diff options
221 files changed, 42319 insertions, 0 deletions
diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/36114-h.zip b/36114-h.zip Binary files differnew file mode 100644 index 0000000..92c5fef --- /dev/null +++ b/36114-h.zip diff --git a/36114-h/36114-h.htm b/36114-h/36114-h.htm new file mode 100644 index 0000000..973b6a4 --- /dev/null +++ b/36114-h/36114-h.htm @@ -0,0 +1,6295 @@ +<!DOCTYPE html> +<html lang="en"> +<head> +<meta charset="UTF-8"> +<title>The Special and the General Theory | Project Gutenberg</title> + +<link href="images/cover.jpg" rel="icon" type="image/x-cover"> + +<style> + +body { + font-family: "Times New Roman", Times, serif; + margin-left: 10%; + margin-right: 10%; +} + + h1,h2,h3,h4,h5,h6 { + text-align: center; + clear: both; +} + +p { + margin-top: .51em; + text-align: justify; + margin-bottom: .49em; + text-indent:4%; +} + +.nind {text-indent:0%;} + +.hanging2 {padding-left: 2em; + text-indent: -1em; + } + +.align-center { +display: block; +text-align: center; +margin-top: 1em; +margin-bottom: 1em; +} + +.center {text-align: center;text-indent:0%;} + +hr { + width: 33%; + margin-top: 2em; + margin-bottom: 2em; + margin-left: auto; + margin-right: auto; + clear: both; + } + +table { + margin-left: auto; + margin-right: auto; +} + +td, th { + padding: 0.2em; + text-align: left; +} + + +.footnote {margin-left: 10%; margin-right: 10%; font-size: 0.9em;} + +.footnote .label {position: absolute; right: 84%; text-align: right;} + +.fnanchor { + vertical-align: super; + font-size: .8em; + text-decoration: + none; +} + +.dropcap { + float: left; + clear: left; + font-size: 250%; + margin-top:-.7%; + margin: 0 0.15em 0 0; + padding: 0; + line-height: 0.85em; + text-indent: 0 +} + +div.chapter { + page-break-before: always; + margin-top: 4em + } + +.caption {font-weight: normal; + font-size: 90%; + text-align: center; + padding-bottom: 1em;} + +.caption p +{ + text-align: center; + text-indent: 0; + margin: 0.25em 0; +} + +p.caption { + margin-top: 0; + font-size: smaller; +} + +.figcenter { + margin: 3% auto 3% auto; + clear: both; + text-align: center; + text-indent: 0% +} + +.figleft { + float:left;clear:left; + margin-left:1em; + margin-bottom:1em; + margin-top:1em; + margin-right:0em; + padding:0; + text-align:center;} + +img.floatleft { + float: left; + margin-right: 1em; + margin-top: 0.5em; + margin-bottom: 0.5em + } + +img.floatright { + float: right; + margin-left: 1em; + margin-top: 0.5em; + margin-bottom: 0.5em + } + +.indx { + font-size: 98%; + margin-left: 10%; + margin-right: 10%; + text-align: left; + text-indent: 0; + line-height: 100% + } + +.pagenum { + position: absolute; + left: 92%; + font-size: small; + text-align: right; + font-style: normal; + font-weight: normal; + font-variant: normal; + text-indent: 0; +} + +.transnote {background-color: #E6E6FA; + color: black; + font-size:smaller; + padding:0.5em; + margin-bottom:5em; + font-family:sans-serif, serif; } + + </style> +</head> + +<body> +<p style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of Relativity: The Special and the General Theory, by Robert W. Lawson</p> +<div style='display:block; margin:1em 0'> +This eBook is for the use of anyone anywhere in the United States and +most other parts of the world at no cost and with almost no restrictions +whatsoever. You may copy it, give it away or re-use it under the terms +of the Project Gutenberg License included with this eBook or online +at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you +are not located in the United States, you will have to check the laws of the +country where you are located before using this eBook. +</div> + +<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Title: Relativity: The Special and the General Theory</p> +<p style='display:block; margin-left:2em; text-indent:0; margin-top:0; margin-bottom:1em;'>A Popular Exposition, 3rd ed.</p> +<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Translator: Robert W. Lawson</p> +<p style='display:block; text-indent:0; margin:1em 0'>Release Date: March 30, 2023 [eBook #36114]</p> +<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p> + <p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em; text-align:left'>Produced by: Andrew D. Hwang. HTML version by Laura Natal. (This ebook was produced using OCR text generously provided by the University of Toronto Robarts Library through the Internet Archive.)</p> +<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK RELATIVITY: THE SPECIAL AND THE GENERAL THEORY ***</div> + +<div class="figcenter" style="width: 500px;"> +<img src="images/cover.jpg" width="500" alt="500"> +</div> + +<div class="figcenter" style="width: 500px;"> +<img src="images/frontispiece.jpg" width="500" alt="frontispiece"> +</div> + +<div class='chapter'> +<h1>RELATIVITY</h1> + +<p class="center"><b>THE SPECIAL & THE GENERAL THEORY</b></p> + +<p class="center">A POPULAR EXPOSITION</p> + +<p><br><br></p> + +<p class="center"><b>BY</b></p> + +<div style='text-align:center; font-size:1.2em;'>ALBERT EINSTEIN, Ph.D.</div> + +<p class="center">PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN</p> + +<p><br><br></p> + +<p class="center">AUTHORISED TRANSLATION BY</p> + +<p class="center"><b>ROBERT W. LAWSON, D.Sc.</b></p> +<p class="center">UNIVERSITY OF SHEFFIELD</p> + +<p><br><br></p> + +<p class="center">WITH FIVE DIAGRAMS<br> +AND A PORTRAIT OF THE AUTHOR +</p> + +<p><br><br></p> + +<p class="center">THIRD EDITION</p> + +<p><br><br></p> + +<p class="center"><b>METHUEN & CO. LTD.</b><br> +36 ESSEX STREET W.C.<br> +LONDON +</p></div> + +<p><br><br><br></p> + +<div class='chapter'> +<p class="nind"> +<i>This Translation was first Published</i><span style="margin-left: 1em;"> +<i>August 19th 1920</i></span><br> +<i>Second Edition</i><span style="margin-left: 10em;"><i>September 1920</i></span><br> +<i>Third Edition</i><span style="margin-left: 13em;"><i>1920</i></span> +<span class="pagenum" id="Page_v">[Pg v]</span> +</p> +</div> + +<p><br><br><br></p> + +<div class='chapter'> +<p class="center"><b>PREFACE</b></p> + +<p class="nind"> +<span class="dropcap">T</span>HE present book is intended, as far as +possible, to give an exact insight into the theory of Relativity +to those readers who, from a general +scientific and philosophical point of view, are interested +in the theory, but who are not conversant with the +mathematical apparatus<a id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a> +of theoretical physics. The +work presumes a standard of education corresponding +to that of a university matriculation examination, +and, despite the shortness of the book, a fair amount +of patience and force of will on the part of the reader. +The author has spared himself no pains in his endeavour +<span class="pagenum" id="Page_vi">[Pg vi]</span> +to present the main ideas in the simplest and most intelligible +form, and on the whole, in the sequence and connection +in which they actually originated. In the interest +of clearness, it appeared to me inevitable that I should +repeat myself frequently, without paying the slightest +attention to the elegance of the presentation. I adhered +scrupulously to the precept of that brilliant theoretical +physicist L. Boltzmann, according to whom matters of +elegance ought to be left to the tailor and to the cobbler. +I make no pretence of having withheld from the reader +difficulties which are inherent to the subject. On the +other hand, I have purposely treated the empirical +physical foundations of the theory in a "step-motherly" +fashion, so that readers unfamiliar with physics may +not feel like the wanderer who was unable to see the +forest for trees. May the book bring some one a few +happy hours of suggestive thought! +</p> + +<p><i>December</i>, 1916</p><p style="text-align:right">A. EINSTEIN</p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a>The mathematical fundaments of the special theory of +relativity are to be found in the original papers of H. A. Lorentz, +A. Einstein, H. Minkowski, published under the title <i>Das +Relativitätsprinzip</i> (The Principle of Relativity) in B. G. +Teubner's collection of monographs <i>Fortschritte der mathematischen +Wissenschaften</i> (Advances in the Mathematical Sciences), +also in M. Laue's exhaustive book <i>Das +Relativitätsprinzip</i>—published +by Friedr. Vieweg & Son, Braunschweig. +The general theory of relativity, together with the necessary +parts of the theory of invariants, is dealt with in the author's +book <i>Die Grundlagen der allgemeinen Relativitätstheorie</i> (The +Foundations of the General Theory of Relativity) Joh. Ambr. +Barth, 1916; this book assumes some familiarity with the special +theory of relativity.</p></div> + +<p><br></p> + +<p class="center">NOTE TO THE THIRD EDITION</p> + +<p class="nind"> +<span class="dropcap">I</span>N the present year (1918) an excellent and +detailed manual on the general theory of relativity, written +by H. Weyl, was published by the firm Julius +Springer (Berlin). This book, entitled <i>Raum—Zeit—Materie</i> +(Space—Time—Matter), may be warmly recommended +to mathematicians and physicists. +<span class="pagenum" id="Page_vii">[Pg vii]</span> +</p></div> + +<p><br><br><br></p> + +<div class='chapter'> +<p class="center"><b>BIOGRAPHICAL NOTE</b></p> + +<p class="nind"> +<span class="dropcap">A</span>LBERT EINSTEIN is the son of German-Jewish +parents. He was born in 1879 in the +town of Ulm, Würtemberg, Germany. His +schooldays were spent in Munich, where he attended +the <i>Gymnasium</i> until his sixteenth year. After leaving +school at Munich, he accompanied his parents to Milan, +whence he proceeded to Switzerland six months later +to continue his studies. +</p> +<p> +From 1896 to 1900 Albert Einstein studied mathematics +and physics at the Technical High School in +Zurich, as he intended becoming a secondary school +(<i>Gymnasium</i>) teacher. For some time afterwards he +was a private tutor, and having meanwhile become +naturalised, he obtained a post as engineer in the Swiss +Patent Office in 1902 which position he occupied till +1909. The main ideas involved in the most important +of Einstein's theories date back to this period. Amongst +these may be mentioned: <i>The Special Theory of Relativity</i>, +<i>Inertia of Energy</i>, <i>Theory of the Brownian Movement</i>, +and the <i>Quantum-Law of the Emission and Absorption of Light</i> (1905). +These were followed some years +<span class="pagenum" id="Page_viii">[Pg viii]</span> +later by the <i>Theory of the Specific Heat of Solid Bodies</i>, +and the fundamental idea of the <i>General Theory of +Relativity</i>. +</p> +<p> +During the interval 1909 to 1911 he occupied the post +of Professor <i>Extraordinarius</i> at the University of Zurich, +afterwards being appointed to the University of Prague, +Bohemia, where he remained as Professor <i>Ordinarius</i> +until 1912. In the latter year Professor Einstein +accepted a similar chair at the <i>Polytechnikum</i>, Zurich, +and continued his activities there until 1914, when he +received a call to the Prussian Academy of Science, +Berlin, as successor to Van't Hoff. Professor Einstein +is able to devote himself freely to his studies at the +Berlin Academy, and it was here that he succeeded in +completing his work on the <i>General Theory of Relativity</i> +(1915-17). Professor Einstein also lectures on various +special branches of physics at the University of Berlin, +and, in addition, he is Director of the Institute for +Physical Research of the <i>Kaiser Wilhelm Gesellschaft</i>. +</p> +<p> +Professor Einstein has been twice married. His first +wife, whom he married at Berne in 1903, was a fellow-student +from Serbia. There were two sons of this +marriage, both of whom are living in Zurich, the elder +being sixteen years of age. Recently Professor Einstein +married a widowed cousin, with whom he is now living +in Berlin. +</p> +<p style="text-align:right">R. W. L. +<span class="pagenum" id="Page_ix">[Pg ix]</span> +</p></div> + +<div class='chapter'> +<p class="center"><b>TRANSLATOR'S NOTE</b></p> + +<p class="nind"> +<span class="dropcap">I</span>N presenting this translation to the +English-reading public, it is hardly necessary for me to +enlarge on the Author's prefatory remarks, except +to draw attention to those additions to the book which +do not appear in the original. +</p> +<p> +At my request, Professor Einstein kindly supplied +me with a portrait of himself, by one of Germany's +most celebrated artists. Appendix III, on "The +Experimental Confirmation of the General Theory of +Relativity," has been written specially for this translation. +Apart from these valuable additions to the book, +I have included a biographical note on the Author, +and, at the end of the book, an Index and a list of +English references to the subject. This list, which is more +suggestive than exhaustive, is intended as a guide to those +readers who wish to pursue the subject farther. +</p> +<p> +I desire to tender my best thanks to my colleagues +Professor S. R. Milner, D.Sc., and Mr. W. E. Curtis, +A.R.C.Sc., F.R.A.S., also to my friend Dr. Arthur +Holmes, A.R.C.Sc., F.G.S., of the Imperial College, +for their kindness in reading through the manuscript, +<span class="pagenum" id="Page_x">[Pg x]</span> +for helpful criticism, and for numerous suggestions. I +owe an expression of thanks also to Messrs. Methuen +for their ready counsel and advice, and for the care +they have bestowed on the work during the course of +its publication. +</p> + +<p style="text-align:right">ROBERT W. LAWSON</p> + +<p class="nind">THE PHYSICS LABORATORY<br> +<span style="margin-left: 1em;">THE UNIVERSITY OF SHEFFIELD</span><br> +<span style="margin-left: 3em;"><i>June</i> 12, 1920</span> +<span class="pagenum" id="Page_xi">[Pg xi]</span> +</p></div> + +<p><br><br><br></p> + +<div class='chapter'> +<h2>CONTENTS</h2> +<p class="nind"> +<a href="#part01">PART I<br> +THE SPECIAL THEORY OF RELATIVITY</a><br> +<br> +I. <a href="#chap01">Physical Meaning of Geometrical Propositions</a><br> +II. <a href="#chap02">The System of Co-ordinates</a><br> +III. <a href="#chap03">Space and Time in Classical Mechanics</a><br> +IV. <a href="#chap04">The Galileian System of Co-ordinates</a><br> +V. <a href="#chap05">The Principle of Relativity (in the Restricted<br> +<span style="margin-left: 3.5em;">Sense)</span></a><br> +VI. <a href="#chap06">The Theorem of the Addition of Velocities employed<br> +<span style="margin-left: 3.5em;">in Classical Mechanics</span></a><br> +VII. <a href="#chap07">The Apparent Incompatibility of the Law of<br> +<span style="margin-left: 3.5em;">Propagation of Light with the Principle of</span><br> +<span style="margin-left: 3.5em;">Relativity</span></a><br> +VIII. <a href="#chap08">On the Idea of Time in Physics</a><br> +IX. <a href="#chap09">The Relativity of Simultaneity</a><br> +X. <a href="#chap10">On the Relativity of the Conception of Distance</a><br> +XI. <a href="#chap11">The Lorentz Transformation</a><br> +XII. <a href="#chap12">The Behaviour of Measuring-Rods and Clocks<br> +<span style="margin-left: 3.5em;">in Motion</span></a><br> +<span class="pagenum" id="Page_xii">[Pg xii]</span> +XIII. <a href="#chap13">Theorem of the Addition of Velocities. The<br> +<span style="margin-left: 3.5em;">Experiment of Fizeau</span></a><br> +XIV. <a href="#chap14">The Heuristic Value of the Theory of Relativity</a><br> +XV. <a href="#chap15">General Results of the Theory</a><br> +XVI. <a href="#chap16">Experience and the Special Theory of Relativity</a><br> +XVII. <a href="#chap17">Minkowski's Four-dimensional Space</a><br> +<br> +<a href="#part02">PART II<br> +THE GENERAL THEORY OF RELATIVITY</a><br> +<br> +XVIII. <a href="#chap18">Special and General Principle of Relativity</a><br> +XIX. <a href="#chap19">The Gravitational Field</a><br> +XX. <a href="#chap20">The Equality of Inertial and Gravitational Mass<br> +<span style="margin-left: 3.5em;">as an Argument for the General Postulate</span><br> +<span style="margin-left: 3.5em;">of Relativity</span></a><br> +XXI. <a href="#chap21">In what Respects are the Foundations of Classical<br> +<span style="margin-left: 3.5em;">Mechanics and of the Special Theory</span><br> +<span style="margin-left: 3.5em;">of Relativity unsatisfactory?</span></a><br> +XXII. <a href="#chap22">A Few Inferences from the General Principle of<br> +<span style="margin-left: 3.5em;">Relativity</span></a><br> +XXIII. <a href="#chap23">Behaviour of Clocks and Measuring-Rods on a<br> +<span style="margin-left: 3.5em;">Rotating Body of Reference</span></a><br> +XXIV. <a href="#chap24">Euclidean and Non-Euclidean Continuum</a><br> +XXV. <a href="#chap25">Gaussian Co-ordinates</a><br> +XXVI. <a href="#chap26">The Space-time Continuum of the Special<br> +<span style="margin-left: 3.5em;">Theory of Relativity considered as a</span><br> +<span style="margin-left: 3.5em;">Euclidean Continuum</span><br> +<span class="pagenum" id="Page_xiii">[Pg xiii]</span></a> +XXVII. <a href="#chap27">The Space-time Continuum of the General<br> +<span style="margin-left: 3.5em;">Theory of Relativity is not a Euclidean</span><br> +<span style="margin-left: 3.5em;">Continuum</span></a><br> +XXVIII. <a href="#chap28">Exact Formulation of the General Principle of<br> +<span style="margin-left: 3.5em;">Relativity</span></a><br> +XXIX. <a href="#chap29">The Solution of the Problem of Gravitation on<br> +<span style="margin-left: 3.5em;">the Basis of the General Principle of</span><br> +<span style="margin-left: 3.5em;">Relativity</span></a><br> +<br> +<a href="#part03">PART III<br> +CONSIDERATIONS ON THE UNIVERSE<br> +AS A WHOLE</a><br> +<br> +XXX. <a href="#chap30">Cosmological Difficulties of Newton's Theory</a><br> +XXXI. <a href="#chap31">The Possibility of a "Finite" and yet "Unbounded"<br> +<span style="margin-left: 3.5em;">Universe</span></a><br> +XXXII. <a href="#chap32">The Structure of Space according to the<br> +<span style="margin-left: 3.5em;">General Theory of Relativity</span></a><br> +<br> +<a href="#APPENDICES">APPENDICES</a><br> +<br> +I. <a href="#appen01">Simple Derivation of the Lorentz Transformation<br> +<span style="margin-left: 3.5em;">[Supplementary to Section XI.]</span></a><br> +II. <a href="#appen02">Minkowski's Four-dimensional Space ("World")<br> +<span style="margin-left: 3.5em;">[Supplementary to Section XVII.]</span></a><br> +III. <a href="#appen03">The Experimental Confirmation of the General<br> +<span style="margin-left: 3.5em;">Theory of Relativity</span><br> +<span style="margin-left: 3em;">(<i>a</i>) Motion of the Perihelion of Mercury</span><br> +<span style="margin-left: 3em;">(<i>b</i>) Deflection of Light by a Gravitational Field</span><br> +<span style="margin-left: 3em;">(<i>c</i>) Displacement of Spectral Lines towards the</span><br> +<span style="margin-left: 3.5em;">Red</span></a><br> +<br> +<a href="#BIBLIOGRAPHY">BIBLIOGRAPHY</a><br> +<br> +<a href="#INDEX">INDEX</a></p> + +<p><span class="pagenum" id="Page_xiv">[Pg xiv]</span></p> +</div> + +<p><br><br><br></p> + +<div class='chapter'> +<h2>RELATIVITY<br> +THE SPECIAL AND THE GENERAL THEORY +</h2></div> + +<p><br><br><br></p> + +<div class="chapter"> +<h2 title="PART I: THE SPECIAL THEORY OF RELATIVITY"><a id="part01"></a>PART I +<br> +THE SPECIAL THEORY OF RELATIVITY</h2> + +<p><br><br></p> + +<h2 title="I: PHYSICAL MEANING OF GEOMETRICAL +PROPOSITIONS"><a id="chap01"></a>I +<br><br> +PHYSICAL MEANING OF GEOMETRICAL<br> +PROPOSITIONS +</h2> + +<p class="nind"> +<span class="dropcap">I</span>N your schooldays most of you who read this +book made acquaintance with the noble building of +Euclid's geometry, and you remember—perhaps +with more respect than love—the magnificent structure, +on the lofty staircase of which you were chased about +for uncounted hours by conscientious teachers. By +reason of your past experience, you would certainly +regard everyone with disdain who should pronounce even +the most out-of-the-way proposition of this science to +be untrue. But perhaps this feeling of proud certainty +would leave you immediately if some one were to ask +you: "What, then, do you mean by the assertion that +these propositions are true?" Let us proceed to give +this question a little consideration. +</p> +<p> +Geometry sets out from certain conceptions such as +"plane," "point," and "straight line," with which +<span class="pagenum" id="Page_1">[Pg 1]</span> +we are able to associate more or less definite ideas, and +from certain simple propositions (axioms) which, +in virtue of these ideas, we are inclined to accept as +"true." Then, on the basis of a logical process, the +justification of which we feel ourselves compelled to +admit, all remaining propositions are shown to follow +from those axioms, <i>i.e.</i> they are proven. A proposition +is then correct ("true") when it has been derived in the +recognised manner from the axioms. The question +of the "truth" of the individual geometrical propositions +is thus reduced to one of the "truth" of the +axioms. Now it has long been known that the last +question is not only unanswerable by the methods of +geometry, but that it is in itself entirely without meaning. +We cannot ask whether it is true that only one +straight line goes through two points. We can only +say that Euclidean geometry deals with things called +"straight lines," to each of which is ascribed the property +of being uniquely determined by two points +situated on it. The concept "true" does not tally with +the assertions of pure geometry, because by the word +"true" we are eventually in the habit of designating +always the correspondence with a "real" object; +geometry, however, is not concerned with the relation +of the ideas involved in it to objects of experience, but +only with the logical connection of these ideas among +themselves. +</p> +<p> +It is not difficult to understand why, in spite of this, +we feel constrained to call the propositions of geometry +"true." Geometrical ideas correspond to more or less +exact objects in nature, and these last are undoubtedly +the exclusive cause of the genesis of those ideas. Geometry +ought to refrain from such a course, in order to +<span class="pagenum" id="Page_2">[Pg 2]</span> +give to its structure the largest possible logical unity. +The practice, for example, of seeing in a "distance" +two marked positions on a practically rigid body is +something which is lodged deeply in our habit of thought. +We are accustomed further to regard three points as +being situated on a straight line, if their apparent +positions can be made to coincide for observation with +one eye, under suitable choice of our place of observation. +</p> +<p> +If, in pursuance of our habit of thought, we now +supplement the propositions of Euclidean geometry by +the single proposition that two points on a practically +rigid body always correspond to the same distance +(line-interval), independently of any changes in position +to which we may subject the body, the propositions of +Euclidean geometry then resolve themselves into propositions +on the possible relative position of practically +rigid bodies.<a id="FNanchor_2_1"></a><a href="#Footnote_2_1" class="fnanchor">[2]</a> +Geometry which has been supplemented +in this way is then to be treated as a branch of physics. +We can now legitimately ask as to the "truth" of +geometrical propositions interpreted in this way, since +we are justified in asking whether these propositions +are satisfied for those real things we have associated +with the geometrical ideas. In less exact terms we can +express this by saying that by the "truth" of a geometrical +proposition in this sense we understand its +validity for a construction with ruler and compasses. +<span class="pagenum" id="Page_3">[Pg 3]</span> +</p> +<p> +Of course the conviction of the "truth" of geometrical +propositions in this sense is founded exclusively +on rather incomplete experience. For the present we +shall assume the "truth" of the geometrical propositions, +then at a later stage (in the general theory of +relativity) we shall see that this "truth" is limited, +and we shall consider the extent of its limitation. +<span class="pagenum" id="Page_4">[Pg 4]</span> +</p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_2_1"></a><a href="#FNanchor_2_1"><span class="label">[2]</span></a>It follows that a natural object is associated also with a +straight line. Three points <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">, <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> and <img style="vertical-align: -0.05ex; width: 1.719ex; height: 1.645ex;" src="images/3.svg" alt=" " data-tex="C"> on a rigid body thus +lie in a straight line when, the points <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: -0.05ex; width: 1.719ex; height: 1.645ex;" src="images/3.svg" alt=" " data-tex="C"> being given, <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> +is chosen such that the sum of the distances <img style="vertical-align: 0; width: 3.414ex; height: 1.62ex;" src="images/4.svg" alt=" " data-tex="AB"> and <img style="vertical-align: -0.05ex; width: 3.437ex; height: 1.645ex;" src="images/5.svg" alt=" " data-tex="BC"> is as +short as possible. This incomplete suggestion will suffice for +our present purpose.</p></div> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="II: THE SYSTEM OF CO-ORDINATES"><a id="chap02"></a>II +<br><br> +THE SYSTEM OF CO-ORDINATES +</h2> + +<p class="nind"> +<span class="dropcap">O</span>N the basis of the physical interpretation of +distance which has been indicated, we are also +in a position to establish the distance between +two points on a rigid body by means of measurements. +For this purpose we require a "distance" (rod <img style="vertical-align: -0.05ex; width: 1.459ex; height: 1.645ex;" src="images/6.svg" alt=" " data-tex="S">) +which is to be used once and for all, and which we +employ as a standard measure. If, now, <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> are +two points on a rigid body, we can construct the +line joining them according to the rules of geometry; +then, starting from <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">, we can mark off the distance <img style="vertical-align: -0.05ex; width: 1.459ex; height: 1.645ex;" src="images/6.svg" alt=" " data-tex="S"> +time after time until we reach <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">. The number of +these operations required is the numerical measure +of the distance <img style="vertical-align: 0; width: 3.414ex; height: 1.62ex;" src="images/4.svg" alt=" " data-tex="AB">. This is the basis of all measurement +of length.<a id="FNanchor_3_1"></a><a href="#Footnote_3_1" class="fnanchor">[3]</a> +</p> +<p> +Every description of the scene of an event or of the +position of an object in space is based on the specification +of the point on a rigid body (body of reference) +with which that event or object coincides. This applies +not only to scientific description, but also to everyday +life. If I analyse the place specification "Trafalgar +<span class="pagenum" id="Page_5">[Pg 5]</span> +Square, London,"<a id="FNanchor_4_1"></a><a href="#Footnote_4_1" class="fnanchor">[4]</a> +I arrive at the following result. +The earth is the rigid body to which the specification +of place refers; "Trafalgar Square, London," is a +well-defined point, to which a name has been assigned, +and with which the event coincides in space.<a id="FNanchor_5_1"></a><a href="#Footnote_5_1" class="fnanchor">[5]</a> +</p> +<p> +This primitive method of place specification deals +only with places on the surface of rigid bodies, and is +dependent on the existence of points on this surface +which are distinguishable from each other. But we +can free ourselves from both of these limitations without +altering the nature of our specification of position. +If, for instance, a cloud is hovering over Trafalgar +Square, then we can determine its position relative to +the surface of the earth by erecting a pole perpendicularly +on the Square, so that it reaches the cloud. The +length of the pole measured with the standard measuring-rod, +combined with the specification of the position of +the foot of the pole, supplies us with a complete place +specification. On the basis of this illustration, we are +able to see the manner in which a refinement of the conception +of position has been developed. +</p> +<p> +(<i>a</i>) We imagine the rigid body, to which the place +specification is referred, supplemented in such a manner +that the object whose position we require is reached by +the completed rigid body. +</p> +<p> +(<i>b</i>) In locating the position of the object, we make +use of a number (here the length of the pole measured +<span class="pagenum" id="Page_6">[Pg 6]</span> +with the measuring-rod) instead of designated points of +reference. +</p> +<p> +(<i>c</i>) We speak of the height of the cloud even when the +pole which reaches the cloud has not been erected. +By means of optical observations of the cloud from +different positions on the ground, and taking into account +the properties of the propagation of light, we determine +the length of the pole we should have required in order +to reach the cloud. +</p> +<p> +From this consideration we see that it will be advantageous +if, in the description of position, it should be +possible by means of numerical measures to make ourselves +independent of the existence of marked positions +(possessing names) on the rigid body of reference. In +the physics of measurement this is attained by the +application of the Cartesian system of co-ordinates. +</p> +<p> +This consists of three plane surfaces perpendicular +to each other and rigidly attached to a rigid body. +Referred to a system of co-ordinates, the scene of any +event will be determined (for the main part) by the +specification of the lengths of the three perpendiculars +or co-ordinates (<img style="vertical-align: -0.464ex; width: 5.467ex; height: 1.464ex;" src="images/7.svg" alt=" " data-tex="x, y, z">) which can be dropped from the +scene of the event to those three plane surfaces. The +lengths of these three perpendiculars can be determined +by a series of manipulations with rigid measuring-rods +performed according to the rules and methods laid +down by Euclidean geometry. +</p> +<p> +In practice, the rigid surfaces which constitute the +system of co-ordinates are generally not available; +furthermore, the magnitudes of the co-ordinates are not +actually determined by constructions with rigid rods, but +by indirect means. If the results of physics and astronomy +are to maintain their clearness, the physical meaning +<span class="pagenum" id="Page_7">[Pg 7]</span> +of specifications of position must always be<a id="FNanchor_6_1"></a><a href="#Footnote_6_1" class="fnanchor">[6]</a> +sought in accordance with the above considerations.</p> +<p> +We thus obtain the following result: Every description +of events in space involves the use of a rigid body +to which such events have to be referred. The resulting +relationship takes for granted that the laws of Euclidean +geometry hold for "distances," the "distance" being +represented physically by means of the convention of +two marks on a rigid body. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_3_1"></a><a href="#FNanchor_3_1"><span class="label">[3]</span></a>Here we have assumed that there is nothing left over, <i>i.e.</i> +that the measurement gives a whole number. This difficulty +is got over by the use of divided measuring-rods, the introduction +of which does not demand any fundamentally new method.</p></div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_4_1"></a><a href="#FNanchor_4_1"><span class="label">[4]</span></a>I have chosen this as being more familiar to the English +reader than the "Potsdamer Platz, Berlin," which is referred to +in the original. (R. W. L.)</p></div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_5_1"></a><a href="#FNanchor_5_1"><span class="label">[5]</span></a>It is not necessary here to investigate further the significance +of the expression "coincidence in space." This conception is +sufficiently obvious to ensure that differences of opinion are +scarcely likely to arise as to its applicability in practice.</p></div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_6_1"></a><a href="#FNanchor_6_1"><span class="label">[6]</span></a>A refinement and modification of these views does not become +necessary until we come to deal with the general theory of +relativity, treated in the second part of this book.</p></div> + +<p><span class="pagenum" id="Page_8">[Pg 8]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="III: SPACE AND TIME IN CLASSICAL MECHANICS"><a id="chap03"></a>III +<br><br> +SPACE AND TIME IN CLASSICAL MECHANICS</h2> + +<p class="nind"> +<span class="dropcap">"T</span>HE purpose of mechanics is to describe how +bodies change their position in space with +time." I should load my conscience with grave +sins against the sacred spirit of lucidity were I to +formulate the aims of mechanics in this way, without +serious reflection and detailed explanations. Let us +proceed to disclose these sins. +</p> +<p> +It is not clear what is to be understood here by +"position" and "space." I stand at the window of a +railway carriage which is travelling uniformly, and drop +a stone on the embankment, without throwing it. Then, +disregarding the influence of the air resistance, I see the +stone descend in a straight line. A pedestrian who +observes the misdeed from the footpath notices that the +stone falls to earth in a parabolic curve. I now ask: +Do the "positions" traversed by the stone lie "in +reality" on a straight line or on a parabola? Moreover, +what is meant here by motion "in space"? From the +considerations of the previous section the answer is +self-evident. In the first place, we entirely shun the +vague word "space," of which, we must honestly +acknowledge, we cannot form the slightest conception, +and we replace it by "motion relative to a +practically rigid body of reference." The positions +relative to the body of reference (railway carriage or +embankment) have already been defined in detail in the +<span class="pagenum" id="Page_9">[Pg 9]</span> +preceding section. If instead of "body of reference" +we insert "system of co-ordinates," which is a useful +idea for mathematical description, we are in a position +to say: The stone traverses a straight line relative to a +system of co-ordinates rigidly attached to the carriage, +but relative to a system of co-ordinates rigidly attached +to the ground (embankment) it describes a parabola. +With the aid of this example it is clearly seen that there +is no such thing as an independently existing trajectory +(lit. "path-curve"<a id="FNanchor_7_1"></a><a href="#Footnote_7_1" class="fnanchor">[7]</a>), +but only a trajectory relative to a +particular body of reference. +</p> +<p> +In order to have a <i>complete</i> description of the motion, +we must specify how the body alters its position <i>with +time</i>; <i>i.e.</i> for every point on the trajectory it must be +stated at what time the body is situated there. These +data must be supplemented by such a definition of +time that, in virtue of this definition, these time-values +can be regarded essentially as magnitudes (results of +measurements) capable of observation. If we take our +stand on the ground of classical mechanics, we can +satisfy this requirement for our illustration in the +following manner. We imagine two clocks of identical +construction; the man at the railway-carriage window +is holding one of them, and the man on the footpath +the other. Each of the observers determines +the position on his own reference-body occupied by the +stone at each tick of the clock he is holding in his +hand. In this connection we have not taken account +of the inaccuracy involved by the finiteness of the +velocity of propagation of light. With this and with a +second difficulty prevailing here we shall have to deal +in detail later. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_7_1"></a><a href="#FNanchor_7_1"><span class="label">[7]</span></a>That is, a curve along which the body moves.</p></div> + +<p><span class="pagenum" id="Page_10">[Pg 10]</span></p> +<p><br><br><br></p> +</div> + +<div class="chapter"> + +<h2 title="IV: THE GALILEIAN SYSTEM OF CO-ORDINATES"><a id="chap04"></a>IV +<br><br> +THE GALILEIAN SYSTEM OF CO-ORDINATES</h2> + +<p class="nind"> +<span class="dropcap">A</span>S is well known, the fundamental law of the +mechanics of Galilei-Newton, which is known +as the <i>law of inertia</i>, can be stated thus: +A body removed sufficiently far from other bodies +continues in a state of rest or of uniform motion +in a straight line. This law not only says something +about the motion of the bodies, but it also +indicates the reference-bodies or systems of co-ordinates, +permissible in mechanics, which can be used +in mechanical description. The visible fixed stars are +bodies for which the law of inertia certainly holds to a +high degree of approximation. Now if we use a system +of co-ordinates which is rigidly attached to the earth, +then, relative to this system, every fixed star describes +a circle of immense radius in the course of an astronomical +day, a result which is opposed to the statement +of the law of inertia. So that if we adhere to this law +we must refer these motions only to systems of co-ordinates +relative to which the fixed stars do not move +in a circle. A system of co-ordinates of which the state +of motion is such that the law of inertia holds relative to +it is called a "Galileian system of co-ordinates." The +laws of the mechanics of Galilei-Newton can be regarded +as valid only for a Galileian system of co-ordinates. +<span class="pagenum" id="Page_11">[Pg 11]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="V: THE PRINCIPLE OF RELATIVITY"><a id="chap05"></a>V +<br><br> +THE PRINCIPLE OF RELATIVITY (IN THE +RESTRICTED SENSE)</h2> + +<p class="nind"> +<span class="dropcap">I</span>N order to attain the greatest possible +clearness, let us return to our example of the railway carriage +supposed to be travelling uniformly. We call its +motion a uniform translation ("uniform" because +it is of constant velocity and direction, "translation" +because although the carriage changes its position +relative to the embankment yet it does not rotate +in so doing). Let us imagine a raven flying through +the air in such a manner that its motion, as observed +from the embankment, is uniform and in a straight +line. If we were to observe the flying raven from +the moving railway carriage, we should find that the +motion of the raven would be one of different velocity +and direction, but that it would still be uniform +and in a straight line. Expressed in an abstract +manner we may say: If a mass <img style="vertical-align: -0.025ex; width: 1.986ex; height: 1.025ex;" src="images/8.svg" alt=" " data-tex="m"> is moving uniformly +in a straight line with respect to a co-ordinate +system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, then it will also be moving uniformly and in a +straight line relative to a second co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', +provided that the latter is executing a uniform +translatory motion with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. In accordance +with the discussion contained in the preceding section, +it follows that: +<span class="pagenum" id="Page_12">[Pg 12]</span> +</p> +<p> +If <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> is a Galileian co-ordinate system, then every other +co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' is a Galileian one, when, in relation +to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, it is in a condition of uniform motion of translation. +Relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' the mechanical laws of Galilei-Newton +hold good exactly as they do with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. +</p> +<p> +We advance a step farther in our generalisation when +we express the tenet thus: If, relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' is +a uniformly moving co-ordinate system devoid of rotation, +then natural phenomena run their course with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +according to exactly the same general laws as with +respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. This statement is called the <i>principle +of relativity</i> (in the restricted sense). +</p> +<p> +As long as one was convinced that all natural phenomena +were capable of representation with the help of +classical mechanics, there was no need to doubt the +validity of this principle of relativity. But in view of +the more recent development of electrodynamics and +optics it became more and more evident that classical +mechanics affords an insufficient foundation for the +physical description of all natural phenomena. At this +juncture the question of the validity of the principle of +relativity became ripe for discussion, and it did not +appear impossible that the answer to this question +might be in the negative. +</p> +<p> +Nevertheless, there are two general facts which at the +outset speak very much in favour of the validity of the +principle of relativity. Even though classical mechanics +does not supply us with a sufficiently broad basis for the +theoretical presentation of all physical phenomena, +still we must grant it a considerable measure of "truth," +since it supplies us with the actual motions of the +heavenly bodies with a delicacy of detail little short of +wonderful. The principle of relativity must therefore +<span class="pagenum" id="Page_13">[Pg 13]</span> +apply with great accuracy in the domain of <i>mechanics</i>. +But that a principle of such broad generality should +hold with such exactness in one domain of phenomena, +and yet should be invalid for another, is <i>a priori</i> not +very probable. +</p> +<p> +We now proceed to the second argument, to which, +moreover, we shall return later. If the principle of relativity +(in the restricted sense) does not hold, then the +Galileian co-ordinate systems <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'<code>'</code>, etc., which are +moving uniformly relative to each other, will not be +<i>equivalent</i> for the description of natural phenomena. +In this case we should be constrained to believe that +natural laws are capable of being formulated in a particularly +simple manner, and of course only on condition +that, from amongst all possible Galileian co-ordinate +systems, we should have chosen <i>one</i> <img style="vertical-align: -0.375ex; width: 2.748ex; height: 1.92ex;" src="images/10.svg" alt=" " data-tex="\mathrm K_{0}"> of a particular +state of motion as our body of reference. We should +then be justified (because of its merits for the description +of natural phenomena) in calling this system "absolutely +at rest," and all other Galileian systems <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> "in motion." +If, for instance, our embankment were the system <img style="vertical-align: -0.375ex; width: 2.748ex; height: 1.92ex;" src="images/10.svg" alt=" " data-tex="\mathrm K_{0}">, +then our railway carriage would be a system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, +relative to which less simple laws would hold than with +respect to <img style="vertical-align: -0.375ex; width: 2.748ex; height: 1.92ex;" src="images/10.svg" alt=" " data-tex="\mathrm K_{0}">. This diminished simplicity would be +due to the fact that the carriage <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> would be in motion +(<i>i.e.</i> "really") with respect to <img style="vertical-align: -0.375ex; width: 2.748ex; height: 1.92ex;" src="images/10.svg" alt=" " data-tex="\mathrm K_{0}">. In the general +laws of nature which have been formulated with reference +to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, the magnitude and direction of the velocity +of the carriage would necessarily play a part. We should +expect, for instance, that the note emitted by an organ-pipe +placed with its axis parallel to the direction of +travel would be different from that emitted if the axis +of the pipe were placed perpendicular to this direction. +<span class="pagenum" id="Page_14">[Pg 14]</span> +Now in virtue of its motion in an orbit round the sun, +our earth is comparable with a railway carriage travelling +with a velocity of about 30 kilometres per second. +If the principle of relativity were not valid we should +therefore expect that the direction of motion of the +earth at any moment would enter into the laws of nature, +and also that physical systems in their behaviour would +be dependent on the orientation in space with respect +to the earth. For owing to the alteration in direction +of the velocity of revolution of the earth in the course +of a year, the earth cannot be at rest relative to the +hypothetical system <img style="vertical-align: -0.375ex; width: 2.748ex; height: 1.92ex;" src="images/10.svg" alt=" " data-tex="\mathrm K_{0}"> throughout the whole year. +However, the most careful observations have never +revealed such anisotropic properties in terrestrial physical +space, <i>i.e.</i> a physical non-equivalence of different +directions. This is very powerful argument in favour +of the principle of relativity. +<span class="pagenum" id="Page_15">[Pg 15]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="VI: THE THEOREM OF THE ADDITION OF VELOCITIES +EMPLOYED IN CLASSICAL MECHANICS"><a id="chap06"></a>VI +<br><br> +THE THEOREM OF THE ADDITION OF VELOCITIES +EMPLOYED IN CLASSICAL MECHANICS</h2> + +<p class="nind"> +<span class="dropcap">L</span>ET us suppose our old friend the railway +carriage to be travelling along the rails with a constant +velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">, and that a man traverses the length of +the carriage in the direction of travel with a velocity <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w">. +How quickly or, in other words, with what velocity <img style="vertical-align: -0.05ex; width: 2.326ex; height: 1.595ex;" src="images/13.svg" alt=" " data-tex="\mathrm W"> +does the man advance relative to the embankment +during the process? The only possible answer seems to +result from the following consideration: If the man were +to stand still for a second, he would advance relative to +the embankment through a distance <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> equal numerically +to the velocity of the carriage. As a consequence of +his walking, however, he traverses an additional distance <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w"> +relative to the carriage, and hence also relative to the +embankment, in this second, the distance <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w"> being +numerically equal to the velocity with which he is +walking. Thus in total he covers the distance <img style="vertical-align: -0.186ex; width: 10.871ex; height: 1.731ex;" src="images/14.svg" alt=" " data-tex="W = v + w"> +relative to the embankment in the second considered. +We shall see later that this result, which expresses +the theorem of the addition of velocities employed in +classical mechanics, cannot be maintained; in other +words, the law that we have just written down does not +hold in reality. For the time being, however, we shall +assume its correctness. +<span class="pagenum" id="Page_16">[Pg 16]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="VII: THE APPARENT INCOMPATIBILITY OF THE +LAW OF PROPAGATION OF LIGHT WITH +THE PRINCIPLE OF RELATIVITY"><a id="chap07"></a>VII +<br><br> +THE APPARENT INCOMPATIBILITY OF THE +LAW OF PROPAGATION OF LIGHT WITH +THE PRINCIPLE OF RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">T</span>HERE is hardly a simpler law in physics than +that according to which light is propagated in +empty space. Every child at school knows, or +believes he knows, that this propagation takes place +in straight lines with a velocity <img style="vertical-align: -0.439ex; width: 11.79ex; height: 1.946ex;" src="images/15.svg" alt=" " data-tex="c = 300,000"> km./sec. +At all events we know with great exactness that this +velocity is the same for all colours, because if this were +not the case, the minimum of emission would not be +observed simultaneously for different colours during +the eclipse of a fixed star by its dark neighbour. By +means of similar considerations based on observations +of double stars, the Dutch astronomer De Sitter +was also able to show that the velocity of propagation +of light cannot depend on the velocity of motion +of the body emitting the light. The assumption that +this velocity of propagation is dependent on the direction +"in space" is in itself improbable. +</p> +<p> +In short, let us assume that the simple law of the +constancy of the velocity of light <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> (in vacuum) is +justifiably believed by the child at school. Who would +imagine that this simple law has plunged the conscientiously +thoughtful physicist into the greatest +<span class="pagenum" id="Page_17">[Pg 17]</span> +intellectual difficulties? Let us consider how these +difficulties arise. +</p> +<p> +Of course we must refer the process of the propagation +of light (and indeed every other process) to a rigid +reference-body (co-ordinate system). As such a system +let us again choose our embankment. We shall imagine +the air above it to have been removed. If a ray of +light be sent along the embankment, we see from the +above that the tip of the ray will be transmitted with +the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> relative to the embankment. Now let +us suppose that our railway carriage is again travelling +along the railway lines with the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">, and that +its direction is the same as that of the ray of light, but +its velocity of course much less. Let us inquire about +the velocity of propagation of the ray of light relative +to the carriage. It is obvious that we can here apply the +consideration of the previous section, since the ray of +light plays the part of the man walking along relatively +to the carriage. The velocity <img style="vertical-align: -0.05ex; width: 2.371ex; height: 1.595ex;" src="images/17.svg" alt=" " data-tex="W"> of the man relative +to the embankment is here replaced by the velocity +of light relative to the embankment. <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w"> is the required +velocity of light with respect to the carriage, and we +have +<span class="align-center"><img style="vertical-align: -0.186ex; width: 10.109ex; height: 1.505ex;" src="images/18.svg" alt=" " data-tex=" +w = c - v. +"></span> +The velocity of propagation of a ray of light relative to +the carriage thus comes out smaller than <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">. +</p> +<p> +But this result comes into conflict with the principle +of relativity set forth in Section V. For, like every +other general law of nature, the law of the transmission +of light <i>in vacuo</i> must, according to the principle of +relativity, be the same for the railway carriage as +reference-body as when the rails are the body of reference. +<span class="pagenum" id="Page_18">[Pg 18]</span> +But, from our above consideration, this would +appear to be impossible. If every ray of light is propagated +relative to the embankment with the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">, +then for this reason it would appear that another law +of propagation of light must necessarily hold with respect +to the carriage—a result contradictory to the principle +of relativity. +</p> +<p> +In view of this dilemma there appears to be nothing +else for it than to abandon either the principle of relativity +or the simple law of the propagation of light <i>in vacuo</i>. +Those of you who have carefully followed the +preceding discussion are almost sure to expect that +we should retain the principle of relativity, which +appeals so convincingly to the intellect because it is so +natural and simple. The law of the propagation of +light <i>in vacuo</i> would then have to be replaced by a +more complicated law conformable to the principle of +relativity. The development of theoretical physics +shows, however, that we cannot pursue this course. +The epoch-making theoretical investigations of H. A. +Lorentz on the electrodynamical and optical phenomena +connected with moving bodies show that experience +in this domain leads conclusively to a theory of electromagnetic +phenomena, of which the law of the constancy +of the velocity of light <i>in vacuo</i> is a necessary consequence. +Prominent theoretical physicists were therefore +more inclined to reject the principle of relativity, +in spite of the fact that no empirical data had been +found which were contradictory to this principle. +</p> +<p> +At this juncture the theory of relativity entered the +arena. As a result of an analysis of the physical conceptions +of time and space, it became evident that <i>in +reality there is not the least incompatibility between the +<span class="pagenum" id="Page_19">[Pg 19]</span> +principle of relativity and the law of propagation of light</i>, +and that by systematically holding fast to both these +laws a logically rigid theory could be arrived at. This +theory has been called the <i>special theory of relativity</i> +to distinguish it from the extended theory, with which +we shall deal later. In the following pages we shall +present the fundamental ideas of the special theory of +relativity. +<span class="pagenum" id="Page_20">[Pg 20]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="VIII: ON THE IDEA OF TIME IN PHYSICS"><a id="chap08"></a>VIII +<br><br> +ON THE IDEA OF TIME IN PHYSICS</h2> + +<p class="nind"> +<span class="dropcap">L</span>IGHTNING has struck the rails on our railway +embankment at two places <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> far distant +from each other. I make the additional assertion +that these two lightning flashes occurred simultaneously. +If I ask you whether there is sense in this statement, +you will answer my question with a decided +"Yes." But if I now approach you with the request +to explain to me the sense of the statement more +precisely, you find after some consideration that the +answer to this question is not so easy as it appears at +first sight. +</p> +<p> +After some time perhaps the following answer would +occur to you: "The significance of the statement is +clear in itself and needs no further explanation; of +course it would require some consideration if I were to +be commissioned to determine by observations whether +in the actual case the two events took place simultaneously +or not." I cannot be satisfied with this answer +for the following reason. Supposing that as a result +of ingenious considerations an able meteorologist were +to discover that the lightning must always strike the +places <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> simultaneously, then we should be faced +with the task of testing whether or not this theoretical +result is in accordance with the reality. We encounter +<span class="pagenum" id="Page_21">[Pg 21]</span> +the same difficulty with all physical statements in which +the conception "simultaneous" plays a part. The +concept does not exist for the physicist until he has the +possibility of discovering whether or not it is fulfilled +in an actual case. We thus require a definition of +simultaneity such that this definition supplies us with +the method by means of which, in the present case, he +can decide by experiment whether or not both the +lightning strokes occurred simultaneously. As long +as this requirement is not satisfied, I allow myself to be +deceived as a physicist (and of course the same applies +if I am not a physicist), when I imagine that I am able +to attach a meaning to the statement of simultaneity. +(I would ask the reader not to proceed farther until he +is fully convinced on this point.) +</p> +<p> +After thinking the matter over for some time you +then offer the following suggestion with which to test +simultaneity. By measuring along the rails, the +connecting line <img style="vertical-align: 0; width: 3.414ex; height: 1.62ex;" src="images/4.svg" alt=" " data-tex="AB"> should be measured up and an +observer placed at the mid-point <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M"> of the distance <img style="vertical-align: 0; width: 3.414ex; height: 1.62ex;" src="images/4.svg" alt=" " data-tex="AB">. +This observer should be supplied with an arrangement +(<i>e.g.</i> two mirrors inclined at <img style="vertical-align: -0.05ex; width: 3.394ex; height: 1.667ex;" src="images/20.svg" alt=" " data-tex="90°">) which allows him +visually to observe both places <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> at the same +time. If the observer perceives the two flashes of +lightning at the same time, then they are simultaneous. +</p> +<p> +I am very pleased with this suggestion, but for all +that I cannot regard the matter as quite settled, because +I feel constrained to raise the following objection: +"Your definition would certainly be right, if I only +knew that the light by means of which the observer +at <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M"> perceives the lightning flashes travels along the +length <img style="vertical-align: -0.025ex; width: 9.037ex; height: 1.645ex;" src="images/21.svg" alt=" " data-tex="A \longrightarrow M"> with the same velocity as along the +length <img style="vertical-align: -0.025ex; width: 9.058ex; height: 1.57ex;" src="images/22.svg" alt=" " data-tex="B \longrightarrow M">. But an examination of this supposition +<span class="pagenum" id="Page_22">[Pg 22]</span> +would only be possible if we already had at our +disposal the means of measuring time. It would thus +appear as though we were moving here in a logical circle." +</p> +<p> +After further consideration you cast a somewhat +disdainful glance at me—and rightly so—and you +declare: "I maintain my previous definition nevertheless, +because in reality it assumes absolutely nothing +about light. There is only <i>one</i> demand to be made of +the definition of simultaneity, namely, that in every +real case it must supply us with an empirical decision +as to whether or not the conception that has to +be defined is fulfilled. That my definition satisfies +this demand is indisputable. That light requires the +same time to traverse the path <img style="vertical-align: -0.025ex; width: 9.037ex; height: 1.645ex;" src="images/21.svg" alt=" " data-tex="A \longrightarrow M"> as for the path +<img style="vertical-align: -0.025ex; width: 9.058ex; height: 1.57ex;" src="images/22.svg" alt=" " data-tex="B \longrightarrow M"> is in reality neither a <i>supposition nor a +hypothesis</i> about the physical nature of light, but a <i>stipulation</i> +which I can make of my own free will in order to arrive +at a definition of simultaneity." +</p> +<p> +It is clear that this definition can be used to give an +exact meaning not only to <i>two</i> events, but to as many +events as we care to choose, and independently of the +positions of the scenes of the events with respect to the +body of reference<a id="FNanchor_8_1"></a><a href="#Footnote_8_1" class="fnanchor">[8]</a> +(here the railway embankment). +We are thus led also to a definition of "time" in physics. +For this purpose we suppose that clocks of identical +construction are placed at the points <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">, <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> and <img style="vertical-align: -0.05ex; width: 1.719ex; height: 1.645ex;" src="images/3.svg" alt=" " data-tex="C"> of +<span class="pagenum" id="Page_23">[Pg 23]</span> +the railway line (co-ordinate system), and that they +are set in such a manner that the positions of their +pointers are simultaneously (in the above sense) the +same. Under these conditions we understand by the +"time" of an event the reading (position of the hands) +of that one of these clocks which is in the immediate +vicinity (in space) of the event. In this manner a +time-value is associated with every event which is +essentially capable of observation. +</p> +<p> +This stipulation contains a further physical hypothesis, +the validity of which will hardly be doubted without +empirical evidence to the contrary. It has been assumed +that all these clocks go <i>at the same rate</i> if they are of +identical construction. Stated more exactly: When +two clocks arranged at rest in different places of a +reference-body are set in such a manner that a <i>particular</i> +position of the pointers of the one clock is <i>simultaneous</i> +(in the above sense) with the <i>same</i> position of the +pointers of the other clock, then identical "settings" +are always simultaneous (in the sense of the above +definition). +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_8_1"></a><a href="#FNanchor_8_1"><span class="label">[8]</span></a>We suppose further, that, when three events <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">, <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> and <img style="vertical-align: -0.05ex; width: 1.719ex; height: 1.645ex;" src="images/3.svg" alt=" " data-tex="C"> +occur in different places in such a manner that <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> is simultaneous +with <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">, and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> is simultaneous with <img style="vertical-align: -0.05ex; width: 1.719ex; height: 1.645ex;" src="images/3.svg" alt=" " data-tex="C"> (simultaneous +in the sense of the above definition), then the criterion for the +simultaneity of the pair of events <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">, <img style="vertical-align: -0.05ex; width: 1.719ex; height: 1.645ex;" src="images/3.svg" alt=" " data-tex="C"> is also satisfied. This +assumption is a physical hypothesis about the law of propagation +of light; it must certainly be fulfilled if we are to maintain the +law of the constancy of the velocity of light <i>in vacuo</i>.</p></div> + +<p><span class="pagenum" id="Page_24">[Pg 24]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="IX: THE RELATIVITY OF SIMULTANEITY"><a id="chap09"></a>IX +<br><br> +THE RELATIVITY OF SIMULTANEITY</h2> + +<p class="nind"> +<span class="dropcap">U</span>P to now our considerations have been +referred to a particular body of reference, which we +have styled a "railway embankment." We +suppose a very long train travelling along the rails +with the constant velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> and in the direction indicated +in Fig. 1. +</p> + +<div class="figcenter" style="width: 400px;"> +<img src="images/figure01.jpg" width="400" alt="fig01"> +<div class="caption"> +<p>FIG. 1.</p> +</div></div> + +<p class="nind"> +People travelling in this train will +with advantage use the train as a rigid reference-body +(co-ordinate system); they regard all events in +reference to the train. Then every event which takes +place along the line also takes place at a particular +point of the train. Also the definition of simultaneity +can be given relative to the train in exactly the same +way as with respect to the embankment. As a natural +consequence, however, the following question arises: +</p> +<p> +Are two events (<i>e.g.</i> the two strokes of lightning <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> +and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">) which are simultaneous <i>with reference to the +railway embankment</i> also simultaneous <i>relatively to the +train</i>? We shall show directly that the answer must +be in the negative. +</p> +<p> +When we say that the lightning strokes <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> are +<span class="pagenum" id="Page_25">[Pg 25]</span> +simultaneous with respect to the embankment, we +mean: the rays of light emitted at the places <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">, +where the lightning occurs, meet each other at the mid-point +<img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M"> of the length <img style="vertical-align: -0.025ex; width: 8.261ex; height: 1.645ex;" src="images/23.svg" alt=" " data-tex="A \longrightarrow \mathrm B"> of the embankment. +But the events <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> also correspond to positions <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> +on the train. Let <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M">' be the mid-point of the +distance <img style="vertical-align: -0.025ex; width: 8.377ex; height: 1.645ex;" src="images/24.svg" alt=" " data-tex="A \longrightarrow B"> on the travelling train. Just when +the flashes<a id="FNanchor_9_1"></a><a href="#Footnote_9_1" class="fnanchor">[9]</a> +of lightning occur, this point <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M">' naturally +coincides with the point <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M">, but it moves towards the +right in the diagram with the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> of the train. If +an observer sitting in the position <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M">' in the train did +not possess this velocity, then he would remain permanently +at <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M">, and the light rays emitted by the +flashes of lightning <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> would reach him simultaneously, +<i>i.e.</i> they would meet just where he is situated. +Now in reality (considered with reference to the railway +embankment) he is hastening towards the beam of light +coming from <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">, whilst he is riding on ahead of the beam +of light coming from <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">. Hence the observer will see +the beam of light emitted from <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> earlier than he will +see that emitted from <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">. Observers who take the railway +train as their reference-body must therefore come +to the conclusion that the lightning flash <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> took place +earlier than the lightning flash <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">. We thus arrive at +the important result: +</p> +<p> +Events which are simultaneous with reference to the +embankment are not simultaneous with respect to the +train, and <i>vice versa</i> (relativity of simultaneity). Every +reference-body (co-ordinate system) has its own particular +time; unless we are told the reference-body to which +the statement of time refers, there is no meaning in a +statement of the time of an event. +<span class="pagenum" id="Page_26">[Pg 26]</span> +</p> +<p> +Now before the advent of the theory of relativity +it had always tacitly been assumed in physics that the +statement of time had an absolute significance, <i>i.e.</i> +that it is independent of the state of motion of the body +of reference. But we have just seen that this assumption +is incompatible with the most natural definition +of simultaneity; if we discard this assumption, then +the conflict between the law of the propagation of +light <i>in vacuo</i> and the principle of relativity (developed +in Section VII) disappears. +</p> +<p> +We were led to that conflict by the considerations +of Section VI, which are now no longer tenable. In +that section we concluded that the man in the carriage, +who traverses the distance <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w"> <i>per second</i> relative to the +carriage, traverses the same distance also with respect to +the embankment <i>in each second</i> of time. But, according +to the foregoing considerations, the time required by a +particular occurrence with respect to the carriage must +not be considered equal to the duration of the same +occurrence as judged from the embankment (as reference-body). +Hence it cannot be contended that the +man in walking travels the distance <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w"> relative to the +railway line in a time which is equal to one second as +judged from the embankment. +</p> +<p> +Moreover, the considerations of Section VI are based +on yet a second assumption, which, in the light of a +strict consideration, appears to be arbitrary, although +it was always tacitly made even before the introduction +of the theory of relativity. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_9_1"></a><a href="#FNanchor_9_1"><span class="label">[9]</span></a>As judged from the embankment.</p></div> + +<p><span class="pagenum" id="Page_27">[Pg 27]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="X: ON THE RELATIVITY OF THE CONCEPTION +OF DISTANCE"><a id="chap10"></a>X +<br><br> +ON THE RELATIVITY OF THE CONCEPTION +OF DISTANCE</h2> + +<p class="nind"> +<span class="dropcap">L</span>ET us consider two particular points on the +train<a id="FNanchor_10_1"></a><a href="#Footnote_10_1" class="fnanchor">[10]</a> +travelling along the embankment with the +velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">, and inquire as to their distance apart. +We already know that it is necessary to have a body of +reference for the measurement of a distance, with respect +to which body the distance can be measured up. It is +the simplest plan to use the train itself as reference-body +(co-ordinate system). An observer in the train +measures the interval by marking off his measuring-rod +in a straight line (<i>e.g.</i> along the floor of the carriage) +as many times as is necessary to take him from the one +marked point to the other. Then the number which +tells us how often the rod has to be laid down is the +required distance. +</p> +<p> +It is a different matter when the distance has to be +judged from the railway line. Here the following +method suggests itself. If we call <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">' and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">' the two +points on the train whose distance apart is required, +then both of these points are moving with the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> +along the embankment. In the first place we require to +determine the points <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> of the embankment which +are just being passed by the two points <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A">' and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">' at a +<span class="pagenum" id="Page_28">[Pg 28]</span> +particular time <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">—judged from the embankment. +These points <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> of the embankment can be determined +by applying the definition of time given in +Section VIII. The distance between these points <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B"> +is then measured by repeated application of the +measuring-rod along the embankment. +</p> +<p> +<i>A priori</i> it is by no means certain that this last +measurement will supply us with the same result as +the first. Thus the length of the train as measured +from the embankment may be different from that +obtained by measuring in the train itself. This +circumstance leads us to a second objection which must +be raised against the apparently obvious consideration +of Section VI. Namely, if the man in the carriage +covers the distance <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w"> in a unit of time—<i>measured from +the train</i>,—then this distance—<i>as measured from the +embankment</i>—is not necessarily also equal to <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w">. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_10_1"></a><a href="#FNanchor_10_1"><span class="label">[10]</span></a><i>e.g.</i> the middle of the first and of the hundredth carriage.</p></div> + +<p><span class="pagenum" id="Page_29">[Pg 29]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XI: THE LORENTZ TRANSFORMATION"><a id="chap11"></a>XI +<br><br> +THE LORENTZ TRANSFORMATION</h2> + +<p class="nind"> +<span class="dropcap">T</span>HE results of the last three sections show +that the apparent incompatibility of the law +of propagation of light with the principle of +relativity (Section VII) has been derived by means of +a consideration which borrowed two unjustifiable +hypotheses from classical mechanics; these are as +follows: +</p> +<p class="hanging2"> +(1) The time-interval (time) between two events is +independent of the condition of motion of the +body of reference. +</p> +<p class="hanging2"> +(2) The space-interval (distance) between two points +of a rigid body is independent of the condition +of motion of the body of reference. +</p> +<p> +If we drop these hypotheses, then the dilemma of +Section VII disappears, because the theorem of the addition +of velocities derived in Section VI becomes invalid. +The possibility presents itself that the law of the propagation +of light <i>in vacuo</i> may be compatible with the +principle of relativity, and the question arises: How +have we to modify the considerations of Section VI +in order to remove the apparent disagreement between +these two fundamental results of experience? This +question leads to a general one. In the discussion of +<span class="pagenum" id="Page_30">[Pg 30]</span> +Section VI we have to do with places and times relative +both to the train and to the embankment. How are +we to find the place and time of an event in relation to +the train, when we know the place and time of the +event with respect to the railway embankment? Is +there a thinkable answer to this question of such a +nature that the law of transmission of light <i>in vacuo</i> +does not contradict the principle of relativity? In +other words: Can we conceive of a relation between +place and time of the individual events relative to both +reference-bodies, such that every ray of light possesses +the velocity of transmission <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> relative to the embankment +and relative to the train? This question leads to +a quite definite positive answer, and to a perfectly definite +transformation law for the space-time magnitudes of +an event when changing over from one body of reference +to another. +</p> +<p> +Before we deal with this, we shall introduce the +following incidental consideration. Up to the present +we have only considered events taking place along the +embankment, which had mathematically to assume the +function of a straight line. In the manner indicated +in Section II we can imagine this reference-body supplemented +laterally and in a vertical direction by means of +a framework of rods, so that an event which takes place +anywhere can be localised with reference to this framework. +Similarly, we can imagine the train travelling +with the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> to be continued across the whole of +space, so that every event, no matter how far off it +may be, could also be localised with respect to the second +framework. Without committing any fundamental error, +we can disregard the fact that in reality these frameworks +would continually interfere with each other, owing +<span class="pagenum" id="Page_31">[Pg 31]</span> +to the impenetrability of solid bodies. In every such +framework we imagine three surfaces perpendicular to +each other marked out, and designated as "co-ordinate +planes" ("co-ordinate system"). A co-ordinate +system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> then corresponds to the embankment, and a +co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' to the train. An event, wherever +it may have taken place, would be fixed in space with +respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> by the three perpendiculars <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z"> +on the co-ordinate planes, and with regard to time by a time-value <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">. +</p> +<a id="figure02"></a> +<img src="images/figure02.jpg" class="floatleft" width="200" alt="fig02"> +<div class="caption"> +<p>FIG. 2.</p> +</div> +<p class="nind"> +Relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', <i>the +same event</i> would be fixed +in respect of space and time +by corresponding values <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">', <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">', +<img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">', <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">', which of course are +not identical with <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">. +It has already been set +forth in detail how these +magnitudes are to be regarded +as results of physical measurements. +</p> +<p> +Obviously our problem can be exactly formulated in +the following manner. What are the values <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">', <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">', <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">', <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">', +of an event with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', when the magnitudes +<img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, of the same event with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +are given? The relations must be so chosen that the law of the +transmission of light <i>in vacuo</i> is satisfied for one and the +same ray of light (and of course for every ray) with +respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> and <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. For the relative orientation +in space of the co-ordinate systems indicated in the diagram +(Fig. 2), this problem is solved by means of the +equations: +<span class="pagenum" id="Page_32">[Pg 32]</span> +<span class="align-center"><img style="vertical-align: -12.409ex; width: 16.037ex; height: 25.95ex;" src="images/29.svg" alt=" " data-tex=" +\begin{align*} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, \\ +y' &= y, \\ +z' &= z, \\ +t' &= \frac{t - \dfrac{v}{c^{2}}·x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{align*} +"></span> +This system of equations is known as the "Lorentz +transformation."<a id="FNanchor_11_1"></a><a href="#Footnote_11_1" class="fnanchor">[11]</a> +</p> +<p> +If in place of the law of transmission of light we had +taken as our basis the tacit assumptions of the older +mechanics as to the absolute character of times and +lengths, then instead of the above we should have +obtained the following equations: +<span class="align-center"><img style="vertical-align: -5.244ex; width: 11.542ex; height: 11.62ex;" src="images/30.svg" alt=" " data-tex=" +\begin{align*} +x' &= x - vt, \\ +y' &= y, \\ +z' &= z, \\ +t' &= t. +\end{align*} +"></span> +This system of equations is often termed the "Galilei +transformation." The Galilei transformation can be +obtained from the Lorentz transformation by substituting +an infinitely large value for the velocity of +light <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> in the latter transformation. +</p> +<p> +Aided by the following illustration, we can readily +see that, in accordance with the Lorentz transformation, +the law of the transmission of light <i>in vacuo</i> +is satisfied both for the reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> and for the +reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. A light-signal is sent along the +positive <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis, and this light-stimulus advances in +accordance with the equation +<span class="align-center"><img style="vertical-align: -0.439ex; width: 6.737ex; height: 1.855ex;" src="images/31.svg" alt=" " data-tex=" +x = ct, +"></span> +<span class="pagenum" id="Page_33">[Pg 33]</span> +<i>i.e.</i> with the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">. According to the equations of +the Lorentz transformation, this simple relation between +<img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x"> and <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> involves a relation between <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">' and <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">'. In point +of fact, if we substitute for <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x"> the value <img style="vertical-align: -0.025ex; width: 1.796ex; height: 1.441ex;" src="images/32.svg" alt=" " data-tex="ct"> in the first +and fourth equations of the Lorentz transformation, +we obtain: +<span class="align-center"><img style="vertical-align: -9.51ex; width: 16.071ex; height: 20.15ex;" src="images/33.svg" alt=" " data-tex=" +\begin{align*} +x' &= \frac{(c - v)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, \\ +t' &= \frac{\left(1 - \dfrac{v}{c}\right)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +\end{align*} +"></span> +from which, by division, the expression +<span class="align-center"><img style="vertical-align: -0.186ex; width: 7.363ex; height: 2.016ex;" src="images/34.svg" alt=" " data-tex=" +x' = ct' +"></span> +immediately follows. If referred to the system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', the +propagation of light takes place according to this +equation. We thus see that the velocity of transmission +relative to the reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' is also equal to <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">. The +same result is obtained for rays of light advancing in +any other direction whatsoever. Of course this is not +surprising, since the equations of the Lorentz transformation +were derived conformably to this point of +view. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_11_1"></a><a href="#FNanchor_11_1"><span class="label">[11]</span></a>A simple derivation of the Lorentz transformation is given +in Appendix I.</p></div> + +<p><span class="pagenum" id="Page_34">[Pg 34]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XII: THE BEHAVIOUR OF MEASURING-RODS AND +CLOCKS IN MOTION"><a id="chap12"></a>XII +<br><br> +THE BEHAVIOUR OF MEASURING-RODS AND +CLOCKS IN MOTION</h2> + +<p class="nind"> +<span class="dropcap">I</span> PLACE a metre-rod in the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">'-axis of +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' in such a manner that one end (the beginning) coincides with +the point <img style="vertical-align: -0.186ex; width: 6.07ex; height: 1.903ex;" src="images/35.svg" alt=" " data-tex="x' = 0">, whilst the other end (the end of the +rod) coincides with the point <img style="vertical-align: -0.186ex; width: 6.07ex; height: 1.903ex;" src="images/36.svg" alt=" " data-tex="x' = 1">. What is the length +of the metre-rod relatively to the system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">? In order +to learn this, we need only ask where the beginning of the +rod and the end of the rod lie with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> at a +particular time <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> of the system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. By means of the first +equation of the Lorentz transformation the values of +these two points at the time <img style="vertical-align: -0.186ex; width: 4.965ex; height: 1.692ex;" src="images/37.svg" alt=" " data-tex="t = 0"> can be shown to be +<span class="align-center"><img style="vertical-align: -5.339ex; width: 29.587ex; height: 11.81ex;" src="images/38.svg" alt=" " data-tex=" +\begin{align*} +x_{\text{(beginning of rod)}} + &= 0·\sqrt{1 - \frac{v^{2}}{c^{2}}}, \\ +x_{\text{(end of rod)}} + &= 1·\sqrt{1 - \frac{v^{2}}{c^{2}}}, +\end{align*} +"></span> +the distance between the points being <img style="vertical-align: -1.681ex; width: 9.285ex; height: 5.566ex;" src="images/39.svg" alt=" " data-tex="\sqrt{1 - \dfrac{v^{2}}{c^{2}}}">. +But the metre-rod is moving with the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> relative to +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. It therefore follows that the length of a rigid metre-rod +moving in the direction of its length with a velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> +is <img style="vertical-align: -0.628ex; width: 11.388ex; height: 2.851ex;" src="images/40.svg" alt=" " data-tex="\sqrt{1 - v^{2}/c^{2}}"> of a metre. The rigid rod is thus +shorter when in motion than when at rest, and the +more quickly it is moving, the shorter is the rod. For +the velocity <img style="vertical-align: -0.186ex; width: 5.094ex; height: 1.505ex;" src="images/41.svg" alt=" " data-tex="v = c"> we should have <img style="vertical-align: -0.628ex; width: 15.536ex; height: 2.851ex;" src="images/42.svg" alt=" " data-tex="\sqrt{1 - v^{2}/c^{2}} = 0">, and +for still greater velocities the square-root becomes +<span class="pagenum" id="Page_35">[Pg 35]</span> +imaginary. From this we conclude that in the theory +of relativity the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> plays the part of a limiting +velocity, which can neither be reached nor exceeded +by any real body. +</p> +<p> +Of course this feature of the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> as a limiting +velocity also clearly follows from the equations of the +Lorentz transformation, for these become meaningless +if we choose values of <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> greater than <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">. +</p> +<p> +If, on the contrary, we had considered a metre-rod +at rest in the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, then we should +have found that the length of the rod as judged from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' +would have been <img style="vertical-align: -0.628ex; width: 11.388ex; height: 2.851ex;" src="images/40.svg" alt=" " data-tex="\sqrt{1 - v^{2}/c^{2}}">; this is quite in accordance +with the principle of relativity which forms the +basis of our considerations. +</p> +<p> +<i>A priori</i> it is quite clear that we must be able to +learn something about the physical behaviour of measuring-rods +and clocks from the equations of transformation, +for the magnitudes <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, are nothing more nor +less than the results of measurements obtainable by +means of measuring-rods and clocks. If we had based +our considerations on the Galilei transformation we +should not have obtained a contraction of the rod as a +consequence of its motion. +</p> +<p> +Let us now consider a seconds-clock which is permanently +situated at the origin (<img style="vertical-align: -0.186ex; width: 6.07ex; height: 1.903ex;" src="images/35.svg" alt=" " data-tex="x' = 0">) of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. <img style="vertical-align: -0.186ex; width: 5.593ex; height: 1.903ex;" src="images/43.svg" alt=" " data-tex="t' = 0"> +and <img style="vertical-align: -0.186ex; width: 5.593ex; height: 1.903ex;" src="images/44.svg" alt=" " data-tex="t' = 1"> are two successive ticks of this clock. The +first and fourth equations of the Lorentz transformation +give for these two ticks: +<span class="align-center"><img style="vertical-align: -5.161ex; width: 19.146ex; height: 11.452ex;" src="images/45.svg" alt=" " data-tex=" +\begin{align*} +t &= 0 \\ +\text{and}\,\, t &= \frac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{align*} +"></span> +<span class="pagenum" id="Page_36">[Pg 36]</span> +</p> +<p> +As judged from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, the clock is moving with the +velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">; as judged from this reference-body, the time +which elapses between two strokes of the clock is not one second, +but <img style="vertical-align: -5.475ex; width: 10.281ex; height: 8.511ex;" src="images/46.svg" alt=" " data-tex="\dfrac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}"> seconds, <i>i.e.</i> +a somewhat larger time. As a consequence of its motion +the clock goes more slowly than when at rest. Here +also the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> plays the part of an unattainable +limiting velocity. +<span class="pagenum" id="Page_37">[Pg 37]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XIII: THEOREM OF THE ADDITION OF VELOCITIES. +THE EXPERIMENT OF FIZEAU"><a id="chap13"></a>XIII +<br><br> +THEOREM OF THE ADDITION OF VELOCITIES. +THE EXPERIMENT OF FIZEAU</h2> + +<p class="nind"> +<span class="dropcap">N</span>OW in practice we can move clocks and +measuring-rods only with velocities that are +small compared with the velocity of light; hence +we shall hardly be able to compare the results of the +previous section directly with the reality. But, on the +other hand, these results must strike you as being very +singular, and for that reason I shall now draw another +conclusion from the theory, one which can easily be +derived from the foregoing considerations, and which +has been most elegantly confirmed by experiment. +</p> +<p> +In Section VI we derived the theorem of the addition +of velocities in one direction in the form which also +results from the hypotheses of classical mechanics. This +theorem can also be deduced readily from the Galilei +transformation (Section XI). In place of the man +walking inside the carriage, we introduce a point moving +relatively to the co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' in accordance +with the equation +<span class="align-center"><img style="vertical-align: -0.186ex; width: 8.632ex; height: 2.016ex;" src="images/47.svg" alt=" " data-tex=" +x' = wt'. +"></span> +By means of the first and fourth equations of the Galilei +transformation we can express <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">' and <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">' in terms of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x"> and +<img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, and we then obtain +<span class="align-center"><img style="vertical-align: -0.566ex; width: 13ex; height: 2.262ex;" src="images/48.svg" alt=" " data-tex=" +x = (v + w)t. +"></span> +<span class="pagenum" id="Page_38">[Pg 38]</span> +This equation expresses nothing else than the law of +motion of the point with reference to the system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +(of the man with reference to the embankment). We +denote this velocity by the symbol <img style="vertical-align: -0.05ex; width: 2.371ex; height: 1.595ex;" src="images/17.svg" alt=" " data-tex="W">, and we then +obtain, as in Section VI, +<span class="align-center"><img style="vertical-align: -0.566ex; width: 19.859ex; height: 2.262ex;" src="images/49.svg" alt=" " data-tex=" +W = v + w. \qquad\text{(A)} +"></span> +</p> +<p> +But we can carry out this consideration just as well +on the basis of the theory of relativity. In the equation +<span class="align-center"><img style="vertical-align: -0.186ex; width: 8.003ex; height: 2.016ex;" src="images/50.svg" alt=" " data-tex=" +x' = wt' +"></span> +we must then express <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">' and <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">' in terms of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x"> and <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, making +use of the first and fourth equations of the <i>Lorentz +transformation</i>. Instead of the equation (A) we then +obtain the equation +<span class="align-center"><img style="vertical-align: -4.095ex; width: 22.886ex; height: 6.943ex;" src="images/51.svg" alt=" " data-tex=" +W = \frac{v + w}{1 + \dfrac{vw}{c^{2}}}, \qquad\text{(B)} +"></span> +which corresponds to the theorem of addition for +velocities in one direction according to the theory of +relativity. The question now arises as to which of these +two theorems is the better in accord with experience. On +this point we are enlightened by a most important experiment +which the brilliant physicist Fizeau performed more +than half a century ago, and which has been repeated +since then by some of the best experimental physicists, +so that there can be no doubt about its result. The +experiment is concerned with the following question. +Light travels in a motionless liquid with a particular +velocity <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w">. How quickly does it travel in the direction +of the arrow in the tube <img style="vertical-align: 0; width: 1.593ex; height: 1.532ex;" src="images/52.svg" alt=" " data-tex="T"> (see the accompanying diagram, +Fig. 3) when the liquid above mentioned is flowing +through the tube with a velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">? +<span class="pagenum" id="Page_39">[Pg 39]</span> +</p> +<p> +In accordance with the principle of relativity we shall +certainly have to take for granted that the propagation +of light always takes place with the same velocity <img style="vertical-align: -0.025ex; width: 1.62ex; height: 1.027ex;" src="images/12.svg" alt=" " data-tex="w"> +<i>with respect to the liquid</i>, whether the latter is in motion +with reference to other bodies or not. The velocity +of light relative to the liquid and the velocity of the +latter relative to the tube are thus known, and we +require the velocity of light relative to the tube. +</p> +<p> +It is clear that we have the problem of Section VI +again before us. The tube plays the part of the railway +embankment or of the co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, the liquid +plays the part of the carriage or of the co-ordinate +system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', and finally, the light plays the part of the +man walking along the carriage, or of the moving point +in the present section. +</p> +<div class="figcenter" style="width: 200px;"> +<img src="images/figure03.jpg" width="200" alt="fig03"> +<div class="caption"> +<p>FIG. 3.</p> +</div></div> +<p class="nind"> +If we denote the velocity of the +light relative to the tube by <img style="vertical-align: -0.05ex; width: 2.371ex; height: 1.595ex;" src="images/17.svg" alt=" " data-tex="W">, then this is given +by the equation (A) or (B), according as the Galilei +transformation or the Lorentz transformation corresponds +to the facts. Experiment<a id="FNanchor_12_1"></a><a href="#Footnote_12_1" class="fnanchor">[12]</a> +decides in favour +of equation (B) derived from the theory of relativity, and +the agreement is, indeed, very exact. According to +<span class="pagenum" id="Page_40">[Pg 40]</span> +recent and most excellent measurements by Zeeman, the +influence of the velocity of flow <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> on the propagation of +light is represented by formula (B) to within one per +cent. +</p> +<p> +Nevertheless we must now draw attention to the fact +that a theory of this phenomenon was given by H. A. +Lorentz long before the statement of the theory of +relativity. This theory was of a purely electrodynamical +nature, and was obtained by the use of particular +hypotheses as to the electromagnetic structure of matter. +This circumstance, however, does not in the least +diminish the conclusiveness of the experiment as a +crucial test in favour of the theory of relativity, for the +electrodynamics of Maxwell-Lorentz, on which the +original theory was based, in no way opposes the theory +of relativity. Rather has the latter been developed +from electrodynamics as an astoundingly simple combination +and generalisation of the hypotheses, formerly +independent of each other, on which electrodynamics +was built. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_12_1"></a><a href="#FNanchor_12_1"><span class="label">[12]</span></a>Fizeau found <img style="vertical-align: -2.148ex; width: 21.816ex; height: 5.428ex;" src="images/53.svg" alt=" " data-tex="W = w + v\left(1 - \dfrac{1}{n^{2}}\right)">, where <img style="vertical-align: -1.577ex; width: 6.99ex; height: 4.106ex;" src="images/54.svg" alt=" " data-tex="n = \dfrac{c}{w}"> is the index of +refraction of the liquid. On the other hand, owing to the smallness +of <img style="vertical-align: -1.654ex; width: 3.713ex; height: 4.185ex;" src="images/55.svg" alt=" " data-tex="\dfrac{vw}{c^{2}}"> as compared with 1, we can replace (B) in the +first place by <img style="vertical-align: -1.654ex; width: 23.319ex; height: 4.254ex;" src="images/56.svg" alt=" " data-tex="W = (w + v) \left(1 - \dfrac{vw}{c^{2}}\right)">, or to +the same order of approximation by +<img style="vertical-align: -2.148ex; width: 16.428ex; height: 5.428ex;" src="images/57.svg" alt=" " data-tex="w + v \left(1 - \dfrac{1}{n^{2}}\right)">, which agrees +with Fizeau's result.</p></div> + +<p><span class="pagenum" id="Page_41">[Pg 41]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XIV: THE HEURISTIC VALUE OF THE THEORY OF +RELATIVITY"><a id="chap14"></a>XIV +<br><br> +THE HEURISTIC VALUE OF THE THEORY OF +RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">O</span>UR train of thought in the foregoing pages +can be epitomised in the following manner. Experience +has led to the conviction that, on the one hand, +the principle of relativity holds true, and that on the +other hand the velocity of transmission of light <i>in vacuo</i> +has to be considered equal to a constant <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">. By uniting +these two postulates we obtained the law of transformation +for the rectangular co-ordinates <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z"> and the time <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> +of the events which constitute the processes of nature. +In this connection we did not obtain the Galilei transformation, +but, differing from classical mechanics, +the <i>Lorentz transformation</i>. +</p> +<p> +The law of transmission of light, the acceptance of +which is justified by our actual knowledge, played an +important part in this process of thought. Once in +possession of the Lorentz transformation, however, +we can combine this with the principle of relativity, +and sum up the theory thus: +</p> +<p> +Every general law of nature must be so constituted +that it is transformed into a law of exactly the same +form when, instead of the space-time variables <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> +of the original co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, we introduce new +space-time variables <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">', <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">', <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">', <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">' of a co-ordinate system +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. +<span class="pagenum" id="Page_42">[Pg 42]</span> +In this connection the relation between the +ordinary and the accented magnitudes is given by the +Lorentz transformation. Or, in brief: General laws +of nature are co-variant with respect to Lorentz transformations. +</p> +<p> +This is a definite mathematical condition that the +theory of relativity demands of a natural law, and in +virtue of this, the theory becomes a valuable heuristic aid +in the search for general laws of nature. If a general +law of nature were to be found which did not satisfy +this condition, then at least one of the two fundamental +assumptions of the theory would have been disproved. +Let us now examine what general results the latter +theory has hitherto evinced. +<span class="pagenum" id="Page_43">[Pg 43]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XV: GENERAL RESULTS OF THE THEORY"><a id="chap15"></a>XV +<br><br> +GENERAL RESULTS OF THE THEORY</h2> + +<p class="nind"> +<span class="dropcap">I</span>T is clear from our previous considerations +that the (special) theory of relativity has grown out of electrodynamics +and optics. In these fields it has not +appreciably altered the predictions of theory, but it +has considerably simplified the theoretical structure, +<i>i.e.</i> the derivation of laws, and—what is incomparably +more important—it has considerably reduced the +number of independent hypotheses forming the basis of +theory. The special theory of relativity has rendered +the Maxwell-Lorentz theory so plausible, that the latter +would have been generally accepted by physicists +even if experiment had decided less unequivocally in its +favour. +</p> +<p> +Classical mechanics required to be modified before it +could come into line with the demands of the special +theory of relativity. For the main part, however, +this modification affects only the laws for rapid motions, +in which the velocities of matter <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> are not very small as +compared with the velocity of light. We have experience +of such rapid motions only in the case of electrons +and ions; for other motions the variations from the laws +of classical mechanics are too small to make themselves +evident in practice. We shall not consider the motion +of stars until we come to speak of the general theory of +relativity. In accordance with the theory of relativity +<span class="pagenum" id="Page_44">[Pg 44]</span> +the kinetic energy of a material point of mass <img style="vertical-align: -0.025ex; width: 1.986ex; height: 1.025ex;" src="images/8.svg" alt=" " data-tex="m"> is no +longer given by the well-known expression +<span class="align-center"><img style="vertical-align: -1.552ex; width: 5.696ex; height: 4.968ex;" src="images/58.svg" alt=" " data-tex=" +m\frac{v^{2}}{2}, +"></span> +but by the expression +<span class="align-center"><img style="vertical-align: -5.475ex; width: 10.909ex; height: 8.891ex;" src="images/59.svg" alt=" " data-tex=" +\frac{mc^{2}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +"></span> +This expression approaches infinity as the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> +approaches the velocity of light <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">. The velocity must +therefore always remain less than <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">, however great may +be the energies used to produce the acceleration. If +we develop the expression for the kinetic energy in the +form of a series, we obtain +<span class="align-center"><img style="vertical-align: -1.654ex; width: 28.169ex; height: 5.087ex;" src="images/60.svg" alt=" " data-tex=" +mc^{2} + m\frac{v^{2}}{2} + \frac{3}{8}m\frac{v^4}{c^{2}} + \dots. +"></span> +</p> +<p> +When <img style="vertical-align: -1.654ex; width: 3.08ex; height: 5.07ex;" src="images/61.svg" alt=" " data-tex="\dfrac{v^{2}}{c^{2}}"> is small compared with unity, the third +of these terms is always small in comparison with the +second, which last is alone considered in classical +mechanics. The first term <img style="vertical-align: -0.025ex; width: 3.954ex; height: 1.912ex;" src="images/62.svg" alt=" " data-tex="mc^{2}"> does not contain +the velocity, and requires no consideration if we are only +dealing with the question as to how the energy of a +point-mass depends on the velocity. We shall speak +of its essential significance later. +</p> +<p> +The most important result of a general character to +which the special theory of relativity has led is concerned +with the conception of mass. Before the advent of +relativity, physics recognised two conservation laws of +fundamental importance, namely, the law of the conservation +of energy and the law of the conservation of +mass; these two fundamental laws appeared to be quite +<span class="pagenum" id="Page_45">[Pg 45]</span> +independent of each other. By means of the theory of +relativity they have been united into one law. We shall +now briefly consider how this unification came about, +and what meaning is to be attached to it. +</p> +<p> +The principle of relativity requires that the law of the +conservation of energy should hold not only with reference +to a co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, but also with respect +to every co-ordinate system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' which is in a state of +uniform motion of translation relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, or, briefly, +relative to every "Galileian" system of co-ordinates. +In contrast to classical mechanics, the Lorentz transformation +is the deciding factor in the transition from +one such system to another. +</p> +<p> +By means of comparatively simple considerations +we are led to draw the following conclusion from +these premises, in conjunction with the fundamental +equations of the electrodynamics of Maxwell: A body +moving with the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">, which absorbs<a id="FNanchor_13_1"></a><a href="#Footnote_13_1" class="fnanchor">[13]</a> +an amount of energy <img style="vertical-align: -0.375ex; width: 2.657ex; height: 1.913ex;" src="images/63.svg" alt=" " data-tex="E_{0}"> in the form of radiation without suffering +an alteration in velocity in the process, has, as a consequence, +its energy increased by an amount +<span class="align-center"><img style="vertical-align: -5.475ex; width: 10.909ex; height: 8.543ex;" src="images/64.svg" alt=" " data-tex=" +\frac{E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +"></span> +</p> +<p> +In consideration of the expression given above for the +kinetic energy of the body, the required energy of the +body comes out to be +<span class="align-center"><img style="vertical-align: -5.475ex; width: 15.327ex; height: 11.943ex;" src="images/65.svg" alt=" " data-tex=" +\frac{\left(m + \dfrac{E_{0}}{c^{2}}\right)c^{2}} + {\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +"></span> +<span class="pagenum" id="Page_46">[Pg 46]</span> +</p> +<p> +Thus the body has the same energy as a body of mass +<img style="vertical-align: -2.148ex; width: 11.735ex; height: 5.428ex;" src="images/66.svg" alt=" " data-tex="\left(m + \dfrac{E_{0}}{c^{2}}\right)"> moving with the velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">. +Hence we can say: If a body takes up an amount of energy <img style="vertical-align: -0.375ex; width: 2.657ex; height: 1.913ex;" src="images/63.svg" alt=" " data-tex="E_{0}">, then +its inertial mass increases by an amount <img style="vertical-align: -1.654ex; width: 3.653ex; height: 4.722ex;" src="images/67.svg" alt=" " data-tex="\dfrac{E_{0}}{c^{2}}">; the +inertial mass of a body is not a constant, but varies +according to the change in the energy of the body. +The inertial mass of a system of bodies can even be +regarded as a measure of its energy. The law of the +conservation of the mass of a system becomes identical +with the law of the conservation of energy, and is only +valid provided that the system neither takes up nor sends +out energy. Writing the expression for the energy in +the form +<span class="align-center"><img style="vertical-align: -5.475ex; width: 11.001ex; height: 8.891ex;" src="images/68.svg" alt=" " data-tex=" +\frac{mc^{2} + E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +"></span> +we see that the term <img style="vertical-align: -0.025ex; width: 3.954ex; height: 1.912ex;" src="images/62.svg" alt=" " data-tex="mc^{2}">, which has hitherto attracted +our attention, is nothing else than the energy possessed +by the body<a id="FNanchor_14_1"></a><a href="#Footnote_14_1" class="fnanchor">[14]</a> +before it absorbed the energy <img style="vertical-align: -0.375ex; width: 2.657ex; height: 1.913ex;" src="images/63.svg" alt=" " data-tex="E_{0}">. +</p> +<p> +A direct comparison of this relation with experiment +is not possible at the present time, owing to the fact that +the changes in energy <img style="vertical-align: -0.375ex; width: 2.657ex; height: 1.913ex;" src="images/63.svg" alt=" " data-tex="E_{0}"> to which we can subject a +system are not large enough to make themselves +perceptible as a change in the inertial mass of the +system. <img style="vertical-align: -1.654ex; width: 3.653ex; height: 4.722ex;" src="images/67.svg" alt=" " data-tex="\dfrac{E_{0}}{c^{2}}"> is too small in comparison with the mass +<img style="vertical-align: -0.025ex; width: 1.986ex; height: 1.025ex;" src="images/8.svg" alt=" " data-tex="m">, which was present before the alteration of the energy. +It is owing to this circumstance that classical mechanics +was able to establish successfully the conservation of +mass as a law of independent validity. +<span class="pagenum" id="Page_47">[Pg 47]</span> +</p> +<p> +Let me add a final remark of a fundamental nature. +The success of the Faraday-Maxwell interpretation of +electromagnetic action at a distance resulted in physicists +becoming convinced that there are no such things as +instantaneous actions at a distance (not involving an +intermediary medium) of the type of Newton's law of +gravitation. According to the theory of relativity, +action at a distance with the velocity of light always +takes the place of instantaneous action at a distance or +of action at a distance with an infinite velocity of transmission. +This is connected with the fact that the +velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> plays a fundamental rôle in this theory. In +Part II we shall see in what way this result becomes +modified in the general theory of relativity. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_13_1"></a><a href="#FNanchor_13_1"><span class="label">[13]</span></a><img style="vertical-align: -0.375ex; width: 2.657ex; height: 1.913ex;" src="images/63.svg" alt=" " data-tex="E_{0}"> is the energy taken up, as judged from a co-ordinate +system moving with the body.</p></div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_14_1"></a><a href="#FNanchor_14_1"><span class="label">[14]</span></a>As judged from a co-ordinate system moving with the body.</p></div> + +<p><span class="pagenum" id="Page_48">[Pg 48]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XVI: EXPERIENCE AND THE SPECIAL THEORY OF +RELATIVITY"><a id="chap16"></a>XVI +<br><br> +EXPERIENCE AND THE SPECIAL THEORY OF +RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">T</span>O what extent is the special theory of +relativity supported by experience? This question is not +easily answered for the reason already mentioned +in connection with the fundamental experiment of Fizeau. +The special theory of relativity has crystallised out +from the Maxwell-Lorentz theory of electromagnetic +phenomena. Thus all facts of experience which support +the electromagnetic theory also support the theory of +relativity. As being of particular importance, I mention +here the fact that the theory of relativity enables us to +predict the effects produced on the light reaching us +from the fixed stars. These results are obtained in an +exceedingly simple manner, and the effects indicated, +which are due to the relative motion of the earth with +reference to those fixed stars, are found to be in accord +with experience. We refer to the yearly movement of +the apparent position of the fixed stars resulting from the +motion of the earth round the sun (aberration), and to the +influence of the radial components of the relative +motions of the fixed stars with respect to the earth on +the colour of the light reaching us from them. The +<span class="pagenum" id="Page_49">[Pg 49]</span> +latter effect manifests itself in a slight displacement +of the spectral lines of the light transmitted to us from +a fixed star, as compared with the position of the same +spectral lines when they are produced by a terrestrial +source of light (Doppler principle). The experimental +arguments in favour of the Maxwell-Lorentz theory, +which are at the same time arguments in favour of the +theory of relativity, are too numerous to be set forth +here. In reality they limit the theoretical possibilities +to such an extent, that no other theory than that of +Maxwell and Lorentz has been able to hold its own when +tested by experience. +</p> +<p> +But there are two classes of experimental facts +hitherto obtained which can be represented in the +Maxwell-Lorentz theory only by the introduction of an +auxiliary hypothesis, which in itself—<i>i.e.</i> without +making use of the theory of relativity—appears extraneous. +</p> +<p> +It is known that cathode rays and the so-called +<img style="vertical-align: -0.439ex; width: 1.281ex; height: 2.034ex;" src="images/69.svg" alt=" " data-tex="\beta">-rays emitted by radioactive substances consist of +negatively electrified particles (electrons) of very small +inertia and large velocity. By examining the deflection +of these rays under the influence of electric and magnetic +fields, we can study the law of motion of these particles +very exactly. +</p> +<p> +In the theoretical treatment of these electrons, we are +faced with the difficulty that electrodynamic theory of +itself is unable to give an account of their nature. For +since electrical masses of one sign repel each other, the +negative electrical masses constituting the electron would +necessarily be scattered under the influence of their +mutual repulsions, unless there are forces of another +kind operating between them, the nature of which has +<span class="pagenum" id="Page_50">[Pg 50]</span> +hitherto remained obscure to us.<a id="FNanchor_15_1"></a><a href="#Footnote_15_1" class="fnanchor">[15]</a> +If we now assume +that the relative distances between the electrical masses +constituting the electron remain unchanged during the +motion of the electron (rigid connection in the sense of +classical mechanics), we arrive at a law of motion of the +electron which does not agree with experience. Guided +by purely formal points of view, H. A. Lorentz was the +first to introduce the hypothesis that the particles +constituting the electron experience a contraction +in the direction of motion in consequence of that motion, +the amount of this contraction being proportional to +the expression <img style="vertical-align: -1.681ex; width: 9.285ex; height: 5.566ex;" src="images/39.svg" alt=" " data-tex="\sqrt{1 - \dfrac{v^{2}}{c^{2}}}">. This hypothesis, which +is not justifiable by any electrodynamical facts, supplies us +then with that particular law of motion which has +been confirmed with great precision in recent years. +</p> +<p> +The theory of relativity leads to the same law of +motion, without requiring any special hypothesis whatsoever +as to the structure and the behaviour of the +electron. We arrived at a similar conclusion in Section XIII +in connection with the experiment of Fizeau, the +result of which is foretold by the theory of relativity +without the necessity of drawing on hypotheses as to +the physical nature of the liquid. +</p> +<p> +The second class of facts to which we have alluded +has reference to the question whether or not the motion +of the earth in space can be made perceptible in terrestrial +experiments. We have already remarked in Section V +that all attempts of this nature led to a negative result. +Before the theory of relativity was put forward, it was +<span class="pagenum" id="Page_51">[Pg 51]</span> +difficult to become reconciled to this negative result, +for reasons now to be discussed. The inherited +prejudices about time and space did not allow any +doubt to arise as to the prime importance of the +Galilei transformation for changing over from one +body of reference to another. Now assuming that the +Maxwell-Lorentz equations hold for a reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, +we then find that they do not hold for a reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' +moving uniformly with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, if we +assume that the relations of the Galileian transformation +exist between the co-ordinates of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> and <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. It +thus appears that of all Galileian co-ordinate systems +one (<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">) corresponding to a particular state of motion +is physically unique. This result was interpreted +physically by regarding <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> as at rest with respect to a +hypothetical æther of space. On the other hand, +all co-ordinate systems <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' moving relatively to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +were to be regarded as in motion with respect to the æther. +To this motion of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' against the æther ("æther-drift" +relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">') were assigned the more complicated +laws which were supposed to hold relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. +Strictly speaking, such an æther-drift ought also to be +assumed relative to the earth, and for a long time the +efforts of physicists were devoted to attempts to detect +the existence of an æther-drift at the earth's surface. +</p> +<p> +In one of the most notable of these attempts Michelson +devised a method which appears as though it must be +decisive. Imagine two mirrors so arranged on a rigid +body that the reflecting surfaces face each other. A +ray of light requires a perfectly definite time <img style="vertical-align: 0; width: 1.593ex; height: 1.532ex;" src="images/52.svg" alt=" " data-tex="T"> to pass +from one mirror to the other and back again, if the whole +system be at rest with respect to the æther. It is found +by calculation, however, that a slightly different time <img style="vertical-align: 0; width: 1.593ex; height: 1.532ex;" src="images/52.svg" alt=" " data-tex="T">' +<span class="pagenum" id="Page_52">[Pg 52]</span> +is required for this process, if the body, together with +the mirrors, be moving relatively to the æther. And +yet another point: it is shown by calculation that for +a given velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> with reference to the æther, this +time <img style="vertical-align: 0; width: 1.593ex; height: 1.532ex;" src="images/52.svg" alt=" " data-tex="T">' is different when the body is moving perpendicularly +to the planes of the mirrors from that resulting +when the motion is parallel to these planes. Although +the estimated difference between these two times is +exceedingly small, Michelson and Morley performed an +experiment involving interference in which this difference +should have been clearly detectable. But the experiment +gave a negative result—a fact very perplexing +to physicists. Lorentz and FitzGerald rescued the +theory from this difficulty by assuming that the motion +of the body relative to the æther produces a contraction +of the body in the direction of motion, the amount of contraction +being just sufficient to compensate for the difference +in time mentioned above. Comparison with the +discussion in Section XII shows that also from the standpoint +of the theory of relativity this solution of the +difficulty was the right one. But on the basis of the +theory of relativity the method of interpretation is +incomparably more satisfactory. According to this +theory there is no such thing as a "specially favoured" +(unique) co-ordinate system to occasion the introduction +of the æther-idea, and hence there can be no æther-drift, +nor any experiment with which to demonstrate it. +Here the contraction of moving bodies follows from +the two fundamental principles of the theory without +the introduction of particular hypotheses; and as the +prime factor involved in this contraction we find, not +the motion in itself, to which we cannot attach any +meaning, but the motion with respect to the body of +<span class="pagenum" id="Page_53">[Pg 53]</span> +reference chosen in the particular case in point. Thus +for a co-ordinate system moving with the earth the +mirror system of Michelson and Morley is not shortened, +but it <i>is</i> shortened for a co-ordinate system which is at +rest relatively to the sun. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_15_1"></a><a href="#FNanchor_15_1"><span class="label">[15]</span></a>The general theory of relativity renders it likely that the +electrical masses of an electron are held together by gravitational +forces.</p></div> + +<p><span class="pagenum" id="Page_54">[Pg 54]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XVII: MINKOWSKI'S FOUR-DIMENSIONAL SPACE"><a id="chap17"></a>XVII +<br><br> +MINKOWSKI'S FOUR-DIMENSIONAL SPACE</h2> + + +<p class="nind"> +<span class="dropcap">T</span>HE non-mathematician is seized by a +mysterious shuddering when he hears of "four-dimensional" +things, by a feeling not unlike that awakened by +thoughts of the occult. And yet there is no more +common-place statement than that the world in which +we live is a four-dimensional space-time continuum. +</p> +<p> +Space is a three-dimensional continuum. By this +we mean that it is possible to describe the position of a +point (at rest) by means of three numbers (co-ordinates) +<img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, and that there is an indefinite number of points +in the neighbourhood of this one, the position of which +can be described by co-ordinates such as <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.464ex; width: 2.096ex; height: 1.464ex;" src="images/71.svg" alt=" " data-tex="y_{1}">, <img style="vertical-align: -0.339ex; width: 2.04ex; height: 1.339ex;" src="images/72.svg" alt=" " data-tex="z_{1}">, +which may be as near as we choose to the respective values of +the co-ordinates <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z"> of the first point. In virtue of the +latter property we speak of a "continuum," and owing +to the fact that there are three co-ordinates we speak of +it as being "three-dimensional." +</p> +<p> +Similarly, the world of physical phenomena which was +briefly called "world" by Minkowski is naturally +four-dimensional in the space-time sense. For it is +composed of individual events, each of which is described +by four numbers, namely, three space +co-ordinates <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z"> and a time co-ordinate, the time-value +<img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">. The "world" is in this sense also a continuum; +for to every event there are as many "neighbouring" +<span class="pagenum" id="Page_55">[Pg 55]</span> +events (realised or at least thinkable) as we care to +choose, the co-ordinates <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.464ex; width: 2.096ex; height: 1.464ex;" src="images/71.svg" alt=" " data-tex="y_{1}">, <img style="vertical-align: -0.339ex; width: 2.04ex; height: 1.339ex;" src="images/72.svg" alt=" " data-tex="z_{1}">, <img style="vertical-align: -0.339ex; width: 1.804ex; height: 1.756ex;" src="images/73.svg" alt=" " data-tex="t_{1}"> of +which differ by an indefinitely small amount from those of the +event <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> originally considered. That we have not +been accustomed to regard the world in this sense as a +four-dimensional continuum is due to the fact that in +physics, before the advent of the theory of relativity, +time played a different and more independent rôle, as +compared with the space co-ordinates. It is for this +reason that we have been in the habit of treating time +as an independent continuum. As a matter of fact, +according to classical mechanics, time is absolute, +<i>i.e.</i> it is independent of the position and the condition +of motion of the system of co-ordinates. We see this +expressed in the last equation of the Galileian transformation +(<img style="vertical-align: -0.186ex; width: 5.278ex; height: 1.903ex;" src="images/74.svg" alt=" " data-tex="t' = t">). +</p> +<p> +The four-dimensional mode of consideration of the +"world" is natural on the theory of relativity, since +according to this theory time is robbed of its independence. +This is shown by the fourth equation of the +Lorentz transformation: +<span class="align-center"><img style="vertical-align: -5.475ex; width: 15.371ex; height: 10.701ex;" src="images/75.svg" alt=" " data-tex=" +t' = \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +"></span> +Moreover, according to this equation the time difference <img style="vertical-align: -0.025ex; width: 2.701ex; height: 1.645ex;" src="images/76.svg" alt=" " data-tex="\Delta t">' +of two events with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' does not in general +vanish, even when the time difference <img style="vertical-align: -0.025ex; width: 2.701ex; height: 1.645ex;" src="images/76.svg" alt=" " data-tex="\Delta t"> of the same +events with reference to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> vanishes. Pure "space-distance" +of two events with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> results in +"time-distance" of the same events with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. +But the discovery of Minkowski, which was of importance +<span class="pagenum" id="Page_56">[Pg 56]</span> +for the formal development of the theory of relativity, +does not lie here. It is to be found rather in +the fact of his recognition that the four-dimensional +space-time continuum of the theory of relativity, in its +most essential formal properties, shows a pronounced +relationship to the three-dimensional continuum of +Euclidean geometrical space.<a id="FNanchor_16_1"></a><a href="#Footnote_16_1" class="fnanchor">[16]</a> +In order to give due +prominence to this relationship, however, we must +replace the usual time co-ordinate <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> by an imaginary +magnitude <img style="vertical-align: -0.318ex; width: 8.252ex; height: 2.398ex;" src="images/77.svg" alt=" " data-tex="\sqrt{-1}·ct"> proportional to it. Under these +conditions, the natural laws satisfying the demands of +the (special) theory of relativity assume mathematical +forms, in which the time co-ordinate plays exactly the +same rôle as the three space co-ordinates. Formally, +these four co-ordinates correspond exactly to the three +space co-ordinates in Euclidean geometry. It must be +clear even to the non-mathematician that, as a consequence +of this purely formal addition to our knowledge, +the theory perforce gained clearness in no mean +measure. +</p> +<p> +These inadequate remarks can give the reader only a +vague notion of the important idea contributed by Minkowski. +Without it the general theory of relativity, of +which the fundamental ideas are developed in the following +pages, would perhaps have got no farther than its +long clothes. Minkowski's work is doubtless difficult of +access to anyone inexperienced in mathematics, but +since it is not necessary to have a very exact grasp of +this work in order to understand the fundamental ideas +of either the special or the general theory of relativity, +I shall at present leave it here, and shall revert to it +only towards the end of Part II. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_16_1"></a><a href="#FNanchor_16_1"><span class="label">[16]</span></a>Cf. the somewhat more detailed discussion in Appendix II.</p></div> + +<p><span class="pagenum" id="Page_57">[Pg 57]</span></p> + +<p><span class="pagenum" id="Page_58">[Pg 58]</span></p> + +</div> + +<p><br><br><br></p> + +<div class="chapter"> +<h2 title="PART II: THE GENERAL THEORY OF RELATIVITY"><a id="part02"></a>PART II +<br> +THE GENERAL THEORY OF RELATIVITY</h2> + +<p><br><br></p> + +<h2 title="XVIII: SPECIAL AND GENERAL PRINCIPLE OF +RELATIVITY"><a id="chap18"></a>XVIII +<br><br> +SPECIAL AND GENERAL PRINCIPLE OF +RELATIVITY +</h2> + +<p class="nind"> +<span class="dropcap">T</span>HE basal principle, which was the pivot of +all our previous considerations, was the <i>special</i> +principle of relativity, <i>i.e.</i> the principle of the +physical relativity of all <i>uniform</i> motion. Let us once +more analyse its meaning carefully. +</p> +<p> +It was at all times clear that, from the point of view +of the idea it conveys to us, every motion must only +be considered as a relative motion. Returning to the +illustration we have frequently used of the embankment +and the railway carriage, we can express the fact of the +motion here taking place in the following two forms, +both of which are equally justifiable: +</p> +<p class="hanging2"> +(<i>a</i>) The carriage is in motion relative to the embankment. +</p> +<p class="hanging2"> +(<i>b</i>) The embankment is in motion relative to the +carriage. +</p> +<p> +In (<i>a</i>) the embankment, in (<i>b</i>) the carriage, serves as +the body of reference in our statement of the motion +taking place. If it is simply a question of detecting +<span class="pagenum" id="Page_59">[Pg 59]</span> +or of describing the motion involved, it is in principle +immaterial to what reference-body we refer the motion. +As already mentioned, this is self-evident, but it must +not be confused with the much more comprehensive +statement called "the principle of relativity," which +we have taken as the basis of our investigations. +</p> +<p> +The principle we have made use of not only maintains +that we may equally well choose the carriage or the +embankment as our reference-body for the description +of any event (for this, too, is self-evident). Our principle +rather asserts what follows: If we formulate the general +laws of nature as they are obtained from experience, +by making use of +</p> +<p class="hanging2"> +(<i>a</i>) the embankment as reference-body, +</p> +<p class="hanging2"> +(<i>b</i>) the railway carriage as reference-body, +</p> +<p class="nind"> +then these general laws of nature (<i>e.g.</i> the laws of +mechanics or the law of the propagation of light <i>in vacuo</i>) +have exactly the same form in both cases. This can +also be expressed as follows: For the <i>physical</i> description +of natural processes, neither of the reference-bodies +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' is unique (lit. "specially marked out") as +compared with the other. Unlike the first, this latter +statement need not of necessity hold <i>a priori</i>; it is +not contained in the conceptions of "motion" and +"reference-body" and derivable from them; only +<i>experience</i> can decide as to its correctness or incorrectness. +</p> +<p> +Up to the present, however, we have by no means +maintained the equivalence of <i>all</i> bodies of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +in connection with the formulation of natural laws. +Our course was more on the following lines. In the +first place, we started out from the assumption that +there exists a reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, whose condition of +<span class="pagenum" id="Page_60">[Pg 60]</span> +motion is such that the Galileian law holds with respect +to it: A particle left to itself and sufficiently far removed +from all other particles moves uniformly in a straight +line. With reference to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> (Galileian reference-body) the +laws of nature were to be as simple as possible. But +in addition to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, all bodies of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' should +be given preference in this sense, and they should be exactly +equivalent to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> for the formulation of natural laws, +provided that they are in a state of <i>uniform rectilinear +and non-rotary motion</i> with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">; all these +bodies of reference are to be regarded as Galileian +reference-bodies. The validity of the principle of +relativity was assumed only for these reference-bodies, +but not for others (<i>e.g.</i> those possessing motion of a +different kind). In this sense we speak of the <i>special</i> +principle of relativity, or special theory of relativity. +</p> +<p> +In contrast to this we wish to understand by the +"general principle of relativity" the following statement: +All bodies of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', etc., are equivalent +for the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion. But before proceeding farther, it +ought to be pointed out that this formulation must be +replaced later by a more abstract one, for reasons which +will become evident at a later stage. +</p> +<p> +Since the introduction of the special principle of +relativity has been justified, every intellect which +strives after generalisation must feel the temptation +to venture the step towards the general principle of +relativity. But a simple and apparently quite reliable +consideration seems to suggest that, for the present +at any rate, there is little hope of success in such an +attempt. Let us imagine ourselves transferred to our +<span class="pagenum" id="Page_61">[Pg 61]</span> +old friend the railway carriage, which is travelling at a +uniform rate. As long as it is moving uniformly, the +occupant of the carriage is not sensible of its motion, +and it is for this reason that he can without reluctance +interpret the facts of the case as indicating that the +carriage is at rest but the embankment in motion. +Moreover, according to the special principle of relativity, +this interpretation is quite justified also from a physical +point of view. +</p> +<p> +If the motion of the carriage is now changed into a +non-uniform motion, as for instance by a powerful +application of the brakes, then the occupant of the +carriage experiences a correspondingly powerful jerk +forwards. The retarded motion is manifested in the +mechanical behaviour of bodies relative to the person +in the railway carriage. The mechanical behaviour is +different from that of the case previously considered, +and for this reason it would appear to be impossible +that the same mechanical laws hold relatively to the non-uniformly +moving carriage, as hold with reference to the +carriage when at rest or in uniform motion. At all +events it is clear that the Galileian law does not hold +with respect to the non-uniformly moving carriage. +Because of this, we feel compelled at the present juncture +to grant a kind of absolute physical reality to non-uniform +motion, in opposition to the general principle +of relativity. But in what follows we shall soon see +that this conclusion cannot be maintained. +<span class="pagenum" id="Page_62">[Pg 62]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XIX: THE GRAVITATIONAL FIELD"><a id="chap19"></a>XIX +<br><br> +THE GRAVITATIONAL FIELD</h2> + +<p class="nind"> +<span class="dropcap">I</span>F we pick up a stone and then let it go, why +does it fall to the ground?" The usual answer to this +question is: "Because it is attracted by the earth." +Modern physics formulates the answer rather differently +for the following reason. As a result of the more careful +study of electromagnetic phenomena, we have come +to regard action at a distance as a process impossible +without the intervention of some intermediary medium. +If, for instance, a magnet attracts a piece of iron, we +cannot be content to regard this as meaning that the +magnet acts directly on the iron through the intermediate +empty space, but we are constrained to imagine—after +the manner of Faraday—that the magnet +always calls into being something physically real in +the space around it, that something being what we call a +"magnetic field." In its turn this magnetic field +operates on the piece of iron, so that the latter strives +to move towards the magnet. We shall not discuss +here the justification for this incidental conception, +which is indeed a somewhat arbitrary one. We shall +only mention that with its aid electromagnetic phenomena +can be theoretically represented much more +satisfactorily than without it, and this applies particularly +to the transmission of electromagnetic waves. +<span class="pagenum" id="Page_63">[Pg 63]</span> +The effects of gravitation also are regarded in an analogous +manner. +</p> +<p> +The action of the earth on the stone takes place indirectly. +The earth produces in its surroundings a +gravitational field, which acts on the stone and produces +its motion of fall. As we know from experience, the +intensity of the action on a body diminishes according +to a quite definite law, as we proceed farther and farther +away from the earth. From our point of view this +means: The law governing the properties of the gravitational +field in space must be a perfectly definite one, in +order correctly to represent the diminution of gravitational +action with the distance from operative bodies. +It is something like this: The body (<i>e.g.</i> the earth) produces +a field in its immediate neighbourhood directly; +the intensity and direction of the field at points farther +removed from the body are thence determined by +the law which governs the properties in space of the +gravitational fields themselves. +</p> +<p> +In contrast to electric and magnetic fields, the gravitational +field exhibits a most remarkable property, which +is of fundamental importance for what follows. Bodies +which are moving under the sole influence of a gravitational +field receive an acceleration, <i>which does not in the +least depend either on the material or on the physical +state of the body</i>. For instance, a piece of lead and +a piece of wood fall in exactly the same manner in a +gravitational field (<i>in vacuo</i>), when they start off from +rest or with the same initial velocity. This law, which +holds most accurately, can be expressed in a different +form in the light of the following consideration. +</p> +<p> +According to Newton's law of motion, we have +<span class="align-center"><img style="vertical-align: -0.566ex; width: 40.298ex; height: 2.262ex;" src="images/78.svg" alt=" " data-tex=" +(\text{Force}) = (\text{inertial mass}) × (\text{acceleration}), +"></span> +<span class="pagenum" id="Page_64">[Pg 64]</span> +where the "inertial mass" is a characteristic constant +of the accelerated body. If now gravitation is the +cause of the acceleration, we then have +<span class="align-center"><img style="vertical-align: -2.036ex; width: 39.12ex; height: 5.204ex;" src="images/79.svg" alt=" " data-tex=" +\begin{align*} +(\text{Force}) + = (\text{gravitational mass})\\ + \mspace{18.0mu} × (\text{intensity of the gravitational field}), +\end{align*} +"></span> +where the "gravitational mass" is likewise a characteristic +constant for the body. From these two relations +follows: +<span class="align-center"><img style="vertical-align: -3.643ex; width: 37.36ex; height: 8.416ex;" src="images/80.svg" alt=" " data-tex=" +\begin{align*} +(\text{acceleration}) + = \frac{(\text{gravitational mass})}{(\text{inertial mass})}\\ + \mspace{18.0mu} (\text{intensity of the gravitational field}). +\end{align*} +"></span> +</p> +<p> +If now, as we find from experience, the acceleration is +to be independent of the nature and the condition of the +body and always the same for a given gravitational +field, then the ratio of the gravitational to the inertial +mass must likewise be the same for all bodies. By a +suitable choice of units we can thus make this ratio +equal to unity. We then have the following law: +The <i>gravitational</i> mass of a body is equal to its <i>inertial</i> +mass. +</p> +<p> +It is true that this important law had hitherto been +recorded in mechanics, but it had not been <i>interpreted</i>. +A satisfactory interpretation can be obtained only if we +recognise the following fact: <i>The same</i> quality of a +body manifests itself according to circumstances as +"inertia" or as "weight" (lit. "heaviness"). In the +following section we shall show to what extent this is +actually the case, and how this question is connected +with the general postulate of relativity. +<span class="pagenum" id="Page_65">[Pg 65]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XX: THE EQUALITY OF INERTIAL AND GRAVITATIONAL +MASS AS AN ARGUMENT FOR THE +GENERAL POSTULATE OF RELATIVITY"><a id="chap20"></a>XX +<br><br> +THE EQUALITY OF INERTIAL AND GRAVITATIONAL +MASS AS AN ARGUMENT FOR THE +GENERAL POSTULATE OF RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">W</span>E imagine a large portion of empty space, so +far removed from stars and other appreciable +masses, that we have before us approximately +the conditions required by the fundamental law of Galilei. +It is then possible to choose a Galileian reference-body for +this part of space (world), relative to which points at +rest remain at rest and points in motion continue permanently +in uniform rectilinear motion. As reference-body +let us imagine a spacious chest resembling a room +with an observer inside who is equipped with apparatus. +Gravitation naturally does not exist for this observer. +He must fasten himself with strings to the floor, +otherwise the slightest impact against the floor will +cause him to rise slowly towards the ceiling of the +room. +</p> +<p> +To the middle of the lid of the chest is fixed externally +a hook with rope attached, and now a "being" (what +kind of a being is immaterial to us) begins pulling at +this with a constant force. The chest together with the +observer then begin to move "upwards" with a +uniformly accelerated motion. In course of time their +velocity will reach unheard-of values—provided that +<span class="pagenum" id="Page_66">[Pg 66]</span> +we are viewing all this from another reference-body +which is not being pulled with a rope. +</p> +<p> +But how does the man in the chest regard the process? +The acceleration of the chest will be transmitted to him +by the reaction of the floor of the chest. He must +therefore take up this pressure by means of his legs if +he does not wish to be laid out full length on the floor. +He is then standing in the chest in exactly the same way +as anyone stands in a room of a house on our earth. +If he release a body which he previously had in his +hand, the acceleration of the chest will no longer be +transmitted to this body, and for this reason the body +will approach the floor of the chest with an accelerated +relative motion. The observer will further convince +himself <i>that the acceleration of the body towards the floor +of the chest is always of the same magnitude, whatever +kind of body he may happen to use for the experiment</i>. +</p> +<p> +Relying on his knowledge of the gravitational field +(as it was discussed in the preceding section), the man +in the chest will thus come to the conclusion that he +and the chest are in a gravitational field which is constant +with regard to time. Of course he will be puzzled for +a moment as to why the chest does not fall, in this +gravitational field. Just then, however, he discovers +the hook in the middle of the lid of the chest and the +rope which is attached to it, and he consequently comes +to the conclusion that the chest is suspended at rest in +the gravitational field. +</p> +<p> +Ought we to smile at the man and say that he errs +in his conclusion? I do not believe we ought to if we +wish to remain consistent; we must rather admit that +his mode of grasping the situation violates neither reason +nor known mechanical laws. Even though it is being +<span class="pagenum" id="Page_67">[Pg 67]</span> +accelerated with respect to the "Galileian space" +first considered, we can nevertheless regard the chest +as being at rest. We have thus good grounds for +extending the principle of relativity to include bodies +of reference which are accelerated with respect to each +other, and as a result we have gained a powerful argument +for a generalised postulate of relativity. +</p> +<p> +We must note carefully that the possibility of this +mode of interpretation rests on the fundamental +property of the gravitational field of giving all bodies +the same acceleration, or, what comes to the same thing, +on the law of the equality of inertial and gravitational +mass. If this natural law did not exist, the man in +the accelerated chest would not be able to interpret +the behaviour of the bodies around him on the supposition +of a gravitational field, and he would not be justified +on the grounds of experience in supposing his reference-body +to be "at rest." +</p> +<p> +Suppose that the man in the chest fixes a rope to the +inner side of the lid, and that he attaches a body to the +free end of the rope. The result of this will be to stretch +the rope so that it will hang "vertically" downwards. +If we ask for an opinion of the cause of tension in the +rope, the man in the chest will say: "The suspended +body experiences a downward force in the gravitational +field, and this is neutralised by the tension of the rope; +what determines the magnitude of the tension of the +rope is the <i>gravitational mass</i> of the suspended body." +On the other hand, an observer who is poised freely in +space will interpret the condition of things thus: "The +rope must perforce take part in the accelerated motion +of the chest, and it transmits this motion to the body +attached to it. The tension of the rope is just large +<span class="pagenum" id="Page_68">[Pg 68]</span> +enough to effect the acceleration of the body. That +which determines the magnitude of the tension of the +rope is the <i>inertial mass</i> of the body." Guided by +this example, we see that our extension of the principle +of relativity implies the <i>necessity</i> of the law of the +equality of inertial and gravitational mass. Thus we +have obtained a physical interpretation of this law. +</p> +<p> +From our consideration of the accelerated chest we +see that a general theory of relativity must yield important +results on the laws of gravitation. In point of +fact, the systematic pursuit of the general idea of relativity +has supplied the laws satisfied by the gravitational +field. Before proceeding farther, however, I +must warn the reader against a misconception suggested +by these considerations. A gravitational field exists +for the man in the chest, despite the fact that there was +no such field for the co-ordinate system first chosen. +Now we might easily suppose that the existence of a +gravitational field is always only an <i>apparent</i> one. We +might also think that, regardless of the kind of gravitational +field which may be present, we could always +choose another reference-body such that <i>no</i> gravitational +field exists with reference to it. This is by no means +true for all gravitational fields, but only for those of +quite special form. It is, for instance, impossible to +choose a body of reference such that, as judged from it, +the gravitational field of the earth (in its entirety) +vanishes. +</p> +<p> +We can now appreciate why that argument is not +convincing, which we brought forward against the +general principle of relativity at the end of Section XVIII. +It is certainly true that the observer in the railway +carriage experiences a jerk forwards as a result of the +<span class="pagenum" id="Page_69">[Pg 69]</span> +application of the brake, and that he recognises in this the +non-uniformity of motion (retardation) of the carriage. +But he is compelled by nobody to refer this jerk to a +"real" acceleration (retardation) of the carriage. He +might also interpret his experience thus: "My body of +reference (the carriage) remains permanently at rest. +With reference to it, however, there exists (during the +period of application of the brakes) a gravitational +field which is directed forwards and which is variable +with respect to time. Under the influence of this field, +the embankment together with the earth moves non-uniformly +in such a manner that their original velocity +in the backwards direction is continuously reduced." +<span class="pagenum" id="Page_70">[Pg 70]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXI: IN WHAT RESPECTS ARE THE FOUNDATIONS +OF CLASSICAL MECHANICS AND OF THE +SPECIAL THEORY OF RELATIVITY UNSATISFACTORY?"><a id="chap21"></a>XXI +<br><br> +IN WHAT RESPECTS ARE THE FOUNDATIONS +OF CLASSICAL MECHANICS AND OF THE +SPECIAL THEORY OF RELATIVITY UNSATISFACTORY?</h2> + +<p class="nind"> +<span class="dropcap">W</span>E have already stated several times that +classical mechanics starts out from the following +law: Material particles sufficiently far +removed from other material particles continue to +move uniformly in a straight line or continue in a +state of rest. We have also repeatedly emphasised +that this fundamental law can only be valid for +bodies of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> which possess certain unique +states of motion, and which are in uniform translational +motion relative to each other. Relative to other reference-bodies +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> the law is not valid. Both in classical +mechanics and in the special theory of relativity we +therefore differentiate between reference-bodies <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +relative to which the recognised "laws of nature" can +be said to hold, and reference-bodies <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> relative to which +these laws do not hold. +</p> +<p> +But no person whose mode of thought is logical can +rest satisfied with this condition of things. He asks: +"How does it come that certain reference-bodies (or +their states of motion) are given priority over other +reference-bodies (or their states of motion)? <i>What is +<span class="pagenum" id="Page_71">[Pg 71]</span> +the reason for this preference?</i>" In order to show clearly +what I mean by this question, I shall make use of a +comparison. +</p> +<p> +I am standing in front of a gas range. Standing +alongside of each other on the range are two pans so +much alike that one may be mistaken for the other. +Both are half full of water. I notice that steam is being +emitted continuously from the one pan, but not from the +other. I am surprised at this, even if I have never seen +either a gas range or a pan before. But if I now notice +a luminous something of bluish colour under the first +pan but not under the other, I cease to be astonished, +even if I have never before seen a gas flame. For I +can only say that this bluish something will cause the +emission of the steam, or at least <i>possibly</i> it may do so. +If, however, I notice the bluish something in neither +case, and if I observe that the one continuously emits +steam whilst the other does not, then I shall remain +astonished and dissatisfied until I have discovered +some circumstance to which I can attribute the different +behaviour of the two pans. +</p> +<p> +Analogously, I seek in vain for a real something in +classical mechanics (or in the special theory of relativity) +to which I can attribute the different behaviour +of bodies considered with respect to the reference-systems +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> and <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'.<a id="FNanchor_17_1"></a><a href="#Footnote_17_1" class="fnanchor">[17]</a> +Newton saw this objection and +attempted to invalidate it, but without success. But +E. Mach recognised it most clearly of all, and because +of this objection he claimed that mechanics must be +<span class="pagenum" id="Page_72">[Pg 72]</span> +placed on a new basis. It can only be got rid of by +means of a physics which is conformable to the general +principle of relativity, since the equations of such a +theory hold for every body of reference, whatever +may be its state of motion. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_17_1"></a><a href="#FNanchor_17_1"><span class="label">[17]</span></a>The objection is of importance more especially when the state +of motion of the reference-body is of such a nature that it does +not require any external agency for its maintenance, <i>e.g.</i> in +the case when the reference-body is rotating uniformly.</p></div> + +<p><span class="pagenum" id="Page_73">[Pg 73]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXII: A FEW INFERENCES FROM THE GENERAL +PRINCIPLE OF RELATIVITY"><a id="chap22"></a>XXII +<br><br> +A FEW INFERENCES FROM THE GENERAL +PRINCIPLE OF RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">T</span>HE considerations of Section XX show that the +general principle of relativity puts us in a position +to derive properties of the gravitational field in a +purely theoretical manner. Let us suppose, for instance, +that we know the space-time "course" for any natural +process whatsoever, as regards the manner in which it +takes place in the Galileian domain relative to a +Galileian body of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. By means of purely +theoretical operations (<i>i.e.</i> simply by calculation) we are +then able to find how this known natural process +appears, as seen from a reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' which is +accelerated relatively to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. But since a gravitational +field exists with respect to this new body of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', +our consideration also teaches us how the gravitational +field influences the process studied. +</p> +<p> +For example, we learn that a body which is in a state +of uniform rectilinear motion with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> (in +accordance with the law of Galilei) is executing an +accelerated and in general curvilinear motion with +respect to the accelerated reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' (chest). +This acceleration or curvature corresponds to the influence +on the moving body of the gravitational field +prevailing relatively to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. It is known that a gravitational +field influences the movement of bodies in this +<span class="pagenum" id="Page_74">[Pg 74]</span> +way, so that our consideration supplies us with nothing +essentially new. +</p> +<p> +However, we obtain a new result of fundamental +importance when we carry out the analogous consideration +for a ray of light. With respect to the Galileian +reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, such a ray of light is transmitted +rectilinearly with the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">. It can easily be shown +that the path of the same ray of light is no longer a +straight line when we consider it with reference to the +accelerated chest (reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'). From this we +conclude, <i>that, in general, rays of light are propagated +curvilinearly in gravitational fields</i>. In two respects +this result is of great importance. +</p> +<p> +In the first place, it can be compared with the reality. +Although a detailed examination of the question shows +that the curvature of light rays required by the general +theory of relativity is only exceedingly small for the +gravitational fields at our disposal in practice, its estimated +magnitude for light rays passing the sun at +grazing incidence is nevertheless 1.7 seconds of arc. +This ought to manifest itself in the following way. +As seen from the earth, certain fixed stars appear to be +in the neighbourhood of the sun, and are thus capable +of observation during a total eclipse of the sun. At such +times, these stars ought to appear to be displaced +outwards from the sun by an amount indicated above, +as compared with their apparent position in the sky +when the sun is situated at another part of the heavens. +The examination of the correctness or otherwise of this +deduction is a problem of the greatest importance, the +early solution of which is to be expected of astronomers.<a id="FNanchor_18_1"></a><a href="#Footnote_18_1" class="fnanchor">[18]</a> +<span class="pagenum" id="Page_75">[Pg 75]</span> +</p> +<p> +In the second place our result shows that, according +to the general theory of relativity, the law of the constancy +of the velocity of light <i>in vacuo</i>, which constitutes +one of the two fundamental assumptions in the +special theory of relativity and to which we have +already frequently referred, cannot claim any unlimited +validity. A curvature of rays of light can only take +place when the velocity of propagation of light varies +with position. Now we might think that as a consequence +of this, the special theory of relativity and with +it the whole theory of relativity would be laid in the +dust. But in reality this is not the case. We can only +conclude that the special theory of relativity cannot +claim an unlimited domain of validity; its results +hold only so long as we are able to disregard the influences +of gravitational fields on the phenomena +(<i>e.g.</i> of light). +</p> +<p> +Since it has often been contended by opponents of +the theory of relativity that the special theory of +relativity is overthrown by the general theory of relativity, +it is perhaps advisable to make the facts of the +case clearer by means of an appropriate comparison. +Before the development of electrodynamics the laws +of electrostatics were looked upon as the laws of +electricity. At the present time we know that +electric fields can be derived correctly from electrostatic +considerations only for the case, which is never +strictly realised, in which the electrical masses are quite +at rest relatively to each other, and to the co-ordinate +system. Should we be justified in saying that for this +<span class="pagenum" id="Page_76">[Pg 76]</span> +reason electrostatics is overthrown by the field-equations +of Maxwell in electrodynamics? Not in the least. +Electrostatics is contained in electrodynamics as a +limiting case; the laws of the latter lead directly to +those of the former for the case in which the fields are +invariable with regard to time. No fairer destiny +could be allotted to any physical theory, than that it +should of itself point out the way to the introduction +of a more comprehensive theory, in which it lives on +as a limiting case. +</p> +<p> +In the example of the transmission of light just dealt +with, we have seen that the general theory of relativity +enables us to derive theoretically the influence of a +gravitational field on the course of natural processes, +the laws of which are already known when a gravitational +field is absent. But the most attractive problem, +to the solution of which the general theory of relativity +supplies the key, concerns the investigation of the laws +satisfied by the gravitational field itself. Let us consider +this for a moment. +</p> +<p> +We are acquainted with space-time domains which +behave (approximately) in a "Galileian" fashion under +suitable choice of reference-body, <i>i.e.</i> domains in which +gravitational fields are absent. If we now refer such +a domain to a reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' possessing any kind +of motion, then relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' there exists a gravitational +field which is variable with respect to space and +time.<a id="FNanchor_19_1"></a><a href="#Footnote_19_1" class="fnanchor">[19]</a> +The character of this field will of course depend +on the motion chosen for <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. According to the general +theory of relativity, the general law of the gravitational +field must be satisfied for all gravitational fields obtainable +<span class="pagenum" id="Page_77">[Pg 77]</span> +in this way. Even though by no means all gravitational +fields can be produced in this way, yet we may +entertain the hope that the general law of gravitation +will be derivable from such gravitational fields of a +special kind. This hope has been realised in the most +beautiful manner. But between the clear vision of +this goal and its actual realisation it was necessary to +surmount a serious difficulty, and as this lies deep at +the root of things, I dare not withhold it from the reader. +We require to extend our ideas of the space-time continuum +still farther. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_18_1"></a><a href="#FNanchor_18_1"><span class="label">[18]</span></a>By means of the star photographs of two expeditions equipped +by a Joint Committee of the Royal and Royal Astronomical +Societies, the existence of the deflection of light demanded by +theory was confirmed during the solar eclipse of 29th May, 1919. +(Cf. Appendix III.)</p></div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_19_1"></a><a href="#FNanchor_19_1"><span class="label">[19]</span></a>This follows from a generalisation of the discussion in Section XX.</p></div> + +<p><span class="pagenum" id="Page_78">[Pg 78]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXIII: BEHAVIOUR OF CLOCKS AND MEASURING-RODS +ON A ROTATING BODY OF REFERENCE"><a id="chap23"></a>XXIII +<br><br> +BEHAVIOUR OF CLOCKS AND MEASURING-RODS +ON A ROTATING BODY OF REFERENCE</h2> + +<p class="nind"> +<span class="dropcap">H</span>ITHERTO I have purposely refrained from +speaking about the physical interpretation of +space- and time-data in the case of the general +theory of relativity. As a consequence, I am guilty of a +certain slovenliness of treatment, which, as we know +from the special theory of relativity, is far from being +unimportant and pardonable. It is now high time that +we remedy this defect; but I would mention at the +outset, that this matter lays no small claims on the +patience and on the power of abstraction of the reader. +</p> +<p> +We start off again from quite special cases, which we +have frequently used before. Let us consider a space-time +domain in which no gravitational field exists +relative to a reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> whose state of motion +has been suitably chosen. <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> is then a Galileian reference-body +as regards the domain considered, and the +results of the special theory of relativity hold relative +to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. Let us suppose the same domain referred to a +second body of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', which is rotating uniformly +with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. In order to fix our ideas, we shall +imagine <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' to be in the form of a plane circular disc, +which rotates uniformly in its own plane about its +centre. An observer who is sitting eccentrically on the +<span class="pagenum" id="Page_79">[Pg 79]</span> +disc <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' is sensible of a force which acts outwards in a +radial direction, and which would be interpreted as an +effect of inertia (centrifugal force) by an observer who +was at rest with respect to the original reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. +But the observer on the disc may regard his disc as a +reference-body which is "at rest"; on the basis of the +general principle of relativity he is justified in doing this. +The force acting on himself, and in fact on all other +bodies which are at rest relative to the disc, he regards +as the effect of a gravitational field. Nevertheless, +the space-distribution of this gravitational field is of a +kind that would not be possible on Newton's theory of +gravitation.<a id="FNanchor_20_1"></a><a href="#Footnote_20_1" class="fnanchor">[20]</a> +But since the observer believes in the +general theory of relativity, this does not disturb him; +he is quite in the right when he believes that a general +law of gravitation can be formulated—a law which not +only explains the motion of the stars correctly, but +also the field of force experienced by himself. +</p> +<p> +The observer performs experiments on his circular +disc with clocks and measuring-rods. In doing so, it +is his intention to arrive at exact definitions for the +signification of time- and space-data with reference +to the circular disc <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', these definitions being based on +his observations. What will be his experience in this +enterprise? +</p> +<p> +To start with, he places one of two identically constructed +clocks at the centre of the circular disc, and the +other on the edge of the disc, so that they are at rest +relative to it. We now ask ourselves whether both +clocks go at the same rate from the standpoint of the +<span class="pagenum" id="Page_80">[Pg 80]</span> +non-rotating Galileian reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. As judged +from this body, the clock at the centre of the disc has +no velocity, whereas the clock at the edge of the disc +is in motion relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> in consequence of the rotation. +According to a result obtained in Section XII, it follows +that the latter clock goes at a rate permanently slower +than that of the clock at the centre of the circular disc, +<i>i.e.</i> as observed from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. It is obvious that the same +effect would be noted by an observer whom we will imagine +sitting alongside his clock at the centre of the circular +disc. Thus on our circular disc, or, to make the case +more general, in every gravitational field, a clock will +go more quickly or less quickly, according to the position +in which the clock is situated (at rest). For this reason +it is not possible to obtain a reasonable definition of time +with the aid of clocks which are arranged at rest with +respect to the body of reference. A similar difficulty +presents itself when we attempt to apply our earlier +definition of simultaneity in such a case, but I do not +wish to go any farther into this question. +</p> +<p> +Moreover, at this stage the definition of the space +co-ordinates also presents insurmountable difficulties. +If the observer applies his standard measuring-rod +(a rod which is short as compared with the radius of +the disc) tangentially to the edge of the disc, then, as +judged from the Galileian system, the length of this rod +will be less than 1, since, according to Section XII, moving +bodies suffer a shortening in the direction of the motion. +On the other hand, the measuring-rod will not experience +a shortening in length, as judged from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, if it is applied +to the disc in the direction of the radius. If, then, the +observer first measures the circumference of the disc +with his measuring-rod and then the diameter of the +<span class="pagenum" id="Page_81">[Pg 81]</span> +disc, on dividing the one by the other, he will not obtain +as quotient the familiar number <img style="vertical-align: -0.186ex; width: 11.358ex; height: 1.717ex;" src="images/81.svg" alt=" " data-tex="\pi = 3.14\dots">, but +a larger number,<a id="FNanchor_21_1"></a><a href="#Footnote_21_1" class="fnanchor">[21]</a> +whereas of course, for a disc which is +at rest with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, this operation would yield <img style="vertical-align: -0.025ex; width: 1.29ex; height: 1ex;" src="images/82.svg" alt=" " data-tex="\pi"> +exactly. This proves that the propositions of Euclidean +geometry cannot hold exactly on the rotating disc, nor +in general in a gravitational field, at least if we attribute +the length 1 to the rod in all positions and in every +orientation. Hence the idea of a straight line also loses +its meaning. We are therefore not in a position to +define exactly the co-ordinates <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z"> relative to the +disc by means of the method used in discussing the +special theory, and as long as the co-ordinates and times +of events have not been defined, we cannot assign an +exact meaning to the natural laws in which these occur. +</p> +<p> +Thus all our previous conclusions based on general +relativity would appear to be called in question. In +reality we must make a subtle detour in order to be +able to apply the postulate of general relativity exactly. +I shall prepare the reader for this in the +following paragraphs. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_20_1"></a><a href="#FNanchor_20_1"><span class="label">[20]</span></a>The field disappears at the centre of the disc and increases +proportionally to the distance from the centre as we proceed +outwards.</p></div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_21_1"></a><a href="#FNanchor_21_1"><span class="label">[21]</span></a>Throughout this consideration we have to use the Galileian +(non-rotating) system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> as reference-body, since we may only +assume the validity of the results of the special theory of relativity +relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> (relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' a gravitational field +prevails).</p></div> + +<p><span class="pagenum" id="Page_82">[Pg 82]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXIV: EUCLIDEAN AND NON-EUCLIDEAN CONTINUUM"><a id="chap24"></a>XXIV +<br><br> +EUCLIDEAN AND NON-EUCLIDEAN CONTINUUM</h2> + +<p class="nind"> +<span class="dropcap">T</span>HE surface of a marble table is spread out in +front of me. I can get from any one point on this +table to any other point by passing continuously +from one point to a "neighbouring" one, and repeating +this process a (large) number of times, or, in other words, +by going from point to point without executing "jumps." +I am sure the reader will appreciate with sufficient +clearness what I mean here by "neighbouring" and by +"jumps" (if he is not too pedantic). We express this +property of the surface by describing the latter as a +continuum. +</p> +<p> +Let us now imagine that a large number of little rods +of equal length have been made, their lengths being +small compared with the dimensions of the marble +slab. When I say they are of equal length, I mean that +one can be laid on any other without the ends overlapping. +We next lay four of these little rods on the +marble slab so that they constitute a quadrilateral +figure (a square), the diagonals of which are equally +long. To ensure the equality of the diagonals, we make +use of a little testing-rod. To this square we add +similar ones, each of which has one rod in common +with the first. We proceed in like manner with each of +these squares until finally the whole marble slab is +<span class="pagenum" id="Page_83">[Pg 83]</span> +laid out with squares. The arrangement is such, that +each side of a square belongs to two squares and each +corner to four squares. +</p> +<p> +It is a veritable wonder that we can carry out this +business without getting into the greatest difficulties. +We only need to think of the following. If at any +moment three squares meet at a corner, then two sides +of the fourth square are already laid, and, as a consequence, +the arrangement of the remaining two sides of +the square is already completely determined. But I +am now no longer able to adjust the quadrilateral so +that its diagonals may be equal. If they are equal +of their own accord, then this is an especial favour +of the marble slab and of the little rods, about which I +can only be thankfully surprised. We must needs +experience many such surprises if the construction is to +be successful. +</p> +<p> +If everything has really gone smoothly, then I say +that the points of the marble slab constitute a Euclidean +continuum with respect to the little rod, which has been +used as a "distance" (line-interval). By choosing +one corner of a square as "origin," I can characterise +every other corner of a square with reference to this +origin by means of two numbers. I only need state +how many rods I must pass over when, starting from the +origin, I proceed towards the "right" and then "upwards," +in order to arrive at the corner of the square +under consideration. These two numbers are then the +"Cartesian co-ordinates" of this corner with reference +to the "Cartesian co-ordinate system" which is determined +by the arrangement of little rods. +</p> +<p> +By making use of the following modification of this +abstract experiment, we recognise that there must also +<span class="pagenum" id="Page_84">[Pg 84]</span> +be cases in which the experiment would be unsuccessful. +We shall suppose that the rods "expand" by an amount +proportional to the increase of temperature. We heat +the central part of the marble slab, but not the periphery, +in which case two of our little rods can still be +brought into coincidence at every position on the table. +But our construction of squares must necessarily come +into disorder during the heating, because the little rods +on the central region of the table expand, whereas +those on the outer part do not. +</p> +<p> +With reference to our little rods—defined as unit +lengths—the marble slab is no longer a Euclidean continuum, +and we are also no longer in the position of defining +Cartesian co-ordinates directly with their aid, +since the above construction can no longer be carried +out. But since there are other things which are not +influenced in a similar manner to the little rods (or +perhaps not at all) by the temperature of the table, it is +possible quite naturally to maintain the point of view +that the marble slab is a "Euclidean continuum." +This can be done in a satisfactory manner by making a +more subtle stipulation about the measurement or the +comparison of lengths. +</p> +<p> +But if rods of every kind (<i>i.e.</i> of every material) were +to behave <i>in the same way</i> as regards the influence of +temperature when they are on the variably heated +marble slab, and if we had no other means of detecting +the effect of temperature than the geometrical behaviour +of our rods in experiments analogous to the one +described above, then our best plan would be to assign +the distance <i>one</i> to two points on the slab, provided that +the ends of one of our rods could be made to coincide +with these two points; for how else should we define +<span class="pagenum" id="Page_85">[Pg 85]</span> +the distance without our proceeding being in the highest +measure grossly arbitrary? The method of Cartesian +co-ordinates must then be discarded, and replaced by +another which does not assume the validity of Euclidean +geometry for rigid bodies.<a id="FNanchor_22_1"></a><a href="#Footnote_22_1" class="fnanchor">[22]</a> +The reader will notice that +the situation depicted here corresponds to the one +brought about by the general postulate of relativity +(Section XXIII). +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_22_1"></a><a href="#FNanchor_22_1"><span class="label">[22]</span></a>Mathematicians have been confronted with our problem in the +following form. If we are given a surface (<i>e.g.</i> an ellipsoid) in +Euclidean three-dimensional space, then there exists for this +surface a two-dimensional geometry, just as much as for a plane +surface. Gauss undertook the task of treating this two-dimensional +geometry from first principles, without making use of the +fact that the surface belongs to a Euclidean continuum of +three dimensions. If we imagine constructions to be made with +rigid rods <i>in the surface</i> (similar to that above with the marble +slab), we should find that different laws hold for these from those +resulting on the basis of Euclidean plane geometry. The surface +is not a Euclidean continuum with respect to the rods, and we +cannot define Cartesian co-ordinates <i>in the surface</i>. Gauss +indicated the principles according to which we can treat the +geometrical relationships in the surface, and thus pointed out +the way to the method of Riemann of treating multi-dimensional, +non-Euclidean <i>continua</i>. Thus it is that mathematicians +long ago solved the formal problems to which we are led by the +general postulate of relativity.</p></div> + +<p><span class="pagenum" id="Page_86">[Pg 86]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXV: GAUSSIAN CO-ORDINATES"><a id="chap25"></a>XXV +<br><br> +GAUSSIAN CO-ORDINATES</h2> + +<p class="nind"> +<span class="dropcap">A</span>CCORDING to Gauss, this combined analytical +and geometrical mode of handling the problem +can be arrived at in the following way. We +imagine a system of arbitrary curves (see Fig. 4) +drawn on the surface of the table. These we designate +as <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u">-curves, and we indicate each of them by +means of a number. The curves <img style="vertical-align: -0.186ex; width: 5.442ex; height: 1.692ex;" src="images/84.svg" alt=" " data-tex="u = 1">, <img style="vertical-align: -0.186ex; width: 5.442ex; height: 1.692ex;" src="images/85.svg" alt=" " data-tex="u = 2"> and +<img style="vertical-align: -0.186ex; width: 5.442ex; height: 1.69ex;" src="images/86.svg" alt=" " data-tex="u = 3"> are drawn in the diagram. Between the curves +<img style="vertical-align: -0.186ex; width: 5.442ex; height: 1.692ex;" src="images/84.svg" alt=" " data-tex="u = 1"> and <img style="vertical-align: -0.186ex; width: 5.442ex; height: 1.692ex;" src="images/85.svg" alt=" " data-tex="u = 2"> we must imagine an infinitely large +number to be drawn, all of which correspond to real +numbers lying between 1 and 2. +</p> +<a id="figure04"></a> +<img src="images/figure04.jpg" class="floatleft" width="200" alt="fig4"> +<div class="caption"> +<p>FIG. 4.</p> +</div> +<p class="nind"> + We have then a system of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u">-curves, and +this "infinitely dense" system +covers the whole surface +of the table. These +<img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u">-curves must not intersect +each other, and through each +point of the surface one and +only one curve must pass. +Thus a perfectly definite +value of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u"> belongs to every point on the surface of the +marble slab. In like manner we imagine a system of +<img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">-curves drawn on the surface. These satisfy the same +conditions as the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u">-curves, they are provided with numbers +<span class="pagenum" id="Page_87">[Pg 87]</span> +in a corresponding manner, and they may likewise +be of arbitrary shape. It follows that a value of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u"> and +a value of <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> belong to every point on the surface of the +table. We call these two numbers the co-ordinates +of the surface of the table (Gaussian co-ordinates). +For example, the point <img style="vertical-align: 0; width: 1.699ex; height: 1.545ex;" src="images/87.svg" alt=" " data-tex="P"> in the diagram has the Gaussian +co-ordinates <img style="vertical-align: -0.186ex; width: 5.442ex; height: 1.69ex;" src="images/86.svg" alt=" " data-tex="u = 3">, <img style="vertical-align: -0.186ex; width: 5.246ex; height: 1.692ex;" src="images/88.svg" alt=" " data-tex="v = 1">. Two neighbouring points <img style="vertical-align: 0; width: 1.699ex; height: 1.545ex;" src="images/87.svg" alt=" " data-tex="P"> +and <img style="vertical-align: 0; width: 1.699ex; height: 1.545ex;" src="images/87.svg" alt=" " data-tex="P">' on the surface then correspond to the co-ordinates +<span class="align-center"><img style="vertical-align: -2.103ex; width: 22.537ex; height: 5.337ex;" src="images/89.svg" alt=" " data-tex=" +\begin{align*} +&P: &&u, v \\ +&P': &&u + du, v + dv, +\end{align*} +"></span> +where <img style="vertical-align: -0.025ex; width: 2.471ex; height: 1.595ex;" src="images/90.svg" alt=" " data-tex="du"> and <img style="vertical-align: -0.025ex; width: 2.274ex; height: 1.595ex;" src="images/91.svg" alt=" " data-tex="dv"> signify very small numbers. In a +similar manner we may indicate the distance (line-interval) +between <img style="vertical-align: 0; width: 1.699ex; height: 1.545ex;" src="images/87.svg" alt=" " data-tex="P"> and <img style="vertical-align: 0; width: 1.699ex; height: 1.545ex;" src="images/87.svg" alt=" " data-tex="P">', as measured with a little +rod, by means of the very small number <img style="vertical-align: -0.023ex; width: 2.238ex; height: 1.593ex;" src="images/92.svg" alt=" " data-tex="ds">. Then +according to Gauss we have +<span class="align-center"><img style="vertical-align: -0.464ex; width: 35.11ex; height: 2.464ex;" src="images/93.svg" alt=" " data-tex=" +ds^{2} = g_{11}\, du^{2} + 2g_{12}\, du\, dv + g_{22}\, dv^{2}, +"></span> +where <img style="vertical-align: -0.464ex; width: 2.867ex; height: 1.464ex;" src="images/94.svg" alt=" " data-tex="g_{11}">, <img style="vertical-align: -0.464ex; width: 2.867ex; height: 1.464ex;" src="images/95.svg" alt=" " data-tex="g_{12}">, <img style="vertical-align: -0.464ex; width: 2.867ex; height: 1.464ex;" src="images/96.svg" alt=" " data-tex="g_{22}">, are magnitudes which depend in a +perfectly definite way on <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u"> and <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">. The magnitudes <img style="vertical-align: -0.464ex; width: 2.867ex; height: 1.464ex;" src="images/94.svg" alt=" " data-tex="g_{11}">, +<img style="vertical-align: -0.464ex; width: 2.867ex; height: 1.464ex;" src="images/95.svg" alt=" " data-tex="g_{12}"> and <img style="vertical-align: -0.464ex; width: 2.867ex; height: 1.464ex;" src="images/96.svg" alt=" " data-tex="g_{22}"> determine the behaviour of the rods relative +to the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u">-curves and <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">-curves, and thus also relative +to the surface of the table. For the case in which the +points of the surface considered form a Euclidean continuum +with reference to the measuring-rods, but +only in this case, it is possible to draw the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u">-curves +and <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">-curves and to attach numbers to them, in such a +manner, that we simply have: +<span class="align-center"><img style="vertical-align: -0.186ex; width: 16.357ex; height: 2.185ex;" src="images/97.svg" alt=" " data-tex=" +ds^{2} = du^{2} + dv^{2}. +"></span> +Under these conditions, the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/83.svg" alt=" " data-tex="u">-curves and <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">-curves are +straight lines in the sense of Euclidean geometry, and +they are perpendicular to each other. Here the Gaussian +co-ordinates are simply Cartesian ones. It is clear +<span class="pagenum" id="Page_88">[Pg 88]</span> +that Gauss co-ordinates are nothing more than an +association of two sets of numbers with the points of +the surface considered, of such a nature that numerical +values differing very slightly from each other are +associated with neighbouring points "in space." +</p> +<p> +So far, these considerations hold for a continuum +of two dimensions. But the Gaussian method can be +applied also to a continuum of three, four or more +dimensions. If, for instance, a continuum of four +dimensions be supposed available, we may represent +it in the following way. With every point of the +continuum we associate arbitrarily four numbers, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, +<img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">, which are known as "co-ordinates." Adjacent +points correspond to adjacent values of the co-ordinates. +If a distance <img style="vertical-align: -0.023ex; width: 2.238ex; height: 1.593ex;" src="images/92.svg" alt=" " data-tex="ds"> is associated with the adjacent points +<img style="vertical-align: 0; width: 1.699ex; height: 1.545ex;" src="images/87.svg" alt=" " data-tex="P"> and <img style="vertical-align: 0; width: 1.699ex; height: 1.545ex;" src="images/87.svg" alt=" " data-tex="P">', this distance being measurable and well-defined +from a physical point of view, then the following +formula holds: +<span class="align-center"><img style="vertical-align: -0.464ex; width: 43.616ex; height: 2.482ex;" src="images/101.svg" alt=" " data-tex=" +ds^{2} = g_{11}\, {dx_{1}}^{2} + + 2g_{12}\, dx_{1}\, dx_{2}\, \dots.\, + + g_{44}\, {dx_{4}}^{2}, +"></span> +where the magnitudes <img style="vertical-align: -0.464ex; width: 2.867ex; height: 1.464ex;" src="images/94.svg" alt=" " data-tex="g_{11}">, etc., have values which vary +with the position in the continuum. Only when the +continuum is a Euclidean one is it possible to associate +the co-ordinates <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}"> ... <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}"> with the points of the +continuum so that we have simply +<span class="align-center"><img style="vertical-align: -0.375ex; width: 32.952ex; height: 2.393ex;" src="images/102.svg" alt=" " data-tex=" +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2}. +"></span> +In this case relations hold in the four-dimensional +continuum which are analogous to those holding in our +three-dimensional measurements. +</p> +<p> +However, the Gauss treatment for <img style="vertical-align: -0.023ex; width: 3.225ex; height: 1.909ex;" src="images/103.svg" alt=" " data-tex="ds^{2}"> which we have +given above is not always possible. It is only possible +when sufficiently small regions of the continuum under +consideration may be regarded as Euclidean continua. +<span class="pagenum" id="Page_89">[Pg 89]</span> +For example, this obviously holds in the case of the +marble slab of the table and local variation of temperature. +The temperature is practically constant for a small +part of the slab, and thus the geometrical behaviour of +the rods is <i>almost</i> as it ought to be according to the +rules of Euclidean geometry. Hence the imperfections +of the construction of squares in the previous section +do not show themselves clearly until this construction +is extended over a considerable portion of the surface +of the table. +</p> +<p> +We can sum this up as follows: Gauss invented a +method for the mathematical treatment of continua in +general, in which "size-relations" ("distances" between +neighbouring points) are defined. To every point of a +continuum are assigned as many numbers (Gaussian co-ordinates) +as the continuum has dimensions. This is +done in such a way, that only one meaning can be attached +to the assignment, and that numbers (Gaussian co-ordinates) +which differ by an indefinitely small amount +are assigned to adjacent points. The Gaussian co-ordinate +system is a logical generalisation of the Cartesian +co-ordinate system. It is also applicable to non-Euclidean +continua, but only when, with respect to the defined +"size" or "distance," small parts of the continuum +under consideration behave more nearly like a Euclidean +system, the smaller the part of the continuum under +our notice. +<span class="pagenum" id="Page_90">[Pg 90]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXVI: THE SPACE-TIME CONTINUUM OF THE SPECIAL +THEORY OF RELATIVITY CONSIDERED AS +A EUCLIDEAN CONTINUUM"><a id="chap26"></a>XXVI +<br><br> +THE SPACE-TIME CONTINUUM OF THE SPECIAL +THEORY OF RELATIVITY CONSIDERED AS +A EUCLIDEAN CONTINUUM</h2> + +<p class="nind"> +<span class="dropcap">W</span>E are now in a position to formulate more +exactly the idea of Minkowski, which was +only vaguely indicated in Section XVII. +In accordance with the special theory of relativity, +certain co-ordinate systems are given preference +for the description of the four-dimensional, space-time +continuum. We called these "Galileian co-ordinate +systems." For these systems, the four co-ordinates +<img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, which determine an event or—in other +words—a point of the four-dimensional continuum, are +defined physically in a simple manner, as set forth in +detail in the first part of this book. For the transition +from one Galileian system to another, which is moving +uniformly with reference to the first, the equations of +the Lorentz transformation are valid. These last +form the basis for the derivation of deductions from the +special theory of relativity, and in themselves they are +nothing more than the expression of the universal +validity of the law of transmission of light for all Galileian +systems of reference. +</p> +<p> +Minkowski found that the Lorentz transformations +satisfy the following simple conditions. Let us consider +<span class="pagenum" id="Page_91">[Pg 91]</span> +two neighbouring events, the relative position of which +in the four-dimensional continuum is given with respect +to a Galileian reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> by the space co-ordinate +differences <img style="vertical-align: -0.025ex; width: 2.471ex; height: 1.595ex;" src="images/104.svg" alt=" " data-tex="dx">, <img style="vertical-align: -0.464ex; width: 2.285ex; height: 2.034ex;" src="images/105.svg" alt=" " data-tex="dy">, <img style="vertical-align: -0.025ex; width: 2.229ex; height: 1.595ex;" src="images/106.svg" alt=" " data-tex="dz"> and the time-difference <img style="vertical-align: -0.025ex; width: 1.993ex; height: 1.595ex;" src="images/107.svg" alt=" " data-tex="dt">. With +reference to a second Galileian system we shall suppose +that the corresponding differences for these two events +are <img style="vertical-align: -0.025ex; width: 2.471ex; height: 1.595ex;" src="images/104.svg" alt=" " data-tex="dx">', <img style="vertical-align: -0.464ex; width: 2.285ex; height: 2.034ex;" src="images/105.svg" alt=" " data-tex="dy">', <img style="vertical-align: -0.025ex; width: 2.229ex; height: 1.595ex;" src="images/106.svg" alt=" " data-tex="dz">', <img style="vertical-align: -0.025ex; width: 1.993ex; height: 1.595ex;" src="images/107.svg" alt=" " data-tex="dt">'. Then these magnitudes always +fulfil the condition<a id="FNanchor_23_1"></a><a href="#Footnote_23_1" class="fnanchor">[23]</a> +<span class="align-center"><img style="vertical-align: -0.464ex; width: 52.547ex; height: 2.464ex;" src="images/108.svg" alt=" " data-tex=" +dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2} + = dx'^{2} + dy'^{2} + dz'^{2} - c^{2}\, dt'^{2}. +"></span> + +The validity of the Lorentz transformation follows +from this condition. We can express this as follows: +The magnitude +<span class="align-center"><img style="vertical-align: -0.464ex; width: 30.442ex; height: 2.464ex;" src="images/109.svg" alt=" " data-tex=" +ds^{2} = dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2}, +"></span> +which belongs to two adjacent points of the four-dimensional +space-time continuum, has the same value +for all selected (Galileian) reference-bodies. If we replace +<img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.318ex; width: 6.995ex; height: 2.398ex;" src="images/110.svg" alt=" " data-tex="\sqrt{-1}\,ct">, by <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, +<img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">, we also obtain the result that +<span class="align-center"><img style="vertical-align: -0.375ex; width: 32.323ex; height: 2.393ex;" src="images/111.svg" alt=" " data-tex=" +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2} +"></span> +is independent of the choice of the body of reference. +We call the magnitude <img style="vertical-align: -0.023ex; width: 2.238ex; height: 1.593ex;" src="images/92.svg" alt=" " data-tex="ds"> the "distance" apart of the +two events or four-dimensional points. +</p> +<p> +Thus, if we choose as time-variable the imaginary +variable <img style="vertical-align: -0.318ex; width: 6.995ex; height: 2.398ex;" src="images/110.svg" alt=" " data-tex="\sqrt{-1}\,ct"> instead of the real quantity <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, we can +regard the space-time continuum—in accordance with +the special theory of relativity—as a "Euclidean" +four-dimensional continuum, a result which follows +from the considerations of the preceding section. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_23_1"></a><a href="#FNanchor_23_1"><span class="label">[23]</span></a>Cf. Appendices I and II. The relations which are derived +there for the co-ordinates themselves are valid also for co-ordinate +<i>differences</i>, and thus also for co-ordinate differentials +(indefinitely small differences).</p></div> + +<p><span class="pagenum" id="Page_92">[Pg 92]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXVII: THE SPACE-TIME CONTINUUM OF THE +GENERAL THEORY OF RELATIVITY IS +NOT A EUCLIDEAN CONTINUUM"><a id="chap27"></a>XXVII +<br><br> +THE SPACE-TIME CONTINUUM OF THE +GENERAL THEORY OF RELATIVITY IS +NOT A EUCLIDEAN CONTINUUM</h2> + +<p class="nind"> +<span class="dropcap">I</span>N the first part of this book we were able to +make use of space-time co-ordinates which allowed of a simple +and direct physical interpretation, and which, according +to Section XXVI, can be regarded as four-dimensional +Cartesian co-ordinates. This was possible on the basis +of the law of the constancy of the velocity of light. But +according to Section XXI, the general theory of relativity +cannot retain this law. On the contrary, we arrived at +the result that according to this latter theory the +velocity of light must always depend on the co-ordinates +when a gravitational field is present. In connection +with a specific illustration in Section XXIII, we found +that the presence of a gravitational field invalidates the +definition of the co-ordinates and the time, which led us +to our objective in the special theory of relativity. +</p> +<p> +In view of the results of these considerations we are +led to the conviction that, according to the general +principle of relativity, the space-time continuum cannot +be regarded as a Euclidean one, but that here we have +the general case, corresponding to the marble slab with +local variations of temperature, and with which we +made acquaintance as an example of a two-dimensional +<span class="pagenum" id="Page_93">[Pg 93]</span> +continuum. Just as it was there impossible to construct +a Cartesian co-ordinate system from equal rods, so +here it is impossible to build up a system (reference-body) +from rigid bodies and clocks, which shall be of +such a nature that measuring-rods and clocks, arranged +rigidly with respect to one another, shall indicate position +and time directly. Such was the essence of the +difficulty with which we were confronted in Section XXIII. +</p> +<p> +But the considerations of Sections Sections XXV and XXVI +show us the way to surmount this difficulty. We refer the +four-dimensional space-time continuum in an arbitrary +manner to Gauss co-ordinates. We assign to every +point of the continuum (event) four numbers, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, +<img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}"> (co-ordinates), which have not the least direct +physical significance, but only serve the purpose of +numbering the points of the continuum in a definite +but arbitrary manner. This arrangement does not even +need to be of such a kind that we must regard <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, +<img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}"> as "space" co-ordinates and <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}"> as a "time" co-ordinate. +</p> +<p> +The reader may think that such a description of the +world would be quite inadequate. What does it mean +to assign to an event the particular co-ordinates <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, +<img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">, if in themselves these co-ordinates have no +significance? More careful consideration shows, however, +that this anxiety is unfounded. Let us consider, +for instance, a material point with any kind of motion. +If this point had only a momentary existence without +duration, then it would be described in space-time by a +single system of values <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">. Thus +its permanent existence must be characterised by an infinitely large +number of such systems of values, the co-ordinate values +of which are so close together as to give continuity; +<span class="pagenum" id="Page_94">[Pg 94]</span> +corresponding to the material point, we thus have a +(uni-dimensional) line in the four-dimensional continuum. +In the same way, any such lines in our continuum +correspond to many points in motion. The only statements +having regard to these points which can claim +a physical existence are in reality the statements about +their encounters. In our mathematical treatment, +such an encounter is expressed in the fact that the two +lines which represent the motions of the points in +question have a particular system of co-ordinate values, +<img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">, in common. After mature +consideration the reader will doubtless admit that in reality such +encounters constitute the only actual evidence of a +time-space nature with which we meet in physical +statements. +</p> +<p> +When we were describing the motion of a material +point relative to a body of reference, we stated +nothing more than the encounters of this point with +particular points of the reference-body. We can also +determine the corresponding values of the time by the +observation of encounters of the body with clocks, in +conjunction with the observation of the encounter of the +hands of clocks with particular points on the dials. +It is just the same in the case of space-measurements by +means of measuring-rods, as a little consideration will +show. +</p> +<p> +The following statements hold generally: Every +physical description resolves itself into a number of +statements, each of which refers to the space-time +coincidence of two events <img style="vertical-align: 0; width: 1.697ex; height: 1.62ex;" src="images/1.svg" alt=" " data-tex="A"> and <img style="vertical-align: 0; width: 1.717ex; height: 1.545ex;" src="images/2.svg" alt=" " data-tex="B">. In terms of +Gaussian co-ordinates, every such statement is expressed +by the agreement of their four co-ordinates <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, +<img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">. Thus in reality, the description of the time-space +<span class="pagenum" id="Page_95">[Pg 95]</span> +continuum by means of Gauss co-ordinates completely +replaces the description with the aid of a body of reference, +without suffering from the defects of the latter +mode of description; it is not tied down to the Euclidean +character of the continuum which has to be represented. +<span class="pagenum" id="Page_96">[Pg 96]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXVIII: EXACT FORMULATION OF THE GENERAL +PRINCIPLE OF RELATIVITY"><a id="chap28"></a>XXVIII +<br><br> +EXACT FORMULATION OF THE GENERAL +PRINCIPLE OF RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">W</span>E are now in a position to replace the +provisional formulation of the general principle +of relativity given in Section XVIII by +an exact formulation. The form there used, "All +bodies of reference <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', etc., are equivalent for +the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion," cannot be maintained, because the +use of rigid reference-bodies, in the sense of the method +followed in the special theory of relativity, is in general +not possible in space-time description. The Gauss +co-ordinate system has to take the place of the body of +reference. The following statement corresponds to the +fundamental idea of the general principle of relativity: +"<i>All Gaussian co-ordinate systems are essentially equivalent +for the formulation of the general laws of nature.</i>" +</p> +<p> +We can state this general principle of relativity in still +another form, which renders it yet more clearly intelligible +than it is when in the form of the natural +extension of the special principle of relativity. According +to the special theory of relativity, the equations +which express the general laws of nature pass over into +equations of the same form when, by making use of the +Lorentz transformation, we replace the space-time +<span class="pagenum" id="Page_97">[Pg 97]</span> +variables <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, of a (Galileian) reference-body +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> by the space-time variables <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">', <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">', <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">', <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">', +of a new reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. According to the general theory +of relativity, on the other hand, by application of +<i>arbitrary substitutions</i> of the Gauss variables <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, +<img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">, the equations must pass over into equations of the +same form; for every transformation (not only the Lorentz +transformation) corresponds to the transition of one +Gauss co-ordinate system into another. +</p> +<p> +If we desire to adhere to our "old-time" three-dimensional +view of things, then we can characterise +the development which is being undergone by the +fundamental idea of the general theory of relativity +as follows: The special theory of relativity has reference +to Galileian domains, <i>i.e.</i> to those in which no gravitational +field exists. In this connection a Galileian reference-body +serves as body of reference, <i>i.e.</i> a rigid +body the state of motion of which is so chosen that the +Galileian law of the uniform rectilinear motion of +"isolated" material points holds relatively to it. +</p> +<p> +Certain considerations suggest that we should refer +the same Galileian domains to <i>non-Galileian</i> reference-bodies +also. A gravitational field of a special kind is +then present with respect to these bodies (cf. Sections XX +and XXIII). +</p> +<p> +In gravitational fields there are no such things as rigid +bodies with Euclidean properties; thus the fictitious rigid +body of reference is of no avail in the general theory of +relativity. The motion of clocks is also influenced by +gravitational fields, and in such a way that a physical +definition of time which is made directly with the aid of +clocks has by no means the same degree of plausibility +as in the special theory of relativity. +<span class="pagenum" id="Page_98">[Pg 98]</span> +</p> +<p> +For this reason non-rigid reference-bodies are used, +which are as a whole not only moving in any way +whatsoever, but which also suffer alterations in form +<i>ad lib.</i> during their motion. Clocks, for which the law of +motion is of any kind, however irregular, serve for the +definition of time. We have to imagine each of these +clocks fixed at a point on the non-rigid reference-body. +These clocks satisfy only the one condition, that the +"readings" which are observed simultaneously on +adjacent clocks (in space) differ from each other by an +indefinitely small amount. This non-rigid reference-body, +which might appropriately be termed a "reference-mollusk," +is in the main equivalent to a Gaussian four-dimensional +co-ordinate system chosen arbitrarily. +That which gives the "mollusk" a certain comprehensibleness +as compared with the Gauss co-ordinate +system is the (really unjustified) formal retention of +the separate existence of the space co-ordinates as +opposed to the time co-ordinate. Every point on the +mollusk is treated as a space-point, and every material +point which is at rest relatively to it as at rest, so long as +the mollusk is considered as reference-body. The +general principle of relativity requires that all these +mollusks can be used as reference-bodies with equal +right and equal success in the formulation of the general +laws of nature; the laws themselves must be quite +independent of the choice of mollusk. +</p> +<p> +The great power possessed by the general principle +of relativity lies in the comprehensive limitation which +is imposed on the laws of nature in consequence of what +we have seen above. +<span class="pagenum" id="Page_99">[Pg 99]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXIX: THE SOLUTION OF THE PROBLEM OF GRAVITATION +ON THE BASIS OF THE GENERAL +PRINCIPLE OF RELATIVITY"><a id="chap29"></a>XXIX +<br><br> +THE SOLUTION OF THE PROBLEM OF GRAVITATION +ON THE BASIS OF THE GENERAL +PRINCIPLE OF RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">I</span>F the reader has followed all our previous +considerations, he will have no further difficulty in +understanding the methods leading to the solution +of the problem of gravitation. +</p> +<p> +We start off from a consideration of a Galileian +domain, <i>i.e.</i> a domain in which there is no gravitational +field relative to the Galileian reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. The +behaviour of measuring-rods and clocks with reference +to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> is known from the special theory of relativity, +likewise the behaviour of "isolated" material points; +the latter move uniformly and in straight lines. +</p> +<p> +Now let us refer this domain to a random Gauss co-ordinate +system or to a "mollusk" as reference-body <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. +Then with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' there is a gravitational +field <img style="vertical-align: -0.05ex; width: 1.776ex; height: 1.645ex;" src="images/112.svg" alt=" " data-tex="\mathrm G"> (of a particular kind). We learn the behaviour +of measuring-rods and clocks and also of freely-moving +material points with reference to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' simply by mathematical +transformation. We interpret this behaviour +as the behaviour of measuring-rods, clocks and material +points under the influence of the gravitational field <img style="vertical-align: -0.05ex; width: 1.776ex; height: 1.645ex;" src="images/112.svg" alt=" " data-tex="\mathrm G">. +Hereupon we introduce a hypothesis: that the influence +of the gravitational field on measuring-rods, +<span class="pagenum" id="Page_100">[Pg 100]</span> +clocks and freely-moving material points continues to +take place according to the same laws, even in the case +when the prevailing gravitational field is <i>not</i> derivable +from the Galileian special case, simply by means of a +transformation of co-ordinates. +</p> +<p> +The next step is to investigate the space-time +behaviour of the gravitational field <img style="vertical-align: -0.05ex; width: 1.776ex; height: 1.645ex;" src="images/112.svg" alt=" " data-tex="\mathrm G">, which was derived +from the Galileian special case simply by transformation +of the co-ordinates. This behaviour is formulated +in a law, which is always valid, no matter how the +reference-body (mollusk) used in the description may +be chosen. +</p> +<p> +This law is not yet the <i>general</i> law of the gravitational +field, since the gravitational field under consideration is +of a special kind. In order to find out the general +law-of-field of gravitation we still require to obtain a +generalisation of the law as found above. This can be +obtained without caprice, however, by taking into +consideration the following demands: +</p> +<p class="hanging2"> +(<i>a</i>) The required generalisation must likewise satisfy +the general postulate of relativity. +</p> +<p class="hanging2"> +(<i>b</i>) If there is any matter in the domain under consideration, +only its inertial mass, and thus +according to Section XV only its energy is of +importance for its effect in exciting a field. +</p> +<p class="hanging2"> +(<i>c</i>) Gravitational field and matter together must +satisfy the law of the conservation of energy +(and of impulse). +</p> +<p> +Finally, the general principle of relativity permits +us to determine the influence of the gravitational field +on the course of all those processes which take place +according to known laws when a gravitational field is +<span class="pagenum" id="Page_101">[Pg 101]</span> +absent, <i>i.e.</i> which have already been fitted into the +frame of the special theory of relativity. In this connection +we proceed in principle according to the method +which has already been explained for measuring-rods, +clocks and freely-moving material points. +</p> +<p> +The theory of gravitation derived in this way from +the general postulate of relativity excels not only in +its beauty; nor in removing the defect attaching to +classical mechanics which was brought to light in Section XXI; +nor in interpreting the empirical law of the equality +of inertial and gravitational mass; but it has also +already explained a result of observation in astronomy, +against which classical mechanics is powerless. +</p> +<p> +If we confine the application of the theory to the +case where the gravitational fields can be regarded as +being weak, and in which all masses move with respect +to the co-ordinate system with velocities which are +small compared with the velocity of light, we then obtain +as a first approximation the Newtonian theory. Thus +the latter theory is obtained here without any particular +assumption, whereas Newton had to introduce the +hypothesis that the force of attraction between mutually +attracting material points is inversely proportional to +the square of the distance between them. If we increase +the accuracy of the calculation, deviations from +the theory of Newton make their appearance, practically +all of which must nevertheless escape the test of +observation owing to their smallness. +</p> +<p> +We must draw attention here to one of these deviations. +According to Newton's theory, a planet moves +round the sun in an ellipse, which would permanently +maintain its position with respect to the fixed stars, +if we could disregard the motion of the fixed stars +<span class="pagenum" id="Page_102">[Pg 102]</span> +themselves and the action of the other planets under +consideration. Thus, if we correct the observed motion +of the planets for these two influences, and if Newton's +theory be strictly correct, we ought to obtain for the +orbit of the planet an ellipse, which is fixed with reference +to the fixed stars. This deduction, which can +be tested with great accuracy, has been confirmed +for all the planets save one, with the precision that is +capable of being obtained by the delicacy of observation +attainable at the present time. The sole exception +is Mercury, the planet which lies nearest the sun. Since +the time of Leverrier, it has been known that the ellipse +corresponding to the orbit of Mercury, after it has been +corrected for the influences mentioned above, is not +stationary with respect to the fixed stars, but that it +rotates exceedingly slowly in the plane of the orbit +and in the sense of the orbital motion. The value +obtained for this rotary movement of the orbital ellipse +was 43 seconds of arc per~century, an amount ensured +to be correct to within a few seconds of arc. This +effect can be explained by means of classical mechanics +only on the assumption of hypotheses which have +little probability, and which were devised solely for +this purpose. +</p> +<p> +On the basis of the general theory of relativity, it +is found that the ellipse of every planet round the sun +must necessarily rotate in the manner indicated above; +that for all the planets, with the exception of Mercury, +this rotation is too small to be detected with the delicacy +of observation possible at the present time; but that in +the case of Mercury it must amount to 43 seconds of +arc per century, a result which is strictly in agreement +with observation. +<span class="pagenum" id="Page_103">[Pg 103]</span> +</p> +<p> +Apart from this one, it has hitherto been possible to +make only two deductions from the theory which admit +of being tested by observation, to wit, the curvature +of light rays by the gravitational field of the sun,<a id="FNanchor_24_1"></a><a href="#Footnote_24_1" class="fnanchor">[24]</a> +and a displacement of the spectral lines of light reaching +us from large stars, as compared with the corresponding +lines for light produced in an analogous manner terrestrially +(<i>i.e.</i> by the same kind of molecule). I do not +doubt that these deductions from the theory will be +confirmed also. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_24_1"></a><a href="#FNanchor_24_1"><span class="label">[24]</span></a>Observed by Eddington and others in 1919. (Cf.Appendix III.)</p></div> + +<p><br></p> + +<p><span class="pagenum" id="Page_104">[Pg 104]</span></p> + +</div> + +<p><br><br><br></p> + +<div class="chapter"> +<h2 title="PART III: CONSIDERATIONS ON THE UNIVERSE AS +A WHOLE"><a id="part03"></a>PART III +<br> +CONSIDERATIONS ON THE UNIVERSE AS +A WHOLE</h2> + +<p><br><br></p> + +<h2 title="XXX: COSMOLOGICAL DIFFICULTIES OF NEWTON'S +THEORY"><a id="chap30"></a>XXX +<br><br> +COSMOLOGICAL DIFFICULTIES OF NEWTON'S +THEORY +</h2> + +<p class="nind"> +<span class="dropcap">A</span>PART from the difficulty discussed in Section +XXI, there is a second fundamental difficulty +attending classical celestial mechanics, which, +to the best of my knowledge, was first discussed in +detail by the astronomer Seeliger. If we ponder over +the question as to how the universe, considered as a +whole, is to be regarded, the first answer that suggests +itself to us is surely this: As regards space (and time) +the universe is infinite. There are stars everywhere, +so that the density of matter, although very variable +in detail, is nevertheless on the average everywhere the +same. In other words: However far we might travel +through space, we should find everywhere an attenuated +swarm of fixed stars of approximately the same kind +and density. +</p> +<p> +This view is not in harmony with the theory of +Newton. The latter theory rather requires that the +universe should have a kind of centre in which the +<span class="pagenum" id="Page_105">[Pg 105]</span> +density of the stars is a maximum, and that as we +proceed outwards from this centre the group-density +of the stars should diminish, until finally, at great +distances, it is succeeded by an infinite region of emptiness. +The stellar universe ought to be a finite island in +the infinite ocean of space.<a id="FNanchor_25_1"></a><a href="#Footnote_25_1" class="fnanchor">[25]</a> +</p> +<p> +This conception is in itself not very satisfactory. +It is still less satisfactory because it leads to the result +that the light emitted by the stars and also individual +stars of the stellar system are perpetually passing out +into infinite space, never to return, and without ever +again coming into interaction with other objects of +nature. Such a finite material universe would be +destined to become gradually but systematically impoverished. +</p> +<p> +In order to escape this dilemma, Seeliger suggested a +modification of Newton's law, in which he assumes that +for great distances the force of attraction between two +masses diminishes more rapidly than would result from +the inverse square law. In this way it is possible for the +mean density of matter to be constant everywhere, +even to infinity, without infinitely large gravitational +fields being produced. We thus free ourselves from the +<span class="pagenum" id="Page_106">[Pg 106]</span> +distasteful conception that the material universe ought +to possess something of the nature of a centre. Of +course we purchase our emancipation from the fundamental +difficulties mentioned, at the cost of a modification +and complication of Newton's law which has +neither empirical nor theoretical foundation. We can +imagine innumerable laws which would serve the same +purpose, without our being able to state a reason why +one of them is to be preferred to the others; for any +one of these laws would be founded just as little on +more general theoretical principles as is the law of +Newton. +</p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_25_1"></a><a href="#FNanchor_25_1"><span class="label">[25]</span></a><i>Proof</i>—According to the theory of Newton, the number of +"lines of force" which come from infinity and terminate in a +mass <img style="vertical-align: -0.025ex; width: 1.986ex; height: 1.025ex;" src="images/8.svg" alt=" " data-tex="m"> is proportional to the mass <img style="vertical-align: -0.025ex; width: 1.986ex; height: 1.025ex;" src="images/8.svg" alt=" " data-tex="m">. If, on the average, the +mass-density <img style="vertical-align: -0.489ex; width: 2.157ex; height: 1.489ex;" src="images/113.svg" alt=" " data-tex="\rho_{0}"> is constant throughout the universe, then a +sphere of volume <img style="vertical-align: -0.05ex; width: 1.74ex; height: 1.595ex;" src="images/114.svg" alt=" " data-tex="V"> will enclose the average mass <img style="vertical-align: -0.489ex; width: 3.897ex; height: 2.034ex;" src="images/115.svg" alt=" " data-tex="\rho_{0}V">. Thus +the number of lines of force passing through the surface <img style="vertical-align: 0; width: 1.695ex; height: 1.538ex;" src="images/116.svg" alt=" " data-tex="F"> of the +sphere into its interior is proportional to <img style="vertical-align: -0.489ex; width: 3.897ex; height: 2.034ex;" src="images/115.svg" alt=" " data-tex="\rho_{0}V">. For unit area +of the surface of the sphere the number of lines of force which +enters the sphere is thus proportional to <img style="vertical-align: -1.552ex; width: 4.893ex; height: 4.627ex;" src="images/117.svg" alt=" " data-tex="\rho_{0}\dfrac{V}{F}"> or to +<img style="vertical-align: -0.489ex; width: 3.875ex; height: 2.034ex;" src="images/118.svg" alt=" " data-tex="\rho_{0}R">. Hence the intensity of the field at the surface would +ultimately become infinite with increasing radius <img style="vertical-align: -0.048ex; width: 1.717ex; height: 1.593ex;" src="images/119.svg" alt=" " data-tex="R"> of the sphere, +which is impossible.</p></div> + +<p><span class="pagenum" id="Page_107">[Pg 107]</span></p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXXI: THE POSSIBILITY OF A FINITE AND YET +UNBOUNDED UNIVERSE"><a id="chap31"></a>XXXI +<br><br> +THE POSSIBILITY OF A "FINITE" AND YET +"UNBOUNDED" UNIVERSE</h2> + +<p class="nind"> +<span class="dropcap">B</span>UT speculations on the structure of the +universe also move in quite another direction. The +development of non-Euclidean geometry led to +the recognition of the fact, that we can cast doubt on the +<i>infiniteness</i> of our space without coming into conflict +with the laws of thought or with experience (Riemann, +Helmholtz). These questions have already been treated +in detail and with unsurpassable lucidity by Helmholtz +and Poincaré, whereas I can only touch on them +briefly here. +</p> +<p> +In the first place, we imagine an existence in two-dimensional +space. Flat beings with flat implements, +and in particular flat rigid measuring-rods, are free to +move in a <i>plane</i>. For them nothing exists outside of +this plane: that which they observe to happen to +themselves and to their flat "things" is the all-inclusive +reality of their plane. In particular, the constructions +of plane Euclidean geometry can be carried out by +means of the rods, <i>e.g.</i> the lattice construction, considered +in Section XXIV. In contrast to ours, the universe of +these beings is two-dimensional; but, like ours, it extends +to infinity. In their universe there is room for an +infinite number of identical squares made up of rods, +<span class="pagenum" id="Page_108">[Pg 108]</span> +<i>i.e.</i> its volume (surface) is infinite. If these beings say +their universe is "plane," there is sense in the statement, +because they mean that they can perform the constructions +of plane Euclidean geometry with their rods. +In this connection the individual rods always represent +the same distance, independently of their position. +</p> +<p> +Let us consider now a second two-dimensional existence, +but this time on a spherical surface instead of on +a plane. The flat beings with their measuring-rods +and other objects fit exactly on this surface and they +are unable to leave it. Their whole universe of observation +extends exclusively over the surface of the sphere. +Are these beings able to regard the geometry of their +universe as being plane geometry and their rods withal +as the realisation of "distance"? They cannot do +this. For if they attempt to realise a straight line, they +will obtain a curve, which we "three-dimensional +beings" designate as a great circle, <i>i.e.</i> a self-contained +line of definite finite length, which can be measured +up by means of a measuring-rod. Similarly, this +universe has a finite area that can be compared with the +area of a square constructed with rods. The great +charm resulting from this consideration lies in the +recognition of the fact that <i>the universe of these beings is +finite and yet has no limits</i>. +</p> +<p> +But the spherical-surface beings do not need to go +on a world-tour in order to perceive that they are not +living in a Euclidean universe. They can convince +themselves of this on every part of their "world," +provided they do not use too small a piece of it. Starting +from a point, they draw "straight lines" (arcs of circles +as judged in three-dimensional space) of equal length +in all directions. They will call the line joining the +<span class="pagenum" id="Page_109">[Pg 109]</span> +free ends of these lines a "circle." For a plane surface, +the ratio of the circumference of a circle to its diameter, +both lengths being measured with the same rod, is, +according to Euclidean geometry of the plane, equal to +a constant value <img style="vertical-align: -0.025ex; width: 1.29ex; height: 1ex;" src="images/82.svg" alt=" " data-tex="\pi">, which is independent of the diameter +of the circle. On their spherical surface our flat beings +would find for this ratio the value +<span class="align-center"><img style="vertical-align: -4.11ex; width: 14.501ex; height: 9.351ex;" src="images/120.svg" alt=" " data-tex=" +\pi = \frac{\sin\left(\dfrac{r}{R}\right)}{\left(\dfrac{r}{R}\right)}, +"></span> +<i>i.e.</i> a smaller value than <img style="vertical-align: -0.025ex; width: 1.29ex; height: 1ex;" src="images/82.svg" alt=" " data-tex="\pi">, the difference being the +more considerable, the greater is the radius of the +circle in comparison with the radius <img style="vertical-align: -0.048ex; width: 1.717ex; height: 1.593ex;" src="images/119.svg" alt=" " data-tex="R"> of the "world-sphere." +By means of this relation the spherical beings +can determine the radius of their universe ("world"), +even when only a relatively small part of their world-sphere +is available for their measurements. But if this +part is very small indeed, they will no longer be able to +demonstrate that they are on a spherical "world" and +not on a Euclidean plane, for a small part of a spherical +surface differs only slightly from a piece of a plane of +the same size. +</p> +<p> +Thus if the spherical-surface beings are living on a +planet of which the solar system occupies only a negligibly +small part of the spherical universe, they have no means +of determining whether they are living in a finite or in +an infinite universe, because the "piece of universe" +to which they have access is in both cases practically +plane, or Euclidean. It follows directly from this +discussion, that for our sphere-beings the circumference +of a circle first increases with the radius until the "circumference +<span class="pagenum" id="Page_110">[Pg 110]</span> +of the universe" is reached, and that it +thenceforward gradually decreases to zero for still +further increasing values of the radius. During this +process the area of the circle continues to increase +more and more, until finally it becomes equal to the +total area of the whole "world-sphere." +</p> +<p> +Perhaps the reader will wonder why we have placed +our "beings" on a sphere rather than on another closed +surface. But this choice has its justification in the fact +that, of all closed surfaces, the sphere is unique in possessing +the property that all points on it are equivalent. I +admit that the ratio of the circumference <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> of a circle +to its radius <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r"> depends on <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r">, but for a given value of <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r"> +it is the same for all points of the "world-sphere"; +in other words, the "world-sphere" is a "surface of +constant curvature." +</p> +<p> +To this two-dimensional sphere-universe there is a +three-dimensional analogy, namely, the three-dimensional +spherical space which was discovered by Riemann. Its +points are likewise all equivalent. It possesses a finite +volume, which is determined by its "radius" (<img style="vertical-align: -0.048ex; width: 6.113ex; height: 1.934ex;" src="images/122.svg" alt=" " data-tex="2\pi^{2}R^{3}">). +Is it possible to imagine a spherical space? To imagine +a space means nothing else than that we imagine an +epitome of our "space" experience, <i>i.e.</i> of experience +that we can have in the movement of "rigid" bodies. +In this sense we <i>can</i> imagine a spherical space. +</p> +<p> +Suppose we draw lines or stretch strings in all directions +from a point, and mark off from each of these +the distance <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r"> with a measuring-rod. All the free end-points +of these lengths lie on a spherical surface. We +can specially measure up the area (<img style="vertical-align: 0; width: 1.695ex; height: 1.538ex;" src="images/116.svg" alt=" " data-tex="F">) of this surface +by means of a square made up of measuring-rods. If +the universe is Euclidean, then <img style="vertical-align: -0.186ex; width: 9.141ex; height: 2.072ex;" src="images/123.svg" alt=" " data-tex="F = 4\pi r^{2}">; if it is spherical, +<span class="pagenum" id="Page_111">[Pg 111]</span> +then <img style="vertical-align: 0; width: 1.695ex; height: 1.538ex;" src="images/116.svg" alt=" " data-tex="F"> is always less than <img style="vertical-align: -0.025ex; width: 4.429ex; height: 1.912ex;" src="images/124.svg" alt=" " data-tex="4\pi r^{2}">. With increasing +values of <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r">, <img style="vertical-align: 0; width: 1.695ex; height: 1.538ex;" src="images/116.svg" alt=" " data-tex="F"> increases from zero up to a maximum +value which is determined by the "world-radius," but +for still further increasing values of <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r">, the area gradually +diminishes to zero. At first, the straight lines which +radiate from the starting point diverge farther and +farther from one another, but later they approach +each other, and finally they run together again at a +"counter-point" to the starting point. Under such +conditions they have traversed the whole spherical +space. It is easily seen that the three-dimensional +spherical space is quite analogous to the two-dimensional +spherical surface. It is finite (<i>i.e.</i> of finite volume), and +has no bounds. +</p> +<p> +It may be mentioned that there is yet another kind +of curved space: "elliptical space." It can be regarded +as a curved space in which the two "counter-points" +are identical (indistinguishable from each other). An +elliptical universe can thus be considered to some +extent as a curved universe possessing central symmetry. +</p> +<p> +It follows from what has been said, that closed spaces +without limits are conceivable. From amongst these, +the spherical space (and the elliptical) excels in its +simplicity, since all points on it are equivalent. As a +result of this discussion, a most interesting question +arises for astronomers and physicists, and that is +whether the universe in which we live is infinite, or +whether it is finite in the manner of the spherical universe. +Our experience is far from being sufficient to +enable us to answer this question. But the general +theory of relativity permits of our answering it with a +moderate degree of certainty, and in this connection the +difficulty mentioned in Section XXX finds its solution. +<span class="pagenum" id="Page_112">[Pg 112]</span> +</p> + +<p><br><br><br></p> +</div> + +<div class="chapter"> +<h2 title="XXXII: THE STRUCTURE OF SPACE ACCORDING TO +THE GENERAL THEORY OF RELATIVITY"><a id="chap32"></a>XXXII +<br><br> +THE STRUCTURE OF SPACE ACCORDING TO +THE GENERAL THEORY OF RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">A</span>CCORDING to the general theory of relativity, +the geometrical properties of space are not independent, +but they are determined by matter. +Thus we can draw conclusions about the geometrical +structure of the universe only if we base our considerations +on the state of the matter as being something +that is known. We know from experience that, for a +suitably chosen co-ordinate system, the velocities of +the stars are small as compared with the velocity of +transmission of light. We can thus as a rough approximation +arrive at a conclusion as to the nature of +the universe as a whole, if we treat the matter as being +at rest. +</p> +<p> +We already know from our previous discussion that the +behaviour of measuring-rods and clocks is influenced by +gravitational fields, <i>i.e.</i> by the distribution of matter. +This in itself is sufficient to exclude the possibility of +the exact validity of Euclidean geometry in our universe. +But it is conceivable that our universe differs +only slightly from a Euclidean one, and this notion +seems all the more probable, since calculations show +that the metrics of surrounding space is influenced only +to an exceedingly small extent by masses even of the +<span class="pagenum" id="Page_113">[Pg 113]</span> +magnitude of our sun. We might imagine that, as +regards geometry, our universe behaves analogously +to a surface which is irregularly curved in its individual +parts, but which nowhere departs appreciably from a +plane: something like the rippled surface of a lake. +Such a universe might fittingly be called a quasi-Euclidean +universe. As regards its space it would be +infinite. But calculation shows that in a quasi-Euclidean +universe the average density of matter +would necessarily be <i>nil</i>. Thus such a universe could +not be inhabited by matter everywhere; it would +present to us that unsatisfactory picture which we +portrayed in Section XXX. +</p> +<p> +If we are to have in the universe an average density +of matter which differs from zero, however small may +be that difference, then the universe cannot be quasi-Euclidean. +On the contrary, the results of calculation +indicate that if matter be distributed uniformly, the +universe would necessarily be spherical (or elliptical). +Since in reality the detailed distribution of matter is +not uniform, the real universe will deviate in individual +parts from the spherical, <i>i.e.</i> the universe will be quasi-spherical. +But it will be necessarily finite. In fact, the +theory supplies us with a simple connection<a id="FNanchor_26_1"></a><a href="#Footnote_26_1" class="fnanchor">[26]</a> +between the space-expanse of the universe and the average +density of matter in it. +</p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_26_1"></a><a href="#FNanchor_26_1"><span class="label">[26]</span></a>For the "radius" <img style="vertical-align: -0.048ex; width: 1.717ex; height: 1.593ex;" src="images/119.svg" alt=" " data-tex="R"> of the universe we obtain the equation +<span class="align-center"><img style="vertical-align: -2.041ex; width: 9.819ex; height: 5.077ex;" src="images/125.svg" alt=" " data-tex=" +R^{2} = \frac{2}{\kappa \rho}. +"></span> +The use of the C.G.S. system in this equation gives +<img style="vertical-align: -1.577ex; width: 15.149ex; height: 4.613ex;" src="images/126.svg" alt=" " data-tex="\dfrac{2}{\kappa} = 1.08 × 10^{27}">; +<img style="vertical-align: -0.489ex; width: 1.17ex; height: 1.489ex;" src="images/127.svg" alt=" " data-tex="\rho"> is the average density of the matter.</p></div> + +<p><span class="pagenum" id="Page_114">[Pg 114]</span></p> + +</div> + +<p><br><br><br></p> + +<div class="chapter"> + +<h2 title="APPENDICES"><a id="APPENDICES"></a>APPENDICES</h2> + +<p><br></p> + +<h2 title="APPENDIX I: SIMPLE DERIVATION OF THE LORENTZ +TRANSFORMATION"><a id="appen01"></a>APPENDIX I +<br> +SIMPLE DERIVATION OF THE LORENTZ +TRANSFORMATION [SUPPLEMENTARY TO SECTION XI]</h2> + +<p class="nind"> +<span class="dropcap">F</span>OR the relative orientation of the +co-ordinate systems indicated in Fig. 2, the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axes of both +systems permanently coincide. In the present +case we can divide the problem into parts by considering +first only events which are localised on the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis. Any +such event is represented with respect to the co-ordinate +system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> by the abscissa <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x"> and the time <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, and with +respect to the system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' by the abscissa <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">' and the +time <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">'. We require to find <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">' and <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">' when <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x"> and <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> are +given. +</p> +<p> +A light-signal, which is proceeding along the positive +axis of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, is transmitted according to the equation +<span class="align-center"><img style="vertical-align: -0.186ex; width: 6.108ex; height: 1.602ex;" src="images/128.svg" alt=" " data-tex=" +x = ct +"></span> +or +<span class="align-center"><img style="vertical-align: -0.566ex; width: 18.679ex; height: 2.262ex;" src="images/129.svg" alt=" " data-tex=" +x - ct = 0. +\qquad\text{(1)}. +"></span> +Since the same light-signal has to be transmitted relative +to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' with the velocity <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">, the propagation relative to +the system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' will be represented by the analogous +formula +<span class="align-center"><img style="vertical-align: -0.566ex; width: 19.934ex; height: 2.396ex;" src="images/130.svg" alt=" " data-tex=" +x' - ct' = 0. +\qquad\text{(2)}. +"></span> +Those space-time points (events) which satisfy (1) must +<span class="pagenum" id="Page_115">[Pg 115]</span> +also satisfy (2). Obviously this will be the case when +the relation +<span class="align-center"><img style="vertical-align: -0.566ex; width: 28.87ex; height: 2.396ex;" src="images/131.svg" alt=" " data-tex=" +(x' - ct') = \lambda(x - ct) +\qquad\text{(3)}. +"></span> +is fulfilled in general, where <img style="vertical-align: -0.027ex; width: 1.319ex; height: 1.597ex;" src="images/132.svg" alt=" " data-tex="\lambda"> indicates a constant; for, +according to (3), the disappearance of <img style="vertical-align: -0.566ex; width: 7.616ex; height: 2.262ex;" src="images/133.svg" alt=" " data-tex="(x - ct)"> involves +the disappearance of <img style="vertical-align: -0.566ex; width: 8.872ex; height: 2.283ex;" src="images/134.svg" alt=" " data-tex="(x' - ct')">. +</p> +<p> +If we apply quite similar considerations to light rays +which are being transmitted along the negative <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis, +we obtain the condition +<span class="align-center"><img style="vertical-align: -0.566ex; width: 28.915ex; height: 2.396ex;" src="images/135.svg" alt=" " data-tex=" +(x' + ct') = \mu(x + ct) +\qquad\text{(4)}. +"></span> +</p> +<p> +By adding (or subtracting) equations (3) and (4), and +introducing for convenience the constants <img style="vertical-align: -0.023ex; width: 1.197ex; height: 1.02ex;" src="images/136.svg" alt=" " data-tex="a"> and <img style="vertical-align: -0.025ex; width: 0.971ex; height: 1.595ex;" src="images/137.svg" alt=" " data-tex="b"> in +place of the constants <img style="vertical-align: -0.027ex; width: 1.319ex; height: 1.597ex;" src="images/132.svg" alt=" " data-tex="\lambda"> and <img style="vertical-align: -0.489ex; width: 1.364ex; height: 1.489ex;" src="images/138.svg" alt=" " data-tex="\mu">, where +<span class="align-center"><img style="vertical-align: -4.425ex; width: 15.464ex; height: 9.982ex;" src="images/139.svg" alt=" " data-tex=" +\begin{align*} +a &= \frac{\lambda + \mu}{2}\\ +\text{and}\,\, b &= \frac{\lambda - \mu}{2}, +\end{align*} +"></span> +we obtain the equations +<span class="align-center"><img style="vertical-align: -2.17ex; width: 23.836ex; height: 5.47ex;" src="images/140.svg" alt=" " data-tex=" +\left. +\begin{align*} +x' &= ax - bct, \\ +ct' &= act - bx. +\end{align*} +\right\} +\qquad\text{(5)}. +"></span> +</p> +<p> +We should thus have the solution of our problem, +if the constants <img style="vertical-align: -0.023ex; width: 1.197ex; height: 1.02ex;" src="images/136.svg" alt=" " data-tex="a"> and <img style="vertical-align: -0.025ex; width: 0.971ex; height: 1.595ex;" src="images/137.svg" alt=" " data-tex="b"> were known. These result +from the following discussion. +</p> +<p> +For the origin of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' we have permanently <img style="vertical-align: -0.186ex; width: 6.07ex; height: 1.903ex;" src="images/35.svg" alt=" " data-tex="x' = 0">, and +hence according to the first of the equations (5) +<span class="align-center"><img style="vertical-align: -1.575ex; width: 8.703ex; height: 4.674ex;" src="images/141.svg" alt=" " data-tex=" +x = \frac{bc}{a} t. +"></span> +</p> +<p> +If we call <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> the velocity with which the origin of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' is +moving relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, we then have +<span class="align-center"><img style="vertical-align: -1.575ex; width: 15.105ex; height: 4.674ex;" src="images/142.svg" alt=" " data-tex=" +v = \frac{bc}{a} +\qquad\text{(6)}. +"></span> +<span class="pagenum" id="Page_116">[Pg 116]</span> +</p> +<p> +The same value <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> can be obtained from equation (5), +if we calculate the velocity of another point of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' +relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, or the velocity (directed towards the +negative <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis) of a point of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> with respect to +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. In short, we can designate <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v"> as the relative velocity +of the two systems. +</p> +<p> +Furthermore, the principle of relativity teaches us +that, as judged from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, the length of a unit measuring-rod +which is at rest with reference to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' must be exactly +the same as the length, as judged from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', of a unit +measuring-rod which is at rest relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. In order +to see how the points of the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">'-axis appear as viewed +from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, we only require to take a "snapshot" of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' +from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">; this means that we have to insert a particular +value of <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> (time of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">), <i>e.g.</i> <img style="vertical-align: -0.186ex; width: 4.965ex; height: 1.692ex;" src="images/37.svg" alt=" " data-tex="t = 0">. For this +value of <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> we then obtain from the first of the equations (5) +<span class="align-center"><img style="vertical-align: -0.186ex; width: 8.059ex; height: 2.016ex;" src="images/143.svg" alt=" " data-tex=" +x' = ax. +"></span> +</p> +<p> +Two points of the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">'-axis which are separated by the +distance <img style="vertical-align: -0.186ex; width: 7.955ex; height: 1.903ex;" src="images/144.svg" alt=" " data-tex="\Delta x' = 1"> when measured in the <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' system are +thus separated in our instantaneous photograph by the +distance +<span class="align-center"><img style="vertical-align: -1.575ex; width: 17.439ex; height: 4.611ex;" src="images/145.svg" alt=" " data-tex=" +\Delta x = \frac{1}{a}. +\qquad\text{(7)}. +"></span> +</p> +<p> +But if the snapshot be taken from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'(<img style="vertical-align: -0.186ex; width: 5.593ex; height: 1.903ex;" src="images/43.svg" alt=" " data-tex="t' = 0">), and if +we eliminate <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t"> from the equations (5), taking into +account the expression (6), we obtain +<span class="align-center"><img style="vertical-align: -2.148ex; width: 18.744ex; height: 5.564ex;" src="images/146.svg" alt=" " data-tex=" +x' = a\left(1 - \frac{v^{2}}{c^{2}}\right)x. +"></span> +</p> +<p> +From this we conclude that two points on the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis +and separated by the distance 1 (relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">) will +be represented on our snapshot by the distance +<span class="align-center"><img style="vertical-align: -2.148ex; width: 28.888ex; height: 5.564ex;" src="images/147.svg" alt=" " data-tex=" +\Delta x' = a\left(1 - \frac{v^{2}}{c^{2}}\right). +\qquad\text{(7a)}. +"></span> +<span class="pagenum" id="Page_117">[Pg 117]</span> +</p> +<p> +But from what has been said, the two snapshots +must be identical; hence <img style="vertical-align: -0.025ex; width: 3.179ex; height: 1.645ex;" src="images/148.svg" alt=" " data-tex="\Delta x"> in (7) must be equal to +<img style="vertical-align: -0.025ex; width: 3.179ex; height: 1.645ex;" src="images/148.svg" alt=" " data-tex="\Delta x">' in (7a), so that we obtain +<span class="align-center"><img style="vertical-align: -4.979ex; width: 23.484ex; height: 8.016ex;" src="images/149.svg" alt=" " data-tex=" +a^{2} = \frac{1}{1 - \dfrac{v^{2}}{c^{2}}}. +\qquad\text{(7b)}. +"></span> +</p> +<p> +The equations (6) and (7b) determine the constants <img style="vertical-align: -0.023ex; width: 1.197ex; height: 1.02ex;" src="images/136.svg" alt=" " data-tex="a"> and <img style="vertical-align: -0.025ex; width: 0.971ex; height: 1.595ex;" src="images/137.svg" alt=" " data-tex="b">. +By inserting the values of these constants in (5), +we obtain the first and the fourth of the equations +given in Section XI. +<span class="align-center"><img style="vertical-align: -9.335ex; width: 25.905ex; height: 19.801ex;" src="images/150.svg" alt=" " data-tex=" +\left. +\begin{aligned} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, \\ +t' &= \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{aligned} +\right\} +\qquad\text{(8)}. +"></span> +</p> +<p> +Thus we have obtained the Lorentz transformation +for events on the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis. It satisfies the condition +<span class="align-center"><img style="vertical-align: -0.566ex; width: 31.718ex; height: 2.565ex;" src="images/151.svg" alt=" " data-tex=" +x'^{2} - c^{2} t'^{2} = x^{2} - c^{2} t^{2}. +\qquad\text{(8a)}. +"></span> +</p> +<p> +The extension of this result, to include events which +take place outside the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis, is obtained by retaining +equations (8) and supplementing them by the relations +<span class="align-center"><img style="vertical-align: -2.17ex; width: 16.233ex; height: 5.47ex;" src="images/152.svg" alt=" " data-tex=" +\left. +\begin{aligned} +y' &= y, \\ +z' &= z. +\end{aligned} +\right\} +\qquad\text{(9)}. +"></span> +In this way we satisfy the postulate of the constancy of +the velocity of light <i>in vacuo</i> for rays of light of arbitrary +direction, both for the system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> and for the system +<img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'. This may be shown in the following manner. +</p> +<p> +We suppose a light-signal sent out from the origin +of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> at the time <img style="vertical-align: -0.186ex; width: 4.965ex; height: 1.692ex;" src="images/37.svg" alt=" " data-tex="t = 0">. It will be propagated according +to the equation +<span class="align-center"><img style="vertical-align: -0.469ex; width: 23.737ex; height: 2.851ex;" src="images/153.svg" alt=" " data-tex=" +r = \sqrt{x^{2} + y^{2} + z^{2}} = ct, +"></span> +<span class="pagenum" id="Page_118">[Pg 118]</span> +or, if we square this equation, according to the equation +<span class="align-center"><img style="vertical-align: -0.566ex; width: 32.44ex; height: 2.565ex;" src="images/154.svg" alt=" " data-tex=" +x^{2} + y^{2} + z^{2} - c^{2} t^{2} = 0. +\qquad\text{(10)}. +"></span> +</p> +<p> +It is required by the law of propagation of light, in +conjunction with the postulate of relativity, that the +transmission of the signal in question should take place—as +judged from <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">'—in accordance with the corresponding +formula +<span class="align-center"><img style="vertical-align: -0.439ex; width: 7.718ex; height: 2.269ex;" src="images/155.svg" alt=" " data-tex=" +r' = ct', +"></span> +or, +<span class="align-center"><img style="vertical-align: -0.566ex; width: 35.331ex; height: 2.565ex;" src="images/156.svg" alt=" " data-tex=" +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} = 0. +\qquad\text{(10a)}. +"></span> +In order that equation (10a) may be a consequence of +equation (10), we must have +<span class="align-center"><img style="vertical-align: -0.566ex; width: 54.985ex; height: 2.565ex;" src="images/157.svg" alt=" " data-tex=" +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = \sigma(x^{2} + y^{2} + z^{2} - c^{2} t^{2}). +\qquad\text{(11)}. +"></span> +</p> +<p> +Since equation (8a) must hold for points on the +<img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis, we thus have <img style="vertical-align: -0.186ex; width: 5.44ex; height: 1.692ex;" src="images/158.svg" alt=" " data-tex="\sigma = 1">. It is easily seen that the +Lorentz transformation really satisfies equation (11) +for <img style="vertical-align: -0.186ex; width: 5.44ex; height: 1.692ex;" src="images/158.svg" alt=" " data-tex="\sigma = 1">; for (11) is a consequence of (8a) and (9), +and hence also of (8) and (9). We have thus derived +the Lorentz transformation. +</p> +<p> +The Lorentz transformation represented by (8) and (9) +still requires to be generalised. Obviously it is +immaterial whether the axes of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' be chosen so that +they are spatially parallel to those of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. It is also not +essential that the velocity of translation of <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' with +respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> should be in the direction of the <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">-axis. +A simple consideration shows that we are able to +construct the Lorentz transformation in this general +sense from two kinds of transformations, viz. from +Lorentz transformations in the special sense and from +purely spatial transformations, which corresponds to +the replacement of the rectangular co-ordinate system +<span class="pagenum" id="Page_119">[Pg 119]</span> +by a new system with its axes pointing in other +directions. +</p> +<p> +Mathematically, we can characterise the generalised +Lorentz transformation thus: +</p> +<p> +It expresses <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">', <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">', <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">', <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">', in terms of linear homogeneous +functions of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, of such a kind that the relation +<span class="align-center"><img style="vertical-align: -0.566ex; width: 52.058ex; height: 2.565ex;" src="images/159.svg" alt=" " data-tex=" +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = x^{2} + y^{2} + z^{2} - c^{2} t^{2} +\qquad\text{(11a)}. +"></span> +is satisfied identically. That is to say: If we substitute +their expressions in <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">, <img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">, <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">, <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, in place of <img style="vertical-align: -0.025ex; width: 1.294ex; height: 1.025ex;" src="images/26.svg" alt=" " data-tex="x">', +<img style="vertical-align: -0.464ex; width: 1.109ex; height: 1.464ex;" src="images/27.svg" alt=" " data-tex="y">', <img style="vertical-align: -0.025ex; width: 1.052ex; height: 1.025ex;" src="images/28.svg" alt=" " data-tex="z">', <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">', on the left-hand side, then the left-hand side of +(11a) agrees with the right-hand side. +<span class="pagenum" id="Page_120">[Pg 120]</span> +</p> + +</div> + +<p><br><br><br></p> + +<div class="chapter"> +<h2 title="APPENDIX II: MINKOWSKI'S FOUR-DIMENSIONAL SPACE +(WORLD)"><a id="appen02"></a>APPENDIX II +<br> +MINKOWSKI'S FOUR-DIMENSIONAL SPACE +("WORLD")</h2> + +<p class="nind"> +<span class="dropcap">W</span>E can characterise the Lorentz transformation +still more simply if we introduce the imaginary <img style="vertical-align: -0.318ex; width: 8.252ex; height: 2.398ex;" src="images/77.svg" alt=" " data-tex="\sqrt{-1}·ct"> +in place of <img style="vertical-align: -0.025ex; width: 0.817ex; height: 1.441ex;" src="images/25.svg" alt=" " data-tex="t">, as time-variable. If, in +accordance with this, we insert +<span class="align-center"><img style="vertical-align: -5.223ex; width: 14.18ex; height: 11.577ex;" src="images/160.svg" alt=" " data-tex=" +\begin{align*} +x_{1} &= x, \\ +x_{2} &= y, \\ +x_{3} &= z, \\ +x_{4} &= \sqrt{-1}·ct, +\end{align*} +"></span> +and similarly for the accented system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">', then the +condition which is identically satisfied by the transformation +can be expressed thus: +<span class="align-center"><img style="vertical-align: -0.594ex; width: 53.759ex; height: 2.594ex;" src="images/161.svg" alt=" " data-tex=" +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + x_{4}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2} + {x_{4}}^{2}. +\qquad\text{(12)}. +"></span> +</p> +<p> +That is, by the afore-mentioned choice of "co-ordinates," +(11a) is transformed into this equation. +</p> +<p> +We see from (12) that the imaginary time co-ordinate <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}"> +enters into the condition of transformation in exactly +the same way as the space co-ordinates <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">. It +is due to this fact that, according to the theory of +<span class="pagenum" id="Page_121">[Pg 121]</span> +relativity, the "time" <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}"> enters into natural laws in the +same form as the space co-ordinates <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">. +</p> +<p> +A four-dimensional continuum described by the +"co-ordinates" <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/100.svg" alt=" " data-tex="x_{4}">, was called +"world" by Minkowski, who also termed a point-event a "world-point." +From a "happening" in three-dimensional +space, physics becomes, as it were, an "existence" in +the four-dimensional "world." +</p> +<p> +This four-dimensional "world" bears a close similarity +to the three-dimensional "space" of (Euclidean) +analytical geometry. If we introduce into the latter a +new Cartesian co-ordinate system (<img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">', <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">', <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">') with +the same origin, then <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">', <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">', <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">', are linear +homogeneous functions of <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/70.svg" alt=" " data-tex="x_{1}">, <img style="vertical-align: -0.339ex; width: 2.282ex; height: 1.339ex;" src="images/98.svg" alt=" " data-tex="x_{2}">, <img style="vertical-align: -0.375ex; width: 2.282ex; height: 1.375ex;" src="images/99.svg" alt=" " data-tex="x_{3}">, which identically +satisfy the equation +<span class="align-center"><img style="vertical-align: -0.594ex; width: 32.683ex; height: 2.594ex;" src="images/162.svg" alt=" " data-tex=" +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2}. +"></span> +The analogy with (12) is a complete one. We can +regard Minkowski's "world" in a formal manner as a +four-dimensional Euclidean space (with imaginary +time co-ordinate); the Lorentz transformation corresponds +to a "rotation" of the co-ordinate system in the +four-dimensional "world." +<span class="pagenum" id="Page_122">[Pg 122]</span> +</p> + +</div> + +<p><br><br><br></p> + +<div class="chapter"> +<h2 title="APPENDIX III: THE EXPERIMENTAL CONFIRMATION OF THE +GENERAL THEORY OF RELATIVITY"><a id="appen03"></a>APPENDIX III +<br> +THE EXPERIMENTAL CONFIRMATION OF THE +GENERAL THEORY OF RELATIVITY</h2> + +<p class="nind"> +<span class="dropcap">F</span>ROM a systematic theoretical point of view, +we may imagine the process of evolution of an empirical +science to be a continuous process of induction. +Theories are evolved and are expressed in +short compass as statements of a large number of individual +observations in the form of empirical laws, +from which the general laws can be ascertained by comparison. +Regarded in this way, the development of a +science bears some resemblance to the compilation of a +classified catalogue. It is, as it were, a purely empirical +enterprise. +</p> +<p> +But this point of view by no means embraces the whole +of the actual process; for it slurs over the important +part played by intuition and deductive thought in the +development of an exact science. As soon as a science +has emerged from its initial stages, theoretical advances +are no longer achieved merely by a process of arrangement. +Guided by empirical data, the investigator +rather develops a system of thought which, in general, +is built up logically from a small number of fundamental +assumptions, the so-called axioms. We call such a +system of thought a <i>theory</i>. The theory finds the +<span class="pagenum" id="Page_123">[Pg 123]</span> +justification for its existence in the fact that it correlates +a large number of single observations, and it is just here +that the "truth" of the theory lies. +</p> +<p> +Corresponding to the same complex of empirical data, +there may be several theories, which differ from one +another to a considerable extent. But as regards the +deductions from the theories which are capable of +being tested, the agreement between the theories may +be so complete, that it becomes difficult to find such +deductions in which the two theories differ from each +other. As an example, a case of general interest is +available in the province of biology, in the Darwinian +theory of the development of species by selection in +the struggle for existence, and in the theory of development +which is based on the hypothesis of the hereditary +transmission of acquired characters. +</p> +<p> +We have another instance of far-reaching agreement +between the deductions from two theories in Newtonian +mechanics on the one hand, and the general theory of +relativity on the other. This agreement goes so far, +that up to the present we have been able to find only +a few deductions from the general theory of relativity +which are capable of investigation, and to which the +physics of pre-relativity days does not also lead, and +this despite the profound difference in the fundamental +assumptions of the two theories. In what follows, we +shall again consider these important deductions, and we +shall also discuss the empirical evidence appertaining to +them which has hitherto been obtained. +</p> + +<p><br><br></p> + +<p class="center">(<i>a</i>) MOTION OF THE PERIHELION OF MERCURY</p> + +<p> +According to Newtonian mechanics and Newton's +law of gravitation, a planet which is revolving round the +<span class="pagenum" id="Page_124">[Pg 124]</span> +sun would describe an ellipse round the latter, or, more +correctly, round the common centre of gravity of the +sun and the planet. In such a system, the sun, or the +common centre of gravity, lies in one of the foci of the +orbital ellipse in such a manner that, in the course of a +planet-year, the distance sun-planet grows from a +minimum to a maximum, and then decreases again to +a minimum. If instead of Newton's law we insert a +somewhat different law of attraction into the calculation, +we find that, according to this new law, the motion +would still take place in such a manner that the distance +sun-planet exhibits periodic variations; but in this +case the angle described by the line joining sun and +planet during such a period (from perihelion—closest +proximity to the sun—to perihelion) would differ from 360°. +The line of the orbit would not then be a closed +one, but in the course of time it would fill up an annular +part of the orbital plane, viz. between the circle of +least and the circle of greatest distance of the planet from +the sun. +</p> +<p> +According also to the general theory of relativity, +which differs of course from the theory of Newton, a +small variation from the Newton-Kepler motion of a +planet in its orbit should take place, and in such a way, +that the angle described by the radius sun-planet +between one perihelion and the next should exceed that +corresponding to one complete revolution by an amount +given by +<span class="align-center"><img style="vertical-align: -2.194ex; width: 15.758ex; height: 5.611ex;" src="images/163.svg" alt=" " data-tex=" ++\frac{24\pi^{3} a^{2}}{T^{2} c^{2} (1-e^{2})}. +"></span> +</p> +<p> +(<i>N.B.</i>—One complete revolution corresponds to the +angle <img style="vertical-align: -0.025ex; width: 2.421ex; height: 1.532ex;" src="images/164.svg" alt=" " data-tex="2\pi"> in the absolute angular measure customary in +physics, and the above expression gives the amount by +<span class="pagenum" id="Page_125">[Pg 125]</span> +which the radius sun-planet exceeds this angle during +the interval between one perihelion and the next.) +In this expression <img style="vertical-align: -0.023ex; width: 1.197ex; height: 1.02ex;" src="images/136.svg" alt=" " data-tex="a"> represents the major semi-axis of +the ellipse, <img style="vertical-align: -0.025ex; width: 1.054ex; height: 1.025ex;" src="images/165.svg" alt=" " data-tex="e"> its eccentricity, <img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c"> the velocity of light, and +<img style="vertical-align: 0; width: 1.593ex; height: 1.532ex;" src="images/52.svg" alt=" " data-tex="T"> the period of revolution of the planet. Our result +may also be stated as follows: According to the general +theory of relativity, the major axis of the ellipse rotates +round the sun in the same sense as the orbital motion +of the planet. Theory requires that this rotation should +amount to 43 seconds of arc per century for the planet +Mercury, but for the other planets of our solar system its +magnitude should be so small that it would necessarily +escape detection.<a id="FNanchor_27_1"></a><a href="#Footnote_27_1" class="fnanchor">[27]</a> +</p> +<p> +In point of fact, astronomers have found that the +theory of Newton does not suffice to calculate the +observed motion of Mercury with an exactness corresponding +to that of the delicacy of observation attainable +at the present time. After taking account of all +the disturbing influences exerted on Mercury by the +remaining planets, it was found (Leverrier—1859—and +Newcomb—1895) that an unexplained perihelial +movement of the orbit of Mercury remained over, the +amount of which does not differ sensibly from the above-mentioned ++43 seconds of arc per~century. The uncertainty +of the empirical result amounts to a few +seconds only. +</p> + +<p><br></p> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_27_1"></a><a href="#FNanchor_27_1"><span class="label">[27]</span></a>Especially since the next planet Venus has an orbit that is +almost an exact circle, which makes it more difficult to locate +the perihelion with precision.</p></div> + +<p><br><br></p> + +<p class="center">(<i>b</i>) DEFLECTION OF LIGHT BY A GRAVITATIONAL +FIELD</p> + +<p> +In XXII it has been already mentioned that, +<span class="pagenum" id="Page_126">[Pg 126]</span> +according to the general theory of relativity, a ray of +light will experience a curvature of its path when passing +through a gravitational field, this curvature being similar +to that experienced by the path of a body which is +projected through a gravitational field. As a result of +this theory, we should expect that a ray of light which +is passing close to a heavenly body would be deviated +towards the latter. For a ray of light which passes the +sun at a distance of <img style="vertical-align: 0; width: 1.885ex; height: 1.62ex;" src="images/166.svg" alt=" " data-tex="\Delta"> sun-radii from its centre, the +angle of deflection (<img style="vertical-align: -0.025ex; width: 1.448ex; height: 1.025ex;" src="images/167.svg" alt=" " data-tex="\alpha">) should amount to +<span class="align-center"><img style="vertical-align: -1.552ex; width: 22.963ex; height: 4.676ex;" src="images/168.svg" alt=" " data-tex=" +\alpha = \frac{\text{1.7 seconds of arc}}{\Delta}. +"></span> +</p> +<p class="nind"> +It may be added that, according to the theory, half of +this deflection is produced by the +Newtonian field of attraction of the +sun, and the other half by the geometrical +modification ("curvature") +of space caused by the sun. +</p> +<a id="figure05"></a> +<img src="images/figure05.jpg" class="floatright" width="200" alt="fig5"> +<div class="caption"> +<p>FIG. 5.</p> +</div> +<p> +This result admits of an experimental +test by means of the photographic +registration of stars during +a total eclipse of the sun. The only +reason why we must wait for a total +eclipse is because at every other +time the atmosphere is so strongly +illuminated by the light from the +sun that the stars situated near the +sun's disc are invisible. The predicted effect can be +seen clearly from the accompanying diagram. If the +sun (<img style="vertical-align: -0.05ex; width: 1.459ex; height: 1.645ex;" src="images/6.svg" alt=" " data-tex="S">) were not present, a star which is practically +infinitely distant would be seen in the direction <img style="vertical-align: -0.339ex; width: 2.861ex; height: 1.885ex;" src="images/169.svg" alt=" " data-tex="D_{1}">, as +observed from the earth. But as a consequence of the +<span class="pagenum" id="Page_127">[Pg 127]</span> +deflection of light from the star by the sun, the star +will be seen in the direction <img style="vertical-align: -0.339ex; width: 2.861ex; height: 1.885ex;" src="images/170.svg" alt=" " data-tex="D_{2}">, <i>i.e.</i> at a somewhat +greater distance from the centre of the sun than corresponds +to its real position. +</p> +<p> +In practice, the question is tested in the following +way. The stars in the neighbourhood of the sun are +photographed during a solar eclipse. In addition, a +second photograph of the same stars is taken when the +sun is situated at another position in the sky, <i>i.e.</i> a few +months earlier or later. As compared with the standard +photograph, the positions of the stars on the eclipse-photograph +ought to appear displaced radially outwards +(away from the centre of the sun) by an amount +corresponding to the angle <img style="vertical-align: -0.025ex; width: 1.448ex; height: 1.025ex;" src="images/167.svg" alt=" " data-tex="\alpha">. +</p> +<p> +We are indebted to the Royal Society and to the +Royal Astronomical Society for the investigation of +this important deduction. Undaunted by the war and +by difficulties of both a material and a psychological +nature aroused by the war, these societies equipped +two expeditions—to Sobral (Brazil), and to the island of +Principe (West Africa)—and sent several of Britain's +most celebrated astronomers (Eddington, Cottingham, +Crommelin, Davidson), in order to obtain photographs +of the solar eclipse of 29th May, 1919. The relative +discrepancies to be expected between the stellar photographs +obtained during the eclipse and the comparison +photographs amounted to a few hundredths of a millimetre +only. Thus great accuracy was necessary in +making the adjustments required for the taking of the +photographs, and in their subsequent measurement. +</p> +<p> +The results of the measurements confirmed the theory +in a thoroughly satisfactory manner. The rectangular +components of the observed and of the calculated +<span class="pagenum" id="Page_128">[Pg 128]</span> +deviations of the stars (in seconds of arc) are set forth +in the following table of results: +</p> + +<table style="border-spacing: 0px;padding: 1px;border-width: 0px;"> +<thead> +<tr> +<th style="width:180px">Number of the Star.</th> +<th colspan="2" style="width:500px">First Co-ordinate.</th> +<th colspan="2" style="width:500px">Second Co-ordinate.</th> +</tr> +<tbody> +<tr> +<td> </td> +<td style="text-align: center;">Observed.</td> +<td style="text-align: center;">Calculated.</td> +<td style="text-align: center;">Observed.</td> +<td style="text-align: center;">Calculated.</td> +</tr> +<tr> +<td style="text-align: center;">11</td> +<td style="text-align: center;">-0.19</td> +<td style="text-align: center;">-0.22</td> +<td style="text-align: center;">+0.16</td> +<td style="text-align: center;">+0.02</td> +</tr> +<tr> +<td style="text-align: center;"> 5</td> +<td style="text-align: center;">+0.29</td> +<td style="text-align: center;">+0.31</td> +<td style="text-align: center;">-0.46</td> +<td style="text-align: center;">-0.43</td> +</tr> +<tr> +<td style="text-align: center;"> 4</td> +<td style="text-align: center;">+0.11</td> +<td style="text-align: center;">+0.10</td> +<td style="text-align: center;">+0.83</td> +<td style="text-align: center;">+0.74</td> +</tr> +<tr> +<td style="text-align: center;"> 3</td> +<td style="text-align: center;">+0.20</td> +<td style="text-align: center;">+0.12</td> +<td style="text-align: center;">+1.00</td> +<td style="text-align: center;">+0.87</td> +</tr> +<tr> +<td style="text-align: center;"> 6</td> +<td style="text-align: center;">+0.10</td> +<td style="text-align: center;">+0.04</td> +<td style="text-align: center;">+0.57</td> +<td style="text-align: center;">+0.40</td> +</tr> +<tr> +<td style="text-align: center;">10</td> +<td style="text-align: center;">-0.08</td> +<td style="text-align: center;">+0.09</td> +<td style="text-align: center;">+0.35</td> +<td style="text-align: center;">+0.32</td> +</tr> +<tr> +<td style="text-align: center;"> 2</td> +<td style="text-align: center;">+0.95</td> +<td style="text-align: center;">+0.85</td> +<td style="text-align: center;">-0.27</td> +<td style="text-align: center;">-0.09</td> +</tr></tbody></table> + +<p><br><br></p> + +<p class="center">(<i>c</i>) DISPLACEMENT OF SPECTRAL LINES TOWARDS +THE RED</p> + +<p>In XXIII it has been shown that in a system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' +which is in rotation with regard to a Galileian system <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">, +clocks of identical construction, and which are considered +at rest with respect to the rotating reference-body, +go at rates which are dependent on the positions +of the clocks. We shall now examine this dependence +quantitatively. A clock, which is situated at a distance <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r"> +from the centre of the disc, has a velocity relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +which is given by +<span class="align-center"><img style="vertical-align: -0.439ex; width: 7.171ex; height: 1.758ex;" src="images/171.svg" alt=" " data-tex=" +v = \omega r, +"></span> +where <img style="vertical-align: -0.025ex; width: 1.407ex; height: 1.027ex;" src="images/172.svg" alt=" " data-tex="\omega"> represents the angular velocity of rotation of the +disc <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">' with respect to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K">. If <img style="vertical-align: -0.375ex; width: 2.105ex; height: 1.375ex;" src="images/173.svg" alt=" " data-tex="\nu_{0}"> +represents the number of ticks of the clock per unit time ("rate" of +the clock) relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> when the clock is at rest, then the +"rate" of the clock (<img style="vertical-align: 0; width: 1.199ex; height: 1ex;" src="images/174.svg" alt=" " data-tex="\nu">) when it is moving relative to <img style="vertical-align: 0; width: 1.76ex; height: 1.545ex;" src="images/9.svg" alt=" " data-tex="\mathrm K"> +with a velocity <img style="vertical-align: -0.025ex; width: 1.097ex; height: 1.027ex;" src="images/11.svg" alt=" " data-tex="v">, but at rest with respect to the disc, will, +in accordance with XII, be given by +<span class="align-center"><img style="vertical-align: -1.657ex; width: 16.236ex; height: 5.566ex;" src="images/175.svg" alt=" " data-tex=" +\nu = \nu_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}, +"></span> +<span class="pagenum" id="Page_129">[Pg 129]</span> +or with sufficient accuracy by +<span class="align-center"><img style="vertical-align: -2.148ex; width: 19.808ex; height: 5.564ex;" src="images/176.svg" alt=" " data-tex=" +\nu = \nu_{0} \left(1 - \tfrac{1}{2}\, \frac{v^{2}}{c^{2}}\right). +"></span> +</p> +<p class="nind"> +This expression may also be stated in the following +form: +<span class="align-center"><img style="vertical-align: -2.148ex; width: 23.294ex; height: 5.564ex;" src="images/177.svg" alt=" " data-tex=" +\nu = \nu_{0} \left(1 - \frac{1}{c^{2}}\, \frac{\omega^{2} r^{2}}{2}\right). +"></span> +</p> +<p class="nind"> +If we represent the difference of potential of the centrifugal +force between the position of the clock and the +centre of the disc by <img style="vertical-align: -0.464ex; width: 1.348ex; height: 2.034ex;" src="images/178.svg" alt=" " data-tex="\phi">, <i>i.e.</i> the work, considered +negatively, which must be performed on the unit of mass +against the centrifugal force in order to transport it +from the position of the clock on the rotating disc to +the centre of the disc, then we have +<span class="align-center"><img style="vertical-align: -1.552ex; width: 12.153ex; height: 4.968ex;" src="images/179.svg" alt=" " data-tex=" +\phi = -\frac{\omega^{2} r^{2}}{2}. +"></span> +</p> +<p class="nind"> +From this it follows that +<span class="align-center"><img style="vertical-align: -2.148ex; width: 17.518ex; height: 5.428ex;" src="images/180.svg" alt=" " data-tex=" +\nu = \nu_{0} \left(1 + \frac{\phi}{c^{2}}\right). +"></span> +</p> +<p class="nind"> +In the first place, we see from this expression that two +clocks of identical construction will go at different rates +when situated at different distances from the centre of +the disc. This result is also valid from the standpoint +of an observer who is rotating with the disc. +</p> +<p> +Now, as judged from the disc, the latter is in a gravitational +field of potential <img style="vertical-align: -0.464ex; width: 1.348ex; height: 2.034ex;" src="images/178.svg" alt=" " data-tex="\phi">, hence the result we have +obtained will hold quite generally for gravitational +fields. Furthermore, we can regard an atom which is +emitting spectral lines as a clock, so that the following +statement will hold: +</p> +<p> +<i>An atom absorbs or emits light of a frequency which is</i> +<span class="pagenum" id="Page_130">[Pg 130]</span> +<i>dependent on the potential of the gravitational field in +which it is situated.</i> +</p> +<p> +The frequency of an atom situated on the surface of a +heavenly body will be somewhat less than the frequency +of an atom of the same element which is situated in free +space (or on the surface of a smaller celestial body). +Now <img style="vertical-align: -1.577ex; width: 11.51ex; height: 4.652ex;" src="images/181.svg" alt=" " data-tex="\phi = -K\dfrac{M}{r}">, where <img style="vertical-align: 0; width: 2.011ex; height: 1.545ex;" src="images/182.svg" alt=" " data-tex="K"> is Newton's constant of +gravitation, and <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M"> is the mass of the heavenly body. +Thus a displacement towards the red ought to take place +for spectral lines produced at the surface of stars as +compared with the spectral lines of the same element +produced at the surface of the earth, the amount of this +displacement being +<span class="align-center"><img style="vertical-align: -1.927ex; width: 17.47ex; height: 5.001ex;" src="images/183.svg" alt=" " data-tex=" +\frac{\nu_{0} - \nu}{\nu_{0}} = \frac{K}{c^{2}}\, \frac{M}{r}. +"></span> +</p> +<p> +For the sun, the displacement towards the red predicted +by theory amounts to about two millionths of +the wave-length. A trustworthy calculation is not +possible in the case of the stars, because in general +neither the mass <img style="vertical-align: 0; width: 2.378ex; height: 1.545ex;" src="images/19.svg" alt=" " data-tex="M"> nor the radius <img style="vertical-align: -0.025ex; width: 1.02ex; height: 1.025ex;" src="images/121.svg" alt=" " data-tex="r"> is known. +</p> +<p> +It is an open question whether or not this effect +exists, and at the present time astronomers are working +with great zeal towards the solution. Owing to the +smallness of the effect in the case of the sun, it is difficult +to form an opinion as to its existence. Whereas +Grebe and Bachem (Bonn), as a result of their own +measurements and those of Evershed and Schwarzschild +on the cyanogen bands, have placed the existence of +the effect almost beyond doubt, other investigators, +particularly St. John, have been led to the opposite +opinion in consequence of their measurements. +<span class="pagenum" id="Page_131">[Pg 131]</span> +</p> +<p> +Mean displacements of lines towards the less refrangible +end of the spectrum are certainly revealed by +statistical investigations of the fixed stars; but up +to the present the examination of the available data +does not allow of any definite decision being arrived at, +as to whether or not these displacements are to be +referred in reality to the effect of gravitation. The +results of observation have been collected together, +and discussed in detail from the standpoint of the +question which has been engaging our attention here, +in a paper by E. Freundlich entitled "Zur Prüfung der +allgemeinen Relativitäts-Theorie" (<i>Die Naturwissenschaften</i>, +1919, No. 35, p. 520: Julius Springer, Berlin). +</p> +<p> +At all events, a definite decision will be reached during +the next few years. If the displacement of spectral +lines towards the red by the gravitational potential +does not exist, then the general theory of relativity +will be untenable. On the other hand, if the cause of +the displacement of spectral lines be definitely traced +to the gravitational potential, then the study of this +displacement will furnish us with important information +as to the mass of the heavenly bodies. +<span class="pagenum" id="Page_132">[Pg 132]</span> +</p> + +</div> + +<p><br><br><br></p> + +<div class="chapter"> +<h2 title="BIBLIOGRAPHY"><a id="BIBLIOGRAPHY"></a> +BIBLIOGRAPHY</h2> + +<p class="center"><b>WORKS IN ENGLISH ON EINSTEIN'S THEORY</b></p> + +<p class="center">INTRODUCTORY</p> + +<p class="hanging2"> +<i>The Foundations of Einstein's Theory of Gravitation</i>: +Erwin Freundlich (translation by H. L. Brose). +Camb. Univ. Press, 1920. +</p> +<p class="hanging2"> +<i>Space and Time in Contemporary Physics</i>: Moritz Schlick +(translation by H. L. Brose). Clarendon Press, +Oxford, 1920. +</p> + +<p><br></p> + +<p class="center">THE SPECIAL THEORY</p> + +<p class="hanging2"> +<i>The Principle of Relativity</i>: E. Cunningham. Camb. +Univ. Press. +</p> +<p class="hanging2"> +<i>Relativity and the Electron Theory</i>: E. Cunningham, Monographs +on Physics. Longmans, Green & Co. +</p> +<p class="hanging2"> +<i>The Theory of Relativity</i>: L. Silberstein. Macmillan & Co. +</p> +<p class="hanging2"> +<i>The Space-Time Manifold of Relativity</i>: E. B. Wilson +and G. N. Lewis, <i>Proc. Amer. Soc. Arts & Science</i>, +vol. XLVIII., No. 11, 1912. +</p> + +<p><br></p> + +<p class="center">THE GENERAL THEORY</p> + +<p class="hanging2"> +<i>Report on the Relativity Theory of Gravitation</i>: A. S. +Eddington. Fleetway Press Ltd., Fleet Street, +London. +<span class="pagenum" id="Page_133">[Pg 133]</span> +</p> +<p class="hanging2"> +<i>On Einstein's Theory of Gravitation and its Astronomical +Consequences</i>: W. de Sitter, <i>M. N. Roy. Astron. +Soc.</i>, LXXVI. p. 699, 1916; LXXVII. p. 155, 1916; LXXVIII. +p. 3, 1917. +</p> +<p class="hanging2"> +<i>On Einstein's Theory of Gravitation</i>: H. A. Lorentz, <i>Proc. +Amsterdam Acad.</i>, vol. XIX. p. 1341, 1917. +</p> +<p class="hanging2"> +<i>Space, Time and Gravitation</i>: W. de Sitter: <i>The +Observatory</i>, No. 505, p. 412. Taylor & Francis, Fleet +Street, London. +</p> +<p class="hanging2"> +<i>The Total Eclipse of 29th May, 1919, and the Influence of +Gravitation on Light</i>: A. S. Eddington, <i>ibid.</i>, +March 1919. +</p> +<p class="hanging2"> +<i>Discussion on the Theory of Relativity</i>: <i>M. N. Roy. Astron. +Soc.</i>, vol. LXXX. No. 2, p. 96, December 1919. +</p> +<p class="hanging2"> +<i>The Displacement of Spectrum Lines and the Equivalence +Hypothesis</i>: W. G. Duffield, <i>M. N. Roy. Astron. Soc.</i>, +vol. LXXX.; No. 3, p. 262, 1920. +</p> +<p class="hanging2"> +<i>Space, Time and Gravitation</i>: A. S. Eddington, Camb. Univ. +Press, 1920. +</p> + +<p><br></p> + +<p class="center">ALSO, CHAPTERS IN</p> + +<p class="hanging2"> +<i>The Mathematical Theory of Electricity and Magnetism</i>: +J. H. Jeans (4th edition). Camb. Univ. Press, 1920. +</p> +<p class="hanging2"> +<i>The Electron Theory of Matter</i>: O. W. Richardson. Camb. +Univ. Press. +<span class="pagenum" id="Page_134">[Pg 134]</span> +</p> +</div> + +<p><br><br><br></p> + +<div class="chapter"> +<h2 title='INDEX'><a id="INDEX"></a>INDEX</h2> +<p class="indx"> +Aberration, <a href="#Page_49">49</a><br> +Absorption of energy, <a href="#Page_46">46</a><br> +Acceleration, <a href="#Page_64">64</a>, <a href="#Page_67">67</a>, <a href="#Page_70">70</a><br> +Action at a distance, <a href="#Page_48">48</a><br> +Addition of velocities, <a href="#Page_16">16</a>, <a href="#Page_38">38</a><br> +Adjacent points, <a href="#Page_89">89</a><br> +Aether, <a href="#Page_52">52</a><br> +—drift, <a href="#Page_52">52</a>, <a href="#Page_53">53</a><br> +Arbitrary substitutions, <a href="#Page_98">98</a><br> +Astronomy, <a href="#Page_7">7</a>, <a href="#Page_102">102</a><br> +Astronomical day, <a href="#Page_11">11</a><br> +Axioms, <a href="#Page_2">2</a>, <a href="#Page_123">123</a><br> +<span style="margin-left: 1em;">truth of, <a href="#Page_2">2</a></span><br> +<br> +Bachem, <a href="#Page_131">131</a><br> +Basis of theory, <a href="#Page_44">44</a><br> +"Being," <a href="#Page_66">66</a>, <a href="#Page_108">108</a><br> +β-rays, <a href="#Page_50">50</a><br> +Biology, <a href="#Page_124">124</a><br> +<br> +Cartesian system of co-ordinates, <a href="#Page_7">7</a>, <a href="#Page_84">84</a>, <a href="#Page_122">122</a><br> +Cathode rays, <a href="#Page_50">50</a><br> +Celestial mechanics, <a href="#Page_105">105</a><br> +Centrifugal force, <a href="#Page_80">80</a>, <a href="#Page_130">130</a><br> +Chest, <a href="#Page_66">66</a><br> +Classical mechanics, <a href="#Page_9">9</a>, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_16">16</a>, <a href="#Page_30">30</a>, <a href="#Page_44">44</a>, <a href="#Page_71">71</a>, <a href="#Page_102">102</a>, <a href="#Page_103">103</a>, <a href="#Page_124">124</a></span><br> +—truth of, <a href="#Page_13">13</a><br> +Clocks, <a href="#Page_10">10</a>, <a href="#Page_23">23</a>, <a href="#Page_80">80</a>, <a href="#Page_81">81</a>, <a href="#Page_94">94</a>, <a href="#Page_95">95</a>, <a href="#Page_98">98</a>-<a href="#Page_100">100</a>, <a href="#Page_102">102</a>, <a href="#Page_113">113</a>, <a href="#Page_129">129</a><br> +—rate of, <a href="#Page_129">129</a><br> +Conception of mass, <a href="#Page_45">45</a><br> +—position, <a href="#Page_6">6</a><br> +Conservation of energy, <a href="#Page_45">45</a>, <a href="#Page_101">101</a><br> +—impulse, <a href="#Page_101">101</a><br> +—mass, <a href="#Page_45">45</a>, <a href="#Page_47">47</a><br> +Continuity, <a href="#Page_95">95</a><br> +Continuum, <a href="#Page_55">55</a>, <a href="#Page_83">83</a><br> +—two-dimensional, <a href="#Page_94">94</a><br> +—three-dimensional, <a href="#Page_57">57</a><br> +—four-dimensional, <a href="#Page_89">89</a>, <a href="#Page_91">91</a>, <a href="#Page_92">92</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_94">94</a>, <a href="#Page_122">122</a></span><br> +—space-time, <a href="#Page_78">78</a>, <a href="#Page_91">91</a>-<a href="#Page_96">96</a><br> +—Euclidean, <a href="#Page_84">84</a>, <a href="#Page_86">86</a>, <a href="#Page_88">88</a>, <a href="#Page_92">92</a><br> +—non-Euclidean, <a href="#Page_86">86</a>, <a href="#Page_90">90</a><br> +Co-ordinate differences, <a href="#Page_92">92</a><br> +—differentials, <a href="#Page_92">92</a><br> +—planes, <a href="#Page_32">32</a><br> +Cottingham, <a href="#Page_128">128</a><br> +Counter-Point, <a href="#Page_112">112</a><br> +Co-variant, <a href="#Page_43">43</a><br> +Crommelin, <a href="#Page_128">128</a><br> +Curvature of light-rays, <a href="#Page_104">104</a>, <a href="#Page_127">127</a><br> +<span style="margin-left: 1em;">space, <a href="#Page_127">127</a></span><br> +Curvilinear motion, <a href="#Page_74">74</a><br> +Cyanogen bands, <a href="#Page_131">131</a><br> +<br> +Darwinian theory, <a href="#Page_124">124</a><br> +Davidson, <a href="#Page_128">128</a><br> +Deductive thought, <a href="#Page_123">123</a><br> +Derivation of laws, <a href="#Page_44">44</a><br> +De Sitter, <a href="#Page_17">17</a><br> +Displacement of spectral lines,<br> +<span style="margin-left: 1em;"><a href="#Page_104">104</a>, <a href="#Page_129">129</a></span><br> +Distance (line-interval), <a href="#Page_3">3</a>, <a href="#Page_5">5</a>, <a href="#Page_8">8</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_28">28</a>, <a href="#Page_29">29</a>, <a href="#Page_84">84</a>, <a href="#Page_88">88</a>, <a href="#Page_109">109</a></span><br> +—physical interpretation of, <a href="#Page_5">5</a><br> +—relativity of, <a href="#Page_28">28</a><br> +Doppler principle, <a href="#Page_50">50</a><br> +Double stars, <a href="#Page_17">17</a><br> +<br> +Eclipse of star, <a href="#Page_17">17</a><br> +Eddington, <a href="#Page_104">104</a>, <a href="#Page_128">128</a><br> +<span class="pagenum" id="Page_135">[Pg 135]</span> +Electricity, <a href="#Page_76">76</a><br> +Electrodynamics, <a href="#Page_13">13</a>, <a href="#Page_19">19</a>, <a href="#Page_41">41</a>, <a href="#Page_44">44</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_76">76</a></span><br> +Electromagnetic theory, <a href="#Page_49">49</a><br> +—waves, <a href="#Page_63">63</a><br> +Electron, <a href="#Page_44">44</a>, <a href="#Page_50">50</a><br> +—electrical masses of, <a href="#Page_51">51</a><br> +Electrostatics, <a href="#Page_76">76</a><br> +Elliptical space, <a href="#Page_112">112</a><br> +Empirical laws, <a href="#Page_123">123</a><br> +Encounter (space-time<br> +<span style="margin-left: 1em;">coincidence), <a href="#Page_95">95</a></span><br> +Equivalent, <a href="#Page_14">14</a><br> +Euclidean geometry, <a href="#Page_1">1</a>, <a href="#Page_2">2</a>, <a href="#Page_57">57</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_82">82</a>, <a href="#Page_86">86</a>, <a href="#Page_88">88</a>, <a href="#Page_108">108</a>, <a href="#Page_109">109</a>, <a href="#Page_113">113</a>, <a href="#Page_122">122</a></span><br> +—propositions of, <a href="#Page_3">3</a>, <a href="#Page_8">8</a><br> +Euclidean space, <a href="#Page_57">57</a>, <a href="#Page_86">86</a>, <a href="#Page_122">122</a><br> +Evershed, <a href="#Page_131">131</a><br> +Experience, <a href="#Page_49">49</a>, <a href="#Page_60">60</a><br> +<br> +Faraday, <a href="#Page_48">48</a>, <a href="#Page_63">63</a><br> +FitzGerald, <a href="#Page_53">53</a><br> +Fixed stars, <a href="#Page_11">11</a><br> +Fizeau, <a href="#Page_39">39</a>, <a href="#Page_49">49</a>, <a href="#Page_51">51</a><br> +—experiment of, <a href="#Page_39">39</a><br> +Frequency of atom, <a href="#Page_131">131</a><br> +<br> +Galilei, <a href="#Page_11">11</a><br> +—transformation, <a href="#Page_33">33</a>, <a href="#Page_36">36</a>, <a href="#Page_38">38</a>, <a href="#Page_42">42</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_52">52</a></span><br> +Galileian system of co-ordinates,<br> +<span style="margin-left: 1em;"><a href="#Page_11">11</a>, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_46">46</a>, <a href="#Page_79">79</a>, <a href="#Page_91">91</a>, <a href="#Page_98">98</a>,</span><br> +<span style="margin-left: 1em;"><a href="#Page_100">100</a></span><br> +Gauss, <a href="#Page_86">86</a>, <a href="#Page_87">87</a>, <a href="#Page_90">90</a><br> +Gaussian co-ordinates, <a href="#Page_88">88</a>-<a href="#Page_90">90</a>, <a href="#Page_94">94</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_96">96</a>-<a href="#Page_100">100</a></span><br> +General theory of relativity,<br> +<span style="margin-left: 1em;"><a href="#Page_59">59</a>-<a href="#Page_104">104</a>, <a href="#Page_97">97</a></span><br> +Geometrical ideas, <a href="#Page_2">2</a>, <a href="#Page_3">3</a><br> +—propositions, 1<br> +——truth of, <a href="#Page_2">2</a>-<a href="#Page_4">4</a><br> +Gravitation, <a href="#Page_64">64</a>, <a href="#Page_69">69</a>, <a href="#Page_78">78</a>, <a href="#Page_102">102</a><br> +Gravitational field, <a href="#Page_64">64</a>, <a href="#Page_67">67</a>, <a href="#Page_74">74</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_77">77</a>, <a href="#Page_93">93</a>, <a href="#Page_98">98</a>, <a href="#Page_100">100</a>, <a href="#Page_101">101</a>, <a href="#Page_113">113</a></span><br> +——potential of, <a href="#Page_130">130</a>, <a href="#Page_131">131</a><br> +Gravitational mass, <a href="#Page_65">65</a>, <a href="#Page_68">68</a>, <a href="#Page_102">102</a><br> +Grebe, <a href="#Page_131">131</a><br> +Group-density of stars, <a href="#Page_106">106</a><br> +<br> +Helmholtz, <a href="#Page_108">108</a><br> +Heuristic value of relativity,<br> +<span style="margin-left: 1em;"><a href="#Page_42">42</a></span><br> +<br> +Induction, <a href="#Page_123">123</a><br> +Inertia, <a href="#Page_65">65</a><br> +Inertial mass, <a href="#Page_47">47</a>, <a href="#Page_65">65</a>, <a href="#Page_69">69</a>, <a href="#Page_101">101</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_102">102</a></span><br> +Instantaneous photograph<br> +<span style="margin-left: 1em;">(snapshot), <a href="#Page_117">117</a></span><br> +Intensity of gravitational field,<br> +<span style="margin-left: 1em;"><a href="#Page_106">106</a></span><br> +Intuition, <a href="#Page_123">123</a><br> +Ions, <a href="#Page_44">44</a><br> +<br> +Kepler, <a href="#Page_125">125</a><br> +Kinetic energy, <a href="#Page_45">45</a>, <a href="#Page_101">101</a><br> +<br> +Lattice, <a href="#Page_108">108</a><br> +Law of inertia, <a href="#Page_11">11</a>, <a href="#Page_61">61</a>, <a href="#Page_62">62</a>, <a href="#Page_98">98</a><br> +Laws of Galilei-Newton, <a href="#Page_13">13</a><br> +—of Nature, <a href="#Page_60">60</a>, <a href="#Page_71">71</a>, <a href="#Page_99">99</a><br> +Leverrier, <a href="#Page_103">103</a>, <a href="#Page_126">126</a><br> +Light-signal, <a href="#Page_33">33</a>, <a href="#Page_115">115</a>, <a href="#Page_118">118</a><br> +Light-stimulus, <a href="#Page_33">33</a><br> +Limiting velocity (<img style="vertical-align: -0.025ex; width: 0.98ex; height: 1.025ex;" src="images/16.svg" alt=" " data-tex="c">), <a href="#Page_36">36</a>, <a href="#Page_37">37</a><br> +Lines of force, <a href="#Page_106">106</a><br> +Lorentz, H. A., <a href="#Page_19">19</a>, <a href="#Page_41">41</a>, <a href="#Page_44">44</a>, <a href="#Page_49">49</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_50">50</a>-<a href="#Page_53">53</a></span><br> +—transformation, <a href="#Page_33">33</a>, <a href="#Page_39">39</a>, <a href="#Page_42">42</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_91">91</a>, <a href="#Page_97">97</a>, <a href="#Page_98">98</a>, <a href="#Page_115">115</a>, <a href="#Page_118">118</a>, <a href="#Page_119">119</a>,</span><br> +<span style="margin-left: 1em;"><a href="#Page_121">121</a></span><br> +——(generalised), <a href="#Page_120">120</a><br> +<br> +Mach, E., <a href="#Page_72">72</a><br> +Magnetic field, <a href="#Page_63">63</a><br> +Manifold (<i>see</i> Continuum)<br> +Mass of heavenly bodies, <a href="#Page_132">132</a><br> +Matter, <a href="#Page_101">101</a><br> +Maxwell, <a href="#Page_41">41</a>, <a href="#Page_44">44</a>, <a href="#Page_48">48</a>-<a href="#Page_50">50</a>, <a href="#Page_52">52</a><br> +—fundamental equations, <a href="#Page_46">46</a>, <a href="#Page_77">77</a><br> +Measurement of length, <a href="#Page_85">85</a><br> +Measuring-rod, <a href="#Page_5">5</a>, <a href="#Page_6">6</a>, <a href="#Page_28">28</a>, <a href="#Page_80">80</a>, <a href="#Page_81">81</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_94">94</a>, <a href="#Page_100">100</a>, <a href="#Page_102">102</a>, <a href="#Page_111">111</a>, <a href="#Page_113">113</a>,</span><br> +<span style="margin-left: 1em;"><a href="#Page_117">117</a></span><br> +Mercury, <a href="#Page_103">103</a>, <a href="#Page_126">126</a><br> +—orbit of, <a href="#Page_103">103</a>, <a href="#Page_126">126</a><br> +Michelson, <a href="#Page_52">52</a>-<a href="#Page_54">54</a><br> +Minkowski, <a href="#Page_55">55</a>-<a href="#Page_57">57</a>, <a href="#Page_91">91</a>, <a href="#Page_122">122</a><br> +<span class="pagenum" id="Page_136">[Pg 136]</span> +Morley, <a href="#Page_53">53</a>, <a href="#Page_54">54</a><br> +Motion, <a href="#Page_14">14</a>, <a href="#Page_60">60</a><br> +—of heavenly bodies, <a href="#Page_13">13</a>, <a href="#Page_15">15</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_44">44</a>, <a href="#Page_102">102</a>, <a href="#Page_113">113</a></span><br> + +Newcomb, <a href="#Page_126">126</a><br> +Newton, <a href="#Page_11">11</a>, <a href="#Page_72">72</a>, <a href="#Page_102">102</a>, <a href="#Page_105">105</a>, <a href="#Page_125">125</a><br> +Newton's constant of,<br> +<span style="margin-left: 1em;">gravitation, <a href="#Page_131">131</a></span><br> +—law of gravitation, <a href="#Page_48">48</a>, <a href="#Page_80">80</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_106">106</a>, <a href="#Page_124">124</a></span><br> +—law of motion, <a href="#Page_64">64</a><br> +Non-Euclidean geometry, <a href="#Page_108">108</a><br> +Non-Galileian reference-bodies, <a href="#Page_98">98</a><br> +Non-uniform motion, <a href="#Page_62">62</a><br> +<br> +Optics, <a href="#Page_13">13</a>, <a href="#Page_19">19</a>, <a href="#Page_44">44</a><br> +Organ-pipe, note of, <a href="#Page_14">14</a><br> +<br> +Parabola, <a href="#Page_9">9</a>, <a href="#Page_10">10</a><br> +Path-curve, <a href="#Page_10">10</a><br> +Perihelion of Mercury, <a href="#Page_124">124</a>-<a href="#Page_126">126</a><br> +Physics, <a href="#Page_7">7</a><br> +—of measurement, <a href="#Page_7">7</a><br> +Place specification, <a href="#Page_5">5</a>, <a href="#Page_6">6</a><br> +Plane, <a href="#Page_1">1</a>, <a href="#Page_108">108</a>, <a href="#Page_109">109</a><br> +Poincaré, <a href="#Page_108">108</a><br> +Point, <a href="#Page_1">1</a><br> +Point-mass, energy of, <a href="#Page_45">45</a><br> +Position, <a href="#Page_9">9</a><br> +Principle of relativity, <a href="#Page_13">13</a>-<a href="#Page_15">15</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_19">19</a>, <a href="#Page_20">20</a>, <a href="#Page_60">60</a></span><br> +Processes of Nature, <a href="#Page_42">42</a><br> +Propagation of light, <a href="#Page_17">17</a>, <a href="#Page_19">19</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_2">2</a>, <a href="#Page_32">32</a>, <a href="#Page_91">91</a>, <a href="#Page_119">119</a></span><br> +——in liquid, <a href="#Page_40">40</a><br> +——in gravitational fields, <a href="#Page_75">75</a><br> +<br> +Quasi-Euclidean universe, <a href="#Page_114">114</a><br> +Quasi-spherical universe, <a href="#Page_114">114</a><br> +<br> +Radiation, <a href="#Page_46">46</a><br> +Radioactive substances, <a href="#Page_50">50</a><br> +<br> +Reference-body, <a href="#Page_5">5</a>, <a href="#Page_7">7</a>, <a href="#Page_9">9</a>-<a href="#Page_11">11</a>, <a href="#Page_18">18</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_23">23</a>, <a href="#Page_25">25</a>, <a href="#Page_26">26</a>, <a href="#Page_37">37</a>, <a href="#Page_60">60</a></span><br> +——rotating, <a href="#Page_79">79</a><br> +Reference-mollusk, <a href="#Page_99">99</a>-<a href="#Page_101">101</a><br> +Relative position, <a href="#Page_3">3</a><br> +—velocity, <a href="#Page_117">117</a><br> +Rest, <a href="#Page_14">14</a><br> +Riemann, <a href="#Page_86">86</a>, <a href="#Page_108">108</a>, <a href="#Page_111">111</a><br> +Rotation, <a href="#Page_81">81</a>, <a href="#Page_122">122</a><br> +<br> +Schwarzschild, <a href="#Page_131">131</a><br> +Seconds-clock, <a href="#Page_36">36</a><br> +Seeliger, <a href="#Page_105">105</a>, <a href="#Page_106">106</a><br> +Simultaneity, <a href="#Page_22">22</a>, <a href="#Page_24">24</a>-<a href="#Page_26">26</a>, <a href="#Page_81">81</a><br> +—relativity of, <a href="#Page_26">26</a><br> +Size-relations, <a href="#Page_90">90</a><br> +Solar eclipse, <a href="#Page_75">75</a>, <a href="#Page_127">127</a>, <a href="#Page_128">128</a><br> +Space, <a href="#Page_9">9</a>, <a href="#Page_52">52</a>, <a href="#Page_55">55</a>, <a href="#Page_105">105</a><br> +—conception of, <a href="#Page_19">19</a><br> +Space co-ordinates, <a href="#Page_55">55</a>, <a href="#Page_81">81</a>, <a href="#Page_99">99</a><br> +Space-interval, <a href="#Page_30">30</a>, <a href="#Page_56">56</a><br> +—point, <a href="#Page_99">99</a><br> +—two-dimensional, <a href="#Page_108">108</a><br> +—three-dimensional, <a href="#Page_122">122</a><br> +Special theory of relativity,<br> +<span style="margin-left: 1em;"><a href="#Page_1">1</a>-<a href="#Page_57">57</a>, <a href="#Page_20">20</a></span><br> +Spherical surface, <a href="#Page_109">109</a><br> +—space, <a href="#Page_111">111</a>, <a href="#Page_112">112</a><br> +St. John, <a href="#Page_131">131</a><br> +Stellar universe, <a href="#Page_106">106</a><br> +—photographs, <a href="#Page_128">128</a><br> +Straight line, <a href="#Page_1">1</a>-<a href="#Page_3">3</a>, <a href="#Page_9">9</a>, <a href="#Page_10">10</a>, <a href="#Page_82">82</a>, <a href="#Page_88">88</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_109">109</a></span><br> +System of co-ordinates, <a href="#Page_5">5</a>, <a href="#Page_10">10</a>, <a href="#Page_11">11</a><br> +<br> +Terrestrial space, <a href="#Page_15">15</a><br> +Theory, <a href="#Page_123">123</a><br> +—truth of, <a href="#Page_124">124</a><br> +Three-dimensional, <a href="#Page_55">55</a><br> +Time, conception of, <a href="#Page_19">19</a>, <a href="#Page_52">52</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_105">105</a></span><br> +—co-ordinate, <a href="#Page_55">55</a>, <a href="#Page_99">99</a><br> +—in Physics, <a href="#Page_21">21</a>, <a href="#Page_98">98</a>, <a href="#Page_122">122</a><br> +—of an event, <a href="#Page_24">24</a>, <a href="#Page_26">26</a><br> +Time-interval, <a href="#Page_30">30</a>, <a href="#Page_56">56</a><br> +Trajectory, <a href="#Page_10">10</a><br> +"Truth," <a href="#Page_2">2</a><br> +<br> +Uniform translation, <a href="#Page_12">12</a>, <a href="#Page_59">59</a><br> +Universe (World) structure of,<br> +<span style="margin-left: 1em;"><a href="#Page_108">108</a>, <a href="#Page_113">113</a></span><br> +—circumference of, <a href="#Page_111">111</a><br> +<span class="pagenum" id="Page_137">[Pg 137]</span> +Universe elliptical, <a href="#Page_112">112</a>, <a href="#Page_114">114</a><br> +—Euclidean, <a href="#Page_109">109</a>, <a href="#Page_111">111</a><br> +—space expanse (radius) of,<br> +<span style="margin-left: 1em;"><a href="#Page_114">114</a></span><br> +—spherical, <a href="#Page_111">111</a>, <a href="#Page_114">114</a><br> +<br> +Value of <img style="vertical-align: -0.025ex; width: 1.29ex; height: 1ex;" src="images/82.svg" alt=" " data-tex="\pi">, <a href="#Page_82">82</a>, <a href="#Page_110">110</a><br> +Velocity of light, <a href="#Page_10">10</a>, <a href="#Page_17">17</a>, <a href="#Page_18">18</a>, <a href="#Page_76">76</a>,<br> +<span style="margin-left: 1em;"><a href="#Page_118">118</a></span><br> +Venus, <a href="#Page_126">126</a><br> +<br> +Weight (heaviness), <a href="#Page_65">65</a><br> +World, <a href="#Page_55">55</a>, <a href="#Page_56">56</a>, <a href="#Page_109">109</a>, <a href="#Page_122">122</a><br> +World-point, <a href="#Page_122">122</a><br> +—radius, <a href="#Page_112">112</a><br> +—sphere, <a href="#Page_110">110</a>, <a href="#Page_111">111</a><br> +<br> +Zeeman, <a href="#Page_41">41</a><br> +<span class="pagenum" id="Page_138">[Pg 138]</span> +</p></div> + +<p class="center"> +PRINTED BY<br> +MORRISON AND GIBB LIMITED<br> +EDINBURGH +</p> + +<p><br><br></p> + +<div class='chapter'> +<div class="transnote"> +<p class="center"><b>TRANSCRIBER'S NOTES</b></p> + +<p> +This ebook was produced using scanned images and OCR text generously +provided by the University of Toronto through the Internet Archive. +</p> +<p> +Minor typographical corrections and presentational changes have been +made without comment. +</p></div></div> + +<p><br><br><br></p> + +<div style='display:block; margin-top:4em'>*** END OF THE PROJECT GUTENBERG EBOOK RELATIVITY: THE SPECIAL AND THE GENERAL THEORY ***</div> +<div style='text-align:left'> + +<div style='display:block; margin:1em 0'> +Updated editions will replace the previous one—the old editions will +be renamed. +</div> + +<div style='display:block; margin:1em 0'> +Creating the works from print editions not protected by U.S. copyright +law means that no one owns a United States copyright in these works, +so the Foundation (and you!) can copy and distribute it in the United +States without permission and without paying copyright +royalties. Special rules, set forth in the General Terms of Use part +of this license, apply to copying and distributing Project +Gutenberg™ electronic works to protect the PROJECT GUTENBERG™ +concept and trademark. Project Gutenberg is a registered trademark, +and may not be used if you charge for an eBook, except by following +the terms of the trademark license, including paying royalties for use +of the Project Gutenberg trademark. If you do not charge anything for +copies of this eBook, complying with the trademark license is very +easy. You may use this eBook for nearly any purpose such as creation +of derivative works, reports, performances and research. Project +Gutenberg eBooks may be modified and printed and given away—you may +do practically ANYTHING in the United States with eBooks not protected +by U.S. copyright law. Redistribution is subject to the trademark +license, especially commercial redistribution. +</div> + +<div style='margin-top:1em; font-size:1.1em; text-align:center'>START: FULL LICENSE</div> +<div style='text-align:center;font-size:0.9em'>THE FULL PROJECT GUTENBERG LICENSE</div> +<div style='text-align:center;font-size:0.9em'>PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK</div> + +<div style='display:block; margin:1em 0'> +To protect the Project Gutenberg™ mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase “Project +Gutenberg”), you agree to comply with all the terms of the Full +Project Gutenberg™ License available with this file or online at +www.gutenberg.org/license. +</div> + +<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'> +Section 1. General Terms of Use and Redistributing Project Gutenberg™ electronic works +</div> + +<div style='display:block; margin:1em 0'> +1.A. By reading or using any part of this Project Gutenberg™ +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or +destroy all copies of Project Gutenberg™ electronic works in your +possession. If you paid a fee for obtaining a copy of or access to a +Project Gutenberg™ electronic work and you do not agree to be bound +by the terms of this agreement, you may obtain a refund from the person +or entity to whom you paid the fee as set forth in paragraph 1.E.8. +</div> + +<div style='display:block; margin:1em 0'> +1.B. “Project Gutenberg” is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg™ electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg™ electronic works if you follow the terms of this +agreement and help preserve free future access to Project Gutenberg™ +electronic works. See paragraph 1.E below. +</div> + +<div style='display:block; margin:1em 0'> +1.C. The Project Gutenberg Literary Archive Foundation (“the +Foundation” or PGLAF), owns a compilation copyright in the collection +of Project Gutenberg™ electronic works. Nearly all the individual +works in the collection are in the public domain in the United +States. If an individual work is unprotected by copyright law in the +United States and you are located in the United States, we do not +claim a right to prevent you from copying, distributing, performing, +displaying or creating derivative works based on the work as long as +all references to Project Gutenberg are removed. Of course, we hope +that you will support the Project Gutenberg™ mission of promoting +free access to electronic works by freely sharing Project Gutenberg™ +works in compliance with the terms of this agreement for keeping the +Project Gutenberg™ name associated with the work. You can easily +comply with the terms of this agreement by keeping this work in the +same format with its attached full Project Gutenberg™ License when +you share it without charge with others. +</div> + +<div style='display:block; margin:1em 0'> +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are +in a constant state of change. If you are outside the United States, +check the laws of your country in addition to the terms of this +agreement before downloading, copying, displaying, performing, +distributing or creating derivative works based on this work or any +other Project Gutenberg™ work. The Foundation makes no +representations concerning the copyright status of any work in any +country other than the United States. +</div> + +<div style='display:block; margin:1em 0'> +1.E. Unless you have removed all references to Project Gutenberg: +</div> + +<div style='display:block; margin:1em 0'> +1.E.1. The following sentence, with active links to, or other +immediate access to, the full Project Gutenberg™ License must appear +prominently whenever any copy of a Project Gutenberg™ work (any work +on which the phrase “Project Gutenberg” appears, or with which the +phrase “Project Gutenberg” is associated) is accessed, displayed, +performed, viewed, copied or distributed: +</div> + +<blockquote> + <div style='display:block; margin:1em 0'> + This eBook is for the use of anyone anywhere in the United States and most + other parts of the world at no cost and with almost no restrictions + whatsoever. You may copy it, give it away or re-use it under the terms + of the Project Gutenberg License included with this eBook or online + at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you + are not located in the United States, you will have to check the laws + of the country where you are located before using this eBook. + </div> +</blockquote> + +<div style='display:block; margin:1em 0'> +1.E.2. If an individual Project Gutenberg™ electronic work is +derived from texts not protected by U.S. copyright law (does not +contain a notice indicating that it is posted with permission of the +copyright holder), the work can be copied and distributed to anyone in +the United States without paying any fees or charges. If you are +redistributing or providing access to a work with the phrase “Project +Gutenberg” associated with or appearing on the work, you must comply +either with the requirements of paragraphs 1.E.1 through 1.E.7 or +obtain permission for the use of the work and the Project Gutenberg™ +trademark as set forth in paragraphs 1.E.8 or 1.E.9. +</div> + +<div style='display:block; margin:1em 0'> +1.E.3. If an individual Project Gutenberg™ electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any +additional terms imposed by the copyright holder. Additional terms +will be linked to the Project Gutenberg™ License for all works +posted with the permission of the copyright holder found at the +beginning of this work. +</div> + +<div style='display:block; margin:1em 0'> +1.E.4. Do not unlink or detach or remove the full Project Gutenberg™ +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg™. +</div> + +<div style='display:block; margin:1em 0'> +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg™ License. +</div> + +<div style='display:block; margin:1em 0'> +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including +any word processing or hypertext form. However, if you provide access +to or distribute copies of a Project Gutenberg™ work in a format +other than “Plain Vanilla ASCII” or other format used in the official +version posted on the official Project Gutenberg™ website +(www.gutenberg.org), you must, at no additional cost, fee or expense +to the user, provide a copy, a means of exporting a copy, or a means +of obtaining a copy upon request, of the work in its original “Plain +Vanilla ASCII” or other form. Any alternate format must include the +full Project Gutenberg™ License as specified in paragraph 1.E.1. +</div> + +<div style='display:block; margin:1em 0'> +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg™ works +unless you comply with paragraph 1.E.8 or 1.E.9. +</div> + +<div style='display:block; margin:1em 0'> +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg™ electronic works +provided that: +</div> + +<div style='margin-left:0.7em;'> + <div style='text-indent:-0.7em'> + • You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg™ works calculated using the method + you already use to calculate your applicable taxes. The fee is owed + to the owner of the Project Gutenberg™ trademark, but he has + agreed to donate royalties under this paragraph to the Project + Gutenberg Literary Archive Foundation. Royalty payments must be paid + within 60 days following each date on which you prepare (or are + legally required to prepare) your periodic tax returns. Royalty + payments should be clearly marked as such and sent to the Project + Gutenberg Literary Archive Foundation at the address specified in + Section 4, “Information about donations to the Project Gutenberg + Literary Archive Foundation.” + </div> + + <div style='text-indent:-0.7em'> + • You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg™ + License. You must require such a user to return or destroy all + copies of the works possessed in a physical medium and discontinue + all use of and all access to other copies of Project Gutenberg™ + works. + </div> + + <div style='text-indent:-0.7em'> + • You provide, in accordance with paragraph 1.F.3, a full refund of + any money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days of + receipt of the work. + </div> + + <div style='text-indent:-0.7em'> + • You comply with all other terms of this agreement for free + distribution of Project Gutenberg™ works. + </div> +</div> + +<div style='display:block; margin:1em 0'> +1.E.9. If you wish to charge a fee or distribute a Project +Gutenberg™ electronic work or group of works on different terms than +are set forth in this agreement, you must obtain permission in writing +from the Project Gutenberg Literary Archive Foundation, the manager of +the Project Gutenberg™ trademark. Contact the Foundation as set +forth in Section 3 below. +</div> + +<div style='display:block; margin:1em 0'> +1.F. +</div> + +<div style='display:block; margin:1em 0'> +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +works not protected by U.S. copyright law in creating the Project +Gutenberg™ collection. Despite these efforts, Project Gutenberg™ +electronic works, and the medium on which they may be stored, may +contain “Defects,” such as, but not limited to, incomplete, inaccurate +or corrupt data, transcription errors, a copyright or other +intellectual property infringement, a defective or damaged disk or +other medium, a computer virus, or computer codes that damage or +cannot be read by your equipment. +</div> + +<div style='display:block; margin:1em 0'> +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right +of Replacement or Refund” described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg™ trademark, and any other party distributing a Project +Gutenberg™ electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. +</div> + +<div style='display:block; margin:1em 0'> +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium +with your written explanation. The person or entity that provided you +with the defective work may elect to provide a replacement copy in +lieu of a refund. If you received the work electronically, the person +or entity providing it to you may choose to give you a second +opportunity to receive the work electronically in lieu of a refund. If +the second copy is also defective, you may demand a refund in writing +without further opportunities to fix the problem. +</div> + +<div style='display:block; margin:1em 0'> +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO +OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT +LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE. +</div> + +<div style='display:block; margin:1em 0'> +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of +damages. If any disclaimer or limitation set forth in this agreement +violates the law of the state applicable to this agreement, the +agreement shall be interpreted to make the maximum disclaimer or +limitation permitted by the applicable state law. The invalidity or +unenforceability of any provision of this agreement shall not void the +remaining provisions. +</div> + +<div style='display:block; margin:1em 0'> +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg™ electronic works in +accordance with this agreement, and any volunteers associated with the +production, promotion and distribution of Project Gutenberg™ +electronic works, harmless from all liability, costs and expenses, +including legal fees, that arise directly or indirectly from any of +the following which you do or cause to occur: (a) distribution of this +or any Project Gutenberg™ work, (b) alteration, modification, or +additions or deletions to any Project Gutenberg™ work, and (c) any +Defect you cause. +</div> + +<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'> +Section 2. Information about the Mission of Project Gutenberg™ +</div> + +<div style='display:block; margin:1em 0'> +Project Gutenberg™ is synonymous with the free distribution of +electronic works in formats readable by the widest variety of +computers including obsolete, old, middle-aged and new computers. It +exists because of the efforts of hundreds of volunteers and donations +from people in all walks of life. +</div> + +<div style='display:block; margin:1em 0'> +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg™’s +goals and ensuring that the Project Gutenberg™ collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg™ and future +generations. To learn more about the Project Gutenberg Literary +Archive Foundation and how your efforts and donations can help, see +Sections 3 and 4 and the Foundation information page at www.gutenberg.org. +</div> + +<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'> +Section 3. Information about the Project Gutenberg Literary Archive Foundation +</div> + +<div style='display:block; margin:1em 0'> +The Project Gutenberg Literary Archive Foundation is a non-profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation’s EIN or federal tax identification +number is 64-6221541. Contributions to the Project Gutenberg Literary +Archive Foundation are tax deductible to the full extent permitted by +U.S. federal laws and your state’s laws. +</div> + +<div style='display:block; margin:1em 0'> +The Foundation’s business office is located at 809 North 1500 West, +Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up +to date contact information can be found at the Foundation’s website +and official page at www.gutenberg.org/contact +</div> + +<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'> +Section 4. Information about Donations to the Project Gutenberg Literary Archive Foundation +</div> + +<div style='display:block; margin:1em 0'> +Project Gutenberg™ depends upon and cannot survive without widespread +public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine-readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. +</div> + +<div style='display:block; margin:1em 0'> +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To SEND +DONATIONS or determine the status of compliance for any particular state +visit <a href="https://www.gutenberg.org/donate/">www.gutenberg.org/donate</a>. +</div> + +<div style='display:block; margin:1em 0'> +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. +</div> + +<div style='display:block; margin:1em 0'> +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. +</div> + +<div style='display:block; margin:1em 0'> +Please check the Project Gutenberg web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including checks, online payments and credit card donations. To +donate, please visit: www.gutenberg.org/donate +</div> + +<div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'> +Section 5. General Information About Project Gutenberg™ electronic works +</div> + +<div style='display:block; margin:1em 0'> +Professor Michael S. Hart was the originator of the Project +Gutenberg™ concept of a library of electronic works that could be +freely shared with anyone. For forty years, he produced and +distributed Project Gutenberg™ eBooks with only a loose network of +volunteer support. +</div> + +<div style='display:block; margin:1em 0'> +Project Gutenberg™ eBooks are often created from several printed +editions, all of which are confirmed as not protected by copyright in +the U.S. unless a copyright notice is included. Thus, we do not +necessarily keep eBooks in compliance with any particular paper +edition. +</div> + +<div style='display:block; margin:1em 0'> +Most people start at our website which has the main PG search +facility: <a href="https://www.gutenberg.org">www.gutenberg.org</a>. +</div> + +<div style='display:block; margin:1em 0'> +This website includes information about Project Gutenberg™, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. +</div> + +</div> +</body> + +</html> diff --git a/36114-h/images/1.svg b/36114-h/images/1.svg new file mode 100644 index 0000000..3af5cd6 --- /dev/null +++ b/36114-h/images/1.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="750px" height="716px" viewBox="0 -716 750 716" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-494-TEX-I-1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-494-TEX-I-1D434"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/10.svg b/36114-h/images/10.svg new file mode 100644 index 0000000..1940177 --- /dev/null +++ b/36114-h/images/10.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.375ex;" xmlns="http://www.w3.org/2000/svg" width="1214.6px" height="848.6px" viewBox="0 -683 1214.6 848.6" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-41-TEX-N-4B" d="M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H313Q235 637 233 620Q232 618 232 462L233 307L379 449Q425 494 479 546Q518 584 524 591T531 607V608Q531 630 503 636Q501 636 498 636T493 637H489V683H499Q517 680 630 680Q704 680 716 683H722V637H708Q633 633 589 597Q584 592 495 506T406 419T515 254T631 80Q644 60 662 54T715 46H736V0H728Q719 3 615 3Q493 3 472 0H461V46H469Q515 46 515 72Q515 78 512 84L336 351Q332 348 278 296L232 251V156Q232 62 235 58Q243 47 302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z"></path><path id="MJX-41-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><g ><use xlink:href="#MJX-41-TEX-N-4B"></use></g></g><g transform="translate(811,-150) scale(0.707)" ><g ><use xlink:href="#MJX-41-TEX-N-30"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/100.svg b/36114-h/images/100.svg new file mode 100644 index 0000000..41f9cc0 --- /dev/null +++ b/36114-h/images/100.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.339ex;" xmlns="http://www.w3.org/2000/svg" width="1008.6px" height="592px" viewBox="0 -442 1008.6 592" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-687-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-687-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-687-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-687-TEX-N-34"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/101.svg b/36114-h/images/101.svg new file mode 100644 index 0000000..62b64fd --- /dev/null +++ b/36114-h/images/101.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="19278.2px" height="1097px" viewBox="0 -892 19278.2 1097" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-441-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-441-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-441-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-441-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-441-TEX-I-1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path><path id="MJX-441-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-441-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-441-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-441-TEX-N-2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path><path id="MJX-441-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-441-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-441-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-441-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D460"></use></g><g transform="translate(502,413) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-32"></use></g></g></g><g transform="translate(1703.3,0)"><use xlink:href="#MJX-441-TEX-N-3D"></use></g><g transform="translate(2759.1,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-31"></use><use xlink:href="#MJX-441-TEX-N-31" transform="translate(500,0)"></use></g></g></g><g transform="translate(4026.2,0)"><g ></g></g><g transform="translate(4193.2,0)"><g ><g ><use xlink:href="#MJX-441-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-31"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-32"></use></g></g></g><g transform="translate(6380.5,0)"><use xlink:href="#MJX-441-TEX-N-2B"></use></g><g transform="translate(7380.8,0)"><use xlink:href="#MJX-441-TEX-N-32"></use></g><g transform="translate(7880.8,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-31"></use><use xlink:href="#MJX-441-TEX-N-32" transform="translate(500,0)"></use></g></g></g><g transform="translate(9147.9,0)"><g ></g></g><g transform="translate(9314.9,0)"><use xlink:href="#MJX-441-TEX-I-1D451"></use></g><g transform="translate(9834.9,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-31"></use></g></g></g><g transform="translate(10843.4,0)"><g ></g></g><g transform="translate(11010.4,0)"><use xlink:href="#MJX-441-TEX-I-1D451"></use></g><g transform="translate(11530.4,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-32"></use></g></g></g><g transform="translate(12539,0)"><g ></g></g><g transform="translate(12872.6,0)"><use xlink:href="#MJX-441-TEX-N-2026"></use></g><g transform="translate(14211.3,0)"><use xlink:href="#MJX-441-TEX-N-2E"></use></g><g transform="translate(14489.3,0)"><g ></g></g><g transform="translate(14823,0)"><use xlink:href="#MJX-441-TEX-N-2B"></use></g><g transform="translate(15601,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-34"></use><use xlink:href="#MJX-441-TEX-N-34" transform="translate(500,0)"></use></g></g></g><g transform="translate(16868.1,0)"><g ></g></g><g transform="translate(17035.1,0)"><g ><g ><use xlink:href="#MJX-441-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-441-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-34"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-441-TEX-N-32"></use></g></g></g><g transform="translate(19000.2,0)"><use xlink:href="#MJX-441-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/102.svg b/36114-h/images/102.svg new file mode 100644 index 0000000..ffe902d --- /dev/null +++ b/36114-h/images/102.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.375ex;" xmlns="http://www.w3.org/2000/svg" width="14564.9px" height="1057.5px" viewBox="0 -892 14564.9 1057.5" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-445-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-445-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-445-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-445-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-445-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-445-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-445-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-445-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-445-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-445-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-445-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-445-TEX-I-1D460"></use></g><g transform="translate(502,413) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-32"></use></g></g></g><g transform="translate(1703.3,0)"><use xlink:href="#MJX-445-TEX-N-3D"></use></g><g transform="translate(2759.1,0)"><g ><g ><use xlink:href="#MJX-445-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-445-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-31"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-32"></use></g></g></g><g transform="translate(4946.4,0)"><use xlink:href="#MJX-445-TEX-N-2B"></use></g><g transform="translate(5946.7,0)"><g ><g ><use xlink:href="#MJX-445-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-445-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-32"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-32"></use></g></g></g><g transform="translate(8134,0)"><use xlink:href="#MJX-445-TEX-N-2B"></use></g><g transform="translate(9134.2,0)"><g ><g ><use xlink:href="#MJX-445-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-445-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-33"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-32"></use></g></g></g><g transform="translate(11321.5,0)"><use xlink:href="#MJX-445-TEX-N-2B"></use></g><g transform="translate(12321.8,0)"><g ><g ><use xlink:href="#MJX-445-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-445-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-34"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-445-TEX-N-32"></use></g></g></g><g transform="translate(14286.9,0)"><use xlink:href="#MJX-445-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/103.svg b/36114-h/images/103.svg new file mode 100644 index 0000000..80cdee8 --- /dev/null +++ b/36114-h/images/103.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1425.6px" height="843.9px" viewBox="0 -833.9 1425.6 843.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-446-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-446-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-446-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-446-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-446-TEX-I-1D460"></use></g><g transform="translate(502,363) scale(0.707)" ><g ><use xlink:href="#MJX-446-TEX-N-32"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/104.svg b/36114-h/images/104.svg new file mode 100644 index 0000000..5410793 --- /dev/null +++ b/36114-h/images/104.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1092px" height="705px" viewBox="0 -694 1092 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-456-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-456-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-456-TEX-I-1D451"></use></g><g transform="translate(520,0)"><use xlink:href="#MJX-456-TEX-I-1D465"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/105.svg b/36114-h/images/105.svg new file mode 100644 index 0000000..f4d5894 --- /dev/null +++ b/36114-h/images/105.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="1010px" height="899px" viewBox="0 -694 1010 899" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-457-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-457-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-457-TEX-I-1D451"></use></g><g transform="translate(520,0)"><use xlink:href="#MJX-457-TEX-I-1D466"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/106.svg b/36114-h/images/106.svg new file mode 100644 index 0000000..48f989f --- /dev/null +++ b/36114-h/images/106.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="985px" height="705px" viewBox="0 -694 985 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-458-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-458-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-458-TEX-I-1D451"></use></g><g transform="translate(520,0)"><use xlink:href="#MJX-458-TEX-I-1D467"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/107.svg b/36114-h/images/107.svg new file mode 100644 index 0000000..18938c5 --- /dev/null +++ b/36114-h/images/107.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="881px" height="705px" viewBox="0 -694 881 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-459-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-459-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-459-TEX-I-1D451"></use></g><g transform="translate(520,0)"><use xlink:href="#MJX-459-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/108.svg b/36114-h/images/108.svg new file mode 100644 index 0000000..1139253 --- /dev/null +++ b/36114-h/images/108.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="23225.6px" height="1088.9px" viewBox="0 -883.9 23225.6 1088.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-460-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-460-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-460-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-460-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-460-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-460-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-460-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-460-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-460-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-460-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-460-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-460-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g><g transform="translate(1750.8,0)"><use xlink:href="#MJX-460-TEX-N-2B"></use></g><g transform="translate(2751,0)"><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(3271,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)" ><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g><g transform="translate(4419.8,0)"><use xlink:href="#MJX-460-TEX-N-2B"></use></g><g transform="translate(5420,0)"><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(5940,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)" ><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g><g transform="translate(7063.8,0)"><use xlink:href="#MJX-460-TEX-N-2212"></use></g><g transform="translate(8064,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g><g transform="translate(8933.5,0)"><g ></g></g><g transform="translate(9100.5,0)"><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(9620.5,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)" ><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g><g transform="translate(10695.9,0)"><use xlink:href="#MJX-460-TEX-N-3D"></use></g><g transform="translate(11751.7,0)"><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(12271.7,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-460-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g></g><g transform="translate(13696.9,0)"><use xlink:href="#MJX-460-TEX-N-2B"></use></g><g transform="translate(14697.1,0)"><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(15217.1,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)"><g ><use xlink:href="#MJX-460-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g></g><g transform="translate(16560.3,0)"><use xlink:href="#MJX-460-TEX-N-2B"></use></g><g transform="translate(17560.6,0)"><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(18080.6,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)"><g ><use xlink:href="#MJX-460-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g></g><g transform="translate(19398.8,0)"><use xlink:href="#MJX-460-TEX-N-2212"></use></g><g transform="translate(20399,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g><g transform="translate(21268.6,0)"><g ></g></g><g transform="translate(21435.6,0)"><use xlink:href="#MJX-460-TEX-I-1D451"></use></g><g transform="translate(21955.6,0)"><g ><use xlink:href="#MJX-460-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><g ><use xlink:href="#MJX-460-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-460-TEX-N-32"></use></g></g></g></g><g transform="translate(22947.6,0)"><use xlink:href="#MJX-460-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/109.svg b/36114-h/images/109.svg new file mode 100644 index 0000000..2c1b78d --- /dev/null +++ b/36114-h/images/109.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="13455.2px" height="1088.9px" viewBox="0 -883.9 13455.2 1088.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-461-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-461-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-461-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-461-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-461-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-461-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-461-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-461-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-461-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-461-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-461-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-461-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-461-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-461-TEX-I-1D460"></use></g><g transform="translate(502,413) scale(0.707)" ><g ><use xlink:href="#MJX-461-TEX-N-32"></use></g></g></g><g transform="translate(1703.3,0)"><use xlink:href="#MJX-461-TEX-N-3D"></use></g><g transform="translate(2759.1,0)"><use xlink:href="#MJX-461-TEX-I-1D451"></use></g><g transform="translate(3279.1,0)"><g ><use xlink:href="#MJX-461-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-461-TEX-N-32"></use></g></g></g><g transform="translate(4509.9,0)"><use xlink:href="#MJX-461-TEX-N-2B"></use></g><g transform="translate(5510.1,0)"><use xlink:href="#MJX-461-TEX-I-1D451"></use></g><g transform="translate(6030.1,0)"><g ><use xlink:href="#MJX-461-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)" ><g ><use xlink:href="#MJX-461-TEX-N-32"></use></g></g></g><g transform="translate(7178.9,0)"><use xlink:href="#MJX-461-TEX-N-2B"></use></g><g transform="translate(8179.1,0)"><use xlink:href="#MJX-461-TEX-I-1D451"></use></g><g transform="translate(8699.1,0)"><g ><use xlink:href="#MJX-461-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)" ><g ><use xlink:href="#MJX-461-TEX-N-32"></use></g></g></g><g transform="translate(9822.9,0)"><use xlink:href="#MJX-461-TEX-N-2212"></use></g><g transform="translate(10823.1,0)"><g ><use xlink:href="#MJX-461-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-461-TEX-N-32"></use></g></g></g><g transform="translate(11692.7,0)"><g ></g></g><g transform="translate(11859.7,0)"><use xlink:href="#MJX-461-TEX-I-1D451"></use></g><g transform="translate(12379.7,0)"><g ><use xlink:href="#MJX-461-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)" ><g ><use xlink:href="#MJX-461-TEX-N-32"></use></g></g></g><g transform="translate(13177.2,0)"><use xlink:href="#MJX-461-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/11.svg b/36114-h/images/11.svg new file mode 100644 index 0000000..3ceaa63 --- /dev/null +++ b/36114-h/images/11.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="485px" height="454px" viewBox="0 -443 485 454" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-723-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-723-TEX-I-1D463"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/110.svg b/36114-h/images/110.svg new file mode 100644 index 0000000..f1d0589 --- /dev/null +++ b/36114-h/images/110.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.318ex;" xmlns="http://www.w3.org/2000/svg" width="3092px" height="1060px" viewBox="0 -919.5 3092 1060" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-472-TEX-N-221A" d="M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z"></path><path id="MJX-472-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-472-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-472-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-472-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(853,0)"><g ><use xlink:href="#MJX-472-TEX-N-2212"></use></g><g transform="translate(778,0)"><use xlink:href="#MJX-472-TEX-N-31"></use></g></g><g transform="translate(0,59.5)"><use xlink:href="#MJX-472-TEX-N-221A"></use></g><rect width="1278" height="60" x="853" y="799.5"></rect></g><g transform="translate(2131,0)"><g ></g></g><g transform="translate(2298,0)"><use xlink:href="#MJX-472-TEX-I-1D450"></use></g><g transform="translate(2731,0)"><use xlink:href="#MJX-472-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/111.svg b/36114-h/images/111.svg new file mode 100644 index 0000000..7efa5af --- /dev/null +++ b/36114-h/images/111.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.375ex;" xmlns="http://www.w3.org/2000/svg" width="14286.9px" height="1057.5px" viewBox="0 -892 14286.9 1057.5" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-470-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-470-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-470-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-470-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-470-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-470-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-470-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-470-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-470-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-470-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-470-TEX-I-1D460"></use></g><g transform="translate(502,413) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-32"></use></g></g></g><g transform="translate(1703.3,0)"><use xlink:href="#MJX-470-TEX-N-3D"></use></g><g transform="translate(2759.1,0)"><g ><g ><use xlink:href="#MJX-470-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-470-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-31"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-32"></use></g></g></g><g transform="translate(4946.4,0)"><use xlink:href="#MJX-470-TEX-N-2B"></use></g><g transform="translate(5946.7,0)"><g ><g ><use xlink:href="#MJX-470-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-470-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-32"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-32"></use></g></g></g><g transform="translate(8134,0)"><use xlink:href="#MJX-470-TEX-N-2B"></use></g><g transform="translate(9134.2,0)"><g ><g ><use xlink:href="#MJX-470-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-470-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-33"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-32"></use></g></g></g><g transform="translate(11321.5,0)"><use xlink:href="#MJX-470-TEX-N-2B"></use></g><g transform="translate(12321.8,0)"><g ><g ><use xlink:href="#MJX-470-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-470-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-34"></use></g></g></g></g><g transform="translate(1561.6,421.1) scale(0.707)" ><g ><use xlink:href="#MJX-470-TEX-N-32"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/112.svg b/36114-h/images/112.svg new file mode 100644 index 0000000..7c0188e --- /dev/null +++ b/36114-h/images/112.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="785px" height="727px" viewBox="0 -705 785 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-523-TEX-N-47" d="M56 342Q56 428 89 500T174 615T283 681T391 705Q394 705 400 705T408 704Q499 704 569 636L582 624L612 663Q639 700 643 704Q644 704 647 704T653 705H657Q660 705 666 699V419L660 413H626Q620 419 619 430Q610 512 571 572T476 651Q457 658 426 658Q401 658 376 654T316 633T254 592T205 519T177 411Q173 369 173 335Q173 259 192 201T238 111T302 58T370 31T431 24Q478 24 513 45T559 100Q562 110 562 160V212Q561 213 557 216T551 220T542 223T526 225T502 226T463 227H437V273H449L609 270Q715 270 727 273H735V227H721Q674 227 668 215Q666 211 666 108V6Q660 0 657 0Q653 0 639 10Q617 25 600 42L587 54Q571 27 524 3T406 -22Q317 -22 238 22T108 151T56 342Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-523-TEX-N-47"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/113.svg b/36114-h/images/113.svg new file mode 100644 index 0000000..8f1e1d1 --- /dev/null +++ b/36114-h/images/113.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.489ex;" xmlns="http://www.w3.org/2000/svg" width="953.6px" height="658px" viewBox="0 -442 953.6 658" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-526-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path><path id="MJX-526-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-526-TEX-I-1D70C"></use></g><g transform="translate(550,-150) scale(0.707)" ><g ><use xlink:href="#MJX-526-TEX-N-30"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/114.svg b/36114-h/images/114.svg new file mode 100644 index 0000000..345bd95 --- /dev/null +++ b/36114-h/images/114.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="769px" height="705px" viewBox="0 -683 769 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-527-TEX-I-1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-527-TEX-I-1D449"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/115.svg b/36114-h/images/115.svg new file mode 100644 index 0000000..885678d --- /dev/null +++ b/36114-h/images/115.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.489ex;" xmlns="http://www.w3.org/2000/svg" width="1722.6px" height="899px" viewBox="0 -683 1722.6 899" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-530-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path><path id="MJX-530-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-530-TEX-I-1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-530-TEX-I-1D70C"></use></g><g transform="translate(550,-150) scale(0.707)" ><g ><use xlink:href="#MJX-530-TEX-N-30"></use></g></g></g><g transform="translate(953.6,0)"><use xlink:href="#MJX-530-TEX-I-1D449"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/116.svg b/36114-h/images/116.svg new file mode 100644 index 0000000..ae6895a --- /dev/null +++ b/36114-h/images/116.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="749px" height="680px" viewBox="0 -680 749 680" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-549-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-549-TEX-I-1D439"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/117.svg b/36114-h/images/117.svg new file mode 100644 index 0000000..48560e2 --- /dev/null +++ b/36114-h/images/117.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.552ex;" xmlns="http://www.w3.org/2000/svg" width="2162.6px" height="2045px" viewBox="0 -1359 2162.6 2045" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-531-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path><path id="MJX-531-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-531-TEX-I-1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path><path id="MJX-531-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-531-TEX-I-1D70C"></use></g><g transform="translate(550,-150) scale(0.707)" ><g ><use xlink:href="#MJX-531-TEX-N-30"></use></g></g></g><g transform="translate(953.6,0)"><g ><g transform="translate(220,676)"><use xlink:href="#MJX-531-TEX-I-1D449"></use></g><g transform="translate(230,-686)"><use xlink:href="#MJX-531-TEX-I-1D439"></use></g><rect width="969" height="60" x="120" y="220"></rect></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/118.svg b/36114-h/images/118.svg new file mode 100644 index 0000000..2648c6c --- /dev/null +++ b/36114-h/images/118.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.489ex;" xmlns="http://www.w3.org/2000/svg" width="1712.6px" height="899px" viewBox="0 -683 1712.6 899" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-532-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path><path id="MJX-532-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-532-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-532-TEX-I-1D70C"></use></g><g transform="translate(550,-150) scale(0.707)" ><g ><use xlink:href="#MJX-532-TEX-N-30"></use></g></g></g><g transform="translate(953.6,0)"><use xlink:href="#MJX-532-TEX-I-1D445"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/119.svg b/36114-h/images/119.svg new file mode 100644 index 0000000..f89317f --- /dev/null +++ b/36114-h/images/119.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.048ex;" xmlns="http://www.w3.org/2000/svg" width="759px" height="704px" viewBox="0 -683 759 704" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-551-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-551-TEX-I-1D445"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/12.svg b/36114-h/images/12.svg new file mode 100644 index 0000000..52e1e50 --- /dev/null +++ b/36114-h/images/12.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="716px" height="454px" viewBox="0 -443 716 454" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-236-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-236-TEX-I-1D464"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/120.svg b/36114-h/images/120.svg new file mode 100644 index 0000000..8cb8509 --- /dev/null +++ b/36114-h/images/120.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -4.11ex;" xmlns="http://www.w3.org/2000/svg" width="6409.2px" height="4133px" viewBox="0 -2316.5 6409.2 4133" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-535-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path id="MJX-535-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-535-TEX-N-73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path id="MJX-535-TEX-N-69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path id="MJX-535-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-535-TEX-N-2061" d=""></path><path id="MJX-535-TEX-LO-28" d="M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z"></path><path id="MJX-535-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-535-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path><path id="MJX-535-TEX-LO-29" d="M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z"></path><path id="MJX-535-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-535-TEX-I-1D70B"></use></g><g transform="translate(847.8,0)"><use xlink:href="#MJX-535-TEX-N-3D"></use></g><g transform="translate(1903.6,0)"><g transform="translate(220,1167)"><g ><use xlink:href="#MJX-535-TEX-N-73"></use><use xlink:href="#MJX-535-TEX-N-69" transform="translate(394,0)"></use><use xlink:href="#MJX-535-TEX-N-6E" transform="translate(672,0)"></use></g><g transform="translate(1228,0)"><use xlink:href="#MJX-535-TEX-N-2061"></use></g><g transform="translate(1394.7,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-535-TEX-LO-28"></use></g><g transform="translate(597,0)"><g ><g transform="translate(374,676)"><use xlink:href="#MJX-535-TEX-I-1D45F"></use></g><g transform="translate(220,-686)"><use xlink:href="#MJX-535-TEX-I-1D445"></use></g><rect width="959" height="60" x="120" y="220"></rect></g></g><g transform="translate(1796,0) translate(0 -0.5)"><use xlink:href="#MJX-535-TEX-LO-29"></use></g></g></g><g transform="translate(917.3,-1109.5)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-535-TEX-LO-28"></use></g><g transform="translate(597,0)"><g ><g transform="translate(374,676)"><use xlink:href="#MJX-535-TEX-I-1D45F"></use></g><g transform="translate(220,-686)"><use xlink:href="#MJX-535-TEX-I-1D445"></use></g><rect width="959" height="60" x="120" y="220"></rect></g></g><g transform="translate(1796,0) translate(0 -0.5)"><use xlink:href="#MJX-535-TEX-LO-29"></use></g></g><rect width="3987.7" height="60" x="120" y="220"></rect></g><g transform="translate(6131.2,0)"><use xlink:href="#MJX-535-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/121.svg b/36114-h/images/121.svg new file mode 100644 index 0000000..0d919ad --- /dev/null +++ b/36114-h/images/121.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="451px" height="453px" viewBox="0 -442 451 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-736-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-736-TEX-I-1D45F"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/122.svg b/36114-h/images/122.svg new file mode 100644 index 0000000..d407d00 --- /dev/null +++ b/36114-h/images/122.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.048ex;" xmlns="http://www.w3.org/2000/svg" width="2702.1px" height="854.9px" viewBox="0 -833.9 2702.1 854.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-542-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-542-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path id="MJX-542-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path><path id="MJX-542-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-542-TEX-N-32"></use></g><g transform="translate(500,0)"><g ><use xlink:href="#MJX-542-TEX-I-1D70B"></use></g><g transform="translate(603,363) scale(0.707)" ><g ><use xlink:href="#MJX-542-TEX-N-32"></use></g></g></g><g transform="translate(1506.6,0)"><g ><use xlink:href="#MJX-542-TEX-I-1D445"></use></g><g transform="translate(792,363) scale(0.707)" ><g ><use xlink:href="#MJX-542-TEX-N-33"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/123.svg b/36114-h/images/123.svg new file mode 100644 index 0000000..1f5dcde --- /dev/null +++ b/36114-h/images/123.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="4040.1px" height="915.9px" viewBox="0 -833.9 4040.1 915.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-545-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path><path id="MJX-545-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-545-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-545-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path id="MJX-545-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-545-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-545-TEX-I-1D439"></use></g><g transform="translate(1026.8,0)"><use xlink:href="#MJX-545-TEX-N-3D"></use></g><g transform="translate(2082.6,0)"><use xlink:href="#MJX-545-TEX-N-34"></use></g><g transform="translate(2582.6,0)"><use xlink:href="#MJX-545-TEX-I-1D70B"></use></g><g transform="translate(3152.6,0)"><g ><use xlink:href="#MJX-545-TEX-I-1D45F"></use></g><g transform="translate(484,363) scale(0.707)" ><g ><use xlink:href="#MJX-545-TEX-N-32"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/124.svg b/36114-h/images/124.svg new file mode 100644 index 0000000..8595bce --- /dev/null +++ b/36114-h/images/124.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1957.6px" height="844.9px" viewBox="0 -833.9 1957.6 844.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-547-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-547-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path id="MJX-547-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-547-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-547-TEX-N-34"></use></g><g transform="translate(500,0)"><use xlink:href="#MJX-547-TEX-I-1D70B"></use></g><g transform="translate(1070,0)"><g ><use xlink:href="#MJX-547-TEX-I-1D45F"></use></g><g transform="translate(484,363) scale(0.707)" ><g ><use xlink:href="#MJX-547-TEX-N-32"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/125.svg b/36114-h/images/125.svg new file mode 100644 index 0000000..02f9907 --- /dev/null +++ b/36114-h/images/125.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.041ex;" xmlns="http://www.w3.org/2000/svg" width="4340.1px" height="2244px" viewBox="0 -1342 4340.1 2244" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-552-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path><path id="MJX-552-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-552-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-552-TEX-I-1D705" d="M83 -11Q70 -11 62 -4T51 8T49 17Q49 30 96 217T147 414Q160 442 193 442Q205 441 213 435T223 422T225 412Q225 401 208 337L192 270Q193 269 208 277T235 292Q252 304 306 349T396 412T467 431Q489 431 500 420T512 391Q512 366 494 347T449 327Q430 327 418 338T405 368Q405 370 407 380L397 375Q368 360 315 315L253 266L240 257H245Q262 257 300 251T366 230Q422 203 422 150Q422 140 417 114T411 67Q411 26 437 26Q484 26 513 137Q516 149 519 151T535 153Q554 153 554 144Q554 121 527 64T457 -7Q447 -10 431 -10Q386 -10 360 17T333 90Q333 108 336 122T339 146Q339 170 320 186T271 209T222 218T185 221H180L155 122Q129 22 126 16Q113 -11 83 -11Z"></path><path id="MJX-552-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path><path id="MJX-552-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-552-TEX-I-1D445"></use></g><g transform="translate(792,413) scale(0.707)" ><g ><use xlink:href="#MJX-552-TEX-N-32"></use></g></g></g><g transform="translate(1473.3,0)"><use xlink:href="#MJX-552-TEX-N-3D"></use></g><g transform="translate(2529.1,0)"><g transform="translate(516.5,676)"><use xlink:href="#MJX-552-TEX-N-32"></use></g><g transform="translate(220,-686)"><g ><use xlink:href="#MJX-552-TEX-I-1D705"></use></g><g transform="translate(576,0)"><use xlink:href="#MJX-552-TEX-I-1D70C"></use></g></g><rect width="1293" height="60" x="120" y="220"></rect></g><g transform="translate(4062.1,0)"><use xlink:href="#MJX-552-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/126.svg b/36114-h/images/126.svg new file mode 100644 index 0000000..0af64c3 --- /dev/null +++ b/36114-h/images/126.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.577ex;" xmlns="http://www.w3.org/2000/svg" width="6695.7px" height="2039px" viewBox="0 -1342 6695.7 2039" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-553-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-553-TEX-I-1D705" d="M83 -11Q70 -11 62 -4T51 8T49 17Q49 30 96 217T147 414Q160 442 193 442Q205 441 213 435T223 422T225 412Q225 401 208 337L192 270Q193 269 208 277T235 292Q252 304 306 349T396 412T467 431Q489 431 500 420T512 391Q512 366 494 347T449 327Q430 327 418 338T405 368Q405 370 407 380L397 375Q368 360 315 315L253 266L240 257H245Q262 257 300 251T366 230Q422 203 422 150Q422 140 417 114T411 67Q411 26 437 26Q484 26 513 137Q516 149 519 151T535 153Q554 153 554 144Q554 121 527 64T457 -7Q447 -10 431 -10Q386 -10 360 17T333 90Q333 108 336 122T339 146Q339 170 320 186T271 209T222 218T185 221H180L155 122Q129 22 126 16Q113 -11 83 -11Z"></path><path id="MJX-553-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-553-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-553-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-553-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-553-TEX-N-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"></path><path id="MJX-553-TEX-I-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path><path id="MJX-553-TEX-N-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><g transform="translate(258,676)"><use xlink:href="#MJX-553-TEX-N-32"></use></g><g transform="translate(220,-686)"><use xlink:href="#MJX-553-TEX-I-1D705"></use></g><rect width="776" height="60" x="120" y="220"></rect></g></g><g transform="translate(1293.8,0)"><use xlink:href="#MJX-553-TEX-N-3D"></use></g><g transform="translate(2349.6,0)"><use xlink:href="#MJX-553-TEX-N-31"></use><use xlink:href="#MJX-553-TEX-N-2E" transform="translate(500,0)"></use><use xlink:href="#MJX-553-TEX-N-30" transform="translate(778,0)"></use><use xlink:href="#MJX-553-TEX-N-38" transform="translate(1278,0)"></use></g><g transform="translate(4127.6,0)"><use xlink:href="#MJX-553-TEX-I-D7"></use></g><g transform="translate(4905.6,0)"><g ><use xlink:href="#MJX-553-TEX-N-31"></use><use xlink:href="#MJX-553-TEX-N-30" transform="translate(500,0)"></use></g><g transform="translate(1033,393.1) scale(0.707)" ><g ><use xlink:href="#MJX-553-TEX-N-32"></use><use xlink:href="#MJX-553-TEX-N-37" transform="translate(500,0)"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/127.svg b/36114-h/images/127.svg new file mode 100644 index 0000000..0f52c15 --- /dev/null +++ b/36114-h/images/127.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.489ex;" xmlns="http://www.w3.org/2000/svg" width="517px" height="658px" viewBox="0 -442 517 658" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-554-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-554-TEX-I-1D70C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/128.svg b/36114-h/images/128.svg new file mode 100644 index 0000000..6039326 --- /dev/null +++ b/36114-h/images/128.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2699.6px" height="708px" viewBox="0 -626 2699.6 708" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-568-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-568-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-568-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-568-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-568-TEX-I-1D465"></use></g><g transform="translate(849.8,0)"><use xlink:href="#MJX-568-TEX-N-3D"></use></g><g transform="translate(1905.6,0)"><use xlink:href="#MJX-568-TEX-I-1D450"></use></g><g transform="translate(2338.6,0)"><use xlink:href="#MJX-568-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/129.svg b/36114-h/images/129.svg new file mode 100644 index 0000000..8fee27a --- /dev/null +++ b/36114-h/images/129.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="8256px" height="1000px" viewBox="0 -750 8256 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-569-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-569-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-569-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-569-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-569-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-569-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-569-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-569-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-569-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-569-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-569-TEX-I-1D465"></use></g><g transform="translate(794.2,0)"><use xlink:href="#MJX-569-TEX-N-2212"></use></g><g transform="translate(1794.4,0)"><use xlink:href="#MJX-569-TEX-I-1D450"></use></g><g transform="translate(2227.4,0)"><use xlink:href="#MJX-569-TEX-I-1D461"></use></g><g transform="translate(2866.2,0)"><use xlink:href="#MJX-569-TEX-N-3D"></use></g><g transform="translate(3922,0)"><use xlink:href="#MJX-569-TEX-N-30"></use><use xlink:href="#MJX-569-TEX-N-2E" transform="translate(500,0)"></use></g><g transform="translate(4700,0)"><g ></g></g><g transform="translate(6700,0)"><use xlink:href="#MJX-569-TEX-N-28"></use><use xlink:href="#MJX-569-TEX-N-31" transform="translate(389,0)"></use><use xlink:href="#MJX-569-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(7978,0)"><use xlink:href="#MJX-569-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/13.svg b/36114-h/images/13.svg new file mode 100644 index 0000000..815b7c1 --- /dev/null +++ b/36114-h/images/13.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1028px" height="705px" viewBox="0 -683 1028 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-44-TEX-N-57" d="M792 683Q810 680 914 680Q991 680 1003 683H1009V637H996Q931 633 915 598Q912 591 863 438T766 135T716 -17Q711 -22 694 -22Q676 -22 673 -15Q671 -13 593 231L514 477L435 234Q416 174 391 92T358 -6T341 -22H331Q314 -21 310 -15Q309 -14 208 302T104 622Q98 632 87 633Q73 637 35 637H18V683H27Q69 681 154 681Q164 681 181 681T216 681T249 682T276 683H287H298V637H285Q213 637 213 620Q213 616 289 381L364 144L427 339Q490 535 492 546Q487 560 482 578T475 602T468 618T461 628T449 633T433 636T408 637H380V683H388Q397 680 508 680Q629 680 650 683H660V637H647Q576 637 576 619L727 146Q869 580 869 600Q869 605 863 612T839 627T794 637H783V683H792Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-44-TEX-N-57"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/130.svg b/36114-h/images/130.svg new file mode 100644 index 0000000..4363325 --- /dev/null +++ b/36114-h/images/130.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="8810.9px" height="1059px" viewBox="0 -809 8810.9 1059" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-573-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-573-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-573-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-573-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-573-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-573-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-573-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-573-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-573-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-573-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-573-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-573-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-573-TEX-V-2032"></use></g></g><g transform="translate(1071.7,0)"><use xlink:href="#MJX-573-TEX-N-2212"></use></g><g transform="translate(2071.9,0)"><use xlink:href="#MJX-573-TEX-I-1D450"></use></g><g transform="translate(2504.9,0)"><g ><use xlink:href="#MJX-573-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-573-TEX-V-2032"></use></g></g><g transform="translate(3421.1,0)"><use xlink:href="#MJX-573-TEX-N-3D"></use></g><g transform="translate(4476.9,0)"><use xlink:href="#MJX-573-TEX-N-30"></use><use xlink:href="#MJX-573-TEX-N-2E" transform="translate(500,0)"></use></g><g transform="translate(5254.9,0)"><g ></g></g><g transform="translate(7254.9,0)"><use xlink:href="#MJX-573-TEX-N-28"></use><use xlink:href="#MJX-573-TEX-N-32" transform="translate(389,0)"></use><use xlink:href="#MJX-573-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(8532.9,0)"><use xlink:href="#MJX-573-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/131.svg b/36114-h/images/131.svg new file mode 100644 index 0000000..8bee2db --- /dev/null +++ b/36114-h/images/131.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="12760.4px" height="1059px" viewBox="0 -809 12760.4 1059" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-574-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-574-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-574-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-574-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-574-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-574-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-574-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-574-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-574-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path><path id="MJX-574-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-574-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-574-TEX-N-28"></use></g><g transform="translate(389,0)"><g ><use xlink:href="#MJX-574-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-574-TEX-V-2032"></use></g></g><g transform="translate(1460.7,0)"><use xlink:href="#MJX-574-TEX-N-2212"></use></g><g transform="translate(2460.9,0)"><use xlink:href="#MJX-574-TEX-I-1D450"></use></g><g transform="translate(2893.9,0)"><g ><use xlink:href="#MJX-574-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-574-TEX-V-2032"></use></g></g><g transform="translate(3532.4,0)"><use xlink:href="#MJX-574-TEX-N-29"></use></g><g transform="translate(4199.1,0)"><use xlink:href="#MJX-574-TEX-N-3D"></use></g><g transform="translate(5254.9,0)"><use xlink:href="#MJX-574-TEX-I-1D706"></use></g><g transform="translate(5837.9,0)"><use xlink:href="#MJX-574-TEX-N-28"></use></g><g transform="translate(6226.9,0)"><use xlink:href="#MJX-574-TEX-I-1D465"></use></g><g transform="translate(7021.1,0)"><use xlink:href="#MJX-574-TEX-N-2212"></use></g><g transform="translate(8021.4,0)"><use xlink:href="#MJX-574-TEX-I-1D450"></use></g><g transform="translate(8454.4,0)"><use xlink:href="#MJX-574-TEX-I-1D461"></use></g><g transform="translate(8815.4,0)"><use xlink:href="#MJX-574-TEX-N-29"></use></g><g transform="translate(9204.4,0)"><g ></g></g><g transform="translate(11204.4,0)"><use xlink:href="#MJX-574-TEX-N-28"></use><use xlink:href="#MJX-574-TEX-N-33" transform="translate(389,0)"></use><use xlink:href="#MJX-574-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(12482.4,0)"><use xlink:href="#MJX-574-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/132.svg b/36114-h/images/132.svg new file mode 100644 index 0000000..b0b688a --- /dev/null +++ b/36114-h/images/132.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.027ex;" xmlns="http://www.w3.org/2000/svg" width="583px" height="706px" viewBox="0 -694 583 706" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-582-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-582-TEX-I-1D706"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/133.svg b/36114-h/images/133.svg new file mode 100644 index 0000000..a6f58c9 --- /dev/null +++ b/36114-h/images/133.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="3366.4px" height="1000px" viewBox="0 -750 3366.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-576-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-576-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-576-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-576-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-576-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-576-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-576-TEX-N-28"></use></g><g transform="translate(389,0)"><use xlink:href="#MJX-576-TEX-I-1D465"></use></g><g transform="translate(1183.2,0)"><use xlink:href="#MJX-576-TEX-N-2212"></use></g><g transform="translate(2183.4,0)"><use xlink:href="#MJX-576-TEX-I-1D450"></use></g><g transform="translate(2616.4,0)"><use xlink:href="#MJX-576-TEX-I-1D461"></use></g><g transform="translate(2977.4,0)"><use xlink:href="#MJX-576-TEX-N-29"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/134.svg b/36114-h/images/134.svg new file mode 100644 index 0000000..b4d60e3 --- /dev/null +++ b/36114-h/images/134.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="3921.4px" height="1009px" viewBox="0 -759 3921.4 1009" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-577-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-577-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-577-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-577-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-577-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-577-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-577-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-577-TEX-N-28"></use></g><g transform="translate(389,0)"><g ><use xlink:href="#MJX-577-TEX-I-1D465"></use></g><g transform="translate(605,363) scale(0.707)"><use xlink:href="#MJX-577-TEX-V-2032"></use></g></g><g transform="translate(1460.7,0)"><use xlink:href="#MJX-577-TEX-N-2212"></use></g><g transform="translate(2460.9,0)"><use xlink:href="#MJX-577-TEX-I-1D450"></use></g><g transform="translate(2893.9,0)"><g ><use xlink:href="#MJX-577-TEX-I-1D461"></use></g><g transform="translate(394,363) scale(0.707)"><use xlink:href="#MJX-577-TEX-V-2032"></use></g></g><g transform="translate(3532.4,0)"><use xlink:href="#MJX-577-TEX-N-29"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/135.svg b/36114-h/images/135.svg new file mode 100644 index 0000000..61d04db --- /dev/null +++ b/36114-h/images/135.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="12780.4px" height="1059px" viewBox="0 -809 12780.4 1059" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-579-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-579-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-579-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-579-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-579-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-579-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-579-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-579-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-579-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-579-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-579-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-579-TEX-N-28"></use></g><g transform="translate(389,0)"><g ><use xlink:href="#MJX-579-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-579-TEX-V-2032"></use></g></g><g transform="translate(1460.7,0)"><use xlink:href="#MJX-579-TEX-N-2B"></use></g><g transform="translate(2460.9,0)"><use xlink:href="#MJX-579-TEX-I-1D450"></use></g><g transform="translate(2893.9,0)"><g ><use xlink:href="#MJX-579-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-579-TEX-V-2032"></use></g></g><g transform="translate(3532.4,0)"><use xlink:href="#MJX-579-TEX-N-29"></use></g><g transform="translate(4199.1,0)"><use xlink:href="#MJX-579-TEX-N-3D"></use></g><g transform="translate(5254.9,0)"><use xlink:href="#MJX-579-TEX-I-1D707"></use></g><g transform="translate(5857.9,0)"><use xlink:href="#MJX-579-TEX-N-28"></use></g><g transform="translate(6246.9,0)"><use xlink:href="#MJX-579-TEX-I-1D465"></use></g><g transform="translate(7041.1,0)"><use xlink:href="#MJX-579-TEX-N-2B"></use></g><g transform="translate(8041.4,0)"><use xlink:href="#MJX-579-TEX-I-1D450"></use></g><g transform="translate(8474.4,0)"><use xlink:href="#MJX-579-TEX-I-1D461"></use></g><g transform="translate(8835.4,0)"><use xlink:href="#MJX-579-TEX-N-29"></use></g><g transform="translate(9224.4,0)"><g ></g></g><g transform="translate(11224.4,0)"><use xlink:href="#MJX-579-TEX-N-28"></use><use xlink:href="#MJX-579-TEX-N-34" transform="translate(389,0)"></use><use xlink:href="#MJX-579-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(12502.4,0)"><use xlink:href="#MJX-579-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/136.svg b/36114-h/images/136.svg new file mode 100644 index 0000000..41e751c --- /dev/null +++ b/36114-h/images/136.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.023ex;" xmlns="http://www.w3.org/2000/svg" width="529px" height="451px" viewBox="0 -441 529 451" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-700-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-700-TEX-I-1D44E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/137.svg b/36114-h/images/137.svg new file mode 100644 index 0000000..de56e5c --- /dev/null +++ b/36114-h/images/137.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="429px" height="705px" viewBox="0 -694 429 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-630-TEX-I-1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-630-TEX-I-1D44F"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/138.svg b/36114-h/images/138.svg new file mode 100644 index 0000000..92a75d3 --- /dev/null +++ b/36114-h/images/138.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.489ex;" xmlns="http://www.w3.org/2000/svg" width="603px" height="658px" viewBox="0 -442 603 658" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-583-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-583-TEX-I-1D707"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/139.svg b/36114-h/images/139.svg new file mode 100644 index 0000000..a20e629 --- /dev/null +++ b/36114-h/images/139.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -4.425ex;" xmlns="http://www.w3.org/2000/svg" width="6835px" height="4412px" viewBox="0 -2456 6835 4412" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-584-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-584-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-584-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path><path id="MJX-584-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-584-TEX-I-1D707" d="M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z"></path><path id="MJX-584-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-584-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-584-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-584-TEX-N-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path><path id="MJX-584-TEX-I-1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path id="MJX-584-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-584-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,1086)"><g transform="translate(1846,0)"><g ><use xlink:href="#MJX-584-TEX-I-1D44E"></use></g></g><g transform="translate(2375,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-584-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-584-TEX-I-1D706"></use></g><g transform="translate(805.2,0)"><use xlink:href="#MJX-584-TEX-N-2B"></use></g><g transform="translate(1805.4,0)"><use xlink:href="#MJX-584-TEX-I-1D707"></use></g></g><g transform="translate(1174.2,-686)"><use xlink:href="#MJX-584-TEX-N-32"></use></g><rect width="2608.4" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,-1270)"><g ><g ><use xlink:href="#MJX-584-TEX-N-61"></use><use xlink:href="#MJX-584-TEX-N-6E" transform="translate(500,0)"></use><use xlink:href="#MJX-584-TEX-N-64" transform="translate(1056,0)"></use></g><g transform="translate(1612,0)"><g ></g></g><g transform="translate(1779,0)"><g ></g></g><g transform="translate(1946,0)"><use xlink:href="#MJX-584-TEX-I-1D44F"></use></g></g><g transform="translate(2375,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-584-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-584-TEX-I-1D706"></use></g><g transform="translate(805.2,0)"><use xlink:href="#MJX-584-TEX-N-2212"></use></g><g transform="translate(1805.4,0)"><use xlink:href="#MJX-584-TEX-I-1D707"></use></g></g><g transform="translate(1174.2,-686)"><use xlink:href="#MJX-584-TEX-N-32"></use></g><rect width="2608.4" height="60" x="120" y="220"></rect></g><g transform="translate(4182,0)"><use xlink:href="#MJX-584-TEX-N-2C"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/14.svg b/36114-h/images/14.svg new file mode 100644 index 0000000..7527b53 --- /dev/null +++ b/36114-h/images/14.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="4805px" height="765px" viewBox="0 -683 4805 765" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-48-TEX-I-1D44A" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 637H297Q236 634 232 620Q262 160 266 136L501 550L499 587Q496 629 489 632Q483 636 447 637Q428 637 422 639T416 648Q416 650 418 660Q419 664 420 669T421 676T424 680T428 682T436 683Z"></path><path id="MJX-48-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-48-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-48-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-48-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-48-TEX-I-1D44A"></use></g><g transform="translate(1325.8,0)"><use xlink:href="#MJX-48-TEX-N-3D"></use></g><g transform="translate(2381.6,0)"><use xlink:href="#MJX-48-TEX-I-1D463"></use></g><g transform="translate(3088.8,0)"><use xlink:href="#MJX-48-TEX-N-2B"></use></g><g transform="translate(4089,0)"><use xlink:href="#MJX-48-TEX-I-1D464"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/140.svg b/36114-h/images/140.svg new file mode 100644 index 0000000..33a6455 --- /dev/null +++ b/36114-h/images/140.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.17ex;" xmlns="http://www.w3.org/2000/svg" width="10535.5px" height="2418px" viewBox="0 -1459 10535.5 2418" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-585-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-585-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-585-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-585-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-585-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-585-TEX-I-1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path id="MJX-585-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-585-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-585-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-585-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-585-TEX-S3-7D" d="M131 1414T131 1429T133 1447T148 1450H153H167L182 1444Q276 1404 336 1343T415 1207Q421 1184 421 1154T423 851L424 531L426 517Q434 462 460 415T518 339T571 296T608 274Q615 270 616 267T618 251Q618 241 618 238T615 232T608 227Q542 194 491 132T426 -15L424 -29L423 -350Q422 -622 422 -652T415 -706Q397 -780 337 -841T182 -943L167 -949H153Q137 -949 134 -946T131 -928Q131 -914 132 -911T144 -904Q146 -903 148 -902Q299 -820 323 -680Q324 -663 325 -349T327 -19Q355 145 541 241L561 250L541 260Q356 355 327 520Q326 537 325 850T323 1181Q315 1227 293 1267T244 1332T193 1374T151 1401T132 1413Q131 1414 131 1429Z"></path><path id="MJX-585-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-585-TEX-N-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path id="MJX-585-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0 250)"></g><g ><g transform="translate(0,650)"><g transform="translate(222,0)"><g ><g ><use xlink:href="#MJX-585-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-585-TEX-V-2032"></use></g></g></g><g transform="translate(1071.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-585-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-585-TEX-I-1D44E"></use></g><g transform="translate(1862.6,0)"><use xlink:href="#MJX-585-TEX-I-1D465"></use></g><g transform="translate(2656.8,0)"><use xlink:href="#MJX-585-TEX-N-2212"></use></g><g transform="translate(3657,0)"><use xlink:href="#MJX-585-TEX-I-1D44F"></use></g><g transform="translate(4086,0)"><use xlink:href="#MJX-585-TEX-I-1D450"></use></g><g transform="translate(4519,0)"><use xlink:href="#MJX-585-TEX-I-1D461"></use></g><g transform="translate(4880,0)"><use xlink:href="#MJX-585-TEX-N-2C"></use></g></g></g><g transform="translate(0,-709)"><g ><g ><use xlink:href="#MJX-585-TEX-I-1D450"></use></g><g transform="translate(433,0)"><g ><use xlink:href="#MJX-585-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-585-TEX-V-2032"></use></g></g></g><g transform="translate(1071.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-585-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-585-TEX-I-1D44E"></use></g><g transform="translate(1862.6,0)"><use xlink:href="#MJX-585-TEX-I-1D450"></use></g><g transform="translate(2295.6,0)"><use xlink:href="#MJX-585-TEX-I-1D461"></use></g><g transform="translate(2878.8,0)"><use xlink:href="#MJX-585-TEX-N-2212"></use></g><g transform="translate(3879,0)"><use xlink:href="#MJX-585-TEX-I-1D44F"></use></g><g transform="translate(4308,0)"><use xlink:href="#MJX-585-TEX-I-1D465"></use></g><g transform="translate(4880,0)"><use xlink:href="#MJX-585-TEX-N-2E"></use></g></g></g></g><g transform="translate(6229.5,0) translate(0 -0.5)"><use xlink:href="#MJX-585-TEX-S3-7D"></use></g></g><g transform="translate(6979.5,0)"><g ></g></g><g transform="translate(8979.5,0)"><use xlink:href="#MJX-585-TEX-N-28"></use><use xlink:href="#MJX-585-TEX-N-35" transform="translate(389,0)"></use><use xlink:href="#MJX-585-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(10257.5,0)"><use xlink:href="#MJX-585-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/141.svg b/36114-h/images/141.svg new file mode 100644 index 0000000..5c1507f --- /dev/null +++ b/36114-h/images/141.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.575ex;" xmlns="http://www.w3.org/2000/svg" width="3846.6px" height="2066px" viewBox="0 -1370 3846.6 2066" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-590-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-590-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-590-TEX-I-1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path id="MJX-590-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-590-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-590-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-590-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-590-TEX-I-1D465"></use></g><g transform="translate(849.8,0)"><use xlink:href="#MJX-590-TEX-N-3D"></use></g><g transform="translate(1905.6,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-590-TEX-I-1D44F"></use></g><g transform="translate(429,0)"><use xlink:href="#MJX-590-TEX-I-1D450"></use></g></g><g transform="translate(386.5,-686)"><use xlink:href="#MJX-590-TEX-I-1D44E"></use></g><rect width="1062" height="60" x="120" y="220"></rect></g><g transform="translate(3207.6,0)"><use xlink:href="#MJX-590-TEX-I-1D461"></use></g><g transform="translate(3568.6,0)"><use xlink:href="#MJX-590-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/142.svg b/36114-h/images/142.svg new file mode 100644 index 0000000..f6ed669 --- /dev/null +++ b/36114-h/images/142.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.575ex;" xmlns="http://www.w3.org/2000/svg" width="6676.6px" height="2066px" viewBox="0 -1370 6676.6 2066" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-594-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-594-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-594-TEX-I-1D44F" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path id="MJX-594-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-594-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-594-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-594-TEX-N-36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"></path><path id="MJX-594-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-594-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-594-TEX-I-1D463"></use></g><g transform="translate(762.8,0)"><use xlink:href="#MJX-594-TEX-N-3D"></use></g><g transform="translate(1818.6,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-594-TEX-I-1D44F"></use></g><g transform="translate(429,0)"><use xlink:href="#MJX-594-TEX-I-1D450"></use></g></g><g transform="translate(386.5,-686)"><use xlink:href="#MJX-594-TEX-I-1D44E"></use></g><rect width="1062" height="60" x="120" y="220"></rect></g><g transform="translate(3120.6,0)"><g ></g></g><g transform="translate(5120.6,0)"><use xlink:href="#MJX-594-TEX-N-28"></use><use xlink:href="#MJX-594-TEX-N-36" transform="translate(389,0)"></use><use xlink:href="#MJX-594-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(6398.6,0)"><use xlink:href="#MJX-594-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/143.svg b/36114-h/images/143.svg new file mode 100644 index 0000000..e46ac5d --- /dev/null +++ b/36114-h/images/143.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="3562px" height="891px" viewBox="0 -809 3562 891" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-614-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-614-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-614-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-614-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-614-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-614-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-614-TEX-V-2032"></use></g></g><g transform="translate(1127.2,0)"><use xlink:href="#MJX-614-TEX-N-3D"></use></g><g transform="translate(2183,0)"><use xlink:href="#MJX-614-TEX-I-1D44E"></use></g><g transform="translate(2712,0)"><use xlink:href="#MJX-614-TEX-I-1D465"></use></g><g transform="translate(3284,0)"><use xlink:href="#MJX-614-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/144.svg b/36114-h/images/144.svg new file mode 100644 index 0000000..db3b257 --- /dev/null +++ b/36114-h/images/144.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="3516px" height="841px" viewBox="0 -759 3516 841" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-616-TEX-N-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"></path><path id="MJX-616-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-616-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-616-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-616-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-616-TEX-N-394"></use></g><g transform="translate(833,0)"><g ><use xlink:href="#MJX-616-TEX-I-1D465"></use></g><g transform="translate(605,363) scale(0.707)"><use xlink:href="#MJX-616-TEX-V-2032"></use></g></g><g transform="translate(1960.2,0)"><use xlink:href="#MJX-616-TEX-N-3D"></use></g><g transform="translate(3016,0)"><use xlink:href="#MJX-616-TEX-N-31"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/145.svg b/36114-h/images/145.svg new file mode 100644 index 0000000..d1c9fc0 --- /dev/null +++ b/36114-h/images/145.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.575ex;" xmlns="http://www.w3.org/2000/svg" width="7708.2px" height="2038px" viewBox="0 -1342 7708.2 2038" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-618-TEX-N-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"></path><path id="MJX-618-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-618-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-618-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-618-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-618-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-618-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-618-TEX-N-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"></path><path id="MJX-618-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-618-TEX-N-394"></use></g><g transform="translate(833,0)"><use xlink:href="#MJX-618-TEX-I-1D465"></use></g><g transform="translate(1682.8,0)"><use xlink:href="#MJX-618-TEX-N-3D"></use></g><g transform="translate(2738.6,0)"><g transform="translate(234.5,676)"><use xlink:href="#MJX-618-TEX-N-31"></use></g><g transform="translate(220,-686)"><use xlink:href="#MJX-618-TEX-I-1D44E"></use></g><rect width="729" height="60" x="120" y="220"></rect></g><g transform="translate(3707.6,0)"><use xlink:href="#MJX-618-TEX-N-2E"></use></g><g transform="translate(3985.6,0)"><g ></g></g><g transform="translate(6152.2,0)"><use xlink:href="#MJX-618-TEX-N-28"></use><use xlink:href="#MJX-618-TEX-N-37" transform="translate(389,0)"></use><use xlink:href="#MJX-618-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(7430.2,0)"><use xlink:href="#MJX-618-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/146.svg b/36114-h/images/146.svg new file mode 100644 index 0000000..66f0546 --- /dev/null +++ b/36114-h/images/146.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="8284.7px" height="2459.4px" viewBox="0 -1509.9 8284.7 2459.4" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-622-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-622-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-622-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-622-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-622-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-622-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-622-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-622-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-622-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-622-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-622-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-622-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-622-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-622-TEX-V-2032"></use></g></g><g transform="translate(1127.2,0)"><use xlink:href="#MJX-622-TEX-N-3D"></use></g><g transform="translate(2183,0)"><use xlink:href="#MJX-622-TEX-I-1D44E"></use></g><g transform="translate(2878.7,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-622-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-622-TEX-N-31"></use></g><g transform="translate(1458.2,0)"><use xlink:href="#MJX-622-TEX-N-2212"></use></g><g transform="translate(2458.4,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-622-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-622-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-622-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-622-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g><g transform="translate(3820,0) translate(0 -0.5)"><use xlink:href="#MJX-622-TEX-S3-29"></use></g></g><g transform="translate(7434.7,0)"><use xlink:href="#MJX-622-TEX-I-1D465"></use></g><g transform="translate(8006.7,0)"><use xlink:href="#MJX-622-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/147.svg b/36114-h/images/147.svg new file mode 100644 index 0000000..62d9c09 --- /dev/null +++ b/36114-h/images/147.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="12768.3px" height="2459.4px" viewBox="0 -1509.9 12768.3 2459.4" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-625-TEX-N-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"></path><path id="MJX-625-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-625-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-625-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-625-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-625-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-625-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-625-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-625-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-625-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-625-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-625-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-625-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-625-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-625-TEX-N-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"></path><path id="MJX-625-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-625-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-625-TEX-N-394"></use></g><g transform="translate(833,0)"><g ><use xlink:href="#MJX-625-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-625-TEX-V-2032"></use></g></g><g transform="translate(1960.2,0)"><use xlink:href="#MJX-625-TEX-N-3D"></use></g><g transform="translate(3016,0)"><use xlink:href="#MJX-625-TEX-I-1D44E"></use></g><g transform="translate(3711.7,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-625-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-625-TEX-N-31"></use></g><g transform="translate(1458.2,0)"><use xlink:href="#MJX-625-TEX-N-2212"></use></g><g transform="translate(2458.4,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-625-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-625-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-625-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-625-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g><g transform="translate(3820,0) translate(0 -0.5)"><use xlink:href="#MJX-625-TEX-S3-29"></use></g></g><g transform="translate(8267.7,0)"><use xlink:href="#MJX-625-TEX-N-2E"></use></g><g transform="translate(8545.7,0)"><g ></g></g><g transform="translate(10712.3,0)"><use xlink:href="#MJX-625-TEX-N-28"></use><use xlink:href="#MJX-625-TEX-N-37" transform="translate(389,0)"></use><use xlink:href="#MJX-625-TEX-N-61" transform="translate(889,0)"></use><use xlink:href="#MJX-625-TEX-N-29" transform="translate(1389,0)"></use></g><g transform="translate(12490.3,0)"><use xlink:href="#MJX-625-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/148.svg b/36114-h/images/148.svg new file mode 100644 index 0000000..bbf27dd --- /dev/null +++ b/36114-h/images/148.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1405px" height="727px" viewBox="0 -716 1405 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-627-TEX-N-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"></path><path id="MJX-627-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-627-TEX-N-394"></use></g><g transform="translate(833,0)"><use xlink:href="#MJX-627-TEX-I-1D465"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/149.svg b/36114-h/images/149.svg new file mode 100644 index 0000000..9b54708 --- /dev/null +++ b/36114-h/images/149.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -4.979ex;" xmlns="http://www.w3.org/2000/svg" width="10379.8px" height="3542.9px" viewBox="0 -1342 10379.8 3542.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-628-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-628-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-628-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-628-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-628-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-628-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-628-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-628-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-628-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-628-TEX-N-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"></path><path id="MJX-628-TEX-N-62" d="M307 -11Q234 -11 168 55L158 37Q156 34 153 28T147 17T143 10L138 1L118 0H98V298Q98 599 97 603Q94 622 83 628T38 637H20V660Q20 683 22 683L32 684Q42 685 61 686T98 688Q115 689 135 690T165 693T176 694H179V543Q179 391 180 391L183 394Q186 397 192 401T207 411T228 421T254 431T286 439T323 442Q401 442 461 379T522 216Q522 115 458 52T307 -11ZM182 98Q182 97 187 90T196 79T206 67T218 55T233 44T250 35T271 29T295 26Q330 26 363 46T412 113Q424 148 424 212Q424 287 412 323Q385 405 300 405Q270 405 239 390T188 347L182 339V98Z"></path><path id="MJX-628-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-628-TEX-I-1D44E"></use></g><g transform="translate(562,413) scale(0.707)" ><g ><use xlink:href="#MJX-628-TEX-N-32"></use></g></g></g><g transform="translate(1243.3,0)"><use xlink:href="#MJX-628-TEX-N-3D"></use></g><g transform="translate(2299.1,0)"><g transform="translate(1512,676)"><use xlink:href="#MJX-628-TEX-N-31"></use></g><g transform="translate(220,-1469.9)"><g ><use xlink:href="#MJX-628-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-628-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-628-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-628-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-628-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-628-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><rect width="3284" height="60" x="120" y="220"></rect></g><g transform="translate(5823.1,0)"><use xlink:href="#MJX-628-TEX-N-2E"></use></g><g transform="translate(6101.1,0)"><g ></g></g><g transform="translate(8267.8,0)"><use xlink:href="#MJX-628-TEX-N-28"></use><use xlink:href="#MJX-628-TEX-N-37" transform="translate(389,0)"></use><use xlink:href="#MJX-628-TEX-N-62" transform="translate(889,0)"></use><use xlink:href="#MJX-628-TEX-N-29" transform="translate(1445,0)"></use></g><g transform="translate(10101.8,0)"><use xlink:href="#MJX-628-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/15.svg b/36114-h/images/15.svg new file mode 100644 index 0000000..5dacf0c --- /dev/null +++ b/36114-h/images/15.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="5211.2px" height="860px" viewBox="0 -666 5211.2 860" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-49-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-49-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-49-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-49-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-49-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-49-TEX-I-1D450"></use></g><g transform="translate(710.8,0)"><use xlink:href="#MJX-49-TEX-N-3D"></use></g><g transform="translate(1766.6,0)"><use xlink:href="#MJX-49-TEX-N-33"></use><use xlink:href="#MJX-49-TEX-N-30" transform="translate(500,0)"></use><use xlink:href="#MJX-49-TEX-N-30" transform="translate(1000,0)"></use></g><g transform="translate(3266.6,0)"><use xlink:href="#MJX-49-TEX-N-2C"></use></g><g transform="translate(3711.2,0)"><use xlink:href="#MJX-49-TEX-N-30"></use><use xlink:href="#MJX-49-TEX-N-30" transform="translate(500,0)"></use><use xlink:href="#MJX-49-TEX-N-30" transform="translate(1000,0)"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/150.svg b/36114-h/images/150.svg new file mode 100644 index 0000000..0df9250 --- /dev/null +++ b/36114-h/images/150.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -9.335ex;" xmlns="http://www.w3.org/2000/svg" width="11450px" height="8751.9px" viewBox="0 -4626 11450 8751.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-631-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-631-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-631-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-631-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-631-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-631-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-631-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-631-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-631-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-631-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-631-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-631-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-631-TEX-S4-23AB" d="M170 875Q170 892 172 895T189 899H194H211L222 893Q345 826 420 715T503 476Q504 467 504 230Q504 51 504 21T499 -9H498Q496 -10 444 -10Q402 -10 394 -9T385 -4Q384 -2 384 240V311V366Q384 469 380 513T358 609Q342 657 319 698T271 767T227 812T189 843T171 856T170 875Z"></path><path id="MJX-631-TEX-S4-23AD" d="M384 -239V-57Q384 4 389 9Q391 10 455 10Q496 10 498 9Q501 8 502 5Q504 -5 504 -230Q504 -261 504 -311T505 -381Q505 -486 492 -551T435 -691Q357 -820 222 -893L211 -899H195Q176 -899 173 -896T170 -874Q170 -858 171 -855T184 -846Q262 -793 312 -709T378 -525Q378 -524 379 -522Q383 -493 384 -351Q384 -345 384 -334Q384 -276 384 -239Z"></path><path id="MJX-631-TEX-S4-23AC" d="M389 1159Q391 1160 455 1160Q496 1160 498 1159Q501 1158 502 1155Q504 1145 504 925V782Q504 676 511 616T546 490Q563 446 587 408T633 345T674 304T705 278T717 268Q718 267 718 250T717 232Q717 231 697 216T648 169T588 93T534 -24T505 -179Q504 -191 504 -425Q504 -600 504 -629T499 -659H498Q496 -660 444 -660T390 -659Q387 -658 386 -655Q384 -645 384 -424Q384 -191 385 -182Q394 -49 463 61T645 241L659 250L645 259Q539 325 467 434T385 682Q384 692 384 873Q384 1153 385 1155L389 1159Z"></path><path id="MJX-631-TEX-S4-23AA" d="M384 150V266Q384 304 389 309Q391 310 455 310Q496 310 498 309Q502 308 503 298Q504 283 504 150Q504 32 504 12T499 -9H498Q496 -10 444 -10T390 -9Q386 -8 385 2Q384 17 384 150Z"></path><path id="MJX-631-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-631-TEX-N-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"></path><path id="MJX-631-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0 250)"></g><g ><g transform="translate(0,3324)"><g ><g ><g ><use xlink:href="#MJX-631-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-631-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-631-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(951.8,676)"><g ><use xlink:href="#MJX-631-TEX-I-1D465"></use></g><g transform="translate(794.2,0)"><use xlink:href="#MJX-631-TEX-N-2212"></use></g><g transform="translate(1794.4,0)"><use xlink:href="#MJX-631-TEX-I-1D463"></use></g><g transform="translate(2279.4,0)"><use xlink:href="#MJX-631-TEX-I-1D461"></use></g></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-631-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-631-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-631-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-631-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-631-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-631-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-631-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(5877.6,0)"><use xlink:href="#MJX-631-TEX-N-2C"></use></g></g></g><g transform="translate(0,-1706)"><g transform="translate(211,0)"><g ><g ><use xlink:href="#MJX-631-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-631-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-631-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(539.5,1190.9)"><g ><use xlink:href="#MJX-631-TEX-I-1D461"></use></g><g transform="translate(583.2,0)"><use xlink:href="#MJX-631-TEX-N-2212"></use></g><g transform="translate(1583.4,0)"><g ><g transform="translate(412.3,676)"><use xlink:href="#MJX-631-TEX-I-1D463"></use></g><g transform="translate(220,-719.9)"><g ><use xlink:href="#MJX-631-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-631-TEX-N-32"></use></g></g></g><rect width="1069.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(2893,0)"><use xlink:href="#MJX-631-TEX-I-1D465"></use></g></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-631-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-631-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-631-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-631-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-631-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-631-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-631-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(5877.6,0)"><use xlink:href="#MJX-631-TEX-N-2E"></use></g></g></g></g><g transform="translate(7005,0)"><use xlink:href="#MJX-631-TEX-S4-23AB" transform="translate(0,3727)"></use><use xlink:href="#MJX-631-TEX-S4-23AD" transform="translate(0,-3227)"></use><use xlink:href="#MJX-631-TEX-S4-23AC" transform="translate(0,0)"></use><svg width="889" height="2757" y="1060" x="0" viewBox="0 485.9 889 2757"><use xlink:href="#MJX-631-TEX-S4-23AA" transform="scale(1,13.559)"></use></svg><svg width="889" height="2757" y="-3317" x="0" viewBox="0 485.9 889 2757"><use xlink:href="#MJX-631-TEX-S4-23AA" transform="scale(1,13.559)"></use></svg></g></g><g transform="translate(7894,0)"><g ></g></g><g transform="translate(9894,0)"><use xlink:href="#MJX-631-TEX-N-28"></use><use xlink:href="#MJX-631-TEX-N-38" transform="translate(389,0)"></use><use xlink:href="#MJX-631-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(11172,0)"><use xlink:href="#MJX-631-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/151.svg b/36114-h/images/151.svg new file mode 100644 index 0000000..c8f9b0e --- /dev/null +++ b/36114-h/images/151.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="14019.3px" height="1133.9px" viewBox="0 -883.9 14019.3 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-633-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-633-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-633-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-633-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-633-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-633-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-633-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-633-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-633-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-633-TEX-N-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"></path><path id="MJX-633-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-633-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-633-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-633-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-633-TEX-N-32"></use></g></g></g></g><g transform="translate(1425.2,0)"><use xlink:href="#MJX-633-TEX-N-2212"></use></g><g transform="translate(2425.5,0)"><g ><use xlink:href="#MJX-633-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-633-TEX-N-32"></use></g></g></g><g transform="translate(3295,0)"><g ><use xlink:href="#MJX-633-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><g ><use xlink:href="#MJX-633-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-633-TEX-N-32"></use></g></g></g></g><g transform="translate(4564.8,0)"><use xlink:href="#MJX-633-TEX-N-3D"></use></g><g transform="translate(5620.6,0)"><g ><use xlink:href="#MJX-633-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-633-TEX-N-32"></use></g></g></g><g transform="translate(6851.3,0)"><use xlink:href="#MJX-633-TEX-N-2212"></use></g><g transform="translate(7851.6,0)"><g ><use xlink:href="#MJX-633-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-633-TEX-N-32"></use></g></g></g><g transform="translate(8721.1,0)"><g ><use xlink:href="#MJX-633-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)" ><g ><use xlink:href="#MJX-633-TEX-N-32"></use></g></g></g><g transform="translate(9518.7,0)"><use xlink:href="#MJX-633-TEX-N-2E"></use></g><g transform="translate(9796.7,0)"><g ></g></g><g transform="translate(11963.3,0)"><use xlink:href="#MJX-633-TEX-N-28"></use><use xlink:href="#MJX-633-TEX-N-38" transform="translate(389,0)"></use><use xlink:href="#MJX-633-TEX-N-61" transform="translate(889,0)"></use><use xlink:href="#MJX-633-TEX-N-29" transform="translate(1389,0)"></use></g><g transform="translate(13741.3,0)"><use xlink:href="#MJX-633-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/152.svg b/36114-h/images/152.svg new file mode 100644 index 0000000..1b19c35 --- /dev/null +++ b/36114-h/images/152.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.17ex;" xmlns="http://www.w3.org/2000/svg" width="7175px" height="2418px" viewBox="0 -1459 7175 2418" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-635-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-635-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-635-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-635-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-635-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-635-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-635-TEX-S3-7D" d="M131 1414T131 1429T133 1447T148 1450H153H167L182 1444Q276 1404 336 1343T415 1207Q421 1184 421 1154T423 851L424 531L426 517Q434 462 460 415T518 339T571 296T608 274Q615 270 616 267T618 251Q618 241 618 238T615 232T608 227Q542 194 491 132T426 -15L424 -29L423 -350Q422 -622 422 -652T415 -706Q397 -780 337 -841T182 -943L167 -949H153Q137 -949 134 -946T131 -928Q131 -914 132 -911T144 -904Q146 -903 148 -902Q299 -820 323 -680Q324 -663 325 -349T327 -19Q355 145 541 241L561 250L541 260Q356 355 327 520Q326 537 325 850T323 1181Q315 1227 293 1267T244 1332T193 1374T151 1401T132 1413Q131 1414 131 1429Z"></path><path id="MJX-635-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-635-TEX-N-39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"></path><path id="MJX-635-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0 250)"></g><g ><g transform="translate(0,650)"><g ><g ><g ><use xlink:href="#MJX-635-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)"><use xlink:href="#MJX-635-TEX-V-2032"></use></g></g></g><g transform="translate(767.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-635-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-635-TEX-I-1D466"></use></g><g transform="translate(1823.6,0)"><use xlink:href="#MJX-635-TEX-N-2C"></use></g></g></g><g transform="translate(0,-709)"><g transform="translate(25,0)"><g ><g ><use xlink:href="#MJX-635-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)"><use xlink:href="#MJX-635-TEX-V-2032"></use></g></g></g><g transform="translate(767.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-635-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-635-TEX-I-1D467"></use></g><g transform="translate(1798.6,0)"><use xlink:href="#MJX-635-TEX-N-2E"></use></g></g></g></g><g transform="translate(2869,0) translate(0 -0.5)"><use xlink:href="#MJX-635-TEX-S3-7D"></use></g></g><g transform="translate(3619,0)"><g ></g></g><g transform="translate(5619,0)"><use xlink:href="#MJX-635-TEX-N-28"></use><use xlink:href="#MJX-635-TEX-N-39" transform="translate(389,0)"></use><use xlink:href="#MJX-635-TEX-N-29" transform="translate(889,0)"></use></g><g transform="translate(6897,0)"><use xlink:href="#MJX-635-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/153.svg b/36114-h/images/153.svg new file mode 100644 index 0000000..3446edb --- /dev/null +++ b/36114-h/images/153.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.469ex;" xmlns="http://www.w3.org/2000/svg" width="10491.7px" height="1260px" viewBox="0 -1052.7 10491.7 1260" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-640-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-640-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-640-TEX-SO-221A" d="M263 249Q264 249 315 130T417 -108T470 -228L725 302Q981 837 982 839Q989 850 1001 850Q1008 850 1013 844T1020 832V826L741 243Q645 43 540 -176Q479 -303 469 -324T453 -348Q449 -350 436 -350L424 -349L315 -96Q206 156 205 156L171 130Q138 104 137 104L111 130L263 249Z"></path><path id="MJX-640-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-640-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-640-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-640-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-640-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-640-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-640-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-640-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-640-TEX-I-1D45F"></use></g><g transform="translate(728.8,0)"><use xlink:href="#MJX-640-TEX-N-3D"></use></g><g transform="translate(1784.6,0)"><g transform="translate(1020,0)"><g ><g ><use xlink:href="#MJX-640-TEX-I-1D465"></use></g><g transform="translate(605,289) scale(0.707)" ><g ><use xlink:href="#MJX-640-TEX-N-32"></use></g></g></g><g transform="translate(1230.8,0)"><use xlink:href="#MJX-640-TEX-N-2B"></use></g><g transform="translate(2231,0)"><g ><use xlink:href="#MJX-640-TEX-I-1D466"></use></g><g transform="translate(523,289) scale(0.707)" ><g ><use xlink:href="#MJX-640-TEX-N-32"></use></g></g></g><g transform="translate(3379.8,0)"><use xlink:href="#MJX-640-TEX-N-2B"></use></g><g transform="translate(4380,0)"><g ><use xlink:href="#MJX-640-TEX-I-1D467"></use></g><g transform="translate(498,289) scale(0.707)" ><g ><use xlink:href="#MJX-640-TEX-N-32"></use></g></g></g></g><g transform="translate(0,142.7)"><use xlink:href="#MJX-640-TEX-SO-221A"></use></g><rect width="5281.5" height="60" x="1020" y="932.7"></rect></g><g transform="translate(8363.9,0)"><use xlink:href="#MJX-640-TEX-N-3D"></use></g><g transform="translate(9419.7,0)"><use xlink:href="#MJX-640-TEX-I-1D450"></use></g><g transform="translate(9852.7,0)"><use xlink:href="#MJX-640-TEX-I-1D461"></use></g><g transform="translate(10213.7,0)"><use xlink:href="#MJX-640-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/154.svg b/36114-h/images/154.svg new file mode 100644 index 0000000..583cac6 --- /dev/null +++ b/36114-h/images/154.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="14338.7px" height="1133.9px" viewBox="0 -883.9 14338.7 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-641-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-641-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-641-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-641-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-641-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-641-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-641-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-641-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-641-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-641-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-641-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-641-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-641-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-641-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-641-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-641-TEX-N-32"></use></g></g></g><g transform="translate(1230.8,0)"><use xlink:href="#MJX-641-TEX-N-2B"></use></g><g transform="translate(2231,0)"><g ><use xlink:href="#MJX-641-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)" ><g ><use xlink:href="#MJX-641-TEX-N-32"></use></g></g></g><g transform="translate(3379.8,0)"><use xlink:href="#MJX-641-TEX-N-2B"></use></g><g transform="translate(4380,0)"><g ><use xlink:href="#MJX-641-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)" ><g ><use xlink:href="#MJX-641-TEX-N-32"></use></g></g></g><g transform="translate(5503.8,0)"><use xlink:href="#MJX-641-TEX-N-2212"></use></g><g transform="translate(6504,0)"><g ><use xlink:href="#MJX-641-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-641-TEX-N-32"></use></g></g></g><g transform="translate(7373.5,0)"><g ><use xlink:href="#MJX-641-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)" ><g ><use xlink:href="#MJX-641-TEX-N-32"></use></g></g></g><g transform="translate(8448.9,0)"><use xlink:href="#MJX-641-TEX-N-3D"></use></g><g transform="translate(9504.7,0)"><use xlink:href="#MJX-641-TEX-N-30"></use><use xlink:href="#MJX-641-TEX-N-2E" transform="translate(500,0)"></use></g><g transform="translate(10282.7,0)"><g ></g></g><g transform="translate(12282.7,0)"><use xlink:href="#MJX-641-TEX-N-28"></use><use xlink:href="#MJX-641-TEX-N-31" transform="translate(389,0)"></use><use xlink:href="#MJX-641-TEX-N-30" transform="translate(889,0)"></use><use xlink:href="#MJX-641-TEX-N-29" transform="translate(1389,0)"></use></g><g transform="translate(14060.7,0)"><use xlink:href="#MJX-641-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/155.svg b/36114-h/images/155.svg new file mode 100644 index 0000000..9c35538 --- /dev/null +++ b/36114-h/images/155.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="3411.5px" height="1003px" viewBox="0 -809 3411.5 1003" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-643-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-643-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-643-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-643-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-643-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-643-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-643-TEX-I-1D45F"></use></g><g transform="translate(484,413) scale(0.707)"><use xlink:href="#MJX-643-TEX-V-2032"></use></g></g><g transform="translate(1006.2,0)"><use xlink:href="#MJX-643-TEX-N-3D"></use></g><g transform="translate(2062,0)"><use xlink:href="#MJX-643-TEX-I-1D450"></use></g><g transform="translate(2495,0)"><g ><use xlink:href="#MJX-643-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-643-TEX-V-2032"></use></g></g><g transform="translate(3133.5,0)"><use xlink:href="#MJX-643-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/156.svg b/36114-h/images/156.svg new file mode 100644 index 0000000..da64584 --- /dev/null +++ b/36114-h/images/156.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="15616.5px" height="1133.9px" viewBox="0 -883.9 15616.5 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-644-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-644-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-644-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-644-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-644-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-644-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-644-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-644-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-644-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-644-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-644-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-644-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-644-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-644-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-644-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-644-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-644-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-644-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-644-TEX-N-32"></use></g></g></g></g><g transform="translate(1425.2,0)"><use xlink:href="#MJX-644-TEX-N-2B"></use></g><g transform="translate(2425.5,0)"><g ><use xlink:href="#MJX-644-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)"><g ><use xlink:href="#MJX-644-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-644-TEX-N-32"></use></g></g></g></g><g transform="translate(3768.7,0)"><use xlink:href="#MJX-644-TEX-N-2B"></use></g><g transform="translate(4768.9,0)"><g ><use xlink:href="#MJX-644-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)"><g ><use xlink:href="#MJX-644-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-644-TEX-N-32"></use></g></g></g></g><g transform="translate(6087.1,0)"><use xlink:href="#MJX-644-TEX-N-2212"></use></g><g transform="translate(7087.4,0)"><g ><use xlink:href="#MJX-644-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-644-TEX-N-32"></use></g></g></g><g transform="translate(7956.9,0)"><g ><use xlink:href="#MJX-644-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><g ><use xlink:href="#MJX-644-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-644-TEX-N-32"></use></g></g></g></g><g transform="translate(9226.7,0)"><use xlink:href="#MJX-644-TEX-N-3D"></use></g><g transform="translate(10282.5,0)"><use xlink:href="#MJX-644-TEX-N-30"></use><use xlink:href="#MJX-644-TEX-N-2E" transform="translate(500,0)"></use></g><g transform="translate(11060.5,0)"><g ></g></g><g transform="translate(13060.5,0)"><use xlink:href="#MJX-644-TEX-N-28"></use><use xlink:href="#MJX-644-TEX-N-31" transform="translate(389,0)"></use><use xlink:href="#MJX-644-TEX-N-30" transform="translate(889,0)"></use><use xlink:href="#MJX-644-TEX-N-61" transform="translate(1389,0)"></use><use xlink:href="#MJX-644-TEX-N-29" transform="translate(1889,0)"></use></g><g transform="translate(15338.5,0)"><use xlink:href="#MJX-644-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/157.svg b/36114-h/images/157.svg new file mode 100644 index 0000000..5f4c28e --- /dev/null +++ b/36114-h/images/157.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24303.2px" height="1133.9px" viewBox="0 -883.9 24303.2 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-645-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-645-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-645-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-645-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-645-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-645-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-645-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-645-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-645-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-645-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-645-TEX-I-1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z"></path><path id="MJX-645-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-645-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-645-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-645-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-645-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-645-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g></g><g transform="translate(1425.2,0)"><use xlink:href="#MJX-645-TEX-N-2B"></use></g><g transform="translate(2425.5,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)"><g ><use xlink:href="#MJX-645-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g></g><g transform="translate(3768.7,0)"><use xlink:href="#MJX-645-TEX-N-2B"></use></g><g transform="translate(4768.9,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)"><g ><use xlink:href="#MJX-645-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g></g><g transform="translate(6087.1,0)"><use xlink:href="#MJX-645-TEX-N-2212"></use></g><g transform="translate(7087.4,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g><g transform="translate(7956.9,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><g ><use xlink:href="#MJX-645-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g></g><g transform="translate(9226.7,0)"><use xlink:href="#MJX-645-TEX-N-3D"></use></g><g transform="translate(10282.5,0)"><use xlink:href="#MJX-645-TEX-I-1D70E"></use></g><g transform="translate(10853.5,0)"><use xlink:href="#MJX-645-TEX-N-28"></use></g><g transform="translate(11242.5,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g><g transform="translate(12473.2,0)"><use xlink:href="#MJX-645-TEX-N-2B"></use></g><g transform="translate(13473.5,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)" ><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g><g transform="translate(14622.2,0)"><use xlink:href="#MJX-645-TEX-N-2B"></use></g><g transform="translate(15622.5,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)" ><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g><g transform="translate(16746.2,0)"><use xlink:href="#MJX-645-TEX-N-2212"></use></g><g transform="translate(17746.5,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g><g transform="translate(18616,0)"><g ><use xlink:href="#MJX-645-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)" ><g ><use xlink:href="#MJX-645-TEX-N-32"></use></g></g></g><g transform="translate(19413.6,0)"><use xlink:href="#MJX-645-TEX-N-29"></use></g><g transform="translate(19802.6,0)"><use xlink:href="#MJX-645-TEX-N-2E"></use></g><g transform="translate(20080.6,0)"><g ></g></g><g transform="translate(22247.2,0)"><use xlink:href="#MJX-645-TEX-N-28"></use><use xlink:href="#MJX-645-TEX-N-31" transform="translate(389,0)"></use><use xlink:href="#MJX-645-TEX-N-31" transform="translate(889,0)"></use><use xlink:href="#MJX-645-TEX-N-29" transform="translate(1389,0)"></use></g><g transform="translate(24025.2,0)"><use xlink:href="#MJX-645-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/158.svg b/36114-h/images/158.svg new file mode 100644 index 0000000..22a0fbb --- /dev/null +++ b/36114-h/images/158.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2404.6px" height="748px" viewBox="0 -666 2404.6 748" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-648-TEX-I-1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z"></path><path id="MJX-648-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-648-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-648-TEX-I-1D70E"></use></g><g transform="translate(848.8,0)"><use xlink:href="#MJX-648-TEX-N-3D"></use></g><g transform="translate(1904.6,0)"><use xlink:href="#MJX-648-TEX-N-31"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/159.svg b/36114-h/images/159.svg new file mode 100644 index 0000000..2df3b4e --- /dev/null +++ b/36114-h/images/159.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="23009.6px" height="1133.9px" viewBox="0 -883.9 23009.6 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-662-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-662-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-662-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-662-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-662-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-662-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-662-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-662-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-662-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-662-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-662-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-662-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-662-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-662-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-662-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-662-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-662-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g></g><g transform="translate(1425.2,0)"><use xlink:href="#MJX-662-TEX-N-2B"></use></g><g transform="translate(2425.5,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)"><g ><use xlink:href="#MJX-662-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g></g><g transform="translate(3768.7,0)"><use xlink:href="#MJX-662-TEX-N-2B"></use></g><g transform="translate(4768.9,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)"><g ><use xlink:href="#MJX-662-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g></g><g transform="translate(6087.1,0)"><use xlink:href="#MJX-662-TEX-N-2212"></use></g><g transform="translate(7087.4,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g><g transform="translate(7956.9,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><g ><use xlink:href="#MJX-662-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g></g><g transform="translate(9226.7,0)"><use xlink:href="#MJX-662-TEX-N-3D"></use></g><g transform="translate(10282.5,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g><g transform="translate(11513.2,0)"><use xlink:href="#MJX-662-TEX-N-2B"></use></g><g transform="translate(12513.5,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)" ><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g><g transform="translate(13662.2,0)"><use xlink:href="#MJX-662-TEX-N-2B"></use></g><g transform="translate(14662.5,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)" ><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g><g transform="translate(15786.2,0)"><use xlink:href="#MJX-662-TEX-N-2212"></use></g><g transform="translate(16786.5,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g><g transform="translate(17656,0)"><g ><use xlink:href="#MJX-662-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)" ><g ><use xlink:href="#MJX-662-TEX-N-32"></use></g></g></g><g transform="translate(18453.6,0)"><g ></g></g><g transform="translate(20453.6,0)"><use xlink:href="#MJX-662-TEX-N-28"></use><use xlink:href="#MJX-662-TEX-N-31" transform="translate(389,0)"></use><use xlink:href="#MJX-662-TEX-N-31" transform="translate(889,0)"></use><use xlink:href="#MJX-662-TEX-N-61" transform="translate(1389,0)"></use><use xlink:href="#MJX-662-TEX-N-29" transform="translate(1889,0)"></use></g><g transform="translate(22731.6,0)"><use xlink:href="#MJX-662-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/16.svg b/36114-h/images/16.svg new file mode 100644 index 0000000..fcb8a9c --- /dev/null +++ b/36114-h/images/16.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="433px" height="453px" viewBox="0 -442 433 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-737-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-737-TEX-I-1D450"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/160.svg b/36114-h/images/160.svg new file mode 100644 index 0000000..de28cad --- /dev/null +++ b/36114-h/images/160.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.223ex;" xmlns="http://www.w3.org/2000/svg" width="6267.6px" height="5117.2px" viewBox="0 -2808.6 6267.6 5117.2" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-673-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-673-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-673-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-673-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-673-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-673-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-673-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-673-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-673-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-673-TEX-N-221A" d="M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z"></path><path id="MJX-673-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-673-TEX-N-B7" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path id="MJX-673-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-673-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,2058.6)"><g ><g ><g ><use xlink:href="#MJX-673-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-673-TEX-N-31"></use></g></g></g></g><g transform="translate(1008.6,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-673-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-673-TEX-I-1D465"></use></g><g transform="translate(1905.6,0)"><use xlink:href="#MJX-673-TEX-N-2C"></use></g></g></g><g transform="translate(0,758.6)"><g ><g ><g ><use xlink:href="#MJX-673-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-673-TEX-N-32"></use></g></g></g></g><g transform="translate(1008.6,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-673-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-673-TEX-I-1D466"></use></g><g transform="translate(1823.6,0)"><use xlink:href="#MJX-673-TEX-N-2C"></use></g></g></g><g transform="translate(0,-541.4)"><g ><g ><g ><use xlink:href="#MJX-673-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-673-TEX-N-33"></use></g></g></g></g><g transform="translate(1008.6,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-673-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-673-TEX-I-1D467"></use></g><g transform="translate(1798.6,0)"><use xlink:href="#MJX-673-TEX-N-2C"></use></g></g></g><g transform="translate(0,-2058.6)"><g ><g ><g ><use xlink:href="#MJX-673-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-673-TEX-N-34"></use></g></g></g></g><g transform="translate(1008.6,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-673-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(853,0)"><g ><use xlink:href="#MJX-673-TEX-N-2212"></use></g><g transform="translate(778,0)"><use xlink:href="#MJX-673-TEX-N-31"></use></g></g><g transform="translate(0,107.3)"><use xlink:href="#MJX-673-TEX-N-221A"></use></g><rect width="1278" height="60" x="853" y="847.3"></rect></g><g transform="translate(3686.8,0)"><use xlink:href="#MJX-673-TEX-N-B7"></use></g><g transform="translate(4187,0)"><use xlink:href="#MJX-673-TEX-I-1D450"></use></g><g transform="translate(4620,0)"><use xlink:href="#MJX-673-TEX-I-1D461"></use></g><g transform="translate(4981,0)"><use xlink:href="#MJX-673-TEX-N-2C"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/161.svg b/36114-h/images/161.svg new file mode 100644 index 0000000..cfc66f9 --- /dev/null +++ b/36114-h/images/161.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.594ex;" xmlns="http://www.w3.org/2000/svg" width="23761.3px" height="1146.5px" viewBox="0 -883.9 23761.3 1146.5" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-675-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-675-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-675-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-675-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-675-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-675-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-675-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-675-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-675-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-675-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-675-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-675-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(605,-247) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-31"></use></g></g></g><g transform="translate(1425.2,0)"><use xlink:href="#MJX-675-TEX-N-2B"></use></g><g transform="translate(2425.5,0)"><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-675-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(605,-247) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(3850.7,0)"><use xlink:href="#MJX-675-TEX-N-2B"></use></g><g transform="translate(4850.9,0)"><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-675-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(605,-247) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-33"></use></g></g></g><g transform="translate(6276.1,0)"><use xlink:href="#MJX-675-TEX-N-2B"></use></g><g transform="translate(7276.4,0)"><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-675-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(605,-247) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-34"></use></g></g></g><g transform="translate(8757.1,0)"><use xlink:href="#MJX-675-TEX-N-3D"></use></g><g transform="translate(9812.9,0)"><g ><g ><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-31"></use></g></g></g></g><g transform="translate(1041.6,413) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(11480.2,0)"><use xlink:href="#MJX-675-TEX-N-2B"></use></g><g transform="translate(12480.5,0)"><g ><g ><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g></g><g transform="translate(1041.6,413) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(14147.8,0)"><use xlink:href="#MJX-675-TEX-N-2B"></use></g><g transform="translate(15148,0)"><g ><g ><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-33"></use></g></g></g></g><g transform="translate(1041.6,413) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(16815.4,0)"><use xlink:href="#MJX-675-TEX-N-2B"></use></g><g transform="translate(17815.6,0)"><g ><g ><g ><use xlink:href="#MJX-675-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-34"></use></g></g></g></g><g transform="translate(1041.6,413) scale(0.707)" ><g ><use xlink:href="#MJX-675-TEX-N-32"></use></g></g></g><g transform="translate(19260.7,0)"><use xlink:href="#MJX-675-TEX-N-2E"></use></g><g transform="translate(19538.7,0)"><g ></g></g><g transform="translate(21705.3,0)"><use xlink:href="#MJX-675-TEX-N-28"></use><use xlink:href="#MJX-675-TEX-N-31" transform="translate(389,0)"></use><use xlink:href="#MJX-675-TEX-N-32" transform="translate(889,0)"></use><use xlink:href="#MJX-675-TEX-N-29" transform="translate(1389,0)"></use></g><g transform="translate(23483.3,0)"><use xlink:href="#MJX-675-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/162.svg b/36114-h/images/162.svg new file mode 100644 index 0000000..a48aebe --- /dev/null +++ b/36114-h/images/162.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.594ex;" xmlns="http://www.w3.org/2000/svg" width="14445.7px" height="1146.5px" viewBox="0 -883.9 14445.7 1146.5" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-697-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-697-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-697-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-697-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-697-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-697-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-697-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-697-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-697-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-697-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g><g transform="translate(605,-247) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-31"></use></g></g></g><g transform="translate(1425.2,0)"><use xlink:href="#MJX-697-TEX-N-2B"></use></g><g transform="translate(2425.5,0)"><g ><use xlink:href="#MJX-697-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-697-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g><g transform="translate(605,-247) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g><g transform="translate(3850.7,0)"><use xlink:href="#MJX-697-TEX-N-2B"></use></g><g transform="translate(4850.9,0)"><g ><use xlink:href="#MJX-697-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><g ><use xlink:href="#MJX-697-TEX-V-2032"></use></g><g transform="translate(275,0)"><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g><g transform="translate(605,-247) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-33"></use></g></g></g><g transform="translate(6331.7,0)"><use xlink:href="#MJX-697-TEX-N-3D"></use></g><g transform="translate(7387.5,0)"><g ><g ><g ><use xlink:href="#MJX-697-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-31"></use></g></g></g></g><g transform="translate(1041.6,413) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g><g transform="translate(9054.8,0)"><use xlink:href="#MJX-697-TEX-N-2B"></use></g><g transform="translate(10055,0)"><g ><g ><g ><use xlink:href="#MJX-697-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g></g><g transform="translate(1041.6,413) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g><g transform="translate(11722.3,0)"><use xlink:href="#MJX-697-TEX-N-2B"></use></g><g transform="translate(12722.6,0)"><g ><g ><g ><use xlink:href="#MJX-697-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-33"></use></g></g></g></g><g transform="translate(1041.6,413) scale(0.707)" ><g ><use xlink:href="#MJX-697-TEX-N-32"></use></g></g></g><g transform="translate(14167.7,0)"><use xlink:href="#MJX-697-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/163.svg b/36114-h/images/163.svg new file mode 100644 index 0000000..97c3e30 --- /dev/null +++ b/36114-h/images/163.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.194ex;" xmlns="http://www.w3.org/2000/svg" width="6965.1px" height="2479.9px" viewBox="0 -1509.9 6965.1 2479.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-698-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-698-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-698-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-698-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path id="MJX-698-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-698-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-698-TEX-I-1D447" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path><path id="MJX-698-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-698-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-698-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-698-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-698-TEX-I-1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path><path id="MJX-698-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-698-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-698-TEX-N-2B"></use></g><g transform="translate(778,0)"><g transform="translate(1468.5,676)"><g ><use xlink:href="#MJX-698-TEX-N-32"></use><use xlink:href="#MJX-698-TEX-N-34" transform="translate(500,0)"></use></g><g transform="translate(1000,0)"><g ><use xlink:href="#MJX-698-TEX-I-1D70B"></use></g><g transform="translate(603,363) scale(0.707)" ><g ><use xlink:href="#MJX-698-TEX-N-33"></use></g></g></g><g transform="translate(2006.6,0)"><g ><use xlink:href="#MJX-698-TEX-I-1D44E"></use></g><g transform="translate(562,363) scale(0.707)" ><g ><use xlink:href="#MJX-698-TEX-N-32"></use></g></g></g></g><g transform="translate(220,-719.9)"><g ><g ><use xlink:href="#MJX-698-TEX-I-1D447"></use></g><g transform="translate(793,289) scale(0.707)" ><g ><use xlink:href="#MJX-698-TEX-N-32"></use></g></g></g><g transform="translate(1196.6,0)"><g ><use xlink:href="#MJX-698-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-698-TEX-N-32"></use></g></g></g><g transform="translate(2066.1,0)"><use xlink:href="#MJX-698-TEX-N-28"></use></g><g transform="translate(2455.1,0)"><use xlink:href="#MJX-698-TEX-N-31"></use></g><g transform="translate(3177.3,0)"><use xlink:href="#MJX-698-TEX-N-2212"></use></g><g transform="translate(4177.6,0)"><g ><use xlink:href="#MJX-698-TEX-I-1D452"></use></g><g transform="translate(499,289) scale(0.707)" ><g ><use xlink:href="#MJX-698-TEX-N-32"></use></g></g></g><g transform="translate(5080.1,0)"><use xlink:href="#MJX-698-TEX-N-29"></use></g></g><rect width="5669.1" height="60" x="120" y="220"></rect></g><g transform="translate(6687.1,0)"><use xlink:href="#MJX-698-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/164.svg b/36114-h/images/164.svg new file mode 100644 index 0000000..0470418 --- /dev/null +++ b/36114-h/images/164.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1070px" height="677px" viewBox="0 -666 1070 677" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-699-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-699-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-699-TEX-N-32"></use></g><g transform="translate(500,0)"><use xlink:href="#MJX-699-TEX-I-1D70B"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/165.svg b/36114-h/images/165.svg new file mode 100644 index 0000000..7cb2c12 --- /dev/null +++ b/36114-h/images/165.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="466px" height="453px" viewBox="0 -442 466 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-701-TEX-I-1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-701-TEX-I-1D452"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/166.svg b/36114-h/images/166.svg new file mode 100644 index 0000000..2c9796e --- /dev/null +++ b/36114-h/images/166.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="833px" height="716px" viewBox="0 -716 833 716" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-704-TEX-N-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-704-TEX-N-394"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/167.svg b/36114-h/images/167.svg new file mode 100644 index 0000000..338c792 --- /dev/null +++ b/36114-h/images/167.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="640px" height="453px" viewBox="0 -442 640 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-710-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-710-TEX-I-1D6FC"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/168.svg b/36114-h/images/168.svg new file mode 100644 index 0000000..3271996 --- /dev/null +++ b/36114-h/images/168.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.552ex;" xmlns="http://www.w3.org/2000/svg" width="10149.6px" height="2067px" viewBox="0 -1381 10149.6 2067" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-706-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-706-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-706-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-706-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-706-TEX-N-37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z"></path><path id="MJX-706-TEX-N-20" d=""></path><path id="MJX-706-TEX-N-73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path id="MJX-706-TEX-N-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z"></path><path id="MJX-706-TEX-N-63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z"></path><path id="MJX-706-TEX-N-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path id="MJX-706-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-706-TEX-N-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path><path id="MJX-706-TEX-N-66" d="M273 0Q255 3 146 3Q43 3 34 0H26V46H42Q70 46 91 49Q99 52 103 60Q104 62 104 224V385H33V431H104V497L105 564L107 574Q126 639 171 668T266 704Q267 704 275 704T289 705Q330 702 351 679T372 627Q372 604 358 590T321 576T284 590T270 627Q270 647 288 667H284Q280 668 273 668Q245 668 223 647T189 592Q183 572 182 497V431H293V385H185V225Q185 63 186 61T189 57T194 54T199 51T206 49T213 48T222 47T231 47T241 46T251 46H282V0H273Z"></path><path id="MJX-706-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-706-TEX-N-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path id="MJX-706-TEX-N-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-706-TEX-I-1D6FC"></use></g><g transform="translate(917.8,0)"><use xlink:href="#MJX-706-TEX-N-3D"></use></g><g transform="translate(1973.6,0)"><g transform="translate(220,676)"><use xlink:href="#MJX-706-TEX-N-31"></use><use xlink:href="#MJX-706-TEX-N-2E" transform="translate(500,0)"></use><use xlink:href="#MJX-706-TEX-N-37" transform="translate(778,0)"></use><use xlink:href="#MJX-706-TEX-N-20" transform="translate(1278,0)"></use><use xlink:href="#MJX-706-TEX-N-73" transform="translate(1528,0)"></use><use xlink:href="#MJX-706-TEX-N-65" transform="translate(1922,0)"></use><use xlink:href="#MJX-706-TEX-N-63" transform="translate(2366,0)"></use><use xlink:href="#MJX-706-TEX-N-6F" transform="translate(2810,0)"></use><use xlink:href="#MJX-706-TEX-N-6E" transform="translate(3310,0)"></use><use xlink:href="#MJX-706-TEX-N-64" transform="translate(3866,0)"></use><use xlink:href="#MJX-706-TEX-N-73" transform="translate(4422,0)"></use><use xlink:href="#MJX-706-TEX-N-20" transform="translate(4816,0)"></use><use xlink:href="#MJX-706-TEX-N-6F" transform="translate(5066,0)"></use><use xlink:href="#MJX-706-TEX-N-66" transform="translate(5566,0)"></use><use xlink:href="#MJX-706-TEX-N-20" transform="translate(5872,0)"></use><use xlink:href="#MJX-706-TEX-N-61" transform="translate(6122,0)"></use><use xlink:href="#MJX-706-TEX-N-72" transform="translate(6622,0)"></use><use xlink:href="#MJX-706-TEX-N-63" transform="translate(7014,0)"></use></g><g transform="translate(3532.5,-686)"><use xlink:href="#MJX-706-TEX-N-394"></use></g><rect width="7658" height="60" x="120" y="220"></rect></g><g transform="translate(9871.6,0)"><use xlink:href="#MJX-706-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/169.svg b/36114-h/images/169.svg new file mode 100644 index 0000000..7f782d6 --- /dev/null +++ b/36114-h/images/169.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.339ex;" xmlns="http://www.w3.org/2000/svg" width="1264.6px" height="833px" viewBox="0 -683 1264.6 833" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-708-TEX-I-1D437" d="M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z"></path><path id="MJX-708-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-708-TEX-I-1D437"></use></g><g transform="translate(861,-150) scale(0.707)" ><g ><use xlink:href="#MJX-708-TEX-N-31"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/17.svg b/36114-h/images/17.svg new file mode 100644 index 0000000..a3b3bfc --- /dev/null +++ b/36114-h/images/17.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1048px" height="705px" viewBox="0 -683 1048 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-239-TEX-I-1D44A" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 637H297Q236 634 232 620Q262 160 266 136L501 550L499 587Q496 629 489 632Q483 636 447 637Q428 637 422 639T416 648Q416 650 418 660Q419 664 420 669T421 676T424 680T428 682T436 683Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-239-TEX-I-1D44A"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/170.svg b/36114-h/images/170.svg new file mode 100644 index 0000000..f3b0375 --- /dev/null +++ b/36114-h/images/170.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.339ex;" xmlns="http://www.w3.org/2000/svg" width="1264.6px" height="833px" viewBox="0 -683 1264.6 833" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-709-TEX-I-1D437" d="M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z"></path><path id="MJX-709-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-709-TEX-I-1D437"></use></g><g transform="translate(861,-150) scale(0.707)" ><g ><use xlink:href="#MJX-709-TEX-N-32"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/171.svg b/36114-h/images/171.svg new file mode 100644 index 0000000..a45e536 --- /dev/null +++ b/36114-h/images/171.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="3169.6px" height="777px" viewBox="0 -583 3169.6 777" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-715-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-715-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-715-TEX-I-1D714" d="M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z"></path><path id="MJX-715-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-715-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-715-TEX-I-1D463"></use></g><g transform="translate(762.8,0)"><use xlink:href="#MJX-715-TEX-N-3D"></use></g><g transform="translate(1818.6,0)"><use xlink:href="#MJX-715-TEX-I-1D714"></use></g><g transform="translate(2440.6,0)"><use xlink:href="#MJX-715-TEX-I-1D45F"></use></g><g transform="translate(2891.6,0)"><use xlink:href="#MJX-715-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/172.svg b/36114-h/images/172.svg new file mode 100644 index 0000000..37decd7 --- /dev/null +++ b/36114-h/images/172.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="622px" height="454px" viewBox="0 -443 622 454" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-716-TEX-I-1D714" d="M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-716-TEX-I-1D714"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/173.svg b/36114-h/images/173.svg new file mode 100644 index 0000000..791f5b1 --- /dev/null +++ b/36114-h/images/173.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.375ex;" xmlns="http://www.w3.org/2000/svg" width="930.6px" height="607.6px" viewBox="0 -442 930.6 607.6" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-719-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path><path id="MJX-719-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-719-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-719-TEX-N-30"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/174.svg b/36114-h/images/174.svg new file mode 100644 index 0000000..843f2c5 --- /dev/null +++ b/36114-h/images/174.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="530px" height="442px" viewBox="0 -442 530 442" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-721-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-721-TEX-I-1D708"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/175.svg b/36114-h/images/175.svg new file mode 100644 index 0000000..b92a232 --- /dev/null +++ b/36114-h/images/175.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.657ex;" xmlns="http://www.w3.org/2000/svg" width="7176.1px" height="2460px" viewBox="0 -1727.8 7176.1 2460" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-724-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path><path id="MJX-724-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-724-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-724-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-724-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-724-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-724-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-724-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-724-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-724-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-724-TEX-I-1D708"></use></g><g transform="translate(807.8,0)"><use xlink:href="#MJX-724-TEX-N-3D"></use></g><g transform="translate(1863.6,0)"><g ><use xlink:href="#MJX-724-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-724-TEX-N-30"></use></g></g></g><g transform="translate(2794.1,0)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-724-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-724-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-724-TEX-I-1D463"></use></g><g transform="translate(518,289) scale(0.707)" ><g ><use xlink:href="#MJX-724-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-724-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-724-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(0,217.8)"><use xlink:href="#MJX-724-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1607.8"></rect></g><g transform="translate(6898.1,0)"><use xlink:href="#MJX-724-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/176.svg b/36114-h/images/176.svg new file mode 100644 index 0000000..866e88a --- /dev/null +++ b/36114-h/images/176.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="8755.3px" height="2459.4px" viewBox="0 -1509.9 8755.3 2459.4" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-725-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path><path id="MJX-725-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-725-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-725-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-725-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-725-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-725-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-725-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-725-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-725-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-725-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-725-TEX-I-1D708"></use></g><g transform="translate(807.8,0)"><use xlink:href="#MJX-725-TEX-N-3D"></use></g><g transform="translate(1863.6,0)"><g ><use xlink:href="#MJX-725-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-725-TEX-N-30"></use></g></g></g><g transform="translate(2960.8,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-725-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-725-TEX-N-31"></use></g><g transform="translate(1458.2,0)"><use xlink:href="#MJX-725-TEX-N-2212"></use></g><g transform="translate(2458.4,0)"><g ><g transform="translate(220,394) scale(0.707)"><use xlink:href="#MJX-725-TEX-N-31"></use></g><g transform="translate(220,-345) scale(0.707)"><use xlink:href="#MJX-725-TEX-N-32"></use></g><rect width="553.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(3252,0)"><g ></g></g><g transform="translate(3419,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-725-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-725-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-725-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-725-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g><g transform="translate(4780.6,0) translate(0 -0.5)"><use xlink:href="#MJX-725-TEX-S3-29"></use></g></g><g transform="translate(8477.3,0)"><use xlink:href="#MJX-725-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/177.svg b/36114-h/images/177.svg new file mode 100644 index 0000000..eb14544 --- /dev/null +++ b/36114-h/images/177.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="10295.9px" height="2459.4px" viewBox="0 -1509.9 10295.9 2459.4" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-726-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path><path id="MJX-726-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-726-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-726-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-726-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-726-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-726-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-726-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-726-TEX-I-1D714" d="M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z"></path><path id="MJX-726-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-726-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-726-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-726-TEX-I-1D708"></use></g><g transform="translate(807.8,0)"><use xlink:href="#MJX-726-TEX-N-3D"></use></g><g transform="translate(1863.6,0)"><g ><use xlink:href="#MJX-726-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-726-TEX-N-30"></use></g></g></g><g transform="translate(2960.8,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-726-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-726-TEX-N-31"></use></g><g transform="translate(1458.2,0)"><use xlink:href="#MJX-726-TEX-N-2212"></use></g><g transform="translate(2458.4,0)"><g transform="translate(404.8,676)"><use xlink:href="#MJX-726-TEX-N-31"></use></g><g transform="translate(220,-719.9)"><g ><use xlink:href="#MJX-726-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-726-TEX-N-32"></use></g></g></g><rect width="1069.6" height="60" x="120" y="220"></rect></g><g transform="translate(3768,0)"><g ></g></g><g transform="translate(3935,0)"><g transform="translate(220,676)"><g ><g ><use xlink:href="#MJX-726-TEX-I-1D714"></use></g><g transform="translate(655,363) scale(0.707)" ><g ><use xlink:href="#MJX-726-TEX-N-32"></use></g></g></g><g transform="translate(1058.6,0)"><g ><use xlink:href="#MJX-726-TEX-I-1D45F"></use></g><g transform="translate(484,363) scale(0.707)" ><g ><use xlink:href="#MJX-726-TEX-N-32"></use></g></g></g></g><g transform="translate(943.1,-686)"><use xlink:href="#MJX-726-TEX-N-32"></use></g><rect width="2146.1" height="60" x="120" y="220"></rect></g><g transform="translate(6321.1,0) translate(0 -0.5)"><use xlink:href="#MJX-726-TEX-S3-29"></use></g></g><g transform="translate(10017.9,0)"><use xlink:href="#MJX-726-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/178.svg b/36114-h/images/178.svg new file mode 100644 index 0000000..154b2ff --- /dev/null +++ b/36114-h/images/178.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="596px" height="899px" viewBox="0 -694 596 899" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-730-TEX-I-1D719" d="M409 688Q413 694 421 694H429H442Q448 688 448 686Q448 679 418 563Q411 535 404 504T392 458L388 442Q388 441 397 441T429 435T477 418Q521 397 550 357T579 260T548 151T471 65T374 11T279 -10H275L251 -105Q245 -128 238 -160Q230 -192 227 -198T215 -205H209Q189 -205 189 -198Q189 -193 211 -103L234 -11Q234 -10 226 -10Q221 -10 206 -8T161 6T107 36T62 89T43 171Q43 231 76 284T157 370T254 422T342 441Q347 441 348 445L378 567Q409 686 409 688ZM122 150Q122 116 134 91T167 53T203 35T237 27H244L337 404Q333 404 326 403T297 395T255 379T211 350T170 304Q152 276 137 237Q122 191 122 150ZM500 282Q500 320 484 347T444 385T405 400T381 404H378L332 217L284 29Q284 27 285 27Q293 27 317 33T357 47Q400 66 431 100T475 170T494 234T500 282Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-730-TEX-I-1D719"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/179.svg b/36114-h/images/179.svg new file mode 100644 index 0000000..796fdbb --- /dev/null +++ b/36114-h/images/179.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.552ex;" xmlns="http://www.w3.org/2000/svg" width="5371.7px" height="2195.9px" viewBox="0 -1509.9 5371.7 2195.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-728-TEX-I-1D719" d="M409 688Q413 694 421 694H429H442Q448 688 448 686Q448 679 418 563Q411 535 404 504T392 458L388 442Q388 441 397 441T429 435T477 418Q521 397 550 357T579 260T548 151T471 65T374 11T279 -10H275L251 -105Q245 -128 238 -160Q230 -192 227 -198T215 -205H209Q189 -205 189 -198Q189 -193 211 -103L234 -11Q234 -10 226 -10Q221 -10 206 -8T161 6T107 36T62 89T43 171Q43 231 76 284T157 370T254 422T342 441Q347 441 348 445L378 567Q409 686 409 688ZM122 150Q122 116 134 91T167 53T203 35T237 27H244L337 404Q333 404 326 403T297 395T255 379T211 350T170 304Q152 276 137 237Q122 191 122 150ZM500 282Q500 320 484 347T444 385T405 400T381 404H378L332 217L284 29Q284 27 285 27Q293 27 317 33T357 47Q400 66 431 100T475 170T494 234T500 282Z"></path><path id="MJX-728-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-728-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-728-TEX-I-1D714" d="M495 384Q495 406 514 424T555 443Q574 443 589 425T604 364Q604 334 592 278T555 155T483 38T377 -11Q297 -11 267 66Q266 68 260 61Q201 -11 125 -11Q15 -11 15 139Q15 230 56 325T123 434Q135 441 147 436Q160 429 160 418Q160 406 140 379T94 306T62 208Q61 202 61 187Q61 124 85 100T143 76Q201 76 245 129L253 137V156Q258 297 317 297Q348 297 348 261Q348 243 338 213T318 158L308 135Q309 133 310 129T318 115T334 97T358 83T393 76Q456 76 501 148T546 274Q546 305 533 325T508 357T495 384Z"></path><path id="MJX-728-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-728-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-728-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-728-TEX-I-1D719"></use></g><g transform="translate(873.8,0)"><use xlink:href="#MJX-728-TEX-N-3D"></use></g><g transform="translate(1929.6,0)"><use xlink:href="#MJX-728-TEX-N-2212"></use></g><g transform="translate(2707.6,0)"><g transform="translate(220,676)"><g ><g ><use xlink:href="#MJX-728-TEX-I-1D714"></use></g><g transform="translate(655,363) scale(0.707)" ><g ><use xlink:href="#MJX-728-TEX-N-32"></use></g></g></g><g transform="translate(1058.6,0)"><g ><use xlink:href="#MJX-728-TEX-I-1D45F"></use></g><g transform="translate(484,363) scale(0.707)" ><g ><use xlink:href="#MJX-728-TEX-N-32"></use></g></g></g></g><g transform="translate(943.1,-686)"><use xlink:href="#MJX-728-TEX-N-32"></use></g><rect width="2146.1" height="60" x="120" y="220"></rect></g><g transform="translate(5093.7,0)"><use xlink:href="#MJX-728-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/18.svg b/36114-h/images/18.svg new file mode 100644 index 0000000..d9feec6 --- /dev/null +++ b/36114-h/images/18.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="4468px" height="665px" viewBox="0 -583 4468 665" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-55-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-55-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-55-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-55-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-55-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-55-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-55-TEX-I-1D464"></use></g><g transform="translate(993.8,0)"><use xlink:href="#MJX-55-TEX-N-3D"></use></g><g transform="translate(2049.6,0)"><use xlink:href="#MJX-55-TEX-I-1D450"></use></g><g transform="translate(2704.8,0)"><use xlink:href="#MJX-55-TEX-N-2212"></use></g><g transform="translate(3705,0)"><use xlink:href="#MJX-55-TEX-I-1D463"></use></g><g transform="translate(4190,0)"><use xlink:href="#MJX-55-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/180.svg b/36114-h/images/180.svg new file mode 100644 index 0000000..b7b992a --- /dev/null +++ b/36114-h/images/180.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="7742.8px" height="2399px" viewBox="0 -1449.5 7742.8 2399" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-729-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path><path id="MJX-729-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-729-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-729-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-729-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-729-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-729-TEX-I-1D719" d="M409 688Q413 694 421 694H429H442Q448 688 448 686Q448 679 418 563Q411 535 404 504T392 458L388 442Q388 441 397 441T429 435T477 418Q521 397 550 357T579 260T548 151T471 65T374 11T279 -10H275L251 -105Q245 -128 238 -160Q230 -192 227 -198T215 -205H209Q189 -205 189 -198Q189 -193 211 -103L234 -11Q234 -10 226 -10Q221 -10 206 -8T161 6T107 36T62 89T43 171Q43 231 76 284T157 370T254 422T342 441Q347 441 348 445L378 567Q409 686 409 688ZM122 150Q122 116 134 91T167 53T203 35T237 27H244L337 404Q333 404 326 403T297 395T255 379T211 350T170 304Q152 276 137 237Q122 191 122 150ZM500 282Q500 320 484 347T444 385T405 400T381 404H378L332 217L284 29Q284 27 285 27Q293 27 317 33T357 47Q400 66 431 100T475 170T494 234T500 282Z"></path><path id="MJX-729-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-729-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-729-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-729-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-729-TEX-I-1D708"></use></g><g transform="translate(807.8,0)"><use xlink:href="#MJX-729-TEX-N-3D"></use></g><g transform="translate(1863.6,0)"><g ><use xlink:href="#MJX-729-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-729-TEX-N-30"></use></g></g></g><g transform="translate(2960.8,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-729-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-729-TEX-N-31"></use></g><g transform="translate(1458.2,0)"><use xlink:href="#MJX-729-TEX-N-2B"></use></g><g transform="translate(2458.4,0)"><g transform="translate(356.8,676)"><use xlink:href="#MJX-729-TEX-I-1D719"></use></g><g transform="translate(220,-719.9)"><g ><use xlink:href="#MJX-729-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-729-TEX-N-32"></use></g></g></g><rect width="1069.6" height="60" x="120" y="220"></rect></g><g transform="translate(3768,0) translate(0 -0.5)"><use xlink:href="#MJX-729-TEX-S3-29"></use></g></g><g transform="translate(7464.8,0)"><use xlink:href="#MJX-729-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/181.svg b/36114-h/images/181.svg new file mode 100644 index 0000000..cfc5e58 --- /dev/null +++ b/36114-h/images/181.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.577ex;" xmlns="http://www.w3.org/2000/svg" width="5087.6px" height="2056px" viewBox="0 -1359 5087.6 2056" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-731-TEX-I-1D719" d="M409 688Q413 694 421 694H429H442Q448 688 448 686Q448 679 418 563Q411 535 404 504T392 458L388 442Q388 441 397 441T429 435T477 418Q521 397 550 357T579 260T548 151T471 65T374 11T279 -10H275L251 -105Q245 -128 238 -160Q230 -192 227 -198T215 -205H209Q189 -205 189 -198Q189 -193 211 -103L234 -11Q234 -10 226 -10Q221 -10 206 -8T161 6T107 36T62 89T43 171Q43 231 76 284T157 370T254 422T342 441Q347 441 348 445L378 567Q409 686 409 688ZM122 150Q122 116 134 91T167 53T203 35T237 27H244L337 404Q333 404 326 403T297 395T255 379T211 350T170 304Q152 276 137 237Q122 191 122 150ZM500 282Q500 320 484 347T444 385T405 400T381 404H378L332 217L284 29Q284 27 285 27Q293 27 317 33T357 47Q400 66 431 100T475 170T494 234T500 282Z"></path><path id="MJX-731-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-731-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-731-TEX-I-1D43E" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z"></path><path id="MJX-731-TEX-I-1D440" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path><path id="MJX-731-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-731-TEX-I-1D719"></use></g><g transform="translate(873.8,0)"><use xlink:href="#MJX-731-TEX-N-3D"></use></g><g transform="translate(1929.6,0)"><use xlink:href="#MJX-731-TEX-N-2212"></use></g><g transform="translate(2707.6,0)"><use xlink:href="#MJX-731-TEX-I-1D43E"></use></g><g transform="translate(3596.6,0)"><g ><g transform="translate(220,676)"><use xlink:href="#MJX-731-TEX-I-1D440"></use></g><g transform="translate(520,-686)"><use xlink:href="#MJX-731-TEX-I-1D45F"></use></g><rect width="1251" height="60" x="120" y="220"></rect></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/182.svg b/36114-h/images/182.svg new file mode 100644 index 0000000..42a3f81 --- /dev/null +++ b/36114-h/images/182.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="889px" height="683px" viewBox="0 -683 889 683" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-732-TEX-I-1D43E" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-732-TEX-I-1D43E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/183.svg b/36114-h/images/183.svg new file mode 100644 index 0000000..e74b133 --- /dev/null +++ b/36114-h/images/183.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.927ex;" xmlns="http://www.w3.org/2000/svg" width="7721.6px" height="2210.6px" viewBox="0 -1359 7721.6 2210.6" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-734-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path><path id="MJX-734-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-734-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-734-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-734-TEX-I-1D43E" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z"></path><path id="MJX-734-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-734-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-734-TEX-I-1D440" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path><path id="MJX-734-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-734-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(220,676)"><g ><g ><use xlink:href="#MJX-734-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-734-TEX-N-30"></use></g></g></g><g transform="translate(1152.8,0)"><use xlink:href="#MJX-734-TEX-N-2212"></use></g><g transform="translate(2153,0)"><use xlink:href="#MJX-734-TEX-I-1D708"></use></g></g><g transform="translate(1096.2,-686)"><g ><use xlink:href="#MJX-734-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-734-TEX-N-30"></use></g></g></g><rect width="2883" height="60" x="120" y="220"></rect></g><g transform="translate(3400.8,0)"><use xlink:href="#MJX-734-TEX-N-3D"></use></g><g transform="translate(4456.6,0)"><g transform="translate(220,676)"><use xlink:href="#MJX-734-TEX-I-1D43E"></use></g><g transform="translate(229.7,-719.9)"><g ><use xlink:href="#MJX-734-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-734-TEX-N-32"></use></g></g></g><rect width="1089" height="60" x="120" y="220"></rect></g><g transform="translate(5785.6,0)"><g ></g></g><g transform="translate(5952.6,0)"><g transform="translate(220,676)"><use xlink:href="#MJX-734-TEX-I-1D440"></use></g><g transform="translate(520,-686)"><use xlink:href="#MJX-734-TEX-I-1D45F"></use></g><rect width="1251" height="60" x="120" y="220"></rect></g><g transform="translate(7443.6,0)"><use xlink:href="#MJX-734-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/184.svg b/36114-h/images/184.svg new file mode 100644 index 0000000..be73cb0 --- /dev/null +++ b/36114-h/images/184.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.927ex;" xmlns="http://www.w3.org/2000/svg" width="7721.6px" height="2210.6px" viewBox="0 -1359 7721.6 2210.6" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-735-TEX-I-1D708" d="M74 431Q75 431 146 436T219 442Q231 442 231 434Q231 428 185 241L137 51H140L150 55Q161 59 177 67T214 86T261 119T312 165Q410 264 445 394Q458 442 496 442Q509 442 519 434T530 411Q530 390 516 352T469 262T388 162T267 70T106 5Q81 -2 71 -2Q66 -2 59 -1T51 1Q45 5 45 11Q45 13 88 188L132 364Q133 377 125 380T86 385H65Q59 391 59 393T61 412Q65 431 74 431Z"></path><path id="MJX-735-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-735-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-735-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-735-TEX-I-1D43E" d="M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z"></path><path id="MJX-735-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-735-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-735-TEX-I-1D440" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path><path id="MJX-735-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-735-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(220,676)"><g ><g ><use xlink:href="#MJX-735-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-735-TEX-N-30"></use></g></g></g><g transform="translate(1152.8,0)"><use xlink:href="#MJX-735-TEX-N-2212"></use></g><g transform="translate(2153,0)"><use xlink:href="#MJX-735-TEX-I-1D708"></use></g></g><g transform="translate(1096.2,-686)"><g ><use xlink:href="#MJX-735-TEX-I-1D708"></use></g><g transform="translate(527,-150) scale(0.707)" ><g ><use xlink:href="#MJX-735-TEX-N-30"></use></g></g></g><rect width="2883" height="60" x="120" y="220"></rect></g><g transform="translate(3400.8,0)"><use xlink:href="#MJX-735-TEX-N-3D"></use></g><g transform="translate(4456.6,0)"><g transform="translate(220,676)"><use xlink:href="#MJX-735-TEX-I-1D43E"></use></g><g transform="translate(229.7,-719.9)"><g ><use xlink:href="#MJX-735-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-735-TEX-N-32"></use></g></g></g><rect width="1089" height="60" x="120" y="220"></rect></g><g transform="translate(5785.6,0)"><g ></g></g><g transform="translate(5952.6,0)"><g transform="translate(220,676)"><use xlink:href="#MJX-735-TEX-I-1D440"></use></g><g transform="translate(520,-686)"><use xlink:href="#MJX-735-TEX-I-1D45F"></use></g><rect width="1251" height="60" x="120" y="220"></rect></g><g transform="translate(7443.6,0)"><use xlink:href="#MJX-735-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/19.svg b/36114-h/images/19.svg new file mode 100644 index 0000000..c173015 --- /dev/null +++ b/36114-h/images/19.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="1051px" height="683px" viewBox="0 -683 1051 683" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-735-TEX-I-1D440" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-735-TEX-I-1D440"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/2.svg b/36114-h/images/2.svg new file mode 100644 index 0000000..35a201d --- /dev/null +++ b/36114-h/images/2.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="759px" height="683px" viewBox="0 -683 759 683" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-495-TEX-I-1D435" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-495-TEX-I-1D435"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/20.svg b/36114-h/images/20.svg new file mode 100644 index 0000000..1b212ac --- /dev/null +++ b/36114-h/images/20.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1500px" height="737px" viewBox="0 -715 1500 737" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-65-TEX-N-39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"></path><path id="MJX-65-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-65-TEX-N-B0" d="M147 628Q147 669 179 692T244 715Q298 715 325 689T352 629Q352 592 323 567T249 542Q202 542 175 567T147 628ZM313 628Q313 660 300 669T259 678H253Q248 678 242 678T234 679Q217 679 207 674T192 659T188 644T187 629Q187 600 198 590Q210 579 250 579H265Q279 579 288 581T305 595T313 628Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-65-TEX-N-39"></use><use xlink:href="#MJX-65-TEX-N-30" transform="translate(500,0)"></use></g><g transform="translate(1000,0)"><g ><use xlink:href="#MJX-65-TEX-N-B0"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/21.svg b/36114-h/images/21.svg new file mode 100644 index 0000000..b662a66 --- /dev/null +++ b/36114-h/images/21.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="3994.6px" height="727px" viewBox="0 -716 3994.6 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-71-TEX-I-1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path><path id="MJX-71-TEX-N-27F6" d="M84 237T84 250T98 270H1444Q1328 357 1301 493Q1301 494 1301 496T1300 499Q1300 511 1317 511H1320Q1329 511 1332 510T1338 506T1341 497T1344 481T1352 456Q1374 389 1425 336T1544 261Q1553 258 1553 250Q1553 244 1548 241T1524 231T1486 212Q1445 186 1415 152T1370 85T1349 35T1341 4Q1339 -6 1336 -8T1320 -11Q1300 -11 1300 0Q1300 7 1305 25Q1337 151 1444 230H98Q84 237 84 250Z"></path><path id="MJX-71-TEX-I-1D440" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-71-TEX-I-1D434"></use></g><g transform="translate(1027.8,0)"><use xlink:href="#MJX-71-TEX-N-27F6"></use></g><g transform="translate(2943.6,0)"><use xlink:href="#MJX-71-TEX-I-1D440"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/22.svg b/36114-h/images/22.svg new file mode 100644 index 0000000..366fadd --- /dev/null +++ b/36114-h/images/22.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="4003.6px" height="694px" viewBox="0 -683 4003.6 694" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-72-TEX-I-1D435" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"></path><path id="MJX-72-TEX-N-27F6" d="M84 237T84 250T98 270H1444Q1328 357 1301 493Q1301 494 1301 496T1300 499Q1300 511 1317 511H1320Q1329 511 1332 510T1338 506T1341 497T1344 481T1352 456Q1374 389 1425 336T1544 261Q1553 258 1553 250Q1553 244 1548 241T1524 231T1486 212Q1445 186 1415 152T1370 85T1349 35T1341 4Q1339 -6 1336 -8T1320 -11Q1300 -11 1300 0Q1300 7 1305 25Q1337 151 1444 230H98Q84 237 84 250Z"></path><path id="MJX-72-TEX-I-1D440" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-72-TEX-I-1D435"></use></g><g transform="translate(1036.8,0)"><use xlink:href="#MJX-72-TEX-N-27F6"></use></g><g transform="translate(2952.6,0)"><use xlink:href="#MJX-72-TEX-I-1D440"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/23.svg b/36114-h/images/23.svg new file mode 100644 index 0000000..153e8cc --- /dev/null +++ b/36114-h/images/23.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="3651.6px" height="727px" viewBox="0 -716 3651.6 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-93-TEX-I-1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path><path id="MJX-93-TEX-N-27F6" d="M84 237T84 250T98 270H1444Q1328 357 1301 493Q1301 494 1301 496T1300 499Q1300 511 1317 511H1320Q1329 511 1332 510T1338 506T1341 497T1344 481T1352 456Q1374 389 1425 336T1544 261Q1553 258 1553 250Q1553 244 1548 241T1524 231T1486 212Q1445 186 1415 152T1370 85T1349 35T1341 4Q1339 -6 1336 -8T1320 -11Q1300 -11 1300 0Q1300 7 1305 25Q1337 151 1444 230H98Q84 237 84 250Z"></path><path id="MJX-93-TEX-N-42" d="M131 622Q124 629 120 631T104 634T61 637H28V683H229H267H346Q423 683 459 678T531 651Q574 627 599 590T624 512Q624 461 583 419T476 360L466 357Q539 348 595 302T651 187Q651 119 600 67T469 3Q456 1 242 0H28V46H61Q103 47 112 49T131 61V622ZM511 513Q511 560 485 594T416 636Q415 636 403 636T371 636T333 637Q266 637 251 636T232 628Q229 624 229 499V374H312L396 375L406 377Q410 378 417 380T442 393T474 417T499 456T511 513ZM537 188Q537 239 509 282T430 336L329 337H229V200V116Q229 57 234 52Q240 47 334 47H383Q425 47 443 53Q486 67 511 104T537 188Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-93-TEX-I-1D434"></use></g><g transform="translate(1027.8,0)"><use xlink:href="#MJX-93-TEX-N-27F6"></use></g><g transform="translate(2943.6,0)"><g ><use xlink:href="#MJX-93-TEX-N-42"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/24.svg b/36114-h/images/24.svg new file mode 100644 index 0000000..945e39e --- /dev/null +++ b/36114-h/images/24.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="3702.6px" height="727px" viewBox="0 -716 3702.6 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-99-TEX-I-1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path><path id="MJX-99-TEX-N-27F6" d="M84 237T84 250T98 270H1444Q1328 357 1301 493Q1301 494 1301 496T1300 499Q1300 511 1317 511H1320Q1329 511 1332 510T1338 506T1341 497T1344 481T1352 456Q1374 389 1425 336T1544 261Q1553 258 1553 250Q1553 244 1548 241T1524 231T1486 212Q1445 186 1415 152T1370 85T1349 35T1341 4Q1339 -6 1336 -8T1320 -11Q1300 -11 1300 0Q1300 7 1305 25Q1337 151 1444 230H98Q84 237 84 250Z"></path><path id="MJX-99-TEX-I-1D435" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-99-TEX-I-1D434"></use></g><g transform="translate(1027.8,0)"><use xlink:href="#MJX-99-TEX-N-27F6"></use></g><g transform="translate(2943.6,0)"><use xlink:href="#MJX-99-TEX-I-1D435"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/25.svg b/36114-h/images/25.svg new file mode 100644 index 0000000..c736382 --- /dev/null +++ b/36114-h/images/25.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="361px" height="637px" viewBox="0 -626 361 637" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-672-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-672-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/26.svg b/36114-h/images/26.svg new file mode 100644 index 0000000..d76bf35 --- /dev/null +++ b/36114-h/images/26.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="572px" height="453px" viewBox="0 -442 572 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-667-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-667-TEX-I-1D465"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/27.svg b/36114-h/images/27.svg new file mode 100644 index 0000000..68ccc48 --- /dev/null +++ b/36114-h/images/27.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="490px" height="647px" viewBox="0 -442 490 647" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-668-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-668-TEX-I-1D466"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/28.svg b/36114-h/images/28.svg new file mode 100644 index 0000000..87bca55 --- /dev/null +++ b/36114-h/images/28.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="465px" height="453px" viewBox="0 -442 465 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-669-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-669-TEX-I-1D467"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/29.svg b/36114-h/images/29.svg new file mode 100644 index 0000000..3828d64 --- /dev/null +++ b/36114-h/images/29.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -12.409ex;" xmlns="http://www.w3.org/2000/svg" width="7088.5px" height="11469.9px" viewBox="0 -5984.9 7088.5 11469.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-160-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-160-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-160-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-160-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-160-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-160-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-160-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-160-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-160-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-160-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-160-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-160-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-160-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-160-TEX-N-B7" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path id="MJX-160-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,4682.9)"><g ><g ><g ><use xlink:href="#MJX-160-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-160-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-160-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(951.8,676)"><g ><use xlink:href="#MJX-160-TEX-I-1D465"></use></g><g transform="translate(794.2,0)"><use xlink:href="#MJX-160-TEX-N-2212"></use></g><g transform="translate(1794.4,0)"><use xlink:href="#MJX-160-TEX-I-1D463"></use></g><g transform="translate(2279.4,0)"><use xlink:href="#MJX-160-TEX-I-1D461"></use></g></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-160-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-160-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-160-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-160-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-160-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-160-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-160-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(5877.6,0)"><use xlink:href="#MJX-160-TEX-N-2C"></use></g></g></g><g transform="translate(0,1154)"><g transform="translate(82,0)"><g ><g ><use xlink:href="#MJX-160-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)"><use xlink:href="#MJX-160-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-160-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-160-TEX-I-1D466"></use></g><g transform="translate(1823.6,0)"><use xlink:href="#MJX-160-TEX-N-2C"></use></g></g></g><g transform="translate(0,-205)"><g transform="translate(107,0)"><g ><g ><use xlink:href="#MJX-160-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)"><use xlink:href="#MJX-160-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-160-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-160-TEX-I-1D467"></use></g><g transform="translate(1798.6,0)"><use xlink:href="#MJX-160-TEX-N-2C"></use></g></g></g><g transform="translate(0,-3064.9)"><g transform="translate(211,0)"><g ><g ><use xlink:href="#MJX-160-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-160-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-160-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(220,1190.9)"><g ><use xlink:href="#MJX-160-TEX-I-1D461"></use></g><g transform="translate(583.2,0)"><use xlink:href="#MJX-160-TEX-N-2212"></use></g><g transform="translate(1583.4,0)"><g ><g transform="translate(412.3,676)"><use xlink:href="#MJX-160-TEX-I-1D463"></use></g><g transform="translate(220,-719.9)"><g ><use xlink:href="#MJX-160-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-160-TEX-N-32"></use></g></g></g><rect width="1069.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(3115.2,0)"><use xlink:href="#MJX-160-TEX-N-B7"></use></g><g transform="translate(3615.4,0)"><use xlink:href="#MJX-160-TEX-I-1D465"></use></g></g><g transform="translate(261.7,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-160-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-160-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-160-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-160-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-160-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-160-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-160-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4387.4" height="60" x="120" y="220"></rect></g><g transform="translate(5961,0)"><use xlink:href="#MJX-160-TEX-N-2E"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/3.svg b/36114-h/images/3.svg new file mode 100644 index 0000000..c2b979f --- /dev/null +++ b/36114-h/images/3.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="760px" height="727px" viewBox="0 -705 760 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-84-TEX-I-1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-84-TEX-I-1D436"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/30.svg b/36114-h/images/30.svg new file mode 100644 index 0000000..36ab799 --- /dev/null +++ b/36114-h/images/30.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.244ex;" xmlns="http://www.w3.org/2000/svg" width="5101.5px" height="5135.9px" viewBox="0 -2818 5101.5 5135.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-161-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-161-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-161-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-161-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-161-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-161-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-161-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-161-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-161-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-161-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,2009)"><g ><g ><g ><use xlink:href="#MJX-161-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-161-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-161-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-161-TEX-I-1D465"></use></g><g transform="translate(2127.8,0)"><use xlink:href="#MJX-161-TEX-N-2212"></use></g><g transform="translate(3128,0)"><use xlink:href="#MJX-161-TEX-I-1D463"></use></g><g transform="translate(3613,0)"><use xlink:href="#MJX-161-TEX-I-1D461"></use></g><g transform="translate(3974,0)"><use xlink:href="#MJX-161-TEX-N-2C"></use></g></g></g><g transform="translate(0,650)"><g transform="translate(82,0)"><g ><g ><use xlink:href="#MJX-161-TEX-I-1D466"></use></g><g transform="translate(523,413) scale(0.707)"><use xlink:href="#MJX-161-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-161-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-161-TEX-I-1D466"></use></g><g transform="translate(1823.6,0)"><use xlink:href="#MJX-161-TEX-N-2C"></use></g></g></g><g transform="translate(0,-709)"><g transform="translate(107,0)"><g ><g ><use xlink:href="#MJX-161-TEX-I-1D467"></use></g><g transform="translate(498,413) scale(0.707)"><use xlink:href="#MJX-161-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-161-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-161-TEX-I-1D467"></use></g><g transform="translate(1798.6,0)"><use xlink:href="#MJX-161-TEX-N-2C"></use></g></g></g><g transform="translate(0,-2068)"><g transform="translate(211,0)"><g ><g ><use xlink:href="#MJX-161-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-161-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-161-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-161-TEX-I-1D461"></use></g><g transform="translate(1694.6,0)"><use xlink:href="#MJX-161-TEX-N-2E"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/31.svg b/36114-h/images/31.svg new file mode 100644 index 0000000..a3ac07b --- /dev/null +++ b/36114-h/images/31.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="2977.6px" height="820px" viewBox="0 -626 2977.6 820" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-166-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-166-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-166-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-166-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-166-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-166-TEX-I-1D465"></use></g><g transform="translate(849.8,0)"><use xlink:href="#MJX-166-TEX-N-3D"></use></g><g transform="translate(1905.6,0)"><use xlink:href="#MJX-166-TEX-I-1D450"></use></g><g transform="translate(2338.6,0)"><use xlink:href="#MJX-166-TEX-I-1D461"></use></g><g transform="translate(2699.6,0)"><use xlink:href="#MJX-166-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/32.svg b/36114-h/images/32.svg new file mode 100644 index 0000000..0b721dc --- /dev/null +++ b/36114-h/images/32.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="794px" height="637px" viewBox="0 -626 794 637" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-173-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-173-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-173-TEX-I-1D450"></use></g><g transform="translate(433,0)"><use xlink:href="#MJX-173-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/33.svg b/36114-h/images/33.svg new file mode 100644 index 0000000..31fd9ac --- /dev/null +++ b/36114-h/images/33.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -9.51ex;" xmlns="http://www.w3.org/2000/svg" width="7103.5px" height="8906.5px" viewBox="0 -4703.3 7103.5 8906.5" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-174-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-174-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-174-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-174-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-174-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-174-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-174-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-174-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-174-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-174-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-174-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-174-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-174-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-174-TEX-LO-28" d="M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z"></path><path id="MJX-174-TEX-LO-29" d="M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,3243.3)"><g ><g ><g ><use xlink:href="#MJX-174-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-174-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-174-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(632.3,710)"><g ><use xlink:href="#MJX-174-TEX-N-28"></use></g><g transform="translate(389,0)"><use xlink:href="#MJX-174-TEX-I-1D450"></use></g><g transform="translate(1044.2,0)"><use xlink:href="#MJX-174-TEX-N-2212"></use></g><g transform="translate(2044.4,0)"><use xlink:href="#MJX-174-TEX-I-1D463"></use></g><g transform="translate(2529.4,0)"><use xlink:href="#MJX-174-TEX-N-29"></use></g><g transform="translate(2918.4,0)"><use xlink:href="#MJX-174-TEX-I-1D461"></use></g></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-174-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-174-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-174-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-174-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-174-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-174-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-174-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(5877.6,0)"><use xlink:href="#MJX-174-TEX-N-2C"></use></g></g></g><g transform="translate(0,-1783.2)"><g transform="translate(211,0)"><g ><g ><use xlink:href="#MJX-174-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-174-TEX-V-2032"></use></g></g></g><g transform="translate(849.5,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-174-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(220,1157)"><g ><g transform="translate(0 -0.5)"><use xlink:href="#MJX-174-TEX-LO-28"></use></g><g transform="translate(597,0)"><use xlink:href="#MJX-174-TEX-N-31"></use></g><g transform="translate(1319.2,0)"><use xlink:href="#MJX-174-TEX-N-2212"></use></g><g transform="translate(2319.4,0)"><g ><g transform="translate(220,676)"><use xlink:href="#MJX-174-TEX-I-1D463"></use></g><g transform="translate(246,-686)"><use xlink:href="#MJX-174-TEX-I-1D450"></use></g><rect width="685" height="60" x="120" y="220"></rect></g></g><g transform="translate(3244.4,0) translate(0 -0.5)"><use xlink:href="#MJX-174-TEX-LO-29"></use></g></g><g transform="translate(3841.4,0)"><use xlink:href="#MJX-174-TEX-I-1D461"></use></g></g><g transform="translate(269.2,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-174-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-174-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-174-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-174-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-174-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-174-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-174-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4402.4" height="60" x="120" y="220"></rect></g><g transform="translate(5976,0)"><use xlink:href="#MJX-174-TEX-N-2C"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/34.svg b/36114-h/images/34.svg new file mode 100644 index 0000000..1cf5b52 --- /dev/null +++ b/36114-h/images/34.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="3254.5px" height="891px" viewBox="0 -809 3254.5 891" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-175-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-175-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-175-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-175-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-175-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-175-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-175-TEX-V-2032"></use></g></g><g transform="translate(1127.2,0)"><use xlink:href="#MJX-175-TEX-N-3D"></use></g><g transform="translate(2183,0)"><use xlink:href="#MJX-175-TEX-I-1D450"></use></g><g transform="translate(2616,0)"><g ><use xlink:href="#MJX-175-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-175-TEX-V-2032"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/35.svg b/36114-h/images/35.svg new file mode 100644 index 0000000..946e021 --- /dev/null +++ b/36114-h/images/35.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2683px" height="841px" viewBox="0 -759 2683 841" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-589-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-589-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-589-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-589-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-589-TEX-I-1D465"></use></g><g transform="translate(605,363) scale(0.707)"><use xlink:href="#MJX-589-TEX-V-2032"></use></g></g><g transform="translate(1127.2,0)"><use xlink:href="#MJX-589-TEX-N-3D"></use></g><g transform="translate(2183,0)"><use xlink:href="#MJX-589-TEX-N-30"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/36.svg b/36114-h/images/36.svg new file mode 100644 index 0000000..f350b5e --- /dev/null +++ b/36114-h/images/36.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2683px" height="841px" viewBox="0 -759 2683 841" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-182-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-182-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-182-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-182-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-182-TEX-I-1D465"></use></g><g transform="translate(605,363) scale(0.707)"><use xlink:href="#MJX-182-TEX-V-2032"></use></g></g><g transform="translate(1127.2,0)"><use xlink:href="#MJX-182-TEX-N-3D"></use></g><g transform="translate(2183,0)"><use xlink:href="#MJX-182-TEX-N-31"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/37.svg b/36114-h/images/37.svg new file mode 100644 index 0000000..f471d6d --- /dev/null +++ b/36114-h/images/37.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2194.6px" height="748px" viewBox="0 -666 2194.6 748" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-639-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-639-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-639-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-639-TEX-I-1D461"></use></g><g transform="translate(638.8,0)"><use xlink:href="#MJX-639-TEX-N-3D"></use></g><g transform="translate(1694.6,0)"><use xlink:href="#MJX-639-TEX-N-30"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/38.svg b/36114-h/images/38.svg new file mode 100644 index 0000000..851c069 --- /dev/null +++ b/36114-h/images/38.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.339ex;" xmlns="http://www.w3.org/2000/svg" width="13077.3px" height="5220px" viewBox="0 -2860 13077.3 5220" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-188-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-188-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-188-TEX-N-62" d="M307 -11Q234 -11 168 55L158 37Q156 34 153 28T147 17T143 10L138 1L118 0H98V298Q98 599 97 603Q94 622 83 628T38 637H20V660Q20 683 22 683L32 684Q42 685 61 686T98 688Q115 689 135 690T165 693T176 694H179V543Q179 391 180 391L183 394Q186 397 192 401T207 411T228 421T254 431T286 439T323 442Q401 442 461 379T522 216Q522 115 458 52T307 -11ZM182 98Q182 97 187 90T196 79T206 67T218 55T233 44T250 35T271 29T295 26Q330 26 363 46T412 113Q424 148 424 212Q424 287 412 323Q385 405 300 405Q270 405 239 390T188 347L182 339V98Z"></path><path id="MJX-188-TEX-N-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z"></path><path id="MJX-188-TEX-N-67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path><path id="MJX-188-TEX-N-69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path id="MJX-188-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-188-TEX-N-20" d=""></path><path id="MJX-188-TEX-N-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path id="MJX-188-TEX-N-66" d="M273 0Q255 3 146 3Q43 3 34 0H26V46H42Q70 46 91 49Q99 52 103 60Q104 62 104 224V385H33V431H104V497L105 564L107 574Q126 639 171 668T266 704Q267 704 275 704T289 705Q330 702 351 679T372 627Q372 604 358 590T321 576T284 590T270 627Q270 647 288 667H284Q280 668 273 668Q245 668 223 647T189 592Q183 572 182 497V431H293V385H185V225Q185 63 186 61T189 57T194 54T199 51T206 49T213 48T222 47T231 47T241 46T251 46H282V0H273Z"></path><path id="MJX-188-TEX-N-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path id="MJX-188-TEX-N-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path><path id="MJX-188-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-188-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-188-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-188-TEX-N-B7" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path id="MJX-188-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-188-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-188-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-188-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-188-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-188-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-188-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,1132.2)"><g ><g ><g ><use xlink:href="#MJX-188-TEX-I-1D465"></use></g><g transform="translate(605,-176.7) scale(0.707)" ><g ><use xlink:href="#MJX-188-TEX-N-28"></use><use xlink:href="#MJX-188-TEX-N-62" transform="translate(389,0)"></use><use xlink:href="#MJX-188-TEX-N-65" transform="translate(945,0)"></use><use xlink:href="#MJX-188-TEX-N-67" transform="translate(1389,0)"></use><use xlink:href="#MJX-188-TEX-N-69" transform="translate(1889,0)"></use><use xlink:href="#MJX-188-TEX-N-6E" transform="translate(2167,0)"></use><use xlink:href="#MJX-188-TEX-N-6E" transform="translate(2723,0)"></use><use xlink:href="#MJX-188-TEX-N-69" transform="translate(3279,0)"></use><use xlink:href="#MJX-188-TEX-N-6E" transform="translate(3557,0)"></use><use xlink:href="#MJX-188-TEX-N-67" transform="translate(4113,0)"></use><use xlink:href="#MJX-188-TEX-N-20" transform="translate(4613,0)"></use><use xlink:href="#MJX-188-TEX-N-6F" transform="translate(4863,0)"></use><use xlink:href="#MJX-188-TEX-N-66" transform="translate(5363,0)"></use><use xlink:href="#MJX-188-TEX-N-20" transform="translate(5669,0)"></use><use xlink:href="#MJX-188-TEX-N-72" transform="translate(5919,0)"></use><use xlink:href="#MJX-188-TEX-N-6F" transform="translate(6311,0)"></use><use xlink:href="#MJX-188-TEX-N-64" transform="translate(6811,0)"></use><use xlink:href="#MJX-188-TEX-N-29" transform="translate(7367,0)"></use></g></g></g></g><g transform="translate(6139.3,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-188-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-188-TEX-N-30"></use></g><g transform="translate(2055.8,0)"><use xlink:href="#MJX-188-TEX-N-B7"></use></g><g transform="translate(2556,0)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-188-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-188-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-188-TEX-I-1D463"></use></g><g transform="translate(518,289) scale(0.707)" ><g ><use xlink:href="#MJX-188-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-188-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-188-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(0,217.8)"><use xlink:href="#MJX-188-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1607.8"></rect></g><g transform="translate(6660,0)"><use xlink:href="#MJX-188-TEX-N-2C"></use></g></g></g><g transform="translate(0,-1627.8)"><g transform="translate(1886.6,0)"><g ><g ><use xlink:href="#MJX-188-TEX-I-1D465"></use></g><g transform="translate(605,-176.7) scale(0.707)" ><g ><use xlink:href="#MJX-188-TEX-N-28"></use><use xlink:href="#MJX-188-TEX-N-65" transform="translate(389,0)"></use><use xlink:href="#MJX-188-TEX-N-6E" transform="translate(833,0)"></use><use xlink:href="#MJX-188-TEX-N-64" transform="translate(1389,0)"></use><use xlink:href="#MJX-188-TEX-N-20" transform="translate(1945,0)"></use><use xlink:href="#MJX-188-TEX-N-6F" transform="translate(2195,0)"></use><use xlink:href="#MJX-188-TEX-N-66" transform="translate(2695,0)"></use><use xlink:href="#MJX-188-TEX-N-20" transform="translate(3001,0)"></use><use xlink:href="#MJX-188-TEX-N-72" transform="translate(3251,0)"></use><use xlink:href="#MJX-188-TEX-N-6F" transform="translate(3643,0)"></use><use xlink:href="#MJX-188-TEX-N-64" transform="translate(4143,0)"></use><use xlink:href="#MJX-188-TEX-N-29" transform="translate(4699,0)"></use></g></g></g></g><g transform="translate(6139.3,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-188-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-188-TEX-N-31"></use></g><g transform="translate(2055.8,0)"><use xlink:href="#MJX-188-TEX-N-B7"></use></g><g transform="translate(2556,0)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-188-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-188-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-188-TEX-I-1D463"></use></g><g transform="translate(518,289) scale(0.707)" ><g ><use xlink:href="#MJX-188-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-188-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-188-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(0,217.8)"><use xlink:href="#MJX-188-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1607.8"></rect></g><g transform="translate(6660,0)"><use xlink:href="#MJX-188-TEX-N-2C"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/39.svg b/36114-h/images/39.svg new file mode 100644 index 0000000..121165e --- /dev/null +++ b/36114-h/images/39.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.681ex;" xmlns="http://www.w3.org/2000/svg" width="4104px" height="2460px" viewBox="0 -1717 4104 2460" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-291-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-291-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-291-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-291-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-291-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-291-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-291-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-291-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-291-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-291-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-291-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-291-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-291-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/4.svg b/36114-h/images/4.svg new file mode 100644 index 0000000..004f3c8 --- /dev/null +++ b/36114-h/images/4.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="1509px" height="716px" viewBox="0 -716 1509 716" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-64-TEX-I-1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path><path id="MJX-64-TEX-I-1D435" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-64-TEX-I-1D434"></use></g><g transform="translate(750,0)"><use xlink:href="#MJX-64-TEX-I-1D435"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/40.svg b/36114-h/images/40.svg new file mode 100644 index 0000000..6b1fd06 --- /dev/null +++ b/36114-h/images/40.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.628ex;" xmlns="http://www.w3.org/2000/svg" width="5033.6px" height="1260px" viewBox="0 -982.5 5033.6 1260" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-203-TEX-SO-221A" d="M263 249Q264 249 315 130T417 -108T470 -228L725 302Q981 837 982 839Q989 850 1001 850Q1008 850 1013 844T1020 832V826L741 243Q645 43 540 -176Q479 -303 469 -324T453 -348Q449 -350 436 -350L424 -349L315 -96Q206 156 205 156L171 130Q138 104 137 104L111 130L263 249Z"></path><path id="MJX-203-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-203-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-203-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-203-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-203-TEX-N-2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path><path id="MJX-203-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-203-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-203-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><use xlink:href="#MJX-203-TEX-I-1D463"></use></g><g transform="translate(518,289) scale(0.707)" ><g ><use xlink:href="#MJX-203-TEX-N-32"></use></g></g></g><g transform="translate(2644,0)"><g ><use xlink:href="#MJX-203-TEX-N-2F"></use></g></g><g transform="translate(3144,0)"><g ><use xlink:href="#MJX-203-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-203-TEX-N-32"></use></g></g></g></g><g transform="translate(0,72.5)"><use xlink:href="#MJX-203-TEX-SO-221A"></use></g><rect width="4013.6" height="60" x="1020" y="862.5"></rect></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/41.svg b/36114-h/images/41.svg new file mode 100644 index 0000000..131b6e1 --- /dev/null +++ b/36114-h/images/41.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2251.6px" height="665px" viewBox="0 -583 2251.6 665" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-194-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-194-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-194-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-194-TEX-I-1D463"></use></g><g transform="translate(762.8,0)"><use xlink:href="#MJX-194-TEX-N-3D"></use></g><g transform="translate(1818.6,0)"><use xlink:href="#MJX-194-TEX-I-1D450"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/42.svg b/36114-h/images/42.svg new file mode 100644 index 0000000..d58c036 --- /dev/null +++ b/36114-h/images/42.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.628ex;" xmlns="http://www.w3.org/2000/svg" width="6867.1px" height="1260px" viewBox="0 -982.5 6867.1 1260" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-195-TEX-SO-221A" d="M263 249Q264 249 315 130T417 -108T470 -228L725 302Q981 837 982 839Q989 850 1001 850Q1008 850 1013 844T1020 832V826L741 243Q645 43 540 -176Q479 -303 469 -324T453 -348Q449 -350 436 -350L424 -349L315 -96Q206 156 205 156L171 130Q138 104 137 104L111 130L263 249Z"></path><path id="MJX-195-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-195-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-195-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-195-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-195-TEX-N-2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path><path id="MJX-195-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-195-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-195-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-195-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-195-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><use xlink:href="#MJX-195-TEX-I-1D463"></use></g><g transform="translate(518,289) scale(0.707)" ><g ><use xlink:href="#MJX-195-TEX-N-32"></use></g></g></g><g transform="translate(2644,0)"><g ><use xlink:href="#MJX-195-TEX-N-2F"></use></g></g><g transform="translate(3144,0)"><g ><use xlink:href="#MJX-195-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-195-TEX-N-32"></use></g></g></g></g><g transform="translate(0,72.5)"><use xlink:href="#MJX-195-TEX-SO-221A"></use></g><rect width="4013.6" height="60" x="1020" y="862.5"></rect></g><g transform="translate(5311.3,0)"><use xlink:href="#MJX-195-TEX-N-3D"></use></g><g transform="translate(6367.1,0)"><use xlink:href="#MJX-195-TEX-N-30"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/43.svg b/36114-h/images/43.svg new file mode 100644 index 0000000..032366c --- /dev/null +++ b/36114-h/images/43.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2472px" height="841px" viewBox="0 -759 2472 841" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-620-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-620-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-620-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-620-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-620-TEX-I-1D461"></use></g><g transform="translate(394,363) scale(0.707)"><use xlink:href="#MJX-620-TEX-V-2032"></use></g></g><g transform="translate(916.2,0)"><use xlink:href="#MJX-620-TEX-N-3D"></use></g><g transform="translate(1972,0)"><use xlink:href="#MJX-620-TEX-N-30"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/44.svg b/36114-h/images/44.svg new file mode 100644 index 0000000..361f64c --- /dev/null +++ b/36114-h/images/44.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2472px" height="841px" viewBox="0 -759 2472 841" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-211-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-211-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-211-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-211-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-211-TEX-I-1D461"></use></g><g transform="translate(394,363) scale(0.707)"><use xlink:href="#MJX-211-TEX-V-2032"></use></g></g><g transform="translate(916.2,0)"><use xlink:href="#MJX-211-TEX-N-3D"></use></g><g transform="translate(1972,0)"><use xlink:href="#MJX-211-TEX-N-31"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/45.svg b/36114-h/images/45.svg new file mode 100644 index 0000000..84c4b6e --- /dev/null +++ b/36114-h/images/45.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.161ex;" xmlns="http://www.w3.org/2000/svg" width="8462.6px" height="5062px" viewBox="0 -2781 8462.6 5062" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-212-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-212-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-212-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-212-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-212-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-212-TEX-N-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path><path id="MJX-212-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-212-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-212-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-212-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-212-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-212-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-212-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,2031)"><g transform="translate(1946,0)"><g ><use xlink:href="#MJX-212-TEX-I-1D461"></use></g></g><g transform="translate(2307,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-212-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><use xlink:href="#MJX-212-TEX-N-30"></use></g></g></g><g transform="translate(0,139)"><g ><g ><use xlink:href="#MJX-212-TEX-N-61"></use><use xlink:href="#MJX-212-TEX-N-6E" transform="translate(500,0)"></use><use xlink:href="#MJX-212-TEX-N-64" transform="translate(1056,0)"></use></g><g transform="translate(1612,0)"><g ></g></g><g transform="translate(1779,0)"><g ></g></g><g transform="translate(1946,0)"><use xlink:href="#MJX-212-TEX-I-1D461"></use></g></g><g transform="translate(2307,0)"><g ></g><g transform="translate(277.8,0)"><use xlink:href="#MJX-212-TEX-N-3D"></use></g><g transform="translate(1333.6,0)"><g transform="translate(2022,676)"><use xlink:href="#MJX-212-TEX-N-31"></use></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-212-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-212-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-212-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-212-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-212-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-212-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-212-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(5877.6,0)"><use xlink:href="#MJX-212-TEX-N-2E"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/46.svg b/36114-h/images/46.svg new file mode 100644 index 0000000..ab74cdb --- /dev/null +++ b/36114-h/images/46.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.475ex;" xmlns="http://www.w3.org/2000/svg" width="4544px" height="3762px" viewBox="0 -1342 4544 3762" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-215-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-215-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-215-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-215-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-215-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-215-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><g transform="translate(2022,676)"><use xlink:href="#MJX-215-TEX-N-31"></use></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-215-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-215-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-215-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-215-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-215-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-215-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-215-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/47.svg b/36114-h/images/47.svg new file mode 100644 index 0000000..3b759cd --- /dev/null +++ b/36114-h/images/47.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="3815.5px" height="891px" viewBox="0 -809 3815.5 891" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-218-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-218-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-218-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-218-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-218-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-218-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-218-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-218-TEX-V-2032"></use></g></g><g transform="translate(1127.2,0)"><use xlink:href="#MJX-218-TEX-N-3D"></use></g><g transform="translate(2183,0)"><use xlink:href="#MJX-218-TEX-I-1D464"></use></g><g transform="translate(2899,0)"><g ><use xlink:href="#MJX-218-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-218-TEX-V-2032"></use></g></g><g transform="translate(3537.5,0)"><use xlink:href="#MJX-218-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/48.svg b/36114-h/images/48.svg new file mode 100644 index 0000000..8f46972 --- /dev/null +++ b/36114-h/images/48.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="5746px" height="1000px" viewBox="0 -750 5746 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-223-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-223-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-223-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-223-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-223-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-223-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-223-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-223-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-223-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-223-TEX-I-1D465"></use></g><g transform="translate(849.8,0)"><use xlink:href="#MJX-223-TEX-N-3D"></use></g><g transform="translate(1905.6,0)"><use xlink:href="#MJX-223-TEX-N-28"></use></g><g transform="translate(2294.6,0)"><use xlink:href="#MJX-223-TEX-I-1D463"></use></g><g transform="translate(3001.8,0)"><use xlink:href="#MJX-223-TEX-N-2B"></use></g><g transform="translate(4002,0)"><use xlink:href="#MJX-223-TEX-I-1D464"></use></g><g transform="translate(4718,0)"><use xlink:href="#MJX-223-TEX-N-29"></use></g><g transform="translate(5107,0)"><use xlink:href="#MJX-223-TEX-I-1D461"></use></g><g transform="translate(5468,0)"><use xlink:href="#MJX-223-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/49.svg b/36114-h/images/49.svg new file mode 100644 index 0000000..a5f17f0 --- /dev/null +++ b/36114-h/images/49.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="8777.7px" height="1000px" viewBox="0 -750 8777.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-226-TEX-I-1D44A" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 637H297Q236 634 232 620Q262 160 266 136L501 550L499 587Q496 629 489 632Q483 636 447 637Q428 637 422 639T416 648Q416 650 418 660Q419 664 420 669T421 676T424 680T428 682T436 683Z"></path><path id="MJX-226-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-226-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-226-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-226-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-226-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-226-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-226-TEX-N-41" d="M255 0Q240 3 140 3Q48 3 39 0H32V46H47Q119 49 139 88Q140 91 192 245T295 553T348 708Q351 716 366 716H376Q396 715 400 709Q402 707 508 390L617 67Q624 54 636 51T687 46H717V0H708Q699 3 581 3Q458 3 437 0H427V46H440Q510 46 510 64Q510 66 486 138L462 209H229L209 150Q189 91 189 85Q189 72 209 59T259 46H264V0H255ZM447 255L345 557L244 256Q244 255 345 255H447Z"></path><path id="MJX-226-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-226-TEX-I-1D44A"></use></g><g transform="translate(1325.8,0)"><use xlink:href="#MJX-226-TEX-N-3D"></use></g><g transform="translate(2381.6,0)"><use xlink:href="#MJX-226-TEX-I-1D463"></use></g><g transform="translate(3088.8,0)"><use xlink:href="#MJX-226-TEX-N-2B"></use></g><g transform="translate(4089,0)"><use xlink:href="#MJX-226-TEX-I-1D464"></use></g><g transform="translate(4805,0)"><use xlink:href="#MJX-226-TEX-N-2E"></use></g><g transform="translate(5083,0)"><g ></g></g><g transform="translate(7249.7,0)"><use xlink:href="#MJX-226-TEX-N-28"></use><use xlink:href="#MJX-226-TEX-N-41" transform="translate(389,0)"></use><use xlink:href="#MJX-226-TEX-N-29" transform="translate(1139,0)"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/5.svg b/36114-h/images/5.svg new file mode 100644 index 0000000..aa4894d --- /dev/null +++ b/36114-h/images/5.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1519px" height="727px" viewBox="0 -705 1519 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-8-TEX-I-1D435" d="M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z"></path><path id="MJX-8-TEX-I-1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-8-TEX-I-1D435"></use></g><g transform="translate(759,0)"><use xlink:href="#MJX-8-TEX-I-1D436"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/50.svg b/36114-h/images/50.svg new file mode 100644 index 0000000..7d8835a --- /dev/null +++ b/36114-h/images/50.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="3537.5px" height="891px" viewBox="0 -809 3537.5 891" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-227-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-227-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-227-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-227-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-227-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-227-TEX-I-1D465"></use></g><g transform="translate(605,413) scale(0.707)"><use xlink:href="#MJX-227-TEX-V-2032"></use></g></g><g transform="translate(1127.2,0)"><use xlink:href="#MJX-227-TEX-N-3D"></use></g><g transform="translate(2183,0)"><use xlink:href="#MJX-227-TEX-I-1D464"></use></g><g transform="translate(2899,0)"><g ><use xlink:href="#MJX-227-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-227-TEX-V-2032"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/51.svg b/36114-h/images/51.svg new file mode 100644 index 0000000..2813e65 --- /dev/null +++ b/36114-h/images/51.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -4.095ex;" xmlns="http://www.w3.org/2000/svg" width="10115.7px" height="3068.9px" viewBox="0 -1259 10115.7 3068.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-232-TEX-I-1D44A" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 637H297Q236 634 232 620Q262 160 266 136L501 550L499 587Q496 629 489 632Q483 636 447 637Q428 637 422 639T416 648Q416 650 418 660Q419 664 420 669T421 676T424 680T428 682T436 683Z"></path><path id="MJX-232-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-232-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-232-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-232-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-232-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-232-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-232-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-232-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-232-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-232-TEX-N-42" d="M131 622Q124 629 120 631T104 634T61 637H28V683H229H267H346Q423 683 459 678T531 651Q574 627 599 590T624 512Q624 461 583 419T476 360L466 357Q539 348 595 302T651 187Q651 119 600 67T469 3Q456 1 242 0H28V46H61Q103 47 112 49T131 61V622ZM511 513Q511 560 485 594T416 636Q415 636 403 636T371 636T333 637Q266 637 251 636T232 628Q229 624 229 499V374H312L396 375L406 377Q410 378 417 380T442 393T474 417T499 456T511 513ZM537 188Q537 239 509 282T430 336L329 337H229V200V116Q229 57 234 52Q240 47 334 47H383Q425 47 443 53Q486 67 511 104T537 188Z"></path><path id="MJX-232-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-232-TEX-I-1D44A"></use></g><g transform="translate(1325.8,0)"><use xlink:href="#MJX-232-TEX-N-3D"></use></g><g transform="translate(2381.6,0)"><g transform="translate(690,676)"><g ><use xlink:href="#MJX-232-TEX-I-1D463"></use></g><g transform="translate(707.2,0)"><use xlink:href="#MJX-232-TEX-N-2B"></use></g><g transform="translate(1707.4,0)"><use xlink:href="#MJX-232-TEX-I-1D464"></use></g></g><g transform="translate(220,-1079)"><g ><use xlink:href="#MJX-232-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-232-TEX-N-2B"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-232-TEX-I-1D463"></use></g><g transform="translate(485,0)"><use xlink:href="#MJX-232-TEX-I-1D464"></use></g></g><g transform="translate(385.7,-719.9)"><g ><use xlink:href="#MJX-232-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-232-TEX-N-32"></use></g></g></g><rect width="1401" height="60" x="120" y="220"></rect></g></g></g><rect width="3563.4" height="60" x="120" y="220"></rect></g><g transform="translate(6185,0)"><use xlink:href="#MJX-232-TEX-N-2C"></use></g><g transform="translate(6463,0)"><g ></g></g><g transform="translate(8629.7,0)"><use xlink:href="#MJX-232-TEX-N-28"></use><use xlink:href="#MJX-232-TEX-N-42" transform="translate(389,0)"></use><use xlink:href="#MJX-232-TEX-N-29" transform="translate(1097,0)"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/52.svg b/36114-h/images/52.svg new file mode 100644 index 0000000..bb71ee6 --- /dev/null +++ b/36114-h/images/52.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="704px" height="677px" viewBox="0 -677 704 677" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-703-TEX-I-1D447" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-703-TEX-I-1D447"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/53.svg b/36114-h/images/53.svg new file mode 100644 index 0000000..6e49630 --- /dev/null +++ b/36114-h/images/53.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="9642.7px" height="2399px" viewBox="0 -1449.5 9642.7 2399" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-241-TEX-I-1D44A" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 637H297Q236 634 232 620Q262 160 266 136L501 550L499 587Q496 629 489 632Q483 636 447 637Q428 637 422 639T416 648Q416 650 418 660Q419 664 420 669T421 676T424 680T428 682T436 683Z"></path><path id="MJX-241-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-241-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-241-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-241-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-241-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-241-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-241-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-241-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-241-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-241-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-241-TEX-I-1D44A"></use></g><g transform="translate(1325.8,0)"><use xlink:href="#MJX-241-TEX-N-3D"></use></g><g transform="translate(2381.6,0)"><use xlink:href="#MJX-241-TEX-I-1D464"></use></g><g transform="translate(3319.8,0)"><use xlink:href="#MJX-241-TEX-N-2B"></use></g><g transform="translate(4320,0)"><use xlink:href="#MJX-241-TEX-I-1D463"></use></g><g transform="translate(4971.7,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-241-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-241-TEX-N-31"></use></g><g transform="translate(1458.2,0)"><use xlink:href="#MJX-241-TEX-N-2212"></use></g><g transform="translate(2458.4,0)"><g ><g transform="translate(488.3,676)"><use xlink:href="#MJX-241-TEX-N-31"></use></g><g transform="translate(220,-719.9)"><g ><use xlink:href="#MJX-241-TEX-I-1D45B"></use></g><g transform="translate(633,289) scale(0.707)" ><g ><use xlink:href="#MJX-241-TEX-N-32"></use></g></g></g><rect width="1236.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(3935,0) translate(0 -0.5)"><use xlink:href="#MJX-241-TEX-S3-29"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/54.svg b/36114-h/images/54.svg new file mode 100644 index 0000000..f5f2980 --- /dev/null +++ b/36114-h/images/54.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.577ex;" xmlns="http://www.w3.org/2000/svg" width="3089.6px" height="1815px" viewBox="0 -1118 3089.6 1815" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-242-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-242-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-242-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-242-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-242-TEX-I-1D45B"></use></g><g transform="translate(877.8,0)"><use xlink:href="#MJX-242-TEX-N-3D"></use></g><g transform="translate(1933.6,0)"><g ><g transform="translate(361.5,676)"><use xlink:href="#MJX-242-TEX-I-1D450"></use></g><g transform="translate(220,-686)"><use xlink:href="#MJX-242-TEX-I-1D464"></use></g><rect width="916" height="60" x="120" y="220"></rect></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/55.svg b/36114-h/images/55.svg new file mode 100644 index 0000000..7b4c0b4 --- /dev/null +++ b/36114-h/images/55.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.654ex;" xmlns="http://www.w3.org/2000/svg" width="1641px" height="1849.9px" viewBox="0 -1119 1641 1849.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-243-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-243-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-243-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-243-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-243-TEX-I-1D463"></use></g><g transform="translate(485,0)"><use xlink:href="#MJX-243-TEX-I-1D464"></use></g></g><g transform="translate(385.7,-719.9)"><g ><use xlink:href="#MJX-243-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-243-TEX-N-32"></use></g></g></g><rect width="1401" height="60" x="120" y="220"></rect></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/56.svg b/36114-h/images/56.svg new file mode 100644 index 0000000..d1f6bb9 --- /dev/null +++ b/36114-h/images/56.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.654ex;" xmlns="http://www.w3.org/2000/svg" width="10307.1px" height="1880.4px" viewBox="0 -1149.5 10307.1 1880.4" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-244-TEX-I-1D44A" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 637H297Q236 634 232 620Q262 160 266 136L501 550L499 587Q496 629 489 632Q483 636 447 637Q428 637 422 639T416 648Q416 650 418 660Q419 664 420 669T421 676T424 680T428 682T436 683Z"></path><path id="MJX-244-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-244-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-244-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-244-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-244-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-244-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-244-TEX-LO-28" d="M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z"></path><path id="MJX-244-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-244-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-244-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-244-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-244-TEX-LO-29" d="M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-244-TEX-I-1D44A"></use></g><g transform="translate(1325.8,0)"><use xlink:href="#MJX-244-TEX-N-3D"></use></g><g transform="translate(2381.6,0)"><use xlink:href="#MJX-244-TEX-N-28"></use></g><g transform="translate(2770.6,0)"><use xlink:href="#MJX-244-TEX-I-1D464"></use></g><g transform="translate(3708.8,0)"><use xlink:href="#MJX-244-TEX-N-2B"></use></g><g transform="translate(4709,0)"><use xlink:href="#MJX-244-TEX-I-1D463"></use></g><g transform="translate(5194,0)"><use xlink:href="#MJX-244-TEX-N-29"></use></g><g transform="translate(5749.7,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-244-TEX-LO-28"></use></g><g transform="translate(597,0)"><use xlink:href="#MJX-244-TEX-N-31"></use></g><g transform="translate(1319.2,0)"><use xlink:href="#MJX-244-TEX-N-2212"></use></g><g transform="translate(2319.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-244-TEX-I-1D463"></use></g><g transform="translate(485,0)"><use xlink:href="#MJX-244-TEX-I-1D464"></use></g></g><g transform="translate(385.7,-719.9)"><g ><use xlink:href="#MJX-244-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-244-TEX-N-32"></use></g></g></g><rect width="1401" height="60" x="120" y="220"></rect></g></g><g transform="translate(3960.4,0) translate(0 -0.5)"><use xlink:href="#MJX-244-TEX-LO-29"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/57.svg b/36114-h/images/57.svg new file mode 100644 index 0000000..5d6978f --- /dev/null +++ b/36114-h/images/57.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="7261.1px" height="2399px" viewBox="0 -1449.5 7261.1 2399" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-245-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-245-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-245-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-245-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-245-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-245-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-245-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-245-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-245-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-245-TEX-I-1D464"></use></g><g transform="translate(938.2,0)"><use xlink:href="#MJX-245-TEX-N-2B"></use></g><g transform="translate(1938.4,0)"><use xlink:href="#MJX-245-TEX-I-1D463"></use></g><g transform="translate(2590.1,0)"><g transform="translate(0 -0.5)"><use xlink:href="#MJX-245-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-245-TEX-N-31"></use></g><g transform="translate(1458.2,0)"><use xlink:href="#MJX-245-TEX-N-2212"></use></g><g transform="translate(2458.4,0)"><g ><g transform="translate(488.3,676)"><use xlink:href="#MJX-245-TEX-N-31"></use></g><g transform="translate(220,-719.9)"><g ><use xlink:href="#MJX-245-TEX-I-1D45B"></use></g><g transform="translate(633,289) scale(0.707)" ><g ><use xlink:href="#MJX-245-TEX-N-32"></use></g></g></g><rect width="1236.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(3935,0) translate(0 -0.5)"><use xlink:href="#MJX-245-TEX-S3-29"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/58.svg b/36114-h/images/58.svg new file mode 100644 index 0000000..8c22a0b --- /dev/null +++ b/36114-h/images/58.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.552ex;" xmlns="http://www.w3.org/2000/svg" width="2517.6px" height="2195.9px" viewBox="0 -1509.9 2517.6 2195.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-263-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-263-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-263-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-263-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-263-TEX-I-1D45A"></use></g><g transform="translate(878,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-263-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-263-TEX-N-32"></use></g></g></g><g transform="translate(430.8,-686)"><use xlink:href="#MJX-263-TEX-N-32"></use></g><rect width="1121.6" height="60" x="120" y="220"></rect></g><g transform="translate(2239.6,0)"><use xlink:href="#MJX-263-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/59.svg b/36114-h/images/59.svg new file mode 100644 index 0000000..6286774 --- /dev/null +++ b/36114-h/images/59.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.475ex;" xmlns="http://www.w3.org/2000/svg" width="4822px" height="3929.9px" viewBox="0 -1509.9 4822 3929.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-264-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-264-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-264-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-264-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-264-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-264-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-264-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-264-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(1398.2,676)"><g ><use xlink:href="#MJX-264-TEX-I-1D45A"></use></g><g transform="translate(878,0)"><g ><use xlink:href="#MJX-264-TEX-I-1D450"></use></g><g transform="translate(466,363) scale(0.707)" ><g ><use xlink:href="#MJX-264-TEX-N-32"></use></g></g></g></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-264-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-264-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-264-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-264-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-264-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-264-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-264-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(4544,0)"><use xlink:href="#MJX-264-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/6.svg b/36114-h/images/6.svg new file mode 100644 index 0000000..cf31a24 --- /dev/null +++ b/36114-h/images/6.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="645px" height="727px" viewBox="0 -705 645 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-707-TEX-I-1D446" d="M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-707-TEX-I-1D446"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/60.svg b/36114-h/images/60.svg new file mode 100644 index 0000000..d691d67 --- /dev/null +++ b/36114-h/images/60.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.654ex;" xmlns="http://www.w3.org/2000/svg" width="12450.7px" height="2248.6px" viewBox="0 -1517.7 12450.7 2248.6" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-268-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-268-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-268-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-268-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-268-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-268-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-268-TEX-N-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"></path><path id="MJX-268-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-268-TEX-N-2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path><path id="MJX-268-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-268-TEX-I-1D45A"></use></g><g transform="translate(878,0)"><g ><use xlink:href="#MJX-268-TEX-I-1D450"></use></g><g transform="translate(466,413) scale(0.707)" ><g ><use xlink:href="#MJX-268-TEX-N-32"></use></g></g></g><g transform="translate(1969.8,0)"><use xlink:href="#MJX-268-TEX-N-2B"></use></g><g transform="translate(2970,0)"><use xlink:href="#MJX-268-TEX-I-1D45A"></use></g><g transform="translate(3848,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-268-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-268-TEX-N-32"></use></g></g></g><g transform="translate(430.8,-686)"><use xlink:href="#MJX-268-TEX-N-32"></use></g><rect width="1121.6" height="60" x="120" y="220"></rect></g><g transform="translate(5431.8,0)"><use xlink:href="#MJX-268-TEX-N-2B"></use></g><g transform="translate(6432,0)"><g transform="translate(220,676)"><use xlink:href="#MJX-268-TEX-N-33"></use></g><g transform="translate(220,-686)"><use xlink:href="#MJX-268-TEX-N-38"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g transform="translate(7372,0)"><use xlink:href="#MJX-268-TEX-I-1D45A"></use></g><g transform="translate(8250,0)"><g transform="translate(220,676)"><g ><use xlink:href="#MJX-268-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)"><use xlink:href="#MJX-268-TEX-N-34"></use></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-268-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-268-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g><g transform="translate(9833.8,0)"><use xlink:href="#MJX-268-TEX-N-2B"></use></g><g transform="translate(10834,0)"><use xlink:href="#MJX-268-TEX-N-2026"></use></g><g transform="translate(12172.7,0)"><use xlink:href="#MJX-268-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/61.svg b/36114-h/images/61.svg new file mode 100644 index 0000000..fd86aaf --- /dev/null +++ b/36114-h/images/61.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.654ex;" xmlns="http://www.w3.org/2000/svg" width="1361.6px" height="2240.9px" viewBox="0 -1509.9 1361.6 2240.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-269-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-269-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-269-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-269-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-269-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-269-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-269-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/62.svg b/36114-h/images/62.svg new file mode 100644 index 0000000..cb205ea --- /dev/null +++ b/36114-h/images/62.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1747.6px" height="844.9px" viewBox="0 -833.9 1747.6 844.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-283-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-283-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-283-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-283-TEX-I-1D45A"></use></g><g transform="translate(878,0)"><g ><use xlink:href="#MJX-283-TEX-I-1D450"></use></g><g transform="translate(466,363) scale(0.707)" ><g ><use xlink:href="#MJX-283-TEX-N-32"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/63.svg b/36114-h/images/63.svg new file mode 100644 index 0000000..57e3387 --- /dev/null +++ b/36114-h/images/63.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.375ex;" xmlns="http://www.w3.org/2000/svg" width="1174.6px" height="845.6px" viewBox="0 -680 1174.6 845.6" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-289-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-289-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-289-TEX-I-1D438"></use></g><g transform="translate(771,-150) scale(0.707)" ><g ><use xlink:href="#MJX-289-TEX-N-30"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/64.svg b/36114-h/images/64.svg new file mode 100644 index 0000000..7afbe5d --- /dev/null +++ b/36114-h/images/64.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.475ex;" xmlns="http://www.w3.org/2000/svg" width="4822px" height="3776px" viewBox="0 -1356 4822 3776" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-276-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-276-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-276-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-276-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-276-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-276-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-276-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-276-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-276-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(1684.7,676)"><g ><use xlink:href="#MJX-276-TEX-I-1D438"></use></g><g transform="translate(771,-150) scale(0.707)" ><g ><use xlink:href="#MJX-276-TEX-N-30"></use></g></g></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-276-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-276-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-276-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-276-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-276-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-276-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-276-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(4544,0)"><use xlink:href="#MJX-276-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/65.svg b/36114-h/images/65.svg new file mode 100644 index 0000000..ff7988e --- /dev/null +++ b/36114-h/images/65.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.475ex;" xmlns="http://www.w3.org/2000/svg" width="6774.6px" height="5279px" viewBox="0 -2859 6774.6 5279" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-277-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-277-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-277-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-277-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-277-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-277-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-277-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-277-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path><path id="MJX-277-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-277-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-277-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-277-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-277-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(220,1409.5)"><g ><g transform="translate(0 -0.5)"><use xlink:href="#MJX-277-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-277-TEX-I-1D45A"></use></g><g transform="translate(1836.2,0)"><use xlink:href="#MJX-277-TEX-N-2B"></use></g><g transform="translate(2836.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-277-TEX-I-1D438"></use></g><g transform="translate(771,-150) scale(0.707)" ><g ><use xlink:href="#MJX-277-TEX-N-30"></use></g></g></g><g transform="translate(372.5,-719.9)"><g ><use xlink:href="#MJX-277-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-277-TEX-N-32"></use></g></g></g><rect width="1374.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(4451,0) translate(0 -0.5)"><use xlink:href="#MJX-277-TEX-S3-29"></use></g></g><g transform="translate(5187,0)"><g ><use xlink:href="#MJX-277-TEX-I-1D450"></use></g><g transform="translate(466,363) scale(0.707)" ><g ><use xlink:href="#MJX-277-TEX-N-32"></use></g></g></g></g><g transform="translate(1196.3,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-277-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-277-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-277-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-277-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-277-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-277-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-277-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="6256.6" height="60" x="120" y="220"></rect></g><g transform="translate(6496.6,0)"><use xlink:href="#MJX-277-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/66.svg b/36114-h/images/66.svg new file mode 100644 index 0000000..5a8e522 --- /dev/null +++ b/36114-h/images/66.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.148ex;" xmlns="http://www.w3.org/2000/svg" width="5187px" height="2399px" viewBox="0 -1449.5 5187 2399" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-278-TEX-S3-28" d="M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z"></path><path id="MJX-278-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-278-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-278-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-278-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-278-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-278-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-278-TEX-S3-29" d="M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0 -0.5)"><use xlink:href="#MJX-278-TEX-S3-28"></use></g><g transform="translate(736,0)"><use xlink:href="#MJX-278-TEX-I-1D45A"></use></g><g transform="translate(1836.2,0)"><use xlink:href="#MJX-278-TEX-N-2B"></use></g><g transform="translate(2836.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-278-TEX-I-1D438"></use></g><g transform="translate(771,-150) scale(0.707)" ><g ><use xlink:href="#MJX-278-TEX-N-30"></use></g></g></g><g transform="translate(372.5,-719.9)"><g ><use xlink:href="#MJX-278-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-278-TEX-N-32"></use></g></g></g><rect width="1374.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(4451,0) translate(0 -0.5)"><use xlink:href="#MJX-278-TEX-S3-29"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/67.svg b/36114-h/images/67.svg new file mode 100644 index 0000000..0e0a19f --- /dev/null +++ b/36114-h/images/67.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -1.654ex;" xmlns="http://www.w3.org/2000/svg" width="1614.6px" height="2086.9px" viewBox="0 -1356 1614.6 2086.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-286-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-286-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-286-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-286-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-286-TEX-I-1D438"></use></g><g transform="translate(771,-150) scale(0.707)" ><g ><use xlink:href="#MJX-286-TEX-N-30"></use></g></g></g><g transform="translate(372.5,-719.9)"><g ><use xlink:href="#MJX-286-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-286-TEX-N-32"></use></g></g></g><rect width="1374.6" height="60" x="120" y="220"></rect></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/68.svg b/36114-h/images/68.svg new file mode 100644 index 0000000..9a2313e --- /dev/null +++ b/36114-h/images/68.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.475ex;" xmlns="http://www.w3.org/2000/svg" width="4862.6px" height="3929.9px" viewBox="0 -1509.9 4862.6 3929.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-282-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-282-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-282-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-282-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-282-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-282-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-282-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-282-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-282-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-282-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-282-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-282-TEX-I-1D45A"></use></g><g transform="translate(878,0)"><g ><use xlink:href="#MJX-282-TEX-I-1D450"></use></g><g transform="translate(466,363) scale(0.707)" ><g ><use xlink:href="#MJX-282-TEX-N-32"></use></g></g></g><g transform="translate(1969.8,0)"><use xlink:href="#MJX-282-TEX-N-2B"></use></g><g transform="translate(2970,0)"><g ><use xlink:href="#MJX-282-TEX-I-1D438"></use></g><g transform="translate(771,-150) scale(0.707)" ><g ><use xlink:href="#MJX-282-TEX-N-30"></use></g></g></g></g><g transform="translate(240.3,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-282-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-282-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-282-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-282-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-282-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-282-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-282-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4344.6" height="60" x="120" y="220"></rect></g><g transform="translate(4584.6,0)"><use xlink:href="#MJX-282-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/69.svg b/36114-h/images/69.svg new file mode 100644 index 0000000..d4354d9 --- /dev/null +++ b/36114-h/images/69.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="566px" height="899px" viewBox="0 -705 566 899" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-290-TEX-I-1D6FD" d="M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-290-TEX-I-1D6FD"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/7.svg b/36114-h/images/7.svg new file mode 100644 index 0000000..c92b801 --- /dev/null +++ b/36114-h/images/7.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="2416.3px" height="647px" viewBox="0 -442 2416.3 647" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-16-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-16-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-16-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-16-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-16-TEX-I-1D465"></use></g><g transform="translate(572,0)"><use xlink:href="#MJX-16-TEX-N-2C"></use></g><g transform="translate(1016.7,0)"><use xlink:href="#MJX-16-TEX-I-1D466"></use></g><g transform="translate(1506.7,0)"><use xlink:href="#MJX-16-TEX-N-2C"></use></g><g transform="translate(1951.3,0)"><use xlink:href="#MJX-16-TEX-I-1D467"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/70.svg b/36114-h/images/70.svg new file mode 100644 index 0000000..0652f6c --- /dev/null +++ b/36114-h/images/70.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.339ex;" xmlns="http://www.w3.org/2000/svg" width="1008.6px" height="592px" viewBox="0 -442 1008.6 592" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-694-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-694-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-694-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-694-TEX-N-31"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/71.svg b/36114-h/images/71.svg new file mode 100644 index 0000000..8946940 --- /dev/null +++ b/36114-h/images/71.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="926.6px" height="647px" viewBox="0 -442 926.6 647" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-322-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-322-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-322-TEX-I-1D466"></use></g><g transform="translate(523,-150) scale(0.707)" ><g ><use xlink:href="#MJX-322-TEX-N-31"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/72.svg b/36114-h/images/72.svg new file mode 100644 index 0000000..8105839 --- /dev/null +++ b/36114-h/images/72.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.339ex;" xmlns="http://www.w3.org/2000/svg" width="901.6px" height="592px" viewBox="0 -442 901.6 592" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-323-TEX-I-1D467" d="M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z"></path><path id="MJX-323-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-323-TEX-I-1D467"></use></g><g transform="translate(498,-150) scale(0.707)" ><g ><use xlink:href="#MJX-323-TEX-N-31"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/73.svg b/36114-h/images/73.svg new file mode 100644 index 0000000..3a7315d --- /dev/null +++ b/36114-h/images/73.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.339ex;" xmlns="http://www.w3.org/2000/svg" width="797.6px" height="776px" viewBox="0 -626 797.6 776" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-324-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-324-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-324-TEX-I-1D461"></use></g><g transform="translate(394,-150) scale(0.707)" ><g ><use xlink:href="#MJX-324-TEX-N-31"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/74.svg b/36114-h/images/74.svg new file mode 100644 index 0000000..12dd30f --- /dev/null +++ b/36114-h/images/74.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2333px" height="841px" viewBox="0 -759 2333 841" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-329-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-329-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-329-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-329-TEX-I-1D461"></use></g><g transform="translate(394,363) scale(0.707)"><use xlink:href="#MJX-329-TEX-V-2032"></use></g></g><g transform="translate(916.2,0)"><use xlink:href="#MJX-329-TEX-N-3D"></use></g><g transform="translate(1972,0)"><use xlink:href="#MJX-329-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/75.svg b/36114-h/images/75.svg new file mode 100644 index 0000000..8b8a16b --- /dev/null +++ b/36114-h/images/75.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -5.475ex;" xmlns="http://www.w3.org/2000/svg" width="6794px" height="4729.9px" viewBox="0 -2309.9 6794 4729.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-330-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-330-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-330-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-330-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-330-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-330-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-330-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-330-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-330-TEX-S3-221A" d="M424 -948Q422 -947 313 -434T202 80L170 31Q165 24 157 10Q137 -21 137 -21Q131 -16 124 -8L111 5L264 248L473 -720Q473 -717 727 359T983 1440Q989 1450 1001 1450Q1007 1450 1013 1445T1020 1433Q1020 1425 742 244T460 -941Q458 -950 439 -950H436Q424 -950 424 -948Z"></path><path id="MJX-330-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-330-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-330-TEX-I-1D461"></use></g><g transform="translate(394,413) scale(0.707)"><use xlink:href="#MJX-330-TEX-V-2032"></use></g></g><g transform="translate(916.2,0)"><use xlink:href="#MJX-330-TEX-N-3D"></use></g><g transform="translate(1972,0)"><g transform="translate(539.5,1190.9)"><g ><use xlink:href="#MJX-330-TEX-I-1D461"></use></g><g transform="translate(583.2,0)"><use xlink:href="#MJX-330-TEX-N-2212"></use></g><g transform="translate(1583.4,0)"><g ><g transform="translate(412.3,676)"><use xlink:href="#MJX-330-TEX-I-1D463"></use></g><g transform="translate(220,-719.9)"><g ><use xlink:href="#MJX-330-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-330-TEX-N-32"></use></g></g></g><rect width="1069.6" height="60" x="120" y="220"></rect></g></g><g transform="translate(2893,0)"><use xlink:href="#MJX-330-TEX-I-1D465"></use></g></g><g transform="translate(220,-1677)"><g transform="translate(1020,0)"><g ><use xlink:href="#MJX-330-TEX-N-31"></use></g><g transform="translate(722.2,0)"><use xlink:href="#MJX-330-TEX-N-2212"></use></g><g transform="translate(1722.4,0)"><g ><g transform="translate(220,676)"><g ><use xlink:href="#MJX-330-TEX-I-1D463"></use></g><g transform="translate(518,363) scale(0.707)" ><g ><use xlink:href="#MJX-330-TEX-N-32"></use></g></g></g><g transform="translate(246,-719.9)"><g ><use xlink:href="#MJX-330-TEX-I-1D450"></use></g><g transform="translate(466,289) scale(0.707)" ><g ><use xlink:href="#MJX-330-TEX-N-32"></use></g></g></g><rect width="1121.6" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,207)"><use xlink:href="#MJX-330-TEX-S3-221A"></use></g><rect width="3084" height="60" x="1020" y="1597"></rect></g><rect width="4304" height="60" x="120" y="220"></rect></g><g transform="translate(6516,0)"><use xlink:href="#MJX-330-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/76.svg b/36114-h/images/76.svg new file mode 100644 index 0000000..aee1d60 --- /dev/null +++ b/36114-h/images/76.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1194px" height="727px" viewBox="0 -716 1194 727" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-333-TEX-N-394" d="M51 0Q46 4 46 7Q46 9 215 357T388 709Q391 716 416 716Q439 716 444 709Q447 705 616 357T786 7Q786 4 781 0H51ZM507 344L384 596L137 92L383 91H630Q630 93 507 344Z"></path><path id="MJX-333-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-333-TEX-N-394"></use></g><g transform="translate(833,0)"><use xlink:href="#MJX-333-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/77.svg b/36114-h/images/77.svg new file mode 100644 index 0000000..223a9db --- /dev/null +++ b/36114-h/images/77.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.318ex;" xmlns="http://www.w3.org/2000/svg" width="3647.4px" height="1060px" viewBox="0 -919.5 3647.4 1060" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-671-TEX-N-221A" d="M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z"></path><path id="MJX-671-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-671-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-671-TEX-N-B7" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path id="MJX-671-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-671-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(853,0)"><g ><use xlink:href="#MJX-671-TEX-N-2212"></use></g><g transform="translate(778,0)"><use xlink:href="#MJX-671-TEX-N-31"></use></g></g><g transform="translate(0,59.5)"><use xlink:href="#MJX-671-TEX-N-221A"></use></g><rect width="1278" height="60" x="853" y="799.5"></rect></g><g transform="translate(2353.2,0)"><use xlink:href="#MJX-671-TEX-N-B7"></use></g><g transform="translate(2853.4,0)"><use xlink:href="#MJX-671-TEX-I-1D450"></use></g><g transform="translate(3286.4,0)"><use xlink:href="#MJX-671-TEX-I-1D461"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/78.svg b/36114-h/images/78.svg new file mode 100644 index 0000000..8df09ef --- /dev/null +++ b/36114-h/images/78.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="17811.6px" height="1000px" viewBox="0 -750 17811.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-350-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-350-TEX-N-46" d="M128 619Q121 626 117 628T101 631T58 634H25V680H582V676Q584 670 596 560T610 444V440H570V444Q563 493 561 501Q555 538 543 563T516 601T477 622T431 631T374 633H334H286Q252 633 244 631T233 621Q232 619 232 490V363H284Q287 363 303 363T327 364T349 367T372 373T389 385Q407 403 410 459V480H450V200H410V221Q407 276 389 296Q381 303 371 307T348 313T327 316T303 317T284 317H232V189L233 61Q240 54 245 52T270 48T333 46H360V0H348Q324 3 182 3Q51 3 36 0H25V46H58Q100 47 109 49T128 61V619Z"></path><path id="MJX-350-TEX-N-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path id="MJX-350-TEX-N-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path id="MJX-350-TEX-N-63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z"></path><path id="MJX-350-TEX-N-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z"></path><path id="MJX-350-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-350-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-350-TEX-N-69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path id="MJX-350-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-350-TEX-N-74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z"></path><path id="MJX-350-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-350-TEX-N-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path id="MJX-350-TEX-N-20" d=""></path><path id="MJX-350-TEX-N-6D" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-350-TEX-N-73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path id="MJX-350-TEX-I-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path><path id="MJX-350-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-350-TEX-N-28"></use></g><g transform="translate(389,0)"><use xlink:href="#MJX-350-TEX-N-46"></use><use xlink:href="#MJX-350-TEX-N-6F" transform="translate(653,0)"></use><use xlink:href="#MJX-350-TEX-N-72" transform="translate(1153,0)"></use><use xlink:href="#MJX-350-TEX-N-63" transform="translate(1545,0)"></use><use xlink:href="#MJX-350-TEX-N-65" transform="translate(1989,0)"></use></g><g transform="translate(2822,0)"><use xlink:href="#MJX-350-TEX-N-29"></use></g><g transform="translate(3488.8,0)"><use xlink:href="#MJX-350-TEX-N-3D"></use></g><g transform="translate(4544.6,0)"><use xlink:href="#MJX-350-TEX-N-28"></use></g><g transform="translate(4933.6,0)"><use xlink:href="#MJX-350-TEX-N-69"></use><use xlink:href="#MJX-350-TEX-N-6E" transform="translate(278,0)"></use><use xlink:href="#MJX-350-TEX-N-65" transform="translate(834,0)"></use><use xlink:href="#MJX-350-TEX-N-72" transform="translate(1278,0)"></use><use xlink:href="#MJX-350-TEX-N-74" transform="translate(1670,0)"></use><use xlink:href="#MJX-350-TEX-N-69" transform="translate(2059,0)"></use><use xlink:href="#MJX-350-TEX-N-61" transform="translate(2337,0)"></use><use xlink:href="#MJX-350-TEX-N-6C" transform="translate(2837,0)"></use><use xlink:href="#MJX-350-TEX-N-20" transform="translate(3115,0)"></use><use xlink:href="#MJX-350-TEX-N-6D" transform="translate(3365,0)"></use><use xlink:href="#MJX-350-TEX-N-61" transform="translate(4198,0)"></use><use xlink:href="#MJX-350-TEX-N-73" transform="translate(4698,0)"></use><use xlink:href="#MJX-350-TEX-N-73" transform="translate(5092,0)"></use></g><g transform="translate(10419.6,0)"><use xlink:href="#MJX-350-TEX-N-29"></use></g><g transform="translate(10808.6,0)"><use xlink:href="#MJX-350-TEX-I-D7"></use></g><g transform="translate(11586.6,0)"><use xlink:href="#MJX-350-TEX-N-28"></use></g><g transform="translate(11975.6,0)"><use xlink:href="#MJX-350-TEX-N-61"></use><use xlink:href="#MJX-350-TEX-N-63" transform="translate(500,0)"></use><use xlink:href="#MJX-350-TEX-N-63" transform="translate(944,0)"></use><use xlink:href="#MJX-350-TEX-N-65" transform="translate(1388,0)"></use><use xlink:href="#MJX-350-TEX-N-6C" transform="translate(1832,0)"></use><use xlink:href="#MJX-350-TEX-N-65" transform="translate(2110,0)"></use><use xlink:href="#MJX-350-TEX-N-72" transform="translate(2554,0)"></use><use xlink:href="#MJX-350-TEX-N-61" transform="translate(2946,0)"></use><use xlink:href="#MJX-350-TEX-N-74" transform="translate(3446,0)"></use><use xlink:href="#MJX-350-TEX-N-69" transform="translate(3835,0)"></use><use xlink:href="#MJX-350-TEX-N-6F" transform="translate(4113,0)"></use><use xlink:href="#MJX-350-TEX-N-6E" transform="translate(4613,0)"></use></g><g transform="translate(17144.6,0)"><use xlink:href="#MJX-350-TEX-N-29"></use></g><g transform="translate(17533.6,0)"><use xlink:href="#MJX-350-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/79.svg b/36114-h/images/79.svg new file mode 100644 index 0000000..e36158a --- /dev/null +++ b/36114-h/images/79.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.036ex;" xmlns="http://www.w3.org/2000/svg" width="17291px" height="2300px" viewBox="0 -1400 17291 2300" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-351-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-351-TEX-N-46" d="M128 619Q121 626 117 628T101 631T58 634H25V680H582V676Q584 670 596 560T610 444V440H570V444Q563 493 561 501Q555 538 543 563T516 601T477 622T431 631T374 633H334H286Q252 633 244 631T233 621Q232 619 232 490V363H284Q287 363 303 363T327 364T349 367T372 373T389 385Q407 403 410 459V480H450V200H410V221Q407 276 389 296Q381 303 371 307T348 313T327 316T303 317T284 317H232V189L233 61Q240 54 245 52T270 48T333 46H360V0H348Q324 3 182 3Q51 3 36 0H25V46H58Q100 47 109 49T128 61V619Z"></path><path id="MJX-351-TEX-N-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path id="MJX-351-TEX-N-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path id="MJX-351-TEX-N-63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z"></path><path id="MJX-351-TEX-N-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z"></path><path id="MJX-351-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-351-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-351-TEX-N-67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path><path id="MJX-351-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-351-TEX-N-76" d="M338 431Q344 429 422 429Q479 429 503 431H508V385H497Q439 381 423 345Q421 341 356 172T288 -2Q283 -11 263 -11Q244 -11 239 -2Q99 359 98 364Q93 378 82 381T43 385H19V431H25L33 430Q41 430 53 430T79 430T104 429T122 428Q217 428 232 431H240V385H226Q187 384 184 370Q184 366 235 234L286 102L377 341V349Q377 363 367 372T349 383T335 385H331V431H338Z"></path><path id="MJX-351-TEX-N-69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path id="MJX-351-TEX-N-74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z"></path><path id="MJX-351-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-351-TEX-N-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path id="MJX-351-TEX-N-20" d=""></path><path id="MJX-351-TEX-N-6D" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-351-TEX-N-73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path id="MJX-351-TEX-I-D7" d="M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z"></path><path id="MJX-351-TEX-N-79" d="M69 -66Q91 -66 104 -80T118 -116Q118 -134 109 -145T91 -160Q84 -163 97 -166Q104 -168 111 -168Q131 -168 148 -159T175 -138T197 -106T213 -75T225 -43L242 0L170 183Q150 233 125 297Q101 358 96 368T80 381Q79 382 78 382Q66 385 34 385H19V431H26L46 430Q65 430 88 429T122 428Q129 428 142 428T171 429T200 430T224 430L233 431H241V385H232Q183 385 185 366L286 112Q286 113 332 227L376 341V350Q376 365 366 373T348 383T334 385H331V431H337H344Q351 431 361 431T382 430T405 429T422 429Q477 429 503 431H508V385H497Q441 380 422 345Q420 343 378 235T289 9T227 -131Q180 -204 113 -204Q69 -204 44 -177T19 -116Q19 -89 35 -78T69 -66Z"></path><path id="MJX-351-TEX-N-66" d="M273 0Q255 3 146 3Q43 3 34 0H26V46H42Q70 46 91 49Q99 52 103 60Q104 62 104 224V385H33V431H104V497L105 564L107 574Q126 639 171 668T266 704Q267 704 275 704T289 705Q330 702 351 679T372 627Q372 604 358 590T321 576T284 590T270 627Q270 647 288 667H284Q280 668 273 668Q245 668 223 647T189 592Q183 572 182 497V431H293V385H185V225Q185 63 186 61T189 57T194 54T199 51T206 49T213 48T222 47T231 47T241 46T251 46H282V0H273Z"></path><path id="MJX-351-TEX-N-68" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-351-TEX-N-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path><path id="MJX-351-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,650)"><g transform="translate(4009.4,0)"><g ><use xlink:href="#MJX-351-TEX-N-28"></use></g><g transform="translate(389,0)"><use xlink:href="#MJX-351-TEX-N-46"></use><use xlink:href="#MJX-351-TEX-N-6F" transform="translate(653,0)"></use><use xlink:href="#MJX-351-TEX-N-72" transform="translate(1153,0)"></use><use xlink:href="#MJX-351-TEX-N-63" transform="translate(1545,0)"></use><use xlink:href="#MJX-351-TEX-N-65" transform="translate(1989,0)"></use></g><g transform="translate(2822,0)"><use xlink:href="#MJX-351-TEX-N-29"></use></g><g transform="translate(3488.8,0)"><use xlink:href="#MJX-351-TEX-N-3D"></use></g><g transform="translate(4544.6,0)"><use xlink:href="#MJX-351-TEX-N-28"></use></g><g transform="translate(4933.6,0)"><use xlink:href="#MJX-351-TEX-N-67"></use><use xlink:href="#MJX-351-TEX-N-72" transform="translate(500,0)"></use><use xlink:href="#MJX-351-TEX-N-61" transform="translate(892,0)"></use><use xlink:href="#MJX-351-TEX-N-76" transform="translate(1392,0)"></use><use xlink:href="#MJX-351-TEX-N-69" transform="translate(1920,0)"></use><use xlink:href="#MJX-351-TEX-N-74" transform="translate(2198,0)"></use><use xlink:href="#MJX-351-TEX-N-61" transform="translate(2587,0)"></use><use xlink:href="#MJX-351-TEX-N-74" transform="translate(3087,0)"></use><use xlink:href="#MJX-351-TEX-N-69" transform="translate(3476,0)"></use><use xlink:href="#MJX-351-TEX-N-6F" transform="translate(3754,0)"></use><use xlink:href="#MJX-351-TEX-N-6E" transform="translate(4254,0)"></use><use xlink:href="#MJX-351-TEX-N-61" transform="translate(4810,0)"></use><use xlink:href="#MJX-351-TEX-N-6C" transform="translate(5310,0)"></use><use xlink:href="#MJX-351-TEX-N-20" transform="translate(5588,0)"></use><use xlink:href="#MJX-351-TEX-N-6D" transform="translate(5838,0)"></use><use xlink:href="#MJX-351-TEX-N-61" transform="translate(6671,0)"></use><use xlink:href="#MJX-351-TEX-N-73" transform="translate(7171,0)"></use><use xlink:href="#MJX-351-TEX-N-73" transform="translate(7565,0)"></use></g><g transform="translate(12892.6,0)"><use xlink:href="#MJX-351-TEX-N-29"></use></g></g></g><g transform="translate(0,-650)"><g ><g ></g><g transform="translate(1000,0)"><use xlink:href="#MJX-351-TEX-I-D7"></use></g><g transform="translate(1778,0)"><use xlink:href="#MJX-351-TEX-N-28"></use></g><g transform="translate(2167,0)"><use xlink:href="#MJX-351-TEX-N-69"></use><use xlink:href="#MJX-351-TEX-N-6E" transform="translate(278,0)"></use><use xlink:href="#MJX-351-TEX-N-74" transform="translate(834,0)"></use><use xlink:href="#MJX-351-TEX-N-65" transform="translate(1223,0)"></use><use xlink:href="#MJX-351-TEX-N-6E" transform="translate(1667,0)"></use><use xlink:href="#MJX-351-TEX-N-73" transform="translate(2223,0)"></use><use xlink:href="#MJX-351-TEX-N-69" transform="translate(2617,0)"></use><use xlink:href="#MJX-351-TEX-N-74" transform="translate(2895,0)"></use><use xlink:href="#MJX-351-TEX-N-79" transform="translate(3284,0)"></use><use xlink:href="#MJX-351-TEX-N-20" transform="translate(3812,0)"></use><use xlink:href="#MJX-351-TEX-N-6F" transform="translate(4062,0)"></use><use xlink:href="#MJX-351-TEX-N-66" transform="translate(4562,0)"></use><use xlink:href="#MJX-351-TEX-N-20" transform="translate(4868,0)"></use><use xlink:href="#MJX-351-TEX-N-74" transform="translate(5118,0)"></use><use xlink:href="#MJX-351-TEX-N-68" transform="translate(5507,0)"></use><use xlink:href="#MJX-351-TEX-N-65" transform="translate(6063,0)"></use><use xlink:href="#MJX-351-TEX-N-20" transform="translate(6507,0)"></use><use xlink:href="#MJX-351-TEX-N-67" transform="translate(6757,0)"></use><use xlink:href="#MJX-351-TEX-N-72" transform="translate(7257,0)"></use><use xlink:href="#MJX-351-TEX-N-61" transform="translate(7649,0)"></use><use xlink:href="#MJX-351-TEX-N-76" transform="translate(8149,0)"></use><use xlink:href="#MJX-351-TEX-N-69" transform="translate(8677,0)"></use><use xlink:href="#MJX-351-TEX-N-74" transform="translate(8955,0)"></use><use xlink:href="#MJX-351-TEX-N-61" transform="translate(9344,0)"></use><use xlink:href="#MJX-351-TEX-N-74" transform="translate(9844,0)"></use><use xlink:href="#MJX-351-TEX-N-69" transform="translate(10233,0)"></use><use xlink:href="#MJX-351-TEX-N-6F" transform="translate(10511,0)"></use><use xlink:href="#MJX-351-TEX-N-6E" transform="translate(11011,0)"></use><use xlink:href="#MJX-351-TEX-N-61" transform="translate(11567,0)"></use><use xlink:href="#MJX-351-TEX-N-6C" transform="translate(12067,0)"></use><use xlink:href="#MJX-351-TEX-N-20" transform="translate(12345,0)"></use><use xlink:href="#MJX-351-TEX-N-66" transform="translate(12595,0)"></use><use xlink:href="#MJX-351-TEX-N-69" transform="translate(12901,0)"></use><use xlink:href="#MJX-351-TEX-N-65" transform="translate(13179,0)"></use><use xlink:href="#MJX-351-TEX-N-6C" transform="translate(13623,0)"></use><use xlink:href="#MJX-351-TEX-N-64" transform="translate(13901,0)"></use></g><g transform="translate(16624,0)"><use xlink:href="#MJX-351-TEX-N-29"></use></g><g transform="translate(17013,0)"><use xlink:href="#MJX-351-TEX-N-2C"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/8.svg b/36114-h/images/8.svg new file mode 100644 index 0000000..9e8b655 --- /dev/null +++ b/36114-h/images/8.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="878px" height="453px" viewBox="0 -442 878 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-525-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-525-TEX-I-1D45A"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/80.svg b/36114-h/images/80.svg new file mode 100644 index 0000000..22c8c2d --- /dev/null +++ b/36114-h/images/80.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -3.643ex;" xmlns="http://www.w3.org/2000/svg" width="16513px" height="3720px" viewBox="0 -2110 16513 3720" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-352-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-352-TEX-N-61" d="M137 305T115 305T78 320T63 359Q63 394 97 421T218 448Q291 448 336 416T396 340Q401 326 401 309T402 194V124Q402 76 407 58T428 40Q443 40 448 56T453 109V145H493V106Q492 66 490 59Q481 29 455 12T400 -6T353 12T329 54V58L327 55Q325 52 322 49T314 40T302 29T287 17T269 6T247 -2T221 -8T190 -11Q130 -11 82 20T34 107Q34 128 41 147T68 188T116 225T194 253T304 268H318V290Q318 324 312 340Q290 411 215 411Q197 411 181 410T156 406T148 403Q170 388 170 359Q170 334 154 320ZM126 106Q126 75 150 51T209 26Q247 26 276 49T315 109Q317 116 318 175Q318 233 317 233Q309 233 296 232T251 223T193 203T147 166T126 106Z"></path><path id="MJX-352-TEX-N-63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z"></path><path id="MJX-352-TEX-N-65" d="M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z"></path><path id="MJX-352-TEX-N-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path id="MJX-352-TEX-N-72" d="M36 46H50Q89 46 97 60V68Q97 77 97 91T98 122T98 161T98 203Q98 234 98 269T98 328L97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 60 434T96 436Q112 437 131 438T160 441T171 442H174V373Q213 441 271 441H277Q322 441 343 419T364 373Q364 352 351 337T313 322Q288 322 276 338T263 372Q263 381 265 388T270 400T273 405Q271 407 250 401Q234 393 226 386Q179 341 179 207V154Q179 141 179 127T179 101T180 81T180 66V61Q181 59 183 57T188 54T193 51T200 49T207 48T216 47T225 47T235 46T245 46H276V0H267Q249 3 140 3Q37 3 28 0H20V46H36Z"></path><path id="MJX-352-TEX-N-74" d="M27 422Q80 426 109 478T141 600V615H181V431H316V385H181V241Q182 116 182 100T189 68Q203 29 238 29Q282 29 292 100Q293 108 293 146V181H333V146V134Q333 57 291 17Q264 -10 221 -10Q187 -10 162 2T124 33T105 68T98 100Q97 107 97 248V385H18V422H27Z"></path><path id="MJX-352-TEX-N-69" d="M69 609Q69 637 87 653T131 669Q154 667 171 652T188 609Q188 579 171 564T129 549Q104 549 87 564T69 609ZM247 0Q232 3 143 3Q132 3 106 3T56 1L34 0H26V46H42Q70 46 91 49Q100 53 102 60T104 102V205V293Q104 345 102 359T88 378Q74 385 41 385H30V408Q30 431 32 431L42 432Q52 433 70 434T106 436Q123 437 142 438T171 441T182 442H185V62Q190 52 197 50T232 46H255V0H247Z"></path><path id="MJX-352-TEX-N-6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z"></path><path id="MJX-352-TEX-N-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-352-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-352-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-352-TEX-N-67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z"></path><path id="MJX-352-TEX-N-76" d="M338 431Q344 429 422 429Q479 429 503 431H508V385H497Q439 381 423 345Q421 341 356 172T288 -2Q283 -11 263 -11Q244 -11 239 -2Q99 359 98 364Q93 378 82 381T43 385H19V431H25L33 430Q41 430 53 430T79 430T104 429T122 428Q217 428 232 431H240V385H226Q187 384 184 370Q184 366 235 234L286 102L377 341V349Q377 363 367 372T349 383T335 385H331V431H338Z"></path><path id="MJX-352-TEX-N-20" d=""></path><path id="MJX-352-TEX-N-6D" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q351 442 364 440T387 434T406 426T421 417T432 406T441 395T448 384T452 374T455 366L457 361L460 365Q463 369 466 373T475 384T488 397T503 410T523 422T546 432T572 439T603 442Q729 442 740 329Q741 322 741 190V104Q741 66 743 59T754 49Q775 46 803 46H819V0H811L788 1Q764 2 737 2T699 3Q596 3 587 0H579V46H595Q656 46 656 62Q657 64 657 200Q656 335 655 343Q649 371 635 385T611 402T585 404Q540 404 506 370Q479 343 472 315T464 232V168V108Q464 78 465 68T468 55T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-352-TEX-N-73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z"></path><path id="MJX-352-TEX-N-79" d="M69 -66Q91 -66 104 -80T118 -116Q118 -134 109 -145T91 -160Q84 -163 97 -166Q104 -168 111 -168Q131 -168 148 -159T175 -138T197 -106T213 -75T225 -43L242 0L170 183Q150 233 125 297Q101 358 96 368T80 381Q79 382 78 382Q66 385 34 385H19V431H26L46 430Q65 430 88 429T122 428Q129 428 142 428T171 429T200 430T224 430L233 431H241V385H232Q183 385 185 366L286 112Q286 113 332 227L376 341V350Q376 365 366 373T348 383T334 385H331V431H337H344Q351 431 361 431T382 430T405 429T422 429Q477 429 503 431H508V385H497Q441 380 422 345Q420 343 378 235T289 9T227 -131Q180 -204 113 -204Q69 -204 44 -177T19 -116Q19 -89 35 -78T69 -66Z"></path><path id="MJX-352-TEX-N-66" d="M273 0Q255 3 146 3Q43 3 34 0H26V46H42Q70 46 91 49Q99 52 103 60Q104 62 104 224V385H33V431H104V497L105 564L107 574Q126 639 171 668T266 704Q267 704 275 704T289 705Q330 702 351 679T372 627Q372 604 358 590T321 576T284 590T270 627Q270 647 288 667H284Q280 668 273 668Q245 668 223 647T189 592Q183 572 182 497V431H293V385H185V225Q185 63 186 61T189 57T194 54T199 51T206 49T213 48T222 47T231 47T241 46T251 46H282V0H273Z"></path><path id="MJX-352-TEX-N-68" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 124T102 167T103 217T103 272T103 329Q103 366 103 407T103 482T102 542T102 586T102 603Q99 622 88 628T43 637H25V660Q25 683 27 683L37 684Q47 685 66 686T103 688Q120 689 140 690T170 693T181 694H184V367Q244 442 328 442Q451 442 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 195 315T187 232V168V108Q187 78 188 68T191 55T200 49Q221 46 249 46H265V0H257L234 1Q210 2 183 2T145 3Q42 3 33 0H25V46H41Z"></path><path id="MJX-352-TEX-N-64" d="M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z"></path><path id="MJX-352-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,650)"><g transform="translate(55.4,0)"><g ><use xlink:href="#MJX-352-TEX-N-28"></use></g><g transform="translate(389,0)"><use xlink:href="#MJX-352-TEX-N-61"></use><use xlink:href="#MJX-352-TEX-N-63" transform="translate(500,0)"></use><use xlink:href="#MJX-352-TEX-N-63" transform="translate(944,0)"></use><use xlink:href="#MJX-352-TEX-N-65" transform="translate(1388,0)"></use><use xlink:href="#MJX-352-TEX-N-6C" transform="translate(1832,0)"></use><use xlink:href="#MJX-352-TEX-N-65" transform="translate(2110,0)"></use><use xlink:href="#MJX-352-TEX-N-72" transform="translate(2554,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(2946,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(3446,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(3835,0)"></use><use xlink:href="#MJX-352-TEX-N-6F" transform="translate(4113,0)"></use><use xlink:href="#MJX-352-TEX-N-6E" transform="translate(4613,0)"></use></g><g transform="translate(5558,0)"><use xlink:href="#MJX-352-TEX-N-29"></use></g><g transform="translate(6224.8,0)"><use xlink:href="#MJX-352-TEX-N-3D"></use></g><g transform="translate(7280.6,0)"><g transform="translate(220,710)"><g ><use xlink:href="#MJX-352-TEX-N-28"></use></g><g transform="translate(389,0)"><use xlink:href="#MJX-352-TEX-N-67"></use><use xlink:href="#MJX-352-TEX-N-72" transform="translate(500,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(892,0)"></use><use xlink:href="#MJX-352-TEX-N-76" transform="translate(1392,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(1920,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(2198,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(2587,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(3087,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(3476,0)"></use><use xlink:href="#MJX-352-TEX-N-6F" transform="translate(3754,0)"></use><use xlink:href="#MJX-352-TEX-N-6E" transform="translate(4254,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(4810,0)"></use><use xlink:href="#MJX-352-TEX-N-6C" transform="translate(5310,0)"></use><use xlink:href="#MJX-352-TEX-N-20" transform="translate(5588,0)"></use><use xlink:href="#MJX-352-TEX-N-6D" transform="translate(5838,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(6671,0)"></use><use xlink:href="#MJX-352-TEX-N-73" transform="translate(7171,0)"></use><use xlink:href="#MJX-352-TEX-N-73" transform="translate(7565,0)"></use></g><g transform="translate(8348,0)"><use xlink:href="#MJX-352-TEX-N-29"></use></g></g><g transform="translate(1456.5,-710)"><g ><use xlink:href="#MJX-352-TEX-N-28"></use></g><g transform="translate(389,0)"><use xlink:href="#MJX-352-TEX-N-69"></use><use xlink:href="#MJX-352-TEX-N-6E" transform="translate(278,0)"></use><use xlink:href="#MJX-352-TEX-N-65" transform="translate(834,0)"></use><use xlink:href="#MJX-352-TEX-N-72" transform="translate(1278,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(1670,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(2059,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(2337,0)"></use><use xlink:href="#MJX-352-TEX-N-6C" transform="translate(2837,0)"></use><use xlink:href="#MJX-352-TEX-N-20" transform="translate(3115,0)"></use><use xlink:href="#MJX-352-TEX-N-6D" transform="translate(3365,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(4198,0)"></use><use xlink:href="#MJX-352-TEX-N-73" transform="translate(4698,0)"></use><use xlink:href="#MJX-352-TEX-N-73" transform="translate(5092,0)"></use></g><g transform="translate(5875,0)"><use xlink:href="#MJX-352-TEX-N-29"></use></g></g><rect width="8937" height="60" x="120" y="220"></rect></g></g></g><g transform="translate(0,-1360)"><g ><g ></g><g transform="translate(1000,0)"><use xlink:href="#MJX-352-TEX-N-28"></use></g><g transform="translate(1389,0)"><use xlink:href="#MJX-352-TEX-N-69"></use><use xlink:href="#MJX-352-TEX-N-6E" transform="translate(278,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(834,0)"></use><use xlink:href="#MJX-352-TEX-N-65" transform="translate(1223,0)"></use><use xlink:href="#MJX-352-TEX-N-6E" transform="translate(1667,0)"></use><use xlink:href="#MJX-352-TEX-N-73" transform="translate(2223,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(2617,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(2895,0)"></use><use xlink:href="#MJX-352-TEX-N-79" transform="translate(3284,0)"></use><use xlink:href="#MJX-352-TEX-N-20" transform="translate(3812,0)"></use><use xlink:href="#MJX-352-TEX-N-6F" transform="translate(4062,0)"></use><use xlink:href="#MJX-352-TEX-N-66" transform="translate(4562,0)"></use><use xlink:href="#MJX-352-TEX-N-20" transform="translate(4868,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(5118,0)"></use><use xlink:href="#MJX-352-TEX-N-68" transform="translate(5507,0)"></use><use xlink:href="#MJX-352-TEX-N-65" transform="translate(6063,0)"></use><use xlink:href="#MJX-352-TEX-N-20" transform="translate(6507,0)"></use><use xlink:href="#MJX-352-TEX-N-67" transform="translate(6757,0)"></use><use xlink:href="#MJX-352-TEX-N-72" transform="translate(7257,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(7649,0)"></use><use xlink:href="#MJX-352-TEX-N-76" transform="translate(8149,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(8677,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(8955,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(9344,0)"></use><use xlink:href="#MJX-352-TEX-N-74" transform="translate(9844,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(10233,0)"></use><use xlink:href="#MJX-352-TEX-N-6F" transform="translate(10511,0)"></use><use xlink:href="#MJX-352-TEX-N-6E" transform="translate(11011,0)"></use><use xlink:href="#MJX-352-TEX-N-61" transform="translate(11567,0)"></use><use xlink:href="#MJX-352-TEX-N-6C" transform="translate(12067,0)"></use><use xlink:href="#MJX-352-TEX-N-20" transform="translate(12345,0)"></use><use xlink:href="#MJX-352-TEX-N-66" transform="translate(12595,0)"></use><use xlink:href="#MJX-352-TEX-N-69" transform="translate(12901,0)"></use><use xlink:href="#MJX-352-TEX-N-65" transform="translate(13179,0)"></use><use xlink:href="#MJX-352-TEX-N-6C" transform="translate(13623,0)"></use><use xlink:href="#MJX-352-TEX-N-64" transform="translate(13901,0)"></use></g><g transform="translate(15846,0)"><use xlink:href="#MJX-352-TEX-N-29"></use></g><g transform="translate(16235,0)"><use xlink:href="#MJX-352-TEX-N-2E"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/81.svg b/36114-h/images/81.svg new file mode 100644 index 0000000..0f79298 --- /dev/null +++ b/36114-h/images/81.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="5020.2px" height="759px" viewBox="0 -677 5020.2 759" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-385-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path id="MJX-385-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-385-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-385-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-385-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-385-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-385-TEX-N-2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-385-TEX-I-1D70B"></use></g><g transform="translate(847.8,0)"><use xlink:href="#MJX-385-TEX-N-3D"></use></g><g transform="translate(1903.6,0)"><use xlink:href="#MJX-385-TEX-N-33"></use><use xlink:href="#MJX-385-TEX-N-2E" transform="translate(500,0)"></use><use xlink:href="#MJX-385-TEX-N-31" transform="translate(778,0)"></use><use xlink:href="#MJX-385-TEX-N-34" transform="translate(1278,0)"></use></g><g transform="translate(3848.2,0)"><use xlink:href="#MJX-385-TEX-N-2026"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/82.svg b/36114-h/images/82.svg new file mode 100644 index 0000000..003591a --- /dev/null +++ b/36114-h/images/82.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="570px" height="442px" viewBox="0 -431 570 442" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-738-TEX-I-1D70B" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-738-TEX-I-1D70B"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/83.svg b/36114-h/images/83.svg new file mode 100644 index 0000000..f133fcd --- /dev/null +++ b/36114-h/images/83.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="572px" height="453px" viewBox="0 -442 572 453" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-432-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-432-TEX-I-1D462"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/84.svg b/36114-h/images/84.svg new file mode 100644 index 0000000..3479046 --- /dev/null +++ b/36114-h/images/84.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2405.6px" height="748px" viewBox="0 -666 2405.6 748" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-398-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-398-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-398-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-398-TEX-I-1D462"></use></g><g transform="translate(849.8,0)"><use xlink:href="#MJX-398-TEX-N-3D"></use></g><g transform="translate(1905.6,0)"><use xlink:href="#MJX-398-TEX-N-31"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/85.svg b/36114-h/images/85.svg new file mode 100644 index 0000000..8bad765 --- /dev/null +++ b/36114-h/images/85.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2405.6px" height="748px" viewBox="0 -666 2405.6 748" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-399-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-399-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-399-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-399-TEX-I-1D462"></use></g><g transform="translate(849.8,0)"><use xlink:href="#MJX-399-TEX-N-3D"></use></g><g transform="translate(1905.6,0)"><use xlink:href="#MJX-399-TEX-N-32"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/86.svg b/36114-h/images/86.svg new file mode 100644 index 0000000..3430b6a --- /dev/null +++ b/36114-h/images/86.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2405.6px" height="747px" viewBox="0 -665 2405.6 747" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-408-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-408-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-408-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-408-TEX-I-1D462"></use></g><g transform="translate(849.8,0)"><use xlink:href="#MJX-408-TEX-N-3D"></use></g><g transform="translate(1905.6,0)"><use xlink:href="#MJX-408-TEX-N-33"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/87.svg b/36114-h/images/87.svg new file mode 100644 index 0000000..390cce8 --- /dev/null +++ b/36114-h/images/87.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="751px" height="683px" viewBox="0 -683 751 683" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-440-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-440-TEX-I-1D443"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/88.svg b/36114-h/images/88.svg new file mode 100644 index 0000000..c511921 --- /dev/null +++ b/36114-h/images/88.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="2318.6px" height="748px" viewBox="0 -666 2318.6 748" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-409-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-409-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-409-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-409-TEX-I-1D463"></use></g><g transform="translate(762.8,0)"><use xlink:href="#MJX-409-TEX-N-3D"></use></g><g transform="translate(1818.6,0)"><use xlink:href="#MJX-409-TEX-N-31"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/89.svg b/36114-h/images/89.svg new file mode 100644 index 0000000..0a6d2ed --- /dev/null +++ b/36114-h/images/89.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -2.103ex;" xmlns="http://www.w3.org/2000/svg" width="9961.2px" height="2359px" viewBox="0 -1429.5 9961.2 2359" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-412-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path id="MJX-412-TEX-N-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-412-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-412-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-412-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-412-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-412-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-412-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g transform="translate(0,679.5)"><g ></g><g ><g ><use xlink:href="#MJX-412-TEX-I-1D443"></use></g><g transform="translate(1028.8,0)"><use xlink:href="#MJX-412-TEX-N-3A"></use></g></g><g transform="translate(3639.7,0)"></g><g transform="translate(3639.7,0)"><g ><use xlink:href="#MJX-412-TEX-I-1D462"></use></g><g transform="translate(572,0)"><use xlink:href="#MJX-412-TEX-N-2C"></use></g><g transform="translate(1016.7,0)"><use xlink:href="#MJX-412-TEX-I-1D463"></use></g></g></g><g transform="translate(0,-679.5)"><g ></g><g ><g ><g ><use xlink:href="#MJX-412-TEX-I-1D443"></use></g><g transform="translate(839.5,413) scale(0.707)"><use xlink:href="#MJX-412-TEX-V-2032"></use></g></g><g transform="translate(1361.7,0)"><use xlink:href="#MJX-412-TEX-N-3A"></use></g></g><g transform="translate(3639.7,0)"></g><g transform="translate(3639.7,0)"><g ><use xlink:href="#MJX-412-TEX-I-1D462"></use></g><g transform="translate(794.2,0)"><use xlink:href="#MJX-412-TEX-N-2B"></use></g><g transform="translate(1794.4,0)"><use xlink:href="#MJX-412-TEX-I-1D451"></use></g><g transform="translate(2314.4,0)"><use xlink:href="#MJX-412-TEX-I-1D462"></use></g><g transform="translate(2886.4,0)"><use xlink:href="#MJX-412-TEX-N-2C"></use></g><g transform="translate(3331.1,0)"><use xlink:href="#MJX-412-TEX-I-1D463"></use></g><g transform="translate(4038.3,0)"><use xlink:href="#MJX-412-TEX-N-2B"></use></g><g transform="translate(5038.6,0)"><use xlink:href="#MJX-412-TEX-I-1D451"></use></g><g transform="translate(5558.6,0)"><use xlink:href="#MJX-412-TEX-I-1D463"></use></g><g transform="translate(6043.6,0)"><use xlink:href="#MJX-412-TEX-N-2C"></use></g></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/9.svg b/36114-h/images/9.svg new file mode 100644 index 0000000..e32542c --- /dev/null +++ b/36114-h/images/9.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="778px" height="683px" viewBox="0 -683 778 683" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-722-TEX-N-4B" d="M128 622Q121 629 117 631T101 634T58 637H25V683H36Q57 680 180 680Q315 680 324 683H335V637H313Q235 637 233 620Q232 618 232 462L233 307L379 449Q425 494 479 546Q518 584 524 591T531 607V608Q531 630 503 636Q501 636 498 636T493 637H489V683H499Q517 680 630 680Q704 680 716 683H722V637H708Q633 633 589 597Q584 592 495 506T406 419T515 254T631 80Q644 60 662 54T715 46H736V0H728Q719 3 615 3Q493 3 472 0H461V46H469Q515 46 515 72Q515 78 512 84L336 351Q332 348 278 296L232 251V156Q232 62 235 58Q243 47 302 46H335V0H324Q303 3 180 3Q45 3 36 0H25V46H58Q100 47 109 49T128 61V622Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-722-TEX-N-4B"></use></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/90.svg b/36114-h/images/90.svg new file mode 100644 index 0000000..8c9605d --- /dev/null +++ b/36114-h/images/90.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1092px" height="705px" viewBox="0 -694 1092 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-413-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-413-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-413-TEX-I-1D451"></use></g><g transform="translate(520,0)"><use xlink:href="#MJX-413-TEX-I-1D462"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/91.svg b/36114-h/images/91.svg new file mode 100644 index 0000000..e8d1d8f --- /dev/null +++ b/36114-h/images/91.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1005px" height="705px" viewBox="0 -694 1005 705" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-414-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-414-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-414-TEX-I-1D451"></use></g><g transform="translate(520,0)"><use xlink:href="#MJX-414-TEX-I-1D463"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/92.svg b/36114-h/images/92.svg new file mode 100644 index 0000000..1afcac5 --- /dev/null +++ b/36114-h/images/92.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.023ex;" xmlns="http://www.w3.org/2000/svg" width="989px" height="704px" viewBox="0 -694 989 704" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-471-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-471-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-471-TEX-I-1D451"></use></g><g transform="translate(520,0)"><use xlink:href="#MJX-471-TEX-I-1D460"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/93.svg b/36114-h/images/93.svg new file mode 100644 index 0000000..6547b1c --- /dev/null +++ b/36114-h/images/93.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="15518.4px" height="1088.9px" viewBox="0 -883.9 15518.4 1088.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-418-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-418-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-418-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-418-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-418-TEX-I-1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path><path id="MJX-418-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-418-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-418-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-418-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-418-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-418-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-418-TEX-I-1D460"></use></g><g transform="translate(502,413) scale(0.707)" ><g ><use xlink:href="#MJX-418-TEX-N-32"></use></g></g></g><g transform="translate(1703.3,0)"><use xlink:href="#MJX-418-TEX-N-3D"></use></g><g transform="translate(2759.1,0)"><g ><use xlink:href="#MJX-418-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-418-TEX-N-31"></use><use xlink:href="#MJX-418-TEX-N-31" transform="translate(500,0)"></use></g></g></g><g transform="translate(4026.2,0)"><g ></g></g><g transform="translate(4193.2,0)"><use xlink:href="#MJX-418-TEX-I-1D451"></use></g><g transform="translate(4713.2,0)"><g ><use xlink:href="#MJX-418-TEX-I-1D462"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-418-TEX-N-32"></use></g></g></g><g transform="translate(5944,0)"><use xlink:href="#MJX-418-TEX-N-2B"></use></g><g transform="translate(6944.2,0)"><use xlink:href="#MJX-418-TEX-N-32"></use></g><g transform="translate(7444.2,0)"><g ><use xlink:href="#MJX-418-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-418-TEX-N-31"></use><use xlink:href="#MJX-418-TEX-N-32" transform="translate(500,0)"></use></g></g></g><g transform="translate(8711.3,0)"><g ></g></g><g transform="translate(8878.3,0)"><use xlink:href="#MJX-418-TEX-I-1D451"></use></g><g transform="translate(9398.3,0)"><use xlink:href="#MJX-418-TEX-I-1D462"></use></g><g transform="translate(9970.3,0)"><g ></g></g><g transform="translate(10137.3,0)"><use xlink:href="#MJX-418-TEX-I-1D451"></use></g><g transform="translate(10657.3,0)"><use xlink:href="#MJX-418-TEX-I-1D463"></use></g><g transform="translate(11364.5,0)"><use xlink:href="#MJX-418-TEX-N-2B"></use></g><g transform="translate(12364.8,0)"><g ><use xlink:href="#MJX-418-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-418-TEX-N-32"></use><use xlink:href="#MJX-418-TEX-N-32" transform="translate(500,0)"></use></g></g></g><g transform="translate(13631.9,0)"><g ></g></g><g transform="translate(13798.9,0)"><use xlink:href="#MJX-418-TEX-I-1D451"></use></g><g transform="translate(14318.9,0)"><g ><use xlink:href="#MJX-418-TEX-I-1D463"></use></g><g transform="translate(518,413) scale(0.707)" ><g ><use xlink:href="#MJX-418-TEX-N-32"></use></g></g></g><g transform="translate(15240.4,0)"><use xlink:href="#MJX-418-TEX-N-2C"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/94.svg b/36114-h/images/94.svg new file mode 100644 index 0000000..402c329 --- /dev/null +++ b/36114-h/images/94.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="1267.1px" height="647px" viewBox="0 -442 1267.1 647" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-442-TEX-I-1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path><path id="MJX-442-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-442-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-442-TEX-N-31"></use><use xlink:href="#MJX-442-TEX-N-31" transform="translate(500,0)"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/95.svg b/36114-h/images/95.svg new file mode 100644 index 0000000..4e6184b --- /dev/null +++ b/36114-h/images/95.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="1267.1px" height="647px" viewBox="0 -442 1267.1 647" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-425-TEX-I-1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path><path id="MJX-425-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-425-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-425-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-425-TEX-N-31"></use><use xlink:href="#MJX-425-TEX-N-32" transform="translate(500,0)"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/96.svg b/36114-h/images/96.svg new file mode 100644 index 0000000..eb13bd8 --- /dev/null +++ b/36114-h/images/96.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="1267.1px" height="647px" viewBox="0 -442 1267.1 647" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-426-TEX-I-1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path><path id="MJX-426-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-426-TEX-I-1D454"></use></g><g transform="translate(510,-150) scale(0.707)" ><g ><use xlink:href="#MJX-426-TEX-N-32"></use><use xlink:href="#MJX-426-TEX-N-32" transform="translate(500,0)"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/97.svg b/36114-h/images/97.svg new file mode 100644 index 0000000..966a962 --- /dev/null +++ b/36114-h/images/97.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="7229.7px" height="965.9px" viewBox="0 -883.9 7229.7 965.9" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-431-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-431-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-431-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-431-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-431-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-431-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-431-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-431-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><use xlink:href="#MJX-431-TEX-I-1D451"></use></g><g transform="translate(520,0)"><g ><use xlink:href="#MJX-431-TEX-I-1D460"></use></g><g transform="translate(502,413) scale(0.707)" ><g ><use xlink:href="#MJX-431-TEX-N-32"></use></g></g></g><g transform="translate(1703.3,0)"><use xlink:href="#MJX-431-TEX-N-3D"></use></g><g transform="translate(2759.1,0)"><use xlink:href="#MJX-431-TEX-I-1D451"></use></g><g transform="translate(3279.1,0)"><g ><use xlink:href="#MJX-431-TEX-I-1D462"></use></g><g transform="translate(605,413) scale(0.707)" ><g ><use xlink:href="#MJX-431-TEX-N-32"></use></g></g></g><g transform="translate(4509.9,0)"><use xlink:href="#MJX-431-TEX-N-2B"></use></g><g transform="translate(5510.1,0)"><use xlink:href="#MJX-431-TEX-I-1D451"></use></g><g transform="translate(6030.1,0)"><g ><use xlink:href="#MJX-431-TEX-I-1D463"></use></g><g transform="translate(518,413) scale(0.707)" ><g ><use xlink:href="#MJX-431-TEX-N-32"></use></g></g></g><g transform="translate(6951.7,0)"><use xlink:href="#MJX-431-TEX-N-2E"></use></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/98.svg b/36114-h/images/98.svg new file mode 100644 index 0000000..5aab306 --- /dev/null +++ b/36114-h/images/98.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.339ex;" xmlns="http://www.w3.org/2000/svg" width="1008.6px" height="592px" viewBox="0 -442 1008.6 592" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-695-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-695-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-695-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-695-TEX-N-32"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/99.svg b/36114-h/images/99.svg new file mode 100644 index 0000000..95656a7 --- /dev/null +++ b/36114-h/images/99.svg @@ -0,0 +1 @@ +<svg version="1.1" style="vertical-align: -0.375ex;" xmlns="http://www.w3.org/2000/svg" width="1008.6px" height="607.6px" viewBox="0 -442 1008.6 607.6" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-696-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-696-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g ><g ><g ><use xlink:href="#MJX-696-TEX-I-1D465"></use></g><g transform="translate(605,-150) scale(0.707)" ><g ><use xlink:href="#MJX-696-TEX-N-33"></use></g></g></g></g></g></svg>
\ No newline at end of file diff --git a/36114-h/images/cover.jpg b/36114-h/images/cover.jpg Binary files differnew file mode 100644 index 0000000..7a78761 --- /dev/null +++ b/36114-h/images/cover.jpg diff --git a/36114-h/images/figure01.jpg b/36114-h/images/figure01.jpg Binary files differnew file mode 100644 index 0000000..81fa112 --- /dev/null +++ b/36114-h/images/figure01.jpg diff --git a/36114-h/images/figure02.jpg b/36114-h/images/figure02.jpg Binary files differnew file mode 100644 index 0000000..ff55c86 --- /dev/null +++ b/36114-h/images/figure02.jpg diff --git a/36114-h/images/figure03.jpg b/36114-h/images/figure03.jpg Binary files differnew file mode 100644 index 0000000..7eb7d4e --- /dev/null +++ b/36114-h/images/figure03.jpg diff --git a/36114-h/images/figure04.jpg b/36114-h/images/figure04.jpg Binary files differnew file mode 100644 index 0000000..cb393cb --- /dev/null +++ b/36114-h/images/figure04.jpg diff --git a/36114-h/images/figure05.jpg b/36114-h/images/figure05.jpg Binary files differnew file mode 100644 index 0000000..1f13e30 --- /dev/null +++ b/36114-h/images/figure05.jpg diff --git a/36114-h/images/frontispiece.jpg b/36114-h/images/frontispiece.jpg Binary files differnew file mode 100644 index 0000000..55be612 --- /dev/null +++ b/36114-h/images/frontispiece.jpg diff --git a/36114-pdf.pdf b/36114-pdf.pdf Binary files differnew file mode 100644 index 0000000..5a0a7f9 --- /dev/null +++ b/36114-pdf.pdf diff --git a/36114-pdf.zip b/36114-pdf.zip Binary files differnew file mode 100644 index 0000000..354685d --- /dev/null +++ b/36114-pdf.zip diff --git a/36114-t.zip b/36114-t.zip Binary files differnew file mode 100644 index 0000000..d9342a8 --- /dev/null +++ b/36114-t.zip diff --git a/36114-t/36114-t.tex b/36114-t/36114-t.tex new file mode 100644 index 0000000..9c7681d --- /dev/null +++ b/36114-t/36114-t.tex @@ -0,0 +1,6999 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% +%% Packages and substitutions: %% +%% %% +%% book: Required. %% +%% inputenc: Latin-1 text encoding. Required. %% +%% %% +%% ifthen: Logical conditionals. Required. %% +%% %% +%% amsmath: AMS mathematics enhancements. Required. %% +%% amssymb: Additional mathematical symbols. Required. %% +%% %% +%% alltt: Fixed-width font environment. Required. %% +%% array: Enhanced tabular features. Required. %% +%% %% +%% perpage: Start footnote numbering on each page. Required. %% +%% %% +%% multicol: Twocolumn environment for index. Required. %% +%% makeidx: Indexing. Required. %% +%% %% +%% caption: Caption customization. Required. %% +%% graphicx: Standard interface for graphics inclusion. Required. %% +%% wrapfig: Illustrations surrounded by text. Required. %% +%% %% +%% calc: Length calculations. Required. %% +%% %% +%% fancyhdr: Enhanced running headers and footers. Required. %% +%% %% +%% geometry: Enhanced page layout package. Required. %% +%% hyperref: Hypertext embellishments for pdf output. Required. %% +%% %% +%% %% +%% Producer's Comments: %% +%% %% +%% OCR text for this ebook was obtained on May 7, 2011, from %% +%% http://www.archive.org/details/relativitythespe00einsuoft. %% +%% %% +%% The Methuen book catalogue from the original has been omitted. %% +%% %% +%% Minor changes to the original are noted in this file in three %% +%% ways: %% +%% 1. \Change{}{} for typographical corrections, showing %% +%% original and replacement text side-by-side. %% +%% 2. \Add{} for inconsistent/missing punctuation. %% +%% 3. [** TN: Note]s for lengthier or stylistic comments. %% +%% \Add is implemented in terms of \Change, so redefining \Change %% +%% will "restore" typographical errors in the original. %% +%% %% +%% %% +%% Compilation Flags: %% +%% %% +%% The following behavior may be controlled by boolean flags. %% +%% %% +%% ForPrinting (false by default): %% +%% If true, compile a print-optimized PDF file: Taller text block,%% +%% two-sided layout, US Letter paper, black hyperlinks. Default: %% +%% screen optimized file (one-sided layout, blue hyperlinks). %% +%% %% +%% %% +%% Things to Check: %% +%% %% +%% %% +%% Spellcheck: .................................. OK %% +%% %% +%% lacheck: ..................................... OK %% +%% Numerous false positives from commented code %% +%% %% +%% PDF pages: 147 (if ForPrinting set to false) %% +%% PDF page size: 4.75 x 7" %% +%% PDF bookmarks: created, point to ToC entries %% +%% PDF document info: filled in %% +%% Images: 5 pdf diagrams %% +%% %% +%% Summary of log file: %% +%% * No over- or under-full boxes. %% +%% %% +%% Compile History: %% +%% %% +%% May, 2011: adhere (Andrew D. Hwang) %% +%% texlive2007, GNU/Linux %% +%% %% +%% Command block: %% +%% %% +%% pdflatex x3 %% +%% makeindex %% +%% pdflatex x3 %% +%% %% +%% March 2023: pglatex. %% +%% Compile this project with: %% +%% pdflatex 36114-t.tex ..... THREE times %% +%% makeindex 36114-t.idx %% +%% pdflatex 36114-t.tex ..... THREE times %% +%% %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\listfiles +\documentclass[12pt]{book}[2005/09/16] + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[latin1]{inputenc}[2006/05/05] + +\usepackage{ifthen}[2001/05/26] %% Logical conditionals + +\usepackage{amsmath}[2000/07/18] %% Displayed equations +\usepackage{amssymb}[2002/01/22] %% and additional symbols + +\usepackage{alltt}[1997/06/16] %% boilerplate, credits, license +\usepackage{array}[2005/08/23] %% extended array/tabular features + +\usepackage{perpage}[2006/07/15] + +\usepackage{multicol}[2006/05/18] +\usepackage{makeidx}[2000/03/29] + +\usepackage[font=footnotesize,labelformat=empty]{caption}[2007/01/07] +\usepackage{graphicx}[1999/02/16]%% For diagrams +\usepackage{wrapfig}[2003/01/31] %% and wrapping text around them + +\usepackage{calc}[2005/08/06] + +% for running heads +\usepackage{fancyhdr} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%% Interlude: Set up PRINTING (default) or SCREEN VIEWING %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% ForPrinting=true false (default) +% Asymmetric margins Symmetric margins +% 1 : 1.62 text block aspect ratio 3 : 4 text block aspect ratio +% Black hyperlinks Blue hyperlinks +% Start major marker pages recto No blank verso pages +% +% Chapter-like ``Sections'' start both recto and verso in the scanned +% book. This behavior has been retained. +\newboolean{ForPrinting} + +%% UNCOMMENT the next line for a PRINT-OPTIMIZED VERSION of the text %% +%\setboolean{ForPrinting}{true} + +%% Initialize values to ForPrinting=false +\newcommand{\Margins}{hmarginratio=1:1} % Symmetric margins +\newcommand{\HLinkColor}{blue} % Hyperlink color +\newcommand{\PDFPageLayout}{SinglePage} +\newcommand{\TransNote}{Transcriber's Note} +\newcommand{\TransNoteCommon}{% + The camera-quality files for this public-domain ebook may be + downloaded \textit{gratis} at + \begin{center} + \texttt{www.gutenberg.org/ebooks/\ebook}. + \end{center} + + This ebook was produced using OCR text provided by the University of + Toronto Robarts Library through the Internet Archive. + \bigskip + + Minor typographical corrections and presentational changes have been + made without comment. + \bigskip +} + +\newcommand{\TransNoteText}{% + \TransNoteCommon + + This PDF file is optimized for screen viewing, but may easily be + recompiled for printing. Please consult the preamble of the \LaTeX\ + source file for instructions and other particulars. +} +%% Re-set if ForPrinting=true +\ifthenelse{\boolean{ForPrinting}}{% + \renewcommand{\Margins}{hmarginratio=2:3} % Asymmetric margins + \renewcommand{\HLinkColor}{black} % Hyperlink color + \renewcommand{\PDFPageLayout}{TwoPageRight} + \renewcommand{\TransNote}{Transcriber's Note} + \renewcommand{\TransNoteText}{% + \TransNoteCommon + + This PDF file is optimized for printing, but may easily be + recompiled for screen viewing. Please consult the preamble + of the \LaTeX\ source file for instructions and other particulars. + } +}{% If ForPrinting=false, don't skip to recto + \renewcommand{\cleardoublepage}{\clearpage} +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%% End of PRINTING/SCREEN VIEWING code; back to packages %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\ifthenelse{\boolean{ForPrinting}}{% + \setlength{\paperwidth}{8.5in}% + \setlength{\paperheight}{11in}% +% ~1:1.62 + \usepackage[body={4.5in,7.3in},\Margins]{geometry}[2002/07/08] +}{% + \setlength{\paperwidth}{4.75in}% + \setlength{\paperheight}{7in}% + \raggedbottom +% ~3:4 + \usepackage[body={4.5in,6in},\Margins,includeheadfoot]{geometry}[2002/07/08] +} + +\providecommand{\ebook}{36114} % Overridden during white-washing +\usepackage[pdftex, + hyperfootnotes=false, + pdftitle={The Project Gutenberg eBook \#\ebook: Relativity}, + pdfauthor={Albert Einstein}, + pdfkeywords={University of Toronto, The Internet Archive, Andrew D. Hwang}, + pdfstartview=Fit, % default value + pdfstartpage=1, % default value + pdfpagemode=UseNone, % default value + bookmarks=true, % default value + linktocpage=false, % default value + pdfpagelayout=\PDFPageLayout, + pdfdisplaydoctitle, + pdfpagelabels=true, + bookmarksopen=true, + bookmarksopenlevel=-1, + colorlinks=true, + linkcolor=\HLinkColor]{hyperref}[2007/02/07] + + +%%%% Fixed-width environment to format PG boilerplate %%%% +\newenvironment{PGtext}{% +\begin{alltt} +\fontsize{8.1}{9}\ttfamily\selectfont}% +{\end{alltt}} + +%% No hrule in page header +\renewcommand{\headrulewidth}{0pt} + +% Top-level footnote numbers restart on each page +\MakePerPage{footnote} + +% Running heads +\newcommand{\FlushRunningHeads}{\clearpage\fancyhf{}\cleardoublepage} +\newcommand{\InitRunningHeads}{% + \setlength{\headheight}{15pt} + \pagestyle{fancy} + \thispagestyle{plain} + \ifthenelse{\boolean{ForPrinting}} + {\fancyhead[RO,LE]{\thepage}} + {\fancyhead[R]{\thepage}} +} + +\newcommand{\SetOddHead}[1]{% + \fancyhead[CO]{\textbf{\MakeUppercase{#1}}} +} + +\newcommand{\SetEvenHead}[1]{% + \fancyhead[CE]{\textbf{\MakeUppercase{#1}}} +} + +\newcommand{\BookMark}[2]{\phantomsection\pdfbookmark[#1]{#2}{#2}} + +% ToC formatting +\AtBeginDocument{\renewcommand{\contentsname}% + {\protect\thispagestyle{plain}% + \protect\centering\normalfont\large\textbf{CONTENTS}}} + +\newcommand{\ToCFont}{\centering\normalfont\normalsize\scshape} +\newcommand{\TableofContents}{% + \FlushRunningHeads + \InitRunningHeads + \SetOddHead{Contents} + \BookMark{0}{Contents} + \tableofcontents +} + +% For internal bookkeeping +\newcommand{\ToCAnchor}{} + +%\ToCLine[type]{<label>}{Title}{xref} +\newcommand{\ToCLine}[4][chapter]{% + \label{toc:#4}% + \ifthenelse{\not\equal{\pageref{toc:#4}}{\ToCAnchor}}{% + \renewcommand{\ToCAnchor}{\pageref{toc:#4}}% + \noindent\makebox[\textwidth][r]{\hfill\scriptsize PAGE}\\% + }{}% + \settowidth{\TmpLen}{\;\pageref{#4}}% + \noindent\strut\parbox[b]{\textwidth-\TmpLen}{\small% + \ifthenelse{\not\equal{#2}{}}{% Write unit number at start of line + \ifthenelse{\equal{#1}{appendix}}{% + \settowidth{\TmpLen}{III.}% Widest appendix number + }{% + \settowidth{\TmpLen}{XXVIII.}% Widest chapter number + } + \makebox[\TmpLen][r]{#2}\hspace{0.5em}% + }{}% Empty second argument => no unit number + \raggedright\hangindent6em #3\dotfill}% + \makebox[\TmpLen][r]{\pageref{#4}}% +} + +% Index formatting +\makeindex +\makeatletter +\renewcommand{\@idxitem}{\par\hangindent 30\p@\global\let\idxbrk\nobreak} +\renewcommand\subitem{\idxbrk\@idxitem --- \let\idxbrk\relax} +\renewcommand\subsubitem{\idxbrk\@idxitem --- --- \let\idxbrk\relax} +\renewcommand{\indexspace}{\par\penalty-3000 \vskip 10pt plus5pt minus3pt\relax} + +\renewenvironment{theindex}{% + \setlength\columnseprule{0.5pt}\setlength\columnsep{18pt}% + \cleardoublepage + \phantomsection + \label{index} + \addtocontents{toc}{\ToCLine{}{\textsc{Index}}{index}} + \SetOddHead{Index} + \BookMark{0}{Index} + \begin{multicols}{2}[\SectTitle{Index}\small]% ** N.B. font size + \setlength\parindent{0pt}\setlength\parskip{0pt plus 0.3pt}% + \thispagestyle{plain}\let\item\@idxitem\raggedright% + }{% + \end{multicols}\FlushRunningHeads +} +\makeatother + +% Allows \Part to communicate with \Chapter +\newboolean{StartPart} +\setboolean{StartPart}{false} + +\newcommand{\SectTitle}[2][\large]{% + \section*{\centering#1\MakeUppercase{#2}} +} +\newcommand{\SectSubtitle}[2][\normalsize]{% + \subsection*{\centering#1\MakeUppercase{#2}} +} + +\newcommand{\Part}[3]{% + \setboolean{StartPart}{true} + \ifthenelse{\equal{#1}{I}}{% + \mainmatter + \begin{center} + \textbf{\LARGE RELATIVITY} + \end{center} + }{% + \FlushRunningHeads + }% + \InitRunningHeads + \BookMark{-1}{Part #1. #2} + \label{part:#1} + \SetEvenHead{Relativity} + \SetOddHead{#3} + \addtocontents{toc}{\protect\section*{\protect\ToCFont PART #1}} + \addtocontents{toc}{\protect\subsection*{\protect\ToCFont #2}} + \SectTitle[\Large]{Part #1} + \SectSubtitle{#2} + \bigskip +} + +%\Chapter[PDF name]{Number.}{Heading title} +\newcommand{\Chapter}[3][]{% + \ifthenelse{\boolean{StartPart}}{% + \setboolean{StartPart}{false}% + }{% + \newpage + } + \BookMark{0}{#2. #3} + \label{chapter:#2} + \thispagestyle{plain} + \addtocontents{toc}{\ToCLine{#2.}{#3}{chapter:#2}} + \SectTitle{#2} + \SectSubtitle{#3} +} + +\newcommand{\Section}[1]{% + \newpage + \thispagestyle{plain} + \SectTitle{#1} +} + +\newcommand{\Subsection}[2]{% + \subsection*{\centering\normalsize\normalfont(\Item{#1}) \textsc{#2}} + \ifthenelse{\not\equal{#1}{}}{% + \phantomsection + \label{subsection:#1} + \addtocontents{toc}{% + \ToCLine{(\protect\Item{#1})}{#2}{subsection:#1}% + }% + }{}% +} + +\newcommand{\Bibsection}[1]{% + \subsection*{\centering\normalsize\normalfont\textsc{#1}} +} + +\newcommand{\Preface}{% + \FlushRunningHeads + \InitRunningHeads + \SetOddHead{Relativity} + \SetEvenHead{Relativity} + \BookMark{0}{Preface} + \SectTitle{Preface}% +} + +\newcommand{\Appendix}[3]{% + \clearpage + \BookMark{0}{Appendix #1. #2} + \label{appendix:#1} + \thispagestyle{plain} + \SetOddHead{Appendix #1}% + \ifthenelse{\equal{#1}{I}}{% + \addtocontents{toc}{\protect\section*{\protect\ToCFont APPENDICES}} + }{} + \addtocontents{toc}{\ToCLine[appendix]{#1.}{#2 #3}{appendix:#1}} + \SectTitle{Appendix #1} + \subsection*{\centering\normalsize\normalfont% + \MakeUppercase{#2} \small\textsc{#3}} +} + +\newcommand{\Bibliography}[1]{% + \cleardoublepage + \phantomsection + \label{biblio} + \addtocontents{toc}{\ToCLine{}{\textsc{Bibliography}}{biblio}} + \thispagestyle{plain} + \SetOddHead{Bibliography} + \BookMark{0}{Bibliography} + \SectTitle{Bibliography}% + \SectSubtitle{#1}% +} + +\renewenvironment{itemize}{% + \begin{list}{}{\setlength{\topsep}{4pt plus 8pt}% + \setlength{\itemsep}{0pt plus 2pt}% + \setlength{\parsep}{4pt plus 2pt}% + \setlength{\leftmargin}{4em}}}{\end{list}} + +\newenvironment{CenterPage}{% + \thispagestyle{empty}% + \null\vfill% + \begin{center} + }{% + \end{center} + \vfill% +} + +\newenvironment{PubInfo}{% + \newpage + \begin{CenterPage} + \footnotesize + \settowidth{\TmpLen}{\textit{This Translation was first Published}\qquad} + \begin{tabular}{p{\TmpLen}@{\,}c}% + }{% + \end{tabular} + \end{CenterPage} +} + +\newcommand{\PubRow}[2]{% + \textit{#1}\dotfill & \textit{#2} \\ +} + +\newcommand{\Signature}[2][]{% + \setlength{\TmpLen}{\textwidth-2\parindent}% + \bigskip% + \parbox{\TmpLen}{\centering\small#1\hfill#2}% +} + +\newcommand{\Bibitem}[2]{% +\par\noindent\hangindent2\parindent\textit{#1}: #2\medskip% +} + +\newcommand{\ColHead}[3]{% +\multicolumn{#1}{c}{\settowidth{\TmpLen}{#2}% + \parbox[c]{\TmpLen}{\centering#3\medskip}}% +} + +\newcommand{\Input}[2][] + {\ifthenelse{\equal{#1}{}} + {\includegraphics{./images/#2.pdf}} + {\includegraphics[width=#1]{./images/#2.pdf}}% +} + +\newcounter{figno} +\newcommand{\Figure}[2][0.8\textwidth]{% +\begin{figure}[hbt!] + \refstepcounter{figno} + \centering + \Input[#1]{#2} + \caption{\textsc{Fig}.~\thefigno.} + \label{fig:\thefigno} +\end{figure} +} + +\newcommand{\WFigure}[2]{% +\begin{wrapfigure}{o}{#1} + \refstepcounter{figno} + \centering + \Input[#1]{#2} + \caption{\textsc{Fig}.~\thefigno.} + \label{fig:\thefigno} +\end{wrapfigure} +} + +\newcommand{\First}[1]{\textsc{\large #1}} + +% For corrections. +\newcommand{\Change}[2]{#2} +\newcommand{\Add}[1]{\Change{}{#1}} + +\newcommand{\PageSep}[1]{\ignorespaces} +\setlength{\emergencystretch}{1em} + +\newlength{\TmpLen} + +\DeclareInputText{176}{\ifmmode{{}^\circ}\else\textdegree\fi} +\DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi} + +\newcommand{\Tag}[1]{% + \phantomsection + \label{eqn:#1} + \tag*{\ensuremath{#1}} +} + +% and links +\newcommand{\Eqref}[1]{\hyperref[eqn:#1]{\ensuremath{#1}}} +\newcommand{\Figref}[1]{\hyperref[fig:#1]{Fig.~#1}} +\newcommand{\Partref}[1]{\hyperref[part:#1]{Part~#1}} +\newcommand{\Sectionref}[1]{\hyperref[chapter:#1]{Section~#1}} +\newcommand{\Srefno}[1]{\hyperref[chapter:#1]{#1}} +\newcommand{\Appendixref}[1]{\hyperref[appendix:#1]{Appendix~#1}} + +\newcommand{\ie}{\textit{i.e.}} +\newcommand{\eg}{\textit{e.g.}} +\newcommand{\NB}{\textit{N.B.}} +\newcommand{\Item}[1]{\textit{#1}} + +\newcommand{\itema}{(\Item{a})} +\newcommand{\itemb}{(\Item{b})} +\newcommand{\itemc}{(\Item{c})} + +\newcommand{\Z}{\phantom{0}} + +%%%%%%%%%%%%%%%%%%%%%%%% START OF DOCUMENT %%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} +\pagenumbering{Alph} +\pagestyle{empty} +\BookMark{-1}{Front Matter} +%%%% PG BOILERPLATE %%%% +\BookMark{0}{PG Boilerplate} +\begin{center} +\begin{minipage}{\textwidth} +\small +\begin{PGtext} +The Project Gutenberg EBook of Relativity: The Special and the General +Theory, by Albert Einstein + +This eBook is for the use of anyone anywhere in the United States and +most other parts of the world at no cost and with almost no restrictions +whatsoever. You may copy it, give it away or re-use it under the terms +of the Project Gutenberg License included with this eBook or online at +www.gutenberg.org. If you are not located in the United States, you +will have to check the laws of the country where you are located before +using this eBook. + +Title: Relativity: The Special and the General Theory + A Popular Exposition, 3rd ed. + +Author: Albert Einstein + +Translator: Robert W. Lawson + +Release Date: May 15, 2011 [eBook #36114] + Most recently updated: March 31, 2023 + +Language: English + +Character set encoding: UTF-8 + +*** START OF THE PROJECT GUTENBERG EBOOK RELATIVITY *** +\end{PGtext} +\end{minipage} +\end{center} +\newpage +%%%% Credits and transcriber's note %%%% +\begin{center} +\begin{minipage}{\textwidth} +\begin{PGtext} +Produced by Andrew D. Hwang. (This ebook was produced using +OCR text generously provided by the University of Toronto +Robarts Library through the Internet Archive.) +\end{PGtext} +\end{minipage} +\end{center} +\vfill + +\begin{minipage}{0.85\textwidth} +\small +\BookMark{0}{Transcriber's Note} +\subsection*{\centering\normalfont\scshape% +\normalsize\MakeLowercase{\TransNote}}% + +\raggedright +\TransNoteText +\end{minipage} +%%%%%%%%%%%%%%%%%%%%%%%%%%% FRONT MATTER %%%%%%%%%%%%%%%%%%%%%%%%%% +\frontmatter +\pagestyle{empty} +\begin{center} +\bfseries \Huge RELATIVITY \\ +\medskip +\normalsize THE SPECIAL \textit{\&} THE GENERAL THEORY \\ +\medskip +\small A POPULAR EXPOSITION +\vfill + +\footnotesize BY \\ +\Large ALBERT EINSTEIN, Ph.D. \\ +\smallskip\normalfont\scriptsize +PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN +\vfill + +\footnotesize AUTHORISED TRANSLATION BY \\ +\normalsize \textbf{ROBERT W. LAWSON, D.Sc.} \\ +\smallskip\scriptsize UNIVERSITY OF SHEFFIELD +\vfill + +\footnotesize WITH FIVE DIAGRAMS \\ +AND A PORTRAIT OF THE AUTHOR +\vfill\vfill + +THIRD EDITION +\vfill\vfill + + +\normalsize\bfseries METHUEN \& CO. LTD. \\ +36 ESSEX STREET W.C. \\ +LONDON +\end{center} +\PageSep{iv} +\begin{PubInfo} +\PubRow{This Translation was first Published}{August 19th 1920} +\PubRow{Second Edition}{September 1920} +\PubRow{Third Edition}{1920} +\end{PubInfo} +\PageSep{v} + + +\Preface + +\First{The} present book is intended, as far as possible, +to give an exact insight into the theory of Relativity +to those readers who, from a general +scientific and philosophical point of view, are interested +in the theory, but who are not conversant with the +mathematical apparatus\footnote + {The mathematical fundaments of the special theory of + relativity are to be found in the original papers of H.~A. Lorentz, + A.~Einstein, H.~Minkowski, published under the title \textit{Das + Relativitätsprinzip} (The Principle of Relativity) in B.~G. + Teubner's collection of monographs \textit{Fortschritte der mathematischen + Wissenschaften} (Advances in the Mathematical + Sciences), also in M.~Laue's exhaustive book \textit{Das Relativitätsprinzip}---published + by Friedr.\ Vieweg \&~Son, Braunschweig. + The general theory of relativity, together with the necessary + parts of the theory of invariants, is dealt with in the author's + book \textit{Die Grundlagen der allgemeinen Relativitätstheorie} (The + Foundations of the General Theory of Relativity) Joh.\ Ambr.\ + Barth,~1916; this book assumes some familiarity with the special + theory of relativity.} +of theoretical physics. The +work presumes a standard of education corresponding +to that of a university matriculation examination, +and, despite the shortness of the book, a fair amount +of patience and force of will on the part of the reader. +The author has spared himself no pains in his endeavour +\PageSep{vi} +to present the main ideas in the simplest and most intelligible +form, and on the whole, in the sequence and connection +in which they actually originated. In the interest +of clearness, it appeared to me inevitable that I should +repeat myself frequently, without paying the slightest +attention to the elegance of the presentation. I adhered +scrupulously to the precept of that brilliant theoretical +physicist L.~Boltzmann, according to whom matters of +elegance ought to be left to the tailor and to the cobbler. +I make no pretence of having withheld from the reader +difficulties which are inherent to the subject. On the +other hand, I have purposely treated the empirical +physical foundations of the theory in a ``step-motherly'' +fashion, so that readers unfamiliar with physics may +not feel like the wanderer who was unable to see the +forest for trees. May the book bring some one a few +happy hours of suggestive thought! + +\Signature[\textit{December}, 1916]{A. EINSTEIN} + + +\SectTitle{Note to the Third Edition} + +\First{In} the present year (1918) an excellent and detailed +manual on the general theory of relativity, written +by H.~Weyl, was published by the firm Julius +Springer (Berlin). This book, entitled \textit{Raum---Zeit---Materie} +(Space---Time---Matter), may be warmly recommended +to mathematicians and physicists. +\PageSep{vii} + + +\Section{Biographical Note} + +\First{Albert Einstein} is the son of German-Jewish +parents. He was born in~1879 in the +town of Ulm, Würtemberg, Germany. His +schooldays were spent in Munich, where he attended +the \textit{Gymnasium} until his sixteenth year. After leaving +school at Munich, he accompanied his parents to Milan, +whence he proceeded to Switzerland six months later +to continue his studies. + +From 1896 to 1900 Albert Einstein studied mathematics +and physics at the Technical High School in +Zurich, as he intended becoming a secondary school +(\textit{Gymnasium}) teacher. For some time afterwards he +was a private tutor, and having meanwhile become +naturalised, he obtained a post as engineer in the Swiss +Patent Office in~1902 which position he occupied till +1909. The main ideas involved in the most important +of Einstein's theories date back to this period. Amongst +these may be mentioned: \textit{The Special Theory of Relativity}, +\textit{Inertia of Energy}, \textit{Theory of the Brownian Movement}, +and the \textit{Quantum-Law of the Emission and Absorption of Light}~(1905). +These were followed some years +\PageSep{viii} +later by the \textit{Theory of the Specific Heat of Solid Bodies}, +and the fundamental idea of the \textit{General Theory of +Relativity}. + +During the interval 1909~to~1911 he occupied the post +of Professor \textit{Extraordinarius} at the University of Zurich, +afterwards being appointed to the University of Prague, +Bohemia, where he remained as Professor \textit{Ordinarius} +until~1912. In the latter year Professor Einstein +accepted a similar chair at the \textit{Polytechnikum}, Zurich, +and continued his activities there until~1914, when he +received a call to the Prussian Academy of Science, +Berlin, as successor to Van't~Hoff. Professor Einstein +is able to devote himself freely to his studies at the +Berlin Academy, and it was here that he succeeded in +completing his work on the \textit{General Theory of Relativity} +(1915--17). Professor Einstein also lectures on various +special branches of physics at the University of Berlin, +and, in addition, he is Director of the Institute for +Physical Research of the \textit{Kaiser Wilhelm Gesellschaft}. + +Professor Einstein has been twice married. His first +wife, whom he married at Berne in~1903, was a fellow-student +from Serbia. There were two sons of this +marriage, both of whom are living in Zurich, the elder +being sixteen years of age. Recently Professor Einstein +married a widowed cousin, with whom he is now living +in Berlin. + +\Signature{R. W. L.} +\PageSep{ix} + +\Section{Translator's Note} + +\First{In} presenting this translation to the English-reading +public, it is hardly necessary for me to +enlarge on the Author's prefatory remarks, except +to draw attention to those additions to the book which +do not appear in the original. + +At my request, Professor Einstein kindly supplied +me with a portrait of himself, by one of Germany's +most celebrated artists. \Appendixref{III}, on ``The +Experimental Confirmation of the General Theory of +Relativity,'' has been written specially for this translation. +Apart from these valuable additions to the book, +I have included a biographical note on the Author, +and, at the end of the book, an Index and a list of +English references to the subject. This list, which is more +suggestive than exhaustive, is intended as a guide to those +readers who wish to pursue the subject farther. + +I desire to tender my best thanks to my colleagues +Professor S.~R. Milner,~D.Sc., and Mr.~W.~E. Curtis, +A.R.C.Sc.,~F.R.A.S., also to my friend Dr.~Arthur +Holmes, A.R.C.Sc.,~F.G.S., of the Imperial College, +for their kindness in reading through the manuscript, +\PageSep{x} +for helpful criticism, and for numerous suggestions. I +owe an expression of thanks also to Messrs.\ Methuen +for their ready counsel and advice, and for the care +they have bestowed on the work during the course of +its publication. + +\Signature{ROBERT W. LAWSON} + +\noindent\textsc{The Physics Laboratory} \\ +\hspace*{\parindent}\textsc{The University of Sheffield} \\ +\hspace*{3\parindent}\textit{June} 12, 1920 +\PageSep{xi} +\TableofContents % [** TN: Auto-generate the table of contents] +\iffalse %%%% Start of table of contents text %%%% +CONTENTS + +PART I + +THE SPECIAL THEORY OF RELATIVITY + +PAGE + + I. Physical Meaning of Geometrical Propositions . 1 + II. The System of Co-ordinates . 5 +III. Space and Time in Classical Mechanics . . 9 + IV. The Galileian System of Co-ordinates . .11 + V. The Principle of Relativity (in the Restricted + Sense) . . . . . .12 + VI. The Theorem of the Addition of Velocities employed + in Classical Mechanics . . 16 +VII. The Apparent Incompatibility of the Law of + Propagation of Light with the Principle of + Relativity . . . . 17 + +VIII. On the Idea of Time in Physics . . .21 + IX. The Relativity of Simultaneity . . .25 + X. On the Relativity of the Conception of Distance 28 + XI. The Lorentz Transformation . . .30 + XII. The Behaviour of Measuring-Rods and Clocks + in Motion . . . . 35 +\PageSep{xii} +XIII. Theorem of the Addition of Velocities. The + Experiment of Fizeau . . 3 %[** TN: Edge of page cut off] + XIV. The Heuristic Value of the Theory of Relativity 4 + XV. General Results of the Theory . . .4, + XVI. Experience and the Special Theory of Relativity 4 +XVII. Minkowski's Four-dimensional Space . . 5; + +PART II +THE GENERAL THEORY OF RELATIVITY + +XVIII. Special and General Principle of Relativity . 5 + XIX. The Gravitational Field . . . .6 + XX. The Equality of Inertial and Gravitational Mass + as an Argument for the General Postulate + of Relativity ..... + XXI. In what Respects are the Foundations of Classical + Mechanics and of the Special Theory + of Relativity unsatisfactory? . + XXII. A Few Inferences from the General Principle of + Relativity ..... +XXIII. Behaviour of Clocks and Measuring-Rods on a + Rotating Body of Reference . + XXIV. Euclidean and Non-Euclidean Continuum + XXV. Gaussian Co-ordinates .... + XXVI. The Space-time Continuum of the Special + Theory of Relativity considered as a + Euclidean Continuum +\PageSep{xiii} +PAGE + + XXVII. The Space-time Continuum of the General + Theory of Relativity is not a Euclidean + Continuum . . . . 93 +XXVIII. Exact Formulation of the General Principle of + Relativity . . . . 97 + XXIX. The Solution of the Problem of Gravitation on + the Basis of the General Principle of + Relativity ..... 100 + +PART III + +CONSIDERATIONS ON THE UNIVERSE +AS A WHOLE + + XXX. Cosmological Difficulties of Newton's Theory 105 + XXXI. The Possibility of a ``Finite'' and yet ``Unbounded'' + Universe. . . . 108 + XXXII. The Structure of Space according to the + General Theory of Relativity . . 113 + +APPENDICES + + I. Simple Derivation of the Lorentz Transformation . 115 + II. Minkowski's Four-dimensional Space (``World'') + [Supplementary to Section XVII.] . . 121 +III. The Experimental Confirmation of the General + Theory of Relativity . . . .123 +(a) Motion of the Perihelion of Mercury . 124 +(b) Deflection of Light by a Gravitational Field 126 +(c) Displacement of Spectral Lines towards the + Red . . . . . 129 + +BIBLIOGRAPHY . . . . . . 133 + +INDEX . . . . . . .135 +\fi %%%% End of table of contents text %%%% +\PageSep{xiv} +\FlushRunningHeads +\begin{CenterPage} + \bfseries\LARGE RELATIVITY \\[8pt] + \normalsize THE SPECIAL AND THE GENERAL THEORY +\end{CenterPage} +\PageSep{1} +\index{Manifold|see{Continuum}}% + + +\Part{I}{The Special Theory of Relativity}{Special Theory of Relativity} +\index{Special theory of relativity|(}% + +\Chapter[Geometrical Propositions] +{I}{Physical Meaning of Geometrical +Propositions} + +\First{In} your schooldays most of you who read this +\index{Euclidean geometry}% +book made acquaintance with the noble building of +Euclid's geometry, and you remember---perhaps +with more respect than love---the magnificent structure, +on the lofty staircase of which you were chased about +for uncounted hours by conscientious teachers. By +reason of your past experience, you would certainly +regard everyone with disdain who should pronounce even +the most out-of-the-way proposition of this science to +be untrue. But perhaps this feeling of proud certainty +would leave you immediately if some one were to ask +you: ``What, then, do you mean by the assertion that +these propositions are true?'' Let us proceed to give +this question a little consideration. + +Geometry sets out from certain conceptions such as +\index{Geometrical ideas!truth of|(}% +``plane,'' ``point,'' and ``straight line,'' with which +\index{Plane}% +\index{Point}% +\index{Straight line|(}% +\PageSep{2} +we are able to associate more or less definite ideas, and +from certain simple propositions (axioms) which, +\index{Axioms}% +\index{Axioms!truth of}% +\index{Geometrical ideas!propositions}% +in virtue of these ideas, we are inclined to accept as +``true.'' Then, on the basis of a logical process, the +justification of which we feel ourselves compelled to +admit, all remaining propositions are shown to follow +from those axioms, \ie\ they are proven. A proposition +is then correct (``true'') when it has been derived in the +recognised manner from the axioms. The question +of the ``truth'' of the individual geometrical propositions +\index{Truth@{``Truth''}}% +is thus reduced to one of the ``truth'' of the +axioms. Now it has long been known that the last +question is not only unanswerable by the methods of +geometry, but that it is in itself entirely without meaning. +We cannot ask whether it is true that only one +straight line goes through two points. We can only +say that Euclidean geometry deals with things called +\index{Euclidean geometry}% +``straight lines,'' to each of which is ascribed the property +of being uniquely determined by two points +situated on it. The concept ``true'' does not tally with +the assertions of pure geometry, because by the word +``true'' we are eventually in the habit of designating +always the correspondence with a ``real'' object; +geometry, however, is not concerned with the relation +of the ideas involved in it to objects of experience, but +only with the logical connection of these ideas among +themselves. + +It is not difficult to understand why, in spite of this, +we feel constrained to call the propositions of geometry +``true.'' Geometrical ideas correspond to more or less +\index{Geometrical ideas}% +exact objects in nature, and these last are undoubtedly +the exclusive cause of the genesis of those ideas. Geometry +ought to refrain from such a course, in order to +\PageSep{3} +give to its structure the largest possible logical unity. +The practice, for example, of seeing in a ``distance'' +two marked positions on a practically rigid body is +something which is lodged deeply in our habit of thought. +We are accustomed further to regard three points as +being situated on a straight line, if their apparent +positions can be made to coincide for observation with +one eye, under suitable choice of our place of observation. + +If, in pursuance of our habit of thought, we now +supplement the propositions of Euclidean geometry by +\index{Euclidean geometry!propositions of}% +the single proposition that two points on a practically +rigid body always correspond to the same distance +\index{Distance (line-interval)}% +(line-interval), independently of any changes in position +to which we may subject the body, the propositions of +Euclidean geometry then resolve themselves into propositions +on the possible relative position of practically +\index{Relative!position}% +rigid bodies.\footnote + {It follows that a natural object is associated also with a + straight line. Three points $A$,~$B$ and~$C$ on a rigid body thus + lie in a straight line when, the points $A$~and~$C$ being given, $B$ + is chosen such that the sum of the distances $AB$~and~$BC$ is as + short as possible. This incomplete suggestion will suffice for + our present purpose.} +Geometry which has been supplemented +in this way is then to be treated as a branch of physics. +We can now legitimately ask as to the ``truth'' of +geometrical propositions interpreted in this way, since +we are justified in asking whether these propositions +are satisfied for those real things we have associated +with the geometrical ideas. In less exact terms we can +\index{Geometrical ideas}% +express this by saying that by the ``truth'' of a geometrical +proposition in this sense we understand its +validity for a construction with ruler and compasses. +\index{Straight line|)}% +\PageSep{4} + +Of course the conviction of the ``truth'' of geometrical +propositions in this sense is founded exclusively +on rather incomplete experience. For the present we +shall assume the ``truth'' of the geometrical propositions, +then at a later stage (in the general theory of +relativity) we shall see that this ``truth'' is limited, +and we shall consider the extent of its limitation. +\index{Geometrical ideas!truth of|)}% +\PageSep{5} + + +\Chapter{II}{The System of Co-ordinates} +\index{System of co-ordinates}% + +\First{On} the basis of the physical interpretation of distance +\index{Distance (line-interval)}% +\index{Distance (line-interval)!physical interpretation of}% +\index{Measuring-rod}% +\index{Reference-body}% +which has been indicated, we are also +in a position to establish the distance between +two points on a rigid body by means of measurements. +For this purpose we require a ``distance'' (rod~$S$) +which is to be used once and for all, and which we +employ as a standard measure. If, now, $A$~and~$B$ are +two points on a rigid body, we can construct the +line joining them according to the rules of geometry; +then, starting from~$A$, we can mark off the distance~$S$ +time after time until we reach~$B$. The number of +these operations required is the numerical measure +of the distance~$AB$. This is the basis of all measurement +of length.\footnote + {Here we have assumed that there is nothing left over, \ie\ + that the measurement gives a whole number. This difficulty + is got over by the use of divided measuring-rods, the introduction + of which does not demand any fundamentally new method.} + +Every description of the scene of an event or of the +position of an object in space is based on the specification +of the point on a rigid body (body of reference) +with which that event or object coincides. This applies +not only to scientific description, but also to everyday +life. If I analyse the place specification ``Trafalgar +\index{Place specification}% +\PageSep{6} +Square, London,''\footnote + {I have chosen this as being more familiar to the English + reader than the ``Potsdamer Platz, Berlin,'' which is referred to + in the original. (R.~W.~L.)} +I arrive at the following result. +The earth is the rigid body to which the specification +of place refers; ``Trafalgar Square, London,'' is a +well-defined point, to which a name has been assigned, +and with which the event coincides in space.\footnote + {It is not necessary here to investigate further the significance + of the expression ``coincidence in space.'' This conception is + sufficiently obvious to ensure that differences of opinion are + scarcely likely to arise as to its applicability in practice.} + +This primitive method of place specification deals +\index{Place specification}% +only with places on the surface of rigid bodies, and is +dependent on the existence of points on this surface +which are distinguishable from each other. But we +can free ourselves from both of these limitations without +altering the nature of our specification of position. +\index{Conception of mass!position}% +If, for instance, a cloud is hovering over Trafalgar +Square, then we can determine its position relative to +the surface of the earth by erecting a pole perpendicularly +on the Square, so that it reaches the cloud. The +length of the pole measured with the standard measuring-rod, +\index{Measuring-rod}% +combined with the specification of the position of +the foot of the pole, supplies us with a complete place +specification. On the basis of this illustration, we are +able to see the manner in which a refinement of the conception +of position has been developed. + +\itema~We imagine the rigid body, to which the place +specification is referred, supplemented in such a manner +that the object whose position we require is reached by +the completed rigid body. + +\itemb~In locating the position of the object, we make +use of a number (here the length of the pole measured +\PageSep{7} +with the measuring-rod) instead of designated points of +reference. + +\itemc~We speak of the height of the cloud even when the +pole which reaches the cloud has not been erected. +By means of optical observations of the cloud from +different positions on the ground, and taking into account +the properties of the propagation of light, we determine +the length of the pole we should have required in order +to reach the cloud. + +From this consideration we see that it will be advantageous +\index{Physics}% +if, in the description of position, it should be +possible by means of numerical measures to make ourselves +independent of the existence of marked positions +(possessing names) on the rigid body of reference. In +\index{Reference-body}% +the physics of measurement this is attained by the +\index{Physics!of measurement}% +application of the Cartesian system of co-ordinates. +\index{Cartesian system of co-ordinates}% + +This consists of three plane surfaces perpendicular +to each other and rigidly attached to a rigid body. +Referred to a system of co-ordinates, the scene of any +event will be determined (for the main part) by the +specification of the lengths of the three perpendiculars +or co-ordinates $(x, y, z)$ which can be dropped from the +scene of the event to those three plane surfaces. The +lengths of these three perpendiculars can be determined +by a series of manipulations with rigid measuring-rods +performed according to the rules and methods laid +down by Euclidean geometry. + +In practice, the rigid surfaces which constitute the +system of co-ordinates are generally not available; +furthermore, the magnitudes of the co-ordinates are not +actually determined by constructions with rigid rods, but +by indirect means. If the results of physics and astronomy +\index{Astronomy}% +are to maintain their clearness, the physical meaning +\PageSep{8} +of specifications of position must always be sought +in accordance with the above considerations.\footnote + {A refinement and modification of these views does not become + necessary until we come to deal with the general theory of + relativity, treated in the second part of this book.} + +We thus obtain the following result: Every description +of events in space involves the use of a rigid body +to which such events have to be referred. The resulting +relationship takes for granted that the laws of Euclidean +\index{Distance (line-interval)}% +\index{Euclidean geometry!propositions of}% +geometry hold for ``distances,'' the ``distance'' being +represented physically by means of the convention of +two marks on a rigid body. +\PageSep{9} + + +\Chapter{III}{Space and Time in Classical Mechanics} +\index{Classical mechanics}% +\index{Space}% + +\Change{}{``}\First{The} purpose of mechanics is to describe how +bodies change their position in space with +\index{Position}% +time.'' I should load my conscience with grave +sins against the sacred spirit of lucidity were I to +formulate the aims of mechanics in this way, without +serious reflection and detailed explanations. Let us +proceed to disclose these sins. + +It is not clear what is to be understood here by +\index{Reference-body|(}% +``position'' and ``space.'' I stand at the window of a +railway carriage which is travelling uniformly, and drop +a stone on the embankment, without throwing it. Then, +disregarding the influence of the air resistance, I see the +stone descend in a straight line. A pedestrian who +\index{Straight line}% +observes the misdeed from the footpath notices that the +stone falls to earth in a parabolic curve. I now ask: +Do the ``positions'' traversed by the stone lie ``in +reality'' on a straight line or on a parabola? Moreover, +\index{Parabola}% +what is meant here by motion ``in space''? From the +considerations of the previous section the answer is +self-evident. In the first place, we entirely shun the +vague word ``space,'' of which, we must honestly +acknowledge, we cannot form the slightest conception, +and we replace it by ``motion relative to a +practically rigid body of reference.'' The positions +relative to the body of reference (railway carriage or +embankment) have already been defined in detail in the +\PageSep{10} +preceding section. If instead of ``body of reference'' +we insert ``system of co-ordinates,'' which is a useful +\index{System of co-ordinates}% +idea for mathematical description, we are in a position +to say: The stone traverses a straight line relative to a +\index{Straight line}% +system of co-ordinates rigidly attached to the carriage, +but relative to a system of co-ordinates rigidly attached +to the ground (embankment) it describes a parabola. +\index{Parabola}% +With the aid of this example it is clearly seen that there +is no such thing as an independently existing trajectory +\index{Trajectory}% +(lit. ``path-curve''\footnotemark), but only a trajectory relative to a +\index{Path-curve}% +particular body of reference. +\footnotetext{That is, a curve along which the body moves.} + +In order to have a \emph{complete} description of the motion, +we must specify how the body alters its position \emph{with +time}; \ie\ for every point on the trajectory it must be +stated at what time the body is situated there. These +data must be supplemented by such a definition of +time that, in virtue of this definition, these time-values +can be regarded essentially as magnitudes (results of +measurements) capable of observation. If we take our +stand on the ground of classical mechanics, we can +satisfy this requirement for our illustration in the +following manner. We imagine two clocks of identical +\index{Clocks}% +construction; the man at the railway-carriage window +is holding one of them, and the man on the footpath +the other. Each of the observers determines +the position on his own reference-body occupied by the +stone at each tick of the clock he is holding in his +hand. In this connection we have not taken account +of the inaccuracy involved by the finiteness of the +velocity of propagation of light. With this and with a +\index{Velocity of light}% +second difficulty prevailing here we shall have to deal +in detail later. +\PageSep{11} + + +\Chapter{IV}{The Galileian System of Co-ordinates} +\index{Galileian system of co-ordinates}% +\index{System of co-ordinates}% + +\First{As} is well known, the fundamental law of the +mechanics of Galilei-Newton, which is known +\index{Galilei}% +\index{Newton}% +as the \emph{law of inertia}, can be stated thus: +\index{Law of inertia}% +A body removed sufficiently far from other bodies +continues in a state of rest or of uniform motion +in a straight line. This law not only says something +about the motion of the bodies, but it also +indicates the reference-bodies or systems of co-ordinates, +permissible in mechanics, which can be used +in mechanical description. The visible fixed stars are +\index{Fixed stars}% +bodies for which the law of inertia certainly holds to a +high degree of approximation. Now if we use a system +of co-ordinates which is rigidly attached to the earth, +then, relative to this system, every fixed star describes +a circle of immense radius in the course of an astronomical +day, a result which is opposed to the statement +\index{Astronomical day}% +of the law of inertia. So that if we adhere to this law +we must refer these motions only to systems of co-ordinates +relative to which the fixed stars do not move +in a circle. A system of co-ordinates of which the state +of motion is such that the law of inertia holds relative to +it is called a ``Galileian system of co-ordinates.'' The +laws of the mechanics of Galilei-Newton can be regarded +as valid only for a Galileian system of co-ordinates. +\index{Reference-body|)}% +\PageSep{12} + + +\Chapter{V}{The Principle of Relativity (In the +Restricted Sense)} + +\First{In} order to attain the greatest possible clearness, +let us return to our example of the railway carriage +supposed to be travelling uniformly. We call its +motion a uniform translation (``uniform'' because +\index{Uniform translation}% +it is of constant velocity and direction, ``translation'' +because although the carriage changes its position +relative to the embankment yet it does not rotate +in so doing). Let us imagine a raven flying through +the air in such a manner that its motion, as observed +from the embankment, is uniform and in a straight +line. If we were to observe the flying raven from +the moving railway carriage, we should find that the +motion of the raven would be one of different velocity +and direction, but that it would still be uniform +and in a straight line. Expressed in an abstract +manner we may say: If a mass~$m$ is moving uniformly +in a straight line with respect to a co-ordinate +system~$K$, then it will also be moving uniformly and in a +straight line relative to a second co-ordinate system~$K'$, +provided that the latter is executing a uniform +translatory motion with respect to~$K$. In accordance +with the discussion contained in the preceding section, +it follows that: +\PageSep{13} + +If $K$~is a Galileian co-ordinate system, then every other +\index{Galileian system of co-ordinates}% +co-ordinate system~$K'$ is a Galileian one, when, in relation +to~$K$, it is in a condition of uniform motion of translation. +\index{Motion!of heavenly bodies}% +Relative to~$K'$ the mechanical laws of Galilei-Newton +\index{Laws of Galilei-Newton}% +hold good exactly as they do with respect to~$K$. + +We advance a step farther in our generalisation when +we express the tenet thus: If, relative to~$K$, $K'$~is a +uniformly moving co-ordinate system devoid of rotation, +then natural phenomena run their course with respect to~$K'$ +according to exactly the same general laws as with +respect to~$K$. This statement is called the \emph{principle +of relativity} (in the restricted sense). + +As long as one was convinced that all natural phenomena +were capable of representation with the help of +classical mechanics, there was no need to doubt the +\index{Classical mechanics}% +\index{Classical mechanics!truth of}% +validity of this principle of relativity. But in view of +\index{Principle of relativity|(}% +the more recent development of electrodynamics and +\index{Electrodynamics}% +optics it became more and more evident that classical +\index{Optics}% +mechanics affords an insufficient foundation for the +physical description of all natural phenomena. At this +juncture the question of the validity of the principle of +relativity became ripe for discussion, and it did not +appear impossible that the answer to this question +might be in the negative. + +Nevertheless, there are two general facts which at the +outset speak very much in favour of the validity of the +principle of relativity. Even though classical mechanics +does not supply us with a sufficiently broad basis for the +theoretical presentation of all physical phenomena, +still we must grant it a considerable measure of ``truth,'' +since it supplies us with the actual motions of the +heavenly bodies with a delicacy of detail little short of +wonderful. The principle of relativity must therefore +\PageSep{14} +apply with great accuracy in the domain of \emph{mechanics}. +\index{Classical mechanics}% +But that a principle of such broad generality should +hold with such exactness in one domain of phenomena, +and yet should be invalid for another, is \textit{a~priori} not +very probable. + +We now proceed to the second argument, to which, +moreover, we shall return later. If the principle of relativity +(in the restricted sense) does not hold, then the +Galileian co-ordinate systems $K$,~$K'$, $K''$,~etc., which are +\index{Galileian system of co-ordinates}% +moving uniformly relative to each other, will not be +\emph{equivalent} for the description of natural phenomena. +\index{Equivalent}% +In this case we should be constrained to believe that +natural laws are capable of being formulated in a particularly +simple manner, and of course only on condition +that, from amongst all possible Galileian co-ordinate +systems, we should have chosen \emph{one}~($K_{0}$) of a particular +state of motion as our body of reference. We should +\index{Motion}% +then be justified (because of its merits for the description +of natural phenomena) in calling this system ``absolutely +at rest,'' and all other Galileian systems~$K$ ``in motion.'' +\index{Rest}% +If, for instance, our embankment were the system~$K_{0}$, +then our railway carriage would be a system~$K$, +relative to which less simple laws would hold than with +respect to~$K_{0}$. This diminished simplicity would be +due to the fact that the carriage~$K$ would be in motion +(\ie\ ``really'') with respect to~$K_{0}$. In the general laws +of nature which have been formulated with reference +to~$K$, the magnitude and direction of the velocity +of the carriage would necessarily play a part. We should +expect, for instance, that the note emitted by an organ-pipe +\index{Organ-pipe, note of}% +placed with its axis parallel to the direction of +travel would be different from that emitted if the axis +of the pipe were placed perpendicular to this direction. +\PageSep{15} +Now in virtue of its motion in an orbit round the sun, +\index{Motion!of heavenly bodies}% +our earth is comparable with a railway carriage travelling +with a velocity of about $30$~kilometres per~second. +If the principle of relativity were not valid we should +therefore expect that the direction of motion of the +earth at any moment would enter into the laws of nature, +and also that physical systems in their behaviour would +be dependent on the orientation in space with respect +to the earth. For owing to the alteration in direction +of the velocity of revolution of the earth in the course +of a year, the earth cannot be at rest relative to the +hypothetical system~$K_{0}$ throughout the whole year. +However, the most careful observations have never +revealed such anisotropic properties in terrestrial physical +\index{Terrestrial space}% +space, \ie\ a physical non-equivalence of different +directions. This is very powerful argument in favour +of the principle of relativity. +\index{Principle of relativity|)}% +\PageSep{16} + + +\Chapter{VI}{The Theorem of the Addition of Velocities +employed in Classical Mechanics} +\index{Addition of velocities}% +\index{Classical mechanics}% + +\First{Let} us suppose our old friend the railway carriage +to be travelling along the rails with a constant +velocity~$v$, and that a man traverses the length of +the carriage in the direction of travel with a velocity~$w$. +How quickly or, in other words, with what velocity~$W$ +does the man advance relative to the embankment +during the process? The only possible answer seems to +result from the following consideration: If the man were +to stand still for a second, he would advance relative to +the embankment through a distance~$v$ equal numerically +to the velocity of the carriage. As a consequence of +his walking, however, he traverses an additional distance~$w$ +relative to the carriage, and hence also relative to the +embankment, in this second, the distance~$w$ being +numerically equal to the velocity with which he is +walking. Thus in total he covers the distance $W = v + w$ +relative to the embankment in the second considered. +We shall see later that this result, which expresses +the theorem of the addition of velocities employed in +classical mechanics, cannot be maintained; in other +words, the law that we have just written down does not +hold in reality. For the time being, however, we shall +assume its correctness. +\PageSep{17} + + +\Chapter{VII}{The Apparent Incompatibility of the +Law of Propagation of Light with +the Principle of Relativity} +\index{Propagation of light}% + +\First{There} is hardly a simpler law in physics than +that according to which light is propagated in +empty space. Every child at school knows, or +believes he knows, that this propagation takes place +in straight lines with a velocity $c = 300,000$~km./sec. +At all events we know with great exactness that this +velocity is the same for all colours, because if this were +not the case, the minimum of emission would not be +observed simultaneously for different colours during +the eclipse of a fixed star by its dark neighbour. By +\index{DeSitter@{De Sitter}}% +\index{Eclipse of star}% +means of similar considerations based on observations +of double stars, the Dutch astronomer De~Sitter +\index{Double stars}% +was also able to show that the velocity of propagation +of light cannot depend on the velocity of motion +of the body emitting the light. The assumption that +this velocity of propagation is dependent on the direction +``in space'' is in itself improbable. + +In short, let us assume that the simple law of the +constancy of the velocity of light~$c$ (in vacuum) is +\index{Velocity of light}% +justifiably believed by the child at school. Who would +imagine that this simple law has plunged the conscientiously +thoughtful physicist into the greatest +\PageSep{18} +intellectual difficulties? Let us consider how these +difficulties arise. + +Of course we must refer the process of the propagation +of light (and indeed every other process) to a rigid +reference-body (co-ordinate system). As such a system +\index{Reference-body}% +let us again choose our embankment. We shall imagine +the air above it to have been removed. If a ray of +light be sent along the embankment, we see from the +above that the tip of the ray will be transmitted with +the velocity~$c$ relative to the embankment. Now let +us suppose that our railway carriage is again travelling +along the railway lines with the velocity~$v$, and that +its direction is the same as that of the ray of light, but +its velocity of course much less. Let us inquire about +the velocity of propagation of the ray of light relative +to the carriage. It is obvious that we can here apply the +consideration of the previous section, since the ray of +light plays the part of the man walking along relatively +to the carriage. The velocity~$W$ of the man relative +to the embankment is here replaced by the velocity +of light relative to the embankment. $w$~is the required +velocity of light with respect to the carriage, and we +\index{Velocity of light}% +have +\[ +w = c - v. +\] +The velocity of propagation of a ray of light relative to +the carriage thus comes out smaller than~$c$. + +But this result comes into conflict with the principle +of relativity set forth in \Sectionref{V}. For, like every +other general law of nature, the law of the transmission +of light \textit{in~vacuo} must, according to the principle of +relativity, be the same for the railway carriage as +reference-body as when the rails are the body of reference. +\PageSep{19} +But, from our above consideration, this would +appear to be impossible. If every ray of light is propagated +relative to the embankment with the velocity~$c$, +then for this reason it would appear that another law +of propagation of light must necessarily hold with respect +\index{Propagation of light}% +to the carriage---a result contradictory to the principle +of relativity. + +In view of this dilemma there appears to be nothing +else for it than to abandon either the principle of relativity +\index{Principle of relativity}% +or the simple law of the propagation of light \textit{in~vacuo}. +Those of you who have carefully followed the +preceding discussion are almost sure to expect that +we should retain the principle of relativity, which +appeals so convincingly to the intellect because it is so +natural and simple. The law of the propagation of +light \textit{in~vacuo} would then have to be replaced by a +more complicated law conformable to the principle of +relativity. The development of theoretical physics +shows, however, that we cannot pursue this course. +The epoch-making theoretical investigations of H.~A. +Lorentz on the electrodynamical and optical phenomena +\index{Electrodynamics}% +\index{Optics}% +\index{Lorentz, H. A.}% +connected with moving bodies show that experience +in this domain leads conclusively to a theory of electromagnetic +phenomena, of which the law of the constancy +of the velocity of light \textit{in~vacuo} is a necessary consequence. +Prominent theoretical physicists were therefore +more inclined to reject the principle of relativity, +in spite of the fact that no empirical data had been +found which were contradictory to this principle. + +At this juncture the theory of relativity entered the +arena. As a result of an analysis of the physical conceptions +of time and space, it became evident that \emph{in +\index{Space!conception of}% +\index{Time!conception of}% +reality there is not the least incompatibility between the +\PageSep{20} +principle of relativity and the law of propagation of light}, +\index{Principle of relativity}% +\index{Propagation of light}% +and that by systematically holding fast to both these +laws a logically rigid theory could be arrived at. This +theory has been called the \emph{special theory of relativity} +\index{Special theory of relativity}% +to distinguish it from the extended theory, with which +we shall deal later. In the following pages we shall +present the fundamental ideas of the special theory of +relativity. +\PageSep{21} + + +\Chapter{VIII}{On the Idea of Time in Physics} +\index{Time!in Physics}% + +\First{Lightning} has struck the rails on our railway +embankment at two places $A$~and~$B$ far distant +from each other. I make the additional assertion +that these two lightning flashes occurred simultaneously. +If I ask you whether there is sense in this statement, +you will answer my question with a decided +``Yes.'' But if I now approach you with the request +to explain to me the sense of the statement more +precisely, you find after some consideration that the +answer to this question is not so easy as it appears at +first sight. + +After some time perhaps the following answer would +occur to you: ``The significance of the statement is +clear in itself and needs no further explanation; of +course it would require some consideration if I were to +be commissioned to determine by observations whether +in the actual case the two events took place simultaneously +or not.'' I cannot be satisfied with this answer +for the following reason. Supposing that as a result +of ingenious considerations an able meteorologist were +to discover that the lightning must always strike the +places $A$~and~$B$ simultaneously, then we should be faced +with the task of testing whether or not this theoretical +result is in accordance with the reality. We encounter +\PageSep{22} +the same difficulty with all physical statements in which +the conception ``simultaneous'' plays a part. The +concept does not exist for the physicist until he has the +possibility of discovering whether or not it is fulfilled +in an actual case. We thus require a definition of +simultaneity such that this definition supplies us with +\index{Simultaneity}% +the method by means of which, in the present case, he +can decide by experiment whether or not both the +lightning strokes occurred simultaneously. As long +as this requirement is not satisfied, I allow myself to be +deceived as a physicist (and of course the same applies +if I am not a physicist), when I imagine that I am able +to attach a meaning to the statement of simultaneity. +(I would ask the reader not to proceed farther until he +is fully convinced on this point.) + +After thinking the matter over for some time you +then offer the following suggestion with which to test +simultaneity. By measuring along the rails, the +connecting line~$AB$ should be measured up and an +observer placed at the mid-point~$M$ of the distance~$AB$. +This observer should be supplied with an arrangement +(\eg\ two mirrors inclined at~$90°$) which allows him +visually to observe both places $A$~and~$B$ at the same +time. If the observer perceives the two flashes of +lightning at the same time, then they are simultaneous. + +I am very pleased with this suggestion, but for all +that I cannot regard the matter as quite settled, because +I feel constrained to raise the following objection: +``Your definition would certainly be right, if I only +knew that the light by means of which the observer +at~$M$ perceives the lightning flashes travels along the +length $A\longrightarrow M$ with the same velocity as along the +length $B\longrightarrow M$. But an examination of this supposition +\PageSep{23} +would only be possible if we already had at our +disposal the means of measuring time. It would thus +appear as though we were moving here in a logical circle.'' + +After further consideration you cast a somewhat +disdainful glance at me---and rightly so---and you +declare: ``I maintain my previous definition nevertheless, +because in reality it assumes absolutely nothing +about light. There is only \emph{one} demand to be made of +the definition of simultaneity, namely, that in every +real case it must supply us with an empirical decision +as to whether or not the conception that has to +be defined is fulfilled. That my definition satisfies +this demand is indisputable. That light requires the +same time to traverse the path $A\longrightarrow M$ as for the path +$B\longrightarrow M$ is in reality neither a \emph{supposition nor a hypothesis} +about the physical nature of light, but a \emph{stipulation} +which I can make of my own \Change{freewill}{free will} in order to arrive +at a definition of simultaneity.'' + +It is clear that this definition can be used to give an +exact meaning not only to \emph{two} events, but to as many +events as we care to choose, and independently of the +positions of the scenes of the events with respect to the +\index{Reference-body}% +body of reference\footnote + {We suppose further, that, when three events $A$,~$B$ and~$C$ + occur in different places in such a manner that $A$~is simultaneous + with~$,$ and $B$~is simultaneous with~$C$ (simultaneous + in the sense of the above definition), then the criterion for the + simultaneity of the pair of events $A$,~$C$ is also satisfied. This + assumption is a physical hypothesis about the law of propagation + of light; it must certainly be fulfilled if we are to maintain the + law of the constancy of the velocity of light \textit{in~vacuo}.} +(here the railway embankment). +We are thus led also to a definition of ``time'' in physics. +For this purpose we suppose that clocks of identical +\index{Clocks}% +construction are placed at the points $A$,~$B$ and~$C$ of +\PageSep{24} +\index{Simultaneity|(}% +the railway line (co-ordinate system), and that they +are set in such a manner that the positions of their +pointers are simultaneously (in the above sense) the +same. Under these conditions we understand by the +``time'' of an event the reading (position of the hands) +\index{Time!of an event}% +of that one of these clocks which is in the immediate +vicinity (in space) of the event. In this manner a +time-value is associated with every event which is +essentially capable of observation. + +This stipulation contains a further physical hypothesis, +the validity of which will hardly be doubted without +empirical evidence to the contrary. It has been assumed +that all these clocks go \emph{at the same rate} if they are of +identical construction. Stated more exactly: When +two clocks arranged at rest in different places of a +reference-body are set in such a manner that a \emph{particular} +position of the pointers of the one clock is \emph{simultaneous} +(in the above sense) with the \emph{same} position of the +pointers of the other clock, then identical ``settings'' +are always simultaneous (in the sense of the above +definition). +\PageSep{25} + + +\Chapter{IX}{The Relativity of Simultaneity} + +\First{Up} to now our considerations have been referred +\index{Reference-body}% +to a particular body of reference, which we +have styled a ``railway embankment.'' We +suppose a very long train travelling along the rails +with the constant velocity~$v$ and in the direction indicated +in \Figref{1}. People travelling in this train will +with advantage use the train as a rigid reference-body +(co-ordinate system); they regard all events in +%[Illustration: Fig. 1.] +\Figure{025} +reference to the train. Then every event which takes +place along the line also takes place at a particular +point of the train. Also the definition of simultaneity +can be given relative to the train in exactly the same +way as with respect to the embankment. As a natural +consequence, however, the following question arises: + +Are two events (\eg\ the two strokes of lightning $A$ +and~$B$) which are simultaneous \emph{with reference to the +railway embankment} also simultaneous \emph{relatively to the +train}? We shall show directly that the answer must +be in the negative. + +When we say that the lightning strokes $A$~and~$B$ are +\PageSep{26} +simultaneous with respect to the embankment, we +mean: the rays of light emitted at the places $A$~and~$B$, +where the lightning occurs, meet each other at the +mid-point~$M$ of the length $A\longrightarrow B$ of the embankment. +But the events $A$~and~$B$ also correspond to positions $A$~and~$B$ +\index{Time!of an event}% +on the train. Let $M'$~be the mid-point of the +distance $A\longrightarrow B$ on the travelling train. Just when +the flashes\footnote + {As judged from the embankment.} +of lightning occur, this point~$M'$ naturally +coincides with the point~$M$, but it moves towards the +right in the diagram with the velocity~$v$ of the train. If +an observer sitting in the position~$M'$ in the train did +not possess this velocity, then he would remain permanently +at~$M$, and the light rays emitted by the +flashes of lightning $A$~and~$B$ would reach him simultaneously, +\ie\ they would meet just where he is situated. +Now in reality (considered with reference to the railway +embankment) he is hastening towards the beam of light +coming from~$B$, whilst he is riding on ahead of the beam +of light coming from~$A$. Hence the observer will see +the beam of light emitted from~$B$ earlier than he will +see that emitted from~$A$. Observers who take the railway +train as their reference-body must therefore come +\index{Reference-body}% +to the conclusion that the lightning flash~$B$ took place +earlier than the lightning flash~$A$. We thus arrive at +the important result: + +Events which are simultaneous with reference to the +embankment are not simultaneous with respect to the +train, and \textit{vice versa} (relativity of simultaneity). Every +\index{Simultaneity|)}% +\index{Simultaneity!relativity of}% +reference-body (co-ordinate system) has its own particular +time; unless we are told the reference-body to which +the statement of time refers, there is no meaning in a +statement of the time of an event. +\PageSep{27} + +Now before the advent of the theory of relativity +it had always tacitly been assumed in physics that the +statement of time had an absolute significance, \ie\ +that it is independent of the state of motion of the body +of reference. But we have just seen that this assumption +is incompatible with the most natural definition +of simultaneity; if we discard this assumption, then +the conflict between the law of the propagation of +light \textit{in~vacuo} and the principle of relativity (developed +in \Sectionref{VII}) disappears. + +We were led to that conflict by the considerations +of \Sectionref{VI}, which are now no longer tenable. In +that section we concluded that the man in the carriage, +who traverses the distance~$w$ \emph{per~second} relative to the +carriage, traverses the same distance also with respect to +the embankment \emph{in each second} of time. But, according +to the foregoing considerations, the time required by a +particular occurrence with respect to the carriage must +not be considered equal to the duration of the same +occurrence as judged from the embankment (as reference-body). +Hence it cannot be contended that the +man in walking travels the distance~$w$ relative to the +railway line in a time which is equal to one second as +judged from the embankment. + +Moreover, the considerations of \Sectionref{VI} are based +on yet a second assumption, which, in the light of a +strict consideration, appears to be arbitrary, although +it was always tacitly made even before the introduction +of the theory of relativity. +\PageSep{28} + + +\Chapter{X}{On the Relativity of the Conception +of Distance} +\index{Distance (line-interval)}% +\index{Distance (line-interval)!relativity of}% + +\First{Let} us consider two particular points on the train\footnote + {\eg\ the middle of the first and of the hundredth carriage.} +travelling along the embankment with the +velocity~$v$, and inquire as to their distance apart. +We already know that it is necessary to have a body of +reference for the measurement of a distance, with respect +to which body the distance can be measured up. It is +the simplest plan to use the train itself as reference-body +(co-ordinate system). An observer in the train +measures the interval by marking off his measuring-rod +\index{Measuring-rod}% +in a straight line (\eg\ along the floor of the carriage) +as many times as is necessary to take him from the one +marked point to the other. Then the number which +tells us how often the rod has to be laid down is the +required distance. + +It is a different matter when the distance has to be +judged from the railway line. Here the following +method suggests itself. If we call $A'$~and~$B'$ the two +points on the train whose distance apart is required, +then both of these points are moving with the velocity~$v$ +along the embankment. In the first place we require to +determine the points $A$~and~$B$ of the embankment which +are just being passed by the two points $A'$~and~$B'$ at a +\PageSep{29} +particular time~$t$---judged from the embankment. +These points $A$~and~$B$ of the embankment can be determined +by applying the definition of time given in +\Sectionref{VIII}. The distance between these points $A$~and~$B$ +\index{Distance (line-interval)}% +is then measured by repeated application of the +measuring-rod along the embankment. + +\textit{A~priori} it is by no means certain that this last +measurement will supply us with the same result as +the first. Thus the length of the train as measured +from the embankment may be different from that +obtained by measuring in the train itself. This +circumstance leads us to a second objection which must +be raised against the apparently obvious consideration +of \Sectionref{VI}. Namely, if the man in the carriage +covers the distance~$w$ in a unit of time---\emph{measured from +the train},---then this distance---\emph{as measured from the +embankment}---is not necessarily also equal to~$w$. +\PageSep{30} + + +\Chapter{XI}{The Lorentz Transformation} + +\First{The} results of the last three sections show +that the apparent incompatibility of the law +of propagation of light with the principle of +relativity (\Sectionref{VII}) has been derived by means of +a consideration which borrowed two unjustifiable +hypotheses from classical mechanics; these are as +\index{Classical mechanics}% +follows: +\begin{itemize} +\item[(1)] The time-interval (time) between two events is +\index{Time-interval}% + independent of the condition of motion of the + body of reference. + +\item[(2)] The space-interval (distance) between two points +\index{Space!interval@{-interval}}% + of a rigid body is independent of the condition + of motion of the body of reference. +\end{itemize} + +If we drop these hypotheses, then the dilemma of +\Sectionref{VII} disappears, because the theorem of the addition +of velocities derived in \Sectionref{VI} becomes invalid. +The possibility presents itself that the law of the propagation +of light \textit{in~vacuo} may be compatible with the +principle of relativity, and the question arises: How +have we to modify the considerations of \Sectionref{VI} +in order to remove the apparent disagreement between +these two fundamental results of experience? This +question leads to a general one. In the discussion of +\PageSep{31} +\Sectionref{VI} we have to do with places and times relative +both to the train and to the embankment. How are +we to find the place and time of an event in relation to +the train, when we know the place and time of the +event with respect to the railway embankment? Is +there a thinkable answer to this question of such a +nature that the law of transmission of light \textit{in~vacuo} +does not contradict the principle of relativity? In +other words: Can we conceive of a relation between +place and time of the individual events relative to both +reference-bodies, such that every ray of light possesses +the velocity of transmission~$c$ relative to the embankment +and relative to the train? This question leads to +a quite definite positive answer, and to a perfectly definite +transformation law for the space-time magnitudes of +an event when changing over from one body of reference +to another. + +Before we deal with this, we shall introduce the +following incidental consideration. Up to the present +we have only considered events taking place along the +embankment, which had mathematically to assume the +function of a straight line. In the manner indicated +in \Sectionref{II} we can imagine this reference-body supplemented +laterally and in a vertical direction by means of +a framework of rods, so that an event which takes place +anywhere can be localised with reference to this framework. +Similarly, we can imagine the train travelling +with the velocity~$v$ to be continued across the whole of +space, so that every event, no matter how far off it +may be, could also be localised with respect to the second +framework. Without committing any fundamental error, +we can disregard the fact that in reality these frameworks +would continually interfere with each other, owing +\PageSep{32} +\index{Propagation of light}% +to the impenetrability of solid bodies. In every such +framework we imagine three surfaces perpendicular to +each other marked out, and designated as ``co-ordinate +\index{Coordinate@{Co-ordinate}!planes}% +planes'' (``co-ordinate system''). A co-ordinate +system~$K$ then corresponds to the embankment, and a +co-ordinate system~$K'$ to the train. An event, wherever +it may have taken place, would be fixed in space with +respect to~$K$ by the three perpendiculars $x$,~$y$,~$z$ on the +co-ordinate planes, and with regard to time by a time-value~$t$. +Relative to~$K'$, \emph{the +same event} would be fixed +in respect of space and time +by corresponding values $x'$,~$y'$, +$z'$,~$t'$, which of course are +not identical with $x$,~$y$, $z$,~$t$. +It has already been set +forth in detail how these +magnitudes are to be regarded +as results of physical measurements. +%[Illustration: Fig. 2.] +\Figure[2in]{032} + +Obviously our problem can be exactly formulated in +the following manner. What are the values $x'$,~$y'$, $z'$,~$t'$, +of an event with respect to~$K'$, when the magnitudes +$x$,~$y$, $z$,~$t$, of the same event with respect to~$K$ are given? +The relations must be so chosen that the law of the +transmission of light \textit{in~vacuo} is satisfied for one and the +same ray of light (and of course for every ray) with +respect to $K$ and~$K'$. For the relative orientation in +space of the co-ordinate systems indicated in the diagram +(\Figref{2}), this problem is solved by means of the +equations: +\begin{align*} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,}\displaybreak[1] \\ +\PageSep{33} +y' &= y\Add{,} \\ +z' &= z\Add{,} \\ +t' &= \frac{t - \dfrac{v}{c^{2}}·x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Change{}{.} +\end{align*} +This system of equations is known as the ``Lorentz +\index{Lorentz, H. A.!transformation}% +transformation.''\footnote + {A simple derivation of the Lorentz transformation is given + in \Appendixref{I}.} + +If in place of the law of transmission of light we had +taken as our basis the tacit assumptions of the older +mechanics as to the absolute character of times and +lengths, then instead of the above we should have +obtained the following equations: +\begin{align*} +x' &= x - vt\Add{,} \\ +y' &= y\Add{,} \\ +z' &= z\Add{,} \\ +t' &= t. +\end{align*} +This system of equations is often termed the ``Galilei +\index{Galilei!transformation}% +transformation.'' The Galilei transformation can be +obtained from the Lorentz transformation by substituting +an infinitely large value for the velocity of +light~$c$ in the latter transformation. + +Aided by the following illustration, we can readily +see that, in accordance with the Lorentz transformation, +the law of the transmission of light \textit{in~vacuo} +is satisfied both for the reference-body~$K$ and for the +reference-body~$K'$. A light-signal is sent along the +\index{Light-signal}% +positive $x$-axis, and this light-stimulus advances in +\index{Light-stimulus}% +accordance with the equation +\[ +x = ct, +\] +\PageSep{34} +\ie\ with the velocity~$c$. According to the equations of +the Lorentz transformation, this simple relation between +$x$~and~$t$ involves a relation between $x'$~and~$t'$. In point +of fact, if we substitute for~$x$ the value~$ct$ in the first +and fourth equations of the Lorentz transformation, +we obtain: +\begin{align*} +x' &= \frac{(c - v)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,} \\ +t' &= \frac{\left(1 - \dfrac{v}{c}\right)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +\end{align*} +from which, by division, the expression +\[ +x' = ct' +\] +immediately follows. If referred to the system~$K'$, the +propagation of light takes place according to this +equation. We thus see that the velocity of transmission +relative to the reference-body~$K'$ is also equal to~$c$. The +same result is obtained for rays of light advancing in +any other direction whatsoever. Of course this is not +surprising, since the equations of the Lorentz transformation +were derived conformably to this point of +view. +\PageSep{35} + + +\Chapter{XII}{The Behaviour of Measuring-Rods and +Clocks in Motion} + +\First{I place} a metre-rod in the $x'$-axis of~$K'$ in such a +manner that one end (the beginning) coincides with +the point $x' = 0$, whilst the other end (the end of the +rod) coincides with the point $x' = 1$. What is the length +of the metre-rod relatively to the system~$K$? In order +to learn this, we need only ask where the beginning of the +rod and the end of the rod lie with respect to~$K$ at a +particular time~$t$ of the system~$K$. By means of the first +equation of the Lorentz transformation the values of +these two points at the time $t = 0$ can be shown to be +\begin{align*} +x_{\text{(beginning of rod)}} + &= 0·\sqrt{1 - \frac{v^{2}}{c^{2}}}\Add{,} \\ +x_{\text{(end of rod)}} + &= 1·\sqrt{1 - \frac{v^{2}}{c^{2}}}, +\end{align*} +the distance between the points being~$\sqrt{1 - \dfrac{v^{2}}{c^{2}}}$. But +the metre-rod is moving with the velocity~$v$ relative to~$K$. +It therefore follows that the length of a rigid metre-rod +moving in the direction of its length with a velocity~$v$ +is $\sqrt{1 - v^{2}/c^{2}}$~of a metre. The rigid rod is thus +shorter when in motion than when at rest, and the +more quickly it is moving, the shorter is the rod. For +the velocity $v = c$ we should have $\sqrt{1 - v^{2}/c^{2}} = 0$, and +for still greater velocities the square-root becomes +\PageSep{36} +imaginary. From this we conclude that in the theory +of relativity the velocity~$c$ plays the part of a limiting +\index{Limiting velocity ($c$)}% +velocity, which can neither be reached nor exceeded +by any real body. + +Of course this feature of the velocity~$c$ as a limiting +velocity also clearly follows from the equations of the +Lorentz transformation, for these become meaningless +if we choose values of~$v$ greater than~$c$. + +If, on the contrary, we had considered a metre-rod +at rest in the $x$-axis with respect to~$K$, then we should +have found that the length of the rod as judged from~$K'$ +would have been~$\sqrt{1 - v^{2}/c^{2}}$; this is quite in accordance +with the principle of relativity which forms the +basis of our considerations. + +\textit{A~priori} it is quite clear that we must be able to +learn something about the physical behaviour of measuring-rods +and clocks from the equations of transformation, +for the magnitudes $x$,~$y$, $z$,~$t$, are nothing more nor +less than the results of measurements obtainable by +means of measuring-rods and clocks. If we had based +our considerations on the Galilei transformation we +\index{Galilei!transformation}% +should not have obtained a contraction of the rod as a +consequence of its motion. + +Let us now consider a seconds-clock which is permanently +\index{Seconds-clock}% +situated at the origin ($x' = 0$) of~$K'$. $t' = 0$ +and $t' = 1$ are two successive ticks of this clock. The +first and fourth equations of the Lorentz transformation +give for these two ticks: +\begin{align*} +t &= 0 \\ +\intertext{and} +t &= \frac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{align*} +\PageSep{37} + +As judged from~$K$, the clock is moving with the +velocity~$v$; as judged from this reference-body, the +\index{Reference-body}% +time which elapses between two strokes of the clock +is not one second, but $\dfrac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}$~seconds, \ie\ a somewhat +larger time. As a consequence of its motion +the clock goes more slowly than when at rest. Here +also the velocity~$c$ plays the part of an unattainable +limiting velocity. +\index{Limiting velocity ($c$)}% +\PageSep{38} + + +\Chapter{XIII}{Theorem of the Addition of Velocities. +The Experiment of Fizeau} +\index{Addition of velocities}% + +\First{Now} in practice we can move clocks and +measuring-rods only with velocities that are +small compared with the velocity of light; hence +we shall hardly be able to compare the results of the +previous section directly with the reality. But, on the +other hand, these results must strike you as being very +singular, and for that reason I shall now draw another +conclusion from the theory, one which can easily be +derived from the foregoing considerations, and which +has been most elegantly confirmed by experiment. + +In \Sectionref{VI} we derived the theorem of the addition +of velocities in one direction in the form which also +results from the hypotheses of classical mechanics. This +theorem can also be deduced readily from the Galilei +\index{Galilei!transformation}% +transformation (\Sectionref{XI}). In place of the man +walking inside the carriage, we introduce a point moving +relatively to the co-ordinate system~$K'$ in accordance +with the equation +\[ +x' = wt'. +\] +By means of the first and fourth equations of the Galilei +transformation we can express $x'$~and~$t'$ in terms of $x$~and~$t$, +and we then obtain +\[ +x = (v + w)t. +\] +\PageSep{39} +This equation expresses nothing else than the law of +motion of the point with reference to the system~$K$ +(of the man with reference to the embankment). We +denote this velocity by the symbol~$W$, and we then +obtain, as in \Sectionref{VI}, +\[ +W = v + w. +\Tag{(A)} +\] + +But we can carry out this consideration just as well +on the basis of the theory of relativity. In the equation +\[ +x' = wt' +\] +we must then express $x'$~and~$t'$ in terms of $x$~and~$t$, making +use of the first and fourth equations of the \emph{Lorentz +\index{Lorentz, H. A.!transformation}% +transformation}. Instead of the equation~\Eqref{(A)} we then +obtain the equation +\[ +W = \frac{v + w}{1 + \dfrac{vw}{c^{2}}}, +\Tag{(B)} +\] +which corresponds to the theorem of addition for +velocities in one direction according to the theory of +relativity. The question now arises as to which of these +two theorems is the better in accord with experience. On +this point we are enlightened by a most important experiment +which the brilliant physicist Fizeau performed more +\index{Fizeau}% +\index{Fizeau!experiment of}% +than half a century ago, and which has been repeated +since then by some of the best experimental physicists, +so that there can be no doubt about its result. The +experiment is concerned with the following question. +Light travels in a motionless liquid with a particular +velocity~$w$. How quickly does it travel in the direction +of the arrow in the tube~$T$ (see the accompanying diagram, +\Figref{3}) when the liquid above mentioned is flowing +through the tube with a velocity~$v$? +\PageSep{40} + +In accordance with the principle of relativity we shall +\index{Propagation of light!in liquid}% +certainly have to take for granted that the propagation +of light always takes place with the same velocity~$w$ +\emph{with respect to the liquid}, whether the latter is in motion +with reference to other bodies or not. The velocity +of light relative to the liquid and the velocity of the +latter relative to the tube are thus known, and we +require the velocity of light relative to the tube. + +It is clear that we have the problem of \Sectionref{VI} +again before us. The tube plays the part of the railway +embankment or of the co-ordinate system~$K$, the liquid +plays the part of the carriage or of the co-ordinate +system~$K'$, and finally, the light plays the part of the +%[Illustration: Fig. 3.] +\Figure[2in]{040} +man walking along the carriage, or of the moving point +in the present section. If we denote the velocity of the +light relative to the tube by~$W$, then this is given +by the equation \Eqref{(A)}~or~\Eqref{(B)}, according as the Galilei +transformation or the Lorentz transformation corresponds +to the facts. Experiment\footnote + {Fizeau found $W = w + v\left(1 - \dfrac{1}{n^{2}}\right)$, where $n = \dfrac{c}{w}$ is the index of + refraction of the liquid. On the other hand, owing to the smallness + of~$\dfrac{vw}{c^{2}}$ as compared with~$1$, we can replace~\Eqref{(B)} in the first + place by $W = (w + v) \left(1 - \dfrac{vw}{c^{2}}\right)$, or to the same order of approximation + by $w + v \left(1 - \dfrac{1}{n^{2}}\right)$, which agrees with Fizeau's result.} +decides in favour +of equation~\Eqref{(B)} derived from the theory of relativity, and +the agreement is, indeed, very exact. According to +\PageSep{41} +recent and most excellent measurements by Zeeman, the +\index{Zeeman}% +influence of the velocity of flow~$v$ on the propagation of +light is represented by formula~\Eqref{(B)} to within one per +cent. %[** TN: [sic] two words] + +Nevertheless we must now draw attention to the fact +that a theory of this phenomenon was given by H.~A. +Lorentz long before the statement of the theory of +\index{Lorentz, H. A.}% +relativity. This theory was of a purely electrodynamical +nature, and was obtained by the use of particular +hypotheses as to the electromagnetic structure of matter. +This circumstance, however, does not in the least +diminish the conclusiveness of the experiment as a +crucial test in favour of the theory of relativity, for the +electrodynamics of Maxwell-Lorentz, on which the +\index{Electrodynamics}% +\index{Maxwell}% +original theory was based, in no way opposes the theory +of relativity. Rather has the latter been developed +from electrodynamics as an astoundingly simple combination +and generalisation of the hypotheses, formerly +independent of each other, on which electrodynamics +was built. +\PageSep{42} + + +\Chapter{XIV}{The Heuristic Value of the Theory of +Relativity} +\index{Heuristic value of relativity}% + +\First{Our} train of thought in the foregoing pages can be +epitomised in the following manner. Experience +has led to the conviction that, on the one hand, +the principle of relativity holds true, and that on the +other hand the velocity of transmission of light \textit{in~vacuo} +has to be considered equal to a constant~$c$. By uniting +these two postulates we obtained the law of transformation +for the rectangular co-ordinates $x$,~$y$,~$z$ and the time~$t$ +of the events which constitute the processes of nature. +\index{Processes of Nature}% +In this connection we did not obtain the Galilei transformation, +\index{Galilei!transformation}% +but, differing from classical mechanics, +the \emph{Lorentz transformation}. +\index{Lorentz, H. A.!transformation}% + +The law of transmission of light, the acceptance of +which is justified by our actual knowledge, played an +important part in this process of thought. Once in +possession of the Lorentz transformation, however, +we can combine this with the principle of relativity, +and sum up the theory thus: + +Every general law of nature must be so constituted +that it is transformed into a law of exactly the same +form when, instead of the space-time variables $x$,~$y$, $z$,~$t$ +of the original co-ordinate system~$K$, we introduce new +space-time variables $x'$,~$y'$, $z'$,~$t'$ of a co-ordinate system~$K'$. +\PageSep{43} +In this connection the relation between the +ordinary and the accented magnitudes is given by the +Lorentz transformation. Or, in brief: General laws +of nature are co-variant with respect to Lorentz transformations. +\index{Covariant@{Co-variant}}% + +This is a definite mathematical condition that the +theory of relativity demands of a natural law, and in +virtue of this, the theory becomes a valuable heuristic aid +in the search for general laws of nature. If a general +law of nature were to be found which did not satisfy +this condition, then at least one of the two fundamental +assumptions of the theory would have been disproved. +Let us now examine what general results the latter +theory has hitherto evinced. +\PageSep{44} + + +\Chapter{XV}{General Results of the Theory} + +\First{It} is clear from our previous considerations that the +(special) theory of relativity has grown out of electrodynamics +\index{Electrodynamics}% +and optics. In these fields it has not +\index{Optics}% +appreciably altered the predictions of theory, but it +has considerably simplified the theoretical structure, +\ie\ the derivation of laws, and---what is incomparably +\index{Derivation of laws}% +more important---it has considerably reduced the +number of independent hypotheses forming the basis of +\index{Basis of theory}% +theory. The special theory of relativity has rendered +the Maxwell-Lorentz theory so plausible, that the latter +\index{Lorentz, H. A.}% +\index{Maxwell}% +would have been generally accepted by physicists +even if experiment had decided less unequivocally in its +favour. + +Classical mechanics required to be modified before it +\index{Classical mechanics}% +could come into line with the demands of the special +theory of relativity. For the main part, however, +this modification affects only the laws for rapid motions, +in which the velocities of matter~$v$ are not very small as +compared with the velocity of light. We have experience +of such rapid motions only in the case of electrons +\index{Electron}% +and ions; for other motions the variations from the laws +\index{Ions}% +of classical mechanics are too small to make themselves +evident in practice. We shall not consider the motion +\index{Motion!of heavenly bodies}% +of stars until we come to speak of the general theory of +relativity. In accordance with the theory of relativity +\PageSep{45} +the kinetic energy of a material point of mass~$m$ is no +\index{Kinetic energy}% +longer given by the well-known expression +\[ +m\frac{v^{2}}{2}\Change{.}{,} +\] +but by the expression +\[ +\frac{mc^{2}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +This expression approaches infinity as the velocity~$v$ +approaches the velocity of light~$c$. The velocity must +therefore always remain less than~$c$, however great may +be the energies used to produce the acceleration. If +we develop the expression for the kinetic energy in the +form of a series, we obtain +\[ +mc^{2} + m\frac{v^{2}}{2} + \frac{3}{8}m\frac{v^4}{c^{2}} + \dots. +\] + +When $\dfrac{v^{2}}{c^{2}}$ is small compared with unity, the third +of these terms is always small in comparison with the +second, which last is alone considered in classical +mechanics. The first term~$mc^{2}$ does not contain +the velocity, and requires no consideration if we are only +dealing with the question as to how the energy of a +point-mass depends on the velocity. We shall speak +\index{Point-mass, energy of}% +of its essential significance later. + +The most important result of a general character to +\index{Conservation of energy}% +\index{Conservation of energy!mass}% +which the special theory of relativity has led is concerned +with the conception of mass. Before the advent of +\index{Conception of mass}% +relativity, physics recognised two conservation laws of +fundamental importance, namely, the law of the conservation +of energy and the law of the conservation of +mass; these two fundamental laws appeared to be quite +\PageSep{46} +independent of each other. By means of the theory of +relativity they have been united into one law. We shall +now briefly consider how this unification came about, +and what meaning is to be attached to it. + +The principle of relativity requires that the law of the +conservation of energy should hold not only with reference +to a co-ordinate system~$K$, but also with respect +to every co-ordinate system~$K'$ which is in a state of +uniform motion of translation relative to~$K$, or, briefly, +relative to every ``Galileian'' system of co-ordinates. +\index{Galileian system of co-ordinates}% +In contrast to classical mechanics, the Lorentz transformation +is the deciding factor in the transition from +one such system to another. + +By means of comparatively simple considerations +we are led to draw the following conclusion from +these premises, in conjunction with the fundamental +equations of the electrodynamics of Maxwell: A body +\index{Maxwell!fundamental equations}% +\index{Absorption of energy}% +moving with the velocity~$v$, which absorbs\footnote + {$E_{0}$~is the energy taken up, as judged from a co-ordinate + system moving with the body.} +an amount +of energy~$E_{0}$ in the form of radiation without suffering +\index{Radiation}% +an alteration in velocity in the process, has, as a consequence, +its energy increased by an amount +\[ +\frac{E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] + +In consideration of the expression given above for the +kinetic energy of the body, the required energy of the +body comes out to be +\[ +\frac{\left(m + \dfrac{E_{0}}{c^{2}}\right)c^{2}} + {\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +\PageSep{47} + +Thus the body has the same energy as a body of mass +$\left(m + \dfrac{E_{0}}{c^{2}}\right)$ moving with the velocity~$v$. Hence we can +say: If a body takes up an amount of energy~$E_{0}$, then +its inertial mass increases by an amount~$\dfrac{E_{0}}{c^{2}}$; the +\index{Inertial mass}% +inertial mass of a body is not a constant, but varies +according to the change in the energy of the body. +The inertial mass of a system of bodies can even be +regarded as a measure of its energy. The law of the +conservation of the mass of a system becomes identical +with the law of the conservation of energy, and is only +\index{Conservation of energy!mass}% +valid provided that the system neither takes up nor sends +out energy. Writing the expression for the energy in +the form +\[ +\frac{mc^{2} + E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +\] +we see that the term~$mc^{2}$, which has hitherto attracted +our attention, is nothing else than the energy possessed +by the body\footnote + {As judged from a co-ordinate system moving with the body.} +before it absorbed the energy~$E_{0}$. + +A direct comparison of this relation with experiment +is not possible at the present time, owing to the fact that +the changes in energy~$E_{0}$ to which we can subject a +system are not large enough to make themselves +perceptible as a change in the inertial mass of the +system. $\dfrac{E_{0}}{c^{2}}$~is too small in comparison with the mass~$m$, +which was present before the alteration of the energy. +It is owing to this circumstance that classical mechanics +was able to establish successfully the conservation of +mass as a law of independent validity. +\PageSep{48} + +Let me add a final remark of a fundamental nature. +The success of the Faraday-Maxwell interpretation of +\index{Faraday}% +\index{Maxwell|(}% +electromagnetic action at a distance resulted in physicists +\index{Action at a distance}% +becoming convinced that there are no such things as +instantaneous actions at a distance (not involving an +intermediary medium) of the type of Newton's law of +\index{Newton's!law of gravitation}% +gravitation. According to the theory of relativity, +action at a distance with the velocity of light always +takes the place of instantaneous action at a distance or +of action at a distance with an infinite velocity of transmission. +This is connected with the fact that the +velocity~$c$ plays a fundamental rôle in this theory. In +\Partref{II} we shall see in what way this result becomes +modified in the general theory of relativity. +\PageSep{49} + + +\Chapter{XVI}{Experience and the Special Theory of +Relativity} +\index{Experience}% + +\First{To} what extent is the special theory of relativity +supported by experience? This question is not +easily answered for the reason already mentioned +in connection with the fundamental experiment of Fizeau. +\index{Fizeau}% +The special theory of relativity has crystallised out +from the Maxwell-Lorentz theory of electromagnetic +\index{Lorentz, H. A.}% +phenomena. Thus all facts of experience which support +the electromagnetic theory also support the theory of +\index{Electromagnetic theory}% +relativity. As being of particular importance, I mention +here the fact that the theory of relativity enables us to +predict the effects produced on the light reaching us +from the fixed stars. These results are obtained in an +exceedingly simple manner, and the effects indicated, +which are due to the relative motion of the earth with +reference to those fixed stars, are found to be in accord +with experience. We refer to the yearly movement of +the apparent position of the fixed stars resulting from the +motion of the earth round the sun (aberration), and to the +\index{Aberration}% +influence of the radial components of the relative +motions of the fixed stars with respect to the earth on +the colour of the light reaching us from them. The +\PageSep{50} +latter effect manifests itself in a slight displacement +of the spectral lines of the light transmitted to us from +a fixed star, as compared with the position of the same +spectral lines when they are produced by a terrestrial +source of light (Doppler principle). The experimental +\index{Doppler principle}% +arguments in favour of the Maxwell-Lorentz theory, +\index{Lorentz, H. A.|(}% +which are at the same time arguments in favour of the +theory of relativity, are too numerous to be set forth +here. In reality they limit the theoretical possibilities +to such an extent, that no other theory than that of +Maxwell and Lorentz has been able to hold its own when +tested by experience. + +But there are two classes of experimental facts +hitherto obtained which can be represented in the +Maxwell-Lorentz theory only by the introduction of an +\index{Maxwell|)}% +auxiliary hypothesis, which in itself---\ie\ without +making use of the theory of relativity---appears extraneous. + +It is known that cathode rays and the so-called +\index{beta-rays@{$\beta$-rays}}% +\index{Cathode rays}% +$\beta$-rays emitted by radioactive substances consist of +\index{Radioactive substances}% +negatively electrified particles (electrons) of very small +inertia and large velocity. By examining the deflection +of these rays under the influence of electric and magnetic +fields, we can study the law of motion of these particles +very exactly. + +In the theoretical treatment of these electrons, we are +faced with the difficulty that electrodynamic theory of +itself is unable to give an account of their nature. For +since electrical masses of one sign repel each other, the +negative electrical masses constituting the electron would +\index{Electron}% +necessarily be scattered under the influence of their +mutual repulsions, unless there are forces of another +kind operating between them, the nature of which has +\PageSep{51} +hitherto remained obscure to us.\footnote + {The general theory of relativity renders it likely that the + electrical masses of an electron are held together by gravitational +\index{Electron!electrical masses of}% + forces.} +If we now assume +that the relative distances between the electrical masses +constituting the electron remain unchanged during the +motion of the electron (rigid connection in the sense of +classical mechanics), we arrive at a law of motion of the +electron which does not agree with experience. Guided +by purely formal points of view, H.~A.~Lorentz was the +first to introduce the hypothesis that the particles +constituting the electron experience a contraction +in the direction of motion in consequence of that motion, +the amount of this contraction being proportional to +the expression~$\sqrt{1 - \dfrac{v^{2}}{c^{2}}}$. This hypothesis, which is +not justifiable by any electrodynamical facts, supplies us +then with that particular law of motion which has +been confirmed with great precision in recent years. + +The theory of relativity leads to the same law of +motion, without requiring any special hypothesis whatsoever +as to the structure and the behaviour of the +electron. We arrived at a similar conclusion in \Sectionref{XIII} +in connection with the experiment of Fizeau, the +\index{Fizeau}% +result of which is foretold by the theory of relativity +without the necessity of drawing on hypotheses as to +the physical nature of the liquid. + +The second class of facts to which we have alluded +has reference to the question whether or not the motion +of the earth in space can be made perceptible in terrestrial +experiments. We have already remarked in \Sectionref{V} +that all attempts of this nature led to a negative result. +Before the theory of relativity was put forward, it was +\PageSep{52} +difficult to become reconciled to this negative result, +for reasons now to be discussed. The inherited +prejudices about time and space did not allow any +\index{Time!conception of}% +\index{Space}% +doubt to arise as to the prime importance of the +Galilei transformation for changing over from one +\index{Galilei!transformation}% +body of reference to another. Now assuming that the +Maxwell-Lorentz equations hold for a reference-body~$K$, +\index{Maxwell}% +we then find that they do not hold for a reference-body~$K'$ +moving uniformly with respect to~$K$, if we +assume that the relations of the Galileian transformation +exist between the co-ordinates of $K$~and~$K'$. It +thus appears that of all Galileian co-ordinate systems +one~($K$) corresponding to a particular state of motion +is physically unique. This result was interpreted +physically by regarding $K$ as at rest with respect to a +hypothetical æther of space. On the other hand, +all co-ordinate systems~$K'$ moving relatively to~$K$ were +to be regarded as in motion with respect to the æther. +\index{Aether}% +\index{Aether!-drift}% +To this motion of~$K'$ against the æther (``æther-drift'' +relative to~$K'$) were assigned the more complicated +laws which were supposed to hold relative to~$K'$. +Strictly speaking, such an æther-drift ought also to be +assumed relative to the earth, and for a long time the +efforts of physicists were devoted to attempts to detect +the existence of an æther-drift at the earth's surface. + +In one of the most notable of these attempts Michelson +\index{Michelson|(}% +devised a method which appears as though it must be +decisive. Imagine two mirrors so arranged on a rigid +body that the reflecting surfaces face each other. A +ray of light requires a perfectly definite time~$T$ to pass +from one mirror to the other and back again, if the whole +system be at rest with respect to the æther. It is found +by calculation, however, that a slightly different time~$T'$ +\PageSep{53} +is required for this process, if the body, together with +the mirrors, be moving relatively to the æther. And +\index{Aether!-drift}% +yet another point: it is shown by calculation that for +a given velocity~$v$ with reference to the æther, this +time~$T'$ is different when the body is moving perpendicularly +to the planes of the mirrors from that resulting +when the motion is parallel to these planes. Although +the estimated difference between these two times is +exceedingly small, Michelson and Morley performed an +\index{Morley}% +experiment involving interference in which this difference +should have been clearly detectable. But the experiment +gave a negative result---a fact very perplexing +to physicists. Lorentz and FitzGerald rescued the +\index{FitzGerald}% +\index{Lorentz, H. A.|)}% +theory from this difficulty by assuming that the motion +of the body relative to the æther produces a contraction +of the body in the direction of motion, the amount of contraction +being just sufficient to compensate for the difference +in time mentioned above. Comparison with the +discussion in \Sectionref{XII} shows that also from the standpoint +of the theory of relativity this solution of the +difficulty was the right one. But on the basis of the +theory of relativity the method of interpretation is +incomparably more satisfactory. According to this +theory there is no such thing as a ``specially favoured'' +(unique) co-ordinate system to occasion the introduction +of the æther-idea, and hence there can be no æther-drift, +nor any experiment with which to demonstrate it. +Here the contraction of moving bodies follows from +the two fundamental principles of the theory without +the introduction of particular hypotheses; and as the +prime factor involved in this contraction we find, not +the motion in itself, to which we cannot attach any +meaning, but the motion with respect to the body of +\PageSep{54} +reference chosen in the particular case in point. Thus +for a co-ordinate system moving with the earth the +mirror system of Michelson and Morley is not shortened, +\index{Michelson|)}% +\index{Morley}% +but it \emph{is} shortened for a co-ordinate system which is at +rest relatively to the sun. +\PageSep{55} + + +\Chapter{XVII}{Minkowski's Four-dimensional Space} +\index{Minkowski|(}% +\index{Space}% + +\First{The} non-mathematician is seized by a mysterious +shuddering when he hears of ``four-dimensional'' +things, by a feeling not unlike that awakened by +thoughts of the occult. And yet there is no more +common-place statement than that the world in which +\index{World}% +we live is a four-dimensional space-time continuum. +\index{Continuum}% + +Space is a three-dimensional continuum. By this +\index{Space co-ordinates}% +\index{Three-dimensional}% +\index{Time!coordinate@{co-ordinate}}% +we mean that it is possible to describe the position of a +point (at rest) by means of three numbers (co-ordinates) +$x$,~$y$,~$z$, and that there is an indefinite number of points +in the neighbourhood of this one, the position of which +can be described by co-ordinates such as $x_{1}$,~$y_{1}$,~$z_{1}$, which +may be as near as we choose to the respective values of +the co-ordinates $x$,~$y$,~$z$ of the first point. In virtue of the +latter property we speak of a ``continuum,'' and owing +to the fact that there are three co-ordinates we speak of +it as being ``three-dimensional.'' + +Similarly, the world of physical phenomena which was +briefly called ``world'' by Minkowski is naturally +four-dimensional in the space-time sense. For it is +composed of individual events, each of which is described +by four numbers, namely, three space +co-ordinates $x$,~$y$,~$z$ and a time co-ordinate, the time-value~$t$. +The ``world'' is in this sense also a continuum; +for to every event there are as many ``neighbouring'' +\PageSep{56} +events (realised or at least thinkable) as we care to +choose, the co-ordinates $x_{1}$,~$y_{1}$, $z_{1}$,~$t_{1}$ of which differ +by an indefinitely small amount from those of the +event $x$,~$y$, $z$,~$t$ originally considered. That we have not +been accustomed to regard the world in this sense as a +\index{World}% +four-dimensional continuum is due to the fact that in +physics, before the advent of the theory of relativity, +time played a different and more independent rôle, as +compared with the space co-ordinates. It is for this +reason that we have been in the habit of treating time +as an independent continuum. As a matter of fact, +according to classical mechanics, time is absolute, +\ie\ it is independent of the position and the condition +of motion of the system of co-ordinates. We see this +expressed in the last equation of the Galileian transformation +($t' = t$). + +The four-dimensional mode of consideration of the +``world'' is natural on the theory of relativity, since +according to this theory time is robbed of its independence. +This is shown by the fourth equation of the +Lorentz transformation: +\[ +t' = \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +Moreover, according to this equation the time difference~$\Delta t'$ +\index{Space!interval@{-interval}}% +\index{Time-interval}% +of two events with respect to~$K'$ does not in general +vanish, even when the time difference~$\Delta t$ of the same +events with reference to~$K$ vanishes. Pure ``space-distance'' +of two events with respect to~$K$ results in +``time-distance'' of the same events with respect to~$K'$. +But the discovery of Minkowski, which was of importance +\PageSep{57} +for the formal development of the theory of relativity, +does not lie here. It is to be found rather in +the fact of his recognition that the four-dimensional +space-time continuum of the theory of relativity, in its +\index{Continuum!three-dimensional}% +most essential formal properties, shows a pronounced +relationship to the three-dimensional continuum of +Euclidean geometrical space.\footnote + {Cf.\ the somewhat more detailed discussion in \Appendixref{II}.} +In order to give due +prominence to this relationship, however, we must +replace the usual time co-ordinate~$t$ by an imaginary +magnitude~$\sqrt{-1}·ct$ proportional to it. Under these +conditions, the natural laws satisfying the demands of +the (special) theory of relativity assume mathematical +forms, in which the time co-ordinate plays exactly the +same rôle as the three space co-ordinates. Formally, +these four co-ordinates correspond exactly to the three +space co-ordinates in Euclidean geometry. It must be +\index{Euclidean geometry}% +\index{Euclidean space}% +clear even to the non-mathematician that, as a consequence +of this purely formal addition to our knowledge, +the theory perforce gained clearness in no mean +measure. + +These inadequate remarks can give the reader only a +vague notion of the important idea contributed by Minkowski. +Without it the general theory of relativity, of +which the fundamental ideas are developed in the following +pages, would perhaps have got no farther than its +long clothes. Minkowski's work is doubtless difficult of +\index{Minkowski|)}% +access to anyone inexperienced in mathematics, but +since it is not necessary to have a very exact grasp of +this work in order to understand the fundamental ideas +of either the special or the general theory of relativity, +I shall at present leave it here, and shall revert to it +only towards the end of \Partref{II}. +\index{Special theory of relativity|)}% +\PageSep{58} +% [Blank page] +\PageSep{59} + + +\Part{II}{The General Theory of Relativity}{General Theory of Relativity} +\index{General theory of relativity|(}% + +\Chapter{XVIII}{Special and General Principle of +Relativity} +\index{Laws of Galilei-Newton!of Nature}% + +\First{The} basal principle, which was the pivot of all +our previous considerations, was the \emph{special} +principle of relativity, \ie\ the principle of the +physical relativity of all \emph{uniform} motion. Let us once +\index{Uniform translation}% +more analyse its meaning carefully. + +It was at all times clear that, from the point of view +of the idea it conveys to us, every motion must only +be considered as a relative motion. Returning to the +illustration we have frequently used of the embankment +and the railway carriage, we can express the fact of the +motion here taking place in the following two forms, +both of which are equally justifiable: +\begin{itemize} +\item[\itema] The carriage is in motion relative to the embankment. + +\item[\itemb] The embankment is in motion relative to the + carriage. +\end{itemize} + +In \itema~the embankment, in \itemb~the carriage, serves as +the body of reference in our statement of the motion +taking place. If it is simply a question of detecting +\PageSep{60} +or of describing the motion involved, it is in principle +\index{Motion}% +immaterial to what reference-body we refer the motion. +\index{Reference-body}% +As already mentioned, this is self-evident, but it must +not be confused with the much more comprehensive +statement called ``the principle of relativity,'' which +\index{Principle of relativity}% +we have taken as the basis of our investigations. + +The principle we have made use of not only maintains +that we may equally well choose the carriage or the +embankment as our reference-body for the description +of any event (for this, too, is self-evident). Our principle +rather asserts what follows: If we formulate the general +laws of nature as they are obtained from experience, +\index{Experience}% +by making use of +\begin{itemize} +\item[\itema] the embankment as reference-body, +\item[\itemb] the railway carriage as reference-body, +\end{itemize} +then these general laws of nature (\eg\ the laws of +mechanics or the law of the propagation of light \textit{in~vacuo}) +have exactly the same form in both cases. This can +also be expressed as follows: For the \emph{physical} description +of natural processes, neither of the reference-bodies +$K$,~$K'$ is unique (lit.\ ``specially marked out'') as +compared with the other. Unlike the first, this latter +statement need not of necessity hold \textit{a~priori}; it is +not contained in the conceptions of ``motion'' and +``reference-body'' and derivable from them; only +\emph{experience} can decide as to its correctness or incorrectness. + +Up to the present, however, we have by no means +maintained the equivalence of \emph{all} bodies of reference~$K$ +in connection with the formulation of natural laws. +Our course was more on the following lines. In the +first place, we started out from the assumption that +there exists a reference-body~$K$, whose condition of +\PageSep{61} +\index{Law of inertia}% +motion is such that the Galileian law holds with respect +to it: A particle left to itself and sufficiently far removed +from all other particles moves uniformly in a straight +line. With reference to~$K$ (Galileian reference-body) the +laws of nature were to be as simple as possible. But +in addition to~$K$, all bodies of reference~$K'$ should be +given preference in this sense, and they should be exactly +equivalent to~$K$ for the formulation of natural laws, +provided that they are in a state of \emph{uniform rectilinear +and non-rotary motion} with respect to~$K$; all these +bodies of reference are to be regarded as Galileian +reference-bodies. The validity of the principle of +relativity was assumed only for these reference-bodies, +but not for others (\eg\ those possessing motion of a +different kind). In this sense we speak of the \emph{special} +principle of relativity, or special theory of relativity. + +In contrast to this we wish to understand by the +``general principle of relativity'' the following statement: +All bodies of reference $K$,~$K'$,~etc., are equivalent +for the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion. But before proceeding farther, it +ought to be pointed out that this formulation must be +replaced later by a more abstract one, for reasons which +will become evident at a later stage. + +Since the introduction of the special principle of +relativity has been justified, every intellect which +strives after generalisation must feel the temptation +to venture the step towards the general principle of +relativity. But a simple and apparently quite reliable +consideration seems to suggest that, for the present +at any rate, there is little hope of success in such an +attempt. Let us imagine ourselves transferred to our +\PageSep{62} +\index{Law of inertia}% +old friend the railway carriage, which is travelling at a +uniform rate. As long as it is moving uniformly, the +occupant of the carriage is not sensible of its motion, +and it is for this reason that he can without reluctance +interpret the facts of the case as indicating that the +carriage is at rest but the embankment in motion. +Moreover, according to the special principle of relativity, +this interpretation is quite justified also from a physical +point of view. + +If the motion of the carriage is now changed into a +non-uniform motion, as for instance by a powerful +\index{Non-uniform motion}% +application of the brakes, then the occupant of the +carriage experiences a correspondingly powerful jerk +forwards. The retarded motion is manifested in the +mechanical behaviour of bodies relative to the person +in the railway carriage. The mechanical behaviour is +different from that of the case previously considered, +and for this reason it would appear to be impossible +that the same mechanical laws hold relatively to the non-uniformly +moving carriage, as hold with reference to the +carriage when at rest or in uniform motion. At all +events it is clear that the Galileian law does not hold +with respect to the non-uniformly moving carriage. +Because of this, we feel compelled at the present juncture +to grant a kind of absolute physical reality to non-uniform +motion, in opposition to the general principle +of relativity. But in what follows we shall soon see +that this conclusion cannot be maintained. +\PageSep{63} + + +\Chapter{XIX}{The Gravitational Field} + +``\First{If} we pick up a stone and then let it go, why does it +fall to the ground?'' The usual answer to this +question is: ``Because it is attracted by the earth.'' +Modern physics formulates the answer rather differently +for the following reason. As a result of the more careful +study of electromagnetic phenomena, we have come +to regard action at a distance as a process impossible +without the intervention of some intermediary medium. +If, for instance, a magnet attracts a piece of iron, we +cannot be content to regard this as meaning that the +magnet acts directly on the iron through the intermediate +empty space, but we are constrained to imagine---after +the manner of Faraday---that the magnet +\index{Faraday}% +always calls into being something physically real in +the space around it, that something being what we call a +``magnetic field.'' In its turn this magnetic field +\index{Magnetic field}% +operates on the piece of iron, so that the latter strives +to move towards the magnet. We shall not discuss +here the justification for this incidental conception, +which is indeed a somewhat arbitrary one. We shall +only mention that with its aid electromagnetic phenomena +can be theoretically represented much more +satisfactorily than without it, and this applies particularly +\index{Electromagnetic theory!waves}% +to the transmission of electromagnetic waves. +\PageSep{64} +The effects of gravitation also are regarded in an analogous +\index{Gravitation}% +manner. + +The action of the earth on the stone takes place indirectly. +The earth produces in its surroundings a +gravitational field, which acts on the stone and produces +\index{Gravitational field}% +its motion of fall. As we know from experience, the +intensity of the action on a body diminishes according +to a quite definite law, as we proceed farther and farther +away from the earth. From our point of view this +means: The law governing the properties of the gravitational +field in space must be a perfectly definite one, in +order correctly to represent the diminution of gravitational +action with the distance from operative bodies. +It is something like this: The body (\eg\ the earth) produces +a field in its immediate neighbourhood directly; +the intensity and direction of the field at points farther +removed from the body are thence determined by +the law which governs the properties in space of the +gravitational fields themselves. + +In contrast to electric and magnetic fields, the gravitational +field exhibits a most remarkable property, which +is of fundamental importance for what follows. Bodies +which are moving under the sole influence of a gravitational +field receive an acceleration, \emph{which does not in the +\index{Acceleration}% +least depend either on the material or on the physical +state of the body}. For instance, a piece of lead and +a piece of wood fall in exactly the same manner in a +gravitational field (\textit{in~vacuo}), when they start off from +rest or with the same initial velocity. This law, which +holds most accurately, can be expressed in a different +form in the light of the following consideration. + +According to Newton's law of motion, we have +\index{Newton's!law of motion}% +\[ +(\text{Force}) = (\text{inertial mass}) × (\text{acceleration}), +\] +\PageSep{65} +where the ``inertial mass'' is a characteristic constant +\index{Inertial mass}% +of the accelerated body. If now gravitation is the +cause of the acceleration, we then have +%[** TN: Re-breaking next two displayed equations] +\begin{multline*} +(\text{Force}) + = (\text{gravitational mass}) \\ + × (\text{intensity of the gravitational field}), +\index{Gravitational mass}% +\end{multline*} +where the ``gravitational mass'' is likewise a characteristic +constant for the body. From these two relations +follows: +\begin{multline*} +(\text{acceleration}) + = \frac{(\text{gravitational mass})}{(\text{inertial mass})} \\ + × (\text{intensity of the gravitational field}). +\end{multline*} + +If now, as we find from experience, the acceleration is +to be independent of the nature and the condition of the +body and always the same for a given gravitational +field, then the ratio of the gravitational to the inertial +mass must likewise be the same for all bodies. By a +suitable choice of units we can thus make this ratio +equal to unity. We then have the following law: +The \emph{gravitational} mass of a body is equal to its \emph{inertial} +mass. + +It is true that this important law had hitherto been +recorded in mechanics, but it had not been \emph{interpreted}. +A satisfactory interpretation can be obtained only if we +recognise the following fact: \emph{The same} quality of a +body manifests itself according to circumstances as +``inertia'' or as ``weight'' (lit.\ ``heaviness''). In the +\index{Inertia}% +\index{Weight (heaviness)}% +following section we shall show to what extent this is +actually the case, and how this question is connected +with the general postulate of relativity. +\PageSep{66} + + +\Chapter{XX}{The Equality of Inertial and Gravitational +Mass as an Argument for the +General Postulate of Relativity} + +\First{We} imagine a large portion of empty space, so far +removed from stars and other appreciable +masses, that we have before us approximately +the conditions required by the fundamental law of Galilei. +It is then possible to choose a Galileian reference-body for +this part of space (world), relative to which points at +rest remain at rest and points in motion continue permanently +in uniform rectilinear motion. As reference-body +let us imagine a spacious chest resembling a room +\index{Chest}% +with an observer inside who is equipped with apparatus. +Gravitation naturally does not exist for this observer. +He must fasten himself with strings to the floor, +otherwise the slightest impact against the floor will +cause him to rise slowly towards the ceiling of the +room. + +To the middle of the lid of the chest is fixed externally +a hook with rope attached, and now a ``being'' (what +\index{Being@{``Being''}}% +kind of a being is immaterial to us) begins pulling at +this with a constant force. The chest together with the +observer then begin to move ``upwards'' with a +uniformly accelerated motion. In course of time their +velocity will reach unheard-of values---provided that +\PageSep{67} +we are viewing all this from another reference-body +which is not being pulled with a rope. + +But how does the man in the chest regard the process? +The acceleration of the chest will be transmitted to him +\index{Acceleration}% +by the reaction of the floor of the chest. He must +therefore take up this pressure by means of his legs if +he does not wish to be laid out full length on the floor. +He is then standing in the chest in exactly the same way +as anyone stands in a room of a house on our earth. +If he release a body which he previously had in his +hand, the acceleration of the chest will no longer be +transmitted to this body, and for this reason the body +will approach the floor of the chest with an accelerated +relative motion. The observer will further convince +himself \emph{that the acceleration of the body towards the floor +of the chest is always of the same magnitude, whatever +kind of body he may happen to use for the experiment}. + +Relying on his knowledge of the gravitational field +\index{Gravitational field}% +(as it was discussed in the preceding section), the man +in the chest will thus come to the conclusion that he +and the chest are in a gravitational field which is constant +with regard to time. Of course he will be puzzled for +a moment as to why the chest does not fall, in this +gravitational field. Just then, however, he discovers +the hook in the middle of the lid of the chest and the +rope which is attached to it, and he consequently comes +to the conclusion that the chest is suspended at rest in +the gravitational field. + +Ought we to smile at the man and say that he errs +in his conclusion? I do not believe we ought to if we +wish to remain consistent; we must rather admit that +his mode of grasping the situation violates neither reason +nor known mechanical laws. Even though it is being +\PageSep{68} +accelerated with respect to the ``Galileian space'' +first considered, we can nevertheless regard the chest +as being at rest. We have thus good grounds for +extending the principle of relativity to include bodies +of reference which are accelerated with respect to each +other, and as a result we have gained a powerful argument +for a generalised postulate of relativity. + +We must note carefully that the possibility of this +mode of interpretation rests on the fundamental +property of the gravitational field of giving all bodies +\index{Gravitational mass}% +the same acceleration, or, what comes to the same thing, +on the law of the equality of inertial and gravitational +mass. If this natural law did not exist, the man in +the accelerated chest would not be able to interpret +the behaviour of the bodies around him on the supposition +of a gravitational field, and he would not be justified +on the grounds of experience in supposing his reference-body +to be ``at rest.'' + +Suppose that the man in the chest fixes a rope to the +inner side of the lid, and that he attaches a body to the +free end of the rope. The result of this will be to stretch +the rope so that it will hang ``vertically'' downwards. +If we ask for an opinion of the cause of tension in the +rope, the man in the chest will say: ``The suspended +body experiences a downward force in the gravitational +field, and this is neutralised by the tension of the rope; +what determines the magnitude of the tension of the +rope is the \emph{gravitational mass} of the suspended body.'' +On the other hand, an observer who is poised freely in +space will interpret the condition of things thus: ``The +rope must perforce take part in the accelerated motion +of the chest, and it transmits this motion to the body +attached to it. The tension of the rope is just large +\PageSep{69} +enough to effect the acceleration of the body. That +which determines the magnitude of the tension of the +rope is the \emph{inertial mass} of the body.'' Guided by +\index{Inertial mass}% +this example, we see that our extension of the principle +of relativity implies the \emph{necessity} of the law of the +equality of inertial and gravitational mass. Thus we +have obtained a physical interpretation of this law. + +From our consideration of the accelerated chest we +see that a general theory of relativity must yield important +results on the laws of gravitation. In point of +\index{Gravitation}% +fact, the systematic pursuit of the general idea of relativity +has supplied the laws satisfied by the gravitational +field. Before proceeding farther, however, I +must warn the reader against a misconception suggested +by these considerations. A gravitational field exists +for the man in the chest, despite the fact that there was +no such field for the co-ordinate system first chosen. +Now we might easily suppose that the existence of a +gravitational field is always only an \emph{apparent} one. We +might also think that, regardless of the kind of gravitational +field which may be present, we could always +choose another reference-body such that \emph{no} gravitational +field exists with reference to it. This is by no means +true for all gravitational fields, but only for those of +quite special form. It is, for instance, impossible to +choose a body of reference such that, as judged from it, +the gravitational field of the earth (in its entirety) +vanishes. + +We can now appreciate why that argument is not +convincing, which we brought forward against the +general principle of relativity at the end of \Sectionref{XVIII}. +It is certainly true that the observer in the railway +carriage experiences a jerk forwards as a result of the +\PageSep{70} +application of the brake, and that he recognises in this the +non-uniformity of motion (retardation) of the carriage. +But he is compelled by nobody to refer this jerk to a +``real'' acceleration (retardation) of the carriage. He +\index{Acceleration}% +might also interpret his experience thus: ``My body of +reference (the carriage) remains permanently at rest. +With reference to it, however, there exists (during the +period of application of the brakes) a gravitational +field which is directed forwards and which is variable +with respect to time. Under the influence of this field, +the embankment together with the earth moves non-uniformly +in such a manner that their original velocity +in the backwards direction is continuously reduced.'' +\PageSep{71} + + +\Chapter{XXI}{In what Respects are the Foundations +of Classical Mechanics and of the +Special Theory of Relativity unsatisfactory?} +\index{Classical mechanics}% +\index{Laws of Galilei-Newton!of Nature}% + +\First{We} have already stated several times that +classical mechanics starts out from the following +law: Material particles sufficiently far +removed from other material particles continue to +move uniformly in a straight line or continue in a +state of rest. We have also repeatedly emphasised +that this fundamental law can only be valid for +bodies of reference~$K$ which possess certain unique +states of motion, and which are in uniform translational +motion relative to each other. Relative to other reference-bodies~$K$ +the law is not valid. Both in classical +mechanics and in the special theory of relativity we +therefore differentiate between reference-bodies~$K$ +relative to which the recognised ``laws of nature'' can +be said to hold, and reference-bodies~$K$ relative to which +these laws do not hold. + +But no person whose mode of thought is logical can +rest satisfied with this condition of things. He asks: +``How does it come that certain reference-bodies (or +their states of motion) are given priority over other +reference-bodies (or their states of motion)? \emph{What is +\PageSep{72} +the reason for this preference?}\Change{}{''} In order to show clearly +what I mean by this question, I shall make use of a +comparison. + +I am standing in front of a gas range. Standing +alongside of each other on the range are two pans so +much alike that one may be mistaken for the other. +Both are half full of water. I notice that steam is being +emitted continuously from the one pan, but not from the +other. I am surprised at this, even if I have never seen +either a gas range or a pan before. But if I now notice +a luminous something of bluish colour under the first +pan but not under the other, I cease to be astonished, +even if I have never before seen a gas flame. For I +can only say that this bluish something will cause the +emission of the steam, or at least \emph{possibly} it may do so. +If, however, I notice the bluish something in neither +case, and if I observe that the one continuously emits +steam whilst the other does not, then I shall remain +astonished and dissatisfied until I have discovered +some circumstance to which I can attribute the different +behaviour of the two pans. + +Analogously, I seek in vain for a real something in +classical mechanics (or in the special theory of relativity) +to which I can attribute the different behaviour +of bodies considered with respect to the reference-systems +$K$~and~$K'$.\footnote + {The objection is of importance more especially when the state + of motion of the reference-body is of such a nature that it does + not require any external agency for its maintenance, \eg\ in + the case when the reference-body is rotating uniformly.} +Newton saw this objection and +\index{Newton}% +attempted to invalidate it, but without success. But +E.~Mach recognised it most clearly of all, and because +\index{Mach, E.}% +of this objection he claimed that mechanics must be +\PageSep{73} +placed on a new basis. It can only be got rid of by +means of a physics which is conformable to the general +principle of relativity, since the equations of such a +theory hold for every body of reference, whatever +may be its state of motion. +\PageSep{74} + + +\Chapter{XXII}{A Few Inferences from the General +Principle of Relativity} + +\First{The} considerations of \Sectionref{XX} show that the +general principle of relativity puts us in a position +to derive properties of the gravitational field in a +\index{Gravitational field}% +purely theoretical manner. Let us suppose, for instance, +that we know the space-time ``course'' for any natural +process whatsoever, as regards the manner in which it +takes place in the Galileian domain relative to a +Galileian body of reference~$K$. By means of purely +theoretical operations (\ie\ simply by calculation) we are +then able to find how this known natural process +appears, as seen from a reference-body~$K'$ which is +accelerated relatively to~$K$. But since a gravitational +field exists with respect to this new body of reference~$K'$, +our consideration also teaches us how the gravitational +field influences the process studied. + +For example, we learn that a body which is in a state +of uniform rectilinear motion with respect to~$K$ (in +accordance with the law of Galilei) is executing an +accelerated and in general curvilinear motion with +\index{Curvilinear motion}% +respect to the accelerated reference-body~$K'$ (chest). +This acceleration or curvature corresponds to the influence +on the moving body of the gravitational field +prevailing relatively to~$K'$. It is known that a gravitational +field influences the movement of bodies in this +\PageSep{75} +way, so that our consideration supplies us with nothing +essentially new. + +However, we obtain a new result of fundamental +\index{Propagation of light!in gravitational fields}% +importance when we carry out the analogous consideration +for a ray of light. With respect to the Galileian +reference-body~$K$, such a ray of light is transmitted +rectilinearly with the velocity~$c$. It can easily be shown +that the path of the same ray of light is no longer a +straight line when we consider it with reference to the +accelerated chest (reference-body~$K'$). From this we +conclude, \emph{that, in general, rays of light are propagated +curvilinearly in gravitational fields}. In two respects +this result is of great importance. + +In the first place, it can be compared with the reality. +Although a detailed examination of the question shows +that the curvature of light rays required by the general +theory of relativity is only exceedingly small for the +gravitational fields at our disposal in practice, its estimated +magnitude for light rays passing the sun at +grazing incidence is nevertheless $1.7$~seconds of arc. +This ought to manifest itself in the following way. +As seen from the earth, certain fixed stars appear to be +in the neighbourhood of the sun, and are thus capable +of observation during a total eclipse of the sun. At such +times, these stars ought to appear to be displaced +outwards from the sun by an amount indicated above, +as compared with their apparent position in the sky +when the sun is situated at another part of the heavens. +The examination of the correctness or otherwise of this +deduction is a problem of the greatest importance, the +early solution of which is to be expected of astronomers.\footnote + {By means of the star photographs of two expeditions equipped + by a Joint Committee of the Royal and Royal Astronomical + Societies, the existence of the deflection of light demanded by + theory was confirmed during the solar eclipse of 29th~May, 1919. +\index{Solar eclipse}% + (Cf.\ \Appendixref{III}.)} +\PageSep{76} + +In the second place our result shows that, according +to the general theory of relativity, the law of the constancy +of the velocity of light \textit{in~vacuo}, which constitutes +\index{Velocity of light}% +one of the two fundamental assumptions in the +special theory of relativity and to which we have +already frequently referred, cannot claim any unlimited +validity. A curvature of rays of light can only take +place when the velocity of propagation of light varies +with position. Now we might think that as a consequence +of this, the special theory of relativity and with +it the whole theory of relativity would be laid in the +dust. But in reality this is not the case. We can only +conclude that the special theory of relativity cannot +claim an unlimited domain of validity; its results +hold only so long as we are able to disregard the influences +of gravitational fields on the phenomena +(\eg\ of light). + +Since it has often been contended by opponents of +the theory of relativity that the special theory of +relativity is overthrown by the general theory of relativity, +it is perhaps advisable to make the facts of the +case clearer by means of an appropriate comparison. +Before the development of electrodynamics the laws +\index{Electrodynamics}% +of electrostatics were looked upon as the laws of +\index{Electrostatics}% +electricity. At the present time we know that +\index{Electricity}% +electric fields can be derived correctly from electrostatic +considerations only for the case, which is never +strictly realised, in which the electrical masses are quite +at rest relatively to each other, and to the co-ordinate +system. Should we be justified in saying that for this +\PageSep{77} +reason electrostatics is overthrown by the field-equations +of Maxwell in electrodynamics? Not in the least. +\index{Maxwell!fundamental equations}% +Electrostatics is contained in electrodynamics as a +limiting case; the laws of the latter lead directly to +those of the former for the case in which the fields are +invariable with regard to time. No fairer destiny +could be allotted to any physical theory, than that it +should of itself point out the way to the introduction +of a more comprehensive theory, in which it lives on +as a limiting case. + +In the example of the transmission of light just dealt +with, we have seen that the general theory of relativity +enables us to derive theoretically the influence of a +gravitational field on the course of natural processes, +\index{Gravitational field}% +the laws of which are already known when a gravitational +field is absent. But the most attractive problem, +to the solution of which the general theory of relativity +supplies the key, concerns the investigation of the laws +satisfied by the gravitational field itself. Let us consider +this for a moment. + +We are acquainted with space-time domains which +behave (approximately) in a ``Galileian'' fashion under +suitable choice of reference-body, \ie\ domains in which +gravitational fields are absent. If we now refer such +a domain to a reference-body~$K'$ possessing any kind +of motion, then relative to~$K'$ there exists a gravitational +field which is variable with respect to space and +time.\footnote + {This follows from a generalisation of the discussion in \Sectionref{XX}.} +The character of this field will of course depend +on the motion chosen for~$K'$. According to the general +theory of relativity, the general law oi the gravitational +field must be satisfied for all gravitational fields obtainable +\PageSep{78} +in this way. Even though by no means all gravitational +fields can be produced in this way, yet we may +entertain the hope that the general law of gravitation +\index{Gravitation}% +will be derivable from such gravitational fields of a +special kind. This hope has been realised in the most +beautiful manner. But between the clear vision of +this goal and its actual realisation it was necessary to +surmount a serious difficulty, and as this lies deep at +the root of things, I dare not withhold it from the reader. +We require to extend our ideas of the space-time continuum +\index{Continuum!space-time}% +still farther. +\PageSep{79} + + +\Chapter{XXIII}{Behaviour of Clocks and Measuring-Rods +on a Rotating Body of Reference} + +\First{Hitherto} I have purposely refrained from +speaking about the physical interpretation of +space- and time-data in the case of the general +theory of relativity. As a consequence, I am guilty of a +certain slovenliness of treatment, which, as we know +from the special theory of relativity, is far from being +unimportant and pardonable. It is now high time that +we remedy this defect; but I would mention at the +outset, that this matter lays no small claims on the +patience and on the power of abstraction of the reader. + +We start off again from quite special cases, which we +\index{Galileian system of co-ordinates}% +have frequently used before. Let us consider a space-time +domain in which no gravitational field exists +relative to a reference-body~$K$ whose state of motion +\index{Reference-body!rotating}% +has been suitably chosen. $K$~is then a Galileian reference-body +as regards the domain considered, and the +results of the special theory of relativity hold relative +to~$K$. Let us suppose the same domain referred to a +second body of reference~$K'$, which is rotating uniformly +with respect to~$K$. In order to fix our ideas, we shall +imagine~$K'$ to be in the form of a plane circular disc, +which rotates uniformly in its own plane about its +centre. An observer who is sitting eccentrically on the +\PageSep{80} +disc~$K'$ is sensible of a force which acts outwards in a +radial direction, and which would be interpreted as an +effect of inertia (centrifugal force) by an observer who +\index{Centrifugal force}% +was at rest with respect to the original reference-body~$K$. +But the observer on the disc may regard his disc as a +reference-body which is ``at rest''; on the basis of the +general principle of relativity he is justified in doing this. +The force acting on himself, and in fact on all other +bodies which are at rest relative to the disc, he regards +as the effect of a gravitational field. Nevertheless, +the space-distribution of this gravitational field is of a +kind that would not be possible on Newton's theory of +\index{Newton's!law of gravitation}% +gravitation.\footnote + {The field disappears at the centre of the disc and increases + proportionally to the distance from the centre as we proceed + outwards.} +But since the observer believes in the +general theory of relativity, this does not disturb him; +he is quite in the right when he believes that a general +law of gravitation can be formulated---a law which not +only explains the motion of the stars correctly, but +also the field of force experienced by himself. + +The observer performs experiments on his circular +disc with clocks and measuring-rods. In doing so, it +\index{Clocks}% +\index{Measuring-rod}% +is his intention to arrive at exact definitions for the +signification of time- and space-data with reference +to the circular disc~$K'$, these definitions being based on +his observations. What will be his experience in this +enterprise? + +To start with, he places one of two identically constructed +clocks at the centre of the circular disc, and the +other on the edge of the disc, so that they are at rest +relative to it. We now ask ourselves whether both +clocks go at the same rate from the standpoint of the +\PageSep{81} +non-rotating Galileian reference-body~$K$. As judged +from this body, the clock at the centre of the disc has +no velocity, whereas the clock at the edge of the disc +is in motion relative to~$K$ in consequence of the rotation. +\index{Rotation}% +According to a result obtained in \Sectionref{XII}, it follows +that the latter clock goes at a rate permanently slower +than that of the clock at the centre of the circular disc, +\ie\ as observed from~$K$. It is obvious that the same effect +would be noted by an observer whom we will imagine +sitting alongside his clock at the centre of the circular +disc. Thus on our circular disc, or, to make the case +more general, in every gravitational field, a clock will +go more quickly or less quickly, according to the position +in which the clock is situated (at rest). For this reason +it is not possible to obtain a reasonable definition of time +with the aid of clocks which are arranged at rest with +\index{Clocks}% +respect to the body of reference. A similar difficulty +presents itself when we attempt to apply our earlier +definition of simultaneity in such a case, but I do not +\index{Simultaneity}% +wish to go any farther into this question. + +Moreover, at this stage the definition of the space +\index{Space co-ordinates}% +co-ordinates also presents insurmountable difficulties. +If the observer applies his standard measuring-rod +\index{Measuring-rod}% +(a rod which is short as compared with the radius of +the disc) tangentially to the edge of the disc, then, as +judged from the Galileian system, the length of this rod +will be less than~$1$, since, according to \Sectionref{XII}, moving +bodies suffer a shortening in the direction of the motion. +On the other hand, the measuring-rod will not experience +a shortening in length, as judged from~$K$, if it is applied +to the disc in the direction of the radius. If, then, the +observer first measures the circumference of the disc +with his measuring-rod and then the diameter of the +\PageSep{82} +disc, on dividing the one by the other, he will not obtain +as quotient the familiar number $\pi = 3.14\dots$, but +a larger number,\footnote + {Throughout this consideration we have to use the Galileian + (non-rotating) system~$K$ as reference-body, since we may only + assume the validity of the results of the special theory of relativity + relative to~$K$ (relative to~$K'$ a gravitational field prevails).} +whereas of course, for a disc which is +at rest with respect to~$K$, this operation would yield~$\pi$ +\index{Value of $\pi$}% +exactly. This proves that the propositions of Euclidean +\index{Euclidean geometry}% +geometry cannot hold exactly on the rotating disc, nor +in general in a gravitational field, at least if we attribute +the length~$1$ to the rod in all positions and in every +orientation. Hence the idea of a straight line also loses +\index{Straight line}% +its meaning. We are therefore not in a position to +define exactly the co-ordinates $x$,~$y$,~$z$ relative to the +disc by means of the method used in discussing the +special theory, and as long as the co-ordinates and times +of events have not been defined, we cannot assign an +exact meaning to the natural laws in which these occur. + +Thus all our previous conclusions based on general +relativity would appear to be called in question. In +reality we must make a subtle detour in order to be +able to apply the postulate of general relativity exactly. +I shall prepare the reader for this in the +following paragraphs. +\PageSep{83} + + +\Chapter{XXIV}{Euclidean and Non-Euclidean Continuum} +\index{Continuum}% + +\First{The} surface of a marble table is spread out in front +of me. I can get from any one point on this +table to any other point by passing continuously +from one point to a ``neighbouring'' one, and repeating +this process a (large) number of times, or, in other words, +by going from point to point without executing ``jumps.'' +I am sure the reader will appreciate with sufficient +clearness what I mean here by ``neighbouring'' and by +``jumps'' (if he is not too pedantic). We express this +property of the surface by describing the latter as a +continuum. + +Let us now imagine that a large number of little rods +of equal length have been made, their lengths being +small compared with the dimensions of the marble +slab. When I say they are of equal length, I mean that +one can be laid on any other without the ends overlapping. +We next lay four of these little rods on the +marble slab so that they constitute a quadrilateral +figure (a square), the diagonals of which are equally +long. To ensure the equality of the diagonals, we make +use of a little testing-rod. To this square we add +similar ones, each of which has one rod in common +with the first. We proceed in like manner with each of +these squares until finally the whole marble slab is +\PageSep{84} +laid out with squares. The arrangement is such, that +each side of a square belongs to two squares and each +corner to four squares. + +It is a veritable wonder that we can carry out this +business without getting into the greatest difficulties. +We only need to think of the following. If at any +moment three squares meet at a corner, then two sides +of the fourth square are already laid, and, as a consequence, +the arrangement of the remaining two sides of +the square is already completely determined. But I +am now no longer able to adjust the quadrilateral so +that its diagonals may be equal. If they are equal +of their own accord, then this is an especial favour +of the marble slab and of the little rods, about which I +can only be thankfully surprised. We must needs +experience many such surprises if the construction is to +be successful. + +If everything has really gone smoothly, then I say +that the points of the marble slab constitute a Euclidean +\index{Distance (line-interval)}% +\index{Continuum!Euclidean}% +continuum with respect to the little rod, which has been +used as a ``distance'' (line-interval). By choosing +one corner of a square as ``origin,'' I can characterise +every other corner of a square with reference to this +origin by means of two numbers. I only need state +how many rods I must pass over when, starting from the +origin, I proceed towards the ``right'' and then ``upwards,'' +in order to arrive at the corner of the square +under consideration. These two numbers are then the +``Cartesian co-ordinates'' of this corner with reference +\index{Cartesian system of co-ordinates}% +to the ``Cartesian co-ordinate system'' which is determined +by the arrangement of little rods. + +By making use of the following modification of this +abstract experiment, we recognise that there must also +\PageSep{85} +\index{Measurement of length}% +be cases in which the experiment would be unsuccessful. +We shall suppose that the rods ``expand'' by an amount +proportional to the increase of temperature. We heat +the central part of the marble slab, but not the periphery, +in which case two of our little rods can still be +brought into coincidence at every position on the table. +But our construction of squares must necessarily come +into disorder during the heating, because the little rods +on the central region of the table expand, whereas +those on the outer part do not. + +With reference to our little rods---defined as unit +lengths---the marble slab is no longer a Euclidean continuum, +and we are also no longer in the position of defining +Cartesian co-ordinates directly with their aid, +since the above construction can no longer be carried +out. But since there are other things which are not +influenced in a similar manner to the little rods (or +perhaps not at all) by the temperature of the table, it is +possible quite naturally to maintain the point of view +that the marble slab is a ``Euclidean continuum.'' +This can be done in a satisfactory manner by making a +more subtle stipulation about the measurement or the +comparison of lengths. + +But if rods of every kind (\ie\ of every material) were +to behave \emph{in the same way} as regards the influence of +temperature when they are on the variably heated +marble slab, and if we had no other means of detecting +the effect of temperature than the geometrical behaviour +of our rods in experiments analogous to the one +described above, then our best plan would be to assign +the distance \emph{one} to two points on the slab, provided that +the ends of one of our rods could be made to coincide +with these two points; for how else should we define +\PageSep{86} +the distance without our proceeding being in the highest +measure grossly arbitrary? The method of Cartesian +co-ordinates must then be discarded, and replaced by +another which does not assume the validity of Euclidean +\index{Continuum!Euclidean}% +\index{Continuum!non-Euclidean}% +\index{Euclidean geometry}% +\index{Euclidean space}% +geometry for rigid bodies.\footnote + {Mathematicians have been confronted with our problem in the + following form. If we are given a surface (\eg\ an ellipsoid) in + Euclidean three-dimensional space, then there exists for this + surface a two-dimensional geometry, just as much as for a plane + surface. Gauss undertook the task of treating this two-dimensional +\index{Gauss}% + geometry from first principles, without making use of the + fact that the surface belongs to a Euclidean continuum of + three dimensions. If we imagine constructions to be made with + rigid rods \emph{in the surface} (similar to that above with the marble + slab), we should find that different laws hold for these from those + resulting on the basis of Euclidean plane geometry. The surface + is not a Euclidean continuum with respect to the rods, and we + cannot define Cartesian co-ordinates \emph{in the surface}. Gauss + indicated the principles according to which we can treat the + geometrical relationships in the surface, and thus pointed out + the way to the method of Riemann of treating multi-dimensional, +\index{Riemann}% + non-Euclidean \textit{continua}. Thus it is that mathematicians + long ago solved the formal problems to which we are led by the + general postulate of relativity.} +The reader will notice that +the situation depicted here corresponds to the one +brought about by the general postulate of relativity +(\Sectionref{XXIII}). +\PageSep{87} + + +\Chapter{XXV}{Gaussian Co-ordinates} + +\First{According} to Gauss, this combined analytical +\index{Gauss}% +and geometrical mode of handling the problem +can be arrived at in the following way. We +imagine a system of arbitrary curves (see \Figref{4}) +drawn on the surface of the table. These we designate +as $u$-curves, and we indicate each of them by +means of a number. The curves $u = 1$, $u = 2$ and +$u = 3$ are drawn in the diagram. Between the curves +$u = 1$ and $u = 2$ we must imagine an infinitely large +number to be drawn, all of which correspond +%[Illustration: Fig. 4.] +\WFigure{2in}{087} +to real +numbers lying between $1$~and~$2$. We have then +a system of $u$-curves, and +this ``infinitely dense'' system +covers the whole surface +of the table. These +$u$-curves must not intersect +each other, and through each +point of the surface one and +only one curve must pass. +Thus a perfectly definite +value of~$u$ belongs to every point on the surface of the +marble slab. In like manner we imagine a system of +$v$-curves drawn on the surface. These satisfy the same +conditions as the $u$-curves, they are provided with numbers +\PageSep{88} +in a corresponding manner, and they may likewise +be of arbitrary shape. It follows that a value of~$u$ and +a value of~$v$ belong to every point on the surface of the +table. We call these two numbers the co-ordinates +of the surface of the table (Gaussian co-ordinates). +\index{Gaussian co-ordinates|(}% +For example, the point~$P$ in the diagram has the Gaussian +co-ordinates $u = 3$, $v = 1$. Two neighbouring points $P$ +and~$P'$ on the surface then correspond to the co-ordinates +\begin{align*} +&P: &&u, v \\ +&P': &&u + du, v + dv, +\end{align*} +where $du$~and~$dv$ signify very small numbers. In a +similar manner we may indicate the distance (line-interval) +\index{Distance (line-interval)}% +between $P$~and~$P'$, as measured with a little +rod, by means of the very small number~$ds$. Then +according to Gauss we have +\[ +ds^{2} = g_{11}\, du^{2} + 2g_{12}\, du\, dv + g_{22}\, dv^{2}, +\] +where $g_{11}$,~$g_{12}$,~$g_{22}$, are magnitudes which depend in a +perfectly definite way on $u$~and~$v$. The magnitudes $g_{11}$,~$g_{12}$ +and~$g_{22}$ determine the behaviour of the rods relative +to the $u$-curves and $v$-curves, and thus also relative +to the surface of the table. For the case in which the +points of the surface considered form a Euclidean continuum +\index{Continuum!Euclidean}% +with reference to the measuring-rods, but +only in this case, it is possible to draw the $u$-curves +and $v$-curves and to attach numbers to them, in such a +manner, that we simply have: +\[ +ds^{2} = du^{2} + dv^{2}. +\] +Under these conditions, the $u$-curves and $v$-curves are +straight lines in the sense of Euclidean geometry, and +\index{Euclidean geometry}% +\index{Straight line}% +they are perpendicular to each other. Here the Gaussian +co-ordinates are simply Cartesian ones. It is clear +\PageSep{89} +that Gauss co-ordinates are nothing more than an +association of two sets of numbers with the points of +the surface considered, of such a nature that numerical +values differing very slightly from each other are +associated with neighbouring points ``in space.'' + +So far, these considerations hold for a continuum +\index{Continuum!four-dimensional}% +of two dimensions. But the Gaussian method can be +applied also to a continuum of three, four or more +dimensions. If, for instance, a continuum of four +dimensions be supposed available, we may represent +it in the following way. With every point of the +continuum we associate arbitrarily four numbers, $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$, which are known as ``co-ordinates.'' Adjacent +points correspond to adjacent values of the co-ordinates. +If a distance~$ds$ is associated with the adjacent points +\index{Adjacent points}% +$P$~and~$P'$, this distance being measurable and well-defined +from a physical point of view, then the following +formula holds: +\[ +ds^{2} = g_{11}\, {dx_{1}}^{2} + + 2g_{12}\, dx_{1}\, dx_{2} \Add{+} \dots + + g_{44}\, {dx_{4}}^{2}, +\] +where the magnitudes $g_{11}$,~etc., have values which vary +with the position in the continuum. Only when the +continuum is a Euclidean one is it possible to associate +the co-ordinates $x_{1}$\Add{,}\ldots\Add{,}~$x_{4}$ with the points of the +continuum so that we have simply +\[ +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2}. +\] +In this case relations hold in the four-dimensional +continuum which are analogous to those holding in our +three-dimensional measurements. + +However, the Gauss treatment for~$ds^{2}$ which we have +given above is not always possible. It is only possible +when sufficiently small regions of the continuum under +consideration may be regarded as Euclidean continua. +\PageSep{90} +For example, this obviously holds in the case of the +marble slab of the table and local variation of temperature. +The temperature is practically constant for a small +part of the slab, and thus the geometrical behaviour of +the rods is \emph{almost} as it ought to be according to the +rules of Euclidean geometry. Hence the imperfections +\index{Continuum!non-Euclidean}% +of the construction of squares in the previous section +do not show themselves clearly until this construction +is extended over a considerable portion of the surface +of the table. + +We can sum this up as follows: Gauss invented a +\index{Gauss}% +method for the mathematical treatment of continua in +general, in which ``size-relations'' (``distances'' between +\index{Size-relations}% +neighbouring points) are defined. To every point of a +continuum are assigned as many numbers (Gaussian co-ordinates) +as the continuum has dimensions. This is +done in such a way, that only one meaning can be attached +to the assignment, and that numbers (Gaussian co-ordinates) +\index{Gaussian co-ordinates|)}% +which differ by an indefinitely small amount +are assigned to adjacent points. The Gaussian co-ordinate +system is a logical generalisation of the Cartesian +co-ordinate system. It is also applicable to non-Euclidean +continua, but only when, with respect to the defined +``size'' or ``distance,'' small parts of the continuum +under consideration behave more nearly like a Euclidean +system, the smaller the part of the continuum under +our notice. +\PageSep{91} + + +\Chapter{XXVI}{The Space-Time Continuum of the Special +Theory of Relativity considered as +a Euclidean Continuum} +\index{Continuum!four-dimensional}% +\index{Continuum!space-time|(}% + +\First{We} are now in a position to formulate more +exactly the idea of Minkowski, which was +\index{Minkowski}% +only vaguely indicated in \Sectionref{XVII}. +In accordance with the special theory of relativity, +certain co-ordinate systems are given preference +for the description of the four-dimensional, space-time +continuum. We called these ``Galileian co-ordinate +\index{Galileian system of co-ordinates}% +systems.'' For these systems, the four co-ordinates +$x$,~$y$, $z$,~$t$, which determine an event or---in other +words---a point of the four-dimensional continuum, are +defined physically in a simple manner, as set forth in +detail in the first part of this book. For the transition +from one Galileian system to another, which is moving +uniformly with reference to the first, the equations of +the Lorentz transformation are valid. These last +\index{Lorentz, H. A.!transformation}% +form the basis for the derivation of deductions from the +special theory of relativity, and in themselves they are +nothing more than the expression of the universal +validity of the law of transmission of light for all Galileian +\index{Propagation of light}% +systems of reference. + +Minkowski found that the Lorentz transformations +satisfy the following simple conditions. Let us consider +\PageSep{92} +two neighbouring events, the relative position of which +in the four-dimensional continuum is given with respect +\index{Continuum!four-dimensional}% +to a Galileian reference-body~$K$ by the space co-ordinate +\index{Coordinate@{Co-ordinate}!differences}% +\index{Coordinate@{Co-ordinate}!differentials}% +differences $dx$,~$dy$,~$dz$ and the time-difference~$dt$. With +reference to a second Galileian system we shall suppose +that the corresponding differences for these two events +are $dx'$,~$dy'$, $dz'$,~$dt'$. Then these magnitudes always +fulfil the condition\footnote + {Cf.\ Appendices I~and~II\@. The relations which are derived + there for the co-ordinates themselves are valid also for co-ordinate + \emph{differences}, and thus also for co-ordinate differentials + (indefinitely small differences).} +\[ +dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2} + = dx'^{2} + dy'^{2} + dz'^{2} - c^{2}\, dt'^{2}. +\] + +The validity of the Lorentz transformation follows +from this condition. We can express this as follows: +The magnitude +\[ +ds^{2} = dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2}, +\] +which belongs to two adjacent points of the four-dimensional +space-time continuum, has the same value +for all selected (Galileian) reference-bodies. If we replace +$x$,~$y$, $z$,~$\sqrt{-1}\,ct$, by $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, we also obtain the +result that +\[ +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2} +\] +is independent of the choice of the body of reference. +We call the magnitude~$ds$ the ``distance'' apart of the +two events or four-dimensional points. + +Thus, if we choose as time-variable the imaginary +variable~$\sqrt{-1}\,ct$ instead of the real quantity~$t$, we can +regard the space-time continuum---in accordance with +the special theory of relativity---as a ``Euclidean'' +\index{Continuum!Euclidean}% +four-dimensional continuum, a result which follows +from the considerations of the preceding section. +\PageSep{93} + + +\Chapter{XXVII}{The Space-Time Continuum of the +General Theory of Relativity is +not a Euclidean Continuum} + +\First{In} the first part of this book we were able to make use +of space-time co-ordinates which allowed of a simple +and direct physical interpretation, and which, according +to \Sectionref{XXVI}, can be regarded as four-dimensional +Cartesian co-ordinates. This was possible on the basis +of the law of the constancy of the velocity of light. But +according to \Sectionref{XXI}, the general theory of relativity +cannot retain this law. On the contrary, we arrived at +the result that according to this latter theory the +velocity of light must always depend on the co-ordinates +when a gravitational field is present. In connection +\index{Gravitational field}% +with a specific illustration in \Sectionref{XXIII}, we found +that the presence of a gravitational field invalidates the +definition of the co-ordinates and the time, which led us +to our objective in the special theory of relativity. + +In view of the results of these considerations we are +led to the conviction that, according to the general +principle of relativity, the space-time continuum cannot +be regarded as a Euclidean one, but that here we have +the general case, corresponding to the marble slab with +local variations of temperature, and with which we +made acquaintance as an example of a two-dimensional +\PageSep{94} +continuum. Just as it was there impossible to construct +\index{Continuum!two-dimensional}% +\index{Continuum!four-dimensional}% +a Cartesian co-ordinate system from equal rods, so +here it is impossible to build up a system (reference-body) +from rigid bodies and clocks, which shall be of +\index{Clocks}% +such a nature that measuring-rods and clocks, arranged +\index{Measuring-rod}% +rigidly with respect to one another, shall indicate position +and time directly. Such was the essence of the +difficulty with which we were confronted in \Sectionref{XXIII}. + +But the considerations of Sections \Srefno{XXV}~and~\Srefno{XXVI} +show us the way to surmount this difficulty. We refer the +four-dimensional space-time continuum in an arbitrary +manner to Gauss co-ordinates. We assign to every +\index{Gaussian co-ordinates}% +point of the continuum (event) four numbers, $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$ (co-ordinates), which have not the least direct +physical significance, but only serve the purpose of +numbering the points of the continuum in a definite +but arbitrary manner. This arrangement does not even +need to be of such a kind that we must regard $x_{1}$,~$x_{2}$,~$x_{3}$ as +``space'' co-ordinates and $x_{4}$~as a ``time'' co-ordinate. + +The reader may think that such a description of the +world would be quite inadequate. What does it mean +to assign to an event the particular co-ordinates $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$, if in themselves these co-ordinates have no +significance? More careful consideration shows, however, +that this anxiety is unfounded. Let us consider, +for instance, a material point with any kind of motion. +If this point had only a momentary existence without +duration, then it would be described in space-time by a +single system of values $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$. Thus its permanent +existence must be characterised by an infinitely large +number of such systems of values, the co-ordinate values +of which are so close together as to give continuity; +\PageSep{95} +corresponding to the material point, we thus have a +(uni-dimensional) line in the four-dimensional continuum. +\index{Continuity}% +In the same way, any such lines in our continuum +correspond to many points in motion. The only statements +having regard to these points which can claim +a physical existence are in reality the statements about +their encounters. In our mathematical treatment, +such an encounter is expressed in the fact that the two +lines which represent the motions of the points in +question have a particular system of co-ordinate values, +$x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, in common. After mature consideration +the reader will doubtless admit that in reality such +encounters constitute the only actual evidence of a +time-space nature with which we meet in physical +statements. + +When we were describing the motion of a material +\index{Encounter (space-time coincidence)}% +point relative to a body of reference, we stated +nothing more than the encounters of this point with +particular points of the reference-body. We can also +determine the corresponding values of the time by the +observation of encounters of the body with clocks, in +\index{Clocks}% +conjunction with the observation of the encounter of the +hands of clocks with particular points on the dials. +It is just the same in the case of space-measurements by +means of measuring-rods, as a little consideration will +show. + +The following statements hold generally: Every +physical description resolves itself into a number of +statements, each of which refers to the space-time +coincidence of two events $A$~and~$B$. In terms of +Gaussian co-ordinates, every such statement is expressed +by the agreement of their four co-ordinates $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$. +Thus in reality, the description of the time-space +\PageSep{96} +continuum by means of Gauss co-ordinates completely +\index{Gaussian co-ordinates|(}% +replaces the description with the aid of a body of reference, +without suffering from the defects of the latter +mode of description; it is not tied down to the Euclidean +character of the continuum which has to be represented. +\index{Continuum!space-time|)}% +\PageSep{97} + + +\Chapter{XXVIII}{Exact Formulation of the General +Principle of Relativity} +\index{General theory of relativity}% + +\First{We} are now in a position to replace the provisional +formulation of the general principle +of relativity given in \Sectionref{XVIII} by +an exact formulation. The form there used, ``All +bodies of reference $K$,~$K'$,~etc., are equivalent for +the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion,'' cannot be maintained, because the +use of rigid reference-bodies, in the sense of the method +followed in the special theory of relativity, is in general +not possible in space-time description. The Gauss +co-ordinate system has to take the place of the body of +reference. The following statement corresponds to the +fundamental idea of the general principle of relativity: +``\emph{All Gaussian co-ordinate systems are essentially equivalent +for the formulation of the general laws of nature.}'' + +We can state this general principle of relativity in still +another form, which renders it yet more clearly intelligible +than it is when in the form of the natural +extension of the special principle of relativity. According +to the special theory of relativity, the equations +which express the general laws of nature pass over into +equations of the same form when, by making use of the +Lorentz transformation, we replace the space-time +\index{Lorentz, H. A.!transformation}% +\PageSep{98} +variables $x$,~$y$, $z$,~$t$, of a (Galileian) reference-body~$K$ +by the space-time variables $x'$,~$y'$, $z'$,~$t'$, of a new reference-body~$K'$. +According to the general theory +of relativity, on the other hand, by application of +\emph{arbitrary substitutions} of the Gauss variables $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, +\index{Arbitrary substitutions}% +the equations must pass over into equations of the same +form; for every transformation (not only the Lorentz +\index{Lorentz, H. A.!transformation}% +transformation) corresponds to the transition of one +Gauss co-ordinate system into another. + +If we desire to adhere to our ``old-time'' three-dimensional +\index{Law of inertia}% +view of things, then we can characterise +the development which is being undergone by the +fundamental idea of the general theory of relativity +as follows: The special theory of relativity has reference +to Galileian domains, \ie\ to those in which no gravitational +field exists. In this connection a Galileian reference-body +\index{Galileian system of co-ordinates}% +serves as body of reference, \ie\ a rigid +body the state of motion of which is so chosen that the +Galileian law of the uniform rectilinear motion of +``isolated'' material points holds relatively to it. + +Certain considerations suggest that we should refer +the same Galileian domains to \emph{non-Galileian} reference-bodies +\index{Non-Galileian reference-bodies}% +also. A gravitational field of a special kind is +\index{Gravitational field}% +then present with respect to these bodies (cf.\ Sections \Srefno{XX} +and~\Srefno{XXIII}). + +In gravitational fields there are no such things as rigid +\index{Time!in Physics}% +bodies with Euclidean properties; thus the fictitious rigid +body of reference is of no avail in the general theory of +relativity. The motion of clocks is also influenced by +\index{Clocks|(}% +gravitational fields, and in such a way that a physical +definition of time which is made directly with the aid of +clocks has by no means the same degree of plausibility +as in the special theory of relativity. +\PageSep{99} +\index{Laws of Galilei-Newton!of Nature}% +\index{Time!coordinate@{co-ordinate}}% + +For this reason non-rigid reference-bodies are used, +which are as a whole not only moving in any way +whatsoever, but which also suffer alterations in form +\textit{ad~lib.}\ during their motion. Clocks, for which the law of +motion is of any kind, however irregular, serve for the +definition of time. We have to imagine each of these +clocks fixed at a point on the non-rigid reference-body. +\index{Reference-mollusk|(}% +These clocks satisfy only the one condition, that the +``readings'' which are observed simultaneously on +adjacent clocks (in space) differ from each other by an +\index{Space!point@{-point}}% +indefinitely small amount. This non-rigid reference-body, +which might appropriately be termed a ``reference-mollusk,'' +is in the main equivalent to a Gaussian four-dimensional +co-ordinate system chosen arbitrarily. +That which gives the ``mollusk'' a certain comprehensibleness +as compared with the Gauss co-ordinate +system is the (really unjustified) formal retention of +the separate existence of the space co-ordinates as +\index{Space co-ordinates}% +opposed to the time co-ordinate. Every point on the +mollusk is treated as a space-point, and every material +point which is at rest relatively to it as at rest, so long as +the mollusk is considered as reference-body. The +general principle of relativity requires that all these +mollusks can be used as reference-bodies with equal +right and equal success in the formulation of the general +laws of nature; the laws themselves must be quite +independent of the choice of mollusk. + +The great power possessed by the general principle +of relativity lies in the comprehensive limitation which +is imposed on the laws of nature in consequence of what +we have seen above. +\PageSep{100} + + +\Chapter{XXIX}{The Solution of the Problem of Gravitation +on the Basis of the General +Principle of Relativity} + +\First{If} the reader has followed all our previous considerations, +he will have no further difficulty in +understanding the methods leading to the solution +of the problem of gravitation. + +We start off from a consideration of a Galileian +domain, \ie\ a domain in which there is no gravitational +field relative to the Galileian reference-body~$K$. The +\index{Galileian system of co-ordinates}% +behaviour of measuring-rods and clocks with reference +\index{Measuring-rod}% +to~$K$ is known from the special theory of relativity, +likewise the behaviour of ``isolated'' material points; +the latter move uniformly and in straight lines. + +Now let us refer this domain to a random Gauss co-ordinate +system or to a ``mollusk'' as reference-body~$K'$. +Then with respect to~$K'$ there is a gravitational +field~$G$ (of a particular kind). We learn the behaviour +of measuring-rods and clocks and also of freely-moving +material points with reference to~$K'$ simply by mathematical +transformation. We interpret this behaviour +as the behaviour of measuring-rods, clocks and material +\index{Clocks|)}% +points under the influence of the gravitational field~$G$. +\index{Gravitational field}% +Hereupon we introduce a hypothesis: that the influence +of the gravitational field on measuring-rods, +\index{Gaussian co-ordinates|)}% +\PageSep{101} +clocks and freely-moving material points continues to +take place according to the same laws, even in the case +when the prevailing gravitational field is \emph{not} derivable +\index{Gravitational field}% +from the Galileian special case, simply by means of a +transformation of co-ordinates. + +The next step is to investigate the space-time +behaviour of the gravitational field~$G$, which was derived +from the Galileian special case simply by transformation +of the co-ordinates. This behaviour is formulated +in a law, which is always valid, no matter how the +\index{Matter}% +reference-body (mollusk) used in the description may +\index{Reference-mollusk|)}% +be chosen. + +This law is not yet the \emph{general} law of the gravitational +field, since the gravitational field under consideration is +of a special kind. In order to find out the general +law-of-field of gravitation we still require to obtain a +generalisation of the law as found above. This can be +obtained without caprice, however, by taking into +consideration the following demands: +\begin{itemize} +\item[\itema] The required generalisation must likewise satisfy + the general postulate of relativity. + +\item[\itemb] If there is any matter in the domain under consideration, + only its inertial mass, and thus +\index{Inertial mass}% + according to \Sectionref{XV} only its energy is of + importance for its effect in exciting a field. + +\item[\itemc] Gravitational field and matter together must + satisfy the law of the conservation of energy +\index{Conservation of energy}% +\index{Conservation of energy!impulse}% +\index{Kinetic energy}% + (and of impulse). +\end{itemize} + +Finally, the general principle of relativity permits +us to determine the influence of the gravitational field +on the course of all those processes which take place +according to known laws when a gravitational field is +\PageSep{102} +absent, \ie\ which have already been fitted into the +frame of the special theory of relativity. In this connection +we proceed in principle according to the method +which has already been explained for measuring-rods, +\index{Measuring-rod}% +clocks and freely-moving material points. +\index{Clocks}% + +The theory of gravitation derived in this way from +\index{Gravitation}% +the general postulate of relativity excels not only in +its beauty; nor in removing the defect attaching to +classical mechanics which was brought to light in \Sectionref{XXI}; +\index{Classical mechanics}% +nor in interpreting the empirical law of the equality +of inertial and gravitational mass; but it has also +\index{Gravitational mass}% +\index{Inertial mass}% +already explained a result of observation in astronomy, +\index{Astronomy}% +against which classical mechanics is powerless. + +If we confine the application of the theory to the +case where the gravitational fields can be regarded as +being weak, and in which all masses move with respect +to the co-ordinate system with velocities which are +small compared with the velocity of light, we then obtain +as a first approximation the Newtonian theory. Thus +the latter theory is obtained here without any particular +assumption, whereas Newton had to introduce the +\index{Newton}% +hypothesis that the force of attraction between mutually +attracting material points is inversely proportional to +the square of the distance between them. If we increase +the accuracy of the calculation, deviations from +the theory of Newton make their appearance, practically +all of which must nevertheless escape the test of +observation owing to their smallness. + +We must draw attention here to one of these deviations. +According to Newton's theory, a planet moves +round the sun in an ellipse, which would permanently +maintain its position with respect to the fixed stars, +if we could disregard the motion of the fixed stars +\index{Motion!of heavenly bodies}% +\PageSep{103} +themselves and the action of the other planets under +consideration. Thus, if we correct the observed motion +of the planets for these two influences, and if Newton's +theory be strictly correct, we ought to obtain for the +orbit of the planet an ellipse, which is fixed with reference +to the fixed stars. This deduction, which can +be tested with great accuracy, has been confirmed +for all the planets save one, with the precision that is +capable of being obtained by the delicacy of observation +attainable at the present time. The sole exception +is Mercury, the planet which lies nearest the sun. Since +\index{Mercury}% +\index{Mercury!orbit of}% +the time of Leverrier, it has been known that the ellipse +\index{Leverrier}% +corresponding to the orbit of Mercury, after it has been +corrected for the influences mentioned above, is not +stationary with respect to the fixed stars, but that it +rotates exceedingly slowly in the plane of the orbit +and in the sense of the orbital motion. The value +obtained for this rotary movement of the orbital ellipse +was $43$~seconds of arc per~century, an amount ensured +to be correct to within a few seconds of arc. This +effect can be explained by means of classical mechanics +\index{Classical mechanics}% +only on the assumption of hypotheses which have +little probability, and which were devised solely for +this purpose. + +On the basis of the general theory of relativity, it +is found that the ellipse of every planet round the sun +must necessarily rotate in the manner indicated above; +that for all the planets, with the exception of Mercury, +this rotation is too small to be detected with the delicacy +of observation possible at the present time; but that in +the case of Mercury it must amount to $43$~seconds of +arc per century, a result which is strictly in agreement +with observation. +\PageSep{104} + +Apart from this one, it has hitherto been possible to +make only two deductions from the theory which admit +of being tested by observation, to wit, the curvature +\index{Curvature of light-rays}% +of light rays by the gravitational field of the sun,\footnote + {Observed by Eddington and others in~1919. (Cf.\ \Appendixref{III}.)} +\index{Eddington}% +and a displacement of the spectral lines of light reaching +\index{Displacement of spectral lines}% +us from large stars, as compared with the corresponding +lines for light produced in an analogous manner terrestrially +(\ie\ by the same kind of molecule). I do not +doubt that these deductions from the theory will be +confirmed also. +\index{General theory of relativity|)}% +\PageSep{105} + + +\Part{III}{Considerations on the Universe as +a Whole}{Considerations on the Universe} + +\Chapter{XXX}{Cosmological Difficulties of Newton's +Theory} +\index{Newton}% + +\First{Apart} from the difficulty discussed in \Sectionref{XXI}, +there is a second fundamental difficulty +attending classical celestial mechanics, which, +\index{Celestial mechanics}% +to the best of my knowledge, was first discussed in +detail by the astronomer Seeliger. If we ponder over +\index{Seeliger}% +the question as to how the universe, considered as a +whole, is to be regarded, the first answer that suggests +itself to us is surely this: As regards space (and time) +\index{Space}% +\index{Time!conception of}% +the universe is infinite. There are stars everywhere, +so that the density of matter, although very variable +in detail, is nevertheless on the average everywhere the +same. In other words: However far we might travel +through space, we should find everywhere an attenuated +swarm of fixed stars of approximately the same kind +and density. + +This view is not in harmony with the theory of +Newton. The latter theory rather requires that the +universe should have a kind of centre in which the +\PageSep{106} +density of the stars is a maximum, and that as we +proceed outwards from this centre the group-density +\index{Group-density of stars}% +of the stars should diminish, until finally, at great +distances, it is succeeded by an infinite region of emptiness. +The stellar universe ought to be a finite island in +\index{Stellar universe}% +the infinite ocean of space.\footnote + {\textit{Proof}---According to the theory of Newton, the number of + ``lines of force'' which come from infinity and terminate in a +\index{Lines of force}% + mass~$m$ is proportional to the mass~$m$. If, on the average, the + mass-density~$\rho_{0}$ is constant throughout the universe, then a + sphere of volume~$V$ will enclose the average mass~$\rho_{0}V$. Thus + the number of lines of force passing through the surface~$F$ of the + sphere into its interior is proportional to~$\rho_{0}V$. For unit area + of the surface of the sphere the number of lines of force which + enters the sphere is thus proportional to~$\rho_{0}\dfrac{V}{F}$ or to~$\rho_{0}R$. Hence + the intensity of the field at the surface would ultimately become + infinite with increasing radius~$R$ of the sphere, which is impossible.} + +This conception is in itself not very satisfactory. +It is still less satisfactory because it leads to the result +that the light emitted by the stars and also individual +stars of the stellar system are perpetually passing out +into infinite space, never to return, and without ever +again coming into interaction with other objects of +nature. Such a finite material universe would be +destined to become gradually but systematically impoverished. + +In order to escape this dilemma, Seeliger suggested a +\index{Intensity of gravitational field}% +\index{Seeliger}% +modification of Newton's law, in which he assumes that +\index{Newton's!law of gravitation}% +for great distances the force of attraction between two +masses diminishes more rapidly than would result from +the inverse square law. In this way it is possible for the +mean density of matter to be constant everywhere, +even to infinity, without infinitely large gravitational +fields being produced. We thus free ourselves from the +\PageSep{107} +distasteful conception that the material universe ought +to possess something of the nature of a centre. Of +course we purchase our emancipation from the fundamental +difficulties mentioned, at the cost of a modification +and complication of Newton's law which has +neither empirical nor theoretical foundation. We can +imagine innumerable laws which would serve the same +purpose, without our being able to state a reason why +one of them is to be preferred to the others; for any +one of these laws would be founded just as little on +more general theoretical principles as is the law of +Newton. +\PageSep{108} + + +\Chapter{XXXI}{The Possibility of a ``Finite'' and yet +``Unbounded'' Universe} +\index{Universe (World) structure of}% + +\First{But} speculations on the structure of the universe +also move in quite another direction. The +development of non-Euclidean geometry led to +\index{Euclidean geometry}% +\index{Non-Euclidean geometry}% +the recognition of the fact, that we can cast doubt on the +\emph{infiniteness} of our space without coming into conflict +with the laws of thought or with experience (Riemann, +\index{Riemann}% +Helmholtz). These questions have already been treated +\index{Helmholtz}% +in detail and with unsurpassable lucidity by Helmholtz +and Poincaré, whereas I can only touch on them +\index{Poincare@{Poincaré}}% +briefly here. + +In the first place, we imagine an existence in two-dimensional +\index{Being@{``Being''}}% +\index{Space!two-dimensional}% +space. Flat beings with flat implements, +and in particular flat rigid measuring-rods, are free to +move in a \emph{plane}. For them nothing exists outside of +\index{Plane}% +this plane: that which they observe to happen to +themselves and to their flat ``things'' is the all-inclusive +reality of their plane. In particular, the constructions +of plane Euclidean geometry can be carried out by +means of the rods, \eg\ the lattice construction, considered +\index{Lattice}% +in \Sectionref{XXIV}. In contrast to ours, the universe of +these beings is two-dimensional; but, like ours, it extends +to infinity. In their universe there is room for an +infinite number of identical squares made up of rods, +\PageSep{109} +\ie\ its volume (surface) is infinite. If these beings say +their universe is ``plane,'' there is sense in the statement, +\index{Plane}% +\index{Universe!Euclidean}% +because they mean that they can perform the constructions +of plane Euclidean geometry with their rods. +\index{Euclidean geometry}% +In this connection the individual rods always represent +\index{Distance (line-interval)}% +the same distance, independently of their position. + +Let us consider now a second two-dimensional existence, +but this time on a spherical surface instead of on +\index{Spherical!surface}% +a plane. The flat beings with their measuring-rods +and other objects fit exactly on this surface and they +are unable to leave it. Their whole universe of observation +extends exclusively over the surface of the sphere. +Are these beings able to regard the geometry of their +universe as being plane geometry and their rods withal +as the realisation of ``distance''? They cannot do +this. For if they attempt to realise a straight line, they +\index{Straight line}% +will obtain a curve, which we ``three-dimensional +beings'' designate as a great circle, \ie\ a self-contained +line of definite finite length, which can be measured +up by means of a measuring-rod. Similarly, this +universe has a finite area that can be compared with the +area of a square constructed with rods. The great +charm resulting from this consideration lies in the +recognition of the fact that \emph{the universe of these beings is +finite and yet has no limits}. + +But the spherical-surface beings do not need to go +on a world-tour in order to perceive that they are not +\index{World}% +living in a Euclidean universe. They can convince +themselves of this on every part of their ``world,'' +provided they do not use too small a piece of it. Starting +from a point, they draw ``straight lines'' (arcs of circles +as judged in three-dimensional space) of equal length +in all directions. They will call the line joining the +\PageSep{110} +free ends of these lines a ``circle.'' For a plane surface, +the ratio of the circumference of a circle to its diameter, +both lengths being measured with the same rod, is, +according to Euclidean geometry of the plane, equal to +a constant value~$\pi$, which is independent of the diameter +\index{Value of $\pi$}% +of the circle. On their spherical surface our flat beings +would find for this ratio the value +\[ +\pi = \frac{\sin\left(\dfrac{r}{R}\right)}{\left(\dfrac{r}{R}\right)}, +\] +\ie\ a smaller value than~$\pi$, the difference being the +more considerable, the greater is the radius of the +circle in comparison with the radius~$R$ of the ``world-sphere.'' +\index{World!sphere@{-sphere}}% +By means of this relation the spherical beings +can determine the radius of their universe (``world''), +even when only a relatively small part of their world-sphere +is available for their measurements. But if this +part is very small indeed, they will no longer be able to +demonstrate that they are on a spherical ``world'' and +not on a Euclidean plane, for a small part of a spherical +surface differs only slightly from a piece of a plane of +the same size. + +Thus if the spherical-surface beings are living on a +planet of which the solar system occupies only a negligibly +small part of the spherical universe, they have no means +of determining whether they are living in a finite or in +an infinite universe, because the ``piece of universe'' +to which they have access is in both cases practically +plane, or Euclidean. It follows directly from this +discussion, that for our sphere-beings the circumference +of a circle first increases with the radius until the ``circumference +\PageSep{111} +\index{Universe (World) structure of!circumference of}% +of the universe'' is reached, and that it +\index{Universe!Euclidean}% +\index{Universe!spherical}% +thenceforward gradually decreases to zero for still +further increasing values of the radius. During this +process the area of the circle continues to increase +more and more, until finally it becomes equal to the +total area of the whole ``world-sphere.'' +\index{World!sphere@{-sphere}}% + +Perhaps the reader will wonder why we have placed +our ``beings'' on a sphere rather than on another closed +surface. But this choice has its justification in the fact +that, of all closed surfaces, the sphere is unique in possessing +the property that all points on it are equivalent. I +admit that the ratio of the circumference~$c$ of a circle +to its radius~$r$ depends on~$r$, but for a given value of~$r$ +it is the same for all points of the ``world-sphere''; +in other words, the ``world-sphere'' is a ``surface of +constant curvature.'' + +To this two-dimensional sphere-universe there is a +three-dimensional analogy, namely, the three-dimensional +spherical space which was discovered by Riemann. Its +\index{Riemann}% +points are likewise all equivalent. It possesses a finite +volume, which is determined by its ``radius'' ($2\pi^{2}R^{3}$). +Is it possible to imagine a spherical space? To imagine +a space means nothing else than that we imagine an +epitome of our ``space'' experience, \ie\ of experience +that we can have in the movement of ``rigid'' bodies. +In this sense we \emph{can} imagine a spherical space. + +Suppose we draw lines or stretch strings in all directions +from a point, and mark off from each of these +the distance~$r$ with a measuring-rod. All the free end-points +\index{Measuring-rod}% +of these lengths lie on a spherical surface. We +\index{Spherical!space}% +can specially measure up the area~($F$) of this surface +by means of a square made up of measuring-rods. If +the universe is Euclidean, then $F = 4\pi r^{2}$; if it is spherical, +\PageSep{112} +then $F$~is always less than~$4\pi r^{2}$. With increasing +values of~$r$, $F$~increases from zero up to a maximum +value which is determined by the ``world-radius,'' but +\index{World!radius@{-radius}}% +for still further increasing values of~$r$, the area gradually +diminishes to zero. At first, the straight lines which +radiate from the starting point diverge farther and +farther from one another, but later they approach +each other, and finally they run together again at a +``counter-point'' to the starting point. Under such +\index{Counter-Point}% +conditions they have traversed the whole spherical +space. It is easily seen that the three-dimensional +spherical space is quite analogous to the two-dimensional +spherical surface. It is finite (\ie\ of finite volume), and +\index{Spherical!space}% +has no bounds. + +It may be mentioned that there is yet another kind +of curved space: ``elliptical space.'' It can be regarded +\index{Elliptical space}% +as a curved space in which the two ``counter-points'' +are identical (indistinguishable from each other). An +elliptical universe can thus be considered to some +\index{Universe!elliptical}% +extent as a curved universe possessing central symmetry. + +It follows from what has been said, that closed spaces +without limits are conceivable. From amongst these, +the spherical space (and the elliptical) excels in its +simplicity, since all points on it are equivalent. As a +result of this discussion, a most interesting question +arises for astronomers and physicists, and that is +whether the universe in which we live is infinite, or +whether it is finite in the manner of the spherical universe. +Our experience is far from being sufficient to +enable us to answer this question. But the general +theory of relativity permits of our answering it with a +moderate degree of certainty, and in this connection the +difficulty mentioned in \Sectionref{XXX} finds its solution. +\PageSep{113} + + +\Chapter{XXXII}{The Structure of Space according to +the General Theory of Relativity} +\index{Motion!of heavenly bodies}% +\index{Universe (World) structure of}% + +\First{According} to the general theory of relativity, +the geometrical properties of space are not independent, +but they are determined by matter. +Thus we can draw conclusions about the geometrical +structure of the universe only if we base our considerations +on the state of the matter as being something +that is known. We know from experience that, for a +suitably chosen co-ordinate system, the velocities of +the stars are small as compared with the velocity of +transmission of light. We can thus as a rough approximation +arrive at a conclusion as to the nature of +the universe as a whole, if we treat the matter as being +at rest. + +We already know from our previous discussion that the +behaviour of measuring-rods and clocks is influenced by +\index{Clocks}% +\index{Measuring-rod}% +gravitational fields, \ie\ by the distribution of matter. +\index{Gravitational field}% +This in itself is sufficient to exclude the possibility of +the exact validity of Euclidean geometry in our universe. +\index{Euclidean geometry}% +But it is conceivable that our universe differs +only slightly from a Euclidean one, and this notion +seems all the more probable, since calculations show +that the metrics of surrounding space is influenced only +to an exceedingly small extent by masses even of the +\PageSep{114} +magnitude of our sun. We might imagine that, as +regards geometry, our universe behaves analogously +\index{Universe!elliptical}% +\index{Universe!space expanse (radius) of}% +\index{Universe!spherical}% +to a surface which is irregularly curved in its individual +parts, but which nowhere departs appreciably from a +plane: something like the rippled surface of a lake. +Such a universe might fittingly be called a quasi-Euclidean +universe. As regards its space it would be +infinite. But calculation shows that in a quasi-Euclidean +universe the average density of matter +would necessarily be \emph{nil}. Thus such a universe could +not be inhabited by matter everywhere; it would +present to us that unsatisfactory picture which we +portrayed in \Sectionref{XXX}. + +If we are to have in the universe an average density +of matter which differs from zero, however small may +be that difference, then the universe cannot be quasi-Euclidean. +\index{Quasi-Euclidean universe}% +On the contrary, the results of calculation +indicate that if matter be distributed uniformly, the +universe would necessarily be spherical (or elliptical). +Since in reality the detailed distribution of matter is +not uniform, the real universe will deviate in individual +parts from the spherical, \ie\ the universe will be quasi-spherical. +\index{Quasi-spherical universe}% +But it will be necessarily finite. In fact, the +theory supplies us with a simple connection\footnote + {For the ``radius''~$R$ of the universe we obtain the equation + \[ + R^{2} = \frac{2}{\kappa \rho}. + \] + The use of the C.G.S. system in this equation gives $\dfrac{2}{\kappa} = 1.08 × 10^{27}$; +is the average density of the matter.} +between +the space-expanse of the universe and the average +density of matter in it. +\PageSep{115} + + +\Appendix{I}{Simple Derivation of the Lorentz +Transformation}{[Supplementary to \Sectionref{XI}]} +\index{Lorentz, H. A.!transformation}% + +\First{For} the relative orientation of the co-ordinate +systems indicated in \Figref{2}, the $x$-axes of both +systems permanently coincide. In the present +case we can divide the problem into parts by considering +first only events which are localised on the $x$-axis. Any +such event is represented with respect to the co-ordinate +system~$K$ by the abscissa~$x$ and the time~$t$, and with +respect to the system~$K'$ by the abscissa~$x'$ and the +time~$t'$. We require to find $x'$~and~$t'$ when $x$~and~$t$ are +given. + +A light-signal, which is proceeding along the positive +\index{Light-signal}% +axis of~$x$, is transmitted according to the equation +\[ +x = ct +\] +or +\[ +x - ct = 0. +\Tag{(1)} +\] +Since the same light-signal has to be transmitted relative +to~$K'$ with the velocity~$c$, the propagation relative to +the system~$K'$ will be represented by the analogous +formula +\[ +x' - ct' = 0. +\Tag{(2)} +\] +Those space-time points (events) which satisfy~\Eqref{(1)} must +\PageSep{116} +also satisfy~\Eqref{(2)}. Obviously this will be the case when +the relation +\[ +(x' - ct') = \lambda(x - ct)\Change{.}{} +\Tag{(3)} +\] +is fulfilled in general, where $\lambda$~indicates a constant; for, +according to~\Eqref{(3)}, the disappearance of~$(x - ct)$ involves +the disappearance of~$(x' - ct')$. + +If we apply quite similar considerations to light rays +which are being transmitted along the negative $x$-axis, +we obtain the condition +\[ +(x' + ct') = \mu(x + ct). +\Tag{(4)} +\] + +By adding (or subtracting) equations \Eqref{(3)}~and~\Eqref{(4)}, and +introducing for convenience the constants $a$~and~$b$ in +place of the constants $\lambda$~and~$\mu$, where +\begin{align*} +a &= \frac{\lambda + \mu}{2} +\intertext{and} +b &= \frac{\lambda - \mu}{2}, +\end{align*} +we obtain the equations +\[ +\left. +\begin{aligned} +x' &= ax - bct\Add{,} \\ +ct' &= act - bx. +\end{aligned} +\right\} +\Tag{(5)} +\] + +We should thus have the solution of our problem, +if the constants $a$~and~$b$ were known. These result +from the following discussion. + +For the origin of~$K'$ we have permanently $x' = 0$, and +hence according to the first of the equations~\Eqref{(5)} +\[ +x = \frac{bc}{a} t. +\] + +If we call~$v$ the velocity with which the origin of~$K'$ is +moving relative to~$K$, we then have +\[ +v = \frac{bc}{a}. +\Tag{(6)} +\] +\PageSep{117} + +The same value~$v$ can be obtained from equation~\Eqref{(5)}, +if we calculate the velocity of another point of~$K'$ +relative to~$K$, or the velocity (directed towards the +\index{Relative!velocity}% +negative $x$-axis) of a point of~$K$ with respect to~$K'$. In +short, we can designate~$v$ as the relative velocity of the +two systems. + +Furthermore, the principle of relativity teaches us +that, as judged from~$K$, the length of a unit measuring-rod +\index{Measuring-rod}% +which is at rest with reference to~$K'$ must be exactly +the same as the length, as judged from~$K'$, of a unit +measuring-rod which is at rest relative to~$K$. In order +to see how the points of the $x'$-axis appear as viewed +from~$K$, we only require to take a ``snapshot'' of~$K'$ +\index{Instantaneous photograph (snapshot)}% +from~$K$; this means that we have to insert a particular +value of~$t$ (time of~$K$), \eg\ $t = 0$. For this value of~$t$ +we then obtain from the first of the equations~\Eqref{(5)} +\[ +x' = ax. +\] + +Two points of the $x'$-axis which are separated by the +distance $\Delta x' = 1$ when measured in the $K'$~system are +thus separated in our instantaneous photograph by the +distance +\[ +\Delta x = \frac{1}{a}. +\Tag{(7)} +\] + +But if the snapshot be taken from~$K'$\Change{}{ }($t' = 0$), and if +we eliminate~$t$ from the equations~\Eqref{(5)}, taking into +account the expression~\Eqref{(6)}, we obtain +\[ +x' = a\left(1 - \frac{v^{2}}{c^{2}}\right)x. +\] + +From this we conclude that two points on the $x$-axis +and separated by the distance~$1$ (relative to~$K$) will +be represented on our snapshot by the distance +\[ +\Delta x' = a\left(1 - \frac{v^{2}}{c^{2}}\right). +\Tag{(7a)} +\] +\PageSep{118} + +But from what has been said, the two snapshots +must be identical; hence $\Delta x$~in~\Eqref{(7)} must be equal to +$\Delta x'$~in~\Eqref{(7a)}, so that we obtain +\[ +a^{2} = \frac{1}{1 - \dfrac{v^{2}}{c^{2}}}. +\Tag{(7b)} +\] + +The equations \Eqref{(6)}~and~\Eqref{(7b)} determine the constants $a$~and~$b$. +By inserting the values of these constants in~\Eqref{(5)}, +we obtain the first and the fourth of the equations +given in \Sectionref{XI}. +\[ +\left. +\begin{aligned} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,} \\ +t' &= \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{aligned} +\right\} +\Tag{(8)} +\] + +Thus we have obtained the Lorentz transformation +\index{Lorentz, H. A.!transformation}% +for events on the $x$-axis. It satisfies the condition +\[ +x'^{2} - c^{2} t'^{2} = x^{2} - c^{2} t^{2}. +\Tag{(8a)} +\] + +The extension of this result, to include events which +take place outside the $x$-axis, is obtained by retaining +equations~\Eqref{(8)} and supplementing them by the relations +\[ +\left. +\begin{aligned} +y' &= y\Add{,} \\ +z' &= z. +\end{aligned} +\right\} +\Tag{(9)} +\] +In this way we satisfy the postulate of the constancy of +the velocity of light \textit{in~vacuo} for rays of light of arbitrary +\index{Velocity of light}% +direction, both for the system~$K$ and for the system~$K'$. +This may be shown in the following manner. + +We suppose a light-signal sent out from the origin +\index{Light-signal}% +of~$K$ at the time $t = 0$. It will be propagated according +to the equation +\[ +r = \sqrt{x^{2} + y^{2} + z^{2}} = ct, +\] +\PageSep{119} +or, if we square this equation, according to the equation +\[ +x^{2} + y^{2} + z^{2} - c^{2} t^{2} = 0. +\Tag{(10)} +\] + +It is required by the law of propagation of light, in +\index{Propagation of light}% +conjunction with the postulate of relativity, that the +transmission of the signal in question should take place---as +judged from~$K'$---in accordance with the corresponding +formula +\[ +r' = ct', +\] +or, +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} = 0. +\Tag{(10a)} +\] +In order that equation~\Eqref{(10a)} may be a consequence of +equation~\Eqref{(10)}, we must have +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = \sigma(x^{2} + y^{2} + z^{2} - c^{2} t^{2}). +\Tag{(11)} +\] + +Since equation~\Eqref{(8a)} must hold for points on the +$x$-axis, we thus have $\sigma = 1$. It is easily seen that the +Lorentz transformation really satisfies equation~\Eqref{(11)} +\index{Lorentz, H. A.!transformation}% +for $\sigma = 1$; for \Eqref{(11)}~is a consequence of \Eqref{(8a)}~and~\Eqref{(9)}, +and hence also of \Eqref{(8)}~and~\Eqref{(9)}. We have thus derived +the Lorentz transformation. + +The Lorentz transformation represented by \Eqref{(8)}~and~\Eqref{(9)} +still requires to be generalised. Obviously it is +immaterial whether the axes of~$K'$ be chosen so that +they are spatially parallel to those of~$K$. It is also not +essential that the velocity of translation of~$K'$ with +respect to~$K$ should be in the direction of the $x$-axis. +A simple consideration shows that we are able to +construct the Lorentz transformation in this general +sense from two kinds of transformations, viz.\ from +Lorentz transformations in the special sense and from +purely spatial transformations, which corresponds to +the replacement of the rectangular co-ordinate system +\PageSep{120} +by a new system with its axes pointing in other +directions. + +Mathematically, we can characterise the generalised +Lorentz transformation thus: +\index{Lorentz, H. A.!transformation!(generalised)}% + +It expresses $x'$,~$y'$, $z'$,~$t'$, in terms of linear homogeneous +functions of $x$,~$y$, $z$,~$t$, of such a kind that the relation +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = x^{2} + y^{2} + z^{2} - c^{2} t^{2} +\Tag{(11a)} +\] +is satisfied identically. That is to say: If we substitute +their expressions in $x$,~$y$, $z$,~$t$, in place of $x'$,~$y'$, +$z'$,~$t'$, on the left-hand side, then the left-hand side of~\Eqref{(11a)} +agrees with the right-hand side. +\PageSep{121} + + +\Appendix{II}{Minkowski's Four-dimensional Space +(``World'')}{[Supplementary to \Sectionref{XVII}]} + +\First{We} can characterise the Lorentz transformation +\index{Lorentz, H. A.!transformation}% +still more simply if we introduce the imaginary~$\sqrt{-1}·ct$ +in place of~$t$, as time-variable. If, in +accordance with this, we insert +\begin{align*} +x_{1} &= x\Add{,} \\ +x_{2} &= y\Add{,} \\ +x_{3} &= z\Add{,} \\ +x_{4} &= \sqrt{-1}·ct, +\end{align*} +and similarly for the accented system~$K'$, then the +condition which is identically satisfied by the transformation +can be expressed thus: +\[ +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + x_{4}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2} + {x_{4}}^{2}. +\Tag{(12)} +\] + +That is, by the afore-mentioned choice of ``co-ordinates,'' +\Eqref{(11a)}~is transformed into this equation. + +We see from~\Eqref{(12)} that the imaginary time co-ordinate~$x_{4}$ +\index{Cartesian system of co-ordinates}% +\index{Euclidean geometry}% +\index{Euclidean space}% +\index{Space!three-dimensional}% +\index{Time!in Physics}% +enters into the condition of transformation in exactly +the same way as the space co-ordinates $x_{1}$,~$x_{2}$,~$x_{3}$. It +is due to this fact that, according to the theory of +\PageSep{122} +relativity, the ``time''~$x_{4}$ enters into natural laws in the +same form as the space co-ordinates $x_{1}$,~$x_{2}$,~$x_{3}$. + +A four-dimensional continuum described by the +\index{Continuum!four-dimensional}% +``co-or\-di\-nates'' $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, was called ``world'' by +\index{World}% +\index{World!point@{-point}}% +Minkowski, who also termed a point-event a ``world-point.'' +\index{Minkowski}% +From a ``happening'' in three-dimensional +space, physics becomes, as it were, an ``existence'' in +the four-dimensional ``world.'' + +This four-dimensional ``world'' bears a close similarity +to the three-dimensional ``space'' of (Euclidean) +analytical geometry. If we introduce into the latter a +new Cartesian co-ordinate system $(x_{1}', x_{2}', x_{3}')$ with +the same origin, then $x_{1}'$,~$x_{2}'$,~$x_{3}'$, are linear homogeneous +functions of $x_{1}$,~$x_{2}$,~$x_{3}$, which identically satisfy the +equation +\[ +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2}. +\] +The analogy with~\Eqref{(12)} is a complete one. We can +regard Minkowski's ``world'' in a formal manner as a +four-dimensional Euclidean space (with imaginary +time co-ordinate); the Lorentz transformation corresponds +to a ``rotation'' of the co-ordinate system in the +\index{Rotation}% +four-dimensional ``world.'' +\PageSep{123} + + +\Appendix{III}{The Experimental Confirmation of the +General Theory of Relativity}{} +\index{Theory}% + +\First{From} a systematic theoretical point of view, we +may imagine the process of evolution of an empirical +science to be a continuous process of induction. +\index{Induction}% +Theories are evolved and are expressed in +short compass as statements of a large number of individual +observations in the form of empirical laws, +\index{Empirical laws}% +from which the general laws can be ascertained by comparison. +Regarded in this way, the development of a +science bears some resemblance to the compilation of a +classified catalogue. It is, as it were, a purely empirical +enterprise. + +But this point of view by no means embraces the whole +of the actual process; for it slurs over the important +part played by intuition and deductive thought in the +\index{Deductive thought}% +\index{Intuition}% +development of an exact science. As soon as a science +has emerged from its initial stages, theoretical advances +are no longer achieved merely by a process of arrangement. +Guided by empirical data, the investigator +rather develops a system of thought which, in general, +is built up logically from a small number of fundamental +assumptions, the so-called axioms. We call such a +\index{Axioms}% +system of thought a \emph{theory}. The theory finds the +\PageSep{124} +\index{Classical mechanics}% +\index{Darwinian theory}% +justification for its existence in the fact that it correlates +a large number of single observations, and it is just here +that the ``truth'' of the theory lies. +\index{Theory!truth of}% + +Corresponding to the same complex of empirical data, +there may be several theories, which differ from one +another to a considerable extent. But as regards the +deductions from the theories which are capable of +being tested, the agreement between the theories may +be so complete, that it becomes difficult to find such +deductions in which the two theories differ from each +other. As an example, a case of general interest is +available in the province of biology, in the Darwinian +\index{Biology}% +theory of the development of species by selection in +the struggle for existence, and in the theory of development +which is based on the hypothesis of the hereditary +transmission of acquired characters. + +We have another instance of far-reaching agreement +between the deductions from two theories in Newtonian +mechanics on the one hand, and the general theory of +relativity on the other. This agreement goes so far, +that up to the present we have been able to find only +a few deductions from the general theory of relativity +which are capable of investigation, and to which the +physics of pre-relativity days does not also lead, and +this despite the profound difference in the fundamental +assumptions of the two theories. In what follows, we +shall again consider these important deductions, and we +shall also discuss the empirical evidence appertaining to +them which has hitherto been obtained. + + +\Subsection{a}{Motion of the Perihelion of Mercury} +\index{Perihelion of Mercury|(}% + +According to Newtonian mechanics and Newton's +\index{Newton's!law of gravitation}% +law of gravitation, a planet which is revolving round the +\PageSep{125} +sun would describe an ellipse round the latter, or, more +correctly, round the common centre of gravity of the +sun and the planet. In such a system, the sun, or the +common centre of gravity, lies in one of the foci of the +orbital ellipse in such a manner that, in the course of a +planet-year, the distance sun-planet grows from a +minimum to a maximum, and then decreases again to +a minimum. If instead of Newton's law we insert a +\index{Newton}% +somewhat different law of attraction into the calculation, +we find that, according to this new law, the motion +would still take place in such a manner that the distance +sun-planet exhibits periodic variations; but in this +case the angle described by the line joining sun and +planet during such a period (from perihelion---closest +proximity to the sun---to perihelion) would differ from~$360°$. +The line of the orbit would not then be a closed +one, but in the course of time it would fill up an annular +part of the orbital plane, viz.\ between the circle of +least and the circle of greatest distance of the planet from +the sun. + +According also to the general theory of relativity, +which differs of course from the theory of Newton, a +small variation from the Newton-Kepler motion of a +\index{Kepler}% +planet in its orbit should take place, and in such a way, +that the angle described by the radius sun-planet +between one perihelion and the next should exceed that +corresponding to one complete revolution by an amount +given by +\[ ++\frac{24\pi^{3} a^{2}}{T^{2} c^{2} (1-e^{2})}. +\] + +(\NB---One complete revolution corresponds to the +angle~$2\pi$ in the absolute angular measure customary in +physics, and the above expression gives the amount by +\PageSep{126} +which the radius sun-planet exceeds this angle during +the interval between one perihelion and the next.) +In this expression $a$~represents the major semi-axis of +the ellipse, $e$~its eccentricity, $c$~the velocity of light, and +$T$~the period of revolution of the planet. Our result +may also be stated as follows: According to the general +theory of relativity, the major axis of the ellipse rotates +round the sun in the same sense as the orbital motion +of the planet. Theory requires that this rotation should +amount to $43$~seconds of arc per~century for the planet +Mercury, but for the other planets of our solar system its +\index{Mercury}% +\index{Mercury!orbit of}% +magnitude should be so small that it would necessarily +escape detection.\footnote + {Especially since the next planet Venus has an orbit that is +\index{Venus}% + almost an exact circle, which makes it more difficult to locate + the perihelion with precision.} + +In point of fact, astronomers have found that the +theory of Newton does not suffice to calculate the +observed motion of Mercury with an exactness corresponding +to that of the delicacy of observation attainable +at the present time. After taking account of all +the disturbing influences exerted on Mercury by the +remaining planets, it was found (Leverrier---1859---and +\index{Leverrier}% +Newcomb---1895) that an unexplained perihelial +\index{Newcomb}% +movement of the orbit of Mercury remained over, the +amount of which does not differ sensibly from the above-mentioned +$+43$~seconds of arc per~century. The uncertainty +of the empirical result amounts to a few +seconds only. +\index{Perihelion of Mercury|)}% + + +\Subsection{b}{Deflection of Light by a Gravitational +Field} + +In \Sectionref{XXII} it has been already mentioned that, +\PageSep{127} +according to the general theory of relativity, a ray of +light will experience a curvature of its path when passing +\index{Curvature of light-rays}% +\index{Curvature of light-rays!space}% +through a gravitational field, this curvature being similar +to that experienced by the path of a body which is +projected through a gravitational field. As a result of +this theory, we should expect that a ray of light which +is passing close to a heavenly body would be deviated +towards the latter. For a ray of light which passes the +sun at a distance of $\Delta$~sun-radii from its centre, the +angle of deflection~($\alpha$) should amount to +\[ +\alpha = \frac{\text{$1.7$~seconds of arc}}{\Delta}. +\] +It may be added that, according to the theory, half of +this deflection is produced by the +Newtonian field of attraction of the +sun, and the other half by the geometrical +modification (``curvature'') +of space caused by the sun. + +%[Illustration: Fig. 5.] +\WFigure{1in}{127} +This result admits of an experimental +\index{Solar eclipse}% +test by means of the photographic +registration of stars during +a total eclipse of the sun. The only +reason why we must wait for a total +eclipse is because at every other +time the atmosphere is so strongly +illuminated by the light from the +sun that the stars situated near the +sun's disc are invisible. The predicted effect can be +seen clearly from the accompanying diagram. If the +sun~($S$) were not present, a star which is practically +infinitely distant would be seen in the direction~$D_{1}$, as +observed from the earth. But as a consequence of the +\PageSep{128} +deflection of light from the star by the sun, the star +will be seen in the direction~$D_{2}$, \ie\ at a somewhat +greater distance from the centre of the sun than corresponds +to its real position. + +In practice, the question is tested in the following +way. The stars in the neighbourhood of the sun are +photographed during a solar eclipse. In addition, a +\index{Solar eclipse}% +\index{Stellar universe!photographs}% +second photograph of the same stars is taken when the +sun is situated at another position in the sky, \ie\ a few +months earlier or later. As compared with the standard +photograph, the positions of the stars on the eclipse-photograph +ought to appear displaced radially outwards +(away from the centre of the sun) by an amount +corresponding to the angle~$\alpha$. + +We are indebted to the Royal Society and to the +Royal Astronomical Society for the investigation of +this important deduction. Undaunted by the war and +by difficulties of both a material and a psychological +nature aroused by the war, these societies equipped +two expeditions---to Sobral (Brazil), and to the island of +Principe (West Africa)---and sent several of Britain's +most celebrated astronomers (Eddington, Cottingham, +\index{Cottingham}% +\index{Eddington}% +Crommelin, Davidson), in order to obtain photographs +\index{Crommelin}% +\index{Davidson}% +of the solar eclipse of 29th~May, 1919. The relative +discrepancies to be expected between the stellar photographs +obtained during the eclipse and the comparison +photographs amounted to a few hundredths of a millimetre +only. Thus great accuracy was necessary in +making the adjustments required for the taking of the +photographs, and in their subsequent measurement. + +The results of the measurements confirmed the theory +in a thoroughly satisfactory manner. The rectangular +components of the observed and of the calculated +\PageSep{129} +deviations of the stars (in seconds of arc) are set forth +in the following table of results: +\[ +\begin{array}{@{}c*{2}{>{\quad}cc}@{}} +%[** TN: Re-break first column heading to improve overall width] +\ColHead{1}{Number of}{Number of\\ the Star.} & +\ColHead{2}{Observed. Calculated.}{First Co-ordinate. \\[2pt] +$\overbrace{\text{Observed. Calculated.}}$} & +\ColHead{2}{Observed. Calculated.}{Second Co-ordinate. \\[2pt] +$\overbrace{\text{Observed. Calculated.}}$} \\ +11 & -0.19 & -0.22 & +0.16 & +0.02 \\ +\Z5 & +0.29 & +0.31 & -0.46 & -0.43 \\ +\Z4 & +0.11 & +0.10 & +0.83 & +0.74 \\ +\Z3 & +0.20 & +0.12 & +1.00 & +0.87 \\ +\Z6 & +0.10 & +0.04 & +0.57 & +0.40 \\ +10 & -0.08 & +0.09 & +0.35 & +0.32 \\ +\Z2 & +0.95 & +0.85 & -0.27 & -0.09 +\end{array} +\] + +\Subsection{c}{Displacement of Spectral Lines towards +the Red} +\index{Displacement of spectral lines}% + +In \Sectionref{XXIII} it has been shown that in a system~$K'$ +which is in rotation with regard to a Galileian system~$K$, +clocks of identical construction, and which are considered +\index{Clocks}% +\index{Clocks!rate of}% +at rest with respect to the rotating reference-body, +go at rates which are dependent on the positions +of the clocks. We shall now examine this dependence +quantitatively. A clock, which is situated at a distance~$r$ +from the centre of the disc, has a velocity relative to~$K$ +which is given by +\[ +v = \omega r, +\] +where $\omega$~represents the angular velocity of rotation of the +disc~$K'$ with respect to~$K$. If $\nu_{0}$~represents the number +of ticks of the clock per unit time (``rate'' of the clock) +relative to~$K$ when the clock is at rest, then the ``rate'' +of the clock~($\nu$) when it is moving relative to~$K$ with +a velocity~$v$, but at rest with respect to the disc, will, +in accordance with \Sectionref{XII}, be given by +\[ +\nu = \nu_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}, +\] +\PageSep{130} +or with sufficient accuracy by +\[ +\nu = \nu_{0} \left(1 - \tfrac{1}{2}\, \frac{v^{2}}{c^{2}}\right). +\] +This expression may also be stated in the following +form: +\[ +\nu = \nu_{0} \left(1 - \frac{1}{c^{2}}\, \frac{\omega^{2} r^{2}}{2}\right). +\] +If we represent the difference of potential of the centrifugal +force between the position of the clock and the +centre of the disc by~$\phi$, \ie\ the work, considered negatively, +which must be performed on the unit of mass +against the centrifugal force in order to transport it +\index{Centrifugal force}% +from the position of the clock on the rotating disc to +the centre of the disc, then we have +\[ +\phi = -\frac{\omega^{2} r^{2}}{2}. +\] +From this it follows that +\[ +\nu = \nu_{0} \left(1 + \frac{\phi}{c^{2}}\right). +\] +In the first place, we see from this expression that two +clocks of identical construction will go at different rates +when situated at different distances from the centre of +the disc. This result is also valid from the standpoint +of an observer who is rotating with the disc. + +Now, as judged from the disc, the latter is in a gravitational +\index{Gravitational field!potential of}% +field of potential~$\phi$, hence the result we have +obtained will hold quite generally for gravitational +fields. Furthermore, we can regard an atom which is +emitting spectral lines as a clock, so that the following +statement will hold: + +\emph{An atom absorbs or emits light of a frequency which is +\PageSep{131} +dependent on the potential of the gravitational field in +\index{Gravitational field!potential of}% +which it is situated.} + +The frequency of an atom situated on the surface of a +\index{Frequency of atom}% +heavenly body will be somewhat less than the frequency +of an atom of the same element which is situated in free +space (or on the surface of a smaller celestial body). +Now $\phi = -K\dfrac{M}{r}$, where $K$~is Newton's constant of +\index{Newton's!constant of gravitation}% +gravitation, and $M$~is the mass of the heavenly body. +Thus a displacement towards the red ought to take place +for spectral lines produced at the surface of stars as +compared with the spectral lines of the same element +produced at the surface of the earth, the amount of this +displacement being +\[ +\frac{\nu_{0} - \nu}{\nu_{0}} = \frac{K}{c^{2}}\, \frac{M}{r}. +\] + +For the sun, the displacement towards the red predicted +by theory amounts to about two millionths of +the wave-length. A trustworthy calculation is not +possible in the case of the stars, because in general +neither the mass~$M$ nor the radius~$r$ is known. + +It is an open question whether or not this effect +exists, and at the present time astronomers are working +with great zeal towards the solution. Owing to the +smallness of the effect in the case of the sun, it is difficult +to form an opinion as to its existence. Whereas +Grebe and Bachem (Bonn), as a result of their own +\index{Bachem}% +\index{Grebe}% +measurements and those of Evershed and Schwarzschild +\index{Evershed}% +\index{Schwarzschild}% +on the cyanogen bands, have placed the existence of +\index{Cyanogen bands}% +the effect almost beyond doubt, other investigators, +particularly St.~John, have been led to the opposite +\index{St. John@{St.\ John}}% +opinion in consequence of their measurements. +\PageSep{132} + +Mean displacements of lines towards the less refrangible +end of the spectrum are certainly revealed by +statistical investigations of the fixed stars; but up +to the present the examination of the available data +does not allow of any definite decision being arrived at, +as to whether or not these displacements are to be +referred in reality to the effect of gravitation. The +results of observation have been collected together, +and discussed in detail from the standpoint of the +question which has been engaging our attention here, +in a paper by E.~Freundlich entitled ``Zur Prüfung der +allgemeinen Relativitäts-Theorie'' (\textit{Die Naturwissenschaften}, +1919, No.~35, p.~520: Julius Springer, Berlin). + +At all events, a definite decision will be reached during +the next few years. If the displacement of spectral +lines towards the red by the gravitational potential +does not exist, then the general theory of relativity +will be untenable. On the other hand, if the cause of +the displacement of spectral lines be definitely traced +to the gravitational potential, then the study of this +displacement will furnish us with important information +\index{Mass of heavenly bodies}% +as to the mass of the heavenly bodies. +\PageSep{133} + + +\backmatter +\BookMark{-1}{Back Matter} +\Bibliography{WORKS IN ENGLISH ON EINSTEIN'S THEORY} + +\Bibsection{Introductory} + +\Bibitem{The Foundations of Einstein's Theory of Gravitation} +{Erwin Freundlich (translation by H.~L.~Brose). +Camb.\ Univ.\ Press, 1920.} + +\Bibitem{Space and Time in Contemporary Physics}{Moritz Schlick +(translation by H.~L.~Brose). Clarendon Press, +Oxford, 1920.} + + +\Bibsection{The Special Theory} + +\Bibitem{The Principle of Relativity}{E.~Cunningham. Camb.\ +Univ.\ Press.} + +\Bibitem{Relativity and the Electron Theory}{E.~Cunningham, Monographs +on Physics. Longmans, Green \&~Co.} + +\Bibitem{The Theory of Relativity}{L.~Silberstein. Macmillan \&~Co.} + +\Bibitem{The Space-Time Manifold of Relativity}{E.~B.~Wilson +and G.~N.~Lewis, \textit{Proc.\ Amer.\ Soc.\ Arts \&~Science}, +vol.~xlviii., No.~11, 1912.} + + +\Bibsection{The General Theory} + +\Bibitem{Report on the Relativity Theory of Gravitation}{A.~S. +Eddington. Fleetway Press Ltd., Fleet Street, +London.} +\PageSep{134} + +\Bibitem{On Einstein's Theory of Gravitation and its Astronomical +Consequences}{W.~de~Sitter, \textit{M.~N.~Roy.\ Astron.\ +Soc.},~lxxvi.\ p.~699, 1916; lxxvii.\ p.~155, 1916; lxxviii.\ +p.~3, 1917.} + +\Bibitem{On Einstein's Theory of Gravitation}{H.~A.~Lorentz, \textit{Proc.\ +Amsterdam Acad.}, vol.~xix. p.~1341, 1917.} + +\Bibitem{Space, Time and Gravitation}{W.~de~Sitter: \textit{The +Observatory}, No.~505, p.~412. Taylor \&~Francis, Fleet +Street, London.} + +\Bibitem{The Total Eclipse of 29th~May, 1919, and the Influence of +Gravitation on Light}{A.~S.~Eddington, \textit{ibid.}, +March~1919.} + +\Bibitem{Discussion on the Theory of Relativity}{\textit{M.~N.~Roy.\ Astron.\ +Soc.}, vol.~lxxx.\ No.~2, p.~96, December~1919.} + +\Bibitem{The Displacement of Spectrum Lines and the Equivalence +Hypothesis}{W.~G.~Duffield, \textit{M.~N.~Roy.\ Astron.\ Soc.}, +vol.~lxxx.\Change{;}{} No.~3, p.~262, 1920.} + +\Bibitem{Space, Time and Gravitation}{A.~S.~Eddington, Camb.\ Univ.\ +Press, 1920.} + + +\Bibsection{Also, Chapters in} + +\Bibitem{The Mathematical Theory of Electricity and Magnetism} +{J.~H. Jeans (4th~edition). Camb.\ Univ.\ Press, 1920.} + +\Bibitem{The Electron Theory of Matter}{O.~W.~Richardson. Camb.\ +Univ.\ Press.} +\PageSep{135} +\printindex % [** TN: Auto-generate the index] +\iffalse %%%% Start of index text %%%% +INDEX + +Aberration 49 + +Absorption of energy 46 + +Acceleration 64, 67, 70 + +Action at a distance 48 + +Addition of velocities 16, 38 + +Adjacent points 89 + +Aether 52 + drift@{-drift}#drift 52, 53 + +Arbitrary substitutions 98 + +Astronomy 7, 102 + +Astronomical day 11 + +Axioms 2, 123 + truth of 2 + +Bachem 131 + +Basis of theory 44 + +Being@{``Being''}#Being 66, 108 + +beta-rays@{$\beta$-rays}#rays 50 + +Biology 124 + +Cartesian system of co-ordinates 7, 84, 122 + +Cathode rays 50 + +Celestial mechanics 105 + +Centrifugal force 80, 130 + +Chest 66 + +Classical mechanics 9, 13, 14, 16, 30, 44, 71, 102, 103, 124 + truth of 13 + +Clocks 10, 23, 80, 81, 94, 95, 98-100, 102, 113, 129 + rate of 129 + +Conception of mass 45 + position 6 + +Conservation of energy 45, 101 + impulse 101 + mass 45, 47 + +Continuity 95 + +Continuum 55, 83 + two-dimensional 94 + three-dimensional 57 + four-dimensional 89, 91, 92, 94, 122 + space-time 78, 91-96 + Euclidean 84, 86, 88, 92 + non-Euclidean 86, 90 + +Coordinate@{Co-ordinate}#Co-ordinate + differences 92 + differentials 92 + planes 32 + +Cottingham 128 + +Counter-Point 112 + +Covariant@{Co-variant}#Co-variant 43 + +Crommelin 128 + +Curvature of light-rays 104, 127 + space 127 + +Curvilinear motion 74 + +Cyanogen bands 131 + +Darwinian theory 124 + +Davidson 128 + +Deductive thought 123 + +Derivation of laws 44 + +Desitter@{De Sitter}#De Sitter 17 + +Displacement of spectral lines 104, 129 + +Distance (line-interval) 3, 5, 8, 28, 29, 84, 88, 109 + physical interpretation of 5 + relativity of 28 + +Doppler principle 50 %. + +Double stars 17 + +Eclipse of star 17 + +Eddington 104, 128 +%\PageSep{136} + +Electricity 76 + +Electrodynamics 13, 19, 41, 44, 76 + +Electromagnetic theory 49 + waves 63 + +Electron 44, 50 %. + electrical masses of 51 + +Electrostatics 76 + +Elliptical space 112 + +Empirical laws 123 + +Encounter (space-time coincidence) 95 + +Equivalent 14 + +Euclidean geometry 1, 2, 57, 82, 86, 88, 108, 109, 113, 122 + propositions of 3, 8 + +%[** TN: Add explicit "Euclidean" heading] +Euclidean space 57, 86, 122 + +Evershed 131 + +Experience 49, 60 + +Faraday 48, 63 + +FitzGerald 53 + +Fixed stars 11 + +Fizeau 39, 49, 51 + experiment of 39 + +Frequency of atom 131 + +Galilei 11 + transformation 33, 36, 38, 42, 52 + +Galileian system of co-ordinates + 11, 13, 14, 46, 79, 91, 98, 100 + +Gauss 86, 87, 90 + +Gaussian co-ordinates 88-90, 94, 96-100 + +General theory of relativity 59-104, 97 + +Geometrical ideas 2, 3 + propositions 1 + truth of 2-4 + +Gravitation 64, 69, 78, 102 + +Gravitational field 64, 67, 74, 77, 93, 98, 100, 101, 113 + potential of 130, 131 + +%[** TN: Add explicit "Gravitational" heading] +Gravitational mass 65, 68, 102 + +Grebe 131 + +Group-density of stars 106 + +Helmholtz 108 + +Heuristic value of relativity#Heuristic 42 + +Induction 123 + +Inertia 65 + +Inertial mass 47, 65, 69, 101, 102 + +Instantaneous photograph (snapshot) 117 + +Intensity of gravitational field 106 + +Intuition 123 + +Ions 44 + +Kepler 125 + +Kinetic energy 45, 101 + +Lattice 108 + +Law of inertia 11, 61, 62, 98 + +Laws of Galilei-Newton 13 + of Nature 60, 71, 99 + +Leverrier 103, 126 + +Light-signal 33, 115, 118 + +Light-stimulus 33 + +Limiting velocity ($c$)#Limiting 36, 37 + +Lines of force 106 + +Lorentz, H. A.#Lorentz 19, 41, 44, 49, 50-53 + transformation 33, 39, 42, 91, 97, 98, 115, 118, 119, 121 + (generalised) 120 + +Mach, E.#Mach 72 + +Magnetic field 63 + +Manifold|see{Continuum} 0 + +Mass of heavenly bodies 132 + +Matter 101 + +Maxwell 41, 44, 48-50, 52 + fundamental equations 46, 77 + +Measurement of length 85 + +Measuring-rod 5, 6, 28, 80, 81, 94, 100, 102, 111, 113, 117 + +Mercury 103, 126 + orbit of 103, 126 + +Michelson 52-54 + +Minkowski 55-57, 91, 122 +%\PageSep{137} + +Morley 53, 54 + +Motion 14, 60 + of heavenly bodies 13, 15, 44, 102, 113 + +Newcomb 126 + +Newton 11, 72, 102, 105, 125 + +Newton's + constant of gravitation 131 + law of gravitation 48, 80, 106, 124 + law of motion 64 + +Non-Euclidean geometry 108 + +Non-Galileian reference-bodies 98 + +Non-uniform motion 62 + +Optics 13, 19, 44 + +Organ-pipe, note of 14 + +Parabola 9, 10 + +Path-curve 10 + +Perihelion of Mercury 124-126 + +Physics 7 + of measurement 7 + +Place specification 5, 6 + +Plane 1, 108, 109 + +Poincare@{Poincaré}#Poincaré 108 + +Point 1 + +Point-mass, energy of#Point-mass 45 + +Position 9 + +Principle of relativity 13-15, 19, 20, 60 + +Processes of Nature 42 + +Propagation of light 17, 19, 20, 32, 91, 119 + in liquid 40 + in gravitational fields 75 + +Quasi-Euclidean universe 114 + +Quasi-spherical universe 114 + +Radiation 46 + +Radioactive substances 50 + +Reference-body 5, 7, 9-11, 18, 23, 25, 26, 37, 60 + rotating 79 + +%[** TN: Add explicit "Reference-" heading] +Reference-mollusk 99-101 + +Relative + position 3 + velocity 117 + +Rest 14 + +Riemann 86, 108, 111 + +Rotation 81, 122 + +Schwarzschild 131 + +Seconds-clock 36 + +Seeliger 105, 106 + +Simultaneity 22, 24-26, 81 + relativity of 26 + +Size-relations 90 + +Solar eclipse 75, 127, 128 + +Space 9, 52, 55, 105 + conception of 19 + +Space co-ordinates 55, 81, 99 + +Space + interval@{-interval}#interval 30, 56 + point@{-point}#point 99 + two-dimensional 108 + three-dimensional 122 + +Special theory of relativity 1-57, 20 + +Spherical + surface 109 + space 111, 112 + +St. John@{St.\ John}#St.~John 131 + +Stellar universe 106 + photographs 128 + +Straight line 1-3, 9, 10, 82, 88, 109 + +System of co-ordinates 5, 10, 11 + +Terrestrial space 15 + +Theory 123 + truth of 124 + +Three-dimensional 55 + +Time + conception of 19, 52, 105 + coordinate@{co-ordinate}#co-ordinate 55, 99 + in Physics 21, 98, 122 + of an event 24, 26 + +Time-interval 30, 56 + +Trajectory 10 + +Truth@{``Truth''}#Truth 2 + +Uniform translation 12, 59 + +Universe (World) structure of 108, 113 + circumference of 111 +%\PageSep{138} + +Universe + elliptical 112, 114 + Euclidean 109, 111 + space expanse (radius) of 114 + spherical 111, 114 + +Value of $\pi$#$\pi$ 82, 110 + +Velocity of light 10, 17, 18, 76, 118 + +Venus 126 + +Weight (heaviness) 65 + +World 55, 56, 109, 122 + +World + point@{-point}#point 122 + radius@{-radius}#radius 112 + sphere@{-sphere}#sphere 110, 111 + +Zeeman 41 +\fi %%%% End of index text %%%% +\PageSep{139} +% [Blank page] +\PageSep{140} +\ifthenelse{\boolean{ForPrinting}}{\cleardoublepage\null}{} +\newpage +\begin{CenterPage} + \scriptsize + PRINTED BY \\[2pt] + MORRISON AND GIBB LIMITED \\[2pt] + EDINBURGH +\end{CenterPage} +%%%%%%%%%%%%%%%%%%%%%%%%% GUTENBERG LICENSE %%%%%%%%%%%%%%%%%%%%%%%%%% + +\cleardoublepage +\BookMark{0}{PG License} +\SetEvenHead{Licensing} +\SetOddHead{Licensing} +\pagenumbering{Roman} +\begin{PGtext} +*** END OF THE PROJECT GUTENBERG EBOOK RELATIVITY *** + +***** This file should be named 36114-pdf.pdf or 36114-pdf.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/6/1/1/36114/ + +Updated editions will replace the previous one--the old editions will +be renamed. + +Creating the works from print editions not protected by U.S. copyright +law means that no one owns a United States copyright in these works, +so the Foundation (and you!) can copy and distribute it in the +United States without permission and without paying copyright +royalties. Special rules, set forth in the General Terms of Use part +of this license, apply to copying and distributing Project +Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm +concept and trademark. Project Gutenberg is a registered trademark, +and may not be used if you charge for an eBook, except by following +the terms of the trademark license, including paying royalties for use +of the Project Gutenberg trademark. If you do not charge anything for +copies of this eBook, complying with the trademark license is very +easy. You may use this eBook for nearly any purpose such as creation +of derivative works, reports, performances and research. Project +Gutenberg eBooks may be modified and printed and given away--you may +do practically ANYTHING in the United States with eBooks not protected +by U.S. copyright law. Redistribution is subject to the trademark +license, especially commercial redistribution. + +START: FULL LICENSE + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase `Project +Gutenberg'), you agree to comply with all the terms of the Full +Project Gutenberg-tm License available with this file or online at +www.gutenberg.org/license. + +Section 1. General Terms of Use and Redistributing Project +Gutenberg-tm electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or +destroy all copies of Project Gutenberg-tm electronic works in your +possession. If you paid a fee for obtaining a copy of or access to a +Project Gutenberg-tm electronic work and you do not agree to be bound +by the terms of this agreement, you may obtain a refund from the +person or entity to whom you paid the fee as set forth in paragraph +1.E.8. + +1.B. `Project Gutenberg' is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this +agreement and help preserve free future access to Project Gutenberg-tm +electronic works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation (`the +Foundation' or PGLAF), owns a compilation copyright in the collection +of Project Gutenberg-tm electronic works. Nearly all the individual +works in the collection are in the public domain in the United +States. If an individual work is unprotected by copyright law in the +United States and you are located in the United States, we do not +claim a right to prevent you from copying, distributing, performing, +displaying or creating derivative works based on the work as long as +all references to Project Gutenberg are removed. Of course, we hope +that you will support the Project Gutenberg-tm mission of promoting +free access to electronic works by freely sharing Project Gutenberg-tm +works in compliance with the terms of this agreement for keeping the +Project Gutenberg-tm name associated with the work. You can easily +comply with the terms of this agreement by keeping this work in the +same format with its attached full Project Gutenberg-tm License when +you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are +in a constant state of change. If you are outside the United States, +check the laws of your country in addition to the terms of this +agreement before downloading, copying, displaying, performing, +distributing or creating derivative works based on this work or any +other Project Gutenberg-tm work. The Foundation makes no +representations concerning the copyright status of any work in any +country other than the United States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other +immediate access to, the full Project Gutenberg-tm License must appear +prominently whenever any copy of a Project Gutenberg-tm work (any work +on which the phrase `Project Gutenberg' appears, or with which the +phrase `Project Gutenberg' is associated) is accessed, displayed, +performed, viewed, copied or distributed: + + This eBook is for the use of anyone anywhere in the United States and + most other parts of the world at no cost and with almost no + restrictions whatsoever. You may copy it, give it away or re-use it + under the terms of the Project Gutenberg License included with this + eBook or online at www.gutenberg.org. If you are not located in the + United States, you will have to check the laws of the country where + you are located before using this eBook. + +1.E.2. If an individual Project Gutenberg-tm electronic work is +derived from texts not protected by U.S. copyright law (does not +contain a notice indicating that it is posted with permission of the +copyright holder), the work can be copied and distributed to anyone in +the United States without paying any fees or charges. If you are +redistributing or providing access to a work with the phrase `Project +Gutenberg' associated with or appearing on the work, you must comply +either with the requirements of paragraphs 1.E.1 through 1.E.7 or +obtain permission for the use of the work and the Project Gutenberg-tm +trademark as set forth in paragraphs 1.E.8 or 1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any +additional terms imposed by the copyright holder. Additional terms +will be linked to the Project Gutenberg-tm License for all works +posted with the permission of the copyright holder found at the +beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including +any word processing or hypertext form. However, if you provide access +to or distribute copies of a Project Gutenberg-tm work in a format +other than `Plain Vanilla ASCII' or other format used in the official +version posted on the official Project Gutenberg-tm website +(www.gutenberg.org), you must, at no additional cost, fee or expense +to the user, provide a copy, a means of exporting a copy, or a means +of obtaining a copy upon request, of the work in its original `Plain +Vanilla ASCII' or other form. Any alternate format must include the +full Project Gutenberg-tm License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works +provided that: + +* You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is owed + to the owner of the Project Gutenberg-tm trademark, but he has + agreed to donate royalties under this paragraph to the Project + Gutenberg Literary Archive Foundation. Royalty payments must be paid + within 60 days following each date on which you prepare (or are + legally required to prepare) your periodic tax returns. Royalty + payments should be clearly marked as such and sent to the Project + Gutenberg Literary Archive Foundation at the address specified in + Section 4, `Information about donations to the Project Gutenberg + Literary Archive Foundation.' + +* You provide a full refund of any money paid by a user who notifies + you in writing (or by email) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or destroy all + copies of the works possessed in a physical medium and discontinue + all use of and all access to other copies of Project Gutenberg-tm + works. + +* You provide, in accordance with paragraph 1.F.3, a full refund of + any money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days of + receipt of the work. + +* You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project +Gutenberg-tm electronic work or group of works on different terms than +are set forth in this agreement, you must obtain permission in writing +from the Project Gutenberg Literary Archive Foundation, the manager of +the Project Gutenberg-tm trademark. Contact the Foundation as set +forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +works not protected by U.S. copyright law in creating the Project +Gutenberg-tm collection. Despite these efforts, Project Gutenberg-tm +electronic works, and the medium on which they may be stored, may +contain `Defects,' such as, but not limited to, incomplete, inaccurate +or corrupt data, transcription errors, a copyright or other +intellectual property infringement, a defective or damaged disk or +other medium, a computer virus, or computer codes that damage or +cannot be read by your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the `Right +of Replacement or Refund' described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium +with your written explanation. The person or entity that provided you +with the defective work may elect to provide a replacement copy in +lieu of a refund. If you received the work electronically, the person +or entity providing it to you may choose to give you a second +opportunity to receive the work electronically in lieu of a refund. If +the second copy is also defective, you may demand a refund in writing +without further opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you--`AS-IS', WITH NO +OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT +LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of +damages. If any disclaimer or limitation set forth in this agreement +violates the law of the state applicable to this agreement, the +agreement shall be interpreted to make the maximum disclaimer or +limitation permitted by the applicable state law. The invalidity or +unenforceability of any provision of this agreement shall not void the +remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in +accordance with this agreement, and any volunteers associated with the +production, promotion and distribution of Project Gutenberg-tm +electronic works, harmless from all liability, costs and expenses, +including legal fees, that arise directly or indirectly from any of +the following which you do or cause to occur: (a) distribution of this +or any Project Gutenberg-tm work, (b) alteration, modification, or +additions or deletions to any Project Gutenberg-tm work, and (c) any +Defect you cause. + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of +computers including obsolete, old, middle-aged and new computers. It +exists because of the efforts of hundreds of volunteers and donations +from people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future +generations. To learn more about the Project Gutenberg Literary +Archive Foundation and how your efforts and donations can help, see +Sections 3 and 4 and the Foundation information page at +www.gutenberg.org + +Section 3. Information about the Project Gutenberg Literary +Archive Foundation + +The Project Gutenberg Literary Archive Foundation is a non-profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Contributions to the Project Gutenberg Literary +Archive Foundation are tax deductible to the full extent permitted by +U.S. federal laws and your state's laws. + +The Foundation's business office is located at 809 North 1500 West, +Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up +to date contact information can be found at the Foundation's website +and official page at www.gutenberg.org/contact + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without +widespread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine-readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To SEND +DONATIONS or determine the status of compliance for any particular +state visit www.gutenberg.org/donate + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including checks, online payments and credit card donations. To +donate, please visit: www.gutenberg.org/donate + +Section 5. General Information About Project Gutenberg-tm electronic works + +Professor Michael S. Hart was the originator of the Project +Gutenberg-tm concept of a library of electronic works that could be +freely shared with anyone. For forty years, he produced and +distributed Project Gutenberg-tm eBooks with only a loose network of +volunteer support. + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as not protected by copyright in +the U.S. unless a copyright notice is included. Thus, we do not +necessarily keep eBooks in compliance with any particular paper +edition. + +Most people start at our website which has the main PG search +facility: www.gutenberg.org + +This website includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. +\end{PGtext} + +\end{document} +### +@ControlwordReplace = ( + ['\\Preface', 'Preface'], + ['\\ie', 'i.e.'], + ['\\eg', 'e.g.'], + ['\\NB', 'N.B.'], + ['\\itema', '(a)'], + ['\\itemb', '(b)'], + ['\\itemc', '(c)'] + ); + +@ControlwordArguments = ( + ['\\BookMark', 1, 0, '', '', 1, 0, '', ''], + ['\\item', 0, 1, '', ' '], + ['\\Part', 1, 1, '', ' ', 1, 1, '', '', 1, 0, '', ''], + ['\\Chapter', 0, 0, '', '', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Section', 1, 1, '', ''], + ['\\Subsection', 1, 1, '(', ') ', 1, 1, '', ''], + ['\\SectTitle', 1, 1, '', ''], + ['\\Appendix', 1, 1, '', ' ', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Bibliography', 1, 1, 'Bibliography: ', ''], + ['\\Bibsection', 1, 1, '', ''], + ['\\Bibitem', 1, 1, '', ' ', 1, 1, '', ''], + ['\\PubRow', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Signature', 0, 1, '', ' ', 1, 1, '', ''], + ['\\Change', 1, 0, '', '', 1, 1, '', ''], + ['\\Add', 1, 1, '', ''], + ['\\PageSep', 1, 0, '', ''], + ['\\Figure', 0, 0, '', '', 1, 1, '', ''], + ['\\WFigure', 1, 0, '', '', 1, 1, '', ''], + ['\\Figref', 1, 1, 'Fig. ', ''], + ['\\Partref', 1, 1, 'Part ', ''], + ['\\Sectionref', 1, 1, 'Section ', ''], + ['\\Srefno', 1, 1, '', ''], + ['\\Appendixref', 1, 1, 'Appendix ', ''], + ['\\Eqref', 1, 1, '', ''], + ['\\First', 1, 1, '', ''] + ); +### +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2010.7.3) 13 MAY 2011 19:40 +entering extended mode + %&-line parsing enabled. +**relativity.tex +(./relativity.tex +LaTeX2e <2005/12/01> +Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, ukrainian, russian, bulgarian, basque, french, german, ngerman, iby +cus, greek, monogreek, ancientgreek, italian, loaded. +(/usr/share/texmf-texlive/tex/latex/base/book.cls +Document Class: book 2005/09/16 v1.4f Standard LaTeX document class +(/usr/share/texmf-texlive/tex/latex/base/bk12.clo +File: bk12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +) +\c@part=\count79 +\c@chapter=\count80 +\c@section=\count81 +\c@subsection=\count82 +\c@subsubsection=\count83 +\c@paragraph=\count84 +\c@subparagraph=\count85 +\c@figure=\count86 +\c@table=\count87 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) +(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty +Package: inputenc 2006/05/05 v1.1b Input encoding file +\inpenc@prehook=\toks14 +\inpenc@posthook=\toks15 + +(/usr/share/texmf-texlive/tex/latex/base/latin1.def +File: latin1.def 2006/05/05 v1.1b Input encoding file +)) +(/usr/share/texmf-texlive/tex/latex/base/ifthen.sty +Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) +) +(/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty +Package: amsmath 2000/07/18 v2.13 AMS math features +\@mathmargin=\skip43 + +For additional information on amsmath, use the `?' option. +(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 + +(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 +\@emptytoks=\toks16 +\ex@=\dimen103 +)) +(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d +\pmbraise@=\dimen104 +) +(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count88 +LaTeX Info: Redefining \frac on input line 211. +\uproot@=\count89 +\leftroot@=\count90 +LaTeX Info: Redefining \overline on input line 307. +\classnum@=\count91 +\DOTSCASE@=\count92 +LaTeX Info: Redefining \ldots on input line 379. +LaTeX Info: Redefining \dots on input line 382. +LaTeX Info: Redefining \cdots on input line 467. +\Mathstrutbox@=\box26 +\strutbox@=\box27 +\big@size=\dimen105 +LaTeX Font Info: Redeclaring font encoding OML on input line 567. +LaTeX Font Info: Redeclaring font encoding OMS on input line 568. +\macc@depth=\count93 +\c@MaxMatrixCols=\count94 +\dotsspace@=\muskip10 +\c@parentequation=\count95 +\dspbrk@lvl=\count96 +\tag@help=\toks17 +\row@=\count97 +\column@=\count98 +\maxfields@=\count99 +\andhelp@=\toks18 +\eqnshift@=\dimen106 +\alignsep@=\dimen107 +\tagshift@=\dimen108 +\tagwidth@=\dimen109 +\totwidth@=\dimen110 +\lineht@=\dimen111 +\@envbody=\toks19 +\multlinegap=\skip44 +\multlinetaggap=\skip45 +\mathdisplay@stack=\toks20 +LaTeX Info: Redefining \[ on input line 2666. +LaTeX Info: Redefining \] on input line 2667. +) +(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2002/01/22 v2.2d + +(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2001/10/25 v2.2f +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 132. +)) +(/usr/share/texmf-texlive/tex/latex/base/alltt.sty +Package: alltt 1997/06/16 v2.0g defines alltt environment +) +(/usr/share/texmf-texlive/tex/latex/tools/array.sty +Package: array 2005/08/23 v2.4b Tabular extension package (FMi) +\col@sep=\dimen112 +\extrarowheight=\dimen113 +\NC@list=\toks21 +\extratabsurround=\skip46 +\backup@length=\skip47 +) +(/usr/share/texmf-texlive/tex/latex/bigfoot/perpage.sty +Package: perpage 2006/07/15 1.12 Reset/sort counters per page +\c@abspage=\count100 +) +(/usr/share/texmf-texlive/tex/latex/tools/multicol.sty +Package: multicol 2006/05/18 v1.6g multicolumn formatting (FMi) +\c@tracingmulticols=\count101 +\mult@box=\box28 +\multicol@leftmargin=\dimen114 +\c@unbalance=\count102 +\c@collectmore=\count103 +\doublecol@number=\count104 +\multicoltolerance=\count105 +\multicolpretolerance=\count106 +\full@width=\dimen115 +\page@free=\dimen116 +\premulticols=\dimen117 +\postmulticols=\dimen118 +\multicolsep=\skip48 +\multicolbaselineskip=\skip49 +\partial@page=\box29 +\last@line=\box30 +\mult@rightbox=\box31 +\mult@grightbox=\box32 +\mult@gfirstbox=\box33 +\mult@firstbox=\box34 +\@tempa=\box35 +\@tempa=\box36 +\@tempa=\box37 +\@tempa=\box38 +\@tempa=\box39 +\@tempa=\box40 +\@tempa=\box41 +\@tempa=\box42 +\@tempa=\box43 +\@tempa=\box44 +\@tempa=\box45 +\@tempa=\box46 +\@tempa=\box47 +\@tempa=\box48 +\@tempa=\box49 +\@tempa=\box50 +\@tempa=\box51 +\c@columnbadness=\count107 +\c@finalcolumnbadness=\count108 +\last@try=\dimen119 +\multicolovershoot=\dimen120 +\multicolundershoot=\dimen121 +\mult@nat@firstbox=\box52 +\colbreak@box=\box53 +) +(/usr/share/texmf-texlive/tex/latex/base/makeidx.sty +Package: makeidx 2000/03/29 v1.0m Standard LaTeX package +) +(/usr/share/texmf-texlive/tex/latex/caption/caption.sty +Package: caption 2007/01/07 v3.0k Customising captions (AR) + +(/usr/share/texmf-texlive/tex/latex/caption/caption3.sty +Package: caption3 2007/01/07 v3.0k caption3 kernel (AR) + +(/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty +Package: keyval 1999/03/16 v1.13 key=value parser (DPC) +\KV@toks@=\toks22 +) +\captionmargin=\dimen122 +\captionmarginx=\dimen123 +\captionwidth=\dimen124 +\captionindent=\dimen125 +\captionparindent=\dimen126 +\captionhangindent=\dimen127 +)) +(/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty +Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) + +(/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty +Package: graphics 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) + +(/usr/share/texmf-texlive/tex/latex/graphics/trig.sty +Package: trig 1999/03/16 v1.09 sin cos tan (DPC) +) +(/etc/texmf/tex/latex/config/graphics.cfg +File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive +) +Package graphics Info: Driver file: pdftex.def on input line 90. + +(/usr/share/texmf-texlive/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX +\Gread@gobject=\count109 +)) +\Gin@req@height=\dimen128 +\Gin@req@width=\dimen129 +) +(/usr/share/texmf-texlive/tex/latex/wrapfig/wrapfig.sty +\wrapoverhang=\dimen130 +\WF@size=\dimen131 +\c@WF@wrappedlines=\count110 +\WF@box=\box54 +\WF@everypar=\toks23 +Package: wrapfig 2003/01/31 v 3.6 +) +(/usr/share/texmf-texlive/tex/latex/tools/calc.sty +Package: calc 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) +\calc@Acount=\count111 +\calc@Bcount=\count112 +\calc@Adimen=\dimen132 +\calc@Bdimen=\dimen133 +\calc@Askip=\skip50 +\calc@Bskip=\skip51 +LaTeX Info: Redefining \setlength on input line 75. +LaTeX Info: Redefining \addtolength on input line 76. +\calc@Ccount=\count113 +\calc@Cskip=\skip52 +) +(/usr/share/texmf-texlive/tex/latex/fancyhdr/fancyhdr.sty +\fancy@headwidth=\skip53 +\f@ncyO@elh=\skip54 +\f@ncyO@erh=\skip55 +\f@ncyO@olh=\skip56 +\f@ncyO@orh=\skip57 +\f@ncyO@elf=\skip58 +\f@ncyO@erf=\skip59 +\f@ncyO@olf=\skip60 +\f@ncyO@orf=\skip61 +) +(/usr/share/texmf-texlive/tex/latex/geometry/geometry.sty +Package: geometry 2002/07/08 v3.2 Page Geometry +\Gm@cnth=\count114 +\Gm@cntv=\count115 +\c@Gm@tempcnt=\count116 +\Gm@bindingoffset=\dimen134 +\Gm@wd@mp=\dimen135 +\Gm@odd@mp=\dimen136 +\Gm@even@mp=\dimen137 +\Gm@dimlist=\toks24 +) +(/usr/share/texmf-texlive/tex/latex/hyperref/hyperref.sty +Package: hyperref 2007/02/07 v6.75r Hypertext links for LaTeX +\@linkdim=\dimen138 +\Hy@linkcounter=\count117 +\Hy@pagecounter=\count118 + +(/usr/share/texmf-texlive/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +) +(/etc/texmf/tex/latex/config/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) +(/usr/share/texmf-texlive/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options ( +HO) +) +Package hyperref Info: Option `hyperfootnotes' set `false' on input line 2238. +Package hyperref Info: Option `bookmarks' set `true' on input line 2238. +Package hyperref Info: Option `linktocpage' set `false' on input line 2238. +Package hyperref Info: Option `pdfdisplaydoctitle' set `true' on input line 223 +8. +Package hyperref Info: Option `pdfpagelabels' set `true' on input line 2238. +Package hyperref Info: Option `bookmarksopen' set `true' on input line 2238. +Package hyperref Info: Option `colorlinks' set `true' on input line 2238. +Package hyperref Info: Hyper figures OFF on input line 2288. +Package hyperref Info: Link nesting OFF on input line 2293. +Package hyperref Info: Hyper index ON on input line 2296. +Package hyperref Info: Plain pages OFF on input line 2303. +Package hyperref Info: Backreferencing OFF on input line 2308. + +Implicit mode ON; LaTeX internals redefined +Package hyperref Info: Bookmarks ON on input line 2444. +(/usr/share/texmf-texlive/tex/latex/ltxmisc/url.sty +\Urlmuskip=\muskip11 +Package: url 2005/06/27 ver 3.2 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 2599. +\Fld@menulength=\count119 +\Field@Width=\dimen139 +\Fld@charsize=\dimen140 +\Choice@toks=\toks25 +\Field@toks=\toks26 +Package hyperref Info: Hyper figures OFF on input line 3102. +Package hyperref Info: Link nesting OFF on input line 3107. +Package hyperref Info: Hyper index ON on input line 3110. +Package hyperref Info: backreferencing OFF on input line 3117. +Package hyperref Info: Link coloring ON on input line 3120. +\Hy@abspage=\count120 +\c@Item=\count121 +) +*hyperref using driver hpdftex* +(/usr/share/texmf-texlive/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX +\Fld@listcount=\count122 +) +\c@pp@a@footnote=\count123 +\@indexfile=\write3 +\openout3 = `relativity.idx'. + + +Writing index file relativity.idx +\c@figno=\count124 +\TmpLen=\skip62 +(./relativity.aux) +\openout1 = `relativity.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 528. +LaTeX Font Info: ... okay on input line 528. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 528. +LaTeX Font Info: ... okay on input line 528. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 528. +LaTeX Font Info: ... okay on input line 528. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 528. +LaTeX Font Info: ... okay on input line 528. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 528. +LaTeX Font Info: ... okay on input line 528. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 528. +LaTeX Font Info: ... okay on input line 528. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 528. +LaTeX Font Info: ... okay on input line 528. + (/usr/share/texmf-texlive/tex/latex/ragged2e/ragged2e.sty +Package: ragged2e 2003/03/25 v2.04 ragged2e Package (MS) + +(/usr/share/texmf-texlive/tex/latex/everysel/everysel.sty +Package: everysel 1999/06/08 v1.03 EverySelectfont Package (MS) +LaTeX Info: Redefining \selectfont on input line 125. +) +\CenteringLeftskip=\skip63 +\RaggedLeftLeftskip=\skip64 +\RaggedRightLeftskip=\skip65 +\CenteringRightskip=\skip66 +\RaggedLeftRightskip=\skip67 +\RaggedRightRightskip=\skip68 +\CenteringParfillskip=\skip69 +\RaggedLeftParfillskip=\skip70 +\RaggedRightParfillskip=\skip71 +\JustifyingParfillskip=\skip72 +\CenteringParindent=\skip73 +\RaggedLeftParindent=\skip74 +\RaggedRightParindent=\skip75 +\JustifyingParindent=\skip76 +) +Package caption Info: hyperref package v6.74m (or newer) detected on input line + 528. +-------------------- Geometry parameters +paper: class default +landscape: -- +twocolumn: -- +twoside: true +asymmetric: -- +h-parts: 9.03374pt, 325.215pt, 9.03375pt +v-parts: 4.15848pt, 495.49379pt, 6.23773pt +hmarginratio: 1:1 +vmarginratio: 2:3 +lines: -- +heightrounded: -- +bindingoffset: 0.0pt +truedimen: -- +includehead: true +includefoot: true +includemp: -- +driver: pdftex +-------------------- Page layout dimensions and switches +\paperwidth 343.28249pt +\paperheight 505.89pt +\textwidth 325.215pt +\textheight 433.62pt +\oddsidemargin -63.23625pt +\evensidemargin -63.23624pt +\topmargin -68.11151pt +\headheight 12.0pt +\headsep 19.8738pt +\footskip 30.0pt +\marginparwidth 98.0pt +\marginparsep 7.0pt +\columnsep 10.0pt +\skip\footins 10.8pt plus 4.0pt minus 2.0pt +\hoffset 0.0pt +\voffset 0.0pt +\mag 1000 +\@twosidetrue \@mparswitchtrue +(1in=72.27pt, 1cm=28.45pt) +----------------------- + +(/usr/share/texmf-texlive/tex/latex/graphics/color.sty +Package: color 2005/11/14 v1.0j Standard LaTeX Color (DPC) + +(/etc/texmf/tex/latex/config/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package color Info: Driver file: pdftex.def on input line 130. +) +Package hyperref Info: Link coloring ON on input line 528. + +(/usr/share/texmf-texlive/tex/latex/hyperref/nameref.sty +Package: nameref 2006/12/27 v2.28 Cross-referencing by name of section + +(/usr/share/texmf-texlive/tex/latex/oberdiek/refcount.sty +Package: refcount 2006/02/20 v3.0 Data extraction from references (HO) +) +\c@section@level=\count125 +) +LaTeX Info: Redefining \ref on input line 528. +LaTeX Info: Redefining \pageref on input line 528. + (./relativity.out) +(./relativity.out) +\@outlinefile=\write4 +\openout4 = `relativity.out'. + +LaTeX Font Info: Try loading font information for U+msa on input line 540. + (/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd +File: umsa.fd 2002/01/19 v2.2g AMS font definitions +) +LaTeX Font Info: Try loading font information for U+msb on input line 540. + +(/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd +File: umsb.fd 2002/01/19 v2.2g AMS font definitions +) [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] [1 + +] [2] [3 + + +] [4] [5] [6] [7] (./relativity.toc [8 + + + +] [9]) +\tf@toc=\write5 +\openout5 = `relativity.toc'. + + [10] [11 + + +] [1 + +] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] +[14] [15] [16] [17] [18] [19] [20] [21] [22] +<./images/025.pdf, id=519, 338.26375pt x 50.1875pt> +File: ./images/025.pdf Graphic file (type pdf) + <use ./images/025.pdf> +[23 <./images/025.pdf>] [24] [25] [26] [27] [28] +<./images/032.pdf, id=581, 194.7275pt x 150.5625pt> +File: ./images/032.pdf Graphic file (type pdf) + <use ./images/032.pdf> +[29] [30 <./images/032.pdf>] [31] [32] [33] [34] [35] [36] [37] +<./images/040.pdf, id=649, 222.8325pt x 39.14626pt> +File: ./images/040.pdf Graphic file (type pdf) + <use ./images/040.pdf> +[38 <./images/040.pdf>] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] +[49] [50] [51] [52] [53] [54] [55 + + +] [56] [57] [58] [59] [60] [61] [62] [63] +[64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] +[79] [80] <./images/087.pdf, id=880, 209.78375pt x 129.48375pt> +File: ./images/087.pdf Graphic file (type pdf) + +<use ./images/087.pdf> [81 <./images/087.pdf>] [82] [83] [84] [85] [86] +[87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98 + + +] [99] [100] [101] +[102] [103] [104] [105] [106] [107] [108 + +] [109] [110] [111] [112] [113] +[114 + +] [115] [116 + +] [117] [118] [119] +<./images/127.pdf, id=1169, 99.37125pt x 212.795pt> +File: ./images/127.pdf Graphic file (type pdf) + <use ./images/127.pdf> +[120 <./images/127.pdf>] [121] [122] [123] [124] [125] [126 + + +] (./relativity.ind +[127] [128 + +] [129] [130] [131] [132]) [133 + + +] [1 + +] (./relativity.aux) + + *File List* + book.cls 2005/09/16 v1.4f Standard LaTeX document class + bk12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +inputenc.sty 2006/05/05 v1.1b Input encoding file + latin1.def 2006/05/05 v1.1b Input encoding file + ifthen.sty 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) + amsmath.sty 2000/07/18 v2.13 AMS math features + amstext.sty 2000/06/29 v2.01 + amsgen.sty 1999/11/30 v2.0 + amsbsy.sty 1999/11/29 v1.2d + amsopn.sty 1999/12/14 v2.01 operator names + amssymb.sty 2002/01/22 v2.2d +amsfonts.sty 2001/10/25 v2.2f + alltt.sty 1997/06/16 v2.0g defines alltt environment + array.sty 2005/08/23 v2.4b Tabular extension package (FMi) + perpage.sty 2006/07/15 1.12 Reset/sort counters per page +multicol.sty 2006/05/18 v1.6g multicolumn formatting (FMi) + makeidx.sty 2000/03/29 v1.0m Standard LaTeX package + caption.sty 2007/01/07 v3.0k Customising captions (AR) +caption3.sty 2007/01/07 v3.0k caption3 kernel (AR) + keyval.sty 1999/03/16 v1.13 key=value parser (DPC) +graphicx.sty 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) +graphics.sty 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) + trig.sty 1999/03/16 v1.09 sin cos tan (DPC) +graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive + pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX + wrapfig.sty 2003/01/31 v 3.6 + calc.sty 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) +fancyhdr.sty +geometry.sty 2002/07/08 v3.2 Page Geometry +hyperref.sty 2007/02/07 v6.75r Hypertext links for LaTeX + pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +kvoptions.sty 2006/08/22 v2.4 Connects package keyval with LaTeX options (HO +) + url.sty 2005/06/27 ver 3.2 Verb mode for urls, etc. + hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX +ragged2e.sty 2003/03/25 v2.04 ragged2e Package (MS) +everysel.sty 1999/06/08 v1.03 EverySelectfont Package (MS) + color.sty 2005/11/14 v1.0j Standard LaTeX Color (DPC) + color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive + nameref.sty 2006/12/27 v2.28 Cross-referencing by name of section +refcount.sty 2006/02/20 v3.0 Data extraction from references (HO) +relativity.out +relativity.out + umsa.fd 2002/01/19 v2.2g AMS font definitions + umsb.fd 2002/01/19 v2.2g AMS font definitions +./images/025.pdf +./images/032.pdf +./images/040.pdf +./images/087.pdf +./images/127.pdf +relativity.ind + *********** + + ) +Here is how much of TeX's memory you used: + 5430 strings out of 94722 + 77862 string characters out of 1176552 + 143128 words of memory out of 1500000 + 8141 multiletter control sequences out of 10000+50000 + 17695 words of font info for 67 fonts, out of 1200000 for 2000 + 257 hyphenation exceptions out of 8191 + 34i,18n,44p,467b,649s stack positions out of 5000i,500n,6000p,200000b,5000s +</usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmbx10.pfb></usr/share/texmf +-texlive/fonts/type1/bluesky/cm/cmbx12.pfb></usr/share/texmf-texlive/fonts/type +1/bluesky/cm/cmbxti10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmcs +c10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmex10.pfb></usr/share +/texmf-texlive/fonts/type1/bluesky/cm/cmmi10.pfb></usr/share/texmf-texlive/font +s/type1/bluesky/cm/cmmi12.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/ +cmr10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmr12.pfb></usr/shar +e/texmf-texlive/fonts/type1/bluesky/cm/cmr7.pfb></usr/share/texmf-texlive/fonts +/type1/bluesky/cm/cmr8.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cms +y10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmsy7.pfb></usr/share/ +texmf-texlive/fonts/type1/bluesky/cm/cmsy8.pfb></usr/share/texmf-texlive/fonts/ +type1/bluesky/cm/cmti10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cm +ti12.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmtt10.pfb></usr/shar +e/texmf-texlive/fonts/type1/bluesky/cm/cmtt8.pfb> +Output written on relativity.pdf (147 pages, 638001 bytes). +PDF statistics: + 1850 PDF objects out of 2073 (max. 8388607) + 394 named destinations out of 1000 (max. 131072) + 418 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/36114-t/images/025.pdf b/36114-t/images/025.pdf Binary files differnew file mode 100644 index 0000000..f91bda1 --- /dev/null +++ b/36114-t/images/025.pdf diff --git a/36114-t/images/032.pdf b/36114-t/images/032.pdf Binary files differnew file mode 100644 index 0000000..3ff495d --- /dev/null +++ b/36114-t/images/032.pdf diff --git a/36114-t/images/040.pdf b/36114-t/images/040.pdf Binary files differnew file mode 100644 index 0000000..6ed50b6 --- /dev/null +++ b/36114-t/images/040.pdf diff --git a/36114-t/images/087.pdf b/36114-t/images/087.pdf Binary files differnew file mode 100644 index 0000000..f0c4b55 --- /dev/null +++ b/36114-t/images/087.pdf diff --git a/36114-t/images/127.pdf b/36114-t/images/127.pdf Binary files differnew file mode 100644 index 0000000..e68ff46 --- /dev/null +++ b/36114-t/images/127.pdf diff --git a/36114-t/images/sources/025.eepic b/36114-t/images/sources/025.eepic new file mode 100644 index 0000000..06602b0 --- /dev/null +++ b/36114-t/images/sources/025.eepic @@ -0,0 +1,42 @@ +%% Generated from 025.xp on Tue May 10 18:52:03 EDT 2011 by +%% ePiX-1.2.4 +%% +%% Cartesian bounding box: [-2,2] x [-0.25,0.25] +%% Actual size: 4 x 0.5in +%% Figure offset: left by 0in, down by 0in +%% +%% usepackages tikz +%% +\xdefinecolor{rgb_000000}{rgb}{0,0,0}% +\begin{tikzpicture} +\pgfsetlinewidth{0.4pt} +\useasboundingbox (0in,0in) rectangle (4in,0.5in); +\pgfsetlinewidth{0.8pt} +\draw (0in,0.25in)--(2in,0.25in)--(4in,0.25in); +\draw (0.25in,0.35in)--(2in,0.35in)--(3.75in,0.35in); +\draw (3.75in,0.35in)--(3.8in,0.4in)--(3.85in,0.45in); +\pgftext[at={\pgfpoint{2in}{0.25in}}] {\makebox(0,0){\hbox{\color{rgb_000000}$\rule{0.5pt}{6pt}$}}} +\pgftext[at={\pgfpoint{2in}{0.35in}}] {\makebox(0,0){\hbox{\color{rgb_000000}$\rule{0.5pt}{6pt}$}}} +\pgftext[at={\pgfpoint{1in}{0.25in}}] {\makebox(0,0){\hbox{\color{rgb_000000}$\rule{0.5pt}{12pt}$}}} +\pgftext[at={\pgfpoint{1in}{0.35in}}] {\makebox(0,0){\hbox{\color{rgb_000000}$\rule{0.5pt}{12pt}$}}} +\pgftext[at={\pgfpoint{3in}{0.25in}}] {\makebox(0,0){\hbox{\color{rgb_000000}$\rule{0.5pt}{12pt}$}}} +\pgftext[at={\pgfpoint{3in}{0.35in}}] {\makebox(0,0){\hbox{\color{rgb_000000}$\rule{0.5pt}{12pt}$}}} +\draw (0.25in,0.45in)--(0.75in,0.45in); +\pgfsetfillcolor{rgb_000000} +\draw [fill](0.736163in,0.45in)--(0.722326in,0.436163in)-- + (0.75in,0.45in)--(0.722326in,0.463837in)--(0.736163in,0.45in)--cycle; +\pgftext[at={\pgfpoint{0.277674in}{0.477674in}}] {\makebox(0,0)[bl]{\hbox{\color{rgb_000000}$v$}}} +\draw (3.25in,0.45in)--(3.75in,0.45in); +\draw [fill](3.73616in,0.45in)--(3.72233in,0.436163in)-- + (3.75in,0.45in)--(3.72233in,0.463837in)--(3.73616in,0.45in)--cycle; +\pgftext[at={\pgfpoint{3.27767in}{0.477674in}}] {\makebox(0,0)[bl]{\hbox{\color{rgb_000000}$v$}}} +\draw (2.125in,0.55in)--(2.625in,0.55in); +\draw [fill](2.61116in,0.55in)--(2.59733in,0.536163in)-- + (2.625in,0.55in)--(2.59733in,0.563837in)--(2.61116in,0.55in)--cycle; +\pgftext[at={\pgfpoint{2.06965in}{0.55in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}$M'$}}} +\pgftext[at={\pgfpoint{1in}{0.11163in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$A$}}} +\pgftext[at={\pgfpoint{2in}{0.11163in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$M$}}} +\pgftext[at={\pgfpoint{3in}{0.11163in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$B$}}} +\pgftext[at={\pgfpoint{3.90535in}{0.45in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}\textit{Train}}}} +\pgftext[at={\pgfpoint{3.66791in}{0.139304in}}] {\makebox(0,0)[tl]{\hbox{\color{rgb_000000}\textit{Embankment}}}} +\end{tikzpicture} diff --git a/36114-t/images/sources/025.xp b/36114-t/images/sources/025.xp new file mode 100644 index 0000000..5bc71f0 --- /dev/null +++ b/36114-t/images/sources/025.xp @@ -0,0 +1,51 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double mA(-1), mB(1), mM(0), dx(0.5), dy(0.1); + +void veloc(const P& loc, const P& off, + const std::string& msg, epix_label_posn A) +{ + arrow(loc, loc + P(dx,0)); + label(loc, off, msg, A); +} + +int main() +{ + picture(P(-2,-0.25), P(2,0.25), "4 x 0.5in"); + + begin(); + bold(); + arrow_inset(0.5); + arrow_ratio(2); + arrow_width(2); + + line(P(xmin(), 0), P(xmax(), 0)); + line(P(xmin()+0.25, dy), P(xmax()-0.25, dy)); + line(P(xmax()-0.25, dy), P(xmax()-0.15, dy + 0.1)); + + h_axis_tick(P(mM,0)); + h_axis_tick(P(mM,dy)); + + tick_size(6); + h_axis_tick(P(mA,0)); + h_axis_tick(P(mA,dy)); + + h_axis_tick(P(mB,0)); + h_axis_tick(P(mB,dy)); + + veloc(P(xmin()+0.25, 2*dy), P(2,2), "$v$", tr); + veloc(P(mB+0.25, 2*dy), P(2,2), "$v$", tr); + veloc(P(mM+0.125, 3*dy), P(-4,0), "$M'$", l); + + label(P(mA,0), P(0,-10), "$A$", b); + label(P(mM,0), P(0,-10), "$M$", b); + label(P(mB,0), P(0,-10), "$B$", b); + + label(P(xmax()-0.15, dy + 0.1), P(4,0), "\\textit{Train}", r); + label(P(xmax(), 0), P(-24,-8), "\\textit{Embankment}", br); + + tikz_format(); + end(); +} diff --git a/36114-t/images/sources/032.eepic b/36114-t/images/sources/032.eepic new file mode 100644 index 0000000..ce754bf --- /dev/null +++ b/36114-t/images/sources/032.eepic @@ -0,0 +1,42 @@ +%% Generated from 032.xp on Wed May 11 10:08:49 EDT 2011 by +%% ePiX-1.2.4 +%% +%% Cartesian bounding box: [0,1.5] x [0,1] +%% Actual size: 2.4 x 1.6in +%% Figure offset: left by 0in, down by 0in +%% +%% usepackages tikz +%% +\xdefinecolor{rgb_000000}{rgb}{0,0,0}% +\begin{tikzpicture} +\pgfsetlinewidth{0.4pt} +\useasboundingbox (0in,0in) rectangle (2.4in,1.6in); +\pgfsetlinewidth{0.8pt} +\draw (0in,0in)--(1.2in,0in)--(2.4in,0in); +\draw (0in,0in)--(0.32in,0.32in)--(0.64in,0.64in); +\draw (0in,0in)--(0in,0.8in)--(0in,1.6in); +\draw (0.8in,0.08in)--(1.6in,0.08in)--(2.4in,0.08in); +\draw (0.8in,0.08in)--(1.12in,0.4in)--(1.44in,0.72in); +\draw (0.8in,0.08in)--(0.8in,0.88in)--(0.8in,1.68in); +\draw (1.04in,0.16in)--(1.44in,0.16in); +\pgfsetfillcolor{rgb_000000} +\draw [fill](1.42616in,0.16in)--(1.41233in,0.146163in)-- + (1.44in,0.16in)--(1.41233in,0.173837in)--(1.42616in,0.16in)--cycle; +\pgftext[at={\pgfpoint{1.12302in}{0.187674in}}] {\makebox(0,0)[bl]{\hbox{\color{rgb_000000}$v$}}} +\draw (1.44in,0.64in)--(1.84in,0.64in); +\draw [fill](1.82616in,0.64in)--(1.81233in,0.626163in)-- + (1.84in,0.64in)--(1.81233in,0.653837in)--(1.82616in,0.64in)--cycle; +\pgftext[at={\pgfpoint{1.46767in}{0.584652in}}] {\makebox(0,0)[tl]{\hbox{\color{rgb_000000}$v$}}} +\draw (0.88in,1.6in)--(1.28in,1.6in); +\draw [fill](1.26616in,1.6in)--(1.25233in,1.58616in)-- + (1.28in,1.6in)--(1.25233in,1.61384in)--(1.26616in,1.6in)--cycle; +\pgftext[at={\pgfpoint{0.907674in}{1.54465in}}] {\makebox(0,0)[tl]{\hbox{\color{rgb_000000}$v$}}} +\pgftext[at={\pgfpoint{0in}{-0.055348in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$K$}}} +\pgftext[at={\pgfpoint{0.8in}{-0.055348in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$K'$}}} +\pgftext[at={\pgfpoint{2.42767in}{-0.027674in}}] {\makebox(0,0)[tl]{\hbox{\color{rgb_000000}$x$}}} +\pgftext[at={\pgfpoint{2.42767in}{0.107674in}}] {\makebox(0,0)[bl]{\hbox{\color{rgb_000000}$x'$}}} +\pgftext[at={\pgfpoint{0.612326in}{0.667674in}}] {\makebox(0,0)[br]{\hbox{\color{rgb_000000}$y$}}} +\pgftext[at={\pgfpoint{1.41233in}{0.747674in}}] {\makebox(0,0)[br]{\hbox{\color{rgb_000000}$y'$}}} +\pgftext[at={\pgfpoint{0in}{1.62767in}}] {\makebox(0,0)[b]{\hbox{\color{rgb_000000}$z$}}} +\pgftext[at={\pgfpoint{0.8in}{1.70767in}}] {\makebox(0,0)[b]{\hbox{\color{rgb_000000}$z'$}}} +\end{tikzpicture} diff --git a/36114-t/images/sources/032.xp b/36114-t/images/sources/032.xp new file mode 100644 index 0000000..b432064 --- /dev/null +++ b/36114-t/images/sources/032.xp @@ -0,0 +1,55 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double dx(0.5), dy(0.05), sc(0.8); + +void veloc(const P& loc, const P& off, + const std::string& msg, epix_label_posn A) +{ + arrow(loc, loc + P(0.5*dx,0)); + label(loc, off, msg, A); +} + +int main() +{ + picture(P(0,0), P(1.5,1), "2.4 x 1.6in"); + + begin(); + bold(); + arrow_inset(0.5); + arrow_ratio(2); + arrow_width(2); + + P O1(0,0), O2(dx, dy), + pX1(xmax(), 0), pX2(xmax(), dy), + pY1(sc*dx, sc*dx), pY2(O2 + pY1), + pZ1(0,ymax()), pZ2(O2 + pZ1); + + line(O1, pX1); + line(O1, pY1); + line(O1, pZ1); + + line(O2, pX2); + line(O2, pY2); + line(O2, pZ2); + + veloc(O2 + P(3*dy, dy), P(6,2), "$v$", tr); + veloc(pY2 + P( 0, -dy), P(2,-4), "$v$", br); + veloc(pZ2 + P(dy, -dy), P(2,-4), "$v$", br); + + label(O1, P(0,-4), "$K$", b); + label(O2 - P(0, dy), P(0,-4), "$K'$", b); + + label(pX1, P(2,-2), "$x$", br); + label(pX2, P(2, 2), "$x'$", tr); + + label(pY1, P(-2, 2), "$y$", tl); + label(pY2, P(-2, 2), "$y'$", tl); + + label(pZ1, P(0, 2), "$z$", t); + label(pZ2, P(0, 2), "$z'$", t); + + tikz_format(); + end(); +} diff --git a/36114-t/images/sources/040.eepic b/36114-t/images/sources/040.eepic new file mode 100644 index 0000000..1eb70f6 --- /dev/null +++ b/36114-t/images/sources/040.eepic @@ -0,0 +1,23 @@ +%% Generated from 040.xp on Wed May 11 10:28:32 EDT 2011 by +%% ePiX-1.2.4 +%% +%% Cartesian bounding box: [0,3] x [-0.125,0.125] +%% Actual size: 3 x 0.3in +%% Figure offset: left by 0in, down by 0in +%% +%% usepackages tikz +%% +\xdefinecolor{rgb_000000}{rgb}{0,0,0}% +\begin{tikzpicture} +\pgfsetlinewidth{0.4pt} +\useasboundingbox (0in,0in) rectangle (3in,0.3in); +\pgfsetlinewidth{0.8pt} +\draw (0in,0in)--(1.5in,0in)--(3in,0in); +\draw (0in,0.3in)--(1.5in,0.3in)--(3in,0.3in); +\draw (0.5in,0.15in)--(1in,0.15in); +\pgfsetfillcolor{rgb_000000} +\draw [fill](0.986163in,0.15in)--(0.972326in,0.136163in)-- + (1in,0.15in)--(0.972326in,0.163837in)--(0.986163in,0.15in)--cycle; +\pgftext[at={\pgfpoint{0.75in}{0.177674in}}] {\makebox(0,0)[b]{\hbox{\color{rgb_000000}$v$}}} +\pgftext[at={\pgfpoint{1.5in}{0.327674in}}] {\makebox(0,0)[b]{\hbox{\color{rgb_000000}$T$}}} +\end{tikzpicture} diff --git a/36114-t/images/sources/040.xp b/36114-t/images/sources/040.xp new file mode 100644 index 0000000..4c2f9c9 --- /dev/null +++ b/36114-t/images/sources/040.xp @@ -0,0 +1,33 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double dx(0.5), rad(0.125); + +void veloc(const P& loc, const P& off, + const std::string& msg, epix_label_posn A) +{ + arrow(loc, loc + P(dx,0)); + label(loc + 0.5*dx, off, msg, A); +} + +int main() +{ + picture(P(0,-rad), P(3,rad), "3 x 0.3in"); + + begin(); + bold(); + arrow_inset(0.5); + arrow_ratio(2); + arrow_width(2); + + line(P(xmin(), -rad), P(xmax(), -rad)); + line(P(xmin(), rad), P(xmax(), rad)); + + veloc(P(dx, 0), P(0,2), "$v$", t); + + label(P(0.5*xmax(), ymax()), P(0,2), "$T$", t); + + tikz_format(); + end(); +} diff --git a/36114-t/images/sources/087.eepic b/36114-t/images/sources/087.eepic new file mode 100644 index 0000000..cda7abd --- /dev/null +++ b/36114-t/images/sources/087.eepic @@ -0,0 +1,199 @@ +%% Generated from 087.xp on Thu May 12 12:37:03 EDT 2011 by +%% ePiX-1.2.4 +%% +%% Cartesian bounding box: [-2,2] x [-2,2] +%% Actual size: 3 x 2in +%% Figure offset: left by 0in, down by 0in +%% +%% usepackages tikz +%% +\xdefinecolor{rgb_000000}{rgb}{0,0,0}% +\begin{tikzpicture} +\pgfsetlinewidth{0.4pt} +\useasboundingbox (0in,0in) rectangle (3in,2in); +\pgfsetlinewidth{0.8pt} +\draw (0.5864in,0.397277in)--(0.587835in,0.432446in)-- + (0.590126in,0.467045in)--(0.593257in,0.501084in)-- + (0.597215in,0.534572in)--(0.601986in,0.567518in)-- + (0.607557in,0.59993in)--(0.613916in,0.631817in)-- + (0.62105in,0.663187in)--(0.628948in,0.694048in)-- + (0.637598in,0.724408in)--(0.64699in,0.754273in)-- + (0.657112in,0.783651in)--(0.667955in,0.812549in)-- + (0.679508in,0.840973in)--(0.691762in,0.86893in)-- + (0.704707in,0.896426in)--(0.718335in,0.923468in)-- + (0.732637in,0.95006in)--(0.747604in,0.976208in)-- + (0.763228in,1.00192in)--(0.779501in,1.0272in)-- + (0.796416in,1.05205in)--(0.813965in,1.07647in)-- + (0.832142in,1.10048in)--(0.850939in,1.12408in)-- + (0.870349in,1.14726in)--(0.890366in,1.17004in)-- + (0.910985in,1.19242in)--(0.932198in,1.21441in)--(0.954in,1.236in)-- + (0.976385in,1.2572in)--(0.999349in,1.27802in)-- + (1.02288in,1.29846in)--(1.04699in,1.31851in)-- + (1.07165in,1.3382in)--(1.09688in,1.35751in)-- + (1.12266in,1.37645in)--(1.14898in,1.39502in)-- + (1.17585in,1.41324in)--(1.20326in,1.43109in)-- + (1.23121in,1.44859in)--(1.25969in,1.46573in)-- + (1.28869in,1.48251in)--(1.31822in,1.49895in)-- + (1.34828in,1.51504in)--(1.37885in,1.53079in)-- + (1.40993in,1.54619in)--(1.44153in,1.56126in)-- + (1.47363in,1.57598in)--(1.50624in,1.59037in)-- + (1.53935in,1.60442in)--(1.57296in,1.61814in)-- + (1.60707in,1.63152in)--(1.64167in,1.64458in)-- + (1.67677in,1.65731in)--(1.71235in,1.66972in)-- + (1.74842in,1.6818in)--(1.78497in,1.69356in)-- + (1.82201in,1.70499in)--(1.85952in,1.71611in); +\draw (0.82279in,0.33057in)--(0.8368in,0.358526in)-- + (0.851281in,0.386169in)--(0.866233in,0.413498in)-- + (0.881652in,0.440516in)--(0.897537in,0.467222in)-- + (0.913887in,0.493619in)--(0.9307in,0.519707in)-- + (0.947974in,0.545488in)--(0.965708in,0.570962in)-- + (0.983902in,0.59613in)--(1.00255in,0.620993in)-- + (1.02166in,0.645552in)--(1.04122in,0.669809in)-- + (1.06123in,0.693763in)--(1.0817in,0.717415in)-- + (1.10262in,0.740767in)--(1.12398in,0.763819in)-- + (1.1458in,0.786571in)--(1.16806in,0.809026in)-- + (1.19078in,0.831182in)--(1.21393in,0.853041in)-- + (1.23753in,0.874604in)--(1.26158in,0.895871in)-- + (1.28607in,0.916842in)--(1.311in,0.937519in)-- + (1.33637in,0.957901in)--(1.36218in,0.97799in)-- + (1.38843in,0.997786in)--(1.41512in,1.01729in)-- + (1.44225in,1.0365in)--(1.46982in,1.05542in)-- + (1.49782in,1.07405in)--(1.52626in,1.09238in)-- + (1.55513in,1.11043in)--(1.58444in,1.12819in)-- + (1.61419in,1.14566in)--(1.64436in,1.16283in)-- + (1.67498in,1.17972in)--(1.70602in,1.19633in)-- + (1.73749in,1.21264in)--(1.7694in,1.22866in)--(1.80174in,1.2444in)-- + (1.83451in,1.25985in)--(1.86771in,1.27502in)-- + (1.90134in,1.28989in)--(1.93539in,1.30449in)-- + (1.96988in,1.31879in)--(2.0048in,1.33281in)-- + (2.04014in,1.34655in)--(2.07591in,1.35999in)-- + (2.11211in,1.37316in)--(2.14874in,1.38604in)-- + (2.18579in,1.39863in)--(2.22327in,1.41094in)-- + (2.26117in,1.42297in)--(2.2995in,1.43471in)-- + (2.33826in,1.44617in)--(2.37744in,1.45735in)-- + (2.41705in,1.46824in)--(2.45708in,1.47885in); +\draw (0.901144in,0.158505in)--(0.928096in,0.179495in)-- + (0.955136in,0.200426in)--(0.982275in,0.221291in)-- + (1.00952in,0.242083in)--(1.03689in,0.262796in)-- + (1.06439in,0.283423in)--(1.09202in,0.303957in)-- + (1.1198in,0.324393in)--(1.14774in,0.344725in)-- + (1.17585in,0.364947in)--(1.20412in,0.385054in)-- + (1.23258in,0.405039in)--(1.26123in,0.424899in)-- + (1.29007in,0.444628in)--(1.31912in,0.464221in)-- + (1.34838in,0.483674in)--(1.37785in,0.502982in)-- + (1.40755in,0.52214in)--(1.43748in,0.541146in)-- + (1.46764in,0.559993in)--(1.49805in,0.57868in)-- + (1.52871in,0.597201in)--(1.55961in,0.615553in)-- + (1.59078in,0.633732in)--(1.62221in,0.651735in)-- + (1.65391in,0.66956in)--(1.68589in,0.687201in)-- + (1.71814in,0.704657in)--(1.75068in,0.721924in)-- + (1.7835in,0.739in)--(1.81661in,0.755881in)-- + (1.85003in,0.772565in)--(1.88374in,0.789049in)-- + (1.91775in,0.805331in)--(1.95207in,0.821408in)-- + (1.9867in,0.837278in)--(2.02165in,0.852938in)-- + (2.05691in,0.868387in)--(2.0925in,0.883621in)-- + (2.12841in,0.89864in)--(2.16464in,0.91344in)-- + (2.20121in,0.92802in)--(2.23811in,0.942379in)-- + (2.27534in,0.956514in)--(2.31291in,0.970423in)-- + (2.35083in,0.984105in)--(2.38909in,0.997558in)-- + (2.42769in,1.01078in)--(2.46664in,1.02377in)-- + (2.50594in,1.03653in)--(2.54559in,1.04905in)-- + (2.5856in,1.06134in)--(2.62597in,1.07338in)-- + (2.66669in,1.08519in)--(2.70777in,1.09676in)-- + (2.74922in,1.10809in)--(2.79103in,1.11917in)-- + (2.83321in,1.13001in)--(2.87575in,1.14061in)--(2.91866in,1.15096in); +\draw (0.52503in,0.80449in)--(0.550736in,0.80121in)-- + (0.576009in,0.797641in)--(0.600847in,0.793782in)-- + (0.625251in,0.789634in)--(0.649219in,0.785195in)-- + (0.672753in,0.780467in)--(0.695852in,0.775448in)-- + (0.718514in,0.770139in)--(0.740741in,0.764539in)-- + (0.762532in,0.758649in)--(0.783887in,0.752468in)-- + (0.804805in,0.745995in)--(0.825286in,0.739232in)-- + (0.84533in,0.732177in)--(0.864937in,0.72483in)-- + (0.884105in,0.717192in)--(0.902836in,0.709261in)-- + (0.921128in,0.701038in)--(0.938982in,0.692523in)-- + (0.956396in,0.683715in)--(0.973372in,0.674614in)-- + (0.989907in,0.66522in)--(1.006in,0.655533in)-- + (1.02166in,0.645552in)--(1.03687in,0.635278in)-- + (1.05165in,0.624709in)--(1.06598in,0.613846in)-- + (1.07987in,0.602689in)--(1.09332in,0.591237in)-- + (1.10632in,0.57949in)--(1.11889in,0.567447in)-- + (1.131in,0.555109in)--(1.14268in,0.542475in)-- + (1.15391in,0.529545in)--(1.1647in,0.516319in)-- + (1.17504in,0.502796in)--(1.18494in,0.488976in)-- + (1.19439in,0.474859in)--(1.20339in,0.460444in)-- + (1.21195in,0.445731in)--(1.22006in,0.430721in)-- + (1.22772in,0.415411in)--(1.23494in,0.399803in)-- + (1.2417in,0.383896in)--(1.24802in,0.367689in)-- + (1.25389in,0.351183in)--(1.2593in,0.334376in)-- + (1.26427in,0.317268in)--(1.26878in,0.29986in)-- + (1.27284in,0.282151in)--(1.27645in,0.264139in)-- + (1.27961in,0.245826in)--(1.28231in,0.22721in)-- + (1.28456in,0.208292in)--(1.28635in,0.18907in)-- + (1.28769in,0.169544in)--(1.28857in,0.149715in)-- + (1.289in,0.129581in)--(1.28897in,0.109141in)--(1.28848in,0.0883968in); +\draw (0.7875in,1.275in)--(0.819633in,1.2683in)-- + (0.851344in,1.26131in)--(0.882633in,1.25405in)-- + (0.9135in,1.2465in)--(0.943945in,1.23867in)-- + (0.973969in,1.23056in)--(1.00357in,1.22217in)-- + (1.03275in,1.2135in)--(1.06151in,1.20455in)-- + (1.08984in,1.19531in)--(1.11776in,1.1858in)--(1.14525in,1.176in)-- + (1.17232in,1.16592in)--(1.19897in,1.15556in)-- + (1.2252in,1.14492in)--(1.251in,1.134in)--(1.27638in,1.1228in)-- + (1.30134in,1.11131in)--(1.32588in,1.09955in)--(1.35in,1.0875in)-- + (1.3737in,1.07517in)--(1.39697in,1.06256in)-- + (1.41982in,1.04967in)--(1.44225in,1.0365in)-- + (1.46426in,1.02305in)--(1.48584in,1.00931in)-- + (1.50701in,0.995297in)--(1.52775in,0.981in)-- + (1.54807in,0.966422in)--(1.56797in,0.951562in)-- + (1.58745in,0.936422in)--(1.6065in,0.921in)-- + (1.62513in,0.905297in)--(1.64334in,0.889313in)-- + (1.66113in,0.873047in)--(1.6785in,0.8565in)-- + (1.69545in,0.839672in)--(1.71197in,0.822562in)-- + (1.72807in,0.805172in)--(1.74375in,0.7875in)-- + (1.75901in,0.769547in)--(1.77384in,0.751313in)-- + (1.78826in,0.732797in)--(1.80225in,0.714in)-- + (1.81582in,0.694922in)--(1.82897in,0.675563in)-- + (1.8417in,0.655922in)--(1.854in,0.636in)--(1.86588in,0.615797in)-- + (1.87734in,0.595313in)--(1.88838in,0.574547in)-- + (1.899in,0.5535in)--(1.9092in,0.532172in)--(1.91897in,0.510563in)--(1.92832in,0.488672in)--(1.93725in,0.4665in)-- + (1.94576in,0.444047in)--(1.95384in,0.421313in)-- + (1.96151in,0.398297in)--(1.96875in,0.375in); +\draw (1.16403in,1.56189in)--(1.19947in,1.5537in)-- + (1.23449in,1.54524in)--(1.26911in,1.5365in)-- + (1.30331in,1.52749in)--(1.3371in,1.5182in)--(1.37048in,1.50864in)-- + (1.40345in,1.49881in)--(1.43601in,1.4887in)-- + (1.46816in,1.47832in)--(1.4999in,1.46767in)-- + (1.53123in,1.45674in)--(1.56215in,1.44554in)-- + (1.59266in,1.43406in)--(1.62277in,1.42232in)-- + (1.65246in,1.4103in)--(1.68174in,1.39801in)-- + (1.71062in,1.38545in)--(1.73909in,1.37261in)-- + (1.76715in,1.3595in)--(1.7948in,1.34612in)--(1.82204in,1.33247in)-- + (1.84888in,1.31855in)--(1.87531in,1.30436in)-- + (1.90134in,1.28989in)--(1.92695in,1.27516in)-- + (1.95217in,1.26015in)--(1.97697in,1.24488in)-- + (2.00138in,1.22933in)--(2.02537in,1.21352in)-- + (2.04896in,1.19743in)--(2.07215in,1.18107in)-- + (2.09493in,1.16445in)--(2.11731in,1.14756in)-- + (2.13929in,1.13039in)--(2.16087in,1.11296in)-- + (2.18204in,1.09526in)--(2.2028in,1.07729in)-- + (2.22317in,1.05906in)--(2.24314in,1.04055in)-- + (2.2627in,1.02178in)--(2.28187in,1.00275in)-- + (2.30063in,0.983441in)--(2.31899in,0.963869in)-- + (2.33696in,0.944032in)--(2.35452in,0.923928in)-- + (2.37169in,0.903558in)--(2.38845in,0.882923in)-- + (2.40482in,0.862023in)--(2.4208in,0.840857in)-- + (2.43637in,0.819428in)--(2.45155in,0.797734in)-- + (2.46634in,0.775776in)--(2.48073in,0.753555in)-- + (2.49472in,0.73107in)--(2.50832in,0.708322in)-- + (2.52152in,0.685312in)--(2.53434in,0.66204in)-- + (2.54676in,0.638506in)--(2.55878in,0.61471in)--(2.57042in,0.590653in); +\pgftext[at={\pgfpoint{1.15591in}{0.277248in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$P$}}} +\filldraw[color=rgb_000000] (1.23258in,0.405039in) circle(0.0207555in); +\pgftext[at={\pgfpoint{1.91487in}{1.71611in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$u=1$}}} +\pgftext[at={\pgfpoint{2.51242in}{1.47885in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$u=2$}}} +\pgftext[at={\pgfpoint{2.97401in}{1.15096in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$u=3$}}} +\pgftext[at={\pgfpoint{1.34383in}{0.0883968in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$v=1$}}} +\pgftext[at={\pgfpoint{2.0241in}{0.375in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$v=2$}}} +\pgftext[at={\pgfpoint{2.62577in}{0.590653in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$v=3$}}} +\end{tikzpicture} diff --git a/36114-t/images/sources/087.xp b/36114-t/images/sources/087.xp new file mode 100644 index 0000000..33695e6 --- /dev/null +++ b/36114-t/images/sources/087.xp @@ -0,0 +1,50 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +P f(double u, double v) +{ + double x(u*(1 - 0.25*exp(-v)) + 0.25*v*v), + y(v*(1 + 0.125*exp(0.5*u)) - 0.2*u*u); + return P(x + y, y - x); +} + +const double MAX(2), maxx(1.25); + +domain R(P(-1,-1), P(maxx,1), mesh(60,60)); + +int main() +{ + picture(P(-MAX,-MAX), P(MAX,MAX), "3 x 2in"); + + begin(); + bold(); + + double mu1(-0.8), mu2(-0.1), mu3(0.6), + mv1(-0.6), mv2(0), mv3(0.5); + + P u1(f(mu1, 1)), u2(f(mu2, 1)), u3(f(mu3, 1)), + v1(f(maxx, mv1)), v2(f(maxx, mv2)), v3(f(maxx, mv3)), + O(f(mu3, mv1)); + + plot(f, R.slice1(mu1)); + plot(f, R.slice1(mu2)); + plot(f, R.slice1(mu3)); + + plot(f, R.slice2(mv1)); + plot(f, R.slice2(mv2)); + plot(f, R.slice2(mv3)); + + dot(O, P(-4,-10), "$P$", b); + + label(u1, P(4,0), "$u=1$", r); + label(u2, P(4,0), "$u=2$", r); + label(u3, P(4,0), "$u=3$", r); + + label(v1, P(4,0), "$v=1$", r); + label(v2, P(4,0), "$v=2$", r); + label(v3, P(4,0), "$v=3$", r); + + tikz_format(); + end(); +} diff --git a/36114-t/images/sources/127.eepic b/36114-t/images/sources/127.eepic new file mode 100644 index 0000000..0a5c284 --- /dev/null +++ b/36114-t/images/sources/127.eepic @@ -0,0 +1,341 @@ +%% Generated from 127.xp on Wed May 11 11:13:40 EDT 2011 by +%% ePiX-1.2.4 +%% +%% Cartesian bounding box: [0,1] x [0,3] +%% Actual size: 1 x 3in +%% Figure offset: left by 0in, down by 0in +%% +%% usepackages tikz +%% +\xdefinecolor{rgb_000000}{rgb}{0,0,0}% +\begin{tikzpicture} +\pgfsetlinewidth{0.4pt} +\useasboundingbox (0in,0in) rectangle (1in,3in); +\pgfsetlinewidth{0.8pt} +\draw (0.25in,1in)--(0.4375in,0.953125in)--(0.625in,0.90625in); +\draw (0.125in,-0.03125in)--(0.134375in,0.00625in); +\draw (0.153125in,0.08125in)--(0.1625in,0.11875in); +\draw (0.1625in,0.11875in)--(0.171875in,0.15625in); +\draw (0.190625in,0.23125in)--(0.2in,0.26875in); +\draw (0.2in,0.26875in)--(0.209375in,0.30625in); +\draw (0.228125in,0.38125in)--(0.2375in,0.41875in); +\draw (0.2375in,0.41875in)--(0.246875in,0.45625in); +\draw (0.265625in,0.53125in)--(0.275in,0.56875in); +\draw (0.275in,0.56875in)--(0.284375in,0.60625in); +\draw (0.303125in,0.68125in)--(0.3125in,0.71875in); +\draw (0.3125in,0.71875in)--(0.321875in,0.75625in); +\draw (0.340625in,0.83125in)--(0.35in,0.86875in); +\draw (0.35in,0.86875in)--(0.359375in,0.90625in); +\draw (0.378125in,0.98125in)--(0.3875in,1.01875in); +\draw (0.3875in,1.01875in)--(0.396875in,1.05625in); +\draw (0.415625in,1.13125in)--(0.425in,1.16875in); +\draw (0.425in,1.16875in)--(0.434375in,1.20625in); +\draw (0.453125in,1.28125in)--(0.4625in,1.31875in); +\draw (0.4625in,1.31875in)--(0.471875in,1.35625in); +\draw (0.490625in,1.43125in)--(0.5in,1.46875in); +\draw (0.5in,1.46875in)--(0.509375in,1.50625in); +\draw (0.528125in,1.58125in)--(0.5375in,1.61875in); +\draw (0.5375in,1.61875in)--(0.546875in,1.65625in); +\draw (0.565625in,1.73125in)--(0.575in,1.76875in); +\draw (0.125in,-0.03125in)--(0.140625in,-0.00195312in); +\draw (0.171875in,0.0566406in)--(0.1875in,0.0859375in); +\draw (0.1875in,0.0859375in)--(0.203125in,0.115234in); +\draw (0.234375in,0.173828in)--(0.25in,0.203125in); +\draw (0.25in,0.203125in)--(0.265625in,0.232422in); +\draw (0.296875in,0.291016in)--(0.3125in,0.320312in); +\draw (0.3125in,0.320312in)--(0.328125in,0.349609in); +\draw (0.359375in,0.408203in)--(0.375in,0.4375in); +\draw (0.375in,0.4375in)--(0.390625in,0.466797in); +\draw (0.421875in,0.525391in)--(0.4375in,0.554688in); +\draw (0.4375in,0.554688in)--(0.453125in,0.583984in); +\draw (0.484375in,0.642578in)--(0.5in,0.671875in); +\draw (0.5in,0.671875in)--(0.515625in,0.701172in); +\draw (0.546875in,0.759766in)--(0.5625in,0.789062in); +\draw (0.5625in,0.789062in)--(0.578125in,0.818359in); +\draw (0.609375in,0.876953in)--(0.625in,0.90625in); +\draw (0.625in,0.90625in)--(0.634375in,0.94375in); +\draw (0.653125in,1.01875in)--(0.6625in,1.05625in); +\draw (0.6625in,1.05625in)--(0.671875in,1.09375in); +\draw (0.690625in,1.16875in)--(0.7in,1.20625in); +\draw (0.7in,1.20625in)--(0.709375in,1.24375in); +\draw (0.728125in,1.31875in)--(0.7375in,1.35625in); +\draw (0.7375in,1.35625in)--(0.746875in,1.39375in); +\draw (0.765625in,1.46875in)--(0.775in,1.50625in); +\draw (0.775in,1.50625in)--(0.784375in,1.54375in); +\draw (0.803125in,1.61875in)--(0.8125in,1.65625in); +\draw (0.8125in,1.65625in)--(0.821875in,1.69375in); +\draw (0.840625in,1.76875in)--(0.85in,1.80625in); +\draw (0.85in,1.80625in)--(0.859375in,1.84375in); +\draw (0.878125in,1.91875in)--(0.8875in,1.95625in); +\draw (0.8875in,1.95625in)--(0.896875in,1.99375in); +\draw (0.915625in,2.06875in)--(0.925in,2.10625in); +\draw (0.925in,2.10625in)--(0.934375in,2.14375in); +\draw (0.953125in,2.21875in)--(0.9625in,2.25625in); +\draw (0.9625in,2.25625in)--(0.971875in,2.29375in); +\draw (0.990625in,2.36875in)--(1in,2.40625in); +\draw (1in,2.40625in)--(1.00937in,2.44375in); +\draw (1.02812in,2.51875in)--(1.0375in,2.55625in); +\draw (1.0375in,2.55625in)--(1.04688in,2.59375in); +\draw (1.06562in,2.66875in)--(1.075in,2.70625in); +\draw (0.275in,0.56875in)--(0.275625in,0.57125in); +\draw (0.276875in,0.57625in)--(0.2775in,0.57875in); +\pgfsetfillcolor{rgb_000000} +\draw [fill](0.274144in,0.565326in)--(0.284212in,0.548546in)-- + (0.2775in,0.57875in)--(0.257364in,0.555258in)--(0.274144in,0.565326in)--cycle; +\draw (0.475in,0.625in)--(0.47625in,0.627344in); +\draw (0.47875in,0.632031in)--(0.48in,0.634375in); +\draw [fill](0.473488in,0.622166in)--(0.479186in,0.603445in)-- + (0.48in,0.634375in)--(0.454768in,0.616468in)--(0.473488in,0.622166in)--cycle; +\draw (1.05in,2.60625in)--(1.05063in,2.60875in); +\draw (1.05187in,2.61375in)--(1.0525in,2.61625in); +\draw [fill](1.04914in,2.60283in)--(1.05921in,2.58605in)-- + (1.0525in,2.61625in)--(1.03236in,2.59276in)--(1.04914in,2.60283in)--cycle; +\pgfsetlinewidth{2pt} +\draw (0.375in,1in)--(0.374957in,1.00164in); +\draw (0.374872in,1.00491in)--(0.374829in,1.00654in); +\draw (0.374829in,1.00654in)--(0.3747in,1.00817in); +\draw (0.374444in,1.01144in)--(0.374315in,1.01307in); +\draw (0.374315in,1.01307in)--(0.374102in,1.01469in); +\draw (0.373675in,1.01793in)--(0.373461in,1.01955in); +\draw (0.373461in,1.01955in)--(0.373163in,1.02116in); +\draw (0.372567in,1.02438in)--(0.372268in,1.02599in); +\draw (0.372268in,1.02599in)--(0.371887in,1.02758in); +\draw (0.371123in,1.03076in)--(0.370741in,1.03235in); +\draw (0.370741in,1.03235in)--(0.370276in,1.03392in); +\draw (0.369347in,1.03706in)--(0.368882in,1.03863in); +\draw (0.368882in,1.03863in)--(0.368336in,1.04017in); +\draw (0.367244in,1.04325in)--(0.366698in,1.0448in); +\draw (0.366698in,1.0448in)--(0.366071in,1.04631in); +\draw (0.364819in,1.04933in)--(0.364193in,1.05084in); +\draw (0.364193in,1.05084in)--(0.363489in,1.05232in); +\draw (0.36208in,1.05527in)--(0.361376in,1.05675in); +\draw (0.361376in,1.05675in)--(0.360595in,1.05819in); +\draw (0.359034in,1.06106in)--(0.358253in,1.0625in); +\draw (0.358253in,1.0625in)--(0.357398in,1.06389in); +\draw (0.355689in,1.06668in)--(0.354834in,1.06808in); +\draw (0.354834in,1.06808in)--(0.353907in,1.06943in); +\draw (0.352054in,1.07212in)--(0.351127in,1.07347in); +\draw (0.351127in,1.07347in)--(0.350131in,1.07477in); +\draw (0.348139in,1.07737in)--(0.347143in,1.07867in); +\draw (0.347143in,1.07867in)--(0.346081in,1.07991in); +\draw (0.343956in,1.0824in)--(0.342893in,1.08364in); +\draw (0.342893in,1.08364in)--(0.341767in,1.08483in); +\draw (0.339515in,1.0872in)--(0.338388in,1.08839in); +\draw (0.338388in,1.08839in)--(0.337202in,1.08951in); +\draw (0.334828in,1.09177in)--(0.333641in,1.09289in); +\draw (0.333641in,1.09289in)--(0.332397in,1.09396in); +\draw (0.329909in,1.09608in)--(0.328665in,1.09714in); +\draw (0.328665in,1.09714in)--(0.327367in,1.09814in); +\draw (0.324771in,1.10013in)--(0.323473in,1.10113in); +\draw (0.323473in,1.10113in)--(0.322125in,1.10205in); +\draw (0.319428in,1.10391in)--(0.31808in,1.10483in); +\draw (0.31808in,1.10483in)--(0.316685in,1.10569in); +\draw (0.313895in,1.1074in)--(0.3125in,1.10825in); +\draw (0.3125in,1.10825in)--(0.311062in,1.10903in); +\draw (0.308187in,1.1106in)--(0.306749in,1.11138in); +\draw (0.306749in,1.11138in)--(0.305272in,1.11208in); +\draw (0.302319in,1.11349in)--(0.300842in,1.11419in); +\draw (0.300842in,1.11419in)--(0.299331in,1.11482in); +\draw (0.296308in,1.11607in)--(0.294796in,1.1167in); +\draw (0.294796in,1.1167in)--(0.293254in,1.11724in); +\draw (0.290169in,1.11834in)--(0.288627in,1.11888in); +\draw (0.288627in,1.11888in)--(0.287058in,1.11935in); +\draw (0.283921in,1.12028in)--(0.282352in,1.12074in); +\draw (0.282352in,1.12074in)--(0.280762in,1.12112in); +\draw (0.27758in,1.12189in)--(0.275989in,1.12227in); +\draw (0.275989in,1.12227in)--(0.27438in,1.12257in); +\draw (0.271163in,1.12316in)--(0.269554in,1.12346in); +\draw (0.269554in,1.12346in)--(0.267932in,1.12367in); +\draw (0.264688in,1.1241in)--(0.263066in,1.12432in); +\draw (0.263066in,1.12432in)--(0.261435in,1.12444in); +\draw (0.258173in,1.1247in)--(0.256542in,1.12483in); +\draw (0.256542in,1.12483in)--(0.254906in,1.12487in); +\draw (0.251635in,1.12496in)--(0.25in,1.125in); +\draw (0.25in,1.125in)--(0.248365in,1.12496in); +\draw (0.245094in,1.12487in)--(0.243458in,1.12483in); +\draw (0.243458in,1.12483in)--(0.241827in,1.1247in); +\draw (0.238565in,1.12444in)--(0.236934in,1.12432in); +\draw (0.236934in,1.12432in)--(0.235312in,1.1241in); +\draw (0.232068in,1.12367in)--(0.230446in,1.12346in); +\draw (0.230446in,1.12346in)--(0.228837in,1.12316in); +\draw (0.22562in,1.12257in)--(0.224011in,1.12227in); +\draw (0.224011in,1.12227in)--(0.22242in,1.12189in); +\draw (0.219238in,1.12112in)--(0.217648in,1.12074in); +\draw (0.217648in,1.12074in)--(0.216079in,1.12028in); +\draw (0.212942in,1.11935in)--(0.211373in,1.11888in); +\draw (0.211373in,1.11888in)--(0.209831in,1.11834in); +\draw (0.206746in,1.11724in)--(0.205204in,1.1167in); +\draw (0.205204in,1.1167in)--(0.203692in,1.11607in); +\draw (0.200669in,1.11482in)--(0.199158in,1.11419in); +\draw (0.199158in,1.11419in)--(0.197681in,1.11349in); +\draw (0.194728in,1.11208in)--(0.193251in,1.11138in); +\draw (0.193251in,1.11138in)--(0.191813in,1.1106in); +\draw (0.188938in,1.10903in)--(0.1875in,1.10825in); +\draw (0.1875in,1.10825in)--(0.186105in,1.1074in); +\draw (0.183315in,1.10569in)--(0.18192in,1.10483in); +\draw (0.18192in,1.10483in)--(0.180572in,1.10391in); +\draw (0.177875in,1.10205in)--(0.176527in,1.10113in); +\draw (0.176527in,1.10113in)--(0.175229in,1.10013in); +\draw (0.172633in,1.09814in)--(0.171335in,1.09714in); +\draw (0.171335in,1.09714in)--(0.170091in,1.09608in); +\draw (0.167603in,1.09396in)--(0.166359in,1.09289in); +\draw (0.166359in,1.09289in)--(0.165172in,1.09177in); +\draw (0.162798in,1.08951in)--(0.161612in,1.08839in); +\draw (0.161612in,1.08839in)--(0.160485in,1.0872in); +\draw (0.158233in,1.08483in)--(0.157107in,1.08364in); +\draw (0.157107in,1.08364in)--(0.156044in,1.0824in); +\draw (0.153919in,1.07991in)--(0.152857in,1.07867in); +\draw (0.152857in,1.07867in)--(0.151861in,1.07737in); +\draw (0.149869in,1.07477in)--(0.148873in,1.07347in); +\draw (0.148873in,1.07347in)--(0.147946in,1.07212in); +\draw (0.146093in,1.06943in)--(0.145166in,1.06808in); +\draw (0.145166in,1.06808in)--(0.144311in,1.06668in); +\draw (0.142602in,1.06389in)--(0.141747in,1.0625in); +\draw (0.141747in,1.0625in)--(0.140966in,1.06106in); +\draw (0.139405in,1.05819in)--(0.138624in,1.05675in); +\draw (0.138624in,1.05675in)--(0.13792in,1.05527in); +\draw (0.136511in,1.05232in)--(0.135807in,1.05084in); +\draw (0.135807in,1.05084in)--(0.135181in,1.04933in); +\draw (0.133929in,1.04631in)--(0.133302in,1.0448in); +\draw (0.133302in,1.0448in)--(0.132756in,1.04325in); +\draw (0.131664in,1.04017in)--(0.131118in,1.03863in); +\draw (0.131118in,1.03863in)--(0.130653in,1.03706in); +\draw (0.129724in,1.03392in)--(0.129259in,1.03235in); +\draw (0.129259in,1.03235in)--(0.128877in,1.03076in); +\draw (0.128113in,1.02758in)--(0.127732in,1.02599in); +\draw (0.127732in,1.02599in)--(0.127433in,1.02438in); +\draw (0.126837in,1.02116in)--(0.126539in,1.01955in); +\draw (0.126539in,1.01955in)--(0.126325in,1.01793in); +\draw (0.125898in,1.01469in)--(0.125685in,1.01307in); +\draw (0.125685in,1.01307in)--(0.125556in,1.01144in); +\draw (0.1253in,1.00817in)--(0.125171in,1.00654in); +\draw (0.125171in,1.00654in)--(0.125128in,1.00491in); +\draw (0.125043in,1.00164in)--(0.125in,1in); +\draw (0.125in,1in)--(0.125043in,0.998365in); +\draw (0.125128in,0.995094in)--(0.125171in,0.993458in); +\draw (0.125171in,0.993458in)--(0.1253in,0.991827in); +\draw (0.125556in,0.988565in)--(0.125685in,0.986934in); +\draw (0.125685in,0.986934in)--(0.125898in,0.985312in); +\draw (0.126325in,0.982068in)--(0.126539in,0.980446in); +\draw (0.126539in,0.980446in)--(0.126837in,0.978837in); +\draw (0.127433in,0.97562in)--(0.127732in,0.974011in); +\draw (0.127732in,0.974011in)--(0.128113in,0.97242in); +\draw (0.128877in,0.969238in)--(0.129259in,0.967648in); +\draw (0.129259in,0.967648in)--(0.129724in,0.966079in); +\draw (0.130653in,0.962942in)--(0.131118in,0.961373in); +\draw (0.131118in,0.961373in)--(0.131664in,0.959831in); +\draw (0.132756in,0.956746in)--(0.133302in,0.955204in); +\draw (0.133302in,0.955204in)--(0.133929in,0.953692in); +\draw (0.135181in,0.950669in)--(0.135807in,0.949158in); +\draw (0.135807in,0.949158in)--(0.136511in,0.947681in); +\draw (0.13792in,0.944728in)--(0.138624in,0.943251in); +\draw (0.138624in,0.943251in)--(0.139405in,0.941813in); +\draw (0.140966in,0.938938in)--(0.141747in,0.9375in); +\draw (0.141747in,0.9375in)--(0.142602in,0.936105in); +\draw (0.144311in,0.933315in)--(0.145166in,0.93192in); +\draw (0.145166in,0.93192in)--(0.146093in,0.930572in); +\draw (0.147946in,0.927875in)--(0.148873in,0.926527in); +\draw (0.148873in,0.926527in)--(0.149869in,0.925229in); +\draw (0.151861in,0.922633in)--(0.152857in,0.921335in); +\draw (0.152857in,0.921335in)--(0.153919in,0.920091in); +\draw (0.156044in,0.917603in)--(0.157107in,0.916359in); +\draw (0.157107in,0.916359in)--(0.158233in,0.915172in); +\draw (0.160485in,0.912798in)--(0.161612in,0.911612in); +\draw (0.161612in,0.911612in)--(0.162798in,0.910485in); +\draw (0.165172in,0.908233in)--(0.166359in,0.907107in); +\draw (0.166359in,0.907107in)--(0.167603in,0.906044in); +\draw (0.170091in,0.903919in)--(0.171335in,0.902857in); +\draw (0.171335in,0.902857in)--(0.172633in,0.901861in); +\draw (0.175229in,0.899869in)--(0.176527in,0.898873in); +\draw (0.176527in,0.898873in)--(0.177875in,0.897946in); +\draw (0.180572in,0.896093in)--(0.18192in,0.895166in); +\draw (0.18192in,0.895166in)--(0.183315in,0.894311in); +\draw (0.186105in,0.892602in)--(0.1875in,0.891747in); +\draw (0.1875in,0.891747in)--(0.188938in,0.890966in); +\draw (0.191813in,0.889405in)--(0.193251in,0.888624in); +\draw (0.193251in,0.888624in)--(0.194728in,0.88792in); +\draw (0.197681in,0.886511in)--(0.199158in,0.885807in); +\draw (0.199158in,0.885807in)--(0.200669in,0.885181in); +\draw (0.203692in,0.883929in)--(0.205204in,0.883302in); +\draw (0.205204in,0.883302in)--(0.206746in,0.882756in); +\draw (0.209831in,0.881664in)--(0.211373in,0.881118in); +\draw (0.211373in,0.881118in)--(0.212942in,0.880653in); +\draw (0.216079in,0.879724in)--(0.217648in,0.879259in); +\draw (0.217648in,0.879259in)--(0.219238in,0.878877in); +\draw (0.22242in,0.878113in)--(0.224011in,0.877732in); +\draw (0.224011in,0.877732in)--(0.22562in,0.877433in); +\draw (0.228837in,0.876837in)--(0.230446in,0.876539in); +\draw (0.230446in,0.876539in)--(0.232068in,0.876325in); +\draw (0.235312in,0.875898in)--(0.236934in,0.875685in); +\draw (0.236934in,0.875685in)--(0.238565in,0.875556in); +\draw (0.241827in,0.8753in)--(0.243458in,0.875171in); +\draw (0.243458in,0.875171in)--(0.245094in,0.875128in); +\draw (0.248365in,0.875043in)--(0.25in,0.875in); +\draw (0.25in,0.875in)--(0.251635in,0.875043in); +\draw (0.254906in,0.875128in)--(0.256542in,0.875171in); +\draw (0.256542in,0.875171in)--(0.258173in,0.8753in); +\draw (0.261435in,0.875556in)--(0.263066in,0.875685in); +\draw (0.263066in,0.875685in)--(0.264688in,0.875898in); +\draw (0.267932in,0.876325in)--(0.269554in,0.876539in); +\draw (0.269554in,0.876539in)--(0.271163in,0.876837in); +\draw (0.27438in,0.877433in)--(0.275989in,0.877732in); +\draw (0.275989in,0.877732in)--(0.27758in,0.878113in); +\draw (0.280762in,0.878877in)--(0.282352in,0.879259in); +\draw (0.282352in,0.879259in)--(0.283921in,0.879724in); +\draw (0.287058in,0.880653in)--(0.288627in,0.881118in); +\draw (0.288627in,0.881118in)--(0.290169in,0.881664in); +\draw (0.293254in,0.882756in)--(0.294796in,0.883302in); +\draw (0.294796in,0.883302in)--(0.296308in,0.883929in); +\draw (0.299331in,0.885181in)--(0.300842in,0.885807in); +\draw (0.300842in,0.885807in)--(0.302319in,0.886511in); +\draw (0.305272in,0.88792in)--(0.306749in,0.888624in); +\draw (0.306749in,0.888624in)--(0.308187in,0.889405in); +\draw (0.311062in,0.890966in)--(0.3125in,0.891747in); +\draw (0.3125in,0.891747in)--(0.313895in,0.892602in); +\draw (0.316685in,0.894311in)--(0.31808in,0.895166in); +\draw (0.31808in,0.895166in)--(0.319428in,0.896093in); +\draw (0.322125in,0.897946in)--(0.323473in,0.898873in); +\draw (0.323473in,0.898873in)--(0.324771in,0.899869in); +\draw (0.327367in,0.901861in)--(0.328665in,0.902857in); +\draw (0.328665in,0.902857in)--(0.329909in,0.903919in); +\draw (0.332397in,0.906044in)--(0.333641in,0.907107in); +\draw (0.333641in,0.907107in)--(0.334828in,0.908233in); +\draw (0.337202in,0.910485in)--(0.338388in,0.911612in); +\draw (0.338388in,0.911612in)--(0.339515in,0.912798in); +\draw (0.341767in,0.915172in)--(0.342893in,0.916359in); +\draw (0.342893in,0.916359in)--(0.343956in,0.917603in); +\draw (0.346081in,0.920091in)--(0.347143in,0.921335in); +\draw (0.347143in,0.921335in)--(0.348139in,0.922633in); +\draw (0.350131in,0.925229in)--(0.351127in,0.926527in); +\draw (0.351127in,0.926527in)--(0.352054in,0.927875in); +\draw (0.353907in,0.930572in)--(0.354834in,0.93192in); +\draw (0.354834in,0.93192in)--(0.355689in,0.933315in); +\draw (0.357398in,0.936105in)--(0.358253in,0.9375in); +\draw (0.358253in,0.9375in)--(0.359034in,0.938938in); +\draw (0.360595in,0.941813in)--(0.361376in,0.943251in); +\draw (0.361376in,0.943251in)--(0.36208in,0.944728in); +\draw (0.363489in,0.947681in)--(0.364193in,0.949158in); +\draw (0.364193in,0.949158in)--(0.364819in,0.950669in); +\draw (0.366071in,0.953692in)--(0.366698in,0.955204in); +\draw (0.366698in,0.955204in)--(0.367244in,0.956746in); +\draw (0.368336in,0.959831in)--(0.368882in,0.961373in); +\draw (0.368882in,0.961373in)--(0.369347in,0.962942in); +\draw (0.370276in,0.966079in)--(0.370741in,0.967648in); +\draw (0.370741in,0.967648in)--(0.371123in,0.969238in); +\draw (0.371887in,0.97242in)--(0.372268in,0.974011in); +\draw (0.372268in,0.974011in)--(0.372567in,0.97562in); +\draw (0.373163in,0.978837in)--(0.373461in,0.980446in); +\draw (0.373461in,0.980446in)--(0.373675in,0.982068in); +\draw (0.374102in,0.985312in)--(0.374315in,0.986934in); +\draw (0.374315in,0.986934in)--(0.374444in,0.988565in); +\draw (0.3747in,0.991827in)--(0.374829in,0.993458in); +\draw (0.374829in,0.993458in)--(0.374872in,0.995094in); +\draw (0.374957in,0.998365in)--(0.375in,1in); +\pgftext[at={\pgfpoint{0.097326in}{1in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}$S$}}} +\pgftext[at={\pgfpoint{0.097326in}{-0.058924in}}] {\makebox(0,0)[tr]{\hbox{\color{rgb_000000}$E$}}} +\filldraw[color=rgb_000000] (0.125in,-0.03125in) circle(0.0207555in); +\pgftext[at={\pgfpoint{0.219652in}{0.56875in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}$D_{1}$}}} +\pgftext[at={\pgfpoint{0.530348in}{0.625in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$D_{2}$}}} +\pgftext[at={\pgfpoint{1.10535in}{2.60625in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$D_{1}$}}} +\pgftext[at={\pgfpoint{0.475in}{1.10312in}}] {\makebox(0,0)[c]{\rotatebox{-14.0362}{\hbox{\color{rgb_000000}$\overbrace{\rule{0.35in}{0pt}}^{\mbox{\;$\Delta$}}$}}}} +\end{tikzpicture} diff --git a/36114-t/images/sources/127.xp b/36114-t/images/sources/127.xp new file mode 100644 index 0000000..9434273 --- /dev/null +++ b/36114-t/images/sources/127.xp @@ -0,0 +1,49 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(0,0), P(1,3), "1 x 3in"); + + begin(); + bold(); + arrow_inset(0.5); + arrow_ratio(2); + arrow_width(2); + double rad(0.125); + + P dir(0.25, 1), perp(-rad*J(dir)), sun(dir), earth(perp), bend(sun + 3*perp), + D1a(earth + 0.6*dir), D2(0.3*earth + 0.7*bend), D1b(bend + 1.7*dir); + + double th(Atan2(perp.x2(), perp.x1())); + + line(sun, sun + 3*perp); + + dashed(); + dash_size(12); + line(earth, earth + 1.8*dir); + line(earth, bend); + line(bend, bend + 1.8*dir); + + arrow(D1a, D1a + 0.01*dir); + arrow(D2, D2 + 0.01*(bend - earth)); + arrow(D1b, D1b + 0.01*dir); + + pen(2); + circle(sun, rad); + + label(sun - P(rad, 0), P(-2,0), "$S$", l); + dot(earth, P(-2,-2), "$E$", bl); + + label(D1a, P(-4,0), "$D_{1}$", l); + label(D2, P( 4,0), "$D_{2}$", r); + label(D1b, P( 4,0), "$D_{1}$", r); + + label_angle(th); + label(sun + 0.15*dir + 1.5*perp, + "$\\overbrace{\\rule{0.35in}{0pt}}^{\\mbox{\\;$\\Delta$}}$"); + + tikz_format(); + end(); +} diff --git a/36114-t/old/36114-t.tex b/36114-t/old/36114-t.tex new file mode 100644 index 0000000..6debb02 --- /dev/null +++ b/36114-t/old/36114-t.tex @@ -0,0 +1,7028 @@ +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % +% % +% The Project Gutenberg EBook of Relativity: The Special and the General % +% Theory, by Albert Einstein % +% % +% This eBook is for the use of anyone anywhere at no cost and with % +% almost no restrictions whatsoever. You may copy it, give it away or % +% re-use it under the terms of the Project Gutenberg License included % +% with this eBook or online at www.gutenberg.org % +% % +% % +% Title: Relativity: The Special and the General Theory % +% A Popular Exposition, 3rd ed. % +% % +% Author: Albert Einstein % +% % +% Translator: Robert W. Lawson % +% % +% Release Date: May 15, 2011 [EBook #36114] % +% % +% Language: English % +% % +% Character set encoding: ISO-8859-1 % +% % +% *** START OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** % +% % +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % + +\def\ebook{36114} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% +%% Packages and substitutions: %% +%% %% +%% book: Required. %% +%% inputenc: Latin-1 text encoding. Required. %% +%% %% +%% ifthen: Logical conditionals. Required. %% +%% %% +%% amsmath: AMS mathematics enhancements. Required. %% +%% amssymb: Additional mathematical symbols. Required. %% +%% %% +%% alltt: Fixed-width font environment. Required. %% +%% array: Enhanced tabular features. Required. %% +%% %% +%% perpage: Start footnote numbering on each page. Required. %% +%% %% +%% multicol: Twocolumn environment for index. Required. %% +%% makeidx: Indexing. Required. %% +%% %% +%% caption: Caption customization. Required. %% +%% graphicx: Standard interface for graphics inclusion. Required. %% +%% wrapfig: Illustrations surrounded by text. Required. %% +%% %% +%% calc: Length calculations. Required. %% +%% %% +%% fancyhdr: Enhanced running headers and footers. Required. %% +%% %% +%% geometry: Enhanced page layout package. Required. %% +%% hyperref: Hypertext embellishments for pdf output. Required. %% +%% %% +%% %% +%% Producer's Comments: %% +%% %% +%% OCR text for this ebook was obtained on May 7, 2011, from %% +%% http://www.archive.org/details/relativitythespe00einsuoft. %% +%% %% +%% The Methuen book catalogue from the original has been omitted. %% +%% %% +%% Minor changes to the original are noted in this file in three %% +%% ways: %% +%% 1. \Change{}{} for typographical corrections, showing %% +%% original and replacement text side-by-side. %% +%% 2. \Add{} for inconsistent/missing punctuation. %% +%% 3. [** TN: Note]s for lengthier or stylistic comments. %% +%% \Add is implemented in terms of \Change, so redefining \Change %% +%% will "restore" typographical errors in the original. %% +%% %% +%% %% +%% Compilation Flags: %% +%% %% +%% The following behavior may be controlled by boolean flags. %% +%% %% +%% ForPrinting (false by default): %% +%% If true, compile a print-optimized PDF file: Taller text block,%% +%% two-sided layout, US Letter paper, black hyperlinks. Default: %% +%% screen optimized file (one-sided layout, blue hyperlinks). %% +%% %% +%% %% +%% Things to Check: %% +%% %% +%% %% +%% Spellcheck: .................................. OK %% +%% %% +%% lacheck: ..................................... OK %% +%% Numerous false positives from commented code %% +%% %% +%% PDF pages: 154 (if ForPrinting set to false) %% +%% PDF page size: 4.75 x 7" %% +%% PDF bookmarks: created, point to ToC entries %% +%% PDF document info: filled in %% +%% Images: 5 pdf diagrams %% +%% %% +%% Summary of log file: %% +%% * No over- or under-full boxes. %% +%% %% +%% Compile History: %% +%% %% +%% May, 2011: adhere (Andrew D. Hwang) %% +%% texlive2007, GNU/Linux %% +%% %% +%% Command block: %% +%% %% +%% pdflatex x3 %% +%% makeindex %% +%% pdflatex x3 %% +%% %% +%% %% +%% May 2011: pglatex. %% +%% Compile this project with: %% +%% pdflatex 36114-t.tex ..... THREE times %% +%% makeindex 36114-t.idx %% +%% pdflatex 36114-t.tex ..... THREE times %% +%% %% +%% pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %% +%% %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\listfiles +\documentclass[12pt]{book}[2005/09/16] + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[latin1]{inputenc}[2006/05/05] + +\usepackage{ifthen}[2001/05/26] %% Logical conditionals + +\usepackage{amsmath}[2000/07/18] %% Displayed equations +\usepackage{amssymb}[2002/01/22] %% and additional symbols + +\usepackage{alltt}[1997/06/16] %% boilerplate, credits, license +\usepackage{array}[2005/08/23] %% extended array/tabular features + +\usepackage{perpage}[2006/07/15] + +\usepackage{multicol}[2006/05/18] +\usepackage{makeidx}[2000/03/29] + +\usepackage[font=footnotesize,labelformat=empty]{caption}[2007/01/07] +\usepackage{graphicx}[1999/02/16]%% For diagrams +\usepackage{wrapfig}[2003/01/31] %% and wrapping text around them + +\usepackage{calc}[2005/08/06] + +% for running heads +\usepackage{fancyhdr} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%% Interlude: Set up PRINTING (default) or SCREEN VIEWING %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% ForPrinting=true false (default) +% Asymmetric margins Symmetric margins +% 1 : 1.62 text block aspect ratio 3 : 4 text block aspect ratio +% Black hyperlinks Blue hyperlinks +% Start major marker pages recto No blank verso pages +% +% Chapter-like ``Sections'' start both recto and verso in the scanned +% book. This behavior has been retained. +\newboolean{ForPrinting} + +%% UNCOMMENT the next line for a PRINT-OPTIMIZED VERSION of the text %% +%\setboolean{ForPrinting}{true} + +%% Initialize values to ForPrinting=false +\newcommand{\Margins}{hmarginratio=1:1} % Symmetric margins +\newcommand{\HLinkColor}{blue} % Hyperlink color +\newcommand{\PDFPageLayout}{SinglePage} +\newcommand{\TransNote}{Transcriber's Note} +\newcommand{\TransNoteCommon}{% + The camera-quality files for this public-domain ebook may be + downloaded \textit{gratis} at + \begin{center} + \texttt{www.gutenberg.org/ebooks/\ebook}. + \end{center} + + This ebook was produced using OCR text provided by the University of + Toronto Robarts Library through the Internet Archive. + \bigskip + + Minor typographical corrections and presentational changes have been + made without comment. + \bigskip +} + +\newcommand{\TransNoteText}{% + \TransNoteCommon + + This PDF file is optimized for screen viewing, but may easily be + recompiled for printing. Please consult the preamble of the \LaTeX\ + source file for instructions and other particulars. +} +%% Re-set if ForPrinting=true +\ifthenelse{\boolean{ForPrinting}}{% + \renewcommand{\Margins}{hmarginratio=2:3} % Asymmetric margins + \renewcommand{\HLinkColor}{black} % Hyperlink color + \renewcommand{\PDFPageLayout}{TwoPageRight} + \renewcommand{\TransNote}{Transcriber's Note} + \renewcommand{\TransNoteText}{% + \TransNoteCommon + + This PDF file is optimized for printing, but may easily be + recompiled for screen viewing. Please consult the preamble + of the \LaTeX\ source file for instructions and other particulars. + } +}{% If ForPrinting=false, don't skip to recto + \renewcommand{\cleardoublepage}{\clearpage} +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%% End of PRINTING/SCREEN VIEWING code; back to packages %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\ifthenelse{\boolean{ForPrinting}}{% + \setlength{\paperwidth}{8.5in}% + \setlength{\paperheight}{11in}% +% ~1:1.62 + \usepackage[body={4.5in,7.3in},\Margins]{geometry}[2002/07/08] +}{% + \setlength{\paperwidth}{4.75in}% + \setlength{\paperheight}{7in}% + \raggedbottom +% ~3:4 + \usepackage[body={4.5in,6in},\Margins,includeheadfoot]{geometry}[2002/07/08] +} + +\providecommand{\ebook}{00000} % Overridden during white-washing +\usepackage[pdftex, + hyperref, + hyperfootnotes=false, + pdftitle={The Project Gutenberg eBook \#\ebook: Relativity}, + pdfauthor={Albert Einstein}, + pdfkeywords={University of Toronto, The Internet Archive, Andrew D. Hwang}, + pdfstartview=Fit, % default value + pdfstartpage=1, % default value + pdfpagemode=UseNone, % default value + bookmarks=true, % default value + linktocpage=false, % default value + pdfpagelayout=\PDFPageLayout, + pdfdisplaydoctitle, + pdfpagelabels=true, + bookmarksopen=true, + bookmarksopenlevel=-1, + colorlinks=true, + linkcolor=\HLinkColor]{hyperref}[2007/02/07] + + +%%%% Fixed-width environment to format PG boilerplate %%%% +\newenvironment{PGtext}{% +\begin{alltt} +\fontsize{8.1}{9}\ttfamily\selectfont}% +{\end{alltt}} + +%% No hrule in page header +\renewcommand{\headrulewidth}{0pt} + +% Top-level footnote numbers restart on each page +\MakePerPage{footnote} + +% Running heads +\newcommand{\FlushRunningHeads}{\clearpage\fancyhf{}\cleardoublepage} +\newcommand{\InitRunningHeads}{% + \setlength{\headheight}{15pt} + \pagestyle{fancy} + \thispagestyle{plain} + \ifthenelse{\boolean{ForPrinting}} + {\fancyhead[RO,LE]{\thepage}} + {\fancyhead[R]{\thepage}} +} + +\newcommand{\SetOddHead}[1]{% + \fancyhead[CO]{\textbf{\MakeUppercase{#1}}} +} + +\newcommand{\SetEvenHead}[1]{% + \fancyhead[CE]{\textbf{\MakeUppercase{#1}}} +} + +\newcommand{\BookMark}[2]{\phantomsection\pdfbookmark[#1]{#2}{#2}} + +% ToC formatting +\AtBeginDocument{\renewcommand{\contentsname}% + {\protect\thispagestyle{plain}% + \protect\centering\normalfont\large\textbf{CONTENTS}}} + +\newcommand{\ToCFont}{\centering\normalfont\normalsize\scshape} +\newcommand{\TableofContents}{% + \FlushRunningHeads + \InitRunningHeads + \SetOddHead{Contents} + \BookMark{0}{Contents} + \tableofcontents +} + +% For internal bookkeeping +\newcommand{\ToCAnchor}{} + +%\ToCLine[type]{<label>}{Title}{xref} +\newcommand{\ToCLine}[4][chapter]{% + \label{toc:#4}% + \ifthenelse{\not\equal{\pageref{toc:#4}}{\ToCAnchor}}{% + \renewcommand{\ToCAnchor}{\pageref{toc:#4}}% + \noindent\makebox[\textwidth][r]{\hfill\scriptsize PAGE}\\% + }{}% + \settowidth{\TmpLen}{\;\pageref{#4}}% + \noindent\strut\parbox[b]{\textwidth-\TmpLen}{\small% + \ifthenelse{\not\equal{#2}{}}{% Write unit number at start of line + \ifthenelse{\equal{#1}{appendix}}{% + \settowidth{\TmpLen}{III.}% Widest appendix number + }{% + \settowidth{\TmpLen}{XXVIII.}% Widest chapter number + } + \makebox[\TmpLen][r]{#2}\hspace{0.5em}% + }{}% Empty second argument => no unit number + \raggedright\hangindent6em #3\dotfill}% + \makebox[\TmpLen][r]{\pageref{#4}}% +} + +% Index formatting +\makeindex +\makeatletter +\renewcommand{\@idxitem}{\par\hangindent 30\p@\global\let\idxbrk\nobreak} +\renewcommand\subitem{\idxbrk\@idxitem --- \let\idxbrk\relax} +\renewcommand\subsubitem{\idxbrk\@idxitem --- --- \let\idxbrk\relax} +\renewcommand{\indexspace}{\par\penalty-3000 \vskip 10pt plus5pt minus3pt\relax} + +\renewenvironment{theindex}{% + \setlength\columnseprule{0.5pt}\setlength\columnsep{18pt}% + \cleardoublepage + \phantomsection + \label{index} + \addtocontents{toc}{\ToCLine{}{\textsc{Index}}{index}} + \SetOddHead{Index} + \BookMark{0}{Index} + \begin{multicols}{2}[\SectTitle{Index}\small]% ** N.B. font size + \setlength\parindent{0pt}\setlength\parskip{0pt plus 0.3pt}% + \thispagestyle{plain}\let\item\@idxitem\raggedright% + }{% + \end{multicols}\FlushRunningHeads +} +\makeatother + +% Allows \Part to communicate with \Chapter +\newboolean{StartPart} +\setboolean{StartPart}{false} + +\newcommand{\SectTitle}[2][\large]{% + \section*{\centering#1\MakeUppercase{#2}} +} +\newcommand{\SectSubtitle}[2][\normalsize]{% + \subsection*{\centering#1\MakeUppercase{#2}} +} + +\newcommand{\Part}[3]{% + \setboolean{StartPart}{true} + \ifthenelse{\equal{#1}{I}}{% + \mainmatter + \begin{center} + \textbf{\LARGE RELATIVITY} + \end{center} + }{% + \FlushRunningHeads + }% + \InitRunningHeads + \BookMark{-1}{Part #1. #2} + \label{part:#1} + \SetEvenHead{Relativity} + \SetOddHead{#3} + \addtocontents{toc}{\protect\section*{\protect\ToCFont PART #1}} + \addtocontents{toc}{\protect\subsection*{\protect\ToCFont #2}} + \SectTitle[\Large]{Part #1} + \SectSubtitle{#2} + \bigskip +} + +%\Chapter[PDF name]{Number.}{Heading title} +\newcommand{\Chapter}[3][]{% + \ifthenelse{\boolean{StartPart}}{% + \setboolean{StartPart}{false}% + }{% + \newpage + } + \BookMark{0}{#2. #3} + \label{chapter:#2} + \thispagestyle{plain} + \addtocontents{toc}{\ToCLine{#2.}{#3}{chapter:#2}} + \SectTitle{#2} + \SectSubtitle{#3} +} + +\newcommand{\Section}[1]{% + \newpage + \thispagestyle{plain} + \SectTitle{#1} +} + +\newcommand{\Subsection}[2]{% + \subsection*{\centering\normalsize\normalfont(\Item{#1}) \textsc{#2}} + \ifthenelse{\not\equal{#1}{}}{% + \phantomsection + \label{subsection:#1} + \addtocontents{toc}{% + \ToCLine{(\protect\Item{#1})}{#2}{subsection:#1}% + }% + }{}% +} + +\newcommand{\Bibsection}[1]{% + \subsection*{\centering\normalsize\normalfont\textsc{#1}} +} + +\newcommand{\Preface}{% + \FlushRunningHeads + \InitRunningHeads + \SetOddHead{Relativity} + \SetEvenHead{Relativity} + \BookMark{0}{Preface} + \SectTitle{Preface}% +} + +\newcommand{\Appendix}[3]{% + \clearpage + \BookMark{0}{Appendix #1. #2} + \label{appendix:#1} + \thispagestyle{plain} + \SetOddHead{Appendix #1}% + \ifthenelse{\equal{#1}{I}}{% + \addtocontents{toc}{\protect\section*{\protect\ToCFont APPENDICES}} + }{} + \addtocontents{toc}{\ToCLine[appendix]{#1.}{#2 #3}{appendix:#1}} + \SectTitle{Appendix #1} + \subsection*{\centering\normalsize\normalfont% + \MakeUppercase{#2} \small\textsc{#3}} +} + +\newcommand{\Bibliography}[1]{% + \cleardoublepage + \phantomsection + \label{biblio} + \addtocontents{toc}{\ToCLine{}{\textsc{Bibliography}}{biblio}} + \thispagestyle{plain} + \SetOddHead{Bibliography} + \BookMark{0}{Bibliography} + \SectTitle{Bibliography}% + \SectSubtitle{#1}% +} + +\renewenvironment{itemize}{% + \begin{list}{}{\setlength{\topsep}{4pt plus 8pt}% + \setlength{\itemsep}{0pt plus 2pt}% + \setlength{\parsep}{4pt plus 2pt}% + \setlength{\leftmargin}{4em}}}{\end{list}} + +\newenvironment{CenterPage}{% + \thispagestyle{empty}% + \null\vfill% + \begin{center} + }{% + \end{center} + \vfill% +} + +\newenvironment{PubInfo}{% + \newpage + \begin{CenterPage} + \footnotesize + \settowidth{\TmpLen}{\textit{This Translation was first Published}\qquad} + \begin{tabular}{p{\TmpLen}@{\,}c}% + }{% + \end{tabular} + \end{CenterPage} +} + +\newcommand{\PubRow}[2]{% + \textit{#1}\dotfill & \textit{#2} \\ +} + +\newcommand{\Signature}[2][]{% + \setlength{\TmpLen}{\textwidth-2\parindent}% + \bigskip% + \parbox{\TmpLen}{\centering\small#1\hfill#2}% +} + +\newcommand{\Bibitem}[2]{% +\par\noindent\hangindent2\parindent\textit{#1}: #2\medskip% +} + +\newcommand{\ColHead}[3]{% +\multicolumn{#1}{c}{\settowidth{\TmpLen}{#2}% + \parbox[c]{\TmpLen}{\centering#3\medskip}}% +} + +\newcommand{\Input}[2][] + {\ifthenelse{\equal{#1}{}} + {\includegraphics{./images/#2.pdf}} + {\includegraphics[width=#1]{./images/#2.pdf}}% +} + +\newcounter{figno} +\newcommand{\Figure}[2][0.8\textwidth]{% +\begin{figure}[hbt!] + \refstepcounter{figno} + \centering + \Input[#1]{#2} + \caption{\textsc{Fig}.~\thefigno.} + \label{fig:\thefigno} +\end{figure} +} + +\newcommand{\WFigure}[2]{% +\begin{wrapfigure}{o}{#1} + \refstepcounter{figno} + \centering + \Input[#1]{#2} + \caption{\textsc{Fig}.~\thefigno.} + \label{fig:\thefigno} +\end{wrapfigure} +} + +\newcommand{\First}[1]{\textsc{\large #1}} + +% For corrections. +\newcommand{\Change}[2]{#2} +\newcommand{\Add}[1]{\Change{}{#1}} + +\newcommand{\PageSep}[1]{\ignorespaces} +\setlength{\emergencystretch}{1em} + +\newlength{\TmpLen} + +\DeclareInputText{176}{\ifmmode{{}^\circ}\else\textdegree\fi} +\DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi} + +\newcommand{\Tag}[1]{% + \phantomsection + \label{eqn:#1} + \tag*{\ensuremath{#1}} +} + +% and links +\newcommand{\Eqref}[1]{\hyperref[eqn:#1]{\ensuremath{#1}}} +\newcommand{\Figref}[1]{\hyperref[fig:#1]{Fig.~#1}} +\newcommand{\Partref}[1]{\hyperref[part:#1]{Part~#1}} +\newcommand{\Sectionref}[1]{\hyperref[chapter:#1]{Section~#1}} +\newcommand{\Srefno}[1]{\hyperref[chapter:#1]{#1}} +\newcommand{\Appendixref}[1]{\hyperref[appendix:#1]{Appendix~#1}} + +\newcommand{\ie}{\textit{i.e.}} +\newcommand{\eg}{\textit{e.g.}} +\newcommand{\NB}{\textit{N.B.}} +\newcommand{\Item}[1]{\textit{#1}} + +\newcommand{\itema}{(\Item{a})} +\newcommand{\itemb}{(\Item{b})} +\newcommand{\itemc}{(\Item{c})} + +\newcommand{\Z}{\phantom{0}} + +%%%%%%%%%%%%%%%%%%%%%%%% START OF DOCUMENT %%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} +\pagenumbering{Alph} +\pagestyle{empty} +\BookMark{-1}{Front Matter} +%%%% PG BOILERPLATE %%%% +\BookMark{0}{PG Boilerplate} +\begin{center} +\begin{minipage}{\textwidth} +\small +\begin{PGtext} +The Project Gutenberg EBook of Relativity: The Special and the General +Theory, by Albert Einstein + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Relativity: The Special and the General Theory + A Popular Exposition, 3rd ed. + +Author: Albert Einstein + +Translator: Robert W. Lawson + +Release Date: May 15, 2011 [EBook #36114] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** +\end{PGtext} +\end{minipage} +\end{center} +\newpage +%%%% Credits and transcriber's note %%%% +\begin{center} +\begin{minipage}{\textwidth} +\begin{PGtext} +Produced by Andrew D. Hwang. (This ebook was produced using +OCR text generously provided by the University of Toronto +Robarts Library through the Internet Archive.) +\end{PGtext} +\end{minipage} +\end{center} +\vfill + +\begin{minipage}{0.85\textwidth} +\small +\BookMark{0}{Transcriber's Note} +\subsection*{\centering\normalfont\scshape% +\normalsize\MakeLowercase{\TransNote}}% + +\raggedright +\TransNoteText +\end{minipage} +%%%%%%%%%%%%%%%%%%%%%%%%%%% FRONT MATTER %%%%%%%%%%%%%%%%%%%%%%%%%% +\frontmatter +\pagestyle{empty} +\begin{center} +\bfseries \Huge RELATIVITY \\ +\medskip +\normalsize THE SPECIAL \textit{\&} THE GENERAL THEORY \\ +\medskip +\small A POPULAR EXPOSITION +\vfill + +\footnotesize BY \\ +\Large ALBERT EINSTEIN, Ph.D. \\ +\smallskip\normalfont\scriptsize +PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN +\vfill + +\footnotesize AUTHORISED TRANSLATION BY \\ +\normalsize \textbf{ROBERT W. LAWSON, D.Sc.} \\ +\smallskip\scriptsize UNIVERSITY OF SHEFFIELD +\vfill + +\footnotesize WITH FIVE DIAGRAMS \\ +AND A PORTRAIT OF THE AUTHOR +\vfill\vfill + +THIRD EDITION +\vfill\vfill + + +\normalsize\bfseries METHUEN \& CO. LTD. \\ +36 ESSEX STREET W.C. \\ +LONDON +\end{center} +\PageSep{iv} +\begin{PubInfo} +\PubRow{This Translation was first Published}{August 19th 1920} +\PubRow{Second Edition}{September 1920} +\PubRow{Third Edition}{1920} +\end{PubInfo} +\PageSep{v} + + +\Preface + +\First{The} present book is intended, as far as possible, +to give an exact insight into the theory of Relativity +to those readers who, from a general +scientific and philosophical point of view, are interested +in the theory, but who are not conversant with the +mathematical apparatus\footnote + {The mathematical fundaments of the special theory of + relativity are to be found in the original papers of H.~A. Lorentz, + A.~Einstein, H.~Minkowski, published under the title \textit{Das + Relativitätsprinzip} (The Principle of Relativity) in B.~G. + Teubner's collection of monographs \textit{Fortschritte der mathematischen + Wissenschaften} (Advances in the Mathematical + Sciences), also in M.~Laue's exhaustive book \textit{Das Relativitätsprinzip}---published + by Friedr.\ Vieweg \&~Son, Braunschweig. + The general theory of relativity, together with the necessary + parts of the theory of invariants, is dealt with in the author's + book \textit{Die Grundlagen der allgemeinen Relativitätstheorie} (The + Foundations of the General Theory of Relativity) Joh.\ Ambr.\ + Barth,~1916; this book assumes some familiarity with the special + theory of relativity.} +of theoretical physics. The +work presumes a standard of education corresponding +to that of a university matriculation examination, +and, despite the shortness of the book, a fair amount +of patience and force of will on the part of the reader. +The author has spared himself no pains in his endeavour +\PageSep{vi} +to present the main ideas in the simplest and most intelligible +form, and on the whole, in the sequence and connection +in which they actually originated. In the interest +of clearness, it appeared to me inevitable that I should +repeat myself frequently, without paying the slightest +attention to the elegance of the presentation. I adhered +scrupulously to the precept of that brilliant theoretical +physicist L.~Boltzmann, according to whom matters of +elegance ought to be left to the tailor and to the cobbler. +I make no pretence of having withheld from the reader +difficulties which are inherent to the subject. On the +other hand, I have purposely treated the empirical +physical foundations of the theory in a ``step-motherly'' +fashion, so that readers unfamiliar with physics may +not feel like the wanderer who was unable to see the +forest for trees. May the book bring some one a few +happy hours of suggestive thought! + +\Signature[\textit{December}, 1916]{A. EINSTEIN} + + +\SectTitle{Note to the Third Edition} + +\First{In} the present year (1918) an excellent and detailed +manual on the general theory of relativity, written +by H.~Weyl, was published by the firm Julius +Springer (Berlin). This book, entitled \textit{Raum---Zeit---Materie} +(Space---Time---Matter), may be warmly recommended +to mathematicians and physicists. +\PageSep{vii} + + +\Section{Biographical Note} + +\First{Albert Einstein} is the son of German-Jewish +parents. He was born in~1879 in the +town of Ulm, Würtemberg, Germany. His +schooldays were spent in Munich, where he attended +the \textit{Gymnasium} until his sixteenth year. After leaving +school at Munich, he accompanied his parents to Milan, +whence he proceeded to Switzerland six months later +to continue his studies. + +From 1896 to 1900 Albert Einstein studied mathematics +and physics at the Technical High School in +Zurich, as he intended becoming a secondary school +(\textit{Gymnasium}) teacher. For some time afterwards he +was a private tutor, and having meanwhile become +naturalised, he obtained a post as engineer in the Swiss +Patent Office in~1902 which position he occupied till +1909. The main ideas involved in the most important +of Einstein's theories date back to this period. Amongst +these may be mentioned: \textit{The Special Theory of Relativity}, +\textit{Inertia of Energy}, \textit{Theory of the Brownian Movement}, +and the \textit{Quantum-Law of the Emission and Absorption of Light}~(1905). +These were followed some years +\PageSep{viii} +later by the \textit{Theory of the Specific Heat of Solid Bodies}, +and the fundamental idea of the \textit{General Theory of +Relativity}. + +During the interval 1909~to~1911 he occupied the post +of Professor \textit{Extraordinarius} at the University of Zurich, +afterwards being appointed to the University of Prague, +Bohemia, where he remained as Professor \textit{Ordinarius} +until~1912. In the latter year Professor Einstein +accepted a similar chair at the \textit{Polytechnikum}, Zurich, +and continued his activities there until~1914, when he +received a call to the Prussian Academy of Science, +Berlin, as successor to Van't~Hoff. Professor Einstein +is able to devote himself freely to his studies at the +Berlin Academy, and it was here that he succeeded in +completing his work on the \textit{General Theory of Relativity} +(1915--17). Professor Einstein also lectures on various +special branches of physics at the University of Berlin, +and, in addition, he is Director of the Institute for +Physical Research of the \textit{Kaiser Wilhelm Gesellschaft}. + +Professor Einstein has been twice married. His first +wife, whom he married at Berne in~1903, was a fellow-student +from Serbia. There were two sons of this +marriage, both of whom are living in Zurich, the elder +being sixteen years of age. Recently Professor Einstein +married a widowed cousin, with whom he is now living +in Berlin. + +\Signature{R. W. L.} +\PageSep{ix} + +\Section{Translator's Note} + +\First{In} presenting this translation to the English-reading +public, it is hardly necessary for me to +enlarge on the Author's prefatory remarks, except +to draw attention to those additions to the book which +do not appear in the original. + +At my request, Professor Einstein kindly supplied +me with a portrait of himself, by one of Germany's +most celebrated artists. \Appendixref{III}, on ``The +Experimental Confirmation of the General Theory of +Relativity,'' has been written specially for this translation. +Apart from these valuable additions to the book, +I have included a biographical note on the Author, +and, at the end of the book, an Index and a list of +English references to the subject. This list, which is more +suggestive than exhaustive, is intended as a guide to those +readers who wish to pursue the subject farther. + +I desire to tender my best thanks to my colleagues +Professor S.~R. Milner,~D.Sc., and Mr.~W.~E. Curtis, +A.R.C.Sc.,~F.R.A.S., also to my friend Dr.~Arthur +Holmes, A.R.C.Sc.,~F.G.S., of the Imperial College, +for their kindness in reading through the manuscript, +\PageSep{x} +for helpful criticism, and for numerous suggestions. I +owe an expression of thanks also to Messrs.\ Methuen +for their ready counsel and advice, and for the care +they have bestowed on the work during the course of +its publication. + +\Signature{ROBERT W. LAWSON} + +\noindent\textsc{The Physics Laboratory} \\ +\hspace*{\parindent}\textsc{The University of Sheffield} \\ +\hspace*{3\parindent}\textit{June} 12, 1920 +\PageSep{xi} +\TableofContents % [** TN: Auto-generate the table of contents] +\iffalse %%%% Start of table of contents text %%%% +CONTENTS + +PART I + +THE SPECIAL THEORY OF RELATIVITY + +PAGE + + I. Physical Meaning of Geometrical Propositions . 1 + II. The System of Co-ordinates . 5 +III. Space and Time in Classical Mechanics . . 9 + IV. The Galileian System of Co-ordinates . .11 + V. The Principle of Relativity (in the Restricted + Sense) . . . . . .12 + VI. The Theorem of the Addition of Velocities employed + in Classical Mechanics . . 16 +VII. The Apparent Incompatibility of the Law of + Propagation of Light with the Principle of + Relativity . . . . 17 + +VIII. On the Idea of Time in Physics . . .21 + IX. The Relativity of Simultaneity . . .25 + X. On the Relativity of the Conception of Distance 28 + XI. The Lorentz Transformation . . .30 + XII. The Behaviour of Measuring-Rods and Clocks + in Motion . . . . 35 +\PageSep{xii} +XIII. Theorem of the Addition of Velocities. The + Experiment of Fizeau . . 3 %[** TN: Edge of page cut off] + XIV. The Heuristic Value of the Theory of Relativity 4 + XV. General Results of the Theory . . .4, + XVI. Experience and the Special Theory of Relativity 4 +XVII. Minkowski's Four-dimensional Space . . 5; + +PART II +THE GENERAL THEORY OF RELATIVITY + +XVIII. Special and General Principle of Relativity . 5 + XIX. The Gravitational Field . . . .6 + XX. The Equality of Inertial and Gravitational Mass + as an Argument for the General Postulate + of Relativity ..... + XXI. In what Respects are the Foundations of Classical + Mechanics and of the Special Theory + of Relativity unsatisfactory? . + XXII. A Few Inferences from the General Principle of + Relativity ..... +XXIII. Behaviour of Clocks and Measuring-Rods on a + Rotating Body of Reference . + XXIV. Euclidean and Non-Euclidean Continuum + XXV. Gaussian Co-ordinates .... + XXVI. The Space-time Continuum of the Special + Theory of Relativity considered as a + Euclidean Continuum +\PageSep{xiii} +PAGE + + XXVII. The Space-time Continuum of the General + Theory of Relativity is not a Euclidean + Continuum . . . . 93 +XXVIII. Exact Formulation of the General Principle of + Relativity . . . . 97 + XXIX. The Solution of the Problem of Gravitation on + the Basis of the General Principle of + Relativity ..... 100 + +PART III + +CONSIDERATIONS ON THE UNIVERSE +AS A WHOLE + + XXX. Cosmological Difficulties of Newton's Theory 105 + XXXI. The Possibility of a ``Finite'' and yet ``Unbounded'' + Universe. . . . 108 + XXXII. The Structure of Space according to the + General Theory of Relativity . . 113 + +APPENDICES + + I. Simple Derivation of the Lorentz Transformation . 115 + II. Minkowski's Four-dimensional Space (``World'') + [Supplementary to Section XVII.] . . 121 +III. The Experimental Confirmation of the General + Theory of Relativity . . . .123 +(a) Motion of the Perihelion of Mercury . 124 +(b) Deflection of Light by a Gravitational Field 126 +(c) Displacement of Spectral Lines towards the + Red . . . . . 129 + +BIBLIOGRAPHY . . . . . . 133 + +INDEX . . . . . . .135 +\fi %%%% End of table of contents text %%%% +\PageSep{xiv} +\FlushRunningHeads +\begin{CenterPage} + \bfseries\LARGE RELATIVITY \\[8pt] + \normalsize THE SPECIAL AND THE GENERAL THEORY +\end{CenterPage} +\PageSep{1} +\index{Manifold|see{Continuum}}% + + +\Part{I}{The Special Theory of Relativity}{Special Theory of Relativity} +\index{Special theory of relativity|(}% + +\Chapter[Geometrical Propositions] +{I}{Physical Meaning of Geometrical +Propositions} + +\First{In} your schooldays most of you who read this +\index{Euclidean geometry}% +book made acquaintance with the noble building of +Euclid's geometry, and you remember---perhaps +with more respect than love---the magnificent structure, +on the lofty staircase of which you were chased about +for uncounted hours by conscientious teachers. By +reason of your past experience, you would certainly +regard everyone with disdain who should pronounce even +the most out-of-the-way proposition of this science to +be untrue. But perhaps this feeling of proud certainty +would leave you immediately if some one were to ask +you: ``What, then, do you mean by the assertion that +these propositions are true?'' Let us proceed to give +this question a little consideration. + +Geometry sets out from certain conceptions such as +\index{Geometrical ideas!truth of|(}% +``plane,'' ``point,'' and ``straight line,'' with which +\index{Plane}% +\index{Point}% +\index{Straight line|(}% +\PageSep{2} +we are able to associate more or less definite ideas, and +from certain simple propositions (axioms) which, +\index{Axioms}% +\index{Axioms!truth of}% +\index{Geometrical ideas!propositions}% +in virtue of these ideas, we are inclined to accept as +``true.'' Then, on the basis of a logical process, the +justification of which we feel ourselves compelled to +admit, all remaining propositions are shown to follow +from those axioms, \ie\ they are proven. A proposition +is then correct (``true'') when it has been derived in the +recognised manner from the axioms. The question +of the ``truth'' of the individual geometrical propositions +\index{Truth@{``Truth''}}% +is thus reduced to one of the ``truth'' of the +axioms. Now it has long been known that the last +question is not only unanswerable by the methods of +geometry, but that it is in itself entirely without meaning. +We cannot ask whether it is true that only one +straight line goes through two points. We can only +say that Euclidean geometry deals with things called +\index{Euclidean geometry}% +``straight lines,'' to each of which is ascribed the property +of being uniquely determined by two points +situated on it. The concept ``true'' does not tally with +the assertions of pure geometry, because by the word +``true'' we are eventually in the habit of designating +always the correspondence with a ``real'' object; +geometry, however, is not concerned with the relation +of the ideas involved in it to objects of experience, but +only with the logical connection of these ideas among +themselves. + +It is not difficult to understand why, in spite of this, +we feel constrained to call the propositions of geometry +``true.'' Geometrical ideas correspond to more or less +\index{Geometrical ideas}% +exact objects in nature, and these last are undoubtedly +the exclusive cause of the genesis of those ideas. Geometry +ought to refrain from such a course, in order to +\PageSep{3} +give to its structure the largest possible logical unity. +The practice, for example, of seeing in a ``distance'' +two marked positions on a practically rigid body is +something which is lodged deeply in our habit of thought. +We are accustomed further to regard three points as +being situated on a straight line, if their apparent +positions can be made to coincide for observation with +one eye, under suitable choice of our place of observation. + +If, in pursuance of our habit of thought, we now +supplement the propositions of Euclidean geometry by +\index{Euclidean geometry!propositions of}% +the single proposition that two points on a practically +rigid body always correspond to the same distance +\index{Distance (line-interval)}% +(line-interval), independently of any changes in position +to which we may subject the body, the propositions of +Euclidean geometry then resolve themselves into propositions +on the possible relative position of practically +\index{Relative!position}% +rigid bodies.\footnote + {It follows that a natural object is associated also with a + straight line. Three points $A$,~$B$ and~$C$ on a rigid body thus + lie in a straight line when, the points $A$~and~$C$ being given, $B$ + is chosen such that the sum of the distances $AB$~and~$BC$ is as + short as possible. This incomplete suggestion will suffice for + our present purpose.} +Geometry which has been supplemented +in this way is then to be treated as a branch of physics. +We can now legitimately ask as to the ``truth'' of +geometrical propositions interpreted in this way, since +we are justified in asking whether these propositions +are satisfied for those real things we have associated +with the geometrical ideas. In less exact terms we can +\index{Geometrical ideas}% +express this by saying that by the ``truth'' of a geometrical +proposition in this sense we understand its +validity for a construction with ruler and compasses. +\index{Straight line|)}% +\PageSep{4} + +Of course the conviction of the ``truth'' of geometrical +propositions in this sense is founded exclusively +on rather incomplete experience. For the present we +shall assume the ``truth'' of the geometrical propositions, +then at a later stage (in the general theory of +relativity) we shall see that this ``truth'' is limited, +and we shall consider the extent of its limitation. +\index{Geometrical ideas!truth of|)}% +\PageSep{5} + + +\Chapter{II}{The System of Co-ordinates} +\index{System of co-ordinates}% + +\First{On} the basis of the physical interpretation of distance +\index{Distance (line-interval)}% +\index{Distance (line-interval)!physical interpretation of}% +\index{Measuring-rod}% +\index{Reference-body}% +which has been indicated, we are also +in a position to establish the distance between +two points on a rigid body by means of measurements. +For this purpose we require a ``distance'' (rod~$S$) +which is to be used once and for all, and which we +employ as a standard measure. If, now, $A$~and~$B$ are +two points on a rigid body, we can construct the +line joining them according to the rules of geometry; +then, starting from~$A$, we can mark off the distance~$S$ +time after time until we reach~$B$. The number of +these operations required is the numerical measure +of the distance~$AB$. This is the basis of all measurement +of length.\footnote + {Here we have assumed that there is nothing left over, \ie\ + that the measurement gives a whole number. This difficulty + is got over by the use of divided measuring-rods, the introduction + of which does not demand any fundamentally new method.} + +Every description of the scene of an event or of the +position of an object in space is based on the specification +of the point on a rigid body (body of reference) +with which that event or object coincides. This applies +not only to scientific description, but also to everyday +life. If I analyse the place specification ``Trafalgar +\index{Place specification}% +\PageSep{6} +Square, London,''\footnote + {I have chosen this as being more familiar to the English + reader than the ``Potsdamer Platz, Berlin,'' which is referred to + in the original. (R.~W.~L.)} +I arrive at the following result. +The earth is the rigid body to which the specification +of place refers; ``Trafalgar Square, London,'' is a +well-defined point, to which a name has been assigned, +and with which the event coincides in space.\footnote + {It is not necessary here to investigate further the significance + of the expression ``coincidence in space.'' This conception is + sufficiently obvious to ensure that differences of opinion are + scarcely likely to arise as to its applicability in practice.} + +This primitive method of place specification deals +\index{Place specification}% +only with places on the surface of rigid bodies, and is +dependent on the existence of points on this surface +which are distinguishable from each other. But we +can free ourselves from both of these limitations without +altering the nature of our specification of position. +\index{Conception of mass!position}% +If, for instance, a cloud is hovering over Trafalgar +Square, then we can determine its position relative to +the surface of the earth by erecting a pole perpendicularly +on the Square, so that it reaches the cloud. The +length of the pole measured with the standard measuring-rod, +\index{Measuring-rod}% +combined with the specification of the position of +the foot of the pole, supplies us with a complete place +specification. On the basis of this illustration, we are +able to see the manner in which a refinement of the conception +of position has been developed. + +\itema~We imagine the rigid body, to which the place +specification is referred, supplemented in such a manner +that the object whose position we require is reached by +the completed rigid body. + +\itemb~In locating the position of the object, we make +use of a number (here the length of the pole measured +\PageSep{7} +with the measuring-rod) instead of designated points of +reference. + +\itemc~We speak of the height of the cloud even when the +pole which reaches the cloud has not been erected. +By means of optical observations of the cloud from +different positions on the ground, and taking into account +the properties of the propagation of light, we determine +the length of the pole we should have required in order +to reach the cloud. + +From this consideration we see that it will be advantageous +\index{Physics}% +if, in the description of position, it should be +possible by means of numerical measures to make ourselves +independent of the existence of marked positions +(possessing names) on the rigid body of reference. In +\index{Reference-body}% +the physics of measurement this is attained by the +\index{Physics!of measurement}% +application of the Cartesian system of co-ordinates. +\index{Cartesian system of co-ordinates}% + +This consists of three plane surfaces perpendicular +to each other and rigidly attached to a rigid body. +Referred to a system of co-ordinates, the scene of any +event will be determined (for the main part) by the +specification of the lengths of the three perpendiculars +or co-ordinates $(x, y, z)$ which can be dropped from the +scene of the event to those three plane surfaces. The +lengths of these three perpendiculars can be determined +by a series of manipulations with rigid measuring-rods +performed according to the rules and methods laid +down by Euclidean geometry. + +In practice, the rigid surfaces which constitute the +system of co-ordinates are generally not available; +furthermore, the magnitudes of the co-ordinates are not +actually determined by constructions with rigid rods, but +by indirect means. If the results of physics and astronomy +\index{Astronomy}% +are to maintain their clearness, the physical meaning +\PageSep{8} +of specifications of position must always be sought +in accordance with the above considerations.\footnote + {A refinement and modification of these views does not become + necessary until we come to deal with the general theory of + relativity, treated in the second part of this book.} + +We thus obtain the following result: Every description +of events in space involves the use of a rigid body +to which such events have to be referred. The resulting +relationship takes for granted that the laws of Euclidean +\index{Distance (line-interval)}% +\index{Euclidean geometry!propositions of}% +geometry hold for ``distances,'' the ``distance'' being +represented physically by means of the convention of +two marks on a rigid body. +\PageSep{9} + + +\Chapter{III}{Space and Time in Classical Mechanics} +\index{Classical mechanics}% +\index{Space}% + +\Change{}{``}\First{The} purpose of mechanics is to describe how +bodies change their position in space with +\index{Position}% +time.'' I should load my conscience with grave +sins against the sacred spirit of lucidity were I to +formulate the aims of mechanics in this way, without +serious reflection and detailed explanations. Let us +proceed to disclose these sins. + +It is not clear what is to be understood here by +\index{Reference-body|(}% +``position'' and ``space.'' I stand at the window of a +railway carriage which is travelling uniformly, and drop +a stone on the embankment, without throwing it. Then, +disregarding the influence of the air resistance, I see the +stone descend in a straight line. A pedestrian who +\index{Straight line}% +observes the misdeed from the footpath notices that the +stone falls to earth in a parabolic curve. I now ask: +Do the ``positions'' traversed by the stone lie ``in +reality'' on a straight line or on a parabola? Moreover, +\index{Parabola}% +what is meant here by motion ``in space''? From the +considerations of the previous section the answer is +self-evident. In the first place, we entirely shun the +vague word ``space,'' of which, we must honestly +acknowledge, we cannot form the slightest conception, +and we replace it by ``motion relative to a +practically rigid body of reference.'' The positions +relative to the body of reference (railway carriage or +embankment) have already been defined in detail in the +\PageSep{10} +preceding section. If instead of ``body of reference'' +we insert ``system of co-ordinates,'' which is a useful +\index{System of co-ordinates}% +idea for mathematical description, we are in a position +to say: The stone traverses a straight line relative to a +\index{Straight line}% +system of co-ordinates rigidly attached to the carriage, +but relative to a system of co-ordinates rigidly attached +to the ground (embankment) it describes a parabola. +\index{Parabola}% +With the aid of this example it is clearly seen that there +is no such thing as an independently existing trajectory +\index{Trajectory}% +(lit. ``path-curve''\footnotemark), but only a trajectory relative to a +\index{Path-curve}% +particular body of reference. +\footnotetext{That is, a curve along which the body moves.} + +In order to have a \emph{complete} description of the motion, +we must specify how the body alters its position \emph{with +time}; \ie\ for every point on the trajectory it must be +stated at what time the body is situated there. These +data must be supplemented by such a definition of +time that, in virtue of this definition, these time-values +can be regarded essentially as magnitudes (results of +measurements) capable of observation. If we take our +stand on the ground of classical mechanics, we can +satisfy this requirement for our illustration in the +following manner. We imagine two clocks of identical +\index{Clocks}% +construction; the man at the railway-carriage window +is holding one of them, and the man on the footpath +the other. Each of the observers determines +the position on his own reference-body occupied by the +stone at each tick of the clock he is holding in his +hand. In this connection we have not taken account +of the inaccuracy involved by the finiteness of the +velocity of propagation of light. With this and with a +\index{Velocity of light}% +second difficulty prevailing here we shall have to deal +in detail later. +\PageSep{11} + + +\Chapter{IV}{The Galileian System of Co-ordinates} +\index{Galileian system of co-ordinates}% +\index{System of co-ordinates}% + +\First{As} is well known, the fundamental law of the +mechanics of Galilei-Newton, which is known +\index{Galilei}% +\index{Newton}% +as the \emph{law of inertia}, can be stated thus: +\index{Law of inertia}% +A body removed sufficiently far from other bodies +continues in a state of rest or of uniform motion +in a straight line. This law not only says something +about the motion of the bodies, but it also +indicates the reference-bodies or systems of co-ordinates, +permissible in mechanics, which can be used +in mechanical description. The visible fixed stars are +\index{Fixed stars}% +bodies for which the law of inertia certainly holds to a +high degree of approximation. Now if we use a system +of co-ordinates which is rigidly attached to the earth, +then, relative to this system, every fixed star describes +a circle of immense radius in the course of an astronomical +day, a result which is opposed to the statement +\index{Astronomical day}% +of the law of inertia. So that if we adhere to this law +we must refer these motions only to systems of co-ordinates +relative to which the fixed stars do not move +in a circle. A system of co-ordinates of which the state +of motion is such that the law of inertia holds relative to +it is called a ``Galileian system of co-ordinates.'' The +laws of the mechanics of Galilei-Newton can be regarded +as valid only for a Galileian system of co-ordinates. +\index{Reference-body|)}% +\PageSep{12} + + +\Chapter{V}{The Principle of Relativity (In the +Restricted Sense)} + +\First{In} order to attain the greatest possible clearness, +let us return to our example of the railway carriage +supposed to be travelling uniformly. We call its +motion a uniform translation (``uniform'' because +\index{Uniform translation}% +it is of constant velocity and direction, ``translation'' +because although the carriage changes its position +relative to the embankment yet it does not rotate +in so doing). Let us imagine a raven flying through +the air in such a manner that its motion, as observed +from the embankment, is uniform and in a straight +line. If we were to observe the flying raven from +the moving railway carriage, we should find that the +motion of the raven would be one of different velocity +and direction, but that it would still be uniform +and in a straight line. Expressed in an abstract +manner we may say: If a mass~$m$ is moving uniformly +in a straight line with respect to a co-ordinate +system~$K$, then it will also be moving uniformly and in a +straight line relative to a second co-ordinate system~$K'$, +provided that the latter is executing a uniform +translatory motion with respect to~$K$. In accordance +with the discussion contained in the preceding section, +it follows that: +\PageSep{13} + +If $K$~is a Galileian co-ordinate system, then every other +\index{Galileian system of co-ordinates}% +co-ordinate system~$K'$ is a Galileian one, when, in relation +to~$K$, it is in a condition of uniform motion of translation. +\index{Motion!of heavenly bodies}% +Relative to~$K'$ the mechanical laws of Galilei-Newton +\index{Laws of Galilei-Newton}% +hold good exactly as they do with respect to~$K$. + +We advance a step farther in our generalisation when +we express the tenet thus: If, relative to~$K$, $K'$~is a +uniformly moving co-ordinate system devoid of rotation, +then natural phenomena run their course with respect to~$K'$ +according to exactly the same general laws as with +respect to~$K$. This statement is called the \emph{principle +of relativity} (in the restricted sense). + +As long as one was convinced that all natural phenomena +were capable of representation with the help of +classical mechanics, there was no need to doubt the +\index{Classical mechanics}% +\index{Classical mechanics!truth of}% +validity of this principle of relativity. But in view of +\index{Principle of relativity|(}% +the more recent development of electrodynamics and +\index{Electrodynamics}% +optics it became more and more evident that classical +\index{Optics}% +mechanics affords an insufficient foundation for the +physical description of all natural phenomena. At this +juncture the question of the validity of the principle of +relativity became ripe for discussion, and it did not +appear impossible that the answer to this question +might be in the negative. + +Nevertheless, there are two general facts which at the +outset speak very much in favour of the validity of the +principle of relativity. Even though classical mechanics +does not supply us with a sufficiently broad basis for the +theoretical presentation of all physical phenomena, +still we must grant it a considerable measure of ``truth,'' +since it supplies us with the actual motions of the +heavenly bodies with a delicacy of detail little short of +wonderful. The principle of relativity must therefore +\PageSep{14} +apply with great accuracy in the domain of \emph{mechanics}. +\index{Classical mechanics}% +But that a principle of such broad generality should +hold with such exactness in one domain of phenomena, +and yet should be invalid for another, is \textit{a~priori} not +very probable. + +We now proceed to the second argument, to which, +moreover, we shall return later. If the principle of relativity +(in the restricted sense) does not hold, then the +Galileian co-ordinate systems $K$,~$K'$, $K''$,~etc., which are +\index{Galileian system of co-ordinates}% +moving uniformly relative to each other, will not be +\emph{equivalent} for the description of natural phenomena. +\index{Equivalent}% +In this case we should be constrained to believe that +natural laws are capable of being formulated in a particularly +simple manner, and of course only on condition +that, from amongst all possible Galileian co-ordinate +systems, we should have chosen \emph{one}~($K_{0}$) of a particular +state of motion as our body of reference. We should +\index{Motion}% +then be justified (because of its merits for the description +of natural phenomena) in calling this system ``absolutely +at rest,'' and all other Galileian systems~$K$ ``in motion.'' +\index{Rest}% +If, for instance, our embankment were the system~$K_{0}$, +then our railway carriage would be a system~$K$, +relative to which less simple laws would hold than with +respect to~$K_{0}$. This diminished simplicity would be +due to the fact that the carriage~$K$ would be in motion +(\ie\ ``really'') with respect to~$K_{0}$. In the general laws +of nature which have been formulated with reference +to~$K$, the magnitude and direction of the velocity +of the carriage would necessarily play a part. We should +expect, for instance, that the note emitted by an organ-pipe +\index{Organ-pipe, note of}% +placed with its axis parallel to the direction of +travel would be different from that emitted if the axis +of the pipe were placed perpendicular to this direction. +\PageSep{15} +Now in virtue of its motion in an orbit round the sun, +\index{Motion!of heavenly bodies}% +our earth is comparable with a railway carriage travelling +with a velocity of about $30$~kilometres per~second. +If the principle of relativity were not valid we should +therefore expect that the direction of motion of the +earth at any moment would enter into the laws of nature, +and also that physical systems in their behaviour would +be dependent on the orientation in space with respect +to the earth. For owing to the alteration in direction +of the velocity of revolution of the earth in the course +of a year, the earth cannot be at rest relative to the +hypothetical system~$K_{0}$ throughout the whole year. +However, the most careful observations have never +revealed such anisotropic properties in terrestrial physical +\index{Terrestrial space}% +space, \ie\ a physical non-equivalence of different +directions. This is very powerful argument in favour +of the principle of relativity. +\index{Principle of relativity|)}% +\PageSep{16} + + +\Chapter{VI}{The Theorem of the Addition of Velocities +employed in Classical Mechanics} +\index{Addition of velocities}% +\index{Classical mechanics}% + +\First{Let} us suppose our old friend the railway carriage +to be travelling along the rails with a constant +velocity~$v$, and that a man traverses the length of +the carriage in the direction of travel with a velocity~$w$. +How quickly or, in other words, with what velocity~$W$ +does the man advance relative to the embankment +during the process? The only possible answer seems to +result from the following consideration: If the man were +to stand still for a second, he would advance relative to +the embankment through a distance~$v$ equal numerically +to the velocity of the carriage. As a consequence of +his walking, however, he traverses an additional distance~$w$ +relative to the carriage, and hence also relative to the +embankment, in this second, the distance~$w$ being +numerically equal to the velocity with which he is +walking. Thus in total he covers the distance $W = v + w$ +relative to the embankment in the second considered. +We shall see later that this result, which expresses +the theorem of the addition of velocities employed in +classical mechanics, cannot be maintained; in other +words, the law that we have just written down does not +hold in reality. For the time being, however, we shall +assume its correctness. +\PageSep{17} + + +\Chapter{VII}{The Apparent Incompatibility of the +Law of Propagation of Light with +the Principle of Relativity} +\index{Propagation of light}% + +\First{There} is hardly a simpler law in physics than +that according to which light is propagated in +empty space. Every child at school knows, or +believes he knows, that this propagation takes place +in straight lines with a velocity $c = 300,000$~km./sec. +At all events we know with great exactness that this +velocity is the same for all colours, because if this were +not the case, the minimum of emission would not be +observed simultaneously for different colours during +the eclipse of a fixed star by its dark neighbour. By +\index{DeSitter@{De Sitter}}% +\index{Eclipse of star}% +means of similar considerations based on observations +of double stars, the Dutch astronomer De~Sitter +\index{Double stars}% +was also able to show that the velocity of propagation +of light cannot depend on the velocity of motion +of the body emitting the light. The assumption that +this velocity of propagation is dependent on the direction +``in space'' is in itself improbable. + +In short, let us assume that the simple law of the +constancy of the velocity of light~$c$ (in vacuum) is +\index{Velocity of light}% +justifiably believed by the child at school. Who would +imagine that this simple law has plunged the conscientiously +thoughtful physicist into the greatest +\PageSep{18} +intellectual difficulties? Let us consider how these +difficulties arise. + +Of course we must refer the process of the propagation +of light (and indeed every other process) to a rigid +reference-body (co-ordinate system). As such a system +\index{Reference-body}% +let us again choose our embankment. We shall imagine +the air above it to have been removed. If a ray of +light be sent along the embankment, we see from the +above that the tip of the ray will be transmitted with +the velocity~$c$ relative to the embankment. Now let +us suppose that our railway carriage is again travelling +along the railway lines with the velocity~$v$, and that +its direction is the same as that of the ray of light, but +its velocity of course much less. Let us inquire about +the velocity of propagation of the ray of light relative +to the carriage. It is obvious that we can here apply the +consideration of the previous section, since the ray of +light plays the part of the man walking along relatively +to the carriage. The velocity~$W$ of the man relative +to the embankment is here replaced by the velocity +of light relative to the embankment. $w$~is the required +velocity of light with respect to the carriage, and we +\index{Velocity of light}% +have +\[ +w = c - v. +\] +The velocity of propagation of a ray of light relative to +the carriage thus comes out smaller than~$c$. + +But this result comes into conflict with the principle +of relativity set forth in \Sectionref{V}. For, like every +other general law of nature, the law of the transmission +of light \textit{in~vacuo} must, according to the principle of +relativity, be the same for the railway carriage as +reference-body as when the rails are the body of reference. +\PageSep{19} +But, from our above consideration, this would +appear to be impossible. If every ray of light is propagated +relative to the embankment with the velocity~$c$, +then for this reason it would appear that another law +of propagation of light must necessarily hold with respect +\index{Propagation of light}% +to the carriage---a result contradictory to the principle +of relativity. + +In view of this dilemma there appears to be nothing +else for it than to abandon either the principle of relativity +\index{Principle of relativity}% +or the simple law of the propagation of light \textit{in~vacuo}. +Those of you who have carefully followed the +preceding discussion are almost sure to expect that +we should retain the principle of relativity, which +appeals so convincingly to the intellect because it is so +natural and simple. The law of the propagation of +light \textit{in~vacuo} would then have to be replaced by a +more complicated law conformable to the principle of +relativity. The development of theoretical physics +shows, however, that we cannot pursue this course. +The epoch-making theoretical investigations of H.~A. +Lorentz on the electrodynamical and optical phenomena +\index{Electrodynamics}% +\index{Optics}% +\index{Lorentz, H. A.}% +connected with moving bodies show that experience +in this domain leads conclusively to a theory of electromagnetic +phenomena, of which the law of the constancy +of the velocity of light \textit{in~vacuo} is a necessary consequence. +Prominent theoretical physicists were therefore +more inclined to reject the principle of relativity, +in spite of the fact that no empirical data had been +found which were contradictory to this principle. + +At this juncture the theory of relativity entered the +arena. As a result of an analysis of the physical conceptions +of time and space, it became evident that \emph{in +\index{Space!conception of}% +\index{Time!conception of}% +reality there is not the least incompatibility between the +\PageSep{20} +principle of relativity and the law of propagation of light}, +\index{Principle of relativity}% +\index{Propagation of light}% +and that by systematically holding fast to both these +laws a logically rigid theory could be arrived at. This +theory has been called the \emph{special theory of relativity} +\index{Special theory of relativity}% +to distinguish it from the extended theory, with which +we shall deal later. In the following pages we shall +present the fundamental ideas of the special theory of +relativity. +\PageSep{21} + + +\Chapter{VIII}{On the Idea of Time in Physics} +\index{Time!in Physics}% + +\First{Lightning} has struck the rails on our railway +embankment at two places $A$~and~$B$ far distant +from each other. I make the additional assertion +that these two lightning flashes occurred simultaneously. +If I ask you whether there is sense in this statement, +you will answer my question with a decided +``Yes.'' But if I now approach you with the request +to explain to me the sense of the statement more +precisely, you find after some consideration that the +answer to this question is not so easy as it appears at +first sight. + +After some time perhaps the following answer would +occur to you: ``The significance of the statement is +clear in itself and needs no further explanation; of +course it would require some consideration if I were to +be commissioned to determine by observations whether +in the actual case the two events took place simultaneously +or not.'' I cannot be satisfied with this answer +for the following reason. Supposing that as a result +of ingenious considerations an able meteorologist were +to discover that the lightning must always strike the +places $A$~and~$B$ simultaneously, then we should be faced +with the task of testing whether or not this theoretical +result is in accordance with the reality. We encounter +\PageSep{22} +the same difficulty with all physical statements in which +the conception ``simultaneous'' plays a part. The +concept does not exist for the physicist until he has the +possibility of discovering whether or not it is fulfilled +in an actual case. We thus require a definition of +simultaneity such that this definition supplies us with +\index{Simultaneity}% +the method by means of which, in the present case, he +can decide by experiment whether or not both the +lightning strokes occurred simultaneously. As long +as this requirement is not satisfied, I allow myself to be +deceived as a physicist (and of course the same applies +if I am not a physicist), when I imagine that I am able +to attach a meaning to the statement of simultaneity. +(I would ask the reader not to proceed farther until he +is fully convinced on this point.) + +After thinking the matter over for some time you +then offer the following suggestion with which to test +simultaneity. By measuring along the rails, the +connecting line~$AB$ should be measured up and an +observer placed at the mid-point~$M$ of the distance~$AB$. +This observer should be supplied with an arrangement +(\eg\ two mirrors inclined at~$90°$) which allows him +visually to observe both places $A$~and~$B$ at the same +time. If the observer perceives the two flashes of +lightning at the same time, then they are simultaneous. + +I am very pleased with this suggestion, but for all +that I cannot regard the matter as quite settled, because +I feel constrained to raise the following objection: +``Your definition would certainly be right, if I only +knew that the light by means of which the observer +at~$M$ perceives the lightning flashes travels along the +length $A\longrightarrow M$ with the same velocity as along the +length $B\longrightarrow M$. But an examination of this supposition +\PageSep{23} +would only be possible if we already had at our +disposal the means of measuring time. It would thus +appear as though we were moving here in a logical circle.'' + +After further consideration you cast a somewhat +disdainful glance at me---and rightly so---and you +declare: ``I maintain my previous definition nevertheless, +because in reality it assumes absolutely nothing +about light. There is only \emph{one} demand to be made of +the definition of simultaneity, namely, that in every +real case it must supply us with an empirical decision +as to whether or not the conception that has to +be defined is fulfilled. That my definition satisfies +this demand is indisputable. That light requires the +same time to traverse the path $A\longrightarrow M$ as for the path +$B\longrightarrow M$ is in reality neither a \emph{supposition nor a hypothesis} +about the physical nature of light, but a \emph{stipulation} +which I can make of my own \Change{freewill}{free will} in order to arrive +at a definition of simultaneity.'' + +It is clear that this definition can be used to give an +exact meaning not only to \emph{two} events, but to as many +events as we care to choose, and independently of the +positions of the scenes of the events with respect to the +\index{Reference-body}% +body of reference\footnote + {We suppose further, that, when three events $A$,~$B$ and~$C$ + occur in different places in such a manner that $A$~is simultaneous + with~$,$ and $B$~is simultaneous with~$C$ (simultaneous + in the sense of the above definition), then the criterion for the + simultaneity of the pair of events $A$,~$C$ is also satisfied. This + assumption is a physical hypothesis about the law of propagation + of light; it must certainly be fulfilled if we are to maintain the + law of the constancy of the velocity of light \textit{in~vacuo}.} +(here the railway embankment). +We are thus led also to a definition of ``time'' in physics. +For this purpose we suppose that clocks of identical +\index{Clocks}% +construction are placed at the points $A$,~$B$ and~$C$ of +\PageSep{24} +\index{Simultaneity|(}% +the railway line (co-ordinate system), and that they +are set in such a manner that the positions of their +pointers are simultaneously (in the above sense) the +same. Under these conditions we understand by the +``time'' of an event the reading (position of the hands) +\index{Time!of an event}% +of that one of these clocks which is in the immediate +vicinity (in space) of the event. In this manner a +time-value is associated with every event which is +essentially capable of observation. + +This stipulation contains a further physical hypothesis, +the validity of which will hardly be doubted without +empirical evidence to the contrary. It has been assumed +that all these clocks go \emph{at the same rate} if they are of +identical construction. Stated more exactly: When +two clocks arranged at rest in different places of a +reference-body are set in such a manner that a \emph{particular} +position of the pointers of the one clock is \emph{simultaneous} +(in the above sense) with the \emph{same} position of the +pointers of the other clock, then identical ``settings'' +are always simultaneous (in the sense of the above +definition). +\PageSep{25} + + +\Chapter{IX}{The Relativity of Simultaneity} + +\First{Up} to now our considerations have been referred +\index{Reference-body}% +to a particular body of reference, which we +have styled a ``railway embankment.'' We +suppose a very long train travelling along the rails +with the constant velocity~$v$ and in the direction indicated +in \Figref{1}. People travelling in this train will +with advantage use the train as a rigid reference-body +(co-ordinate system); they regard all events in +%[Illustration: Fig. 1.] +\Figure{025} +reference to the train. Then every event which takes +place along the line also takes place at a particular +point of the train. Also the definition of simultaneity +can be given relative to the train in exactly the same +way as with respect to the embankment. As a natural +consequence, however, the following question arises: + +Are two events (\eg\ the two strokes of lightning $A$ +and~$B$) which are simultaneous \emph{with reference to the +railway embankment} also simultaneous \emph{relatively to the +train}? We shall show directly that the answer must +be in the negative. + +When we say that the lightning strokes $A$~and~$B$ are +\PageSep{26} +simultaneous with respect to the embankment, we +mean: the rays of light emitted at the places $A$~and~$B$, +where the lightning occurs, meet each other at the +mid-point~$M$ of the length $A\longrightarrow B$ of the embankment. +But the events $A$~and~$B$ also correspond to positions $A$~and~$B$ +\index{Time!of an event}% +on the train. Let $M'$~be the mid-point of the +distance $A\longrightarrow B$ on the travelling train. Just when +the flashes\footnote + {As judged from the embankment.} +of lightning occur, this point~$M'$ naturally +coincides with the point~$M$, but it moves towards the +right in the diagram with the velocity~$v$ of the train. If +an observer sitting in the position~$M'$ in the train did +not possess this velocity, then he would remain permanently +at~$M$, and the light rays emitted by the +flashes of lightning $A$~and~$B$ would reach him simultaneously, +\ie\ they would meet just where he is situated. +Now in reality (considered with reference to the railway +embankment) he is hastening towards the beam of light +coming from~$B$, whilst he is riding on ahead of the beam +of light coming from~$A$. Hence the observer will see +the beam of light emitted from~$B$ earlier than he will +see that emitted from~$A$. Observers who take the railway +train as their reference-body must therefore come +\index{Reference-body}% +to the conclusion that the lightning flash~$B$ took place +earlier than the lightning flash~$A$. We thus arrive at +the important result: + +Events which are simultaneous with reference to the +embankment are not simultaneous with respect to the +train, and \textit{vice versa} (relativity of simultaneity). Every +\index{Simultaneity|)}% +\index{Simultaneity!relativity of}% +reference-body (co-ordinate system) has its own particular +time; unless we are told the reference-body to which +the statement of time refers, there is no meaning in a +statement of the time of an event. +\PageSep{27} + +Now before the advent of the theory of relativity +it had always tacitly been assumed in physics that the +statement of time had an absolute significance, \ie\ +that it is independent of the state of motion of the body +of reference. But we have just seen that this assumption +is incompatible with the most natural definition +of simultaneity; if we discard this assumption, then +the conflict between the law of the propagation of +light \textit{in~vacuo} and the principle of relativity (developed +in \Sectionref{VII}) disappears. + +We were led to that conflict by the considerations +of \Sectionref{VI}, which are now no longer tenable. In +that section we concluded that the man in the carriage, +who traverses the distance~$w$ \emph{per~second} relative to the +carriage, traverses the same distance also with respect to +the embankment \emph{in each second} of time. But, according +to the foregoing considerations, the time required by a +particular occurrence with respect to the carriage must +not be considered equal to the duration of the same +occurrence as judged from the embankment (as reference-body). +Hence it cannot be contended that the +man in walking travels the distance~$w$ relative to the +railway line in a time which is equal to one second as +judged from the embankment. + +Moreover, the considerations of \Sectionref{VI} are based +on yet a second assumption, which, in the light of a +strict consideration, appears to be arbitrary, although +it was always tacitly made even before the introduction +of the theory of relativity. +\PageSep{28} + + +\Chapter{X}{On the Relativity of the Conception +of Distance} +\index{Distance (line-interval)}% +\index{Distance (line-interval)!relativity of}% + +\First{Let} us consider two particular points on the train\footnote + {\eg\ the middle of the first and of the hundredth carriage.} +travelling along the embankment with the +velocity~$v$, and inquire as to their distance apart. +We already know that it is necessary to have a body of +reference for the measurement of a distance, with respect +to which body the distance can be measured up. It is +the simplest plan to use the train itself as reference-body +(co-ordinate system). An observer in the train +measures the interval by marking off his measuring-rod +\index{Measuring-rod}% +in a straight line (\eg\ along the floor of the carriage) +as many times as is necessary to take him from the one +marked point to the other. Then the number which +tells us how often the rod has to be laid down is the +required distance. + +It is a different matter when the distance has to be +judged from the railway line. Here the following +method suggests itself. If we call $A'$~and~$B'$ the two +points on the train whose distance apart is required, +then both of these points are moving with the velocity~$v$ +along the embankment. In the first place we require to +determine the points $A$~and~$B$ of the embankment which +are just being passed by the two points $A'$~and~$B'$ at a +\PageSep{29} +particular time~$t$---judged from the embankment. +These points $A$~and~$B$ of the embankment can be determined +by applying the definition of time given in +\Sectionref{VIII}. The distance between these points $A$~and~$B$ +\index{Distance (line-interval)}% +is then measured by repeated application of the +measuring-rod along the embankment. + +\textit{A~priori} it is by no means certain that this last +measurement will supply us with the same result as +the first. Thus the length of the train as measured +from the embankment may be different from that +obtained by measuring in the train itself. This +circumstance leads us to a second objection which must +be raised against the apparently obvious consideration +of \Sectionref{VI}. Namely, if the man in the carriage +covers the distance~$w$ in a unit of time---\emph{measured from +the train},---then this distance---\emph{as measured from the +embankment}---is not necessarily also equal to~$w$. +\PageSep{30} + + +\Chapter{XI}{The Lorentz Transformation} + +\First{The} results of the last three sections show +that the apparent incompatibility of the law +of propagation of light with the principle of +relativity (\Sectionref{VII}) has been derived by means of +a consideration which borrowed two unjustifiable +hypotheses from classical mechanics; these are as +\index{Classical mechanics}% +follows: +\begin{itemize} +\item[(1)] The time-interval (time) between two events is +\index{Time-interval}% + independent of the condition of motion of the + body of reference. + +\item[(2)] The space-interval (distance) between two points +\index{Space!interval@{-interval}}% + of a rigid body is independent of the condition + of motion of the body of reference. +\end{itemize} + +If we drop these hypotheses, then the dilemma of +\Sectionref{VII} disappears, because the theorem of the addition +of velocities derived in \Sectionref{VI} becomes invalid. +The possibility presents itself that the law of the propagation +of light \textit{in~vacuo} may be compatible with the +principle of relativity, and the question arises: How +have we to modify the considerations of \Sectionref{VI} +in order to remove the apparent disagreement between +these two fundamental results of experience? This +question leads to a general one. In the discussion of +\PageSep{31} +\Sectionref{VI} we have to do with places and times relative +both to the train and to the embankment. How are +we to find the place and time of an event in relation to +the train, when we know the place and time of the +event with respect to the railway embankment? Is +there a thinkable answer to this question of such a +nature that the law of transmission of light \textit{in~vacuo} +does not contradict the principle of relativity? In +other words: Can we conceive of a relation between +place and time of the individual events relative to both +reference-bodies, such that every ray of light possesses +the velocity of transmission~$c$ relative to the embankment +and relative to the train? This question leads to +a quite definite positive answer, and to a perfectly definite +transformation law for the space-time magnitudes of +an event when changing over from one body of reference +to another. + +Before we deal with this, we shall introduce the +following incidental consideration. Up to the present +we have only considered events taking place along the +embankment, which had mathematically to assume the +function of a straight line. In the manner indicated +in \Sectionref{II} we can imagine this reference-body supplemented +laterally and in a vertical direction by means of +a framework of rods, so that an event which takes place +anywhere can be localised with reference to this framework. +Similarly, we can imagine the train travelling +with the velocity~$v$ to be continued across the whole of +space, so that every event, no matter how far off it +may be, could also be localised with respect to the second +framework. Without committing any fundamental error, +we can disregard the fact that in reality these frameworks +would continually interfere with each other, owing +\PageSep{32} +\index{Propagation of light}% +to the impenetrability of solid bodies. In every such +framework we imagine three surfaces perpendicular to +each other marked out, and designated as ``co-ordinate +\index{Coordinate@{Co-ordinate}!planes}% +planes'' (``co-ordinate system''). A co-ordinate +system~$K$ then corresponds to the embankment, and a +co-ordinate system~$K'$ to the train. An event, wherever +it may have taken place, would be fixed in space with +respect to~$K$ by the three perpendiculars $x$,~$y$,~$z$ on the +co-ordinate planes, and with regard to time by a time-value~$t$. +Relative to~$K'$, \emph{the +same event} would be fixed +in respect of space and time +by corresponding values $x'$,~$y'$, +$z'$,~$t'$, which of course are +not identical with $x$,~$y$, $z$,~$t$. +It has already been set +forth in detail how these +magnitudes are to be regarded +as results of physical measurements. +%[Illustration: Fig. 2.] +\Figure[2in]{032} + +Obviously our problem can be exactly formulated in +the following manner. What are the values $x'$,~$y'$, $z'$,~$t'$, +of an event with respect to~$K'$, when the magnitudes +$x$,~$y$, $z$,~$t$, of the same event with respect to~$K$ are given? +The relations must be so chosen that the law of the +transmission of light \textit{in~vacuo} is satisfied for one and the +same ray of light (and of course for every ray) with +respect to $K$ and~$K'$. For the relative orientation in +space of the co-ordinate systems indicated in the diagram +(\Figref{2}), this problem is solved by means of the +equations: +\begin{align*} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,}\displaybreak[1] \\ +\PageSep{33} +y' &= y\Add{,} \\ +z' &= z\Add{,} \\ +t' &= \frac{t - \dfrac{v}{c^{2}}·x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Change{}{.} +\end{align*} +This system of equations is known as the ``Lorentz +\index{Lorentz, H. A.!transformation}% +transformation.''\footnote + {A simple derivation of the Lorentz transformation is given + in \Appendixref{I}.} + +If in place of the law of transmission of light we had +taken as our basis the tacit assumptions of the older +mechanics as to the absolute character of times and +lengths, then instead of the above we should have +obtained the following equations: +\begin{align*} +x' &= x - vt\Add{,} \\ +y' &= y\Add{,} \\ +z' &= z\Add{,} \\ +t' &= t. +\end{align*} +This system of equations is often termed the ``Galilei +\index{Galilei!transformation}% +transformation.'' The Galilei transformation can be +obtained from the Lorentz transformation by substituting +an infinitely large value for the velocity of +light~$c$ in the latter transformation. + +Aided by the following illustration, we can readily +see that, in accordance with the Lorentz transformation, +the law of the transmission of light \textit{in~vacuo} +is satisfied both for the reference-body~$K$ and for the +reference-body~$K'$. A light-signal is sent along the +\index{Light-signal}% +positive $x$-axis, and this light-stimulus advances in +\index{Light-stimulus}% +accordance with the equation +\[ +x = ct, +\] +\PageSep{34} +\ie\ with the velocity~$c$. According to the equations of +the Lorentz transformation, this simple relation between +$x$~and~$t$ involves a relation between $x'$~and~$t'$. In point +of fact, if we substitute for~$x$ the value~$ct$ in the first +and fourth equations of the Lorentz transformation, +we obtain: +\begin{align*} +x' &= \frac{(c - v)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,} \\ +t' &= \frac{\left(1 - \dfrac{v}{c}\right)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +\end{align*} +from which, by division, the expression +\[ +x' = ct' +\] +immediately follows. If referred to the system~$K'$, the +propagation of light takes place according to this +equation. We thus see that the velocity of transmission +relative to the reference-body~$K'$ is also equal to~$c$. The +same result is obtained for rays of light advancing in +any other direction whatsoever. Of course this is not +surprising, since the equations of the Lorentz transformation +were derived conformably to this point of +view. +\PageSep{35} + + +\Chapter{XII}{The Behaviour of Measuring-Rods and +Clocks in Motion} + +\First{I place} a metre-rod in the $x'$-axis of~$K'$ in such a +manner that one end (the beginning) coincides with +the point $x' = 0$, whilst the other end (the end of the +rod) coincides with the point $x' = 1$. What is the length +of the metre-rod relatively to the system~$K$? In order +to learn this, we need only ask where the beginning of the +rod and the end of the rod lie with respect to~$K$ at a +particular time~$t$ of the system~$K$. By means of the first +equation of the Lorentz transformation the values of +these two points at the time $t = 0$ can be shown to be +\begin{align*} +x_{\text{(beginning of rod)}} + &= 0·\sqrt{1 - \frac{v^{2}}{c^{2}}}\Add{,} \\ +x_{\text{(end of rod)}} + &= 1·\sqrt{1 - \frac{v^{2}}{c^{2}}}, +\end{align*} +the distance between the points being~$\sqrt{1 - \dfrac{v^{2}}{c^{2}}}$. But +the metre-rod is moving with the velocity~$v$ relative to~$K$. +It therefore follows that the length of a rigid metre-rod +moving in the direction of its length with a velocity~$v$ +is $\sqrt{1 - v^{2}/c^{2}}$~of a metre. The rigid rod is thus +shorter when in motion than when at rest, and the +more quickly it is moving, the shorter is the rod. For +the velocity $v = c$ we should have $\sqrt{1 - v^{2}/c^{2}} = 0$, and +for still greater velocities the square-root becomes +\PageSep{36} +imaginary. From this we conclude that in the theory +of relativity the velocity~$c$ plays the part of a limiting +\index{Limiting velocity ($c$)}% +velocity, which can neither be reached nor exceeded +by any real body. + +Of course this feature of the velocity~$c$ as a limiting +velocity also clearly follows from the equations of the +Lorentz transformation, for these become meaningless +if we choose values of~$v$ greater than~$c$. + +If, on the contrary, we had considered a metre-rod +at rest in the $x$-axis with respect to~$K$, then we should +have found that the length of the rod as judged from~$K'$ +would have been~$\sqrt{1 - v^{2}/c^{2}}$; this is quite in accordance +with the principle of relativity which forms the +basis of our considerations. + +\textit{A~priori} it is quite clear that we must be able to +learn something about the physical behaviour of measuring-rods +and clocks from the equations of transformation, +for the magnitudes $x$,~$y$, $z$,~$t$, are nothing more nor +less than the results of measurements obtainable by +means of measuring-rods and clocks. If we had based +our considerations on the Galilei transformation we +\index{Galilei!transformation}% +should not have obtained a contraction of the rod as a +consequence of its motion. + +Let us now consider a seconds-clock which is permanently +\index{Seconds-clock}% +situated at the origin ($x' = 0$) of~$K'$. $t' = 0$ +and $t' = 1$ are two successive ticks of this clock. The +first and fourth equations of the Lorentz transformation +give for these two ticks: +\begin{align*} +t &= 0 \\ +\intertext{and} +t &= \frac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{align*} +\PageSep{37} + +As judged from~$K$, the clock is moving with the +velocity~$v$; as judged from this reference-body, the +\index{Reference-body}% +time which elapses between two strokes of the clock +is not one second, but $\dfrac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}$~seconds, \ie\ a somewhat +larger time. As a consequence of its motion +the clock goes more slowly than when at rest. Here +also the velocity~$c$ plays the part of an unattainable +limiting velocity. +\index{Limiting velocity ($c$)}% +\PageSep{38} + + +\Chapter{XIII}{Theorem of the Addition of Velocities. +The Experiment of Fizeau} +\index{Addition of velocities}% + +\First{Now} in practice we can move clocks and +measuring-rods only with velocities that are +small compared with the velocity of light; hence +we shall hardly be able to compare the results of the +previous section directly with the reality. But, on the +other hand, these results must strike you as being very +singular, and for that reason I shall now draw another +conclusion from the theory, one which can easily be +derived from the foregoing considerations, and which +has been most elegantly confirmed by experiment. + +In \Sectionref{VI} we derived the theorem of the addition +of velocities in one direction in the form which also +results from the hypotheses of classical mechanics. This +theorem can also be deduced readily from the Galilei +\index{Galilei!transformation}% +transformation (\Sectionref{XI}). In place of the man +walking inside the carriage, we introduce a point moving +relatively to the co-ordinate system~$K'$ in accordance +with the equation +\[ +x' = wt'. +\] +By means of the first and fourth equations of the Galilei +transformation we can express $x'$~and~$t'$ in terms of $x$~and~$t$, +and we then obtain +\[ +x = (v + w)t. +\] +\PageSep{39} +This equation expresses nothing else than the law of +motion of the point with reference to the system~$K$ +(of the man with reference to the embankment). We +denote this velocity by the symbol~$W$, and we then +obtain, as in \Sectionref{VI}, +\[ +W = v + w. +\Tag{(A)} +\] + +But we can carry out this consideration just as well +on the basis of the theory of relativity. In the equation +\[ +x' = wt' +\] +we must then express $x'$~and~$t'$ in terms of $x$~and~$t$, making +use of the first and fourth equations of the \emph{Lorentz +\index{Lorentz, H. A.!transformation}% +transformation}. Instead of the equation~\Eqref{(A)} we then +obtain the equation +\[ +W = \frac{v + w}{1 + \dfrac{vw}{c^{2}}}, +\Tag{(B)} +\] +which corresponds to the theorem of addition for +velocities in one direction according to the theory of +relativity. The question now arises as to which of these +two theorems is the better in accord with experience. On +this point we are enlightened by a most important experiment +which the brilliant physicist Fizeau performed more +\index{Fizeau}% +\index{Fizeau!experiment of}% +than half a century ago, and which has been repeated +since then by some of the best experimental physicists, +so that there can be no doubt about its result. The +experiment is concerned with the following question. +Light travels in a motionless liquid with a particular +velocity~$w$. How quickly does it travel in the direction +of the arrow in the tube~$T$ (see the accompanying diagram, +\Figref{3}) when the liquid above mentioned is flowing +through the tube with a velocity~$v$? +\PageSep{40} + +In accordance with the principle of relativity we shall +\index{Propagation of light!in liquid}% +certainly have to take for granted that the propagation +of light always takes place with the same velocity~$w$ +\emph{with respect to the liquid}, whether the latter is in motion +with reference to other bodies or not. The velocity +of light relative to the liquid and the velocity of the +latter relative to the tube are thus known, and we +require the velocity of light relative to the tube. + +It is clear that we have the problem of \Sectionref{VI} +again before us. The tube plays the part of the railway +embankment or of the co-ordinate system~$K$, the liquid +plays the part of the carriage or of the co-ordinate +system~$K'$, and finally, the light plays the part of the +%[Illustration: Fig. 3.] +\Figure[2in]{040} +man walking along the carriage, or of the moving point +in the present section. If we denote the velocity of the +light relative to the tube by~$W$, then this is given +by the equation \Eqref{(A)}~or~\Eqref{(B)}, according as the Galilei +transformation or the Lorentz transformation corresponds +to the facts. Experiment\footnote + {Fizeau found $W = w + v\left(1 - \dfrac{1}{n^{2}}\right)$, where $n = \dfrac{c}{w}$ is the index of + refraction of the liquid. On the other hand, owing to the smallness + of~$\dfrac{vw}{c^{2}}$ as compared with~$1$, we can replace~\Eqref{(B)} in the first + place by $W = (w + v) \left(1 - \dfrac{vw}{c^{2}}\right)$, or to the same order of approximation + by $w + v \left(1 - \dfrac{1}{n^{2}}\right)$, which agrees with Fizeau's result.} +decides in favour +of equation~\Eqref{(B)} derived from the theory of relativity, and +the agreement is, indeed, very exact. According to +\PageSep{41} +recent and most excellent measurements by Zeeman, the +\index{Zeeman}% +influence of the velocity of flow~$v$ on the propagation of +light is represented by formula~\Eqref{(B)} to within one per +cent. %[** TN: [sic] two words] + +Nevertheless we must now draw attention to the fact +that a theory of this phenomenon was given by H.~A. +Lorentz long before the statement of the theory of +\index{Lorentz, H. A.}% +relativity. This theory was of a purely electrodynamical +nature, and was obtained by the use of particular +hypotheses as to the electromagnetic structure of matter. +This circumstance, however, does not in the least +diminish the conclusiveness of the experiment as a +crucial test in favour of the theory of relativity, for the +electrodynamics of Maxwell-Lorentz, on which the +\index{Electrodynamics}% +\index{Maxwell}% +original theory was based, in no way opposes the theory +of relativity. Rather has the latter been developed +from electrodynamics as an astoundingly simple combination +and generalisation of the hypotheses, formerly +independent of each other, on which electrodynamics +was built. +\PageSep{42} + + +\Chapter{XIV}{The Heuristic Value of the Theory of +Relativity} +\index{Heuristic value of relativity}% + +\First{Our} train of thought in the foregoing pages can be +epitomised in the following manner. Experience +has led to the conviction that, on the one hand, +the principle of relativity holds true, and that on the +other hand the velocity of transmission of light \textit{in~vacuo} +has to be considered equal to a constant~$c$. By uniting +these two postulates we obtained the law of transformation +for the rectangular co-ordinates $x$,~$y$,~$z$ and the time~$t$ +of the events which constitute the processes of nature. +\index{Processes of Nature}% +In this connection we did not obtain the Galilei transformation, +\index{Galilei!transformation}% +but, differing from classical mechanics, +the \emph{Lorentz transformation}. +\index{Lorentz, H. A.!transformation}% + +The law of transmission of light, the acceptance of +which is justified by our actual knowledge, played an +important part in this process of thought. Once in +possession of the Lorentz transformation, however, +we can combine this with the principle of relativity, +and sum up the theory thus: + +Every general law of nature must be so constituted +that it is transformed into a law of exactly the same +form when, instead of the space-time variables $x$,~$y$, $z$,~$t$ +of the original co-ordinate system~$K$, we introduce new +space-time variables $x'$,~$y'$, $z'$,~$t'$ of a co-ordinate system~$K'$. +\PageSep{43} +In this connection the relation between the +ordinary and the accented magnitudes is given by the +Lorentz transformation. Or, in brief: General laws +of nature are co-variant with respect to Lorentz transformations. +\index{Covariant@{Co-variant}}% + +This is a definite mathematical condition that the +theory of relativity demands of a natural law, and in +virtue of this, the theory becomes a valuable heuristic aid +in the search for general laws of nature. If a general +law of nature were to be found which did not satisfy +this condition, then at least one of the two fundamental +assumptions of the theory would have been disproved. +Let us now examine what general results the latter +theory has hitherto evinced. +\PageSep{44} + + +\Chapter{XV}{General Results of the Theory} + +\First{It} is clear from our previous considerations that the +(special) theory of relativity has grown out of electrodynamics +\index{Electrodynamics}% +and optics. In these fields it has not +\index{Optics}% +appreciably altered the predictions of theory, but it +has considerably simplified the theoretical structure, +\ie\ the derivation of laws, and---what is incomparably +\index{Derivation of laws}% +more important---it has considerably reduced the +number of independent hypotheses forming the basis of +\index{Basis of theory}% +theory. The special theory of relativity has rendered +the Maxwell-Lorentz theory so plausible, that the latter +\index{Lorentz, H. A.}% +\index{Maxwell}% +would have been generally accepted by physicists +even if experiment had decided less unequivocally in its +favour. + +Classical mechanics required to be modified before it +\index{Classical mechanics}% +could come into line with the demands of the special +theory of relativity. For the main part, however, +this modification affects only the laws for rapid motions, +in which the velocities of matter~$v$ are not very small as +compared with the velocity of light. We have experience +of such rapid motions only in the case of electrons +\index{Electron}% +and ions; for other motions the variations from the laws +\index{Ions}% +of classical mechanics are too small to make themselves +evident in practice. We shall not consider the motion +\index{Motion!of heavenly bodies}% +of stars until we come to speak of the general theory of +relativity. In accordance with the theory of relativity +\PageSep{45} +the kinetic energy of a material point of mass~$m$ is no +\index{Kinetic energy}% +longer given by the well-known expression +\[ +m\frac{v^{2}}{2}\Change{.}{,} +\] +but by the expression +\[ +\frac{mc^{2}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +This expression approaches infinity as the velocity~$v$ +approaches the velocity of light~$c$. The velocity must +therefore always remain less than~$c$, however great may +be the energies used to produce the acceleration. If +we develop the expression for the kinetic energy in the +form of a series, we obtain +\[ +mc^{2} + m\frac{v^{2}}{2} + \frac{3}{8}m\frac{v^4}{c^{2}} + \dots. +\] + +When $\dfrac{v^{2}}{c^{2}}$ is small compared with unity, the third +of these terms is always small in comparison with the +second, which last is alone considered in classical +mechanics. The first term~$mc^{2}$ does not contain +the velocity, and requires no consideration if we are only +dealing with the question as to how the energy of a +point-mass depends on the velocity. We shall speak +\index{Point-mass, energy of}% +of its essential significance later. + +The most important result of a general character to +\index{Conservation of energy}% +\index{Conservation of energy!mass}% +which the special theory of relativity has led is concerned +with the conception of mass. Before the advent of +\index{Conception of mass}% +relativity, physics recognised two conservation laws of +fundamental importance, namely, the law of the conservation +of energy and the law of the conservation of +mass; these two fundamental laws appeared to be quite +\PageSep{46} +independent of each other. By means of the theory of +relativity they have been united into one law. We shall +now briefly consider how this unification came about, +and what meaning is to be attached to it. + +The principle of relativity requires that the law of the +conservation of energy should hold not only with reference +to a co-ordinate system~$K$, but also with respect +to every co-ordinate system~$K'$ which is in a state of +uniform motion of translation relative to~$K$, or, briefly, +relative to every ``Galileian'' system of co-ordinates. +\index{Galileian system of co-ordinates}% +In contrast to classical mechanics, the Lorentz transformation +is the deciding factor in the transition from +one such system to another. + +By means of comparatively simple considerations +we are led to draw the following conclusion from +these premises, in conjunction with the fundamental +equations of the electrodynamics of Maxwell: A body +\index{Maxwell!fundamental equations}% +\index{Absorption of energy}% +moving with the velocity~$v$, which absorbs\footnote + {$E_{0}$~is the energy taken up, as judged from a co-ordinate + system moving with the body.} +an amount +of energy~$E_{0}$ in the form of radiation without suffering +\index{Radiation}% +an alteration in velocity in the process, has, as a consequence, +its energy increased by an amount +\[ +\frac{E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] + +In consideration of the expression given above for the +kinetic energy of the body, the required energy of the +body comes out to be +\[ +\frac{\left(m + \dfrac{E_{0}}{c^{2}}\right)c^{2}} + {\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +\PageSep{47} + +Thus the body has the same energy as a body of mass +$\left(m + \dfrac{E_{0}}{c^{2}}\right)$ moving with the velocity~$v$. Hence we can +say: If a body takes up an amount of energy~$E_{0}$, then +its inertial mass increases by an amount~$\dfrac{E_{0}}{c^{2}}$; the +\index{Inertial mass}% +inertial mass of a body is not a constant, but varies +according to the change in the energy of the body. +The inertial mass of a system of bodies can even be +regarded as a measure of its energy. The law of the +conservation of the mass of a system becomes identical +with the law of the conservation of energy, and is only +\index{Conservation of energy!mass}% +valid provided that the system neither takes up nor sends +out energy. Writing the expression for the energy in +the form +\[ +\frac{mc^{2} + E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +\] +we see that the term~$mc^{2}$, which has hitherto attracted +our attention, is nothing else than the energy possessed +by the body\footnote + {As judged from a co-ordinate system moving with the body.} +before it absorbed the energy~$E_{0}$. + +A direct comparison of this relation with experiment +is not possible at the present time, owing to the fact that +the changes in energy~$E_{0}$ to which we can subject a +system are not large enough to make themselves +perceptible as a change in the inertial mass of the +system. $\dfrac{E_{0}}{c^{2}}$~is too small in comparison with the mass~$m$, +which was present before the alteration of the energy. +It is owing to this circumstance that classical mechanics +was able to establish successfully the conservation of +mass as a law of independent validity. +\PageSep{48} + +Let me add a final remark of a fundamental nature. +The success of the Faraday-Maxwell interpretation of +\index{Faraday}% +\index{Maxwell|(}% +electromagnetic action at a distance resulted in physicists +\index{Action at a distance}% +becoming convinced that there are no such things as +instantaneous actions at a distance (not involving an +intermediary medium) of the type of Newton's law of +\index{Newton's!law of gravitation}% +gravitation. According to the theory of relativity, +action at a distance with the velocity of light always +takes the place of instantaneous action at a distance or +of action at a distance with an infinite velocity of transmission. +This is connected with the fact that the +velocity~$c$ plays a fundamental rôle in this theory. In +\Partref{II} we shall see in what way this result becomes +modified in the general theory of relativity. +\PageSep{49} + + +\Chapter{XVI}{Experience and the Special Theory of +Relativity} +\index{Experience}% + +\First{To} what extent is the special theory of relativity +supported by experience? This question is not +easily answered for the reason already mentioned +in connection with the fundamental experiment of Fizeau. +\index{Fizeau}% +The special theory of relativity has crystallised out +from the Maxwell-Lorentz theory of electromagnetic +\index{Lorentz, H. A.}% +phenomena. Thus all facts of experience which support +the electromagnetic theory also support the theory of +\index{Electromagnetic theory}% +relativity. As being of particular importance, I mention +here the fact that the theory of relativity enables us to +predict the effects produced on the light reaching us +from the fixed stars. These results are obtained in an +exceedingly simple manner, and the effects indicated, +which are due to the relative motion of the earth with +reference to those fixed stars, are found to be in accord +with experience. We refer to the yearly movement of +the apparent position of the fixed stars resulting from the +motion of the earth round the sun (aberration), and to the +\index{Aberration}% +influence of the radial components of the relative +motions of the fixed stars with respect to the earth on +the colour of the light reaching us from them. The +\PageSep{50} +latter effect manifests itself in a slight displacement +of the spectral lines of the light transmitted to us from +a fixed star, as compared with the position of the same +spectral lines when they are produced by a terrestrial +source of light (Doppler principle). The experimental +\index{Doppler principle}% +arguments in favour of the Maxwell-Lorentz theory, +\index{Lorentz, H. A.|(}% +which are at the same time arguments in favour of the +theory of relativity, are too numerous to be set forth +here. In reality they limit the theoretical possibilities +to such an extent, that no other theory than that of +Maxwell and Lorentz has been able to hold its own when +tested by experience. + +But there are two classes of experimental facts +hitherto obtained which can be represented in the +Maxwell-Lorentz theory only by the introduction of an +\index{Maxwell|)}% +auxiliary hypothesis, which in itself---\ie\ without +making use of the theory of relativity---appears extraneous. + +It is known that cathode rays and the so-called +\index{beta-rays@{$\beta$-rays}}% +\index{Cathode rays}% +$\beta$-rays emitted by radioactive substances consist of +\index{Radioactive substances}% +negatively electrified particles (electrons) of very small +inertia and large velocity. By examining the deflection +of these rays under the influence of electric and magnetic +fields, we can study the law of motion of these particles +very exactly. + +In the theoretical treatment of these electrons, we are +faced with the difficulty that electrodynamic theory of +itself is unable to give an account of their nature. For +since electrical masses of one sign repel each other, the +negative electrical masses constituting the electron would +\index{Electron}% +necessarily be scattered under the influence of their +mutual repulsions, unless there are forces of another +kind operating between them, the nature of which has +\PageSep{51} +hitherto remained obscure to us.\footnote + {The general theory of relativity renders it likely that the + electrical masses of an electron are held together by gravitational +\index{Electron!electrical masses of}% + forces.} +If we now assume +that the relative distances between the electrical masses +constituting the electron remain unchanged during the +motion of the electron (rigid connection in the sense of +classical mechanics), we arrive at a law of motion of the +electron which does not agree with experience. Guided +by purely formal points of view, H.~A.~Lorentz was the +first to introduce the hypothesis that the particles +constituting the electron experience a contraction +in the direction of motion in consequence of that motion, +the amount of this contraction being proportional to +the expression~$\sqrt{1 - \dfrac{v^{2}}{c^{2}}}$. This hypothesis, which is +not justifiable by any electrodynamical facts, supplies us +then with that particular law of motion which has +been confirmed with great precision in recent years. + +The theory of relativity leads to the same law of +motion, without requiring any special hypothesis whatsoever +as to the structure and the behaviour of the +electron. We arrived at a similar conclusion in \Sectionref{XIII} +in connection with the experiment of Fizeau, the +\index{Fizeau}% +result of which is foretold by the theory of relativity +without the necessity of drawing on hypotheses as to +the physical nature of the liquid. + +The second class of facts to which we have alluded +has reference to the question whether or not the motion +of the earth in space can be made perceptible in terrestrial +experiments. We have already remarked in \Sectionref{V} +that all attempts of this nature led to a negative result. +Before the theory of relativity was put forward, it was +\PageSep{52} +difficult to become reconciled to this negative result, +for reasons now to be discussed. The inherited +prejudices about time and space did not allow any +\index{Time!conception of}% +\index{Space}% +doubt to arise as to the prime importance of the +Galilei transformation for changing over from one +\index{Galilei!transformation}% +body of reference to another. Now assuming that the +Maxwell-Lorentz equations hold for a reference-body~$K$, +\index{Maxwell}% +we then find that they do not hold for a reference-body~$K'$ +moving uniformly with respect to~$K$, if we +assume that the relations of the Galileian transformation +exist between the co-ordinates of $K$~and~$K'$. It +thus appears that of all Galileian co-ordinate systems +one~($K$) corresponding to a particular state of motion +is physically unique. This result was interpreted +physically by regarding $K$ as at rest with respect to a +hypothetical æther of space. On the other hand, +all co-ordinate systems~$K'$ moving relatively to~$K$ were +to be regarded as in motion with respect to the æther. +\index{Aether}% +\index{Aether!-drift}% +To this motion of~$K'$ against the æther (``æther-drift'' +relative to~$K'$) were assigned the more complicated +laws which were supposed to hold relative to~$K'$. +Strictly speaking, such an æther-drift ought also to be +assumed relative to the earth, and for a long time the +efforts of physicists were devoted to attempts to detect +the existence of an æther-drift at the earth's surface. + +In one of the most notable of these attempts Michelson +\index{Michelson|(}% +devised a method which appears as though it must be +decisive. Imagine two mirrors so arranged on a rigid +body that the reflecting surfaces face each other. A +ray of light requires a perfectly definite time~$T$ to pass +from one mirror to the other and back again, if the whole +system be at rest with respect to the æther. It is found +by calculation, however, that a slightly different time~$T'$ +\PageSep{53} +is required for this process, if the body, together with +the mirrors, be moving relatively to the æther. And +\index{Aether!-drift}% +yet another point: it is shown by calculation that for +a given velocity~$v$ with reference to the æther, this +time~$T'$ is different when the body is moving perpendicularly +to the planes of the mirrors from that resulting +when the motion is parallel to these planes. Although +the estimated difference between these two times is +exceedingly small, Michelson and Morley performed an +\index{Morley}% +experiment involving interference in which this difference +should have been clearly detectable. But the experiment +gave a negative result---a fact very perplexing +to physicists. Lorentz and FitzGerald rescued the +\index{FitzGerald}% +\index{Lorentz, H. A.|)}% +theory from this difficulty by assuming that the motion +of the body relative to the æther produces a contraction +of the body in the direction of motion, the amount of contraction +being just sufficient to compensate for the difference +in time mentioned above. Comparison with the +discussion in \Sectionref{XII} shows that also from the standpoint +of the theory of relativity this solution of the +difficulty was the right one. But on the basis of the +theory of relativity the method of interpretation is +incomparably more satisfactory. According to this +theory there is no such thing as a ``specially favoured'' +(unique) co-ordinate system to occasion the introduction +of the æther-idea, and hence there can be no æther-drift, +nor any experiment with which to demonstrate it. +Here the contraction of moving bodies follows from +the two fundamental principles of the theory without +the introduction of particular hypotheses; and as the +prime factor involved in this contraction we find, not +the motion in itself, to which we cannot attach any +meaning, but the motion with respect to the body of +\PageSep{54} +reference chosen in the particular case in point. Thus +for a co-ordinate system moving with the earth the +mirror system of Michelson and Morley is not shortened, +\index{Michelson|)}% +\index{Morley}% +but it \emph{is} shortened for a co-ordinate system which is at +rest relatively to the sun. +\PageSep{55} + + +\Chapter{XVII}{Minkowski's Four-dimensional Space} +\index{Minkowski|(}% +\index{Space}% + +\First{The} non-mathematician is seized by a mysterious +shuddering when he hears of ``four-dimensional'' +things, by a feeling not unlike that awakened by +thoughts of the occult. And yet there is no more +common-place statement than that the world in which +\index{World}% +we live is a four-dimensional space-time continuum. +\index{Continuum}% + +Space is a three-dimensional continuum. By this +\index{Space co-ordinates}% +\index{Three-dimensional}% +\index{Time!coordinate@{co-ordinate}}% +we mean that it is possible to describe the position of a +point (at rest) by means of three numbers (co-ordinates) +$x$,~$y$,~$z$, and that there is an indefinite number of points +in the neighbourhood of this one, the position of which +can be described by co-ordinates such as $x_{1}$,~$y_{1}$,~$z_{1}$, which +may be as near as we choose to the respective values of +the co-ordinates $x$,~$y$,~$z$ of the first point. In virtue of the +latter property we speak of a ``continuum,'' and owing +to the fact that there are three co-ordinates we speak of +it as being ``three-dimensional.'' + +Similarly, the world of physical phenomena which was +briefly called ``world'' by Minkowski is naturally +four-dimensional in the space-time sense. For it is +composed of individual events, each of which is described +by four numbers, namely, three space +co-ordinates $x$,~$y$,~$z$ and a time co-ordinate, the time-value~$t$. +The ``world'' is in this sense also a continuum; +for to every event there are as many ``neighbouring'' +\PageSep{56} +events (realised or at least thinkable) as we care to +choose, the co-ordinates $x_{1}$,~$y_{1}$, $z_{1}$,~$t_{1}$ of which differ +by an indefinitely small amount from those of the +event $x$,~$y$, $z$,~$t$ originally considered. That we have not +been accustomed to regard the world in this sense as a +\index{World}% +four-dimensional continuum is due to the fact that in +physics, before the advent of the theory of relativity, +time played a different and more independent rôle, as +compared with the space co-ordinates. It is for this +reason that we have been in the habit of treating time +as an independent continuum. As a matter of fact, +according to classical mechanics, time is absolute, +\ie\ it is independent of the position and the condition +of motion of the system of co-ordinates. We see this +expressed in the last equation of the Galileian transformation +($t' = t$). + +The four-dimensional mode of consideration of the +``world'' is natural on the theory of relativity, since +according to this theory time is robbed of its independence. +This is shown by the fourth equation of the +Lorentz transformation: +\[ +t' = \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +Moreover, according to this equation the time difference~$\Delta t'$ +\index{Space!interval@{-interval}}% +\index{Time-interval}% +of two events with respect to~$K'$ does not in general +vanish, even when the time difference~$\Delta t$ of the same +events with reference to~$K$ vanishes. Pure ``space-distance'' +of two events with respect to~$K$ results in +``time-distance'' of the same events with respect to~$K'$. +But the discovery of Minkowski, which was of importance +\PageSep{57} +for the formal development of the theory of relativity, +does not lie here. It is to be found rather in +the fact of his recognition that the four-dimensional +space-time continuum of the theory of relativity, in its +\index{Continuum!three-dimensional}% +most essential formal properties, shows a pronounced +relationship to the three-dimensional continuum of +Euclidean geometrical space.\footnote + {Cf.\ the somewhat more detailed discussion in \Appendixref{II}.} +In order to give due +prominence to this relationship, however, we must +replace the usual time co-ordinate~$t$ by an imaginary +magnitude~$\sqrt{-1}·ct$ proportional to it. Under these +conditions, the natural laws satisfying the demands of +the (special) theory of relativity assume mathematical +forms, in which the time co-ordinate plays exactly the +same rôle as the three space co-ordinates. Formally, +these four co-ordinates correspond exactly to the three +space co-ordinates in Euclidean geometry. It must be +\index{Euclidean geometry}% +\index{Euclidean space}% +clear even to the non-mathematician that, as a consequence +of this purely formal addition to our knowledge, +the theory perforce gained clearness in no mean +measure. + +These inadequate remarks can give the reader only a +vague notion of the important idea contributed by Minkowski. +Without it the general theory of relativity, of +which the fundamental ideas are developed in the following +pages, would perhaps have got no farther than its +long clothes. Minkowski's work is doubtless difficult of +\index{Minkowski|)}% +access to anyone inexperienced in mathematics, but +since it is not necessary to have a very exact grasp of +this work in order to understand the fundamental ideas +of either the special or the general theory of relativity, +I shall at present leave it here, and shall revert to it +only towards the end of \Partref{II}. +\index{Special theory of relativity|)}% +\PageSep{58} +% [Blank page] +\PageSep{59} + + +\Part{II}{The General Theory of Relativity}{General Theory of Relativity} +\index{General theory of relativity|(}% + +\Chapter{XVIII}{Special and General Principle of +Relativity} +\index{Laws of Galilei-Newton!of Nature}% + +\First{The} basal principle, which was the pivot of all +our previous considerations, was the \emph{special} +principle of relativity, \ie\ the principle of the +physical relativity of all \emph{uniform} motion. Let us once +\index{Uniform translation}% +more analyse its meaning carefully. + +It was at all times clear that, from the point of view +of the idea it conveys to us, every motion must only +be considered as a relative motion. Returning to the +illustration we have frequently used of the embankment +and the railway carriage, we can express the fact of the +motion here taking place in the following two forms, +both of which are equally justifiable: +\begin{itemize} +\item[\itema] The carriage is in motion relative to the embankment. + +\item[\itemb] The embankment is in motion relative to the + carriage. +\end{itemize} + +In \itema~the embankment, in \itemb~the carriage, serves as +the body of reference in our statement of the motion +taking place. If it is simply a question of detecting +\PageSep{60} +or of describing the motion involved, it is in principle +\index{Motion}% +immaterial to what reference-body we refer the motion. +\index{Reference-body}% +As already mentioned, this is self-evident, but it must +not be confused with the much more comprehensive +statement called ``the principle of relativity,'' which +\index{Principle of relativity}% +we have taken as the basis of our investigations. + +The principle we have made use of not only maintains +that we may equally well choose the carriage or the +embankment as our reference-body for the description +of any event (for this, too, is self-evident). Our principle +rather asserts what follows: If we formulate the general +laws of nature as they are obtained from experience, +\index{Experience}% +by making use of +\begin{itemize} +\item[\itema] the embankment as reference-body, +\item[\itemb] the railway carriage as reference-body, +\end{itemize} +then these general laws of nature (\eg\ the laws of +mechanics or the law of the propagation of light \textit{in~vacuo}) +have exactly the same form in both cases. This can +also be expressed as follows: For the \emph{physical} description +of natural processes, neither of the reference-bodies +$K$,~$K'$ is unique (lit.\ ``specially marked out'') as +compared with the other. Unlike the first, this latter +statement need not of necessity hold \textit{a~priori}; it is +not contained in the conceptions of ``motion'' and +``reference-body'' and derivable from them; only +\emph{experience} can decide as to its correctness or incorrectness. + +Up to the present, however, we have by no means +maintained the equivalence of \emph{all} bodies of reference~$K$ +in connection with the formulation of natural laws. +Our course was more on the following lines. In the +first place, we started out from the assumption that +there exists a reference-body~$K$, whose condition of +\PageSep{61} +\index{Law of inertia}% +motion is such that the Galileian law holds with respect +to it: A particle left to itself and sufficiently far removed +from all other particles moves uniformly in a straight +line. With reference to~$K$ (Galileian reference-body) the +laws of nature were to be as simple as possible. But +in addition to~$K$, all bodies of reference~$K'$ should be +given preference in this sense, and they should be exactly +equivalent to~$K$ for the formulation of natural laws, +provided that they are in a state of \emph{uniform rectilinear +and non-rotary motion} with respect to~$K$; all these +bodies of reference are to be regarded as Galileian +reference-bodies. The validity of the principle of +relativity was assumed only for these reference-bodies, +but not for others (\eg\ those possessing motion of a +different kind). In this sense we speak of the \emph{special} +principle of relativity, or special theory of relativity. + +In contrast to this we wish to understand by the +``general principle of relativity'' the following statement: +All bodies of reference $K$,~$K'$,~etc., are equivalent +for the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion. But before proceeding farther, it +ought to be pointed out that this formulation must be +replaced later by a more abstract one, for reasons which +will become evident at a later stage. + +Since the introduction of the special principle of +relativity has been justified, every intellect which +strives after generalisation must feel the temptation +to venture the step towards the general principle of +relativity. But a simple and apparently quite reliable +consideration seems to suggest that, for the present +at any rate, there is little hope of success in such an +attempt. Let us imagine ourselves transferred to our +\PageSep{62} +\index{Law of inertia}% +old friend the railway carriage, which is travelling at a +uniform rate. As long as it is moving uniformly, the +occupant of the carriage is not sensible of its motion, +and it is for this reason that he can without reluctance +interpret the facts of the case as indicating that the +carriage is at rest but the embankment in motion. +Moreover, according to the special principle of relativity, +this interpretation is quite justified also from a physical +point of view. + +If the motion of the carriage is now changed into a +non-uniform motion, as for instance by a powerful +\index{Non-uniform motion}% +application of the brakes, then the occupant of the +carriage experiences a correspondingly powerful jerk +forwards. The retarded motion is manifested in the +mechanical behaviour of bodies relative to the person +in the railway carriage. The mechanical behaviour is +different from that of the case previously considered, +and for this reason it would appear to be impossible +that the same mechanical laws hold relatively to the non-uniformly +moving carriage, as hold with reference to the +carriage when at rest or in uniform motion. At all +events it is clear that the Galileian law does not hold +with respect to the non-uniformly moving carriage. +Because of this, we feel compelled at the present juncture +to grant a kind of absolute physical reality to non-uniform +motion, in opposition to the general principle +of relativity. But in what follows we shall soon see +that this conclusion cannot be maintained. +\PageSep{63} + + +\Chapter{XIX}{The Gravitational Field} + +``\First{If} we pick up a stone and then let it go, why does it +fall to the ground?'' The usual answer to this +question is: ``Because it is attracted by the earth.'' +Modern physics formulates the answer rather differently +for the following reason. As a result of the more careful +study of electromagnetic phenomena, we have come +to regard action at a distance as a process impossible +without the intervention of some intermediary medium. +If, for instance, a magnet attracts a piece of iron, we +cannot be content to regard this as meaning that the +magnet acts directly on the iron through the intermediate +empty space, but we are constrained to imagine---after +the manner of Faraday---that the magnet +\index{Faraday}% +always calls into being something physically real in +the space around it, that something being what we call a +``magnetic field.'' In its turn this magnetic field +\index{Magnetic field}% +operates on the piece of iron, so that the latter strives +to move towards the magnet. We shall not discuss +here the justification for this incidental conception, +which is indeed a somewhat arbitrary one. We shall +only mention that with its aid electromagnetic phenomena +can be theoretically represented much more +satisfactorily than without it, and this applies particularly +\index{Electromagnetic theory!waves}% +to the transmission of electromagnetic waves. +\PageSep{64} +The effects of gravitation also are regarded in an analogous +\index{Gravitation}% +manner. + +The action of the earth on the stone takes place indirectly. +The earth produces in its surroundings a +gravitational field, which acts on the stone and produces +\index{Gravitational field}% +its motion of fall. As we know from experience, the +intensity of the action on a body diminishes according +to a quite definite law, as we proceed farther and farther +away from the earth. From our point of view this +means: The law governing the properties of the gravitational +field in space must be a perfectly definite one, in +order correctly to represent the diminution of gravitational +action with the distance from operative bodies. +It is something like this: The body (\eg\ the earth) produces +a field in its immediate neighbourhood directly; +the intensity and direction of the field at points farther +removed from the body are thence determined by +the law which governs the properties in space of the +gravitational fields themselves. + +In contrast to electric and magnetic fields, the gravitational +field exhibits a most remarkable property, which +is of fundamental importance for what follows. Bodies +which are moving under the sole influence of a gravitational +field receive an acceleration, \emph{which does not in the +\index{Acceleration}% +least depend either on the material or on the physical +state of the body}. For instance, a piece of lead and +a piece of wood fall in exactly the same manner in a +gravitational field (\textit{in~vacuo}), when they start off from +rest or with the same initial velocity. This law, which +holds most accurately, can be expressed in a different +form in the light of the following consideration. + +According to Newton's law of motion, we have +\index{Newton's!law of motion}% +\[ +(\text{Force}) = (\text{inertial mass}) × (\text{acceleration}), +\] +\PageSep{65} +where the ``inertial mass'' is a characteristic constant +\index{Inertial mass}% +of the accelerated body. If now gravitation is the +cause of the acceleration, we then have +%[** TN: Re-breaking next two displayed equations] +\begin{multline*} +(\text{Force}) + = (\text{gravitational mass}) \\ + × (\text{intensity of the gravitational field}), +\index{Gravitational mass}% +\end{multline*} +where the ``gravitational mass'' is likewise a characteristic +constant for the body. From these two relations +follows: +\begin{multline*} +(\text{acceleration}) + = \frac{(\text{gravitational mass})}{(\text{inertial mass})} \\ + × (\text{intensity of the gravitational field}). +\end{multline*} + +If now, as we find from experience, the acceleration is +to be independent of the nature and the condition of the +body and always the same for a given gravitational +field, then the ratio of the gravitational to the inertial +mass must likewise be the same for all bodies. By a +suitable choice of units we can thus make this ratio +equal to unity. We then have the following law: +The \emph{gravitational} mass of a body is equal to its \emph{inertial} +mass. + +It is true that this important law had hitherto been +recorded in mechanics, but it had not been \emph{interpreted}. +A satisfactory interpretation can be obtained only if we +recognise the following fact: \emph{The same} quality of a +body manifests itself according to circumstances as +``inertia'' or as ``weight'' (lit.\ ``heaviness''). In the +\index{Inertia}% +\index{Weight (heaviness)}% +following section we shall show to what extent this is +actually the case, and how this question is connected +with the general postulate of relativity. +\PageSep{66} + + +\Chapter{XX}{The Equality of Inertial and Gravitational +Mass as an Argument for the +General Postulate of Relativity} + +\First{We} imagine a large portion of empty space, so far +removed from stars and other appreciable +masses, that we have before us approximately +the conditions required by the fundamental law of Galilei. +It is then possible to choose a Galileian reference-body for +this part of space (world), relative to which points at +rest remain at rest and points in motion continue permanently +in uniform rectilinear motion. As reference-body +let us imagine a spacious chest resembling a room +\index{Chest}% +with an observer inside who is equipped with apparatus. +Gravitation naturally does not exist for this observer. +He must fasten himself with strings to the floor, +otherwise the slightest impact against the floor will +cause him to rise slowly towards the ceiling of the +room. + +To the middle of the lid of the chest is fixed externally +a hook with rope attached, and now a ``being'' (what +\index{Being@{``Being''}}% +kind of a being is immaterial to us) begins pulling at +this with a constant force. The chest together with the +observer then begin to move ``upwards'' with a +uniformly accelerated motion. In course of time their +velocity will reach unheard-of values---provided that +\PageSep{67} +we are viewing all this from another reference-body +which is not being pulled with a rope. + +But how does the man in the chest regard the process? +The acceleration of the chest will be transmitted to him +\index{Acceleration}% +by the reaction of the floor of the chest. He must +therefore take up this pressure by means of his legs if +he does not wish to be laid out full length on the floor. +He is then standing in the chest in exactly the same way +as anyone stands in a room of a house on our earth. +If he release a body which he previously had in his +hand, the acceleration of the chest will no longer be +transmitted to this body, and for this reason the body +will approach the floor of the chest with an accelerated +relative motion. The observer will further convince +himself \emph{that the acceleration of the body towards the floor +of the chest is always of the same magnitude, whatever +kind of body he may happen to use for the experiment}. + +Relying on his knowledge of the gravitational field +\index{Gravitational field}% +(as it was discussed in the preceding section), the man +in the chest will thus come to the conclusion that he +and the chest are in a gravitational field which is constant +with regard to time. Of course he will be puzzled for +a moment as to why the chest does not fall, in this +gravitational field. Just then, however, he discovers +the hook in the middle of the lid of the chest and the +rope which is attached to it, and he consequently comes +to the conclusion that the chest is suspended at rest in +the gravitational field. + +Ought we to smile at the man and say that he errs +in his conclusion? I do not believe we ought to if we +wish to remain consistent; we must rather admit that +his mode of grasping the situation violates neither reason +nor known mechanical laws. Even though it is being +\PageSep{68} +accelerated with respect to the ``Galileian space'' +first considered, we can nevertheless regard the chest +as being at rest. We have thus good grounds for +extending the principle of relativity to include bodies +of reference which are accelerated with respect to each +other, and as a result we have gained a powerful argument +for a generalised postulate of relativity. + +We must note carefully that the possibility of this +mode of interpretation rests on the fundamental +property of the gravitational field of giving all bodies +\index{Gravitational mass}% +the same acceleration, or, what comes to the same thing, +on the law of the equality of inertial and gravitational +mass. If this natural law did not exist, the man in +the accelerated chest would not be able to interpret +the behaviour of the bodies around him on the supposition +of a gravitational field, and he would not be justified +on the grounds of experience in supposing his reference-body +to be ``at rest.'' + +Suppose that the man in the chest fixes a rope to the +inner side of the lid, and that he attaches a body to the +free end of the rope. The result of this will be to stretch +the rope so that it will hang ``vertically'' downwards. +If we ask for an opinion of the cause of tension in the +rope, the man in the chest will say: ``The suspended +body experiences a downward force in the gravitational +field, and this is neutralised by the tension of the rope; +what determines the magnitude of the tension of the +rope is the \emph{gravitational mass} of the suspended body.'' +On the other hand, an observer who is poised freely in +space will interpret the condition of things thus: ``The +rope must perforce take part in the accelerated motion +of the chest, and it transmits this motion to the body +attached to it. The tension of the rope is just large +\PageSep{69} +enough to effect the acceleration of the body. That +which determines the magnitude of the tension of the +rope is the \emph{inertial mass} of the body.'' Guided by +\index{Inertial mass}% +this example, we see that our extension of the principle +of relativity implies the \emph{necessity} of the law of the +equality of inertial and gravitational mass. Thus we +have obtained a physical interpretation of this law. + +From our consideration of the accelerated chest we +see that a general theory of relativity must yield important +results on the laws of gravitation. In point of +\index{Gravitation}% +fact, the systematic pursuit of the general idea of relativity +has supplied the laws satisfied by the gravitational +field. Before proceeding farther, however, I +must warn the reader against a misconception suggested +by these considerations. A gravitational field exists +for the man in the chest, despite the fact that there was +no such field for the co-ordinate system first chosen. +Now we might easily suppose that the existence of a +gravitational field is always only an \emph{apparent} one. We +might also think that, regardless of the kind of gravitational +field which may be present, we could always +choose another reference-body such that \emph{no} gravitational +field exists with reference to it. This is by no means +true for all gravitational fields, but only for those of +quite special form. It is, for instance, impossible to +choose a body of reference such that, as judged from it, +the gravitational field of the earth (in its entirety) +vanishes. + +We can now appreciate why that argument is not +convincing, which we brought forward against the +general principle of relativity at the end of \Sectionref{XVIII}. +It is certainly true that the observer in the railway +carriage experiences a jerk forwards as a result of the +\PageSep{70} +application of the brake, and that he recognises in this the +non-uniformity of motion (retardation) of the carriage. +But he is compelled by nobody to refer this jerk to a +``real'' acceleration (retardation) of the carriage. He +\index{Acceleration}% +might also interpret his experience thus: ``My body of +reference (the carriage) remains permanently at rest. +With reference to it, however, there exists (during the +period of application of the brakes) a gravitational +field which is directed forwards and which is variable +with respect to time. Under the influence of this field, +the embankment together with the earth moves non-uniformly +in such a manner that their original velocity +in the backwards direction is continuously reduced.'' +\PageSep{71} + + +\Chapter{XXI}{In what Respects are the Foundations +of Classical Mechanics and of the +Special Theory of Relativity unsatisfactory?} +\index{Classical mechanics}% +\index{Laws of Galilei-Newton!of Nature}% + +\First{We} have already stated several times that +classical mechanics starts out from the following +law: Material particles sufficiently far +removed from other material particles continue to +move uniformly in a straight line or continue in a +state of rest. We have also repeatedly emphasised +that this fundamental law can only be valid for +bodies of reference~$K$ which possess certain unique +states of motion, and which are in uniform translational +motion relative to each other. Relative to other reference-bodies~$K$ +the law is not valid. Both in classical +mechanics and in the special theory of relativity we +therefore differentiate between reference-bodies~$K$ +relative to which the recognised ``laws of nature'' can +be said to hold, and reference-bodies~$K$ relative to which +these laws do not hold. + +But no person whose mode of thought is logical can +rest satisfied with this condition of things. He asks: +``How does it come that certain reference-bodies (or +their states of motion) are given priority over other +reference-bodies (or their states of motion)? \emph{What is +\PageSep{72} +the reason for this preference?}\Change{}{''} In order to show clearly +what I mean by this question, I shall make use of a +comparison. + +I am standing in front of a gas range. Standing +alongside of each other on the range are two pans so +much alike that one may be mistaken for the other. +Both are half full of water. I notice that steam is being +emitted continuously from the one pan, but not from the +other. I am surprised at this, even if I have never seen +either a gas range or a pan before. But if I now notice +a luminous something of bluish colour under the first +pan but not under the other, I cease to be astonished, +even if I have never before seen a gas flame. For I +can only say that this bluish something will cause the +emission of the steam, or at least \emph{possibly} it may do so. +If, however, I notice the bluish something in neither +case, and if I observe that the one continuously emits +steam whilst the other does not, then I shall remain +astonished and dissatisfied until I have discovered +some circumstance to which I can attribute the different +behaviour of the two pans. + +Analogously, I seek in vain for a real something in +classical mechanics (or in the special theory of relativity) +to which I can attribute the different behaviour +of bodies considered with respect to the reference-systems +$K$~and~$K'$.\footnote + {The objection is of importance more especially when the state + of motion of the reference-body is of such a nature that it does + not require any external agency for its maintenance, \eg\ in + the case when the reference-body is rotating uniformly.} +Newton saw this objection and +\index{Newton}% +attempted to invalidate it, but without success. But +E.~Mach recognised it most clearly of all, and because +\index{Mach, E.}% +of this objection he claimed that mechanics must be +\PageSep{73} +placed on a new basis. It can only be got rid of by +means of a physics which is conformable to the general +principle of relativity, since the equations of such a +theory hold for every body of reference, whatever +may be its state of motion. +\PageSep{74} + + +\Chapter{XXII}{A Few Inferences from the General +Principle of Relativity} + +\First{The} considerations of \Sectionref{XX} show that the +general principle of relativity puts us in a position +to derive properties of the gravitational field in a +\index{Gravitational field}% +purely theoretical manner. Let us suppose, for instance, +that we know the space-time ``course'' for any natural +process whatsoever, as regards the manner in which it +takes place in the Galileian domain relative to a +Galileian body of reference~$K$. By means of purely +theoretical operations (\ie\ simply by calculation) we are +then able to find how this known natural process +appears, as seen from a reference-body~$K'$ which is +accelerated relatively to~$K$. But since a gravitational +field exists with respect to this new body of reference~$K'$, +our consideration also teaches us how the gravitational +field influences the process studied. + +For example, we learn that a body which is in a state +of uniform rectilinear motion with respect to~$K$ (in +accordance with the law of Galilei) is executing an +accelerated and in general curvilinear motion with +\index{Curvilinear motion}% +respect to the accelerated reference-body~$K'$ (chest). +This acceleration or curvature corresponds to the influence +on the moving body of the gravitational field +prevailing relatively to~$K'$. It is known that a gravitational +field influences the movement of bodies in this +\PageSep{75} +way, so that our consideration supplies us with nothing +essentially new. + +However, we obtain a new result of fundamental +\index{Propagation of light!in gravitational fields}% +importance when we carry out the analogous consideration +for a ray of light. With respect to the Galileian +reference-body~$K$, such a ray of light is transmitted +rectilinearly with the velocity~$c$. It can easily be shown +that the path of the same ray of light is no longer a +straight line when we consider it with reference to the +accelerated chest (reference-body~$K'$). From this we +conclude, \emph{that, in general, rays of light are propagated +curvilinearly in gravitational fields}. In two respects +this result is of great importance. + +In the first place, it can be compared with the reality. +Although a detailed examination of the question shows +that the curvature of light rays required by the general +theory of relativity is only exceedingly small for the +gravitational fields at our disposal in practice, its estimated +magnitude for light rays passing the sun at +grazing incidence is nevertheless $1.7$~seconds of arc. +This ought to manifest itself in the following way. +As seen from the earth, certain fixed stars appear to be +in the neighbourhood of the sun, and are thus capable +of observation during a total eclipse of the sun. At such +times, these stars ought to appear to be displaced +outwards from the sun by an amount indicated above, +as compared with their apparent position in the sky +when the sun is situated at another part of the heavens. +The examination of the correctness or otherwise of this +deduction is a problem of the greatest importance, the +early solution of which is to be expected of astronomers.\footnote + {By means of the star photographs of two expeditions equipped + by a Joint Committee of the Royal and Royal Astronomical + Societies, the existence of the deflection of light demanded by + theory was confirmed during the solar eclipse of 29th~May, 1919. +\index{Solar eclipse}% + (Cf.\ \Appendixref{III}.)} +\PageSep{76} + +In the second place our result shows that, according +to the general theory of relativity, the law of the constancy +of the velocity of light \textit{in~vacuo}, which constitutes +\index{Velocity of light}% +one of the two fundamental assumptions in the +special theory of relativity and to which we have +already frequently referred, cannot claim any unlimited +validity. A curvature of rays of light can only take +place when the velocity of propagation of light varies +with position. Now we might think that as a consequence +of this, the special theory of relativity and with +it the whole theory of relativity would be laid in the +dust. But in reality this is not the case. We can only +conclude that the special theory of relativity cannot +claim an unlimited domain of validity; its results +hold only so long as we are able to disregard the influences +of gravitational fields on the phenomena +(\eg\ of light). + +Since it has often been contended by opponents of +the theory of relativity that the special theory of +relativity is overthrown by the general theory of relativity, +it is perhaps advisable to make the facts of the +case clearer by means of an appropriate comparison. +Before the development of electrodynamics the laws +\index{Electrodynamics}% +of electrostatics were looked upon as the laws of +\index{Electrostatics}% +electricity. At the present time we know that +\index{Electricity}% +electric fields can be derived correctly from electrostatic +considerations only for the case, which is never +strictly realised, in which the electrical masses are quite +at rest relatively to each other, and to the co-ordinate +system. Should we be justified in saying that for this +\PageSep{77} +reason electrostatics is overthrown by the field-equations +of Maxwell in electrodynamics? Not in the least. +\index{Maxwell!fundamental equations}% +Electrostatics is contained in electrodynamics as a +limiting case; the laws of the latter lead directly to +those of the former for the case in which the fields are +invariable with regard to time. No fairer destiny +could be allotted to any physical theory, than that it +should of itself point out the way to the introduction +of a more comprehensive theory, in which it lives on +as a limiting case. + +In the example of the transmission of light just dealt +with, we have seen that the general theory of relativity +enables us to derive theoretically the influence of a +gravitational field on the course of natural processes, +\index{Gravitational field}% +the laws of which are already known when a gravitational +field is absent. But the most attractive problem, +to the solution of which the general theory of relativity +supplies the key, concerns the investigation of the laws +satisfied by the gravitational field itself. Let us consider +this for a moment. + +We are acquainted with space-time domains which +behave (approximately) in a ``Galileian'' fashion under +suitable choice of reference-body, \ie\ domains in which +gravitational fields are absent. If we now refer such +a domain to a reference-body~$K'$ possessing any kind +of motion, then relative to~$K'$ there exists a gravitational +field which is variable with respect to space and +time.\footnote + {This follows from a generalisation of the discussion in \Sectionref{XX}.} +The character of this field will of course depend +on the motion chosen for~$K'$. According to the general +theory of relativity, the general law oi the gravitational +field must be satisfied for all gravitational fields obtainable +\PageSep{78} +in this way. Even though by no means all gravitational +fields can be produced in this way, yet we may +entertain the hope that the general law of gravitation +\index{Gravitation}% +will be derivable from such gravitational fields of a +special kind. This hope has been realised in the most +beautiful manner. But between the clear vision of +this goal and its actual realisation it was necessary to +surmount a serious difficulty, and as this lies deep at +the root of things, I dare not withhold it from the reader. +We require to extend our ideas of the space-time continuum +\index{Continuum!space-time}% +still farther. +\PageSep{79} + + +\Chapter{XXIII}{Behaviour of Clocks and Measuring-Rods +on a Rotating Body of Reference} + +\First{Hitherto} I have purposely refrained from +speaking about the physical interpretation of +space- and time-data in the case of the general +theory of relativity. As a consequence, I am guilty of a +certain slovenliness of treatment, which, as we know +from the special theory of relativity, is far from being +unimportant and pardonable. It is now high time that +we remedy this defect; but I would mention at the +outset, that this matter lays no small claims on the +patience and on the power of abstraction of the reader. + +We start off again from quite special cases, which we +\index{Galileian system of co-ordinates}% +have frequently used before. Let us consider a space-time +domain in which no gravitational field exists +relative to a reference-body~$K$ whose state of motion +\index{Reference-body!rotating}% +has been suitably chosen. $K$~is then a Galileian reference-body +as regards the domain considered, and the +results of the special theory of relativity hold relative +to~$K$. Let us suppose the same domain referred to a +second body of reference~$K'$, which is rotating uniformly +with respect to~$K$. In order to fix our ideas, we shall +imagine~$K'$ to be in the form of a plane circular disc, +which rotates uniformly in its own plane about its +centre. An observer who is sitting eccentrically on the +\PageSep{80} +disc~$K'$ is sensible of a force which acts outwards in a +radial direction, and which would be interpreted as an +effect of inertia (centrifugal force) by an observer who +\index{Centrifugal force}% +was at rest with respect to the original reference-body~$K$. +But the observer on the disc may regard his disc as a +reference-body which is ``at rest''; on the basis of the +general principle of relativity he is justified in doing this. +The force acting on himself, and in fact on all other +bodies which are at rest relative to the disc, he regards +as the effect of a gravitational field. Nevertheless, +the space-distribution of this gravitational field is of a +kind that would not be possible on Newton's theory of +\index{Newton's!law of gravitation}% +gravitation.\footnote + {The field disappears at the centre of the disc and increases + proportionally to the distance from the centre as we proceed + outwards.} +But since the observer believes in the +general theory of relativity, this does not disturb him; +he is quite in the right when he believes that a general +law of gravitation can be formulated---a law which not +only explains the motion of the stars correctly, but +also the field of force experienced by himself. + +The observer performs experiments on his circular +disc with clocks and measuring-rods. In doing so, it +\index{Clocks}% +\index{Measuring-rod}% +is his intention to arrive at exact definitions for the +signification of time- and space-data with reference +to the circular disc~$K'$, these definitions being based on +his observations. What will be his experience in this +enterprise? + +To start with, he places one of two identically constructed +clocks at the centre of the circular disc, and the +other on the edge of the disc, so that they are at rest +relative to it. We now ask ourselves whether both +clocks go at the same rate from the standpoint of the +\PageSep{81} +non-rotating Galileian reference-body~$K$. As judged +from this body, the clock at the centre of the disc has +no velocity, whereas the clock at the edge of the disc +is in motion relative to~$K$ in consequence of the rotation. +\index{Rotation}% +According to a result obtained in \Sectionref{XII}, it follows +that the latter clock goes at a rate permanently slower +than that of the clock at the centre of the circular disc, +\ie\ as observed from~$K$. It is obvious that the same effect +would be noted by an observer whom we will imagine +sitting alongside his clock at the centre of the circular +disc. Thus on our circular disc, or, to make the case +more general, in every gravitational field, a clock will +go more quickly or less quickly, according to the position +in which the clock is situated (at rest). For this reason +it is not possible to obtain a reasonable definition of time +with the aid of clocks which are arranged at rest with +\index{Clocks}% +respect to the body of reference. A similar difficulty +presents itself when we attempt to apply our earlier +definition of simultaneity in such a case, but I do not +\index{Simultaneity}% +wish to go any farther into this question. + +Moreover, at this stage the definition of the space +\index{Space co-ordinates}% +co-ordinates also presents insurmountable difficulties. +If the observer applies his standard measuring-rod +\index{Measuring-rod}% +(a rod which is short as compared with the radius of +the disc) tangentially to the edge of the disc, then, as +judged from the Galileian system, the length of this rod +will be less than~$1$, since, according to \Sectionref{XII}, moving +bodies suffer a shortening in the direction of the motion. +On the other hand, the measuring-rod will not experience +a shortening in length, as judged from~$K$, if it is applied +to the disc in the direction of the radius. If, then, the +observer first measures the circumference of the disc +with his measuring-rod and then the diameter of the +\PageSep{82} +disc, on dividing the one by the other, he will not obtain +as quotient the familiar number $\pi = 3.14\dots$, but +a larger number,\footnote + {Throughout this consideration we have to use the Galileian + (non-rotating) system~$K$ as reference-body, since we may only + assume the validity of the results of the special theory of relativity + relative to~$K$ (relative to~$K'$ a gravitational field prevails).} +whereas of course, for a disc which is +at rest with respect to~$K$, this operation would yield~$\pi$ +\index{Value of $\pi$}% +exactly. This proves that the propositions of Euclidean +\index{Euclidean geometry}% +geometry cannot hold exactly on the rotating disc, nor +in general in a gravitational field, at least if we attribute +the length~$1$ to the rod in all positions and in every +orientation. Hence the idea of a straight line also loses +\index{Straight line}% +its meaning. We are therefore not in a position to +define exactly the co-ordinates $x$,~$y$,~$z$ relative to the +disc by means of the method used in discussing the +special theory, and as long as the co-ordinates and times +of events have not been defined, we cannot assign an +exact meaning to the natural laws in which these occur. + +Thus all our previous conclusions based on general +relativity would appear to be called in question. In +reality we must make a subtle detour in order to be +able to apply the postulate of general relativity exactly. +I shall prepare the reader for this in the +following paragraphs. +\PageSep{83} + + +\Chapter{XXIV}{Euclidean and Non-Euclidean Continuum} +\index{Continuum}% + +\First{The} surface of a marble table is spread out in front +of me. I can get from any one point on this +table to any other point by passing continuously +from one point to a ``neighbouring'' one, and repeating +this process a (large) number of times, or, in other words, +by going from point to point without executing ``jumps.'' +I am sure the reader will appreciate with sufficient +clearness what I mean here by ``neighbouring'' and by +``jumps'' (if he is not too pedantic). We express this +property of the surface by describing the latter as a +continuum. + +Let us now imagine that a large number of little rods +of equal length have been made, their lengths being +small compared with the dimensions of the marble +slab. When I say they are of equal length, I mean that +one can be laid on any other without the ends overlapping. +We next lay four of these little rods on the +marble slab so that they constitute a quadrilateral +figure (a square), the diagonals of which are equally +long. To ensure the equality of the diagonals, we make +use of a little testing-rod. To this square we add +similar ones, each of which has one rod in common +with the first. We proceed in like manner with each of +these squares until finally the whole marble slab is +\PageSep{84} +laid out with squares. The arrangement is such, that +each side of a square belongs to two squares and each +corner to four squares. + +It is a veritable wonder that we can carry out this +business without getting into the greatest difficulties. +We only need to think of the following. If at any +moment three squares meet at a corner, then two sides +of the fourth square are already laid, and, as a consequence, +the arrangement of the remaining two sides of +the square is already completely determined. But I +am now no longer able to adjust the quadrilateral so +that its diagonals may be equal. If they are equal +of their own accord, then this is an especial favour +of the marble slab and of the little rods, about which I +can only be thankfully surprised. We must needs +experience many such surprises if the construction is to +be successful. + +If everything has really gone smoothly, then I say +that the points of the marble slab constitute a Euclidean +\index{Distance (line-interval)}% +\index{Continuum!Euclidean}% +continuum with respect to the little rod, which has been +used as a ``distance'' (line-interval). By choosing +one corner of a square as ``origin,'' I can characterise +every other corner of a square with reference to this +origin by means of two numbers. I only need state +how many rods I must pass over when, starting from the +origin, I proceed towards the ``right'' and then ``upwards,'' +in order to arrive at the corner of the square +under consideration. These two numbers are then the +``Cartesian co-ordinates'' of this corner with reference +\index{Cartesian system of co-ordinates}% +to the ``Cartesian co-ordinate system'' which is determined +by the arrangement of little rods. + +By making use of the following modification of this +abstract experiment, we recognise that there must also +\PageSep{85} +\index{Measurement of length}% +be cases in which the experiment would be unsuccessful. +We shall suppose that the rods ``expand'' by an amount +proportional to the increase of temperature. We heat +the central part of the marble slab, but not the periphery, +in which case two of our little rods can still be +brought into coincidence at every position on the table. +But our construction of squares must necessarily come +into disorder during the heating, because the little rods +on the central region of the table expand, whereas +those on the outer part do not. + +With reference to our little rods---defined as unit +lengths---the marble slab is no longer a Euclidean continuum, +and we are also no longer in the position of defining +Cartesian co-ordinates directly with their aid, +since the above construction can no longer be carried +out. But since there are other things which are not +influenced in a similar manner to the little rods (or +perhaps not at all) by the temperature of the table, it is +possible quite naturally to maintain the point of view +that the marble slab is a ``Euclidean continuum.'' +This can be done in a satisfactory manner by making a +more subtle stipulation about the measurement or the +comparison of lengths. + +But if rods of every kind (\ie\ of every material) were +to behave \emph{in the same way} as regards the influence of +temperature when they are on the variably heated +marble slab, and if we had no other means of detecting +the effect of temperature than the geometrical behaviour +of our rods in experiments analogous to the one +described above, then our best plan would be to assign +the distance \emph{one} to two points on the slab, provided that +the ends of one of our rods could be made to coincide +with these two points; for how else should we define +\PageSep{86} +the distance without our proceeding being in the highest +measure grossly arbitrary? The method of Cartesian +co-ordinates must then be discarded, and replaced by +another which does not assume the validity of Euclidean +\index{Continuum!Euclidean}% +\index{Continuum!non-Euclidean}% +\index{Euclidean geometry}% +\index{Euclidean space}% +geometry for rigid bodies.\footnote + {Mathematicians have been confronted with our problem in the + following form. If we are given a surface (\eg\ an ellipsoid) in + Euclidean three-dimensional space, then there exists for this + surface a two-dimensional geometry, just as much as for a plane + surface. Gauss undertook the task of treating this two-dimensional +\index{Gauss}% + geometry from first principles, without making use of the + fact that the surface belongs to a Euclidean continuum of + three dimensions. If we imagine constructions to be made with + rigid rods \emph{in the surface} (similar to that above with the marble + slab), we should find that different laws hold for these from those + resulting on the basis of Euclidean plane geometry. The surface + is not a Euclidean continuum with respect to the rods, and we + cannot define Cartesian co-ordinates \emph{in the surface}. Gauss + indicated the principles according to which we can treat the + geometrical relationships in the surface, and thus pointed out + the way to the method of Riemann of treating multi-dimensional, +\index{Riemann}% + non-Euclidean \textit{continua}. Thus it is that mathematicians + long ago solved the formal problems to which we are led by the + general postulate of relativity.} +The reader will notice that +the situation depicted here corresponds to the one +brought about by the general postulate of relativity +(\Sectionref{XXIII}). +\PageSep{87} + + +\Chapter{XXV}{Gaussian Co-ordinates} + +\First{According} to Gauss, this combined analytical +\index{Gauss}% +and geometrical mode of handling the problem +can be arrived at in the following way. We +imagine a system of arbitrary curves (see \Figref{4}) +drawn on the surface of the table. These we designate +as $u$-curves, and we indicate each of them by +means of a number. The curves $u = 1$, $u = 2$ and +$u = 3$ are drawn in the diagram. Between the curves +$u = 1$ and $u = 2$ we must imagine an infinitely large +number to be drawn, all of which correspond +%[Illustration: Fig. 4.] +\WFigure{2in}{087} +to real +numbers lying between $1$~and~$2$. We have then +a system of $u$-curves, and +this ``infinitely dense'' system +covers the whole surface +of the table. These +$u$-curves must not intersect +each other, and through each +point of the surface one and +only one curve must pass. +Thus a perfectly definite +value of~$u$ belongs to every point on the surface of the +marble slab. In like manner we imagine a system of +$v$-curves drawn on the surface. These satisfy the same +conditions as the $u$-curves, they are provided with numbers +\PageSep{88} +in a corresponding manner, and they may likewise +be of arbitrary shape. It follows that a value of~$u$ and +a value of~$v$ belong to every point on the surface of the +table. We call these two numbers the co-ordinates +of the surface of the table (Gaussian co-ordinates). +\index{Gaussian co-ordinates|(}% +For example, the point~$P$ in the diagram has the Gaussian +co-ordinates $u = 3$, $v = 1$. Two neighbouring points $P$ +and~$P'$ on the surface then correspond to the co-ordinates +\begin{align*} +&P: &&u, v \\ +&P': &&u + du, v + dv, +\end{align*} +where $du$~and~$dv$ signify very small numbers. In a +similar manner we may indicate the distance (line-interval) +\index{Distance (line-interval)}% +between $P$~and~$P'$, as measured with a little +rod, by means of the very small number~$ds$. Then +according to Gauss we have +\[ +ds^{2} = g_{11}\, du^{2} + 2g_{12}\, du\, dv + g_{22}\, dv^{2}, +\] +where $g_{11}$,~$g_{12}$,~$g_{22}$, are magnitudes which depend in a +perfectly definite way on $u$~and~$v$. The magnitudes $g_{11}$,~$g_{12}$ +and~$g_{22}$ determine the behaviour of the rods relative +to the $u$-curves and $v$-curves, and thus also relative +to the surface of the table. For the case in which the +points of the surface considered form a Euclidean continuum +\index{Continuum!Euclidean}% +with reference to the measuring-rods, but +only in this case, it is possible to draw the $u$-curves +and $v$-curves and to attach numbers to them, in such a +manner, that we simply have: +\[ +ds^{2} = du^{2} + dv^{2}. +\] +Under these conditions, the $u$-curves and $v$-curves are +straight lines in the sense of Euclidean geometry, and +\index{Euclidean geometry}% +\index{Straight line}% +they are perpendicular to each other. Here the Gaussian +co-ordinates are simply Cartesian ones. It is clear +\PageSep{89} +that Gauss co-ordinates are nothing more than an +association of two sets of numbers with the points of +the surface considered, of such a nature that numerical +values differing very slightly from each other are +associated with neighbouring points ``in space.'' + +So far, these considerations hold for a continuum +\index{Continuum!four-dimensional}% +of two dimensions. But the Gaussian method can be +applied also to a continuum of three, four or more +dimensions. If, for instance, a continuum of four +dimensions be supposed available, we may represent +it in the following way. With every point of the +continuum we associate arbitrarily four numbers, $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$, which are known as ``co-ordinates.'' Adjacent +points correspond to adjacent values of the co-ordinates. +If a distance~$ds$ is associated with the adjacent points +\index{Adjacent points}% +$P$~and~$P'$, this distance being measurable and well-defined +from a physical point of view, then the following +formula holds: +\[ +ds^{2} = g_{11}\, {dx_{1}}^{2} + + 2g_{12}\, dx_{1}\, dx_{2} \Add{+} \dots + + g_{44}\, {dx_{4}}^{2}, +\] +where the magnitudes $g_{11}$,~etc., have values which vary +with the position in the continuum. Only when the +continuum is a Euclidean one is it possible to associate +the co-ordinates $x_{1}$\Add{,}\ldots\Add{,}~$x_{4}$ with the points of the +continuum so that we have simply +\[ +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2}. +\] +In this case relations hold in the four-dimensional +continuum which are analogous to those holding in our +three-dimensional measurements. + +However, the Gauss treatment for~$ds^{2}$ which we have +given above is not always possible. It is only possible +when sufficiently small regions of the continuum under +consideration may be regarded as Euclidean continua. +\PageSep{90} +For example, this obviously holds in the case of the +marble slab of the table and local variation of temperature. +The temperature is practically constant for a small +part of the slab, and thus the geometrical behaviour of +the rods is \emph{almost} as it ought to be according to the +rules of Euclidean geometry. Hence the imperfections +\index{Continuum!non-Euclidean}% +of the construction of squares in the previous section +do not show themselves clearly until this construction +is extended over a considerable portion of the surface +of the table. + +We can sum this up as follows: Gauss invented a +\index{Gauss}% +method for the mathematical treatment of continua in +general, in which ``size-relations'' (``distances'' between +\index{Size-relations}% +neighbouring points) are defined. To every point of a +continuum are assigned as many numbers (Gaussian co-ordinates) +as the continuum has dimensions. This is +done in such a way, that only one meaning can be attached +to the assignment, and that numbers (Gaussian co-ordinates) +\index{Gaussian co-ordinates|)}% +which differ by an indefinitely small amount +are assigned to adjacent points. The Gaussian co-ordinate +system is a logical generalisation of the Cartesian +co-ordinate system. It is also applicable to non-Euclidean +continua, but only when, with respect to the defined +``size'' or ``distance,'' small parts of the continuum +under consideration behave more nearly like a Euclidean +system, the smaller the part of the continuum under +our notice. +\PageSep{91} + + +\Chapter{XXVI}{The Space-Time Continuum of the Special +Theory of Relativity considered as +a Euclidean Continuum} +\index{Continuum!four-dimensional}% +\index{Continuum!space-time|(}% + +\First{We} are now in a position to formulate more +exactly the idea of Minkowski, which was +\index{Minkowski}% +only vaguely indicated in \Sectionref{XVII}. +In accordance with the special theory of relativity, +certain co-ordinate systems are given preference +for the description of the four-dimensional, space-time +continuum. We called these ``Galileian co-ordinate +\index{Galileian system of co-ordinates}% +systems.'' For these systems, the four co-ordinates +$x$,~$y$, $z$,~$t$, which determine an event or---in other +words---a point of the four-dimensional continuum, are +defined physically in a simple manner, as set forth in +detail in the first part of this book. For the transition +from one Galileian system to another, which is moving +uniformly with reference to the first, the equations of +the Lorentz transformation are valid. These last +\index{Lorentz, H. A.!transformation}% +form the basis for the derivation of deductions from the +special theory of relativity, and in themselves they are +nothing more than the expression of the universal +validity of the law of transmission of light for all Galileian +\index{Propagation of light}% +systems of reference. + +Minkowski found that the Lorentz transformations +satisfy the following simple conditions. Let us consider +\PageSep{92} +two neighbouring events, the relative position of which +in the four-dimensional continuum is given with respect +\index{Continuum!four-dimensional}% +to a Galileian reference-body~$K$ by the space co-ordinate +\index{Coordinate@{Co-ordinate}!differences}% +\index{Coordinate@{Co-ordinate}!differentials}% +differences $dx$,~$dy$,~$dz$ and the time-difference~$dt$. With +reference to a second Galileian system we shall suppose +that the corresponding differences for these two events +are $dx'$,~$dy'$, $dz'$,~$dt'$. Then these magnitudes always +fulfil the condition\footnote + {Cf.\ Appendices I~and~II\@. The relations which are derived + there for the co-ordinates themselves are valid also for co-ordinate + \emph{differences}, and thus also for co-ordinate differentials + (indefinitely small differences).} +\[ +dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2} + = dx'^{2} + dy'^{2} + dz'^{2} - c^{2}\, dt'^{2}. +\] + +The validity of the Lorentz transformation follows +from this condition. We can express this as follows: +The magnitude +\[ +ds^{2} = dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2}, +\] +which belongs to two adjacent points of the four-dimensional +space-time continuum, has the same value +for all selected (Galileian) reference-bodies. If we replace +$x$,~$y$, $z$,~$\sqrt{-1}\,ct$, by $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, we also obtain the +result that +\[ +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2} +\] +is independent of the choice of the body of reference. +We call the magnitude~$ds$ the ``distance'' apart of the +two events or four-dimensional points. + +Thus, if we choose as time-variable the imaginary +variable~$\sqrt{-1}\,ct$ instead of the real quantity~$t$, we can +regard the space-time continuum---in accordance with +the special theory of relativity---as a ``Euclidean'' +\index{Continuum!Euclidean}% +four-dimensional continuum, a result which follows +from the considerations of the preceding section. +\PageSep{93} + + +\Chapter{XXVII}{The Space-Time Continuum of the +General Theory of Relativity is +not a Euclidean Continuum} + +\First{In} the first part of this book we were able to make use +of space-time co-ordinates which allowed of a simple +and direct physical interpretation, and which, according +to \Sectionref{XXVI}, can be regarded as four-dimensional +Cartesian co-ordinates. This was possible on the basis +of the law of the constancy of the velocity of light. But +according to \Sectionref{XXI}, the general theory of relativity +cannot retain this law. On the contrary, we arrived at +the result that according to this latter theory the +velocity of light must always depend on the co-ordinates +when a gravitational field is present. In connection +\index{Gravitational field}% +with a specific illustration in \Sectionref{XXIII}, we found +that the presence of a gravitational field invalidates the +definition of the co-ordinates and the time, which led us +to our objective in the special theory of relativity. + +In view of the results of these considerations we are +led to the conviction that, according to the general +principle of relativity, the space-time continuum cannot +be regarded as a Euclidean one, but that here we have +the general case, corresponding to the marble slab with +local variations of temperature, and with which we +made acquaintance as an example of a two-dimensional +\PageSep{94} +continuum. Just as it was there impossible to construct +\index{Continuum!two-dimensional}% +\index{Continuum!four-dimensional}% +a Cartesian co-ordinate system from equal rods, so +here it is impossible to build up a system (reference-body) +from rigid bodies and clocks, which shall be of +\index{Clocks}% +such a nature that measuring-rods and clocks, arranged +\index{Measuring-rod}% +rigidly with respect to one another, shall indicate position +and time directly. Such was the essence of the +difficulty with which we were confronted in \Sectionref{XXIII}. + +But the considerations of Sections \Srefno{XXV}~and~\Srefno{XXVI} +show us the way to surmount this difficulty. We refer the +four-dimensional space-time continuum in an arbitrary +manner to Gauss co-ordinates. We assign to every +\index{Gaussian co-ordinates}% +point of the continuum (event) four numbers, $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$ (co-ordinates), which have not the least direct +physical significance, but only serve the purpose of +numbering the points of the continuum in a definite +but arbitrary manner. This arrangement does not even +need to be of such a kind that we must regard $x_{1}$,~$x_{2}$,~$x_{3}$ as +``space'' co-ordinates and $x_{4}$~as a ``time'' co-ordinate. + +The reader may think that such a description of the +world would be quite inadequate. What does it mean +to assign to an event the particular co-ordinates $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$, if in themselves these co-ordinates have no +significance? More careful consideration shows, however, +that this anxiety is unfounded. Let us consider, +for instance, a material point with any kind of motion. +If this point had only a momentary existence without +duration, then it would be described in space-time by a +single system of values $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$. Thus its permanent +existence must be characterised by an infinitely large +number of such systems of values, the co-ordinate values +of which are so close together as to give continuity; +\PageSep{95} +corresponding to the material point, we thus have a +(uni-dimensional) line in the four-dimensional continuum. +\index{Continuity}% +In the same way, any such lines in our continuum +correspond to many points in motion. The only statements +having regard to these points which can claim +a physical existence are in reality the statements about +their encounters. In our mathematical treatment, +such an encounter is expressed in the fact that the two +lines which represent the motions of the points in +question have a particular system of co-ordinate values, +$x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, in common. After mature consideration +the reader will doubtless admit that in reality such +encounters constitute the only actual evidence of a +time-space nature with which we meet in physical +statements. + +When we were describing the motion of a material +\index{Encounter (space-time coincidence)}% +point relative to a body of reference, we stated +nothing more than the encounters of this point with +particular points of the reference-body. We can also +determine the corresponding values of the time by the +observation of encounters of the body with clocks, in +\index{Clocks}% +conjunction with the observation of the encounter of the +hands of clocks with particular points on the dials. +It is just the same in the case of space-measurements by +means of measuring-rods, as a little consideration will +show. + +The following statements hold generally: Every +physical description resolves itself into a number of +statements, each of which refers to the space-time +coincidence of two events $A$~and~$B$. In terms of +Gaussian co-ordinates, every such statement is expressed +by the agreement of their four co-ordinates $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$. +Thus in reality, the description of the time-space +\PageSep{96} +continuum by means of Gauss co-ordinates completely +\index{Gaussian co-ordinates|(}% +replaces the description with the aid of a body of reference, +without suffering from the defects of the latter +mode of description; it is not tied down to the Euclidean +character of the continuum which has to be represented. +\index{Continuum!space-time|)}% +\PageSep{97} + + +\Chapter{XXVIII}{Exact Formulation of the General +Principle of Relativity} +\index{General theory of relativity}% + +\First{We} are now in a position to replace the provisional +formulation of the general principle +of relativity given in \Sectionref{XVIII} by +an exact formulation. The form there used, ``All +bodies of reference $K$,~$K'$,~etc., are equivalent for +the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion,'' cannot be maintained, because the +use of rigid reference-bodies, in the sense of the method +followed in the special theory of relativity, is in general +not possible in space-time description. The Gauss +co-ordinate system has to take the place of the body of +reference. The following statement corresponds to the +fundamental idea of the general principle of relativity: +``\emph{All Gaussian co-ordinate systems are essentially equivalent +for the formulation of the general laws of nature.}'' + +We can state this general principle of relativity in still +another form, which renders it yet more clearly intelligible +than it is when in the form of the natural +extension of the special principle of relativity. According +to the special theory of relativity, the equations +which express the general laws of nature pass over into +equations of the same form when, by making use of the +Lorentz transformation, we replace the space-time +\index{Lorentz, H. A.!transformation}% +\PageSep{98} +variables $x$,~$y$, $z$,~$t$, of a (Galileian) reference-body~$K$ +by the space-time variables $x'$,~$y'$, $z'$,~$t'$, of a new reference-body~$K'$. +According to the general theory +of relativity, on the other hand, by application of +\emph{arbitrary substitutions} of the Gauss variables $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, +\index{Arbitrary substitutions}% +the equations must pass over into equations of the same +form; for every transformation (not only the Lorentz +\index{Lorentz, H. A.!transformation}% +transformation) corresponds to the transition of one +Gauss co-ordinate system into another. + +If we desire to adhere to our ``old-time'' three-dimensional +\index{Law of inertia}% +view of things, then we can characterise +the development which is being undergone by the +fundamental idea of the general theory of relativity +as follows: The special theory of relativity has reference +to Galileian domains, \ie\ to those in which no gravitational +field exists. In this connection a Galileian reference-body +\index{Galileian system of co-ordinates}% +serves as body of reference, \ie\ a rigid +body the state of motion of which is so chosen that the +Galileian law of the uniform rectilinear motion of +``isolated'' material points holds relatively to it. + +Certain considerations suggest that we should refer +the same Galileian domains to \emph{non-Galileian} reference-bodies +\index{Non-Galileian reference-bodies}% +also. A gravitational field of a special kind is +\index{Gravitational field}% +then present with respect to these bodies (cf.\ Sections \Srefno{XX} +and~\Srefno{XXIII}). + +In gravitational fields there are no such things as rigid +\index{Time!in Physics}% +bodies with Euclidean properties; thus the fictitious rigid +body of reference is of no avail in the general theory of +relativity. The motion of clocks is also influenced by +\index{Clocks|(}% +gravitational fields, and in such a way that a physical +definition of time which is made directly with the aid of +clocks has by no means the same degree of plausibility +as in the special theory of relativity. +\PageSep{99} +\index{Laws of Galilei-Newton!of Nature}% +\index{Time!coordinate@{co-ordinate}}% + +For this reason non-rigid reference-bodies are used, +which are as a whole not only moving in any way +whatsoever, but which also suffer alterations in form +\textit{ad~lib.}\ during their motion. Clocks, for which the law of +motion is of any kind, however irregular, serve for the +definition of time. We have to imagine each of these +clocks fixed at a point on the non-rigid reference-body. +\index{Reference-mollusk|(}% +These clocks satisfy only the one condition, that the +``readings'' which are observed simultaneously on +adjacent clocks (in space) differ from each other by an +\index{Space!point@{-point}}% +indefinitely small amount. This non-rigid reference-body, +which might appropriately be termed a ``reference-mollusk,'' +is in the main equivalent to a Gaussian four-dimensional +co-ordinate system chosen arbitrarily. +That which gives the ``mollusk'' a certain comprehensibleness +as compared with the Gauss co-ordinate +system is the (really unjustified) formal retention of +the separate existence of the space co-ordinates as +\index{Space co-ordinates}% +opposed to the time co-ordinate. Every point on the +mollusk is treated as a space-point, and every material +point which is at rest relatively to it as at rest, so long as +the mollusk is considered as reference-body. The +general principle of relativity requires that all these +mollusks can be used as reference-bodies with equal +right and equal success in the formulation of the general +laws of nature; the laws themselves must be quite +independent of the choice of mollusk. + +The great power possessed by the general principle +of relativity lies in the comprehensive limitation which +is imposed on the laws of nature in consequence of what +we have seen above. +\PageSep{100} + + +\Chapter{XXIX}{The Solution of the Problem of Gravitation +on the Basis of the General +Principle of Relativity} + +\First{If} the reader has followed all our previous considerations, +he will have no further difficulty in +understanding the methods leading to the solution +of the problem of gravitation. + +We start off from a consideration of a Galileian +domain, \ie\ a domain in which there is no gravitational +field relative to the Galileian reference-body~$K$. The +\index{Galileian system of co-ordinates}% +behaviour of measuring-rods and clocks with reference +\index{Measuring-rod}% +to~$K$ is known from the special theory of relativity, +likewise the behaviour of ``isolated'' material points; +the latter move uniformly and in straight lines. + +Now let us refer this domain to a random Gauss co-ordinate +system or to a ``mollusk'' as reference-body~$K'$. +Then with respect to~$K'$ there is a gravitational +field~$G$ (of a particular kind). We learn the behaviour +of measuring-rods and clocks and also of freely-moving +material points with reference to~$K'$ simply by mathematical +transformation. We interpret this behaviour +as the behaviour of measuring-rods, clocks and material +\index{Clocks|)}% +points under the influence of the gravitational field~$G$. +\index{Gravitational field}% +Hereupon we introduce a hypothesis: that the influence +of the gravitational field on measuring-rods, +\index{Gaussian co-ordinates|)}% +\PageSep{101} +clocks and freely-moving material points continues to +take place according to the same laws, even in the case +when the prevailing gravitational field is \emph{not} derivable +\index{Gravitational field}% +from the Galileian special case, simply by means of a +transformation of co-ordinates. + +The next step is to investigate the space-time +behaviour of the gravitational field~$G$, which was derived +from the Galileian special case simply by transformation +of the co-ordinates. This behaviour is formulated +in a law, which is always valid, no matter how the +\index{Matter}% +reference-body (mollusk) used in the description may +\index{Reference-mollusk|)}% +be chosen. + +This law is not yet the \emph{general} law of the gravitational +field, since the gravitational field under consideration is +of a special kind. In order to find out the general +law-of-field of gravitation we still require to obtain a +generalisation of the law as found above. This can be +obtained without caprice, however, by taking into +consideration the following demands: +\begin{itemize} +\item[\itema] The required generalisation must likewise satisfy + the general postulate of relativity. + +\item[\itemb] If there is any matter in the domain under consideration, + only its inertial mass, and thus +\index{Inertial mass}% + according to \Sectionref{XV} only its energy is of + importance for its effect in exciting a field. + +\item[\itemc] Gravitational field and matter together must + satisfy the law of the conservation of energy +\index{Conservation of energy}% +\index{Conservation of energy!impulse}% +\index{Kinetic energy}% + (and of impulse). +\end{itemize} + +Finally, the general principle of relativity permits +us to determine the influence of the gravitational field +on the course of all those processes which take place +according to known laws when a gravitational field is +\PageSep{102} +absent, \ie\ which have already been fitted into the +frame of the special theory of relativity. In this connection +we proceed in principle according to the method +which has already been explained for measuring-rods, +\index{Measuring-rod}% +clocks and freely-moving material points. +\index{Clocks}% + +The theory of gravitation derived in this way from +\index{Gravitation}% +the general postulate of relativity excels not only in +its beauty; nor in removing the defect attaching to +classical mechanics which was brought to light in \Sectionref{XXI}; +\index{Classical mechanics}% +nor in interpreting the empirical law of the equality +of inertial and gravitational mass; but it has also +\index{Gravitational mass}% +\index{Inertial mass}% +already explained a result of observation in astronomy, +\index{Astronomy}% +against which classical mechanics is powerless. + +If we confine the application of the theory to the +case where the gravitational fields can be regarded as +being weak, and in which all masses move with respect +to the co-ordinate system with velocities which are +small compared with the velocity of light, we then obtain +as a first approximation the Newtonian theory. Thus +the latter theory is obtained here without any particular +assumption, whereas Newton had to introduce the +\index{Newton}% +hypothesis that the force of attraction between mutually +attracting material points is inversely proportional to +the square of the distance between them. If we increase +the accuracy of the calculation, deviations from +the theory of Newton make their appearance, practically +all of which must nevertheless escape the test of +observation owing to their smallness. + +We must draw attention here to one of these deviations. +According to Newton's theory, a planet moves +round the sun in an ellipse, which would permanently +maintain its position with respect to the fixed stars, +if we could disregard the motion of the fixed stars +\index{Motion!of heavenly bodies}% +\PageSep{103} +themselves and the action of the other planets under +consideration. Thus, if we correct the observed motion +of the planets for these two influences, and if Newton's +theory be strictly correct, we ought to obtain for the +orbit of the planet an ellipse, which is fixed with reference +to the fixed stars. This deduction, which can +be tested with great accuracy, has been confirmed +for all the planets save one, with the precision that is +capable of being obtained by the delicacy of observation +attainable at the present time. The sole exception +is Mercury, the planet which lies nearest the sun. Since +\index{Mercury}% +\index{Mercury!orbit of}% +the time of Leverrier, it has been known that the ellipse +\index{Leverrier}% +corresponding to the orbit of Mercury, after it has been +corrected for the influences mentioned above, is not +stationary with respect to the fixed stars, but that it +rotates exceedingly slowly in the plane of the orbit +and in the sense of the orbital motion. The value +obtained for this rotary movement of the orbital ellipse +was $43$~seconds of arc per~century, an amount ensured +to be correct to within a few seconds of arc. This +effect can be explained by means of classical mechanics +\index{Classical mechanics}% +only on the assumption of hypotheses which have +little probability, and which were devised solely for +this purpose. + +On the basis of the general theory of relativity, it +is found that the ellipse of every planet round the sun +must necessarily rotate in the manner indicated above; +that for all the planets, with the exception of Mercury, +this rotation is too small to be detected with the delicacy +of observation possible at the present time; but that in +the case of Mercury it must amount to $43$~seconds of +arc per century, a result which is strictly in agreement +with observation. +\PageSep{104} + +Apart from this one, it has hitherto been possible to +make only two deductions from the theory which admit +of being tested by observation, to wit, the curvature +\index{Curvature of light-rays}% +of light rays by the gravitational field of the sun,\footnote + {Observed by Eddington and others in~1919. (Cf.\ \Appendixref{III}.)} +\index{Eddington}% +and a displacement of the spectral lines of light reaching +\index{Displacement of spectral lines}% +us from large stars, as compared with the corresponding +lines for light produced in an analogous manner terrestrially +(\ie\ by the same kind of molecule). I do not +doubt that these deductions from the theory will be +confirmed also. +\index{General theory of relativity|)}% +\PageSep{105} + + +\Part{III}{Considerations on the Universe as +a Whole}{Considerations on the Universe} + +\Chapter{XXX}{Cosmological Difficulties of Newton's +Theory} +\index{Newton}% + +\First{Apart} from the difficulty discussed in \Sectionref{XXI}, +there is a second fundamental difficulty +attending classical celestial mechanics, which, +\index{Celestial mechanics}% +to the best of my knowledge, was first discussed in +detail by the astronomer Seeliger. If we ponder over +\index{Seeliger}% +the question as to how the universe, considered as a +whole, is to be regarded, the first answer that suggests +itself to us is surely this: As regards space (and time) +\index{Space}% +\index{Time!conception of}% +the universe is infinite. There are stars everywhere, +so that the density of matter, although very variable +in detail, is nevertheless on the average everywhere the +same. In other words: However far we might travel +through space, we should find everywhere an attenuated +swarm of fixed stars of approximately the same kind +and density. + +This view is not in harmony with the theory of +Newton. The latter theory rather requires that the +universe should have a kind of centre in which the +\PageSep{106} +density of the stars is a maximum, and that as we +proceed outwards from this centre the group-density +\index{Group-density of stars}% +of the stars should diminish, until finally, at great +distances, it is succeeded by an infinite region of emptiness. +The stellar universe ought to be a finite island in +\index{Stellar universe}% +the infinite ocean of space.\footnote + {\textit{Proof}---According to the theory of Newton, the number of + ``lines of force'' which come from infinity and terminate in a +\index{Lines of force}% + mass~$m$ is proportional to the mass~$m$. If, on the average, the + mass-density~$\rho_{0}$ is constant throughout the universe, then a + sphere of volume~$V$ will enclose the average mass~$\rho_{0}V$. Thus + the number of lines of force passing through the surface~$F$ of the + sphere into its interior is proportional to~$\rho_{0}V$. For unit area + of the surface of the sphere the number of lines of force which + enters the sphere is thus proportional to~$\rho_{0}\dfrac{V}{F}$ or to~$\rho_{0}R$. Hence + the intensity of the field at the surface would ultimately become + infinite with increasing radius~$R$ of the sphere, which is impossible.} + +This conception is in itself not very satisfactory. +It is still less satisfactory because it leads to the result +that the light emitted by the stars and also individual +stars of the stellar system are perpetually passing out +into infinite space, never to return, and without ever +again coming into interaction with other objects of +nature. Such a finite material universe would be +destined to become gradually but systematically impoverished. + +In order to escape this dilemma, Seeliger suggested a +\index{Intensity of gravitational field}% +\index{Seeliger}% +modification of Newton's law, in which he assumes that +\index{Newton's!law of gravitation}% +for great distances the force of attraction between two +masses diminishes more rapidly than would result from +the inverse square law. In this way it is possible for the +mean density of matter to be constant everywhere, +even to infinity, without infinitely large gravitational +fields being produced. We thus free ourselves from the +\PageSep{107} +distasteful conception that the material universe ought +to possess something of the nature of a centre. Of +course we purchase our emancipation from the fundamental +difficulties mentioned, at the cost of a modification +and complication of Newton's law which has +neither empirical nor theoretical foundation. We can +imagine innumerable laws which would serve the same +purpose, without our being able to state a reason why +one of them is to be preferred to the others; for any +one of these laws would be founded just as little on +more general theoretical principles as is the law of +Newton. +\PageSep{108} + + +\Chapter{XXXI}{The Possibility of a ``Finite'' and yet +``Unbounded'' Universe} +\index{Universe (World) structure of}% + +\First{But} speculations on the structure of the universe +also move in quite another direction. The +development of non-Euclidean geometry led to +\index{Euclidean geometry}% +\index{Non-Euclidean geometry}% +the recognition of the fact, that we can cast doubt on the +\emph{infiniteness} of our space without coming into conflict +with the laws of thought or with experience (Riemann, +\index{Riemann}% +Helmholtz). These questions have already been treated +\index{Helmholtz}% +in detail and with unsurpassable lucidity by Helmholtz +and Poincaré, whereas I can only touch on them +\index{Poincare@{Poincaré}}% +briefly here. + +In the first place, we imagine an existence in two-dimensional +\index{Being@{``Being''}}% +\index{Space!two-dimensional}% +space. Flat beings with flat implements, +and in particular flat rigid measuring-rods, are free to +move in a \emph{plane}. For them nothing exists outside of +\index{Plane}% +this plane: that which they observe to happen to +themselves and to their flat ``things'' is the all-inclusive +reality of their plane. In particular, the constructions +of plane Euclidean geometry can be carried out by +means of the rods, \eg\ the lattice construction, considered +\index{Lattice}% +in \Sectionref{XXIV}. In contrast to ours, the universe of +these beings is two-dimensional; but, like ours, it extends +to infinity. In their universe there is room for an +infinite number of identical squares made up of rods, +\PageSep{109} +\ie\ its volume (surface) is infinite. If these beings say +their universe is ``plane,'' there is sense in the statement, +\index{Plane}% +\index{Universe!Euclidean}% +because they mean that they can perform the constructions +of plane Euclidean geometry with their rods. +\index{Euclidean geometry}% +In this connection the individual rods always represent +\index{Distance (line-interval)}% +the same distance, independently of their position. + +Let us consider now a second two-dimensional existence, +but this time on a spherical surface instead of on +\index{Spherical!surface}% +a plane. The flat beings with their measuring-rods +and other objects fit exactly on this surface and they +are unable to leave it. Their whole universe of observation +extends exclusively over the surface of the sphere. +Are these beings able to regard the geometry of their +universe as being plane geometry and their rods withal +as the realisation of ``distance''? They cannot do +this. For if they attempt to realise a straight line, they +\index{Straight line}% +will obtain a curve, which we ``three-dimensional +beings'' designate as a great circle, \ie\ a self-contained +line of definite finite length, which can be measured +up by means of a measuring-rod. Similarly, this +universe has a finite area that can be compared with the +area of a square constructed with rods. The great +charm resulting from this consideration lies in the +recognition of the fact that \emph{the universe of these beings is +finite and yet has no limits}. + +But the spherical-surface beings do not need to go +on a world-tour in order to perceive that they are not +\index{World}% +living in a Euclidean universe. They can convince +themselves of this on every part of their ``world,'' +provided they do not use too small a piece of it. Starting +from a point, they draw ``straight lines'' (arcs of circles +as judged in three-dimensional space) of equal length +in all directions. They will call the line joining the +\PageSep{110} +free ends of these lines a ``circle.'' For a plane surface, +the ratio of the circumference of a circle to its diameter, +both lengths being measured with the same rod, is, +according to Euclidean geometry of the plane, equal to +a constant value~$\pi$, which is independent of the diameter +\index{Value of $\pi$}% +of the circle. On their spherical surface our flat beings +would find for this ratio the value +\[ +\pi = \frac{\sin\left(\dfrac{r}{R}\right)}{\left(\dfrac{r}{R}\right)}, +\] +\ie\ a smaller value than~$\pi$, the difference being the +more considerable, the greater is the radius of the +circle in comparison with the radius~$R$ of the ``world-sphere.'' +\index{World!sphere@{-sphere}}% +By means of this relation the spherical beings +can determine the radius of their universe (``world''), +even when only a relatively small part of their world-sphere +is available for their measurements. But if this +part is very small indeed, they will no longer be able to +demonstrate that they are on a spherical ``world'' and +not on a Euclidean plane, for a small part of a spherical +surface differs only slightly from a piece of a plane of +the same size. + +Thus if the spherical-surface beings are living on a +planet of which the solar system occupies only a negligibly +small part of the spherical universe, they have no means +of determining whether they are living in a finite or in +an infinite universe, because the ``piece of universe'' +to which they have access is in both cases practically +plane, or Euclidean. It follows directly from this +discussion, that for our sphere-beings the circumference +of a circle first increases with the radius until the ``circumference +\PageSep{111} +\index{Universe (World) structure of!circumference of}% +of the universe'' is reached, and that it +\index{Universe!Euclidean}% +\index{Universe!spherical}% +thenceforward gradually decreases to zero for still +further increasing values of the radius. During this +process the area of the circle continues to increase +more and more, until finally it becomes equal to the +total area of the whole ``world-sphere.'' +\index{World!sphere@{-sphere}}% + +Perhaps the reader will wonder why we have placed +our ``beings'' on a sphere rather than on another closed +surface. But this choice has its justification in the fact +that, of all closed surfaces, the sphere is unique in possessing +the property that all points on it are equivalent. I +admit that the ratio of the circumference~$c$ of a circle +to its radius~$r$ depends on~$r$, but for a given value of~$r$ +it is the same for all points of the ``world-sphere''; +in other words, the ``world-sphere'' is a ``surface of +constant curvature.'' + +To this two-dimensional sphere-universe there is a +three-dimensional analogy, namely, the three-dimensional +spherical space which was discovered by Riemann. Its +\index{Riemann}% +points are likewise all equivalent. It possesses a finite +volume, which is determined by its ``radius'' ($2\pi^{2}R^{3}$). +Is it possible to imagine a spherical space? To imagine +a space means nothing else than that we imagine an +epitome of our ``space'' experience, \ie\ of experience +that we can have in the movement of ``rigid'' bodies. +In this sense we \emph{can} imagine a spherical space. + +Suppose we draw lines or stretch strings in all directions +from a point, and mark off from each of these +the distance~$r$ with a measuring-rod. All the free end-points +\index{Measuring-rod}% +of these lengths lie on a spherical surface. We +\index{Spherical!space}% +can specially measure up the area~($F$) of this surface +by means of a square made up of measuring-rods. If +the universe is Euclidean, then $F = 4\pi r^{2}$; if it is spherical, +\PageSep{112} +then $F$~is always less than~$4\pi r^{2}$. With increasing +values of~$r$, $F$~increases from zero up to a maximum +value which is determined by the ``world-radius,'' but +\index{World!radius@{-radius}}% +for still further increasing values of~$r$, the area gradually +diminishes to zero. At first, the straight lines which +radiate from the starting point diverge farther and +farther from one another, but later they approach +each other, and finally they run together again at a +``counter-point'' to the starting point. Under such +\index{Counter-Point}% +conditions they have traversed the whole spherical +space. It is easily seen that the three-dimensional +spherical space is quite analogous to the two-dimensional +spherical surface. It is finite (\ie\ of finite volume), and +\index{Spherical!space}% +has no bounds. + +It may be mentioned that there is yet another kind +of curved space: ``elliptical space.'' It can be regarded +\index{Elliptical space}% +as a curved space in which the two ``counter-points'' +are identical (indistinguishable from each other). An +elliptical universe can thus be considered to some +\index{Universe!elliptical}% +extent as a curved universe possessing central symmetry. + +It follows from what has been said, that closed spaces +without limits are conceivable. From amongst these, +the spherical space (and the elliptical) excels in its +simplicity, since all points on it are equivalent. As a +result of this discussion, a most interesting question +arises for astronomers and physicists, and that is +whether the universe in which we live is infinite, or +whether it is finite in the manner of the spherical universe. +Our experience is far from being sufficient to +enable us to answer this question. But the general +theory of relativity permits of our answering it with a +moderate degree of certainty, and in this connection the +difficulty mentioned in \Sectionref{XXX} finds its solution. +\PageSep{113} + + +\Chapter{XXXII}{The Structure of Space according to +the General Theory of Relativity} +\index{Motion!of heavenly bodies}% +\index{Universe (World) structure of}% + +\First{According} to the general theory of relativity, +the geometrical properties of space are not independent, +but they are determined by matter. +Thus we can draw conclusions about the geometrical +structure of the universe only if we base our considerations +on the state of the matter as being something +that is known. We know from experience that, for a +suitably chosen co-ordinate system, the velocities of +the stars are small as compared with the velocity of +transmission of light. We can thus as a rough approximation +arrive at a conclusion as to the nature of +the universe as a whole, if we treat the matter as being +at rest. + +We already know from our previous discussion that the +behaviour of measuring-rods and clocks is influenced by +\index{Clocks}% +\index{Measuring-rod}% +gravitational fields, \ie\ by the distribution of matter. +\index{Gravitational field}% +This in itself is sufficient to exclude the possibility of +the exact validity of Euclidean geometry in our universe. +\index{Euclidean geometry}% +But it is conceivable that our universe differs +only slightly from a Euclidean one, and this notion +seems all the more probable, since calculations show +that the metrics of surrounding space is influenced only +to an exceedingly small extent by masses even of the +\PageSep{114} +magnitude of our sun. We might imagine that, as +regards geometry, our universe behaves analogously +\index{Universe!elliptical}% +\index{Universe!space expanse (radius) of}% +\index{Universe!spherical}% +to a surface which is irregularly curved in its individual +parts, but which nowhere departs appreciably from a +plane: something like the rippled surface of a lake. +Such a universe might fittingly be called a quasi-Euclidean +universe. As regards its space it would be +infinite. But calculation shows that in a quasi-Euclidean +universe the average density of matter +would necessarily be \emph{nil}. Thus such a universe could +not be inhabited by matter everywhere; it would +present to us that unsatisfactory picture which we +portrayed in \Sectionref{XXX}. + +If we are to have in the universe an average density +of matter which differs from zero, however small may +be that difference, then the universe cannot be quasi-Euclidean. +\index{Quasi-Euclidean universe}% +On the contrary, the results of calculation +indicate that if matter be distributed uniformly, the +universe would necessarily be spherical (or elliptical). +Since in reality the detailed distribution of matter is +not uniform, the real universe will deviate in individual +parts from the spherical, \ie\ the universe will be quasi-spherical. +\index{Quasi-spherical universe}% +But it will be necessarily finite. In fact, the +theory supplies us with a simple connection\footnote + {For the ``radius''~$R$ of the universe we obtain the equation + \[ + R^{2} = \frac{2}{\kappa \rho}. + \] + The use of the C.G.S. system in this equation gives $\dfrac{2}{\kappa} = 1.08 × 10^{27}$; +is the average density of the matter.} +between +the space-expanse of the universe and the average +density of matter in it. +\PageSep{115} + + +\Appendix{I}{Simple Derivation of the Lorentz +Transformation}{[Supplementary to \Sectionref{XI}]} +\index{Lorentz, H. A.!transformation}% + +\First{For} the relative orientation of the co-ordinate +systems indicated in \Figref{2}, the $x$-axes of both +systems permanently coincide. In the present +case we can divide the problem into parts by considering +first only events which are localised on the $x$-axis. Any +such event is represented with respect to the co-ordinate +system~$K$ by the abscissa~$x$ and the time~$t$, and with +respect to the system~$K'$ by the abscissa~$x'$ and the +time~$t'$. We require to find $x'$~and~$t'$ when $x$~and~$t$ are +given. + +A light-signal, which is proceeding along the positive +\index{Light-signal}% +axis of~$x$, is transmitted according to the equation +\[ +x = ct +\] +or +\[ +x - ct = 0. +\Tag{(1)} +\] +Since the same light-signal has to be transmitted relative +to~$K'$ with the velocity~$c$, the propagation relative to +the system~$K'$ will be represented by the analogous +formula +\[ +x' - ct' = 0. +\Tag{(2)} +\] +Those space-time points (events) which satisfy~\Eqref{(1)} must +\PageSep{116} +also satisfy~\Eqref{(2)}. Obviously this will be the case when +the relation +\[ +(x' - ct') = \lambda(x - ct)\Change{.}{} +\Tag{(3)} +\] +is fulfilled in general, where $\lambda$~indicates a constant; for, +according to~\Eqref{(3)}, the disappearance of~$(x - ct)$ involves +the disappearance of~$(x' - ct')$. + +If we apply quite similar considerations to light rays +which are being transmitted along the negative $x$-axis, +we obtain the condition +\[ +(x' + ct') = \mu(x + ct). +\Tag{(4)} +\] + +By adding (or subtracting) equations \Eqref{(3)}~and~\Eqref{(4)}, and +introducing for convenience the constants $a$~and~$b$ in +place of the constants $\lambda$~and~$\mu$, where +\begin{align*} +a &= \frac{\lambda + \mu}{2} +\intertext{and} +b &= \frac{\lambda - \mu}{2}, +\end{align*} +we obtain the equations +\[ +\left. +\begin{aligned} +x' &= ax - bct\Add{,} \\ +ct' &= act - bx. +\end{aligned} +\right\} +\Tag{(5)} +\] + +We should thus have the solution of our problem, +if the constants $a$~and~$b$ were known. These result +from the following discussion. + +For the origin of~$K'$ we have permanently $x' = 0$, and +hence according to the first of the equations~\Eqref{(5)} +\[ +x = \frac{bc}{a} t. +\] + +If we call~$v$ the velocity with which the origin of~$K'$ is +moving relative to~$K$, we then have +\[ +v = \frac{bc}{a}. +\Tag{(6)} +\] +\PageSep{117} + +The same value~$v$ can be obtained from equation~\Eqref{(5)}, +if we calculate the velocity of another point of~$K'$ +relative to~$K$, or the velocity (directed towards the +\index{Relative!velocity}% +negative $x$-axis) of a point of~$K$ with respect to~$K'$. In +short, we can designate~$v$ as the relative velocity of the +two systems. + +Furthermore, the principle of relativity teaches us +that, as judged from~$K$, the length of a unit measuring-rod +\index{Measuring-rod}% +which is at rest with reference to~$K'$ must be exactly +the same as the length, as judged from~$K'$, of a unit +measuring-rod which is at rest relative to~$K$. In order +to see how the points of the $x'$-axis appear as viewed +from~$K$, we only require to take a ``snapshot'' of~$K'$ +\index{Instantaneous photograph (snapshot)}% +from~$K$; this means that we have to insert a particular +value of~$t$ (time of~$K$), \eg\ $t = 0$. For this value of~$t$ +we then obtain from the first of the equations~\Eqref{(5)} +\[ +x' = ax. +\] + +Two points of the $x'$-axis which are separated by the +distance $\Delta x' = 1$ when measured in the $K'$~system are +thus separated in our instantaneous photograph by the +distance +\[ +\Delta x = \frac{1}{a}. +\Tag{(7)} +\] + +But if the snapshot be taken from~$K'$\Change{}{ }($t' = 0$), and if +we eliminate~$t$ from the equations~\Eqref{(5)}, taking into +account the expression~\Eqref{(6)}, we obtain +\[ +x' = a\left(1 - \frac{v^{2}}{c^{2}}\right)x. +\] + +From this we conclude that two points on the $x$-axis +and separated by the distance~$1$ (relative to~$K$) will +be represented on our snapshot by the distance +\[ +\Delta x' = a\left(1 - \frac{v^{2}}{c^{2}}\right). +\Tag{(7a)} +\] +\PageSep{118} + +But from what has been said, the two snapshots +must be identical; hence $\Delta x$~in~\Eqref{(7)} must be equal to +$\Delta x'$~in~\Eqref{(7a)}, so that we obtain +\[ +a^{2} = \frac{1}{1 - \dfrac{v^{2}}{c^{2}}}. +\Tag{(7b)} +\] + +The equations \Eqref{(6)}~and~\Eqref{(7b)} determine the constants $a$~and~$b$. +By inserting the values of these constants in~\Eqref{(5)}, +we obtain the first and the fourth of the equations +given in \Sectionref{XI}. +\[ +\left. +\begin{aligned} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,} \\ +t' &= \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{aligned} +\right\} +\Tag{(8)} +\] + +Thus we have obtained the Lorentz transformation +\index{Lorentz, H. A.!transformation}% +for events on the $x$-axis. It satisfies the condition +\[ +x'^{2} - c^{2} t'^{2} = x^{2} - c^{2} t^{2}. +\Tag{(8a)} +\] + +The extension of this result, to include events which +take place outside the $x$-axis, is obtained by retaining +equations~\Eqref{(8)} and supplementing them by the relations +\[ +\left. +\begin{aligned} +y' &= y\Add{,} \\ +z' &= z. +\end{aligned} +\right\} +\Tag{(9)} +\] +In this way we satisfy the postulate of the constancy of +the velocity of light \textit{in~vacuo} for rays of light of arbitrary +\index{Velocity of light}% +direction, both for the system~$K$ and for the system~$K'$. +This may be shown in the following manner. + +We suppose a light-signal sent out from the origin +\index{Light-signal}% +of~$K$ at the time $t = 0$. It will be propagated according +to the equation +\[ +r = \sqrt{x^{2} + y^{2} + z^{2}} = ct, +\] +\PageSep{119} +or, if we square this equation, according to the equation +\[ +x^{2} + y^{2} + z^{2} - c^{2} t^{2} = 0. +\Tag{(10)} +\] + +It is required by the law of propagation of light, in +\index{Propagation of light}% +conjunction with the postulate of relativity, that the +transmission of the signal in question should take place---as +judged from~$K'$---in accordance with the corresponding +formula +\[ +r' = ct', +\] +or, +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} = 0. +\Tag{(10a)} +\] +In order that equation~\Eqref{(10a)} may be a consequence of +equation~\Eqref{(10)}, we must have +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = \sigma(x^{2} + y^{2} + z^{2} - c^{2} t^{2}). +\Tag{(11)} +\] + +Since equation~\Eqref{(8a)} must hold for points on the +$x$-axis, we thus have $\sigma = 1$. It is easily seen that the +Lorentz transformation really satisfies equation~\Eqref{(11)} +\index{Lorentz, H. A.!transformation}% +for $\sigma = 1$; for \Eqref{(11)}~is a consequence of \Eqref{(8a)}~and~\Eqref{(9)}, +and hence also of \Eqref{(8)}~and~\Eqref{(9)}. We have thus derived +the Lorentz transformation. + +The Lorentz transformation represented by \Eqref{(8)}~and~\Eqref{(9)} +still requires to be generalised. Obviously it is +immaterial whether the axes of~$K'$ be chosen so that +they are spatially parallel to those of~$K$. It is also not +essential that the velocity of translation of~$K'$ with +respect to~$K$ should be in the direction of the $x$-axis. +A simple consideration shows that we are able to +construct the Lorentz transformation in this general +sense from two kinds of transformations, viz.\ from +Lorentz transformations in the special sense and from +purely spatial transformations, which corresponds to +the replacement of the rectangular co-ordinate system +\PageSep{120} +by a new system with its axes pointing in other +directions. + +Mathematically, we can characterise the generalised +Lorentz transformation thus: +\index{Lorentz, H. A.!transformation!(generalised)}% + +It expresses $x'$,~$y'$, $z'$,~$t'$, in terms of linear homogeneous +functions of $x$,~$y$, $z$,~$t$, of such a kind that the relation +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = x^{2} + y^{2} + z^{2} - c^{2} t^{2} +\Tag{(11a)} +\] +is satisfied identically. That is to say: If we substitute +their expressions in $x$,~$y$, $z$,~$t$, in place of $x'$,~$y'$, +$z'$,~$t'$, on the left-hand side, then the left-hand side of~\Eqref{(11a)} +agrees with the right-hand side. +\PageSep{121} + + +\Appendix{II}{Minkowski's Four-dimensional Space +(``World'')}{[Supplementary to \Sectionref{XVII}]} + +\First{We} can characterise the Lorentz transformation +\index{Lorentz, H. A.!transformation}% +still more simply if we introduce the imaginary~$\sqrt{-1}·ct$ +in place of~$t$, as time-variable. If, in +accordance with this, we insert +\begin{align*} +x_{1} &= x\Add{,} \\ +x_{2} &= y\Add{,} \\ +x_{3} &= z\Add{,} \\ +x_{4} &= \sqrt{-1}·ct, +\end{align*} +and similarly for the accented system~$K'$, then the +condition which is identically satisfied by the transformation +can be expressed thus: +\[ +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + x_{4}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2} + {x_{4}}^{2}. +\Tag{(12)} +\] + +That is, by the afore-mentioned choice of ``co-ordinates,'' +\Eqref{(11a)}~is transformed into this equation. + +We see from~\Eqref{(12)} that the imaginary time co-ordinate~$x_{4}$ +\index{Cartesian system of co-ordinates}% +\index{Euclidean geometry}% +\index{Euclidean space}% +\index{Space!three-dimensional}% +\index{Time!in Physics}% +enters into the condition of transformation in exactly +the same way as the space co-ordinates $x_{1}$,~$x_{2}$,~$x_{3}$. It +is due to this fact that, according to the theory of +\PageSep{122} +relativity, the ``time''~$x_{4}$ enters into natural laws in the +same form as the space co-ordinates $x_{1}$,~$x_{2}$,~$x_{3}$. + +A four-dimensional continuum described by the +\index{Continuum!four-dimensional}% +``co-or\-di\-nates'' $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, was called ``world'' by +\index{World}% +\index{World!point@{-point}}% +Minkowski, who also termed a point-event a ``world-point.'' +\index{Minkowski}% +From a ``happening'' in three-dimensional +space, physics becomes, as it were, an ``existence'' in +the four-dimensional ``world.'' + +This four-dimensional ``world'' bears a close similarity +to the three-dimensional ``space'' of (Euclidean) +analytical geometry. If we introduce into the latter a +new Cartesian co-ordinate system $(x_{1}', x_{2}', x_{3}')$ with +the same origin, then $x_{1}'$,~$x_{2}'$,~$x_{3}'$, are linear homogeneous +functions of $x_{1}$,~$x_{2}$,~$x_{3}$, which identically satisfy the +equation +\[ +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2}. +\] +The analogy with~\Eqref{(12)} is a complete one. We can +regard Minkowski's ``world'' in a formal manner as a +four-dimensional Euclidean space (with imaginary +time co-ordinate); the Lorentz transformation corresponds +to a ``rotation'' of the co-ordinate system in the +\index{Rotation}% +four-dimensional ``world.'' +\PageSep{123} + + +\Appendix{III}{The Experimental Confirmation of the +General Theory of Relativity}{} +\index{Theory}% + +\First{From} a systematic theoretical point of view, we +may imagine the process of evolution of an empirical +science to be a continuous process of induction. +\index{Induction}% +Theories are evolved and are expressed in +short compass as statements of a large number of individual +observations in the form of empirical laws, +\index{Empirical laws}% +from which the general laws can be ascertained by comparison. +Regarded in this way, the development of a +science bears some resemblance to the compilation of a +classified catalogue. It is, as it were, a purely empirical +enterprise. + +But this point of view by no means embraces the whole +of the actual process; for it slurs over the important +part played by intuition and deductive thought in the +\index{Deductive thought}% +\index{Intuition}% +development of an exact science. As soon as a science +has emerged from its initial stages, theoretical advances +are no longer achieved merely by a process of arrangement. +Guided by empirical data, the investigator +rather develops a system of thought which, in general, +is built up logically from a small number of fundamental +assumptions, the so-called axioms. We call such a +\index{Axioms}% +system of thought a \emph{theory}. The theory finds the +\PageSep{124} +\index{Classical mechanics}% +\index{Darwinian theory}% +justification for its existence in the fact that it correlates +a large number of single observations, and it is just here +that the ``truth'' of the theory lies. +\index{Theory!truth of}% + +Corresponding to the same complex of empirical data, +there may be several theories, which differ from one +another to a considerable extent. But as regards the +deductions from the theories which are capable of +being tested, the agreement between the theories may +be so complete, that it becomes difficult to find such +deductions in which the two theories differ from each +other. As an example, a case of general interest is +available in the province of biology, in the Darwinian +\index{Biology}% +theory of the development of species by selection in +the struggle for existence, and in the theory of development +which is based on the hypothesis of the hereditary +transmission of acquired characters. + +We have another instance of far-reaching agreement +between the deductions from two theories in Newtonian +mechanics on the one hand, and the general theory of +relativity on the other. This agreement goes so far, +that up to the present we have been able to find only +a few deductions from the general theory of relativity +which are capable of investigation, and to which the +physics of pre-relativity days does not also lead, and +this despite the profound difference in the fundamental +assumptions of the two theories. In what follows, we +shall again consider these important deductions, and we +shall also discuss the empirical evidence appertaining to +them which has hitherto been obtained. + + +\Subsection{a}{Motion of the Perihelion of Mercury} +\index{Perihelion of Mercury|(}% + +According to Newtonian mechanics and Newton's +\index{Newton's!law of gravitation}% +law of gravitation, a planet which is revolving round the +\PageSep{125} +sun would describe an ellipse round the latter, or, more +correctly, round the common centre of gravity of the +sun and the planet. In such a system, the sun, or the +common centre of gravity, lies in one of the foci of the +orbital ellipse in such a manner that, in the course of a +planet-year, the distance sun-planet grows from a +minimum to a maximum, and then decreases again to +a minimum. If instead of Newton's law we insert a +\index{Newton}% +somewhat different law of attraction into the calculation, +we find that, according to this new law, the motion +would still take place in such a manner that the distance +sun-planet exhibits periodic variations; but in this +case the angle described by the line joining sun and +planet during such a period (from perihelion---closest +proximity to the sun---to perihelion) would differ from~$360°$. +The line of the orbit would not then be a closed +one, but in the course of time it would fill up an annular +part of the orbital plane, viz.\ between the circle of +least and the circle of greatest distance of the planet from +the sun. + +According also to the general theory of relativity, +which differs of course from the theory of Newton, a +small variation from the Newton-Kepler motion of a +\index{Kepler}% +planet in its orbit should take place, and in such a way, +that the angle described by the radius sun-planet +between one perihelion and the next should exceed that +corresponding to one complete revolution by an amount +given by +\[ ++\frac{24\pi^{3} a^{2}}{T^{2} c^{2} (1-e^{2})}. +\] + +(\NB---One complete revolution corresponds to the +angle~$2\pi$ in the absolute angular measure customary in +physics, and the above expression gives the amount by +\PageSep{126} +which the radius sun-planet exceeds this angle during +the interval between one perihelion and the next.) +In this expression $a$~represents the major semi-axis of +the ellipse, $e$~its eccentricity, $c$~the velocity of light, and +$T$~the period of revolution of the planet. Our result +may also be stated as follows: According to the general +theory of relativity, the major axis of the ellipse rotates +round the sun in the same sense as the orbital motion +of the planet. Theory requires that this rotation should +amount to $43$~seconds of arc per~century for the planet +Mercury, but for the other planets of our solar system its +\index{Mercury}% +\index{Mercury!orbit of}% +magnitude should be so small that it would necessarily +escape detection.\footnote + {Especially since the next planet Venus has an orbit that is +\index{Venus}% + almost an exact circle, which makes it more difficult to locate + the perihelion with precision.} + +In point of fact, astronomers have found that the +theory of Newton does not suffice to calculate the +observed motion of Mercury with an exactness corresponding +to that of the delicacy of observation attainable +at the present time. After taking account of all +the disturbing influences exerted on Mercury by the +remaining planets, it was found (Leverrier---1859---and +\index{Leverrier}% +Newcomb---1895) that an unexplained perihelial +\index{Newcomb}% +movement of the orbit of Mercury remained over, the +amount of which does not differ sensibly from the above-mentioned +$+43$~seconds of arc per~century. The uncertainty +of the empirical result amounts to a few +seconds only. +\index{Perihelion of Mercury|)}% + + +\Subsection{b}{Deflection of Light by a Gravitational +Field} + +In \Sectionref{XXII} it has been already mentioned that, +\PageSep{127} +according to the general theory of relativity, a ray of +light will experience a curvature of its path when passing +\index{Curvature of light-rays}% +\index{Curvature of light-rays!space}% +through a gravitational field, this curvature being similar +to that experienced by the path of a body which is +projected through a gravitational field. As a result of +this theory, we should expect that a ray of light which +is passing close to a heavenly body would be deviated +towards the latter. For a ray of light which passes the +sun at a distance of $\Delta$~sun-radii from its centre, the +angle of deflection~($\alpha$) should amount to +\[ +\alpha = \frac{\text{$1.7$~seconds of arc}}{\Delta}. +\] +It may be added that, according to the theory, half of +this deflection is produced by the +Newtonian field of attraction of the +sun, and the other half by the geometrical +modification (``curvature'') +of space caused by the sun. + +%[Illustration: Fig. 5.] +\WFigure{1in}{127} +This result admits of an experimental +\index{Solar eclipse}% +test by means of the photographic +registration of stars during +a total eclipse of the sun. The only +reason why we must wait for a total +eclipse is because at every other +time the atmosphere is so strongly +illuminated by the light from the +sun that the stars situated near the +sun's disc are invisible. The predicted effect can be +seen clearly from the accompanying diagram. If the +sun~($S$) were not present, a star which is practically +infinitely distant would be seen in the direction~$D_{1}$, as +observed from the earth. But as a consequence of the +\PageSep{128} +deflection of light from the star by the sun, the star +will be seen in the direction~$D_{2}$, \ie\ at a somewhat +greater distance from the centre of the sun than corresponds +to its real position. + +In practice, the question is tested in the following +way. The stars in the neighbourhood of the sun are +photographed during a solar eclipse. In addition, a +\index{Solar eclipse}% +\index{Stellar universe!photographs}% +second photograph of the same stars is taken when the +sun is situated at another position in the sky, \ie\ a few +months earlier or later. As compared with the standard +photograph, the positions of the stars on the eclipse-photograph +ought to appear displaced radially outwards +(away from the centre of the sun) by an amount +corresponding to the angle~$\alpha$. + +We are indebted to the Royal Society and to the +Royal Astronomical Society for the investigation of +this important deduction. Undaunted by the war and +by difficulties of both a material and a psychological +nature aroused by the war, these societies equipped +two expeditions---to Sobral (Brazil), and to the island of +Principe (West Africa)---and sent several of Britain's +most celebrated astronomers (Eddington, Cottingham, +\index{Cottingham}% +\index{Eddington}% +Crommelin, Davidson), in order to obtain photographs +\index{Crommelin}% +\index{Davidson}% +of the solar eclipse of 29th~May, 1919. The relative +discrepancies to be expected between the stellar photographs +obtained during the eclipse and the comparison +photographs amounted to a few hundredths of a millimetre +only. Thus great accuracy was necessary in +making the adjustments required for the taking of the +photographs, and in their subsequent measurement. + +The results of the measurements confirmed the theory +in a thoroughly satisfactory manner. The rectangular +components of the observed and of the calculated +\PageSep{129} +deviations of the stars (in seconds of arc) are set forth +in the following table of results: +\[ +\begin{array}{@{}c*{2}{>{\quad}cc}@{}} +%[** TN: Re-break first column heading to improve overall width] +\ColHead{1}{Number of}{Number of\\ the Star.} & +\ColHead{2}{Observed. Calculated.}{First Co-ordinate. \\[2pt] +$\overbrace{\text{Observed. Calculated.}}$} & +\ColHead{2}{Observed. Calculated.}{Second Co-ordinate. \\[2pt] +$\overbrace{\text{Observed. Calculated.}}$} \\ +11 & -0.19 & -0.22 & +0.16 & +0.02 \\ +\Z5 & +0.29 & +0.31 & -0.46 & -0.43 \\ +\Z4 & +0.11 & +0.10 & +0.83 & +0.74 \\ +\Z3 & +0.20 & +0.12 & +1.00 & +0.87 \\ +\Z6 & +0.10 & +0.04 & +0.57 & +0.40 \\ +10 & -0.08 & +0.09 & +0.35 & +0.32 \\ +\Z2 & +0.95 & +0.85 & -0.27 & -0.09 +\end{array} +\] + +\Subsection{c}{Displacement of Spectral Lines towards +the Red} +\index{Displacement of spectral lines}% + +In \Sectionref{XXIII} it has been shown that in a system~$K'$ +which is in rotation with regard to a Galileian system~$K$, +clocks of identical construction, and which are considered +\index{Clocks}% +\index{Clocks!rate of}% +at rest with respect to the rotating reference-body, +go at rates which are dependent on the positions +of the clocks. We shall now examine this dependence +quantitatively. A clock, which is situated at a distance~$r$ +from the centre of the disc, has a velocity relative to~$K$ +which is given by +\[ +v = \omega r, +\] +where $\omega$~represents the angular velocity of rotation of the +disc~$K'$ with respect to~$K$. If $\nu_{0}$~represents the number +of ticks of the clock per unit time (``rate'' of the clock) +relative to~$K$ when the clock is at rest, then the ``rate'' +of the clock~($\nu$) when it is moving relative to~$K$ with +a velocity~$v$, but at rest with respect to the disc, will, +in accordance with \Sectionref{XII}, be given by +\[ +\nu = \nu_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}, +\] +\PageSep{130} +or with sufficient accuracy by +\[ +\nu = \nu_{0} \left(1 - \tfrac{1}{2}\, \frac{v^{2}}{c^{2}}\right). +\] +This expression may also be stated in the following +form: +\[ +\nu = \nu_{0} \left(1 - \frac{1}{c^{2}}\, \frac{\omega^{2} r^{2}}{2}\right). +\] +If we represent the difference of potential of the centrifugal +force between the position of the clock and the +centre of the disc by~$\phi$, \ie\ the work, considered negatively, +which must be performed on the unit of mass +against the centrifugal force in order to transport it +\index{Centrifugal force}% +from the position of the clock on the rotating disc to +the centre of the disc, then we have +\[ +\phi = -\frac{\omega^{2} r^{2}}{2}. +\] +From this it follows that +\[ +\nu = \nu_{0} \left(1 + \frac{\phi}{c^{2}}\right). +\] +In the first place, we see from this expression that two +clocks of identical construction will go at different rates +when situated at different distances from the centre of +the disc. This result is also valid from the standpoint +of an observer who is rotating with the disc. + +Now, as judged from the disc, the latter is in a gravitational +\index{Gravitational field!potential of}% +field of potential~$\phi$, hence the result we have +obtained will hold quite generally for gravitational +fields. Furthermore, we can regard an atom which is +emitting spectral lines as a clock, so that the following +statement will hold: + +\emph{An atom absorbs or emits light of a frequency which is +\PageSep{131} +dependent on the potential of the gravitational field in +\index{Gravitational field!potential of}% +which it is situated.} + +The frequency of an atom situated on the surface of a +\index{Frequency of atom}% +heavenly body will be somewhat less than the frequency +of an atom of the same element which is situated in free +space (or on the surface of a smaller celestial body). +Now $\phi = -K\dfrac{M}{r}$, where $K$~is Newton's constant of +\index{Newton's!constant of gravitation}% +gravitation, and $M$~is the mass of the heavenly body. +Thus a displacement towards the red ought to take place +for spectral lines produced at the surface of stars as +compared with the spectral lines of the same element +produced at the surface of the earth, the amount of this +displacement being +\[ +\frac{\nu_{0} - \nu}{\nu_{0}} = \frac{K}{c^{2}}\, \frac{M}{r}. +\] + +For the sun, the displacement towards the red predicted +by theory amounts to about two millionths of +the wave-length. A trustworthy calculation is not +possible in the case of the stars, because in general +neither the mass~$M$ nor the radius~$r$ is known. + +It is an open question whether or not this effect +exists, and at the present time astronomers are working +with great zeal towards the solution. Owing to the +smallness of the effect in the case of the sun, it is difficult +to form an opinion as to its existence. Whereas +Grebe and Bachem (Bonn), as a result of their own +\index{Bachem}% +\index{Grebe}% +measurements and those of Evershed and Schwarzschild +\index{Evershed}% +\index{Schwarzschild}% +on the cyanogen bands, have placed the existence of +\index{Cyanogen bands}% +the effect almost beyond doubt, other investigators, +particularly St.~John, have been led to the opposite +\index{St. John@{St.\ John}}% +opinion in consequence of their measurements. +\PageSep{132} + +Mean displacements of lines towards the less refrangible +end of the spectrum are certainly revealed by +statistical investigations of the fixed stars; but up +to the present the examination of the available data +does not allow of any definite decision being arrived at, +as to whether or not these displacements are to be +referred in reality to the effect of gravitation. The +results of observation have been collected together, +and discussed in detail from the standpoint of the +question which has been engaging our attention here, +in a paper by E.~Freundlich entitled ``Zur Prüfung der +allgemeinen Relativitäts-Theorie'' (\textit{Die Naturwissenschaften}, +1919, No.~35, p.~520: Julius Springer, Berlin). + +At all events, a definite decision will be reached during +the next few years. If the displacement of spectral +lines towards the red by the gravitational potential +does not exist, then the general theory of relativity +will be untenable. On the other hand, if the cause of +the displacement of spectral lines be definitely traced +to the gravitational potential, then the study of this +displacement will furnish us with important information +\index{Mass of heavenly bodies}% +as to the mass of the heavenly bodies. +\PageSep{133} + + +\backmatter +\BookMark{-1}{Back Matter} +\Bibliography{WORKS IN ENGLISH ON EINSTEIN'S THEORY} + +\Bibsection{Introductory} + +\Bibitem{The Foundations of Einstein's Theory of Gravitation} +{Erwin Freundlich (translation by H.~L.~Brose). +Camb.\ Univ.\ Press, 1920.} + +\Bibitem{Space and Time in Contemporary Physics}{Moritz Schlick +(translation by H.~L.~Brose). Clarendon Press, +Oxford, 1920.} + + +\Bibsection{The Special Theory} + +\Bibitem{The Principle of Relativity}{E.~Cunningham. Camb.\ +Univ.\ Press.} + +\Bibitem{Relativity and the Electron Theory}{E.~Cunningham, Monographs +on Physics. Longmans, Green \&~Co.} + +\Bibitem{The Theory of Relativity}{L.~Silberstein. Macmillan \&~Co.} + +\Bibitem{The Space-Time Manifold of Relativity}{E.~B.~Wilson +and G.~N.~Lewis, \textit{Proc.\ Amer.\ Soc.\ Arts \&~Science}, +vol.~xlviii., No.~11, 1912.} + + +\Bibsection{The General Theory} + +\Bibitem{Report on the Relativity Theory of Gravitation}{A.~S. +Eddington. Fleetway Press Ltd., Fleet Street, +London.} +\PageSep{134} + +\Bibitem{On Einstein's Theory of Gravitation and its Astronomical +Consequences}{W.~de~Sitter, \textit{M.~N.~Roy.\ Astron.\ +Soc.},~lxxvi.\ p.~699, 1916; lxxvii.\ p.~155, 1916; lxxviii.\ +p.~3, 1917.} + +\Bibitem{On Einstein's Theory of Gravitation}{H.~A.~Lorentz, \textit{Proc.\ +Amsterdam Acad.}, vol.~xix. p.~1341, 1917.} + +\Bibitem{Space, Time and Gravitation}{W.~de~Sitter: \textit{The +Observatory}, No.~505, p.~412. Taylor \&~Francis, Fleet +Street, London.} + +\Bibitem{The Total Eclipse of 29th~May, 1919, and the Influence of +Gravitation on Light}{A.~S.~Eddington, \textit{ibid.}, +March~1919.} + +\Bibitem{Discussion on the Theory of Relativity}{\textit{M.~N.~Roy.\ Astron.\ +Soc.}, vol.~lxxx.\ No.~2, p.~96, December~1919.} + +\Bibitem{The Displacement of Spectrum Lines and the Equivalence +Hypothesis}{W.~G.~Duffield, \textit{M.~N.~Roy.\ Astron.\ Soc.}, +vol.~lxxx.\Change{;}{} No.~3, p.~262, 1920.} + +\Bibitem{Space, Time and Gravitation}{A.~S.~Eddington, Camb.\ Univ.\ +Press, 1920.} + + +\Bibsection{Also, Chapters in} + +\Bibitem{The Mathematical Theory of Electricity and Magnetism} +{J.~H. Jeans (4th~edition). Camb.\ Univ.\ Press, 1920.} + +\Bibitem{The Electron Theory of Matter}{O.~W.~Richardson. Camb.\ +Univ.\ Press.} +\PageSep{135} +\printindex % [** TN: Auto-generate the index] +\iffalse %%%% Start of index text %%%% +INDEX + +Aberration 49 + +Absorption of energy 46 + +Acceleration 64, 67, 70 + +Action at a distance 48 + +Addition of velocities 16, 38 + +Adjacent points 89 + +Aether 52 + drift@{-drift}#drift 52, 53 + +Arbitrary substitutions 98 + +Astronomy 7, 102 + +Astronomical day 11 + +Axioms 2, 123 + truth of 2 + +Bachem 131 + +Basis of theory 44 + +Being@{``Being''}#Being 66, 108 + +beta-rays@{$\beta$-rays}#rays 50 + +Biology 124 + +Cartesian system of co-ordinates 7, 84, 122 + +Cathode rays 50 + +Celestial mechanics 105 + +Centrifugal force 80, 130 + +Chest 66 + +Classical mechanics 9, 13, 14, 16, 30, 44, 71, 102, 103, 124 + truth of 13 + +Clocks 10, 23, 80, 81, 94, 95, 98-100, 102, 113, 129 + rate of 129 + +Conception of mass 45 + position 6 + +Conservation of energy 45, 101 + impulse 101 + mass 45, 47 + +Continuity 95 + +Continuum 55, 83 + two-dimensional 94 + three-dimensional 57 + four-dimensional 89, 91, 92, 94, 122 + space-time 78, 91-96 + Euclidean 84, 86, 88, 92 + non-Euclidean 86, 90 + +Coordinate@{Co-ordinate}#Co-ordinate + differences 92 + differentials 92 + planes 32 + +Cottingham 128 + +Counter-Point 112 + +Covariant@{Co-variant}#Co-variant 43 + +Crommelin 128 + +Curvature of light-rays 104, 127 + space 127 + +Curvilinear motion 74 + +Cyanogen bands 131 + +Darwinian theory 124 + +Davidson 128 + +Deductive thought 123 + +Derivation of laws 44 + +Desitter@{De Sitter}#De Sitter 17 + +Displacement of spectral lines 104, 129 + +Distance (line-interval) 3, 5, 8, 28, 29, 84, 88, 109 + physical interpretation of 5 + relativity of 28 + +Doppler principle 50 %. + +Double stars 17 + +Eclipse of star 17 + +Eddington 104, 128 +%\PageSep{136} + +Electricity 76 + +Electrodynamics 13, 19, 41, 44, 76 + +Electromagnetic theory 49 + waves 63 + +Electron 44, 50 %. + electrical masses of 51 + +Electrostatics 76 + +Elliptical space 112 + +Empirical laws 123 + +Encounter (space-time coincidence) 95 + +Equivalent 14 + +Euclidean geometry 1, 2, 57, 82, 86, 88, 108, 109, 113, 122 + propositions of 3, 8 + +%[** TN: Add explicit "Euclidean" heading] +Euclidean space 57, 86, 122 + +Evershed 131 + +Experience 49, 60 + +Faraday 48, 63 + +FitzGerald 53 + +Fixed stars 11 + +Fizeau 39, 49, 51 + experiment of 39 + +Frequency of atom 131 + +Galilei 11 + transformation 33, 36, 38, 42, 52 + +Galileian system of co-ordinates + 11, 13, 14, 46, 79, 91, 98, 100 + +Gauss 86, 87, 90 + +Gaussian co-ordinates 88-90, 94, 96-100 + +General theory of relativity 59-104, 97 + +Geometrical ideas 2, 3 + propositions 1 + truth of 2-4 + +Gravitation 64, 69, 78, 102 + +Gravitational field 64, 67, 74, 77, 93, 98, 100, 101, 113 + potential of 130, 131 + +%[** TN: Add explicit "Gravitational" heading] +Gravitational mass 65, 68, 102 + +Grebe 131 + +Group-density of stars 106 + +Helmholtz 108 + +Heuristic value of relativity#Heuristic 42 + +Induction 123 + +Inertia 65 + +Inertial mass 47, 65, 69, 101, 102 + +Instantaneous photograph (snapshot) 117 + +Intensity of gravitational field 106 + +Intuition 123 + +Ions 44 + +Kepler 125 + +Kinetic energy 45, 101 + +Lattice 108 + +Law of inertia 11, 61, 62, 98 + +Laws of Galilei-Newton 13 + of Nature 60, 71, 99 + +Leverrier 103, 126 + +Light-signal 33, 115, 118 + +Light-stimulus 33 + +Limiting velocity ($c$)#Limiting 36, 37 + +Lines of force 106 + +Lorentz, H. A.#Lorentz 19, 41, 44, 49, 50-53 + transformation 33, 39, 42, 91, 97, 98, 115, 118, 119, 121 + (generalised) 120 + +Mach, E.#Mach 72 + +Magnetic field 63 + +Manifold|see{Continuum} 0 + +Mass of heavenly bodies 132 + +Matter 101 + +Maxwell 41, 44, 48-50, 52 + fundamental equations 46, 77 + +Measurement of length 85 + +Measuring-rod 5, 6, 28, 80, 81, 94, 100, 102, 111, 113, 117 + +Mercury 103, 126 + orbit of 103, 126 + +Michelson 52-54 + +Minkowski 55-57, 91, 122 +%\PageSep{137} + +Morley 53, 54 + +Motion 14, 60 + of heavenly bodies 13, 15, 44, 102, 113 + +Newcomb 126 + +Newton 11, 72, 102, 105, 125 + +Newton's + constant of gravitation 131 + law of gravitation 48, 80, 106, 124 + law of motion 64 + +Non-Euclidean geometry 108 + +Non-Galileian reference-bodies 98 + +Non-uniform motion 62 + +Optics 13, 19, 44 + +Organ-pipe, note of 14 + +Parabola 9, 10 + +Path-curve 10 + +Perihelion of Mercury 124-126 + +Physics 7 + of measurement 7 + +Place specification 5, 6 + +Plane 1, 108, 109 + +Poincare@{Poincaré}#Poincaré 108 + +Point 1 + +Point-mass, energy of#Point-mass 45 + +Position 9 + +Principle of relativity 13-15, 19, 20, 60 + +Processes of Nature 42 + +Propagation of light 17, 19, 20, 32, 91, 119 + in liquid 40 + in gravitational fields 75 + +Quasi-Euclidean universe 114 + +Quasi-spherical universe 114 + +Radiation 46 + +Radioactive substances 50 + +Reference-body 5, 7, 9-11, 18, 23, 25, 26, 37, 60 + rotating 79 + +%[** TN: Add explicit "Reference-" heading] +Reference-mollusk 99-101 + +Relative + position 3 + velocity 117 + +Rest 14 + +Riemann 86, 108, 111 + +Rotation 81, 122 + +Schwarzschild 131 + +Seconds-clock 36 + +Seeliger 105, 106 + +Simultaneity 22, 24-26, 81 + relativity of 26 + +Size-relations 90 + +Solar eclipse 75, 127, 128 + +Space 9, 52, 55, 105 + conception of 19 + +Space co-ordinates 55, 81, 99 + +Space + interval@{-interval}#interval 30, 56 + point@{-point}#point 99 + two-dimensional 108 + three-dimensional 122 + +Special theory of relativity 1-57, 20 + +Spherical + surface 109 + space 111, 112 + +St. John@{St.\ John}#St.~John 131 + +Stellar universe 106 + photographs 128 + +Straight line 1-3, 9, 10, 82, 88, 109 + +System of co-ordinates 5, 10, 11 + +Terrestrial space 15 + +Theory 123 + truth of 124 + +Three-dimensional 55 + +Time + conception of 19, 52, 105 + coordinate@{co-ordinate}#co-ordinate 55, 99 + in Physics 21, 98, 122 + of an event 24, 26 + +Time-interval 30, 56 + +Trajectory 10 + +Truth@{``Truth''}#Truth 2 + +Uniform translation 12, 59 + +Universe (World) structure of 108, 113 + circumference of 111 +%\PageSep{138} + +Universe + elliptical 112, 114 + Euclidean 109, 111 + space expanse (radius) of 114 + spherical 111, 114 + +Value of $\pi$#$\pi$ 82, 110 + +Velocity of light 10, 17, 18, 76, 118 + +Venus 126 + +Weight (heaviness) 65 + +World 55, 56, 109, 122 + +World + point@{-point}#point 122 + radius@{-radius}#radius 112 + sphere@{-sphere}#sphere 110, 111 + +Zeeman 41 +\fi %%%% End of index text %%%% +\PageSep{139} +% [Blank page] +\PageSep{140} +\ifthenelse{\boolean{ForPrinting}}{\cleardoublepage\null}{} +\newpage +\begin{CenterPage} + \scriptsize + PRINTED BY \\[2pt] + MORRISON AND GIBB LIMITED \\[2pt] + EDINBURGH +\end{CenterPage} +%%%%%%%%%%%%%%%%%%%%%%%%% GUTENBERG LICENSE %%%%%%%%%%%%%%%%%%%%%%%%%% + +\cleardoublepage +\BookMark{0}{PG License} +\SetEvenHead{Licensing} +\SetOddHead{Licensing} +\pagenumbering{Roman} +\begin{PGtext} +End of the Project Gutenberg EBook of Relativity: The Special and the +General Theory, by Albert Einstein + +*** END OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** + +***** This file should be named 36114-pdf.pdf or 36114-pdf.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/6/1/1/36114/ + +Produced by Andrew D. Hwang. (This ebook was produced using +OCR text generously provided by the University of Toronto +Robarts Library through the Internet Archive.) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +http://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need, are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at http://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +http://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at http://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit http://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including checks, online payments and credit card donations. +To donate, please visit: http://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart is the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + http://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. +\end{PGtext} + +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % +% % +% End of the Project Gutenberg EBook of Relativity: The Special and the % +% General Theory, by Albert Einstein % +% % +% *** END OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** % +% % +% ***** This file should be named 36114-t.tex or 36114-t.zip ***** % +% This and all associated files of various formats will be found in: % +% http://www.gutenberg.org/3/6/1/1/36114/ % +% % +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % + +\end{document} +### +@ControlwordReplace = ( + ['\\Preface', 'Preface'], + ['\\ie', 'i.e.'], + ['\\eg', 'e.g.'], + ['\\NB', 'N.B.'], + ['\\itema', '(a)'], + ['\\itemb', '(b)'], + ['\\itemc', '(c)'] + ); + +@ControlwordArguments = ( + ['\\BookMark', 1, 0, '', '', 1, 0, '', ''], + ['\\item', 0, 1, '', ' '], + ['\\Part', 1, 1, '', ' ', 1, 1, '', '', 1, 0, '', ''], + ['\\Chapter', 0, 0, '', '', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Section', 1, 1, '', ''], + ['\\Subsection', 1, 1, '(', ') ', 1, 1, '', ''], + ['\\SectTitle', 1, 1, '', ''], + ['\\Appendix', 1, 1, '', ' ', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Bibliography', 1, 1, 'Bibliography: ', ''], + ['\\Bibsection', 1, 1, '', ''], + ['\\Bibitem', 1, 1, '', ' ', 1, 1, '', ''], + ['\\PubRow', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Signature', 0, 1, '', ' ', 1, 1, '', ''], + ['\\Change', 1, 0, '', '', 1, 1, '', ''], + ['\\Add', 1, 1, '', ''], + ['\\PageSep', 1, 0, '', ''], + ['\\Figure', 0, 0, '', '', 1, 1, '', ''], + ['\\WFigure', 1, 0, '', '', 1, 1, '', ''], + ['\\Figref', 1, 1, 'Fig. ', ''], + ['\\Partref', 1, 1, 'Part ', ''], + ['\\Sectionref', 1, 1, 'Section ', ''], + ['\\Srefno', 1, 1, '', ''], + ['\\Appendixref', 1, 1, 'Appendix ', ''], + ['\\Eqref', 1, 1, '', ''], + ['\\First', 1, 1, '', ''] + ); +### +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2010.5.6) 15 MAY 2011 15:31 +entering extended mode + %&-line parsing enabled. +**36114-t.tex +(./36114-t.tex +LaTeX2e <2005/12/01> +Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov +ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon +ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i +nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp +eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia +n, swedish, ukenglish, pinyin, loaded. +(/usr/share/texmf-texlive/tex/latex/base/book.cls +Document Class: book 2005/09/16 v1.4f Standard LaTeX document class +(/usr/share/texmf-texlive/tex/latex/base/bk12.clo +File: bk12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +) +\c@part=\count79 +\c@chapter=\count80 +\c@section=\count81 +\c@subsection=\count82 +\c@subsubsection=\count83 +\c@paragraph=\count84 +\c@subparagraph=\count85 +\c@figure=\count86 +\c@table=\count87 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) (/usr/share/texmf-texlive/tex/latex/base/inputenc.sty +Package: inputenc 2006/05/05 v1.1b Input encoding file +\inpenc@prehook=\toks14 +\inpenc@posthook=\toks15 +(/usr/share/texmf-texlive/tex/latex/base/latin1.def +File: latin1.def 2006/05/05 v1.1b Input encoding file +)) (/usr/share/texmf-texlive/tex/latex/base/ifthen.sty +Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) +) (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty +Package: amsmath 2000/07/18 v2.13 AMS math features +\@mathmargin=\skip43 +For additional information on amsmath, use the `?' option. +(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 +(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 +\@emptytoks=\toks16 +\ex@=\dimen103 +)) (/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d +\pmbraise@=\dimen104 +) (/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count88 +LaTeX Info: Redefining \frac on input line 211. +\uproot@=\count89 +\leftroot@=\count90 +LaTeX Info: Redefining \overline on input line 307. +\classnum@=\count91 +\DOTSCASE@=\count92 +LaTeX Info: Redefining \ldots on input line 379. +LaTeX Info: Redefining \dots on input line 382. +LaTeX Info: Redefining \cdots on input line 467. +\Mathstrutbox@=\box26 +\strutbox@=\box27 +\big@size=\dimen105 +LaTeX Font Info: Redeclaring font encoding OML on input line 567. +LaTeX Font Info: Redeclaring font encoding OMS on input line 568. +\macc@depth=\count93 +\c@MaxMatrixCols=\count94 +\dotsspace@=\muskip10 +\c@parentequation=\count95 +\dspbrk@lvl=\count96 +\tag@help=\toks17 +\row@=\count97 +\column@=\count98 +\maxfields@=\count99 +\andhelp@=\toks18 +\eqnshift@=\dimen106 +\alignsep@=\dimen107 +\tagshift@=\dimen108 +\tagwidth@=\dimen109 +\totwidth@=\dimen110 +\lineht@=\dimen111 +\@envbody=\toks19 +\multlinegap=\skip44 +\multlinetaggap=\skip45 +\mathdisplay@stack=\toks20 +LaTeX Info: Redefining \[ on input line 2666. +LaTeX Info: Redefining \] on input line 2667. +) (/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2002/01/22 v2.2d +(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2001/10/25 v2.2f +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 132. +)) (/usr/share/texmf-texlive/tex/latex/base/alltt.sty +Package: alltt 1997/06/16 v2.0g defines alltt environment +) (/usr/share/texmf-texlive/tex/latex/tools/array.sty +Package: array 2005/08/23 v2.4b Tabular extension package (FMi) +\col@sep=\dimen112 +\extrarowheight=\dimen113 +\NC@list=\toks21 +\extratabsurround=\skip46 +\backup@length=\skip47 +) (/usr/share/texmf-texlive/tex/latex/bigfoot/perpage.sty +Package: perpage 2006/07/15 1.12 Reset/sort counters per page +\c@abspage=\count100 +) (/usr/share/texmf-texlive/tex/latex/tools/multicol.sty +Package: multicol 2006/05/18 v1.6g multicolumn formatting (FMi) +\c@tracingmulticols=\count101 +\mult@box=\box28 +\multicol@leftmargin=\dimen114 +\c@unbalance=\count102 +\c@collectmore=\count103 +\doublecol@number=\count104 +\multicoltolerance=\count105 +\multicolpretolerance=\count106 +\full@width=\dimen115 +\page@free=\dimen116 +\premulticols=\dimen117 +\postmulticols=\dimen118 +\multicolsep=\skip48 +\multicolbaselineskip=\skip49 +\partial@page=\box29 +\last@line=\box30 +\mult@rightbox=\box31 +\mult@grightbox=\box32 +\mult@gfirstbox=\box33 +\mult@firstbox=\box34 +\@tempa=\box35 +\@tempa=\box36 +\@tempa=\box37 +\@tempa=\box38 +\@tempa=\box39 +\@tempa=\box40 +\@tempa=\box41 +\@tempa=\box42 +\@tempa=\box43 +\@tempa=\box44 +\@tempa=\box45 +\@tempa=\box46 +\@tempa=\box47 +\@tempa=\box48 +\@tempa=\box49 +\@tempa=\box50 +\@tempa=\box51 +\c@columnbadness=\count107 +\c@finalcolumnbadness=\count108 +\last@try=\dimen119 +\multicolovershoot=\dimen120 +\multicolundershoot=\dimen121 +\mult@nat@firstbox=\box52 +\colbreak@box=\box53 +) (/usr/share/texmf-texlive/tex/latex/base/makeidx.sty +Package: makeidx 2000/03/29 v1.0m Standard LaTeX package +) (/usr/share/texmf-texlive/tex/latex/caption/caption.sty +Package: caption 2007/01/07 v3.0k Customising captions (AR) +(/usr/share/texmf-texlive/tex/latex/caption/caption3.sty +Package: caption3 2007/01/07 v3.0k caption3 kernel (AR) +(/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty +Package: keyval 1999/03/16 v1.13 key=value parser (DPC) +\KV@toks@=\toks22 +) +\captionmargin=\dimen122 +\captionmarginx=\dimen123 +\captionwidth=\dimen124 +\captionindent=\dimen125 +\captionparindent=\dimen126 +\captionhangindent=\dimen127 +)) (/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty +Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) +(/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty +Package: graphics 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) +(/usr/share/texmf-texlive/tex/latex/graphics/trig.sty +Package: trig 1999/03/16 v1.09 sin cos tan (DPC) +) (/etc/texmf/tex/latex/config/graphics.cfg +File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive +) +Package graphics Info: Driver file: pdftex.def on input line 90. +(/usr/share/texmf-texlive/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX +\Gread@gobject=\count109 +)) +\Gin@req@height=\dimen128 +\Gin@req@width=\dimen129 +) (/usr/share/texmf-texlive/tex/latex/wrapfig/wrapfig.sty +\wrapoverhang=\dimen130 +\WF@size=\dimen131 +\c@WF@wrappedlines=\count110 +\WF@box=\box54 +\WF@everypar=\toks23 +Package: wrapfig 2003/01/31 v 3.6 +) (/usr/share/texmf-texlive/tex/latex/tools/calc.sty +Package: calc 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) +\calc@Acount=\count111 +\calc@Bcount=\count112 +\calc@Adimen=\dimen132 +\calc@Bdimen=\dimen133 +\calc@Askip=\skip50 +\calc@Bskip=\skip51 +LaTeX Info: Redefining \setlength on input line 75. +LaTeX Info: Redefining \addtolength on input line 76. +\calc@Ccount=\count113 +\calc@Cskip=\skip52 +) (/usr/share/texmf-texlive/tex/latex/fancyhdr/fancyhdr.sty +\fancy@headwidth=\skip53 +\f@ncyO@elh=\skip54 +\f@ncyO@erh=\skip55 +\f@ncyO@olh=\skip56 +\f@ncyO@orh=\skip57 +\f@ncyO@elf=\skip58 +\f@ncyO@erf=\skip59 +\f@ncyO@olf=\skip60 +\f@ncyO@orf=\skip61 +) (/usr/share/texmf-texlive/tex/latex/geometry/geometry.sty +Package: geometry 2002/07/08 v3.2 Page Geometry +\Gm@cnth=\count114 +\Gm@cntv=\count115 +\c@Gm@tempcnt=\count116 +\Gm@bindingoffset=\dimen134 +\Gm@wd@mp=\dimen135 +\Gm@odd@mp=\dimen136 +\Gm@even@mp=\dimen137 +\Gm@dimlist=\toks24 +(/usr/share/texmf-texlive/tex/xelatex/xetexconfig/geometry.cfg)) (/usr/share/te +xmf-texlive/tex/latex/hyperref/hyperref.sty +Package: hyperref 2007/02/07 v6.75r Hypertext links for LaTeX +\@linkdim=\dimen138 +\Hy@linkcounter=\count117 +\Hy@pagecounter=\count118 +(/usr/share/texmf-texlive/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +) (/etc/texmf/tex/latex/config/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) (/usr/share/texmf-texlive/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options ( +HO) +) +Package hyperref Info: Option `hyperfootnotes' set `false' on input line 2238. +Package hyperref Info: Option `bookmarks' set `true' on input line 2238. +Package hyperref Info: Option `linktocpage' set `false' on input line 2238. +Package hyperref Info: Option `pdfdisplaydoctitle' set `true' on input line 223 +8. +Package hyperref Info: Option `pdfpagelabels' set `true' on input line 2238. +Package hyperref Info: Option `bookmarksopen' set `true' on input line 2238. +Package hyperref Info: Option `colorlinks' set `true' on input line 2238. +Package hyperref Info: Hyper figures OFF on input line 2288. +Package hyperref Info: Link nesting OFF on input line 2293. +Package hyperref Info: Hyper index ON on input line 2296. +Package hyperref Info: Plain pages OFF on input line 2303. +Package hyperref Info: Backreferencing OFF on input line 2308. +Implicit mode ON; LaTeX internals redefined +Package hyperref Info: Bookmarks ON on input line 2444. +(/usr/share/texmf-texlive/tex/latex/ltxmisc/url.sty +\Urlmuskip=\muskip11 +Package: url 2005/06/27 ver 3.2 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 2599. +\Fld@menulength=\count119 +\Field@Width=\dimen139 +\Fld@charsize=\dimen140 +\Choice@toks=\toks25 +\Field@toks=\toks26 +Package hyperref Info: Hyper figures OFF on input line 3102. +Package hyperref Info: Link nesting OFF on input line 3107. +Package hyperref Info: Hyper index ON on input line 3110. +Package hyperref Info: backreferencing OFF on input line 3117. +Package hyperref Info: Link coloring ON on input line 3120. +\Hy@abspage=\count120 +\c@Item=\count121 +) +*hyperref using driver hpdftex* +(/usr/share/texmf-texlive/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX +\Fld@listcount=\count122 +) +\c@pp@a@footnote=\count123 +\@indexfile=\write3 +\openout3 = `36114-t.idx'. + +Writing index file 36114-t.idx +\c@figno=\count124 +\TmpLen=\skip62 +(./36114-t.aux) +\openout1 = `36114-t.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +(/usr/share/texmf-texlive/tex/latex/ragged2e/ragged2e.sty +Package: ragged2e 2003/03/25 v2.04 ragged2e Package (MS) +(/usr/share/texmf-texlive/tex/latex/everysel/everysel.sty +Package: everysel 1999/06/08 v1.03 EverySelectfont Package (MS) +LaTeX Info: Redefining \selectfont on input line 125. +) +\CenteringLeftskip=\skip63 +\RaggedLeftLeftskip=\skip64 +\RaggedRightLeftskip=\skip65 +\CenteringRightskip=\skip66 +\RaggedLeftRightskip=\skip67 +\RaggedRightRightskip=\skip68 +\CenteringParfillskip=\skip69 +\RaggedLeftParfillskip=\skip70 +\RaggedRightParfillskip=\skip71 +\JustifyingParfillskip=\skip72 +\CenteringParindent=\skip73 +\RaggedLeftParindent=\skip74 +\RaggedRightParindent=\skip75 +\JustifyingParindent=\skip76 +) +Package caption Info: hyperref package v6.74m (or newer) detected on input line + 566. +(/usr/share/texmf/tex/context/base/supp-pdf.tex +[Loading MPS to PDF converter (version 2006.09.02).] +\scratchcounter=\count125 +\scratchdimen=\dimen141 +\scratchbox=\box55 +\nofMPsegments=\count126 +\nofMParguments=\count127 +\everyMPshowfont=\toks27 +\MPscratchCnt=\count128 +\MPscratchDim=\dimen142 +\MPnumerator=\count129 +\everyMPtoPDFconversion=\toks28 +) +-------------------- Geometry parameters +paper: class default +landscape: -- +twocolumn: -- +twoside: true +asymmetric: -- +h-parts: 9.03374pt, 325.215pt, 9.03375pt +v-parts: 4.15848pt, 495.49379pt, 6.23773pt +hmarginratio: 1:1 +vmarginratio: 2:3 +lines: -- +heightrounded: -- +bindingoffset: 0.0pt +truedimen: -- +includehead: true +includefoot: true +includemp: -- +driver: pdftex +-------------------- Page layout dimensions and switches +\paperwidth 343.28249pt +\paperheight 505.89pt +\textwidth 325.215pt +\textheight 433.62pt +\oddsidemargin -63.23625pt +\evensidemargin -63.23624pt +\topmargin -68.11151pt +\headheight 12.0pt +\headsep 19.8738pt +\footskip 30.0pt +\marginparwidth 98.0pt +\marginparsep 7.0pt +\columnsep 10.0pt +\skip\footins 10.8pt plus 4.0pt minus 2.0pt +\hoffset 0.0pt +\voffset 0.0pt +\mag 1000 +\@twosidetrue \@mparswitchtrue +(1in=72.27pt, 1cm=28.45pt) +----------------------- +(/usr/share/texmf-texlive/tex/latex/graphics/color.sty +Package: color 2005/11/14 v1.0j Standard LaTeX Color (DPC) +(/etc/texmf/tex/latex/config/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package color Info: Driver file: pdftex.def on input line 130. +) +Package hyperref Info: Link coloring ON on input line 566. +(/usr/share/texmf-texlive/tex/latex/hyperref/nameref.sty +Package: nameref 2006/12/27 v2.28 Cross-referencing by name of section +(/usr/share/texmf-texlive/tex/latex/oberdiek/refcount.sty +Package: refcount 2006/02/20 v3.0 Data extraction from references (HO) +) +\c@section@level=\count130 +) +LaTeX Info: Redefining \ref on input line 566. +LaTeX Info: Redefining \pageref on input line 566. +(./36114-t.out) (./36114-t.out) +\@outlinefile=\write4 +\openout4 = `36114-t.out'. + +LaTeX Font Info: Try loading font information for U+msa on input line 600. +(/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd +File: umsa.fd 2002/01/19 v2.2g AMS font definitions +) +LaTeX Font Info: Try loading font information for U+msb on input line 600. +(/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd +File: umsb.fd 2002/01/19 v2.2g AMS font definitions +) [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] [1 + +] [2] [3 + + +] [4] [5] [6] [7] (./36114-t.toc [8 + + + +] [9]) +\tf@toc=\write5 +\openout5 = `36114-t.toc'. + +[10] [11 + + +] [1 + +] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] +[19] [20] [21] [22] <./images/025.pdf, id=519, 338.26375pt x 50.1875pt> +File: ./images/025.pdf Graphic file (type pdf) +<use ./images/025.pdf> [23 <./images/025.pdf>] [24] [25] [26] [27] [28] <./imag +es/032.pdf, id=581, 194.7275pt x 150.5625pt> +File: ./images/032.pdf Graphic file (type pdf) +<use ./images/032.pdf> [29] [30 <./images/032.pdf>] [31] [32] [33] [34] [35] [3 +6] [37] <./images/040.pdf, id=649, 222.8325pt x 39.14626pt> +File: ./images/040.pdf Graphic file (type pdf) +<use ./images/040.pdf> [38 <./images/040.pdf>] [39] [40] [41] [42] [43] [44] [4 +5] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55 + + +] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [7 +1] [72] [73] [74] [75] [76] [77] [78] [79] [80] <./images/087.pdf, id=880, 209. +78375pt x 129.48375pt> +File: ./images/087.pdf Graphic file (type pdf) +<use ./images/087.pdf> [81 <./images/087.pdf>] [82] [83] [84] [85] [86] [87] [8 +8] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98 + + +] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108 + +] [109] [110] [111] [112] [113] [114 + +] [115] [116 + +] [117] [118] [119] <./images/127.pdf, id=1169, 99.37125pt x 212.795pt> +File: ./images/127.pdf Graphic file (type pdf) +<use ./images/127.pdf> [120 <./images/127.pdf>] [121] [122] [123] [124] [125] [ +126 + + +] (./36114-t.ind [127] [128 + +] [129] [130] [131] [132]) [133 + + +] [1 + +] [2] [3] [4] [5] [6] [7] [8] (./36114-t.aux) + + *File List* + book.cls 2005/09/16 v1.4f Standard LaTeX document class + bk12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +inputenc.sty 2006/05/05 v1.1b Input encoding file + latin1.def 2006/05/05 v1.1b Input encoding file + ifthen.sty 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) + amsmath.sty 2000/07/18 v2.13 AMS math features + amstext.sty 2000/06/29 v2.01 + amsgen.sty 1999/11/30 v2.0 + amsbsy.sty 1999/11/29 v1.2d + amsopn.sty 1999/12/14 v2.01 operator names + amssymb.sty 2002/01/22 v2.2d +amsfonts.sty 2001/10/25 v2.2f + alltt.sty 1997/06/16 v2.0g defines alltt environment + array.sty 2005/08/23 v2.4b Tabular extension package (FMi) + perpage.sty 2006/07/15 1.12 Reset/sort counters per page +multicol.sty 2006/05/18 v1.6g multicolumn formatting (FMi) + makeidx.sty 2000/03/29 v1.0m Standard LaTeX package + caption.sty 2007/01/07 v3.0k Customising captions (AR) +caption3.sty 2007/01/07 v3.0k caption3 kernel (AR) + keyval.sty 1999/03/16 v1.13 key=value parser (DPC) +graphicx.sty 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) +graphics.sty 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) + trig.sty 1999/03/16 v1.09 sin cos tan (DPC) +graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive + pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX + wrapfig.sty 2003/01/31 v 3.6 + calc.sty 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) +fancyhdr.sty +geometry.sty 2002/07/08 v3.2 Page Geometry +geometry.cfg +hyperref.sty 2007/02/07 v6.75r Hypertext links for LaTeX + pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +kvoptions.sty 2006/08/22 v2.4 Connects package keyval with LaTeX options (HO +) + url.sty 2005/06/27 ver 3.2 Verb mode for urls, etc. + hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX +ragged2e.sty 2003/03/25 v2.04 ragged2e Package (MS) +everysel.sty 1999/06/08 v1.03 EverySelectfont Package (MS) +supp-pdf.tex + color.sty 2005/11/14 v1.0j Standard LaTeX Color (DPC) + color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive + nameref.sty 2006/12/27 v2.28 Cross-referencing by name of section +refcount.sty 2006/02/20 v3.0 Data extraction from references (HO) + 36114-t.out + 36114-t.out + umsa.fd 2002/01/19 v2.2g AMS font definitions + umsb.fd 2002/01/19 v2.2g AMS font definitions +./images/025.pdf +./images/032.pdf +./images/040.pdf +./images/087.pdf +./images/127.pdf + 36114-t.ind + *********** + + ) +Here is how much of TeX's memory you used: + 5734 strings out of 94074 + 81940 string characters out of 1165154 + 147634 words of memory out of 1500000 + 8516 multiletter control sequences out of 10000+50000 + 17695 words of font info for 67 fonts, out of 1200000 for 2000 + 645 hyphenation exceptions out of 8191 + 34i,18n,44p,464b,649s stack positions out of 5000i,500n,6000p,200000b,5000s +</usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmbx10.pfb></usr/share/texmf +-texlive/fonts/type1/bluesky/cm/cmbx12.pfb></usr/share/texmf-texlive/fonts/type +1/bluesky/cm/cmbxti10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmcs +c10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmex10.pfb></usr/share +/texmf-texlive/fonts/type1/bluesky/cm/cmmi10.pfb></usr/share/texmf-texlive/font +s/type1/bluesky/cm/cmmi12.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/ +cmr10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmr12.pfb></usr/shar +e/texmf-texlive/fonts/type1/bluesky/cm/cmr7.pfb></usr/share/texmf-texlive/fonts +/type1/bluesky/cm/cmr8.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cms +y10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmsy7.pfb></usr/share/ +texmf-texlive/fonts/type1/bluesky/cm/cmsy8.pfb></usr/share/texmf-texlive/fonts/ +type1/bluesky/cm/cmti10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cm +ti12.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmtt10.pfb></usr/shar +e/texmf-texlive/fonts/type1/bluesky/cm/cmtt8.pfb> +Output written on 36114-t.pdf (154 pages, 664963 bytes). +PDF statistics: + 1881 PDF objects out of 2073 (max. 8388607) + 401 named destinations out of 1000 (max. 131072) + 418 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/36114-t/old/36114-t.zip b/36114-t/old/36114-t.zip Binary files differnew file mode 100644 index 0000000..a83f3e3 --- /dev/null +++ b/36114-t/old/36114-t.zip diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..a4c7568 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #36114 (https://www.gutenberg.org/ebooks/36114) diff --git a/old/36114-pdf 2011-05-11.pdf b/old/36114-pdf 2011-05-11.pdf new file mode 100644 index 0000000..8c8c4b6 --- /dev/null +++ b/old/36114-pdf 2011-05-11.pdf @@ -0,0 +1,13884 @@ +%PDF-1.4 +%ÐÔÅØ +5 0 obj +<< /S /GoTo /D (Front\040Matter.-1) >> +endobj +8 0 obj +(Front Matter) +endobj +9 0 obj +<< /S /GoTo /D (PG\040Boilerplate.0) >> +endobj +12 0 obj +(PG Boilerplate) +endobj +13 0 obj +<< /S /GoTo /D (Transcriber's\040Note.0) >> +endobj +16 0 obj +(Transcriber's Note) +endobj +17 0 obj +<< /S /GoTo /D (Preface.0) >> +endobj +20 0 obj +(Preface) +endobj +21 0 obj +<< /S /GoTo /D (Contents.0) >> +endobj +24 0 obj +(Contents) +endobj +25 0 obj +<< /S /GoTo /D (Part\040I.\040The\040Special\040Theory\040of\040Relativity.-1) >> +endobj +28 0 obj +(Part I. The Special Theory of Relativity) +endobj +29 0 obj +<< /S /GoTo /D (I.\040Physical\040Meaning\040of\040Geometrical\040Propositions.0) >> +endobj +32 0 obj +(I. Physical Meaning of Geometrical Propositions) +endobj +33 0 obj +<< /S /GoTo /D (II.\040The\040System\040of\040Co-ordinates.0) >> +endobj +36 0 obj +(II. The System of Co-ordinates) +endobj +37 0 obj +<< /S /GoTo /D (III.\040Space\040and\040Time\040in\040Classical\040Mechanics.0) >> +endobj +40 0 obj +(III. Space and Time in Classical Mechanics) +endobj +41 0 obj +<< /S /GoTo /D (IV.\040The\040Galileian\040System\040of\040Co-ordinates.0) >> +endobj +44 0 obj +(IV. The Galileian System of Co-ordinates) +endobj +45 0 obj +<< /S /GoTo /D (V.\040The\040Principle\040of\040Relativity\040\(In\040the\040Restricted\040Sense\).0) >> +endobj +48 0 obj +(V. The Principle of Relativity \(In the Restricted Sense\)) +endobj +49 0 obj +<< /S /GoTo /D (VI.\040The\040Theorem\040of\040the\040Addition\040of\040Velocities\040employed\040in\040Classical\040Mechanics.0) >> +endobj +52 0 obj +(VI. The Theorem of the Addition of Velocities employed in Classical Mechanics) +endobj +53 0 obj +<< /S /GoTo /D (VII.\040The\040Apparent\040Incompatibility\040of\040the\040Law\040of\040Propagation\040of\040Light\040with\040the\040Principle\040of\040Relativity.0) >> +endobj +56 0 obj +(VII. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity) +endobj +57 0 obj +<< /S /GoTo /D (VIII.\040On\040the\040Idea\040of\040Time\040in\040Physics.0) >> +endobj +60 0 obj +(VIII. On the Idea of Time in Physics) +endobj +61 0 obj +<< /S /GoTo /D (IX.\040The\040Relativity\040of\040Simultaneity.0) >> +endobj +64 0 obj +(IX. The Relativity of Simultaneity) +endobj +65 0 obj +<< /S /GoTo /D (X.\040On\040the\040Relativity\040of\040the\040Conception\040of\040Distance.0) >> +endobj +68 0 obj +(X. On the Relativity of the Conception of Distance) +endobj +69 0 obj +<< /S /GoTo /D (XI.\040The\040Lorentz\040Transformation.0) >> +endobj +72 0 obj +(XI. The Lorentz Transformation) +endobj +73 0 obj +<< /S /GoTo /D (XII.\040The\040Behaviour\040of\040Measuring-Rods\040and\040Clocks\040in\040Motion.0) >> +endobj +76 0 obj +(XII. The Behaviour of Measuring-Rods and Clocks in Motion) +endobj +77 0 obj +<< /S /GoTo /D (XIII.\040Theorem\040of\040the\040Addition\040of\040Velocities.\040The\040Experiment\040of\040Fizeau.0) >> +endobj +80 0 obj +(XIII. Theorem of the Addition of Velocities. The Experiment of Fizeau) +endobj +81 0 obj +<< /S /GoTo /D (XIV.\040The\040Heuristic\040Value\040of\040the\040Theory\040of\040Relativity.0) >> +endobj +84 0 obj +(XIV. The Heuristic Value of the Theory of Relativity) +endobj +85 0 obj +<< /S /GoTo /D (XV.\040General\040Results\040of\040the\040Theory.0) >> +endobj +88 0 obj +(XV. General Results of the Theory) +endobj +89 0 obj +<< /S /GoTo /D (XVI.\040Experience\040and\040the\040Special\040Theory\040of\040Relativity.0) >> +endobj +92 0 obj +(XVI. Experience and the Special Theory of Relativity) +endobj +93 0 obj +<< /S /GoTo /D (XVII.\040Minkowski's\040Four-dimensional\040Space.0) >> +endobj +96 0 obj +(XVII. Minkowski's Four-dimensional Space) +endobj +97 0 obj +<< /S /GoTo /D (Part\040II.\040The\040General\040Theory\040of\040Relativity.-1) >> +endobj +100 0 obj +(Part II. The General Theory of Relativity) +endobj +101 0 obj +<< /S /GoTo /D (XVIII.\040Special\040and\040General\040Principle\040of\040Relativity.0) >> +endobj +104 0 obj +(XVIII. Special and General Principle of Relativity) +endobj +105 0 obj +<< /S /GoTo /D (XIX.\040The\040Gravitational\040Field.0) >> +endobj +108 0 obj +(XIX. The Gravitational Field) +endobj +109 0 obj +<< /S /GoTo /D (XX.\040The\040Equality\040of\040Inertial\040and\040Gravitational\040Mass\040as\040an\040Argument\040for\040the\040General\040Postulate\040of\040Relativity.0) >> +endobj +112 0 obj +(XX. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity) +endobj +113 0 obj +<< /S /GoTo /D (XXI.\040In\040what\040Respects\040are\040the\040Foundations\040of\040Classical\040Mechanics\040and\040of\040the\040Special\040Theory\040of\040Relativity\040unsatisfactory?.0) >> +endobj +116 0 obj +(XXI. In what Respects are the Foundations of Classical Mechanics and of the Special Theory of Relativity unsatisfactory?) +endobj +117 0 obj +<< /S /GoTo /D (XXII.\040A\040Few\040Inferences\040from\040the\040General\040Principle\040of\040Relativity.0) >> +endobj +120 0 obj +(XXII. A Few Inferences from the General Principle of Relativity) +endobj +121 0 obj +<< /S /GoTo /D (XXIII.\040Behaviour\040of\040Clocks\040and\040Measuring-Rods\040on\040a\040Rotating\040Body\040of\040Reference.0) >> +endobj +124 0 obj +(XXIII. Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference) +endobj +125 0 obj +<< /S /GoTo /D (XXIV.\040Euclidean\040and\040Non-Euclidean\040Continuum.0) >> +endobj +128 0 obj +(XXIV. Euclidean and Non-Euclidean Continuum) +endobj +129 0 obj +<< /S /GoTo /D (XXV.\040Gaussian\040Co-ordinates.0) >> +endobj +132 0 obj +(XXV. Gaussian Co-ordinates) +endobj +133 0 obj +<< /S /GoTo /D (XXVI.\040The\040Space-Time\040Continuum\040of\040the\040Special\040Theory\040of\040Relativity\040considered\040as\040a\040Euclidean\040Continuum.0) >> +endobj +136 0 obj +(XXVI. The Space-Time Continuum of the Special Theory of Relativity considered as a Euclidean Continuum) +endobj +137 0 obj +<< /S /GoTo /D (XXVII.\040The\040Space-Time\040Continuum\040of\040the\040General\040Theory\040of\040Relativity\040is\040not\040a\040Euclidean\040Continuum.0) >> +endobj +140 0 obj +(XXVII. The Space-Time Continuum of the General Theory of Relativity is not a Euclidean Continuum) +endobj +141 0 obj +<< /S /GoTo /D (XXVIII.\040Exact\040Formulation\040of\040the\040General\040Principle\040of\040Relativity.0) >> +endobj +144 0 obj +(XXVIII. Exact Formulation of the General Principle of Relativity) +endobj +145 0 obj +<< /S /GoTo /D (XXIX.\040The\040Solution\040of\040the\040Problem\040of\040Gravitation\040on\040the\040Basis\040of\040the\040General\040Principle\040of\040Relativity.0) >> +endobj +148 0 obj +(XXIX. The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity) +endobj +149 0 obj +<< /S /GoTo /D (Part\040III.\040Considerations\040on\040the\040Universe\040as\040a\040Whole.-1) >> +endobj +152 0 obj +(Part III. Considerations on the Universe as a Whole) +endobj +153 0 obj +<< /S /GoTo /D (XXX.\040Cosmological\040Difficulties\040of\040Newton's\040Theory.0) >> +endobj +156 0 obj +(XXX. Cosmological Difficulties of Newton's Theory) +endobj +157 0 obj +<< /S /GoTo /D (XXXI.\040The\040Possibility\040of\040a\040``Finite''\040and\040yet\040``Unbounded''\040Universe.0) >> +endobj +160 0 obj +(XXXI. The Possibility of a ``Finite'' and yet ``Unbounded'' Universe) +endobj +161 0 obj +<< /S /GoTo /D (XXXII.\040The\040Structure\040of\040Space\040according\040to\040the\040General\040Theory\040of\040Relativity.0) >> +endobj +164 0 obj +(XXXII. The Structure of Space according to the General Theory of Relativity) +endobj +165 0 obj +<< /S /GoTo /D (Appendix\040I.\040Simple\040Derivation\040of\040the\040Lorentz\040Transformation.0) >> +endobj +168 0 obj +(Appendix I. Simple Derivation of the Lorentz Transformation) +endobj +169 0 obj +<< /S /GoTo /D (Appendix\040II.\040Minkowski's\040Four-dimensional\040Space\040\(``World''\).0) >> +endobj +172 0 obj +(Appendix II. Minkowski's Four-dimensional Space \(``World''\)) +endobj +173 0 obj +<< /S /GoTo /D (Appendix\040III.\040The\040Experimental\040Confirmation\040of\040the\040General\040Theory\040of\040Relativity.0) >> +endobj +176 0 obj +(Appendix III. The Experimental Confirmation of the General Theory of Relativity) +endobj +177 0 obj +<< /S /GoTo /D (Back\040Matter.-1) >> +endobj +180 0 obj +(Back Matter) +endobj +181 0 obj +<< /S /GoTo /D (Bibliography.0) >> +endobj +184 0 obj +(Bibliography) +endobj +185 0 obj +<< /S /GoTo /D (Index.0) >> +endobj +188 0 obj +(Index) +endobj +189 0 obj +<< /S /GoTo /D (PG\040License.0) >> +endobj +192 0 obj +(PG License) +endobj +193 0 obj +<< /S /GoTo /D [194 0 R /Fit ] >> +endobj +196 0 obj << +/Length 589 +/Filter /FlateDecode +>> +stream +xÚTKsÚ0¾ó+<Ó‹ajÛÁ`n:””–¨íd29(öb«5#ɸüû*Hâ‘úCO»+íãÛÝOê;…Ówfþåu>Ü#gè'Ã~à “87qä‡Qè ÜytQ ]oî7Î~A&µ1«%Ðgà…6Ó)c¿µÊ6Z® Â’ì‰<ŒõÁ)ÑzÁ•60͵"íõ (puý„îBoä'ñð…ñÃ{íö|ÐrR)UJ¨@¨
TWç>ˆÐ^pk6Œ_¡ÝZt•§ÖmK˜ …“Þ”Àe +?Ž’«IOÌ£b»ºÂúgÇyY»Ù_ÄMÈýc"Ïf:2;2©jY2>~ãs0Aˆc*T›§À;þôµ\àF°ÖפFØ2å#–vt_,½‚é!ìÖ /~‰wQ 7OmȘ5.lÆ”e›çm‰9Τe§ +endstream +endobj +194 0 obj << +/Type /Page +/Contents 196 0 R +/Resources 195 0 R +/MediaBox [0 0 342 504] +/Parent 202 0 R +>> endobj +197 0 obj << +/D [194 0 R /XYZ 9 487.902 null] +>> endobj +198 0 obj << +/D [194 0 R /XYZ 9 468.102 null] +>> endobj +199 0 obj << +/D [194 0 R /XYZ 9 468.102 null] +>> endobj +6 0 obj << +/D [194 0 R /XYZ 9 468.102 null] +>> endobj +200 0 obj << +/D [194 0 R /XYZ 9 468.102 null] +>> endobj +10 0 obj << +/D [194 0 R /XYZ 9 468.102 null] +>> endobj +195 0 obj << +/Font << /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +205 0 obj << +/Length 870 +/Filter /FlateDecode +>> +stream +xÚUM¤6½Ï¯à‚Çæ›ã$»“l´QF+"EÊæ`hX ¸cÌɯOÙe:ݳ(Ê¥)TÕ«WõÜ4èüpGÿç÷»æîþ‘UAIê’² yê +’UÐœ‚ßÃ'Nk'NQœ§,l_ñû0Ÿ´ØÐ~GðûãÆçÞÛŸiN›A.¸R_ÐܸÛKÂsÄ›Ðë"ç>ú£ù pÅ©‹üòý'¼`Ä_^ÌB«u=š³V/òô£¿ÎòEèE žñÛ(f£®s˜ó“j¹6 ýGÙj®/A!q?¼Éða6BÏÂÃ{ÐÝ +¿ìl±”äY™' ÁÙ+†°×ËPàâ¤ìÉ6ŠÛþ 캒º"¬J ¢‹Ôë(g!7€ç êÔV[íw¹±w¾šhp*o¨*+’SË f únÛFúÕˆøî‰Òý½›Ñå>-ËŽr³’‘ +¶|râxˆ“$!zx ÿˆ;·¹YJøN¸ÆÃ4´Å Lw
õàL'k v?pócoÏZìÁA{Ì>Vö–K£!ãb
Æõ˜XyØoU° +B »î0Þ_¶Ypµý›gZº_wèB†œ£×ÛÑ‹,g¿NÙmÝ +ÊÛ™IÉn ¹^Èá›ö¾¹ûŠ¥ ‘ +endstream +endobj +204 0 obj << +/Type /Page +/Contents 205 0 R +/Resources 203 0 R +/MediaBox [0 0 342 504] +/Parent 202 0 R +>> endobj +206 0 obj << +/D [204 0 R /XYZ 9 487.902 null] +>> endobj +207 0 obj << +/D [204 0 R /XYZ 26.559 259.997 null] +>> endobj +14 0 obj << +/D [204 0 R /XYZ 26.559 259.997 null] +>> endobj +209 0 obj << +/D [204 0 R /XYZ 26.559 244.65 null] +>> endobj +203 0 obj << +/Font << /F18 201 0 R /F40 208 0 R /F16 210 0 R /F41 211 0 R /F17 212 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +216 0 obj << +/Length 559 +/Filter /FlateDecode +>> +stream +xÚuTË’Û ¼û+8mIUÑ,OGÙÂ)P ¼Jå”T’ÿÿ‚Œ@vÙçb<Ýt÷ ¢ä7¡ä´£ÿY÷i÷|”†p ÚhFÒ/b8˜Ö©PÛ’ô“|«7vµ•Uò¯>}ÔßÓ׌b ¬R|E5Ò—¤á$®•W7B«*Îîà»qÃÙ[œm1†Z2âé5kQÈåÄ•óä&· g.p7,«ÀM›¢„Q°ÔfGRÀ´&
³ ¸.D "¨æ0ŸÇnY Y¹÷9DŸ|˜®4lËÛ•E£"ÉÑ(fm!Ùßd¡3%ó}Œq ÏrÄ0³]8î]Ö˜Šf秘ðçK)ç?ÐCac–h°šñ(Ò6H)•(TóR Z…£‹1¬Ò•Âb]e5 Ñ b)üTÖþ9O¾nXõê–¸ö1ï]¨nô›qÖÞ—h†~2ÞÕÜTç4„ÅG×#À[–nŠ8'f“0•Íýãi±°ö¦a¤¼ÌX-Xî3zƒ²"+ãXÆp‰«‡øãQ\‚‚hÕ}\èú¡ã8¸ãÑ»±`šCËí½ç7Ÿ†Õ”¨ŽÈWìõ>'qZº—¸²`»i×@³›³nê ®+ ›fr^>•¬”Få“\—|3«¢@9æÕÌK\^‚_6^×ß í§¤…ĹÄîi|b{˜/.
g7•$ŸÊr—¬sþeq‚Áp¾5J´h·ŽÑ½o<-Î]{v(X©Asßä1L}úϧȥÝ_Bs +endstream +endobj +215 0 obj << +/Type /Page +/Contents 216 0 R +/Resources 214 0 R +/MediaBox [0 0 342 504] +/Parent 202 0 R +>> endobj +217 0 obj << +/D [215 0 R /XYZ 9 487.902 null] +>> endobj +214 0 obj << +/Font << /F48 218 0 R /F49 219 0 R /F50 220 0 R /F19 213 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +223 0 obj << +/Length 276 +/Filter /FlateDecode +>> +stream +xÚÅ“=OÃ0†÷ü +ökîü µHLHõ ) M¤’¢|ˆ¿O+@•¢HtñYw~tｶ¶g »‹’_âV…Ì3d˜eŠÀ"1ÒÐ!ó9{侬ZKr/¬åÐȳº=d]u¬Cá#›NXþ” jÚ.d úÝ¡jËbrñìïW4?š¡v`õ dj"FC'AaÂN4¢Ê»dx¿ïç¦èºrÞQ2â,Fë@J9lœÖÜNº^ÆåXçYçÕ4ÔR«±`
]кHþ÷‘eíŒ}¨A5²-Þ»âm7ÚP4 ãR 4`Á8óõ šp¥—<#H¥¼ªgÁÏX§Ð÷+˜}Zü«µ>Öé¾3 +endstream +endobj +222 0 obj << +/Type /Page +/Contents 223 0 R +/Resources 221 0 R +/MediaBox [0 0 342 504] +/Parent 202 0 R +>> endobj +224 0 obj << +/D [222 0 R /XYZ 9 487.902 null] +>> endobj +221 0 obj << +/Font << /F41 211 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +227 0 obj << +/Length 2102 +/Filter /FlateDecode +>> +stream +xÚ…XKã6¾÷¯Ði#mEïö4ÌÌN0dgŒÝC’[¦-¢õpH©;=¿ž¯X”-{5Ø‹YdÉRÕW:ôŽ^轿 Ýø°»ûþ]ZzQ$i {»ƒ%I†‘—fIe¥·Û{¿ø?~ûnÅ™ÿf“Dþo7¿í~ÂÆp¹qũݹó .SÞ¹k$ G™EA•eV—ÄE ¬ÐIK#ûM\øãf›&™ÿ¸Ùb2ðï¯)ãF–þ(û½Üßc)}áX¡™˜N|‚1걕Nx ˜wTÏtt;zRÓÛ:Ŷø°4ÍY=ù‡¨¡X&¸Ü¨cc˜¬ÚÏF|-ˆ˜ˆA¿òâpàñ³lŨžÕHÛ ï²q0’I-Å^n"_ž¿4ýÕ-¼Öê ‡Ž¾¨ð
¥”½Ô¢å5S+gQõk¥5‹ˆ~ÏìS£ÚÁ êyÙªôg^–'Õ‰÷¬ä Ì—A ¡åš6Ξ %]–´†±b«8b /{Ý”‘Oîˆ+ÿq™‰ïämtƒ]éǪ«Ô3]!µg¨@úEÍåšÍ:~øK“¾>„ãd 2+¯ªÈ%øÄY˜yÀuRñÑ€Ë Ì½íBÊz‡[ÏËÅm§†´}5ª6b–õBœA?9A-· BŠÁ$Ï®¿ÃL$HÖá4˜þzÏ3« +´*&Ä¿fº¡ÜE„Á1IvQuF¶î°~àñ$˜¤Hc¹U«Q®ôù6ã
“½*² ñ*ýÆY8«!vøäÈW8Á0w^:KÕZÄ=³íæ—°¹ß®©5ʶUGJÍKc2{wO;*wÖ”=“| d +›ÍIPÝ2ü}b—Òì|RH/k‹Ë@ÛSª'«šìÐð‡¾2…0‰¶u³ACm€ZîÉ“qâèϘX¦C·çÀcÝJ¡ ÞôUá#†VLƒe!- ’œ½…±£+l ”¨%‚G|ÈD}`ÒÔºÍZÎç9™Ž“ƒ +óƒ†Ýó¬xëRôŠj”p‡Éz¶í96«ÐÜa¢òM;×I øt ç’4ôN|¸Ù&[y콬tá³`ŸSäN3|mž±Ñ•Z+ä©/öd戩ZO§© &c] ¶Õ€F{\acÿ4òÜê`„[yÔHJ¸:¹†ë«/K€"c$qî x|Ú×}íDO ’–DœíuÌ~§C€úŽW:²¤þv~,â… “ihºô,…k: ĹSò¤•‡‘)fÏÍ -4 š9G®IÕÃ#°H¹-Ãò‡µ0ëÄ“ toÊy¬´uot‹™µ7¸
',FÖ v´x—› ZgÇ@j…!‘]yº§¾'G1B†·¦:7½oww¿ßE Ѿz•‘Www¿üz{,Aé ©JïÅ +thª Ã<ôZïËÝ¿¹e.¼ CRR'ÇAš'^”'Aš×-CîUA•Ç9ÉÁè+“ ²KkŒ/¿íPB …½“ 1ÃRÜFÎ¥B†;6Y+Þ–/ºÎ‹¸¾t…ïx¶Ã²×p JŒÔà8(ÑgH¨Ÿ6g.ýçsPæs6lyvN-m ûÀûþðü?"Fø¿R*‚fÎ[ÔµQªÞ.GçŸTÿdëý¼˜'uIO¶/sÅwzl•ilÄW%ZFD5g"ÔغWI-<… ãr~•üH"ïó5l6ã_˜P£cNZõ_ÕiÅÓQHHçs~
³p7ßý3vÕêÔº)W…r~¸þ/Žb`0¾þ0÷nÀiÙ…Ûk ß»q·)_Nx
|gx© ÚÖU?;·×bì†~8jjÜNY±H …Ašœ¿ä݆ÚD=šºÑj ‰p8>ï½úˆQa¯¤Þ0*üÿ*ƒÄq Ê°fÈ,¨ÐŒ/ ùfÿ¼É¨U«m3\±’Ù½D|‚ܽQ3GJí—Ú6{†LxÏEB´f8 áàî¼Rû“ó…ÿQL’lJ´ü£“/¯H¬]Þ%½[W 'AÆWKÓôÛãöÄ7ÀyqvÑŸ ü³FüØ$úÝ™S+¹G’fÅ””òëoýÞzö“Žô2Nýðð…xá-ÐL£í#½jµÅ…7©#LU¤9g7Úxy–&É9CÃ>.1êëw1Àë.¢Â8Ð%G‰}ú*ÚÍEÐ\ÀA ÍCw%ô+OÑEãJ¢4ãx[HÏ +-™Ê½6 gz.ôÔ¯ÑË^¹“з#“³®_ /¦íZ’¢vÿ;×»ÿ_Ìd^™ç øQ¹òù^Û” Ü´âH!Ãr®ü°™u” 2)³—0ƒM–H#…ÁB*—+#œ„yõ¿
ê[P¡:ÌQ_dAÞDýÞöe¯iä Êîù@Äû 4ÙÍ%ì,ßüq ø?
MÀÔ›ŽXÚM ð +endstream +endobj +226 0 obj << +/Type /Page +/Contents 227 0 R +/Resources 225 0 R +/MediaBox [0 0 342 504] +/Parent 202 0 R +>> endobj +228 0 obj << +/D [226 0 R /XYZ 9 484.913 null] +>> endobj +229 0 obj << +/D [226 0 R /XYZ 9 465.114 null] +>> endobj +18 0 obj << +/D [226 0 R /XYZ 9 465.114 null] +>> endobj +230 0 obj << +/D [226 0 R /XYZ 9 441.319 null] +>> endobj +225 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +235 0 obj << +/Length 937 +/Filter /FlateDecode +>> +stream +xÚmUKoÜ6¾ûW¨=Q@¤ˆõ:&°SoÐÄ€-´h› ¸»Ük½@Qvðï ‡Š½Á^Ä™áÌp^ß( ŽAüvõ±¹zÿITçqçiÐ žVq–æ¨ê8eÐìƒØýÍï ÂZ°fóǦù+ü·ùüþÏÏÌê Ôsðê ô*]%þ ʸˆóÎ"Nªš”ž[½ Ó’µa”Õ“F!Q3=´Ê¨¯,]Ù‘nlëUæeF¹`ÿ©Ã¨ÈSv7œéTlʬ•Ãþ] ^²
]¶Ý?áGa¨f! +HÁÅ6-f +#¸ gÕ€BÏFI«BÎöžÇ—Rp¦úI½“ ɧݞæUR±Ã¸ {iõ8Ì$?¹ +x"f-¥:¢:ý¦Pâ\žH<£tl¼¤ ß^y÷Ë ·Ýjìf¥.…F
TÙ¨'&«‘&!4MÍ0"¢ÌÙ‰!üÅj¶¥>Ó÷ÑËŒ Žäi {¯8ŠDÒ¿§ž‰h±¦ÓD¹a;.Xï,-\ã3Л—ã‚œP‘PfAïØ¢ÀþB<àI\'5w+ã<¯èlÌ3¡kæœíð£ú;ŒÇgñÖVä1/Àó æ‘1^ó"Œx–'%û“ìfóõ¡ +n7÷×DÞ\ošÍÝê49s +ÎD‘‘óÊÃo3\\2°šÖ¨}IÅ&húë²H°¿ÔÐ ¤fß’<²€ä¤%:Õ÷êº30žDì••ºSžë¥SZÔÈ.Fè4Fua"ë’ Õ ŒÓ¯±½Ê¡9«ý€Ì¨Ö“¶4;UÊÜš mHk롆–·Ð0ýgXA¿O³¯ +¶ØžPíþOpöÊ ½Ór˜ Õ4MpùºBõla%½ýA®çMsõ?L)õú +endstream +endobj +234 0 obj << +/Type /Page +/Contents 235 0 R +/Resources 233 0 R +/MediaBox [0 0 342 504] +/Parent 202 0 R +>> endobj +236 0 obj << +/D [234 0 R /XYZ 9 484.913 null] +>> endobj +237 0 obj << +/D [234 0 R /XYZ 9 306.741 null] +>> endobj +233 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F41 211 0 R /F16 210 0 R /F40 208 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +241 0 obj << +/Length 1984 +/Filter /FlateDecode +>> +stream +xÚÉrã6öÞ_¡[¨ªC€ + Yñ\æ×ç- ,¹èN."ððððöEÉj·JV·ï’ð½Þ¾ûþU¬„ŠS•ÉÕöqU$±ÈÕJé4ºXmëÕ/Ñõ‡Ï·_®îï>üýêãz“æ:úççíÍú·íp;9¿½É]ßÈ,–…âëWíƒ ×Y y¸,DtãúÉ[×3¡WBÄ¥ÖD@ˆ2NŠ ¸£«nZ©4òÅ…Š¦¡gÈðÈ€[;vk™~ó£=º©aèÞŒ¶_Ë"òS¼Þ(¡£;‹Ï6óàZ©ŒŸ9®e x+-Dô +|$˜úÀ¬¹èƒ}’“ûÃÛÀwà gÍŒ`ÚBeÑÕ£ÿ¢“Ö’ž@4í¦fE +<¦à†ïχñ̲’Ó 4¼ ¡ïQT,X0Ä7xŒëwœ & +ÜϪs]B÷W, YøøÄܤ%TqÈ;-Î{#¯ŸI fœ xH_5;'¦ÁVÅy³ `UÙ=kwü™\ƒQÀg»¶ìÅ[±+UèäI÷Cûì97A£ÿûr 5«|i˜ß³$)v¶ «\ø™JÎG*)/¦'ãm +endstream +endobj +240 0 obj << +/Type /Page +/Contents 241 0 R +/Resources 239 0 R +/MediaBox [0 0 342 504] +/Parent 244 0 R +>> endobj +242 0 obj << +/D [240 0 R /XYZ 9 484.913 null] +>> endobj +243 0 obj << +/D [240 0 R /XYZ 9 441.319 null] +>> endobj +239 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +247 0 obj << +/Length 840 +/Filter /FlateDecode +>> +stream +xÚuUKoÛ8¾çWèH1KR¤, [4Íf·‡"õnÑm{P$:"ªH)ÇkôÏw†C¹vá=̓ÃáÌ7Šì1ÙíÕ›ÍÕ«wºÊ¤äµ1*Ûl3©*^(“éªæJ¯³M—}a÷7ï_çµf›»î6Ÿóo›?_½“æìZmÀÜ€×xáÅ¡Ñ•Hïd«BjnÖ@K.ªšŒzëm¾*ª’Í}3×'MصµíHt#Ñvzz ììÆÇdî1û\Ùä¿“4‹_KÁ–Åi°ªÒ¼Õì Ï`Í€ÖÙj9_AÐ’ŠVð6“?€omØ´%zZ;4³{qóá"6¢äe-—ç¾ +#d-͹Vò|¥‹‚}ðÓÖ†0yðª$»qc˜mL¤&—l ƒmç·b]œS¬%=ù+pú’Íï¦] Exºf¶ukÔ<øfl¼Þ&L ésêCpm:À!ET#ó÷è^ÐÆúàæh|îáõƒ¯c â<Âfì®ó•QE,® Ì®s³›Æ¤Æ7PFúÖyÈáA _@:/fw +TÀ4Lc £Ø±h +žÅ¼šG‹1 ‘æþÜžð@ûÆÛKý5ÀVˆËªLP +Î7<.áD2‡øÆ +endstream +endobj +246 0 obj << +/Type /Page +/Contents 247 0 R +/Resources 245 0 R +/MediaBox [0 0 342 504] +/Parent 244 0 R +>> endobj +248 0 obj << +/D [246 0 R /XYZ 9 484.913 null] +>> endobj +245 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +252 0 obj << +/Length 1543 +/Filter /FlateDecode +>> +stream +xÚuËrÛ6ðî¯ÐôhFb ¾ytÇu¦‰;’:94=À"$¢¦H mëï»P’]ùB,vûÞN¶“pr{úõãêê×/I1‘I'Y4Ym&… Š(›$i È´˜¬ªÉ_bµ¸þ¾üýzZ&bu¿ø°œÎã<ßïW7Ó¿W_ABx.ažG$b eAT$,â®eV™N¤ Ê4%VYE–ËÞj§Ûi”‹Þ´[Бf¢¯CpVµ®Q½éZOê<¡ÖŒ¸i·qõÜjUy¹ØYÏ`“%ÂôhÄdÎjç`s’d¬œÔÄRÔÊVÍáP´zSöÀ¤MgØi^ÉàÓm£ìÖ#É<$Ö q=ôug?8æ'7ªï@&Z¾6Â견2)ôËZï{€v6JRQY…zæêû1`¨Q##ètšÏªª2ÈàÞrxú,¹èøûxÉ®çÚ¬QM
>D™¨:^Û®G j¿§ÓZY¦˜– }=?î¬ÙšV5iy¦åk5×ä +H*C±Cø€°„°ü;h×cXÊBüa;ºÌ`>~cZ×kÔ‰»GÓRQŠöûÆèŠ)˜7Ä>°‹0Ê×ÃcØ£ÎBÝ´)+D·áµ6;§›
ÚS„>o)r´ú5ë¶;E):` j×9/oý`UOöÁ^ÙÞ¸ÞQ€ E¡©&ûÅíÕ1+©×õ¶2/X]¥¸#~ ø²îtàŸ1h)~Ê8Yq‘–âæÅ˲f‡%Uˆ^5LúÔµ?C™€ ¾÷PƆ×~<«Ûù¥ÊÑÅ$ ŽZcՌǓ(
ýñ…‡i!Åì $%´¡cV.N
6ÑöÙªy:î¼Ík£šÆ‹¦&E€&Ç‹ÎæH0gYq„Àá0ÛíÏ°|š¦‰PÍ îBÆÐT°9öèŽ'x 4Œ}5»d d*&o1 +!ýR«©…ÐsÈT‚3Ç„Ò†öÅËv0•fï®dœÒâ¥?ñ\{†gŠÒù‘ý`Ý0Š¹œÁóñìÝ@…×Ú¾?zqd”0Ùµ3˜Ò߀#,Ã;nT‚}gÒ0C6ˆÙ£ópÇ"NC<ë®i´ÚÚó¼ãïNáe€™,Ä‚Ö\|3M«íŒ‘Ÿƒå:˜±*ª9D~³žõ‡?zã÷Ÿ ¯3Ö~ ,‚OÁ,` À÷P×Á2¸˜dÕ8ð)•ì®£oo¬¡®Ie.>£~D^CÈ‘g°¼ÿkvõ§ð!ý Ý{€¿·¤ è16Ê{=ÃÈºÛ Ç5@¡4 ñVc›çãs%£dä»±…3niXO¦ ß-¶¶õñè¥hø+mpkköØlq˜{}0÷jÝì7šs8z³6nç¹(OÈåÙcÁ¢vÔ:&- £5xojJ¸„ø%ä‡& °iqÕ/ø”t|[I[ÉòX¢ÄK %¬_¿Á +ýÆ'O{l. Áh^|¼© +_Š)8Ý
-¼xà #P=,8JPž,;ǧ,PV Q$4¢K"?]@;vàY$ªK¦Q "?Écæ…+Ã>ò®,§ÿÄ‚ý +ƒf|ºmü³®w ð«Ú_¢ü®Ï&2 Ê°”ô®/à ˆSøÈ—lÅ•Þ¼YL‹F6¼bjÒ8Nü\H‰ Ëûï§_ŠÓÂü(PÆA Ž¿%dkOÂúàÌÚñæwõÐÁ+9ƒY qÍ°Iÿ7õÒ7þlÍ _Ó xOç¹XÖz³1º©Ø¨,>7*N)ßüF| Z}éG'*™e㟎Œf GYFáëgZ Ärž†AšäÌþdÌ+¦›ÕÕ-:Æ +endstream +endobj +251 0 obj << +/Type /Page +/Contents 252 0 R +/Resources 250 0 R +/MediaBox [0 0 342 504] +/Parent 244 0 R +/Annots [ 249 0 R ] +>> endobj +249 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 336.878 77.115 349.497] +/Subtype /Link +/A << /S /GoTo /D (section*.168) >> +>> endobj +253 0 obj << +/D [251 0 R /XYZ 9 484.913 null] +>> endobj +254 0 obj << +/D [251 0 R /XYZ 9 441.319 null] +>> endobj +250 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F16 210 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +292 0 obj << +/Length 1066 +/Filter /FlateDecode +>> +stream +xÚíXKoã6¾çWèH Ìò%‰<fÓ¬á"Ù5bc íAµ›¨-’’mö×wø ù{],Ü=Q¢†ç›oæ‰D³ˆDý+Æã«Ÿ> +Q¹HY4~Š(K°YÄ%Œ¦¦Ñ¯èæó§ñí§ñ(þ}ü , ¥X%‰[À8&*‹z‰ÀL¥Þ~K‰® b™¡qÜã™D»4êI†Á£ K1“‰7 ϵ·ôÄä ³e§zõ÷å“ 3ô yœ¦¨1/¦yõ¢*Ê°Êuç s8H1LÓl} …®c¦Pÿ6¬I#J°"Ê-‚eXp "œl€ã^BÎc&Ñkm&ît\ û˜"85EyW¦˜ùiwHÎQ_—KÝT=Gê\Å=ؤ¬McÊ¢†µ$A°?MYgàû&š€+LˆGTÙˆÚ‹‡>Ä”&A,)Íà±s‹†ež»PH…y¢!¢wú 2ðkôZ7zÙuþ¦ì•ÕÔy£›É?ñïr&g€ìa ‹# +ŽSÂö‚Üz´Ê'켘ú‹±Yj¹)拼®7t»×“˜ehîÙ9±D…P(y|O/ÀÀ“ÇÁcj›¡_¶ÉÙÏf¡M^x¬6\凸ªÈÈv*½2çk›ÃäXsœ´ ÑBÃʳZènÛëê«+{~î7’A@²i×?èÚV¹FbŽtQk°¤@a’}7 ™[Ö)H2˜l]ì–(„ÄÅ ª¿ó&›öéõtê +²¿k ‰%GzQºLœ€e‡} —+˜eV•ìÝÔÏBZu8l%Ü*(ç¡Ä4K8JßWU<ÑäÄx‹K¾®˜49–õ§RnÇ{¿0]¯Vy¥ ¥Æ“vPLÊå +xý‡‰ Kî¬%wKü@lîr»òëú© ¯ÀR¨nx®ç³<0èÍNwf6·/hüíWÓÌ;¯Ø—{ö%¤»ÿv&2™¾wnü“óø– ã[‚ߪ û$ús±ÚÁTçoé ÖŠÍ׊=tô°=%ÔÆä9É¿
_X ¯:µ|¿ñÇíD~“;é:2K›Ï‹&/ô:G¨JþCœíÊ>ãß#ûá3æq?OÅ^ß)…7e1Ñ«Ý +÷³©vÛ›2%Oƒã¬6€¥gðèqGîJ'P‘¿…&Új|•õSY-CgŒ¼¿x ‘äbûx@l?è¹ÓËS>WÝVò^çõ3(ݬ÷໩i½õ1sÓ¶Yv‡?ëõwÍ!ɽ/C¬èÿRøCû1ÎOÔÇ= ÙæIèÀ÷ÕèÀmCÖ˜
uÞ4árß° }/îÚf!„ã cŠÂö\ ¦Üþåÿ¹è +ÔwÓ +nTù£}ñ7»›ÎŸaô.øI¹ïn¡mGÀ4‘˜¥ +endstream +endobj +291 0 obj << +/Type /Page +/Contents 292 0 R +/Resources 290 0 R +/MediaBox [0 0 342 504] +/Parent 244 0 R +/Annots [ 257 0 R 259 0 R 261 0 R 263 0 R 265 0 R 267 0 R 269 0 R 271 0 R 273 0 R 275 0 R 277 0 R 279 0 R 281 0 R ] +>> endobj +257 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [326.151 267.222 333.996 276.919] +/Subtype /Link +/A << /S /GoTo /D (section*.22) >> +>> endobj +259 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [326.151 252.776 333.996 262.473] +/Subtype /Link +/A << /S /GoTo /D (section*.25) >> +>> endobj +261 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [326.151 238.331 333.996 248.028] +/Subtype /Link +/A << /S /GoTo /D (section*.28) >> +>> endobj +263 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 223.885 333.996 233.582] +/Subtype /Link +/A << /S /GoTo /D (section*.31) >> +>> endobj +265 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 209.439 333.996 219.136] +/Subtype /Link +/A << /S /GoTo /D (section*.34) >> +>> endobj +267 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 182.984 333.996 192.681] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +269 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 142.98 333.996 152.677] +/Subtype /Link +/A << /S /GoTo /D (section*.40) >> +>> endobj +271 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 128.534 333.996 138.231] +/Subtype /Link +/A << /S /GoTo /D (section*.43) >> +>> endobj +273 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 114.088 333.996 123.785] +/Subtype /Link +/A << /S /GoTo /D (section*.46) >> +>> endobj +275 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 99.642 333.996 109.339] +/Subtype /Link +/A << /S /GoTo /D (section*.49) >> +>> endobj +277 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 85.196 333.996 94.893] +/Subtype /Link +/A << /S /GoTo /D (section*.52) >> +>> endobj +279 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 58.741 333.996 68.438] +/Subtype /Link +/A << /S /GoTo /D (section*.55) >> +>> endobj +281 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 32.287 333.996 41.983] +/Subtype /Link +/A << /S /GoTo /D (section*.58) >> +>> endobj +293 0 obj << +/D [291 0 R /XYZ 9 484.913 null] +>> endobj +294 0 obj << +/D [291 0 R /XYZ 9 465.114 null] +>> endobj +22 0 obj << +/D [291 0 R /XYZ 9 465.114 null] +>> endobj +295 0 obj << +/D [291 0 R /XYZ 9 345.562 null] +>> endobj +296 0 obj << +/D [291 0 R /XYZ 9 319.277 null] +>> endobj +297 0 obj << +/D [291 0 R /XYZ 9 297.11 null] +>> endobj +290 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F19 213 0 R /F16 210 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +343 0 obj << +/Length 1240 +/Filter /FlateDecode +>> +stream +xÚíXßoœ8~Ï_ÁÛÁ®±
ØOUmr9)¹(AU¥Ó=PÖ›X!ãG“ü÷ Ø`¶¶[]Ó«îeYvÇØóÍ7ßÌ€;§GÉÁ»Æ @" ‰“¬œ€R„cê0.a±“,¿Üã?/’ÅEríýüñî$#&bxž1UOÚè +endstream +endobj +342 0 obj << +/Type /Page +/Contents 343 0 R +/Resources 341 0 R +/MediaBox [0 0 342 504] +/Parent 244 0 R +/Annots [ 283 0 R 285 0 R 287 0 R 289 0 R 312 0 R 314 0 R 316 0 R 318 0 R 320 0 R 322 0 R 324 0 R 326 0 R 328 0 R 330 0 R 332 0 R 334 0 R ] +>> endobj +283 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 437.716 333.996 447.413] +/Subtype /Link +/A << /S /GoTo /D (section*.65) >> +>> endobj +285 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 423.27 333.996 432.967] +/Subtype /Link +/A << /S /GoTo /D (section*.68) >> +>> endobj +287 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 408.825 333.996 418.522] +/Subtype /Link +/A << /S /GoTo /D (section*.71) >> +>> endobj +289 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 394.379 333.996 404.076] +/Subtype /Link +/A << /S /GoTo /D (section*.74) >> +>> endobj +312 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 313.466 333.996 323.162] +/Subtype /Link +/A << /S /GoTo /D (section*.80) >> +>> endobj +314 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 299.02 333.996 308.717] +/Subtype /Link +/A << /S /GoTo /D (section*.83) >> +>> endobj +316 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 272.565 333.996 282.262] +/Subtype /Link +/A << /S /GoTo /D (section*.86) >> +>> endobj +318 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 232.561 333.996 242.257] +/Subtype /Link +/A << /S /GoTo /D (section*.89) >> +>> endobj +320 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 206.106 333.996 215.802] +/Subtype /Link +/A << /S /GoTo /D (section*.92) >> +>> endobj +322 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 179.651 333.996 189.348] +/Subtype /Link +/A << /S /GoTo /D (section*.95) >> +>> endobj +324 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 165.205 333.996 174.902] +/Subtype /Link +/A << /S /GoTo /D (section*.98) >> +>> endobj +326 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 150.759 333.996 160.456] +/Subtype /Link +/A << /S /GoTo /D (section*.101) >> +>> endobj +328 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 124.304 333.996 134.001] +/Subtype /Link +/A << /S /GoTo /D (section*.104) >> +>> endobj +330 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 97.849 333.996 107.546] +/Subtype /Link +/A << /S /GoTo /D (section*.107) >> +>> endobj +332 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 71.394 333.996 81.091] +/Subtype /Link +/A << /S /GoTo /D (section*.110) >> +>> endobj +334 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 44.939 333.996 54.636] +/Subtype /Link +/A << /S /GoTo /D (section*.113) >> +>> endobj +344 0 obj << +/D [342 0 R /XYZ 9 484.913 null] +>> endobj +345 0 obj << +/D [342 0 R /XYZ 9 351.075 null] +>> endobj +346 0 obj << +/D [342 0 R /XYZ 9 328.908 null] +>> endobj +341 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F16 210 0 R /F40 208 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +383 0 obj << +/Length 1077 +/Filter /FlateDecode +>> +stream +xÚíXËnÛ8Ýç+„l*-Ìò%’Z¦M dFìN¤](²bU$C’Û¤_?—"e[¶§iL»±øº|Üsîᥱ7ó°wzðfrðzHB…!õ&7 £)J=®"D¹ô&SïÊ¿ >Oþ:ÀÎêõãM“Q qz&V‘µJùG’þ$0©ü³`@£Õ/Ì–X"!©7€U©âÖòm‘Wzš–q ¤_k¨Yû"·ßzžÚ‡\M˪©I?vÃbûù8/²Ô¬'Œ<‰"‰‰Ù-• Ij–¤ˆ¹Úlä °±Óg#<‚Q„£Æh@•B˜0Ø1Gœ kuyy‰‚Aˆ1l¹º-²b¦“8ƒåóõ'LD²Ìjš1î7¶ë}ú.òW•MæiQÞB˜³A øìbat¼Ò`e +§;Ó(BJBosŠHm¡»ut†R8‚£Sh\ ýÌ}ÒÀ'TúEUékÄ×µ©ßÛ¾öì±uÅ'ÂøPçºN]{>µ…û€*?×Ã>ä¦åX XÂ0âÃzÄ7…ÆE¡ +endstream +endobj +382 0 obj << +/Type /Page +/Contents 383 0 R +/Resources 381 0 R +/MediaBox [0 0 342 504] +/Parent 244 0 R +/Annots [ 336 0 R 338 0 R 340 0 R 364 0 R 365 0 R 367 0 R 368 0 R 370 0 R 372 0 R 374 0 R 376 0 R 378 0 R 380 0 R ] +>> endobj +336 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [320.298 389.265 333.996 398.962] +/Subtype /Link +/A << /S /GoTo /D (section*.119) >> +>> endobj +338 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 362.81 333.996 372.507] +/Subtype /Link +/A << /S /GoTo /D (section*.122) >> +>> endobj +340 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 336.355 333.996 346.052] +/Subtype /Link +/A << /S /GoTo /D (section*.125) >> +>> endobj +364 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [165.004 267.206 217.3 280.107] +/Subtype /Link +/A << /S /GoTo /D (section*.52) >> +>> endobj +365 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 269.933 333.996 279.63] +/Subtype /Link +/A << /S /GoTo /D (section*.128) >> +>> endobj +367 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [165.004 240.145 229.724 253.046] +/Subtype /Link +/A << /S /GoTo /D (section*.74) >> +>> endobj +368 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 242.872 333.996 252.569] +/Subtype /Link +/A << /S /GoTo /D (section*.163) >> +>> endobj +370 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 216.417 333.996 226.114] +/Subtype /Link +/A << /S /GoTo /D (section*.168) >> +>> endobj +372 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 201.971 333.996 211.668] +/Subtype /Link +/A << /S /GoTo /D (section*.172) >> +>> endobj +374 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 187.525 333.996 197.222] +/Subtype /Link +/A << /S /GoTo /D (section*.174) >> +>> endobj +376 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 173.079 333.996 182.776] +/Subtype /Link +/A << /S /GoTo /D (section*.176) >> +>> endobj +378 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 158.634 333.996 168.33] +/Subtype /Link +/A << /S /GoTo /D (section*.178) >> +>> endobj +380 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.445 144.188 333.996 153.885] +/Subtype /Link +/A << /S /GoTo /D (section*.186) >> +>> endobj +384 0 obj << +/D [382 0 R /XYZ 9 484.913 null] +>> endobj +385 0 obj << +/D [382 0 R /XYZ 9 441.319 null] +>> endobj +386 0 obj << +/D [382 0 R /XYZ 9 419.153 null] +>> endobj +387 0 obj << +/D [382 0 R /XYZ 9 293.05 null] +>> endobj +381 0 obj << +/Font << /F15 231 0 R /F40 208 0 R /F19 213 0 R /F16 210 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +400 0 obj << +/Length 145 +/Filter /FlateDecode +>> +stream +xÚuŽ»Â0 E÷~…ÇdHÈËI3%¨*(XH±!øÿ? +endstream +endobj +399 0 obj << +/Type /Page +/Contents 400 0 R +/Resources 398 0 R +/MediaBox [0 0 342 504] +/Parent 402 0 R +>> endobj +401 0 obj << +/D [399 0 R /XYZ 9 484.913 null] +>> endobj +398 0 obj << +/Font << /F48 218 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +405 0 obj << +/Length 1362 +/Filter /FlateDecode +>> +stream +xÚu]Û6콿"èËl öü!Åö^†k‘^3´½Ã]°¡X÷ ³•D«me–Ý6@üH‘¾KÚô%")’â7d±[$‹ëgÉOΗ›g¿¾å"Kâå2“‹ÍvQq&ò…I\åÅbÓ,þîVo¯ÂJ›õŸë͇ðŸÍ ^*ÖT +” @¦‹Hq‘ ’ºE‘«»°ÊƒMå… ÖO¢i\I™¡h”&Iœ¢p¶Œ³R’ðæÍŠdîoW¯ÖWo êÍ ªý@øÍk:ÁÀ0Jƒ‹FŠ8KÿRš'qF¹Œó¬¤‡~bS.âÜ?³éö͇ûõ«Ù–w««÷ë÷×ç†\¯nÞ6wž ô.J Y‚> 1«¹ ó4¸¹½¹_oÖ7ïïÙ€äÔÔ(M“X¤K0 ‹Ó%çaÝo*OM+ÈX ùô<Ç0+;
`OY®Ftoém£=:ºì¬ ²[<KÓ`"ü J"à UCи7Ž. H)ý~b•ªÑt«êÈG bó(K2ò¿I™ ßU_ƒ@–åÁ3îð“zûÐ2ø0™¶1ýŽ8Ð^¤®¦º5Í/Ž¨;m;=Ç°Ì‚@"P}Cœ oRrnÌ ;Ýá59¤‡oöꀾŠ„C¨³ƒ&hÐŽë‘(ã^õµ~³2Ðß¼?^Vízó1IEtÉŽZSH€wYn &HD=Nƒ~ÅU•/ Šò´v;ú„Î"Ê µršØ|R—˜DCU@è²ß…ÞQÖWãÕ 4—ìSœð ,Ì Ä[; +±¤Ú#Óø1Ãá’e˜Mó ÷:ÊŒžÊ}"€‡Èo“$
>Â’øk¯F 5z®{{ÆOH§q8d²zê|c¯çG „À|Wël# Œxåù}—Õ9vÄ¡¾‡¢ F°Øƒ·šå'æa/[kÝ0»¥›¡bdê÷ù”ó׎ +[BéÁQG ØHÂV7 rÅ^|/HY{v=Ïl0¦ +œ ýHH0ji0¼ lG÷s•b¡rì¹—žæ9‡RŠ©˜¦C«zýâ9/¤ fx& +&!pƒÉV;²ÀPVf·Ç’‰ +EgVÞ`@=¹ åzEØ§Ç´Û +NEGkw¦V-!œhlL?k{Ôò/–.4¦£VÑ¥î¡ÎÉ$-i<O+ѹb +endstream +endobj +404 0 obj << +/Type /Page +/Contents 405 0 R +/Resources 403 0 R +/MediaBox [0 0 342 504] +/Parent 402 0 R +>> endobj +406 0 obj << +/D [404 0 R /XYZ 9 484.913 null] +>> endobj +407 0 obj << +/D [404 0 R /XYZ 9 442.547 null] +>> endobj +26 0 obj << +/D [404 0 R /XYZ 9 442.547 null] +>> endobj +408 0 obj << +/D [404 0 R /XYZ 9 391.364 null] +>> endobj +409 0 obj << +/D [404 0 R /XYZ 9 369.197 null] +>> endobj +298 0 obj << +/D [404 0 R /XYZ 9 359.523 null] +>> endobj +30 0 obj << +/D [404 0 R /XYZ 9 359.523 null] +>> endobj +410 0 obj << +/D [404 0 R /XYZ 9 329.751 null] +>> endobj +411 0 obj << +/D [404 0 R /XYZ 9 293.138 null] +>> endobj +403 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +414 0 obj << +/Length 1811 +/Filter /FlateDecode +>> +stream +xÚuXKã6¾Ï¯0ú$ÝŠ$Kj9eI0AⱋÅNj‰¶¹#‹IMOÿûýê!Ù=¹˜Åª"Yï*9Û 7Ùæ·ÿxúðÓ¯e³Éót_UÅæé°É‹&ÝÕ¦löiQ>nžúÍ“~üã—í¾Lž>ýëÓÓ¶=ýþÓ¯yõæؾI›¢À| ž™>³yØåMšã¶‡]fÍ^˜.Þ]¶Åcâ‚Ö›ªNZoxLÂÉmA}ÙæÉ(˜è„åà†Ai²÷î¬ 8“'¸)OŒ^÷ͺs¸¡ëÝÐE½K릞…¶©I×uK‹¬œ¹âɼ^ûæ¡hŠJ=äeZ–Õ¢ ø•~ in Ê¢I~Ù>ì²âî„Ý%6o(¦sÞ›. +úsVeŸó]ýdî°É…çE¹‹ÄFÁœZ½è™ß0 “ ™ŠX‹ˆ½ñVäëÁÝ<&–®iz^ +jMQxDⲊ±zš#“ñÁ ÁÁ ¸?Zo û”š/2ðÕ¨\gÓŽv<’ùwûäßÛFD¥CL;檒6|$R +Fô²±Jea°§ôL„Æ"36lÃkqØû: Ñ·öÈq ÿXª F6G1˜  OÞMàfZ”b‡˜q‚ÐÀ¶bƒÀÅ¥"½ŠD¯ƒ^r‘ø–hÕ]|% ¾"îÇ©loZ¶x}õï€ ‚xÌ+Èx‚eƒÀH¾ó0¥Ä[ ;ØÑ„û;Mx·&‚i;:@×W¹DN•Á'öÍÞÀÚ†Î[ÍŒ^P’s +`|œ#•n„ÕÒÁ&1–¢þ(¨i´È–Ay{g(ÒS'¨(
¶kU-®zdWñ«Y&¨HSçón”ÕFrdžKñ$LçÆÎ\¢l´ÆPšÝ ¦¿‰l)×jœò*I3{T#hC€y´>"Çœæ×eòʱ–³òn×Ná])¸¹[ìàûµü\:XËLXÀ<`¾’e5Ó'U£Ì¤ ”™>àÔ>sš–Ú+°ö&ØãØFKå“o 8ƒ$ Âõ‚‹qÛ
ê¹±7p‚„à elÔle!E<ãNâÔÁ6ððÿж¦Þ½³ æ”y´!í¤{¥H\g?ò%„—ÈCïöÎbŸ¡w
”zB“5®dê6Èá œ’Œ(nX&fÒÓ6 +'^tÛU·Õ^ůAcómÎ;K¶»§M%…¾¨‹¹$Qå¯ ¨Á ¥‡êŽxLÔQ `î ü¢ÐZ›:sçÜT¢ÌCt <åmòÇ´ª¾›Ú>Q Á&ì¬Tœâzû9ËëntÏcVÊG„ˆ± {A½œ$Ôßtá(k¸Øh”™† +±
ʵä +=`N¶Lês&õ¹·”ž 7 âvÎ6'ˆsë¿h\±×»ÏÔ¢”žµ•E–Eo¶P† ‡•lõš@ÉwbÑi{3äÜr
zø¸._oÌ…[c£ÊcEP,±ÑQª¡È]âŒ&â,[&G¢J÷¥€ê:N†{A &¯ƒ1]³:½ysl=±—öÞp‡ÞÝŽA
A„äïÔrùNÕV½»ˆÊŸ‰%8癲ᙚ)) Ê:±‡ùecýj™¸\ à¸$YöÞ»PM¦gU2ÁžÛÞzNÌ +u4ôÊ‘J îcÕ×-ÊØÒ3iw?úF Fe^9 +ïe7’§@…ÉFýîAbÄÙN÷ÒKju:h—¡}G{+Púæ/šyýøôáÿ¥Õ +endstream +endobj +413 0 obj << +/Type /Page +/Contents 414 0 R +/Resources 412 0 R +/MediaBox [0 0 342 504] +/Parent 402 0 R +>> endobj +415 0 obj << +/D [413 0 R /XYZ 9 484.913 null] +>> endobj +412 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +418 0 obj << +/Length 1842 +/Filter /FlateDecode +>> +stream +xÚXKÛ6¾ï¯r’µ*êclÚ-¤£EÑô µ¹[YrEi·ù÷ý†3ôc#l{1‡Ã!9œÇ7#ÇÁ>ˆƒooÞmn¾ùURQçI°y ò,RE dU %YlvÁïáÏ?ܽ¿ûqµNË<Ü|w÷é§U…¿ñüÓ ºûøvU§áæþ—ûÍo«?6ßóAå—G'eÕU‚›Ý©)ÉÜÄ¢J°Nã8Ê« +DÅUÍB÷·8>®BÓÓ˜…Çy´sÓo5O‡GÓp˜Gf´Íƒ™.ײpj‡yß®’*œÜauøL9¡ VI Ž›ØùxìôA¯TØ{" ƒµ*£<¯1fQ–å¬ÙÔâ€$«ÃãéáˆIÖLfè-TN’¸›·Ùé¦gö^=_xñtZάBkú}w:ß ^úÃJ±(Sxeš‰d4v¯!qfˆb° €4+“pèy±áéql¶“Ù6]÷…ù£Ù› “¼ßi°“å¦s74ôóÅ2o;Œ£¶¢i¿ãƒ§aY[²}s7GåáÎØI¼ +þç8;Óëµa/èñi•ç¸ Š|³˜~§ù6
ŠåH}Úï<S›^ŒK“-‰´M¿×vI)`¾¶µcán|n
"S¢Ic ¶/ØFƒ¾êí$'´ˆÍô ƒVIH/JÄûN…qX ç#jAe_eø‚ø9ÄÀ¹1¤&><4tOýÄÀÒÁjbá)–ÅÅèKüoeÜ¥Ä0oHk :í¯ïšÉ<‰Ý.…ÄÚÄâW•”ô2 —å9.KgÆÒ›Ñh äÔAÕe¬ âÔ9è4È¢4@QKÈTGeZë ±oõšS?ó¨Tשïm›æñUL`Ú6– VO“áiêEâyÇ\#«SkdÛE^‰ˆõ"þ(çlÔ»$K‹4ÊR:Õ
#òŒ" å9™›ÄŽ-g³Ù”ë²(Â_)65Km)²ˆè ì1iÞé=|wÀuä#¾ï¯%œa”¨¯b‰vŸUšMã<µoxî’£Ä0Á3^¡ xˆã¨Ù²J,«Ä² Ú\ÚY20u°ë ¯8%w +…ùçl'ó9V™» w
¿ˆíwª°ÕxÞÈsPVöý‚%CÑm™R@ÇÉX1 ‡‘ˆ„*š!xºc +Oí÷–i¯=Ñ{æÓ§±–ófk$Lh‹™ZúbP]ù#S@`à‹•…÷ IŒp°–Wõ?
¡ ‘ðÍÁòº¯¼DsL9Q¸Îïã\ u©Œ—ªHZö ›¼È¤üå«)s5WVHyÀØðp h`,Tt^0®/×ËêÞ¹æ"„(MfÔ(l ©Êí˜e&Ër¨mÐðm&I|â²³)¶$.xÄ–µqç³Ç@s‡h[Š%º,M +ì> ávÉડÙO„»Ü‚^ŠžJÀÜ1]–=¹ŸÙ BÊÛyEûÞ\Ë\٘Ω°^è±¼1OyžHJ'ʃ%8bk·hyñq KÿÙv³•zãz0¹¨ÇáØHŠbÒ~8P•ë€ K‡e´ D èst‹ :ÈMÐܘP, Î3ã% m‹bÆ$Ü1»öÇm–þ ‡ãf¦þŸi©¾™[ +’D*ˆËÿIF P“õ(35{ êÁLï¡E34ì]g¬GܵÜ×
Ta6.+¥äSh#1©cþ)9@‹Q ©…Ç)Í”P—–¡¹çwæ`€c·¯fÀ¹[+N^H8 +¶‡›ßÿˆƒ ¸Ð0JÁzv2‡@%u”c ]ðóÍüMV5.•kb’(+Ò Ê ùuS s©‹¤ 1¼-LJ„î $–H‰®ÈúÏ– -K@ÔôfšG?D
õ®…ï]Á0²MªFuªŽÙ“(F£‹SV‘ï.æPK ²½NSŒÔ„‰«6í¨]$¾-<}´ðsÕÅsó:R*óß’o R §ÍÛ…#Š()j/ðná(—ç•— Húúïå©—y¿| +š/áà'w¹G•†–8çï‚Ê}horæ›- wF3›ûÆ„Q/-í${}FÖߊÍU ¥±£_~Æf@è “—Ë&ÏjWõšÉ¢=O^7XGÅëöB¼«“[E»RŸåu¸8ï—<šWQ–—¯º4Áí…—p +endstream +endobj +417 0 obj << +/Type /Page +/Contents 418 0 R +/Resources 416 0 R +/MediaBox [0 0 342 504] +/Parent 402 0 R +>> endobj +419 0 obj << +/D [417 0 R /XYZ 9 484.913 null] +>> endobj +416 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F11 420 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +423 0 obj << +/Length 2135 +/Filter /FlateDecode +>> +stream +xÚËrã6òî¯`åWY ñà«ö4“x6ÞÊî$±ª¶¶’ `’˜P¤†¤Æåýúí@R z6 @£Ñhô»™D‡(‰þ~“øñýöæÛ¦ˆ¤‰µÉT´ÝG23qž¥‘Iu,Ó"ÚVѯâáv£%üÿ¾ýã˸LSÂßÈÄÄ™ÔÑFe±* ØþpGòT<þçq{ÿOžüÀãw 7 ùþá_ïnK#¶÷žl²dc“J¸^UË,gª [F•é’•ÆE¢à=„3 ÝíÆ$¥x²C=ð´ÛãXÌ{çãÊÅËPïlúEÈèúsïÆ[)ìXwíòt)ªzm»ó$žõ ‘%`“™ØÀŒÉ˜•£ÅûµO·Àt®åeÝVp1\2ºê@™ÏHÊñ¶ía+Ì›¡ ‡<-Î@²ÝP{>4zLl>5õpä%>YL®™›_£M8 ‘
æ™Å +5 ™¢ +œê3¦i51ú«6 +!¡œÆøf¤Ø =uºúr zÞ +U`›Õ˜J!EÎj(ÒY
°ò±h[ÆätØ4›Ê!C-Õ¨ùÔÔ”ëÑtïø8› œ;bNŠÒÜ‚=V3ÔZ©<ìÞÔàÒC}h©R…/‡î}:¿öé\Q&¯ƒ*‚&_å%Å?8Bño-C`Q¯²+;Ôˆ6µÛ÷Û›O7¦ÐêF%˜f Œv§›_O¢ +ÀðÐX—EôLH§Hª2NaDMôxó37ìy”Áxd%HúR*:w•–2¨(ÊLeT
Å&‡¶:uï[?8JâÐŽ‡r çG‹‹Ï H +€Š y6§ªFŒYR ÉCpݸ½Gîf¢½oàÙ3s*Mâ<ª€:žÄ»|¤S“—sŸ¿`ÅW@$Þ ›*òyÆ[&|J*:ËÄÁ»ûÀKËÃó±k O}áƒÿÞÂz †F…ºp*tºlQ „ÍÌ;ÞÐù«–ogÈÔýÂœ# L Ÿ›ì|Á=ås™À]ŸÁ+^`9 +Qž…^Ó 6Ô¤¢ÐdÈþ2 _5B MÇ`™xÊ¡,Èïð"&E’‘ ç!D«Ü‰ûG +RÀÕúJ]øUhÙb{ÏŸ´ÿbÀߌ®òX‡ùÒ7¦-“R}ôKÌ[ÿöãqøJñÿt£ÿJ˜y@'Õ… fÈ Ðº‹1.}8Á8?ÑÎê Æú`G°¿ô}‹;˜`Ü÷Y¿ÑiÿåNO*˜âp¿h4ŒŒáÐq¡¼u™×!üƒÞ_¦ +endstream +endobj +422 0 obj << +/Type /Page +/Contents 423 0 R +/Resources 421 0 R +/MediaBox [0 0 342 504] +/Parent 402 0 R +>> endobj +424 0 obj << +/D [422 0 R /XYZ 9 484.913 null] +>> endobj +299 0 obj << +/D [422 0 R /XYZ 9 465.114 null] +>> endobj +34 0 obj << +/D [422 0 R /XYZ 9 465.114 null] +>> endobj +425 0 obj << +/D [422 0 R /XYZ 9 441.319 null] +>> endobj +426 0 obj << +/D [422 0 R /XYZ 9 419.153 null] +>> endobj +421 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +430 0 obj << +/Length 1779 +/Filter /FlateDecode +>> +stream +xÚ¥XK“Û6 ¾ï¯ÐôDÏÄŠ Ôë˜t6ív2“&ñ´“Ir %Úb#K%e“_€€dÙÑ :=!ÄãèÀ;z÷ÛÝËÝÝóW2÷ÂÐ/’$òv/‘~˜&žÌ ?’™·«¼âýŸ÷¿>¼x½ÙÆY"v¿ß¿y·)¤ø@û7¯h}wÿúŦˆÅîᯇ݇ÍçÝ Ï_…ÉRu”E~‘GðËNk‚2w›âmã ð“<"õƒ¼ ¡]mzÐ âlÍÉ æÛ&Ê„FV.Nz¨»Í6ÊEEŒîÀ²*5‘ýà‹Ò| +BYªÁt-TZ5¬»k› D=š¡F»¼m˜ùIRÀ*})²Æé…o¢¿Á5C‰Ñöà~¹h 29šŠX{giçÌ©ŒîŸ! ÕV$jz’«4›ÜVºÅÛOü þ¾u¦ldJFš~л¾ŒÈ#°’ÊΞ[Zr2Pó póX›ÅkÚ*Ëü +~Á´ÇÑôµÚ7Ì<Øî´fV“Ž¨HDÆ[³•Q"^Žx±" R(UK̃ÕÌêFÛë†âÞO‡ðcîpO÷j:pn‡ö!HkÚ5˜9jÕY˜¨4M\è;gSš +Õ ¨ÁÂ=‰A^±V
£eÚý ‚‰ÄX϶¥(¢7x䯙ôpx†.MÄ¡³ä[Óöƒ‚2_·lºó^†b + T('W‘éxºdg·ÉCaÕA5GŬ÷_G0ÿ\¶]3mŽ|N‘Ê! ÐQƒ¶'ÓjâL0”¹º,YÝ(WŹ`é¡#aò0—BÊ)¯Nµ²\¢ÁuqîÑ8(c™ÇpQ]Î2—è0d²5˜±ÈåPÙ¹ÚL96Ê6¬
F1÷ÃȘ=”D±è;bµHÎ k ³SþcêÊhR\ø 2ðÄŽ˜R4º=b.£ +D ÅÛ=€ñ¤ )gO fOBë„ÃÙS¦Ü¦…Ì(Ì2ã0qè.C‡2ÿYdö"i +1ÏçÆ8Œ€Ó‘W2 )E \ïÜ@²×*Öüµr;D.hoÐè¬`K2€vÕ;ôž³Ò'¦iÆ~°NZšç—:A«(GXê¾íˆÓëUË( +ËPæÌq\\l¥öj…¥ÜäÀîP Ì*MÐÓtìЊP謹òÍ>I@“C/'é#ÁsƒZ›-R?Ïf PB¤ÒHü½ÑD›“::ˆÂ
Ü ‘ä^Bµð!Â%¡É`<P`áÛ+ <n yÉj7à
˜yâÛk^ÊEf©ƒo™a”ÚBE#Æ„œÏsÈ\¡£0Ô%‚hM;EË”H» èÐ)KŸªÄîœHñ %‚G +iq±”3zÄ2¦Âdƒx¹=
ÖÜ‘Qks¬'p]˜ç5)4Í?-í k¢âIvÙê§tó›QlóQq=g ƒT1ý,ŒÒ…h»Î ÷û°ucôV‚/Ûò‡
XÏOLÓ¥j°Æ1í{m¿mhA<c;îV†‚|²Iꑪ°åÆnö§Œ¨Öò©Ö&u-Ýf$cÂÑvc[MSs[ñkG}áÑ'k â»{á”%|0Ç0œâo§îe7a,ßVøRX +ªãÓo
T"yH€qÏ¥ àæ‚‘Æb8«3u&§Yã2"FY<뙌ÛËœ!E›¦¢ïjuy\½Âïww_ïB /ô +/ý ¯<Ý}ü xpáR~\äÞ£“9yaTø ì¯ñÞß½¥ÂÔ+ü"R¬ÂËà]?½¿Ÿî{0 ³~ +cYBÅ—¦â7+<× @ögè¬þ/€›q0ýPÜÌ)°Ÿøý‰“–1@îa¯È=n¿™æÂ)6 +endstream +endobj +429 0 obj << +/Type /Page +/Contents 430 0 R +/Resources 428 0 R +/MediaBox [0 0 342 504] +/Parent 402 0 R +>> endobj +431 0 obj << +/D [429 0 R /XYZ 9 484.913 null] +>> endobj +428 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +434 0 obj << +/Length 1819 +/Filter /FlateDecode +>> +stream +xÚuWK“Û6 ¾ï¯ÐQž‰Q¢^Í)íl:Û饧N’W¢mÎÊ’CJ»q}ÒÊù" H‚À‡ãàÄÁ¯w?ïîÞ’e DTeYìöHÊ(M²@–U”È"Ø5ÁçðÏûß?n*î þ~Øý»ùºûíý'‘]-«Ê¨LØÕ/ÈQæ.æc‚m*ÊHÀnÛ4â²"!«¿Æêf³M“<4 þ‹°·ÞˆÐÒhèiÖjUo`|¤ápÔ4_·ýØ€x„¢ˆ²¬ +¶BFRftʧM™„¶?¼L`¡qDÕ}çL£Lßëe“”¡&Úi=PQ†ÿ/¦m‘áãf;¡jž7™ U‡zê ûÑy¶Wj外ٿƒeBÒ½EÂW"l´«9³Z0Óïiâ §}œÁ)¿:#`Î û±mHþÑËiL‹œylù€GTðBôI«Ž´Œ¯õó‡Æ"ô·OÚšZµÄ‚5n´ÚÑÈ{¹êi2 ŒúÑ:Ý>ãâIÐt&m4Pd%æ³È@èïÛ5ŒtWƒL"¥_„ÿ“²Oþ˜†ÆWVrÈËÂ/qφÐ`‹î@Â:i³‚÷ìèïAšƒá}É׽ߥ¹Ü4Y–tá{mQ×h³Í’8|èhŠn(9 ½œ© 1¦ÅlܨôòË ‹Ñ? Õ0(ÓùØÉääÑ8PòPÏ-¸Q ú`’øEÙA;£xÞ]ÀÚ'ŽÉ=ñê~ ái:‚·#n絕1ǘx„»à8Z . Ž>·ªÓÄ…[ïUY–bgÀ˜zl•å
zúÏ9áf”õp;‹Ž+!."¼OÛ ªP¯À”´f ÜŸ&_I¡5ƒ Äij•Iþ‰·76`SÞ€L’¤W†}·Ä ̹ZwLNâ”c.4Ðe^’Dr†ÂÉ9à у¶'‚
Ž1,ö½¥ž·¢áIù•åáðA¡‚£9‰dS6±»jó%rF[Æh[Š¶º; Gwc–!âe$¬f„7ðÀíl‡ÅCWV¥¼1•¯D\•/™Gòµ|}ÿ°ÙŠœî—‡~‡ÿÕ½«d9cóÀA/G3×+Ö>ª@¥EnÎÃÆög¾ACÓ{,TŒæ,Ê‹•`NŠl† …|{…ƒÏ¯~®§©áØ;=‘ÞÀHr ¢àƒjQB ³È䬥²EÒ+}ù½Ó2WÞ cG‚d•rY±Êk”Ò$#
hE"Ê‘wié³Ê*l;s†£¸È,† ŽH‰) ‘IéêÁÖrT³ô™J»…ø8iVuíñtXÍ´ý›ÖĎדoÇMÎIƒæsPªU†çš /úÂéw¾5Ð÷cÝB«¢¸C:`}éa+Ëè‡DÌ*aÕI*ȲVÕà–ar©JFK5›"©âEƉ€q3ù`†qàu¼A<— d²+V3ñ›XÌÁ—Vq +eTáà + XEÉhÿŸ<è¤ ‘à/ntÄè ÙOyLš"±ïÛ–Ò™ X„œŸ6Û"NÃ{Rß^h|q-_)~ßµàg…®k’W%…öÈ›þîŒm˜7$q'{õÀ^<"ÊŠm =ÕèXœ +PI¥¡šcéÇfÖ÷4·¬Ï¨ÁXc × +-ì
žÅðÖÐ\®Žæ̪'¾ûò5}¿»ûv'€ŒTA)¢B”A}ºûü5àÂ
¢´*ƒ/s‚'}e6)mð×Ý ôê/‚ Ж– mI$ó4(d]Ç5Úò Šª<ÉQ l‚/ø(,ô‘ºM«1»Å›%™²NŸ|3 6W=!NP7›M²ž~qÄEŒÑJÍ Ÿ‹QŠ£µ†HŒNCÝ)x„cºÌH¬Òþ>^Hå‘T4ø”-ò×?Ð5®÷[âÈ¥ÀL¯&Y +ðb +p ¸rÍÜ iÊ"gŸ>Ã+Ýgoh]0¯— l5T›†¤| ð¾ +endstream +endobj +433 0 obj << +/Type /Page +/Contents 434 0 R +/Resources 432 0 R +/MediaBox [0 0 342 504] +/Parent 436 0 R +>> endobj +435 0 obj << +/D [433 0 R /XYZ 9 484.913 null] +>> endobj +432 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +439 0 obj << +/Length 342 +/Filter /FlateDecode +>> +stream +xÚUQQOƒ0~çW4>µ‰t´(Ó0Y23“E}@è‘ÑPÿ·p`¶î¾»ï¾û®x¨@ zpX ‰£qp¤(”…2¦\DHåè
¿<'÷ë冸~`õ˜lw$xx»‚¸K6KûX_×jO>ÔÓbÅ‚Ki qKn7ªÑÀq¼É +r}&)³+]?¤žŒt0Í /pѤ5áît…î˜vs¦!©RÂ%þm™Ää;«Ê\ÛqÒ椻¦t4Õ¤÷¿éù"/[w°g¹LP!°Ó¥u¦ÛÛâ +ÏŸK9ŒÝ(}׺Õe] +endstream +endobj +438 0 obj << +/Type /Page +/Contents 439 0 R +/Resources 437 0 R +/MediaBox [0 0 342 504] +/Parent 436 0 R +>> endobj +440 0 obj << +/D [438 0 R /XYZ 9 484.913 null] +>> endobj +437 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +443 0 obj << +/Length 1671 +/Filter /FlateDecode +>> +stream +xÚWKÛ6¾çW{’µJ=¨G/Åv“´.’ ÀúÖôÀ•h›ˆ,¤´îþû̃’åD ôbŽ†Ãáp曇Åê°«?Þ ¿þ¾{÷ËÇ´XEi˜¤Y¼ÚíWQ…2‘«T&a$‹Õ®^ýl×›$š~ÿÝýŧ¢°”’Nm¢T†Q¾ÚÄY)Ÿzú{]¦ÁÃ=~€³¹ ¾¼gb·ýìYÛ/¼>~zxzÚ>>|âÏÏ ÿ|ø²}|âë"ys] &™„Ûâ0Êr¾ík”¤Þ41 ™ÀkIhwÔKú’8̲r:ö¼ÞÄyÐ9
ÆiÐíy=éj
ü£jMå˜eüÚw¼ÖÚUÖ<ÓyúØã"¸ðîAGûµÑþ4«]Gjdá +Ø¡Œcôl˜¦[Ö µ±p"–Áh¡éM×"+ LË[î¬*ÍäÅôG¦zsÒáÝz“&’‰rÇnhj¦›NÕ¬å„ƾ2]u«Œn+¶IÜZÃÊÓ4
Vá©—5?Yδ©$PtÏlxßW•ÕðàÚž5^½›¡250Aé+ï\ðm½ŠWÙ-·ïì OêQ^Žw¡ÌÉ1EWI Øb +,²Ð›|ÊxÎõ)6§ˆƒ{ày¡zqÚšnpKYýUDRW>^©€X×LÔºW¦Ñôè•ÿÎjŠº4çyðI÷¼=À¶còlG•Ö^¡5W5ß¹!ráâ‹A +I&ÊC)Ë[‹·x#\MÏ‹ í<£j´²L^Žªç]–ÊÙXèš?†¶ÖÖõl®? ;R8ù +:DØgœ'\°ÊÀõ +|ÆRe@öÂÚcºi¦/¦;¼þš(ßQ–?-Dg |bVÊZ££†£a-…ž +OÒcy(Åìꂯ†Í1²ÓÕ BŠy·æI¶ón
_Ýb/š5ONPÁµ%N†ó9ª²„æÄåè
Çè³ÆY/m±è¡¨™Ø8ç1Í<ß&©Zéz±!q¿MÒ1{©pCâ¡`œÇéZÓøžøÆ +ÿ§˜Íö'ÇÝñ÷” ¶ThvýU{… NK.Cmq*¿›ç˜µ &_œE³‘ˆD°ŠàªxœÞߪ5qSÌf8~Ìá?VçÍbŸäÄIâòú •õÿ3âvËOÿ + l9 ñ¨ù Â1³}‡Šç ÆænTÿÏN$“ ²Aò$‹÷:Ñ5Xç~öj0E)_ñdß+ö9Ï#W¾œNÿüW‘,C‘§+¨!!€ˆ+nd>ìÞ}jtB3 +endstream +endobj +442 0 obj << +/Type /Page +/Contents 443 0 R +/Resources 441 0 R +/MediaBox [0 0 342 504] +/Parent 436 0 R +>> endobj +444 0 obj << +/D [442 0 R /XYZ 9 484.913 null] +>> endobj +300 0 obj << +/D [442 0 R /XYZ 9 465.114 null] +>> endobj +38 0 obj << +/D [442 0 R /XYZ 9 465.114 null] +>> endobj +445 0 obj << +/D [442 0 R /XYZ 9 441.319 null] +>> endobj +446 0 obj << +/D [442 0 R /XYZ 9 419.153 null] +>> endobj +441 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F40 208 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +449 0 obj << +/Length 1714 +/Filter /FlateDecode +>> +stream +xÚuWKÛ6¾ï¯z’X%ê…œÒbÓn mb´’ ¸m±+KŽHíÖÿ¾ó ´^W¹Häp8œçÇa ‚8øõæçÝÍëw² „ˆª,K‚Ý>Èd$ò,e%²vMð%üôÇí/woßo¶i‘…»ßn?|ÜT2üÌóïøÿñöýÛM•†»»¿îvŸ7ßv¿¿~'²KÑI‘DU™ÀÉ$µBž›Ø«lSQFŽÜ¦y—3Õj :èW›m’áýF„“ƒ±ŒÃQwÊ™ÇMR†š)n€Z…Šöl>òxØ3K=lAÄ06¦WN[/É LÓýfçTB[Ý † ÝVÈHÊŒ5ÂCÒT„®Õ8HÂÃ8L}ÃįqÑ hªú‡£îQª`^㘯Ѷ Í=œX„¨®)^:©QñÂЩh³•Y þm\û|ê¥R9+¥ *dd'þ]k,ô¿êxê4Oè|üÓb ÖV#ZŽD«A_¿[¹y¤G}¹' ûÁ³O5Ú.ö‡UÕÐÉ9˜×óßô>±á0êQ„#ßçt5Ö¡ ât#¸$ËÂ4„¬vÃxf::¹3}#døU¤ò¤\»§‘“á'Ÿ|UPDU ʽ*Žr È(MKVL¬å¨ŒŠ4
¶l<Ì>Hñ{H=´p›TY”††=;2§H¢Y¤¿ý½ò¸¶dmj¦PBÁTñâïL=ujä¹Ïø–aã…p”QØ ÂÓ×:"½DeYõR«;p»LRLy=ò”I¶ +µ˜UÁÅ.ÉÓK—ˆ8‰b±”m½„ 0¥œ^õ`•e6ss¢Ÿœf=ö^‰V³ÇÁÃRá+CNyÉ,iÕÖd);Eh}"ÕffJ; ÃO¸DaðìÃÂûò±s˜W£å©q–yYä`
é¼â$•Q’W³…O\›JÀ ×=RFyVÎüoÖd‘xö°‰8ž×rD鼜» FöS*bˆOù¥4‡•J¦¨f£ ãÓ0"ø'/Ñà:_‘h<÷w’ãqæ‘‹'Ö”6<Vžá©åQÉ^YZˆëà`Q#Öà ¢0±pœAÙçUîZm5“åž•ÄÙ¢$IšN²G8³Ä{œ×´º@7¸!ÿý5²çÔ +U"^=d%ÀòW8+<ӣݤ¯60@_ ¥T vÕWxÌöq ¨º /4"´Ê8¾08Æëñ æžik½éFuˆSHT^ÀQ @ƒ©™e"ÆŽÚN ”ÅŠ dEž‚ô•ÆųÖ_v°X«“º§›@{Þ1Ü[À!°™¦Ðæ“N†w{f|š¡˜ 0ª‡ Â0Ì9×7«šÑ53gu^.×3© +endstream +endobj +448 0 obj << +/Type /Page +/Contents 449 0 R +/Resources 447 0 R +/MediaBox [0 0 342 504] +/Parent 436 0 R +>> endobj +450 0 obj << +/D [448 0 R /XYZ 9 484.913 null] +>> endobj +447 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F63 238 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +453 0 obj << +/Length 1314 +/Filter /FlateDecode +>> +stream +xÚWKoã6¾çW=I@¤Jõpoi›MSì&@c(º=0 •Ä€”“Í¿ï<(G´@/ž‡Ãy| ÊÙæi“mn.²@Þ]üøI6›\¦…¬Äf·ßäUžn³|#Ë"ÍËf³ë6G·Æÿì~gSX.K2Mr)Ò|[nQ¥¢‘l»ûí:NŠºŒn®>ß~¾¾½ºcñᯇÝõæï?1ýå>¹ÿã×Û»«x[D»ë‡pJ¶ (ɳ´Î*8«j>äʳi^.°9dF6Ælj¬ëè5u¤ûž¥G‹òëx'e^FÓAãBíc§†8ôˆ“êYß«X4à„»g/aW
ºEëƒMΈ
âåh J©”Çt£zÓk“Üé×Éb²Î¢×ƒa' JÁqËü=RV« Æ£)÷ª8Ë=Û¦¹(çä{…—G ÔŒÚMF•Îag=ï¤ ò¨U#Ÿ÷'X¿S“¥v%å'5é:*±0óÑÿ„^ªè +µMðaé·{cK§ÊïËËÛ›È ¿fyÕ
}à6ôÁ|¯\`œ ˜³PŠ Äšù +ÃT!Ùb2pö¤Y‰ÕCê´Ÿ‚Ư G³·n`a°“±ãŠ_ÈlrÊ<Qu¦µèzhP'Ì¢Ý P Â^MØ« vb ±(¨ò´þæƒd= ÌøÄf*Tý8ñ2cæ(QÀ:Sr0dZäõyã ®—¨ÞFè×
QH²÷6hÆδ€ÏâÉ“Ó{íôØêä£O^§ºõo~ÒÃj ÊUL¬ë̈§à-ÎdôÌ uƒñÞ<ö”è–Z€Î.iر¼tè“à{f¸“öè˜+‘˜`¼tŒ°éYÝiß:óŒUÆ–V0Û!¤³ˆ°.¿!ôQ +Ûª ã +‘ ÞÙ€ìza0¨¬ÄIÝ`鑇Òó¢b¸à5JtK °fÑUr¼Z1gžL‡™ +LkšoÁFˆ°˜ ˆŒVn:\b+2TâØõÝCF/1Ã…vœvâFŽ£4Ûº·µ+w‚(ë0„ Œ¦€KÏ:…¤ŠZãZª°(¨3à G ”NuæèÃÂÈ:Î ˜ÖÂ!GçÏ €ïqµ‘0Àìh +`X û‰ù%(¿mHí3ßXëiòƒ†`†”` ½*CxŒÃ®Uˆq>Mþ>-E#8P†w`—E–W§ƒšÂúž5¯s A§:xX?vPO? 3CùŸ¾à˜Þwâ%lËy{x¬#Gµ +endstream +endobj +452 0 obj << +/Type /Page +/Contents 453 0 R +/Resources 451 0 R +/MediaBox [0 0 342 504] +/Parent 436 0 R +>> endobj +454 0 obj << +/D [452 0 R /XYZ 9 484.913 null] +>> endobj +301 0 obj << +/D [452 0 R /XYZ 9 465.114 null] +>> endobj +42 0 obj << +/D [452 0 R /XYZ 9 465.114 null] +>> endobj +455 0 obj << +/D [452 0 R /XYZ 9 441.319 null] +>> endobj +456 0 obj << +/D [452 0 R /XYZ 9 419.153 null] +>> endobj +451 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +459 0 obj << +/Length 1717 +/Filter /FlateDecode +>> +stream +xÚXMÛ6½çW=É@’"õ•[›:©Û`lŒEÓWâz…ÊÒB’³ëß7 Ê+;Ú
ôb’Ã!93|ó†²Xìbñî•ðíOÛW?¼ÕÙBêPé$Zlo2Ña.’…ŽU(ãl±-,ÿÙþÊš2ÌãØi®¤Ra§‹U”„Q¦YuûËz¹Ri |¸Þ\½Ù|x¿åözýþÇe®‚íf)±ïJ›í_<õIÄbsÅ}Úg.’,ÌS‰³t¨uÂG\¯?n¯7o¶ëŸY÷ãúêã‹¥·RLýYå2”lŒB™¤¼Á¦aMOý‘Y˜d ââtÚ®´ ö×"Zje`†6›ªáápgy~×Y3Ø~àÑýr¥AÛ÷ÕMmY³¨éÛ÷ßÓXµ xâÐóšÎ‡ÎOÙŒ3É‚(×A{訣ûhö÷´½“Þrë ¢Ng*Z?,aˆ¡Ÿ#Ë Óu•ÙYÞ£?Ü“lµ%‹Æsnœ~·¡s{|^BÕÖuÕ육âÜÄCSݶݾ>.³(—+uð'õ)QŽ³ëš{Õ@^+ìÛ¡jahÃCÃÓ~# à즯
ôF>I¥½Öws¦xë sè-R
¾í©U.b4.Ú¦ LCîy
ïeëS` š#O™¦äNYu¶ “p:UÙ31ôܦxΦˆ¶«‡»ö°»£‘òw§Ïîâ‚L»3ÍÎö,pÁ#½fdžD%Ø–¸ûÔŒŒ™@Ù=mcš÷¶¡eB¤4 &[Ý@¹Ø‘°lÙ…žÅMëå]; +à³]ámQ5Ž4IÖ ûÁîç<Ž" +™Žîü6ë±³'ªHÈ ¾áÍ«a´‘€ã,©ÁÎÎ-G˜)=[<9¹§£ñ$p4dD£Sy20œð§ºŠB©œ©) nz‹ª\Îe`1œÊÓ"'… }¸(^¤xM +yŠ[¶ÀCQùG®˜ o¦y¼XMÔ(Äõ·ó±))KÈŸ½®‡kö6ÂÛÁ=$Ñ'<Rk mq8ªyâ‹ÞJ¼Q¬žÉe-ôé5ÔvG®§\šxÒ£Ò B2´³ðBBi%¿^ ‡$ô~vGš¢À…˜¦° PZ†>ÎIÀÙ¥c%D§¬ú′{¸`Œ wÙf%2(YZ5ËÀI…-¹êcØŸH4Êü3ÒÛ¶®ÝÍ<ÌVjº¤×nB¦a ç_TÌ90¡›Ä/‡ M™žò•1‡è<xgꪶ•iXzcÆT bíS—–YN’îÈÃ3Ýi¸Öa,.â=Ù;})E2|´IùÕI]Šä/¤H*¡8Eò‰ÿL¨ÔLýÇ…”|ÍEð +ßi,®Ï"7rŽ)Æ2}[Újue ç7Äw{¢ ·ã§ÿz¾V‹¡>Ž×€Zz‘w†N‰²‰ÐN+[–0{PïœÕHç™ÁÁ¯b#{b4æ^”Âè’
NŸ¯Ožòó2ŽÇuø*Î @=£ì= nMÇJÇ]hý;ÂbñFBìzn’=pªc—‡± ¢O øèòûô7
ùÆ «.ÐCWÊ3¥õöÕ>›. +endstream +endobj +458 0 obj << +/Type /Page +/Contents 459 0 R +/Resources 457 0 R +/MediaBox [0 0 342 504] +/Parent 436 0 R +>> endobj +460 0 obj << +/D [458 0 R /XYZ 9 484.913 null] +>> endobj +302 0 obj << +/D [458 0 R /XYZ 9 465.114 null] +>> endobj +46 0 obj << +/D [458 0 R /XYZ 9 465.114 null] +>> endobj +461 0 obj << +/D [458 0 R /XYZ 9 441.319 null] +>> endobj +462 0 obj << +/D [458 0 R /XYZ 9 401.718 null] +>> endobj +457 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +466 0 obj << +/Length 1869 +/Filter /FlateDecode +>> +stream +xÚXKã6 ¾Ï¯zr€‰×’ß½í»‹i‹ Š EÑíAc+‰ZÇJ%y¦ù÷%EÙ±S϶—X¢(Šâã#•dsÜ$›Ï öï>eÕ†±¸Îs¾Ù 6ŒWqÊóMVÕ1ÏÊ;Ýüýôñ‡÷Û:‹öO??íÝþ¾ÿîÝ'–/¶Õ<®‹¤ú
Œ#ÓCÎÙìRÆc^g0(⤪‰ëb¤µÛ ¯‹È$òÈÉ^º‘¶åe4Øo·»Œ'ÑÓáq»K ™-‹d'œzÁu˜5©ÅÙBn“Z}¿ªyW¬Y פqUÜÉ +6Š503ª¸eQˆO+{+™Ådÿ\VYèôÞ" ÔQ§Ñ›„·ÝK"¼¢
Fj£{ÌH£m€$w.lí:"MÔeàƒiâ<¯—Zø#¤ÁK¾ˆg¸Fæh(ü‰|â3Žè Y‚I'Ù]–››NX«¯LÏr·ÈÃ1ÿQöIôª±˜ÍE…"wX}3DZ$Q¯ÃWúX€e( ž
É;0xÙæ9˜GµÊ¡+Q)Ђ*H¥ÙA„›ŒqºÃd€ta‘Z1 ä¢N£ƒ#fŒü¾(ùºÜN¶ÂY›02²™" ç ðÀ1¾L©°¢Jä5Æ0¤¥Ñ>AÛk/Î`EZ}K}qQùÂÄ¢çш~Z컑ä‹j¿¢ #Oë¹ÃydƒK¾%’ø’°€ÌÒÑÓWõv€•¢Q“1|ÐC߆¨ÃÝ°½640ð/—ù’{
Z@ +œÞA’ZB5¦>ìp`‡Ë¥óhžBk½ç¡8ABüà–%¸@»ÒʳѢ%Þga1àJ™qlÔ [v@DêÐf• ¦Þ€jh›Ü@wvQ°„˜ƒÐ†°ó86Cª «¯hIã3=( ÍŽ«Ña¢lõ‡ÑQÐ:XÀn#0 Wt;Ka_k“œM²è K3gwzü ud±ó / ¾Þ Êûv –¨¡kLò€0€„ü5í¬ÑFö-#e,
^@7q‹cÙ“»ÆdåÎ ›Fäo„üŒÛ\iF² :¡:¢uÊ9*îp—“6ŽXÖ#œÒ½; †.&XÛû<®9Â+*.ø½‡g¤Ýœ‡3.*² GPT㊿ϊ G#=Œ@/Ï(YxCœaîã—À¥DìÆh#®uß1³^cÅÔâBÍ€¦¸ )¸ö(áq’äóö•ÔõÐÙ“nøIf† o¿ N+–™J!WA8P†ñ’ºÞª 2’taý¤iTO±·VÑ ©÷ÏtdóÈØj¯˜¸
VKY*íÔLc¦ùìä¡Iµ«OG¯Xx Àƒ•—ùÊ„Oá±ä‡Ç ø‚«1"ÂÊ®yì¾rÒc ZóX–Å<ŸÞd„ Po¥Ä7<F?#>„ /bèf—ý‚¨î³¥Æ& ß‹8©p¯¿dƒÖñFM¹ÿR.ƒ]$àPXæ8øÆÊŒï6øÄO|èØ€îÞ.ôß]%< &¤„¶Þžp |¿C«ÖSßY)
(hížwO† ÜbÖmÏ/bJçj|JLoÂâÍÞfz!âí“äö<¤é¬Äá”:+`T?NFì‰Hæ„Ág N*èóÿOæYßû‡ +endstream +endobj +465 0 obj << +/Type /Page +/Contents 466 0 R +/Resources 464 0 R +/MediaBox [0 0 342 504] +/Parent 468 0 R +>> endobj +467 0 obj << +/D [465 0 R /XYZ 9 484.913 null] +>> endobj +464 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +471 0 obj << +/Length 2068 +/Filter /FlateDecode +>> +stream +xÚµXKÛ6¾çW9É@Ìò¥×±-’tÛ¢)Z£EÑôÀ•¹k6²äJò&ûï;J– í9äb‡#>æñÍŒåê~%Wo_|·}ñÍ[¬”ešêÕön•Z¡²te‹Rh›¯¶»ÕßÉ￾þþæ۟ד§Éö‡×ï~[—6ù‹çïÞðøÛ럿]—&ÙÞüq³ýkýÏöÇoÞ¨t¾µÎr¡t 'Ó®Ê Ð ï²Ú¥….-™EÉRýc?øCÏûi5ßÏjQh;n÷ÓÒ‘JŠB£È«¥]2‘šôj®rQæRÍö°Â˜x'¹ø:‘—éj3{â¸,-¿ð¸ÅóR!K}uÞFƒ!üP $‹4ù¸ÕZÉžW\ç™8´È}Í=ÏOM¸k»CýˆS›t¾vCxXë<‰ -^aµ)3aàúe…µ) ë]…’p†1yÒ{ßÁñƪäc¨käIÓ¼|‹ƒ]éA™¹°•*E®³Q7~Êä¿Sxpµo†E
¤Â“qá|\€ÏÚù¾êÂqmÃ+í]¼N«ùI*O…R6¾)ãÍŽ{ß´ß8±ÞäÖ&7°ƒÕ%ì z¦*×Ã1ÖÈäãš^Dt¿oOõŽ%ð©¤@o›~è\h|\ÒQª>ê/%/o3ì ªÏfÓÍiR;üâcÏ3מ†tåŽî¶Žz5Œñ$2:ÎÑâ¸Á Œ·B^hâf< ]7„ê´YºTí:ô#m҇ÑN“&9¸¦aEâš KÐ `¬ÚS×ûÈkàÂãd"hv!Z v×Ó^er×µ‡¥{¸CÛÜ÷kÓ¡ÃY£’#=¶íû@z@Ö[W U\ÃœªÝ´Ý.€RGó1ØÀ‰6ÍÑ°ù•aÎß“¦`IMÂáÐÂI`´‰Jš%‡Ï´ÈÊ ÚÆ/ŠE:áÓ{™ÊE(H\!a9C•D1n¤Ì3 fEnôj&*~šG‡ƒ ]¼€Ùý@ZœK Z6$}Õógí ´Ñ1ÍÙÒïî1F£4px~‰0ìÁàÒï|SyˆJ[–ÉŸëB³ËSä!
@~œŸcÙÿžú!¼—Êú(‡ÚŒ•;õQŒOË“0ôÌ8øéÛæXks¸À dàn8N‘‹“ ^X½È +Q¾¦åm n€Ï\ŒBpW¸¤Î’÷ÊXwÛ·õiðTÀ#Ô€±óýðêeäQH"AØ !6“ " 8}&÷êÒˆ,ÏžO¾àMjÁ †† Ø f¯ùSØ]ÄKÆÇ›;Œ{¥#®˜@P‡˜Qù¸`ÂKž€ìÖ5 @©Çó9‚;Ï3N @ð»–že$” iþ5"éU|º–"‡’ë +àÑaµMùIH@®¨éú/̬\×wïyFËPèøú ñ¼ìxxú±Z¡uùEÔFgêº>°T ð•¨àÀb€ «ÒæW‰Ã÷XyyÎy1Of°ŸF
‹û–)LÀäœ(†=¯‚{ ¹¬¨æp¹òÙ{S°bf¿†qÒR'[ŠW¼Ý.l¢ +r@y + ¬ìR—÷ J'ªîŠ| ELJÀ¥4â™>M/ äDcP2„ég_1* )J®‹93.È”åêƒ>L‚1¿F¬Šži¥„šñ¾ Ù.r8K•G ëA˜’ð"ûx#~nÍEÄ9„FYÜkÒy +ýb¡.ßvFTt˜YÔá´ñ`•ë&Td Ñ(Eg.2¡"3›© AöÔ + +q^¤Ö ƇÐ
'Ï47¬6–¢@ŒHzþ %[“pw&»öÔì–µ¡¡?5¯¢•¨ˆ–?Þ3ÚÐ…Uµ49·’3´(¨ADи®Rè«)¦p6ZZb±kì”СëwÌx*¶mÄ”Œ=Äi`¾‘Ìÿjpè½ÈÌ-Ç‚Sg†
'fo™BÉÉk#`\Åæ± M¸`ÑŠ¯ §b¯GÈ€¼™ÿÀŒÿü +í¨B#—zâ,yƒ)ˆZ&‹½5ªvúÇç³]
Ö¯5ýý“3P-÷›Ý³ˆîÙˆþÙSá:—íøO.lRŸÚ'§¨dOÄYh®ŽÿBŠßÎÿB Ç×Ûÿß×àÛ +endstream +endobj +470 0 obj << +/Type /Page +/Contents 471 0 R +/Resources 469 0 R +/MediaBox [0 0 342 504] +/Parent 468 0 R +>> endobj +472 0 obj << +/D [470 0 R /XYZ 9 484.913 null] +>> endobj +469 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F63 238 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +475 0 obj << +/Length 558 +/Filter /FlateDecode +>> +stream +xÚmSMoÜ ½ï¯ðK11pl¥¤MÛSeUªÚ ˆ—]#y‹íDûï;0x7[å<f†yï
yrLòäÓîc»»M•eÉ“ö0ÞЂ—‰h$å¢NÚ}ò‹|øö!•‚´O?žÚŸéŸöËý#+oÒ$§²’P5$0áƒvy|'É +Æ)—6͉Q*ÍŠ²"ç”×D+wǪ K¯héqÛ©1ed´ ŸÓŒ7$„•DEÐéù²Ôb^BYD×>&õþò<AšX@Ó©Á÷ ýfLP!Jìq>Ï‹>!eÎÞR.Z1¶1þU‘IMe3 !!VB9Z󕿧]COÞ-½³ë±·«§“7±é\’×Þ±M3šf‚KòÙúó+2f©A¿æŸì KvÊé,ÐÍÊŠJ9WØÀa 0Ó>ÏÚ½¤¥ +@§» w0·$mof¼ÂuÓÞS| +endstream +endobj +474 0 obj << +/Type /Page +/Contents 475 0 R +/Resources 473 0 R +/MediaBox [0 0 342 504] +/Parent 468 0 R +>> endobj +476 0 obj << +/D [474 0 R /XYZ 9 484.913 null] +>> endobj +473 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +479 0 obj << +/Length 1455 +/Filter /FlateDecode +>> +stream +xÚWKoã6¾ï¯ðQFcUõlQiâíz‘lŠÆhQ=0 ³‘¥,%'ÝßyŠõf‹^ÌÑÌœù8/G³ûY4ûùMäÖŸÖo¾}›3‘„2ÉâÙz3™ËHÌ’T†"-fëzögðÛjþ×ú=«‚8MIu!D ñlga\$¬»~·œ/dž"qóëòš?nÞŽL&Î//WëÕ͇Q Ì2Ló NÂ$ÉÜÝË«› P]Þ²êòú—«›¹Á ËKæ¬Ü!Wç··«‹ó+:«ŒÀ¦ÉY×Ë‹wç V·ÎèÐsr'KKp'E–ó–+=°²H}—pzžˆ¤´ïÁ™ýþñq¾ˆó ë5sº½EB]S3gcn =l5K2Íó 6*üùÄÒj.eQ÷î°¡ãõŽîðL {ŠàiádÃŽÜÖMcÚ{ØTÂMçIº ¼½gòÙ [§ÈKÕµý Z4k`ÎÒºéÈˆÊ l1a‹CŒb‡QYxžNᘅQ1jœG‘ ÂêáȘ B^ƲE‘ »IHxû,€> €‰ˆ8•Îá4ÝÞ“Ÿ@w^Ga5bŽ_¦ìÕÕ`ºv²ýðò†y&Ú9CS6¼‘‰üï@B*&"ö(=ŸÂ±³¢ôá|‘yð®ÃÀxÆË’àãÞTxÁCó‰oï,Âä!1ÀEËÊϸ±³uïT8*HBOò¹õ.ú2È ( GÏòŠc" ËBx³?å¨DѨRóu 4/Ü£ +¨®G•_LÒ„£Ä$Þðº5W%c¯š +߆òÑ7¤]èáx’ýÎk†žåUgqBo!‚B´dü·;PÈE‚ÿ !óÒÌýaé‘Örýæ_–Íßr +endstream +endobj +478 0 obj << +/Type /Page +/Contents 479 0 R +/Resources 477 0 R +/MediaBox [0 0 342 504] +/Parent 468 0 R +>> endobj +480 0 obj << +/D [478 0 R /XYZ 9 484.913 null] +>> endobj +303 0 obj << +/D [478 0 R /XYZ 9 465.114 null] +>> endobj +50 0 obj << +/D [478 0 R /XYZ 9 465.114 null] +>> endobj +481 0 obj << +/D [478 0 R /XYZ 9 441.319 null] +>> endobj +482 0 obj << +/D [478 0 R /XYZ 9 390.261 null] +>> endobj +477 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +485 0 obj << +/Length 1658 +/Filter /FlateDecode +>> +stream +xÚ}ÙnÛFð=_!ô‰"†ç’DQIã$*ÜØp…EÓ‡5µ·æ!pÉ8þûÎE .“íììì\;,ö‹`ñþE ë›Í‹Wï’|&~œ¨h±Ù-Â4÷U.’4ö^l¶‹¿½Oëå*½õòŸÍï|!ô‹4¥ «0V~å‹U¤ü(OøÆæÃ\ÉRïõíí²H¼×wW 7ŒYüíæå*ôø +´LÅü¯_/Ã(õ>_Þ¸½[‚š7ÂÀ÷Âþæã%áõúýQçózóáR^Zø‰J/åÝÞÚëÛë«K>wW×"áªÏî Îý¹R¸ +œù¡ÊÄ9•é
‡é¹/“ÂÏbx¢²n¹J«t¿ŸÖ¼8Û jÓó¦ÖË(ó yc[^"Ÿœ-…ËPéö
Â,»~»b'³ì £m»3£À:^ +[.£Ü«x[Û=‰x‹ +ãz軃^†Þ^f+G-¯¦9 ¤oÝA—ÆeâØ»‚_ñÌôrZ⮲µð +å¬PNýÉw¼6Ôë3Ü‘…ýnå"äÏ0pû;‘†§†çÏéº!2($Ú¹ ‹Äêƒ5Zɱ!ô Oâ)©žy2æEëÖ =3åÛŒFÜ£”€öÙÞ”SïRÞ—0N¬ÀÔ‹b˜›]æMga¦Þ ®Álí»{Œ öC˜ùiZ\FüºåîñÔ/¹UÖf`ä(“9Ê0î¼Ù‚ +UùĽæB§É T‚³©Âfß}<;ÒžBv®ãF¯òä‡ ·ð•:¶Ü/ASI8Ö0µ ÇBFswȼG7`EMÀÏ¢Óóñe;¡§‰ +'²Ê´%ô ðóS-Ÿñ(jTv+øî±-|Ÿ +endstream +endobj +484 0 obj << +/Type /Page +/Contents 485 0 R +/Resources 483 0 R +/MediaBox [0 0 342 504] +/Parent 468 0 R +>> endobj +486 0 obj << +/D [484 0 R /XYZ 9 484.913 null] +>> endobj +304 0 obj << +/D [484 0 R /XYZ 9 465.114 null] +>> endobj +54 0 obj << +/D [484 0 R /XYZ 9 465.114 null] +>> endobj +487 0 obj << +/D [484 0 R /XYZ 9 441.319 null] +>> endobj +488 0 obj << +/D [484 0 R /XYZ 9 390.261 null] +>> endobj +483 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +492 0 obj << +/Length 1783 +/Filter /FlateDecode +>> +stream +xÚ•WKÛ6¾çWø(1#R/ª@I±Ûn4Eb¤’ ¸²¼"K®$¯±@|çAJ”W ¤‹äŒ‡óüf® Váê×WﶯÞÜÆz%¥È“D¶ûU ™&«XçBÅÙj»[}
>ýyóËÝÛ÷ëM”%Áö·› ×y |áý‡[þ~¼yÿvGÁöîóÝöËúïíïoneâ‹Vi&¤Êáf’*3dzZ]V›H*¡ò©uÎ\]yl×* ×JåN¬7±RÁÝ~½Q: :ƒÔ'Þ´–VWüçÀÛ{ødAÉ›¾l<’©×2h›Þ
ËT ‘çÞ4ß–ý5ÀÄËÚIŠAR‰f€ ‹8NXí}× Á/QÌâ¢( + kà¬! Ì +l>1 +S"VÉÕl bŸ’8 9¾…a¸ÜÔp955pBðÓ’N™å"BG¨PäJùµù%dÆa`Ï,sdV¡%H -#åaŽÿ'sˆg^N8´Lœ&ÁÍ Ø‘#5Hj=°+Ú#cdzþhêºì ;Tó’ï²LÄSœ´D„Ñ8›Qi,`èžeÔ;î¿òT +8u€ñÕ©¶[îß)yscuÊD’äW^=zm_AÛ ¢`ßv|E„ÚðÓ"\ÉU‡ï \|„GÆWúϧq¾æÏóg:„Îo×ZmG£ˆ†ƒmß]ˆ\r¼;«F fuLy(è{5ojêëÞ€‰ 9ИáÜ•xOæÕ<÷±Ë DFª ðûžÍx†3vfxs›F³'˜Ê„ÊÔˆjvÄ{4Ź]J”X‹ jË~ä ¬ª¦°aRY*d¦¯€nG¨<™8ëðÀ‹=žS3ÏRWI.À + Ú¥észnJ¨·#ÿ§…|¼¯IÝHÒ# Þô³Jæ QFY ‡>¢¢ÀžÉ©ÏâçH+íà”ÆÐÅ1ÌwO.7ñÀâ‡1™Â:J~ a±^rzþ4|ek4FW]iúÖ’+RÒŒEèTäcÓ·ÎÕºJ! Jx< n(ëR|–`rLýϘ¦gs5l]íó®) xD™®ª«êÐÖ4ŠDÎÏ*¾ s€ÆM2rM2 ‹ñ_ı×Àú iÓ™ ô”–’i”¿~¿Å@ÏäþQå>ÒHÛg-Çæú Æêï±*/¼â´M]ü`µ«êòx4î˜^J¸ôâc99cS¿‚Ò +endstream +endobj +491 0 obj << +/Type /Page +/Contents 492 0 R +/Resources 490 0 R +/MediaBox [0 0 342 504] +/Parent 468 0 R +/Annots [ 489 0 R ] +>> endobj +489 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [99.284 183.337 150.74 195.956] +/Subtype /Link +/A << /S /GoTo /D (section*.34) >> +>> endobj +493 0 obj << +/D [491 0 R /XYZ 9 484.913 null] +>> endobj +490 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F24 494 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +497 0 obj << +/Length 1733 +/Filter /FlateDecode +>> +stream +xÚ}XKã6 ¾Ï¯ÈÑl¼±ü>NÝv‹=EP (zÐØJ¬b»–<Óô×—)Ç™zöIEQäLJsØw‡Ý? >~Ϊ]’Äuž‹Ýñ´KD§"ßeU ‹¬Ü ÛÝ Ñ¯Ÿ¾>=ÖYtüòÛ—ãï þø9ÉïŽÕ"®‹¤úI…L¾g·O‹:ƒI ªš¸´{ܧ™ˆ\'{œ%‘ˆ"Ÿeß=-”vš˜¡SD 'Ý7z4¼ N´?)#~É¢Œ®¼÷ö¬Õ—=êºí“,βœôY¤‰Ç_é‰ë«‡Qžáš `à0úÜ=Š*rd¡"½³Puˆ“t±Æ³E½Èf ¶,š¥q~¨{ü¸Ï* »Á†?&ß{Em‡™¯·Û ‘ÆxžXœÎ¿ìPNrˆ9©Ól +‘ƒ1½ ^¢Z¢ÒÛa2NªQîÏt¸Õ¶™%KÀ6È≹ ÖÑÜÎ@]››uAg‹*Ô?#L@¡Æ!¡@<8ÚzeEqn»a6-Í'å$Z¸™a \¢Wˆ÷`Å°h~ítƒ´nK99²RÒXxF¨hlà±hC¼¬?{»Õñ.Y*OÐÁÀå”1þ]¸÷ÌÏ”³w"P4ïè7wôÒÍ“4›Šõ-Ù P< +$pÖi\oðÐ)tiVÜPZyçÅcF6!-&5Ù Fi‹B ç‡<º ³6K7Òî%Äi·?
Ó !ŸÚJ
x–³q²[–ÕÞÌHþ?ØÀ;Õ¡ ï G«(úÌ0â…Š`B{A +Üš;Ðw£wÒÕêÆ"Ä+
ÿë‘
ö ÷Ðmï„Ъ9¾iÞȾ ˜>ΓÉu¶Ì1 +I7(”µrbeA÷}(»Eœa§³¶´UÏàO @EýfÕ=â›H£å›à +Ìߨ.Á[@\7UUPâݨ i™sSDvÔîÍ–™G'Ù¸ÍêϘO¢~ Q]F=q ²•NÒ¬“-M8ûû2QèU +¢{ ÿZ û¢—ùB§Ø˜,ôî†ÄYoÁ + +×ÐQx²ÓÏšo5¼¯q¯þˆêé[³ºë`I–«Yg²+í‘ÕDõ^a3³*´±¢d{H©¥Á[2Ÿ ÝæÇ[šÇy¶d: îªàF³ Õ gÏœrqn¯Ö©‹ôË0Lªá>H½ÓúäˆéÊGZ +Ö¡i«¶[ZxššÀò9$·/ˆÛ²älWV«oRê%Ÿ0ØQá44²8ç›<$½% Å•Ñ J¤ÚÛVR´T ¼ DÐF`ã”E^+Ø!ODÛúXÿ%ÆOLJÿ +endstream +endobj +496 0 obj << +/Type /Page +/Contents 497 0 R +/Resources 495 0 R +/MediaBox [0 0 342 504] +/Parent 499 0 R +>> endobj +498 0 obj << +/D [496 0 R /XYZ 9 484.913 null] +>> endobj +495 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +502 0 obj << +/Length 1706 +/Filter /FlateDecode +>> +stream +xÚXKoÜ6¾çW,rÒ^U¢¨W{JÚ¤qÑ6b´š h‰kÖJ[Q²ãßyiWk(I/9r8of mî6Ñæç‘|_ß¼øî.6±©ÍÍ~§i¨µÚè4 ã´ØÜÔ›¿ƒ?¯·»$æ¿ÿÜüÂjqX¦)©íâH‡:/6;•…ªÐ¬÷þwÐÈÓàæÝ^\ÿôæ¯Þ¿Öõo3O„ÿx÷ñÃõ ä–hiÜNÙ†KTg9_ò«»kÆÎuw¬§K»ò,Œ#%ÑÆx¸#Ó ‡©Úª<¸çýØX\¤Á`\+2}'ßi8ó ·ª j>1× pskºûƒíp9¢›\¼ëµÎøz3‚ŽV rø§g±5•õl¿Š/ìÃTe³ý¯Öž«°ÈÊYÄtõÚ9à°2Mf¡×«ç$az:fo6v~4ò0"ì‡þ€«$°¦Bo4¼ëÁ‡C¸Ýé"¡Dу¹GEËã6ÀÍäXEa™ÏÜS×nt}gZ8%WñÞ@ +R–¡Ì‚™Úõr˜küSŒˆ8‘€ÈP=X3ø5 ¶ ïñ¥Å„=YŒ!©Äy˜z\è½oÀåâ
´ÛÍ+¹thÌÑ ¯Ö¾oÛžA2¨ˆ‘ºÌgÜsÍOmÍÛsQ Ƭ˜DÙ¢³9õ¾G8Дà7t7°àaçVäýJÈ”5zÎN”{–5š}ߪÅÚgͨ¶é;BÉ)‚ÒÏ릳¶FˆŠS¬ øê`?
"H´Ÿprk:ƒÿˆiI–!³‚FE˜ZZ¤=r¦¢‹p‹å‘¡˜¬„û”¯œT ´|·ç/Öu¢‰‚e"ù¾· O©úÃÁy' Š,Åj Yqpµ¤—º¿]-èÛTFzgéÇf†W´P,åð$ +Œ=<¹þbç i&BÁ&R°Gñ\¹À¡"‰¸aõÇfFUP®<ºŠÊZçƒsÔ0|íÈÔYœaºFUõC½Åza,Ïg‹—h•Ðº‘±H&½2 þ¢©‡%l·[Gˉ1ƒt&MLeÔñAV5ö“¬Â‚‘ ,›@¶¡
džóÍ<ñ¢Ïx¦Ñ¸ˆg4NªUÏÑošK¯²GAóŒÛ %HqN—Ì:bç:e=R Ÿq4tú] +ŽàN ,<Ýqä}ÍpiW럱ö3•66 ¨,Ç ˆÄ–_îËi0üSîBWÀ‹2Âa·îRR饋±c5¢vàŸ
‘>'ªŽJT$ÒKpAMÎó~?µÛm‹•A ˜Ž÷sOÂ5ö$phQœ³ É#9`ZÃNÝ[å9á0|j‹Wb3q2‘ +x§ó
88LÉǸ¼zsóâ?80|8 +endstream +endobj +501 0 obj << +/Type /Page +/Contents 502 0 R +/Resources 500 0 R +/MediaBox [0 0 342 504] +/Parent 499 0 R +>> endobj +503 0 obj << +/D [501 0 R /XYZ 9 484.913 null] +>> endobj +305 0 obj << +/D [501 0 R /XYZ 9 465.114 null] +>> endobj +58 0 obj << +/D [501 0 R /XYZ 9 465.114 null] +>> endobj +504 0 obj << +/D [501 0 R /XYZ 9 441.319 null] +>> endobj +505 0 obj << +/D [501 0 R /XYZ 9 419.153 null] +>> endobj +500 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +508 0 obj << +/Length 1988 +/Filter /FlateDecode +>> +stream +xÚXK㸾ϯpr’6G"õÜÛ °x±¹ +—Õ¹Ý8ØJŒ|ü¢³ÛD®sÌû&&òOŸ—²½6ª®g™pbd¢Ú˜]Ⱥ2*ÓåÒ09$“éÂ#%žðØ¿7Ì·‹œKkwñ3Œc ùx˜íü~Ã5‚ †ñ·t¸¦TYSEÃÿ¾XÉ þUóÙ$¿AýÊUQ-!£N“=¤$ A°´eÙ¨\WîNØRW:Êàõ7UòL!„ê ]‘^=ó9ŸÓÂD©U–Ž +çxŠu‰ò¾¦¯Þ˜gÇ“ÇvNý±P‰Æ-æð’Ú åÈoL]ZÈp‚@ÄŠK"ήUã £³N^¦‘W¨€‘æ¶_YYÛ¾_¢ ¦šŸkˆ*w´n®µ$(`Ʋ‰slðp:ÏQ–ƒÇ–ÚI +U]SÇrM+U]ÎYû>(å…sÝ{8å}¼÷62Qz°Ò€AX·AÐi´*aïû#O "ö«0i]w„ÈX8O]«,Ì„:¿£ªòšä¾¦iºÎàÅõ—wb–×ÿÓ;é,Â{g¬¤D˜±¿Zi§cÏFKôºÃñþ´ì–<…;zˆÚ÷]` +eʇ þÔYõz@«¢Öî©ò›$×yòy¢˜¦– G÷›=ûÎJà£?ðÈ©
gØpÍ €"51º©
Tesï7|ÕÌAŠ„tuv€•üVƒ¢„á:?Ž„g[ì,à1$°’Û½¬,O©'зEí¶½{På1nIþ°”ënqmêX,ó25úÍ4·6$GÊ5S`Ê^$ íÀ +lˆbýt<1ïUz‰ë|p,uFßRü=þ¿(ã¿•XÖ¼T<ËdÛ ýŽŽ Äλ֩¿¾[é⓬jàåߌ='‚‡§ Á@·ùÆÇebgÃÈ’–|’½òû(ðü ²2<&߯jÇ–zj€_ Žg÷_þõ +ູ–'ŠlO ƶÞÒñRð-ôûÚ`Ã?gš>> ú}ôœ@÷î,¿‡ùéTK#ìî~ +ÆñÇç¿ãLPj +endstream +endobj +507 0 obj << +/Type /Page +/Contents 508 0 R +/Resources 506 0 R +/MediaBox [0 0 342 504] +/Parent 499 0 R +>> endobj +509 0 obj << +/D [507 0 R /XYZ 9 484.913 null] +>> endobj +506 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F63 238 0 R /F25 463 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +512 0 obj << +/Length 2298 +/Filter /FlateDecode +>> +stream +xÚXK“㶾ϯP|¢ª,.$Q>]»É¤ìrlO’ry}ÀP˜j)Jæcý{÷¤HgsHN + «› +^¹Tš³ZLCLgŠ'©Ò³3f-/g›.˜è¸HÒaEÌÆN¢S;ÂFÉÒpÇrs¸²,Ý‚ +fîDçNôÜ‹–çÔ#˜˜, tΓז %µíú&ÌjA˱ + +àæ úÿÆ:‹r +™&tº×H<ª0Qh¾jOAZEÙÃEöƒ„ÚOB¥HÛ_Ý "ŽÎà·‚[0,U&úˆ†=¢ÅœÞ rî›E¨8žâûD#kJ0`¦¬8nKtÈç–…t—Ðz*„8bˆVŒ‡‚íš¾ <e +vŸ4`ceKô ;nÙ!ÆN~HÂ"&&NåÉ<NŠ8Ïõ ñõÚ*0¿Z 6Ò#¾`Þ®W© ‘ê»Õudœ›ÑæËɉC¤‘e:âHÕìË™O+_S~K +úò´.òÀÅAØ^ÛÎ 1x öÌ + +³TdzIÏ77ÍÛC™ÊbÎ6ø„8±œxêÛêÊ +è&å×ئç%ÍÆ×^ç[‡ŽÂáðÊ€ÖÒ_ÚÈèŸ5Ñ<jc! ª÷> +Ó7h.èu–ÈáSR»'b¥uÀÁCex[oòÑŒkùyþÍËTð°<Õ.tp¡BŒž +\ ¾øÒ×ceŒ’p·kÒÀ# Á„#AÌE«›Óó®ˆîë ÇHiÄÍôt´a®b÷²Õå½ã©Aݶ-[‰¥ ˜¾zË5e6}‚O†eI4u– DÔiÛpãÞVôôF/Û3>Y“aÚÇÖ5l.Þy<û!ñááî;Ä¥d#60H˜éMy¼ûí÷d³1 +Sl.¤tkƒxWm~¹û‰¯ä€“&WÅ +ønÔâ5, ‰‹T/™a±Jv+`Cx•}ÇöÃ{¦Èc¥ñÉK”ÂÊ{%…‚²g|¨!±R¼ò£Û’ãÈrs‹ýŒÓýµõ"ö“Ù—Üö¤BL_»´áô sꃔãõ.ÊçO³²IçIöeG èæ‹×ž3ÙÄRr¬‚@VɱK¶A~)Þ2¿P ůw· :Y߀‰, øj4‡uY=)ÐPÊô9ªK†+ÅiÉÉ Ùh°ÌÌOÜqšÉaU„›Æ‡j5çß03…Õw*Ípe;Q=[ß̧Ü`(Õo¥qfèÅÿ–ƉTÿ%“¢˜F0ÚGu<§žÉb +óøá¿C
<úÀ¤¢²D ~SjÉI¡©‚ÂéY%OKaŽþš\(†Ÿ6üÑ#ËúŽÇám£¢ +–¡bñÂüƒѹ9w#-¡ÉïglRüöÀvüaó
Ž1:–sx¶aTº¦³žÞë8d“ &QYàÃÒ—íM‰ê8ìÐs×·ž¯Ýú` M¢ÇÚev}+›•R7]z`غ¼²üÕ<YPuŒÑ©îìwë»é ÿ€Æ’Û¿¼šŸ•/¶ìO+‘Ksû5§âe Ôü'FACo +endstream +endobj +511 0 obj << +/Type /Page +/Contents 512 0 R +/Resources 510 0 R +/MediaBox [0 0 342 504] +/Parent 499 0 R +>> endobj +513 0 obj << +/D [511 0 R /XYZ 9 484.913 null] +>> endobj +510 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F24 494 0 R /F63 238 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F11 420 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +516 0 obj << +/Length 828 +/Filter /FlateDecode +>> +stream +xÚuUMoÜ8 ½çW=ÉÀZµ¾Ævo»@Zd±§vТØô Œ•X¨Ç Hr²óïK‰rZÞ‹EQE¾GÒuñTÔŇ›¿Ž7oß˶`ŒvJñâøX0ÞRÁU!ÛŽrÙǾø—|¼ýçϲ“äx÷ùîøµüvüûí{¦6×:N»C^ÓΣÑMß)*ÞIÚUTâ@ë¶C«ã`}Y‰† ìeu°ó„Š¼!AÛ)›h\ ãps¢ÑÕÛ“ QƒŠKYÁ2ƒ¡·þ8i%MŒ©¨XC•ê`•TJ…‘<—J=ÚÞ–Œ„änÉ™ q}ì©ä-øÇ G”íú1?¤gMÜ(ÒÏËC0ýj †y ¸1ç‹u9d04϶J‘Õ9¦ÆÔ›é¾x×’0ǵK9$Å +ÓîZ¶œÐ²’ü@îÚ
Ú£]Œ¨%ÆL¸ÕÞ/ç:Ó!«c2Ù¿__ç”Í)¾óÝïø4c% Ħ• _ A§œF ¯ÏYr¥ªáÜì•SÛPˆgub# ¬‰N"Òì@´3¨Jü€ÂZ ‘Œ+ F>¸å‹*â#ùt¤Ë æ´éØ6¥ó ËFóŸ>…ñú®¬Þ‘/C„0êSq¼ÄÏŒŠß%””‘szzŠ`'E@kg|–ì„'½½¯™ +{X_F}2±$Ï5‰ ‹3p @¹TH8FÔ_³[±75ñí¸ú%E=lüõ4¥j$5D>ß¡[Ô‚*Þ¬T]© ºZ7© +endstream +endobj +515 0 obj << +/Type /Page +/Contents 516 0 R +/Resources 514 0 R +/MediaBox [0 0 342 504] +/Parent 499 0 R +>> endobj +517 0 obj << +/D [515 0 R /XYZ 9 484.913 null] +>> endobj +514 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +522 0 obj << +/Length 1636 +/Filter /FlateDecode +>> +stream +xÚ…WKsÜ6 ¾ï¯P{’f,F|é‘ :ÎÔIÝIúH7M;MŒ–ÞÕD+9’Ö®ÿ}‚’¥ÏÎ,I@ø +D*™¤-›Ï›„eiÁ3·?Ÿ»Íñ3? <»>òà‡vóüÆ؉Œg2 Û“ `E*RÁZ³\J@ʜ兜ÂËG{:gM™*²1ØáÌRBü±ÅyÎ$æ¨\‚Kõ˜§s +Læ +ÌTK ”Àù/{â444´
§ÎÔ´F$·ŸOc „:pðe Õù|»X3ɇNÞ´5à>0ÞS}ìéž$ º«zÛ?wBxÆ´.–’.;ç"Œ ”QÉF‚¥K˜ iˆT”F©œçDy$¦ºbÙž¶.ôNËáKŠû¡k?9Ý^«ë`¬«ýÁYÓàaWë[Êò|²ãrµ¾Ièáä¼¾‚ÆêóÈôbMN1G„ij‰$‡
è —Uü $˜é,MæÉcÛDG¿æ].2×£&‹ž@ë°‹tšG1÷s¨28жCv ]Ckãx°E2´c ilâQÕA ª‡5HÎD¢'WvAÑ8;Öê™ +Í9 ‰Œw™o1UBi¦’„àÍoÖÛ–„é|ºï¡e³^:¸êHSÊ™±‹…¨‘Ë£îÆ! +ˆºØ…!ÈùÔjzÊÔŽ¸èÐý@«ò «Ã)'ÈçmE{ðÈǾ˜œïÔ”' ±È€ 6¼inæ÷—iâö|J¹z²î ÖAýõ¼à¤ü©¼¬ò«yù‡ç å8øQ>frˆ™ñi‘A +fgo‹1žœ )
°ÁffièÜC´ È_øû ¢!˜.¼”éahMó bMêñCMÎö:‰VÐxr8!AW5¸.Æ@œ¸J¾z âT>u ÐÀ<y Bé'Ákž… +endstream +endobj +521 0 obj << +/Type /Page +/Contents 522 0 R +/Resources 520 0 R +/MediaBox [0 0 342 504] +/Parent 499 0 R +/Annots [ 518 0 R ] +>> endobj +519 0 obj << +/Type /XObject +/Subtype /Form +/FormType 1 +/PTEX.FileName (./images/025.pdf) +/PTEX.PageNumber 1 +/PTEX.InfoDict 528 0 R +/BBox [-2 -2 335 48] +/Resources << +/ProcSet [ /PDF /ImageB /Text ] +/ExtGState << +/R7 529 0 R +>>/Font << /R12 532 0 R /R10 535 0 R /R8 538 0 R >> +>> +/Length 539 0 R +/Filter /FlateDecode +>> +stream +xœµUMoÓ@弿böÁëÙï#¨© –8 PÚ‚¨‘ +ü}ÞÚ±k'½(Š’užß¼}ž™ o¥V$uþì×›VÔ› ï‰ RÐ$ÿ +-¯ð¥HÊk–àµÒvD Ä{AÆÎ +endstream +endobj +528 0 obj +<< +/Producer (GPL Ghostscript 8.62) +/CreationDate (D:20110510185203-04'00') +/ModDate (D:20110510185203-04'00') +>> +endobj +529 0 obj +<< +/Type /ExtGState +/OPM 1 +>> +endobj +532 0 obj +<< +/Type /Font +/FirstChar 69 +/LastChar 116 +/Widths [ 663 0 0 0 0 0 0 0 0 0 0 0 0 0 0 700 0 0 0 0 0 0 0 0 0 0 0 0 500 450 0 0 450 0 0 0 300 0 450 0 800 550 0 0 0 413 0 325] +/Subtype /Type1 +/FontDescriptor 530 0 R +/BaseFont 540 0 R +/Encoding 531 0 R +>> +endobj +535 0 obj +<< +/ToUnicode 541 0 R +/Type /Font +/FirstChar 48 +/LastChar 48 +/Widths [ 288] +/Subtype /Type1 +/FontDescriptor 533 0 R +/BaseFont 542 0 R +/Encoding 534 0 R +>> +endobj +538 0 obj +<< +/Type /Font +/FirstChar 65 +/LastChar 118 +/Widths [ 734 744 0 0 0 0 0 0 0 0 0 0 947 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 473] +/Subtype /Type1 +/FontDescriptor 536 0 R +/BaseFont 543 0 R +/Encoding 537 0 R +>> +endobj +539 0 obj +589 +endobj +541 0 obj +<< +/Filter /FlateDecode +/Length 161 +>> +stream +xœ]O»Ã Üù +ÿyL•¢,é’¡UÕöˆ1C "dèß7Ò¡ÃY:ß|–Ãx ÙFàðEŒe hu[@‚‰fË¢n@[Œ…剋òB7åß O°È ü®’Ïú’7õ‘A§iõ +)(žItUÕwÆô‚XÿI%0™âlwgBSµMöŸJŠ¦çIÀ-☋æ"©€eúýâO)Ø!¾ïžRõ +endstream +endobj +537 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +534 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/prime/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +531 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +518 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 343.603 40.669 356.222] +/Subtype /Link +/A << /S /GoTo /D (figure.0.1) >> +>> endobj +523 0 obj << +/D [521 0 R /XYZ 9 484.913 null] +>> endobj +306 0 obj << +/D [521 0 R /XYZ 9 465.114 null] +>> endobj +62 0 obj << +/D [521 0 R /XYZ 9 465.114 null] +>> endobj +524 0 obj << +/D [521 0 R /XYZ 9 441.319 null] +>> endobj +525 0 obj << +/D [521 0 R /XYZ 9 419.153 null] +>> endobj +526 0 obj << +/D [521 0 R /XYZ 9 301.759 null] +>> endobj +527 0 obj << +/D [521 0 R /XYZ 155.833 250.848 null] +>> endobj +520 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F16 210 0 R /F63 238 0 R /F24 494 0 R >> +/XObject << /Im1 519 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +547 0 obj << +/Length 2162 +/Filter /FlateDecode +>> +stream +xÚ•XKs䶾ëW07NUÆ‹Ÿv«Öɺœ¤l«’JÙ>P3†^¹!9Réß»Ý|()¹Ì +¼ï®Txá}ÔYÐLƤwX¡b¥ÿŸ[4Å@O$(/0{Ÿ²;F¢"ã×®z gð>
/¢ï +R |èÊ3Q£ÂQOˆ~•«µš¼& C +¢Áßó–Úy&2;Õ¥ÇMµ•ù\sîé„é¨1¸´égþXF ²´½ëCG²tôªè@1Ru±×Tj÷¤£ËÅ ¡¿Òœù_ëš³®§(™
ÅÔÞsŽâ +] at«Uiì% .%¸ DýW4âiˆ´9qYŽµÌ î×Øæ2y +%Åàz¦Œ½nâ%;htë'}¢£ÊFSm}Ë +,h^`å—NÈ—NÈeúÏ…m9’žN-‹P~Ù1ÞÉæJŽ:]׫eÂ1a‹x[ÙQõÀY‰=²ˆ-¡êh8–ÄÉû;B¡Ñ}Çgb *5„-–0œBpò(Öbî6WéuèP_ú*âùXfÊáªà¬[W°Øœ¶ï¹€[rûÞENʹR“^íÚûk]ŽµoŒ—X¾(4FÉÈÜp¡Ëó|Ñ•¸Fço‰ ÒZçÿ¯µ&Kÿ½“Ú}8‘'hVv]õ8ÆÎ1TQœxã¡quf ÔA 3xármñ/¤\ Àgë¼ÿ´~fØ[W©ê€u¢i» ®û,sÓ¥F‹>ƒSôBü?1!œ÷ã¥B@MZyê4\5$k¼"0ˆ”— •@Æé)" xÊ€_¸`I›»¤›aÊ#\Åó##“i¼PÊô2·ÜòiÀ.sóÝ8“]¨Ë¡zœµñ±@âÔ¤`M˜û+ƒÌG¯t¼j2ìžêí"má+56-‹±Ò í [Ü@T ^|†ö|¦fŽ(ù„¥?TCO”xåzjhòµì†êp©ËŽ¸†ê ¾ÝáSWziêˆÊ‘ü4¨ä€‰ +endstream +endobj +546 0 obj << +/Type /Page +/Contents 547 0 R +/Resources 545 0 R +/MediaBox [0 0 342 504] +/Parent 549 0 R +>> endobj +548 0 obj << +/D [546 0 R /XYZ 9 484.913 null] +>> endobj +545 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F24 494 0 R /F19 213 0 R /F63 238 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +554 0 obj << +/Length 1402 +/Filter /FlateDecode +>> +stream +xÚ…VKÛ6¾ï¯ðQbE”HJBOI±Ûl‘"ÅÆH$=p%Úb#‹.%íbÿ}g8”m¹Úö"’3Cj ß<’Õ~•¬~¹y¿½y{Ç‹cq)DºÚîV‚ÇLŠ/Ê8åùj[¯¾EŸ¿ýùþÝÇõ&ËE´ýpûéa]òè+?ÝÑúpûñݺ̢íý—ûí×õŸÛ_ßÞ1qùt*ó˜¥%üÙ¿š +ºI‚.«MÆÒ8-9ldœ%I
Ö›´ÌagzÜ‘êûñp ŒíˆCtX»Ê Žj0&Ég3¬YÔÐah4É l?©SÃNµt®õnƒZFÆcÎia:C¿Ë$ì×,êÍaæÑتÓð#Ø¿ü¬"ÌŽDŸ‘¨i_›¾R®¦»d ’ÏƼAG"K‡ ¡Â—ÊHR¦²Ý÷„ S¡BF°À_¼ôC| +23^odQD÷á?Ájà÷SL¾zþU;ÖÚgÒäµL<ãæ :â™îŠ èŒÚƒ—´Ï6ˆIcƒŒSøKBëu?»*0â‹¥’¿Ò„÷”]â=c±<ãýy)…X'œM"ǵH"tVVpž*üXJ•ë|Âôrº Râ¢Þ 6¬X-ØOÆóe›ùd3zuÐ+Is™Î#.!ë¡vÊHµ½ÅÀªÛÍé>$‰/V% 9¡ËH P…GÕý8@ÙÑåb=¡äò²Ød)&øGU
þßgy Ë”O¯Ø](A`”ȯá€HE ½ ôWQŸ*ëjÓíÑ}9yWï/Øì¬Ó{{âO + $ÅgÊä,?Y‚¸ÓÆy„³ô”ý¤…"ÒQ¹ÁTc« wrUÎi $Rp7R¼ê¸6AÁ±¤u:l›<I!»ý&›Z À\x0Ä"¬Ì`¸¯pÀs°ÃâU_ì’,”1 Ô£ ÉXá½X õô$´±ˆªÍbM8Î +"°èS~JƇhégªÀšM.o–Rèr¶‚ЋP7ÄeÅ¢rï^pÈÂñ¤€yº ;î’ÀÄ•ÀÞR—XœÞW•Ú: T½XÃlÙD‚*Xô R'ðBŒ ¥b ÑC–wËhþ’u/sæ4߆ጋg1ŸÖÛíÍ?ï–¡ +endstream +endobj +553 0 obj << +/Type /Page +/Contents 554 0 R +/Resources 552 0 R +/MediaBox [0 0 342 504] +/Parent 549 0 R +/Annots [ 544 0 R 550 0 R 556 0 R 551 0 R ] +>> endobj +544 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [209.132 405.836 269.075 419.784] +/Subtype /Link +/A << /S /GoTo /D (section*.40) >> +>> endobj +550 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [311.193 392.054 333.996 404.674] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +556 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 377.608 48.064 390.228] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +551 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [186.223 218.704 241.218 231.324] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +555 0 obj << +/D [553 0 R /XYZ 9 484.913 null] +>> endobj +552 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +561 0 obj << +/Length 1930 +/Filter /FlateDecode +>> +stream +xÚÛ’£Dô}¾‚GReZúô㪫Že¹ê¦¼Ôêz\#Ú*?Þsid˜Ù}I ºO÷¹ß’D‡(‰¾»IÂúÕîæËoM I#´IU´»dj„KÒÈX-¤Í£]½‹ÿØü½û1¥pÖæVŠ36ÚªT¨Ü0ꛟ6[Ùx÷ýk~}ýã«3ñîö·ÛÝŸ¼÷æÛi³•q@üúÍO_¿þyw;¾ +RÈaLÊT¾¹}»ÃG_Á•À[2—b+§<WÀ›2ÍøÖ~`diç‚èD¤™…Ò¹òiïÛ¦¯Jßñ×°QYü¸QyÜòÆCÑ
Õþ\áa³Œ¶jqo´M¸}ôè +À` \” —%YP:&qH ƒÎå«NHi†"ÁÈ™¯ëª9Ò€°Ir¥µ¢ná|k´aŽŒÖ±?áý»¢yòÌ;#<VÑ1ªA"iIÒ}E*ùÈ\‚}f\*™ Œ~X“$Iž_ +"Àh z¤äïe±ÛÅp P‡¾¥óxwôÍÕ1Ý=söæ€ëÖ‚C:Ã6(=ƒç° [dí‘?Úû)*å} +¾Z!è„qég4 ‚!lÜÔÈQ]çh„7åf×BY³Çc;ª< N.Ä^‘X‘¹ CjCÀÖ6åP€uôyl~rªô
„²Ký|b®Ã°Úk‰çœyΉg</¨aàDnóÜ¿ŸôóüŠ¤?»±K3hôÕ‹} ‚*_¦øQ> uœù¢ã„ €?¾maâ ‚ÙtXüqŠÿ>ìß%mgN\A±˜9C–‚–²ôNTÈh{ì¯Í¿"µLpi~Wbã(”Nb?ãÞF$Z^¹÷Õ;F¤0®2ýœÛ«n s\艕Hq4˜ëa–úµ þ¡…,Æ
Õèižø~(úž’0…ªéƦ.!zðƧէ̢×9ä/D5d[ð¬ùô󜞵°N^ùA·$W°Úu¢E’\U€Ådˆ
´ k\æR¨)–VS“/üGŧä7C¿ae0Å\$ã'³ D–M¨} Fn~†Á¶¹i²¥Të^¯DrQôóI]fÙË^¯D.õÜëUZ •ås¯!/ íq"@ä©Nãîìåx +o†áCý‘Kj–Oý4'à¤z™´K¨©†ª
£
õ˜ÌЦ *ž½›©—†çnEF þË‚À¯ßÝDïè·0s…×òø·[bzüå‹üÏ PŒ´;JË+È{)gÞ7Ï$y2½¼þ‹‚jØZŽ7Â]’Ôsf·©ü´ÙSc_6»ž—êåd +¡–‹ÙQ’sJH +endstream +endobj +560 0 obj << +/Type /Page +/Contents 561 0 R +/Resources 559 0 R +/MediaBox [0 0 342 504] +/Parent 549 0 R +/Annots [ 557 0 R ] +>> endobj +557 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [147.909 83.578 213.699 96.197] +/Subtype /Link +/A << /S /GoTo /D (section*.43) >> +>> endobj +562 0 obj << +/D [560 0 R /XYZ 9 484.913 null] +>> endobj +307 0 obj << +/D [560 0 R /XYZ 9 465.114 null] +>> endobj +66 0 obj << +/D [560 0 R /XYZ 9 465.114 null] +>> endobj +563 0 obj << +/D [560 0 R /XYZ 9 441.319 null] +>> endobj +564 0 obj << +/D [560 0 R /XYZ 9 404.707 null] +>> endobj +559 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F19 213 0 R /F21 427 0 R /F63 238 0 R /F25 463 0 R /F7 232 0 R /F41 211 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +567 0 obj << +/Length 841 +/Filter /FlateDecode +>> +stream +xÚ}UKoã6¾ûWèH+Æ|J:¦E²M±èYaŶZ¦m¶z¸¢Ü @~ür8TBOšÎ㛧¶Ù1Ûf 7?5››{YeŒÑZ)ž5‡LIÊ´ÊdUS.ˬÙgßÉ—ßï~~¸ý”¢T¤ùåîóc^Kò
ùÏ÷ø}¼ût›×‚4_ šoùŸÍ¯7÷L½wÍuI¯Cäè•— ´Ù&,7÷Z¼×.x-i)TVM·UF·y!EMΓ'·DÖ”Õ|‰áæ Ïq ¾’ìr^’g”
#Êzk¢ÖN³q2óĘ́1Ÿ\R茟_üe²`È +i©XV0I¥T»·D}]‘'×u@ÕÄ_Îçîé‹_^çJæ“EQxaÄä,øÁ—ÉúK7#m’]Ò®É [&'?Ó¼¨4'Í "ç +䯚V;¯g﯆`TTb¹Ok‡…ñ°âÕëat¡>¡é\Ä5‚ö»Þ¾ Ÿë»VkªÞTXn¼„Y…od ™Z„yf 8L
ˆ(†É]ÅÈ©Rrqþá%˜% ñ†Å[ŵ ¼*¯*‹³ +Y *Þ Ã%ࡃëÐyõ :èEè ¶ý.Zij0¯â/Õᯓ"½ÀÎq§z‚“Á¶Ö{3¹î9%ÃKºõu2¦óaù×Äþs1 %ìãJãuEu©þ·ñAãõŸE¯&{ùÞ5› ¤Üÿ +endstream +endobj +566 0 obj << +/Type /Page +/Contents 567 0 R +/Resources 565 0 R +/MediaBox [0 0 342 504] +/Parent 549 0 R +/Annots [ 558 0 R ] +>> endobj +558 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 363.163 64.805 375.782] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +568 0 obj << +/D [566 0 R /XYZ 9 484.913 null] +>> endobj +565 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +576 0 obj << +/Length 1542 +/Filter /FlateDecode +>> +stream +xÚ…WKã6 ¾Ï¯ÈÑÖ®$˯í¡Øû˜¢Ýfƒ¢h·M¢LÔuìÔvf:ÿ¾¤H9vÖÓ^b‰¤(Š _«‡•X½¿üýqsóÝ;]®¤NR«Õf¿’¹L*!W:K™•«ÍnõGôÛíúÏÍO$ +ì,ó¢±e’eÅ*Vy¢JM²›o×qZdÑÏŸîÞ~ÜüN›ÍÝ›ŸßS}ºûåͺÒÑæöÓGÖ*¦Ä×”ªDæ+=X’•ÙÔ‚T%Y.á)^¨³ý¹ zº°ÝÓw€“~Q›~¤Î2±·ÛÁµÍZF| >2:À¾]«"z +Ìp¥ÍœN¦³
+
hÙ*f[bxŠÖ9Yäšm{<™ÁÝ»Ú
(ü ÇEIÖÁ—ô‰ +¬ ÷M¸§®=™ã-ôRQ»‡]í·On8 +™c·í¿'šWƒË"‚@"šw|÷m]“ýë¹W!Ñ„Lá²2Ñ)Ý…HIïë¹ÿc] ÈeЮÙÁ mì(dm÷¸Î Škb¡Ž$A‚PC"ƒuq‘ÇMû°›x
–Pl0€0ñ¸ë‰çš¥HT")åU†S-È4! Ó”O9œa ïоu‘cû-m<ÆÈûßÝó\¨³ûűÖ[›Ì½¶£ãåÅóêÿ<ŸB˜ô'³]r=òPÉÎõƒK9crý‚ï‘3ó=8,Y{OZý#i^t|ç &AQ}ã%¤!zª(=zßb„xJxg#1b€NüjˆÏ,xœàRùÄ’àš |® 2 +Å<ÿ<<”›.¡%Ú…_H¯–í/}/-rXÌæ@OÁL~€ó8£^ô’›i¥²8«ô¥Œöçfg‚Zß?J5zKF¾ö .%Ã’ùÃ:Î…„Tr,7Âèwµ5;f í"²ØÉÓèÁ6 +ÞÌ +9IœBñd‹1_@Â+/pD—Ú_X„…=‘Lx ¥?EÈ¢ïen c®K§G* º%PIv¹ KrÔ
5Ìß4)Š n2úÚ´øO,OE°iÞb¯Õ[Œ¤«‰!›L :Wð$‚Wœ[æy«3q9F×ÞFÃÿ}¼Ò#R¦Ø@•"½ wöÅDA4\óÕy¾ # þË/:iù ~=Ш<MKÜù.ßþ þÌx ±1ù³á:ßÓ…Á,{d–'RÃ?t’R±•ªœ ½ÝÜü Ã*"x +endstream +endobj +575 0 obj << +/Type /Page +/Contents 576 0 R +/Resources 574 0 R +/MediaBox [0 0 342 504] +/Parent 549 0 R +/Annots [ 569 0 R 570 0 R 571 0 R 572 0 R 573 0 R ] +>> endobj +569 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [103.785 371.83 164.355 385.778] +/Subtype /Link +/A << /S /GoTo /D (section*.40) >> +>> endobj +570 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [274.387 230.527 333.996 243.146] +/Subtype /Link +/A << /S /GoTo /D (section*.40) >> +>> endobj +571 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [53.556 201.635 110.833 214.254] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +572 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [278.115 158.297 333.996 170.917] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +573 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [197.458 114.96 254.577 127.579] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +577 0 obj << +/D [575 0 R /XYZ 9 484.913 null] +>> endobj +308 0 obj << +/D [575 0 R /XYZ 9 465.114 null] +>> endobj +70 0 obj << +/D [575 0 R /XYZ 9 465.114 null] +>> endobj +578 0 obj << +/D [575 0 R /XYZ 9 441.319 null] +>> endobj +579 0 obj << +/D [575 0 R /XYZ 9 419.153 null] +>> endobj +574 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +584 0 obj << +/Length 1999 +/Filter /FlateDecode +>> +stream +xÚXKã6¾Ï¯0r’±"Rï\“`f·wd1ã$’=p$ºM´,9¢ÜÞ_ŸzQ– %Ðh‘UÅb±øÕƒN6›dóÏ7_ïß|ù!«6JÅužëÍþ°É³Xù&«êXgåfßn~Ž>ý÷ý7ï¾ÝîÒ2öÿzÿÝÇmE?ñü»üýøþÛwÛ:ö?<ìÚþoÿï/?¨|©Ze¬t
;“V]£Ð›DlÙìR¥c]g0(⤪Yª3[]F/Û]–•Ñpàï4šÞŸœ÷nè—œ*êÜãq««hbŠti€Êê¸ÊÒ`€Ãµ…ŠžMsÖ Î“¸ÌŠ ÞÛ ˜b=ïØoÙ€
¸ãhZ×LbàÑ¢ÂÍN'IœÃYv*‹³,gMçÑõ;w„µbÛá;ÚÎLîÙM¨îõ Û]©êè¡!P9òð=2Œÿj»+t }³U‘é<Ñ †5Ö=/(a'CÆ%bUÁVñöèP]ÖÑg>,ÙÂJpÎi,+صeÚäN–G¸²ÐDp} gj/¦c†eƒzü?y–- ÏÆ®X7÷ÓB‹]à
œ¢Ïv´pÎ0àµÎú·Ë$ò—u yõt4/3ÆWfŒ†œÎ<~¯`¢é™wðÞâߪ‘xè´Ê£g\f;¶¦‘e)‡ï
† |ZÝ‚µŒÁЀ¾f
u\¤UøÈu§UÆ>ÂYö„ÜϦ:Ã嘅WIˆUy×u½† [—štë2
÷œây\ ÍTíÎ3õ׋õ“ƒÍWiÔYÓ +/¨0¬ñ׋›DWkITÖËœ=_çwkNw‹C Ä3^GB@Æ M‹\ ”á~8åë´ãÁ6S÷Ê´åÆ(J—tÆ“DÊt†c‚&À»±)_ +êXáÊ8Ë^°@בM3BÃRœfÐÇ¡“•ž Ëöœ}Ë‘ ÂÂNÎu¬’ö*Ϫ0Ix¿ Ð' &¥‰ó@ ‡Ðûã`„:@‰N™æ&&ŒÄ¥s}Ë£.]ËR¦óÃO‚ÿÄF—µÚ#{iÊp\ é˲ˆ¼÷¶L¼‡_Ýú z¸Èêf8Ü4q1¯‹+²ú²^BZsZ–4 +$##'kF¨Ü“a•_íÍoŽ‰&3 c#ßãôr’á؆a& ¥)8²&¤œQ§ÔY]k?±¦áOÛqt«;ÿÐWYˆÐÏîz4tõ +Ÿ›£hèÿâ(iW:¿; + Å—‰"PÕ&‹ÓT~*IÖ\ĺÊ7»…g, ¢Csñ"l§Ñ»ži75 c®®¹èC” +ìYÐMâx®Öººï0CŒuËÕÜ-#%ô =OÏÝ\Tð‡Ž Î EqÍÙ8ÁWÚoV8NÖÓ[ ‡yH!EqŸ±‹+þXbÓXU
ž]ºë¥ö$á}’ d¶ØžÈìOÂÖ¯¿ûJåü#Õoë—ºÀùÛ5-Uœ”3|^×u¨´øû:þ¿MI\Ö³©Ô/pxä@~èñ—™eg ¾ï÷o~ùT\€ +endstream +endobj +583 0 obj << +/Type /Page +/Contents 584 0 R +/Resources 582 0 R +/MediaBox [0 0 342 504] +/Parent 549 0 R +/Annots [ 580 0 R ] +>> endobj +580 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [117.828 262.042 170.619 274.661] +/Subtype /Link +/A << /S /GoTo /D (section*.25) >> +>> endobj +585 0 obj << +/D [583 0 R /XYZ 9 484.913 null] +>> endobj +582 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +589 0 obj << +/Length 1656 +/Filter /FlateDecode +>> +stream +xÚ½XYÛ6~÷¯Ð£ Ô oR-Š¢E³Á6Š¦F‹"Ƀbkm¶´‘do6¿¾3 ʶ í:g±¦†CÎõqŽåÉ*áɳÉ/óÉ“+í!XfŒLæ7‰ž)ií3&µKæËäeúâéï?O3ίÿ¾žÿ;}=ÿíÉ•0ƒc™d™ÍàÖp@qdšð('™)!™Ì4,,ã>#®¼ZNgÊdé]ÙiÕ«¼‰Ô®Ž¿å¶ Õ›©té=sø± 6§"ݳýÔè4ßì +ÒNŠSí$H÷Ö÷Úuch&¥ë9Øtf”N_› ®ïÊ= +.jˆpœinûóÏ#‹I Ë ÁEœyá@ŽRÑ~>¦‡d.3Éì„í;b³j YƒÙà]î™3.™ Í´6´Ûæä?û¢5Þ +f¥ì¯»CkëÝã 8x}W"}Å…~WIJ"bS´·Ä´èh§¾¡ö6_D¢h+ÞÇvñê¢nfdDT†l°¤ÒAB]-ËjEÇ!æ&ļ ‹H¦™9FôÝHD,³ÀŠžö ?È +ÐÊx + WdÚÄì/܇ +ëM,û<ƒ wö\)´Ö@\fuƒ tDhïۮضôQÂL‚±¿ú=\°,óU“oéC Û"lšUìÆ^<›PwňOÿ‰ñ + Yœ†›Ëv,èÇîHZ‚9¸¡7”–ôý& ˆÖÛ") +£×‚âèÑ·;ÊßV‰Õ +{È,´qû˜LÙG@„>æÀöã(Ð8³Ú%žqï†"õ` +òË×<Y D€ièžïç6†Ö*¬„›ä/è´CG
Õdð˜â]†©˜5›‰0©8¯ ÚÑG*Ŭ³Cg¯7^¥0e*’(Æ<æ™ù)&ŒÞ÷½×(–Ù à¸}Ò|È3 À½2&|ÌFL Rœ9U|ø@Ÿ@Õ彋½ Lº>Ôu¢×‡³¬…RŠàvˆ? ÞâÉ`ö Áç! +endstream +endobj +588 0 obj << +/Type /Page +/Contents 589 0 R +/Resources 587 0 R +/MediaBox [0 0 342 504] +/Parent 594 0 R +/Annots [ 586 0 R ] +>> endobj +581 0 obj << +/Type /XObject +/Subtype /Form +/FormType 1 +/PTEX.FileName (./images/032.pdf) +/PTEX.PageNumber 1 +/PTEX.InfoDict 595 0 R +/BBox [-2 -2 192 148] +/Resources << +/ProcSet [ /PDF /Text ] +/ExtGState << +/R7 596 0 R +>>/Font << /R10 598 0 R /R8 600 0 R >> +>> +/Length 601 0 R +/Filter /FlateDecode +>> +stream +xœµT=oÜ0 Ýõ+4ÖÃ1$%‘ÔZ ÐN¹z+:¥h2ÄCZ _¿¾”|w9åÜ¡²Ÿ Ég~=FŠØžÃy»„«½Æ»ïA¡*Rü0^‡,‘¸‚ Ç%j;"áãH`È(1 ¢9¡ €a‰¥b¿¹0é F «;aî–d +Œé<èÙfYáî?“B©-2¡1GÉvвewBRªÀÔYZs×Ìy=—“¯#ÒX=yñÛ_ª_Žtq¤FNŽä3-Oö'JÉ ÚÑËCøújžïOò÷×áÑ ýýpÜ.ñíì½à9!¨¥pœ]ÉʈV —Î묜⼄Oo~L^>4©Ÿç÷áÝ nzç • +ïâ“"
½@U¬ ¬‚M1Gr«È¥Ý‘#ˆtåŒ~zú^Í÷ËH„Àšb® £è@²!¢>#”N㱄*ê¼: Œ;É圕 © ŠÕ‘&÷Òî‰S JŽç~Z_Ï÷Ë(Õ¡ÔYI6:pçÕFÙ™9Åù‹s>L;_JªlÜXE€šne$`EiŒ«½ëY—!uÞ1C¢ZyµÀ‰˜mer)i$¯6™ü_“›Ò.Ó&ƒ‡â»ç¡Å5nDö*l„ÞQNYcò¿oß-~O;÷ †]miëû TzÏ)oKàT}åü‡ ôÕš-z¦µíúnñgJž÷Lr^ƒAÆÊp [* +˜µuýÏ2ôé¹ aˆaC +endstream +endobj +595 0 obj +<< +/Producer (GPL Ghostscript 8.62) +/CreationDate (D:20110511100850-04'00') +/ModDate (D:20110511100850-04'00') +>> +endobj +596 0 obj +<< +/Type /ExtGState +/OPM 1 +>> +endobj +598 0 obj +<< +/ToUnicode 602 0 R +/Type /Font +/FirstChar 48 +/LastChar 48 +/Widths [ 288] +/Subtype /Type1 +/FontDescriptor 533 0 R +/BaseFont 542 0 R +/Encoding 597 0 R +>> +endobj +600 0 obj +<< +/Type /Font +/FirstChar 75 +/LastChar 122 +/Widths [ 833 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 473 0 556 477 455] +/Subtype /Type1 +/FontDescriptor 536 0 R +/BaseFont 543 0 R +/Encoding 599 0 R +>> +endobj +601 0 obj +545 +endobj +602 0 obj +<< +/Filter /FlateDecode +/Length 161 +>> +stream +xœ]O»Ã Üù +ÿyH¢,é’¡UÕöˆ1C "dèß7Ò¡ÃY:ß|–Ãx ÙFàðEŒe hu[@‚‰fË¢n@[Œ…剋òB7åß O°È ü®’Ïú’7õ‘A§iõ +)(žItUÕwÆô‚XÿI%0™âlwgBSµMöŸJŠ¦çIÀ-☋æ"©€eúýâO)Ø!¾íÄRò +endstream +endobj +599 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +597 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/prime/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +586 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [270.585 95.224 302.789 109.172] +/Subtype /Link +/A << /S /GoTo /D (figure.0.2) >> +>> endobj +590 0 obj << +/D [588 0 R /XYZ 9 484.913 null] +>> endobj +591 0 obj << +/D [588 0 R /XYZ 9 367.522 null] +>> endobj +592 0 obj << +/D [588 0 R /XYZ 155.833 243.725 null] +>> endobj +587 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F63 238 0 R /F40 208 0 R /F16 210 0 R /F24 494 0 R /F27 593 0 R /F19 213 0 R >> +/XObject << /Im2 581 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +606 0 obj << +/Length 1583 +/Filter /FlateDecode +>> +stream +xÚÍXKoÛF¾ëW,z¢€p³ïGŠ ÜÂNÝH›‚$Z¢%"鈔 ç×wöA™+ÓJ)Ћ¸áÌ7ï¡Z#‚^Î~]Ìž_ƒ(ÅVJ†×H +L•DÂXÌ„F‹zŸ½ýëü·Ë³Wóœk™-~?ýfnEö.ì__„ç›óWgs˳Åå?—‹wó‹?ž_P9f͔ƔYì¹rêˆf$by~Áè˜:§Æ`.PÎ&Ɔwî_&‘ÆVê¦\#-pÉ”p ¢ +å#²_"¯D*eX +×Ywßõå6¬Ûëð,?j›H2~jÚ9ÓÙ]¶E<î7eX| \ÌiöªÝ•#ì¿F‚]Ñt×ín[ä¾ì€GÄÀr’ðOV`Ð?\ ¥q¬ Åš(Wí±61Û.*ZeUž7u±,C—iãUÀ
‹ºðj…M¸•ô¶ê:@7¾òj½ñê…íÝœ™,rÚ«È»øäHÀ¾ÎBÝ‘Pw‚ÚÑWÞ|Âdí~WEWų +¾½êÚzßÇ]ä²+@ì²÷ÜiŒxöÕ¶ìâkÍ*,ê²Y÷›î™ÛYǶ çUÑV¬Ž€Ô 0ÅÕ<¹>æn½5œyƒ ÖݦÝ׫°ÞÇ”íU_TMéï‡8…ã붮C$WÍ: "þÅt95”Šœ), áGs„‚7þ“¾ýeªZ̉ýf1ôËêÖÏ#} +s +GU]ï;àX». ÙC݃“a±ƒnPÕ‘aW–ç¢ötëôjY’Ëe»[ïì°¿«úMXhö0Œ˜pÐC¤%Š:AÔÃn0~€÷Jä7Õ/“!ænÿŒxÎ hìIøÖ{’h˜ñtê(–ÝË};åU¡a:PwAX +t.:wœÔØ1ܽ@·ðÊ9‚]y]‚A–e +Ýç‚N“wè»îwu?‡œÀwÁΟS€©ÄÚ Š˜ U’ˆMߟ<@ú¶\*8pµG‚“Jì¦pjÆCãd)f ]>"Ãó\™T‡4Ì»jÝu8u†wà»X\’ ’ï‹ÌåâÑ·£p%ì“/
]Âj +@B#€°‘ÐíˆH'`½ß* ß|@N_X4:t‚d]µ½©Ë°†™° +Å*Ô?wæbÕ=½+Ü"I)裪鈜
Üs]…j6 7ÑNûÝ:šáÍËzïYÝ䇄¶œû©Ý% ð/ˆe³ª¾¸Ož]&–õÞ ?Áôÿ_‹y’ +endstream +endobj +605 0 obj << +/Type /Page +/Contents 606 0 R +/Resources 604 0 R +/MediaBox [0 0 342 504] +/Parent 594 0 R +/Annots [ 603 0 R 608 0 R ] +>> endobj +603 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [315.676 49.355 333.996 61.654] +/Subtype /Link +/A << /S /GoTo /D (section*.128) >> +>> endobj +608 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 35.751 46.249 48.248] +/Subtype /Link +/A << /S /GoTo /D (section*.128) >> +>> endobj +607 0 obj << +/D [605 0 R /XYZ 9 484.913 null] +>> endobj +604 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F24 494 0 R /F19 213 0 R /F27 593 0 R /F63 238 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +611 0 obj << +/Length 1655 +/Filter /FlateDecode +>> +stream +xÚ½XKoÛF¾ëWðHÑfß=¤@R8
P´Zq´DÙD%Ñ!©8é¯ï·J¢LÉISôÄár8³óÍcg–f·Í~œü0Ÿ<-mÆqJñl¾Ê·Dp•Ië—&›/³wù¯¯Þ¾œ:™Ï¯~¿šÿ9}?óü5Sƒß 'N;H
?î™&4éÉf‚q¡ µ.rëz{;I-óÄýtÆM^·UW}œ‚*£6ÎŽµ9G4×½²OcÒDƒH ³âSÕ>ƒgób»ìUVm¤ÖÕí×ÕÍÚ®Úxj·Þ¥oÅòãT)üµ(ÓJµõú²£špcAH"¥J&-u³ôÜÓ™à:¨º»H …·èîèªz;f“’(ɳ×DRvÁ>Gœ½}ßÊâD @Zt/"“ÇL3¦5q’
5V¤$cJ9DÒ=ªÑ6Å“÷ytÙºN\Tý<êAC˜bûÍ)S„ +Ûs)ð†°—ßʇMP\6 =¸S–|Û¸R¯,Ño ;–ü¦£ü·uSnC üí½Ìò®)¶íªn6AVˆCÈ°¼6÷ë2ÒM¹Ž
o7Áö2˜þà(G]Í \\b¸iÕ³øÈ $‰0{§tcr~ŽÄËÀæ* \V¯ñ°¹qAŸÐ#ÃüÛ—Æ$¾üÄ0”ƒõÖ''ö
&:žÂªlvÄv„¥:` OÎí“ú81n¨Q‡Ê¯¶–T›"n]DŇ—®ŠE÷Ì“:¯ÒR)Òíîf–Â~G(]ºÓíºÀ«rDݘ• +aËØåx¡ûÜ#q—¢‚¡w£µT:b8”‰3qè˜ìyªm»—M™lÚ.¾„úÍØ5¡ø’I™Ê^W"nê8-
ÑÌ]HËPEOÓ2Ù hÐõMWTÛïÆ "#V#8<ütp:¡/'cÚËž-ጡœÂ»§\ +¢kªè(ðD N¨T¹<æ +ÌÎ\ò`Ÿ‹ç YÊ J%'”šay0CÔŒ‚NùlÆhn; +Uù@·€ý§ã?‚¥à“ +endstream +endobj +610 0 obj << +/Type /Page +/Contents 611 0 R +/Resources 609 0 R +/MediaBox [0 0 342 504] +/Parent 594 0 R +>> endobj +612 0 obj << +/D [610 0 R /XYZ 9 484.913 null] +>> endobj +609 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F63 238 0 R /F25 463 0 R /F24 494 0 R /F27 593 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +615 0 obj << +/Length 2006 +/Filter /FlateDecode +>> +stream +xÚÍYÛrÛF}×Wð¬2'sP[®-;±åbÕÚÊîVÅy@HHB…m”£|ýžž €$QrÉ›ÊæÚ3Ó}ºçô@N®'rò홌ߗ—g_½¶ÙDYa¬×“Ë«‰r™ð©šXgÊ“ËÅä—ä¿çÓ™QÉùô×Ëïy‚¹saÂLY%´ô“™öBg–g\~÷ +SR—¼|õÝ‹©Ò.ù÷ùÅÏo¹íâ5zõâÝÏoÏß|;{;…ø‹oÞqû‹7ßÐJ“Ì +ç- ¬õ,øë /¾þ!Ž;å\\ž_¼‰›“û§™åFHcoZ(Ÿ² Æf&ù°,¦Z'ó’'*·*hAy%…f૲mÊY³žÎtš,¸ªùÛÞD9ZíËQR —¥ ?â7IEžJEC¼ð‹=›¨m9¶!-Ò :Þ6+þ¨6¼øújlmk„Éu·ô#K+)2•>¸v*²ôpíîÔ›í| +]Üp-¨É&«¢®Ë&Xp¦(Ô¡
Û›¢ÅP)“u]RA%e½à–÷ÒIÒe¨ü4]^Wu]Õ×èRÜ>_Wõ¼Z”žü©jo¸£Ÿù!ÌÄ0Ú^;¦ Añ¹zœeò“ÚñZ³vâ°ç´›Èg¬#¥È½;ÔÁ§›j¹!-xwÂ¥†Š6*m;… Ò·Ââ‡S›©J˜Y²ˆzBãœwªBKT•ï‹ó ìëaŀƸ§ëÍ —Ú¡ÞŒò‰Ó™“&ùO€‰±yB876ãÓRò¬¯é T&UÐ·ï º)µ5å²h«Û)ôS.ïâ„5ÛÇZ!}Q×A”„¥&ÙÜmÚr5¦/…ÌÓ{ 1úW òO ‹¢VÍ’×Íæ!{S
› ßeY4q@{Smž¡˜ÙäY#î¨.ËE”P‡£ Tl~§‚¬Ê†í:K:e‡žGBÔг¸-(RÉÝ =¢VÔ‹AÉ-<•\qñžÉË*63 +™e#¬‹ ê‘S‚ÂxÜoÚ‚Êà¦?qJr[O9` †ö…Ò^s>²1‡îã ]Aè7¸hSÏøŽJ§"U laµÏ…"‡õþ +X"0g8¼6OÅTæm Š'1¥¾$¤öHõ(¤Rƒ}¥íž +)ĺ}œYî? Sì`€)AI¥L^nÛ͇ùg‘ùàöÕ”êG2ÀÞåêƇ4Âäñáf¿
÷,µÇ¤Ètéšnö–<}^Âr7j\¾iÖ3‹ÛQ6§„Þe +}*}Xu”éâRëû<š˜z“œ·|Ê%K°¶Ž:
6È®ÖË%Ó RM ï!5ïˆ<–”¥pºEÕyâ[𧩮«žG¨m_Õ¨‡‡ƒ}é‹j6Æ$L4ùy_›TÌ Ý.ýÓ!£Åc¥àÏã7Ï}~Òz9Ü› .À +oj¿‡Ü
UËCÂ#ê;—¢ÇÜvBänÛaÚ†§õ½cR6‰Í½ž"†®›ƒí <~óx?òHi½Àœµ»l …Bz¬ÎÇ…HÕ{kÿ(‚âèÛå‚Ë7±‡`G¼5S`Ž½UÝëÄ‘àI ¤~š³FQÈûÕ¡«šÇ¹ªyœ«š“®ª°æ4ò²œÞ@aãàBŠk«å²{$†«ËÁÕtÝ”û`– ±*7ÜÙ +endstream +endobj +614 0 obj << +/Type /Page +/Contents 615 0 R +/Resources 613 0 R +/MediaBox [0 0 342 504] +/Parent 594 0 R +>> endobj +616 0 obj << +/D [614 0 R /XYZ 9 484.913 null] +>> endobj +309 0 obj << +/D [614 0 R /XYZ 9 465.114 null] +>> endobj +74 0 obj << +/D [614 0 R /XYZ 9 465.114 null] +>> endobj +617 0 obj << +/D [614 0 R /XYZ 9 441.319 null] +>> endobj +618 0 obj << +/D [614 0 R /XYZ 9 404.707 null] +>> endobj +613 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R /F24 494 0 R /F27 593 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +621 0 obj << +/Length 1907 +/Filter /FlateDecode +>> +stream +xÚµXKÛ6¾ï¯ÐQb†oJ)rH¤H h»(P$9heÙV+KIÞG~}g8”,9Zo[ ‹ ‡Ãá<¾1v~¸úþúêå;DB°Ô]o#!¦¤‰t’2©]t½‰>Æ¿¾ýðf•êøúýïï¯ÿX}¾þñå;afÛRÉR›‚T¿Aidºâáœh„d2Õ0°Œ')qõûbµ–©‹o³¶§Q³¥o†Ÿ$®ÊCÙ—õJÄ;"ÜdU³$ÎË §«DÄ/VkÅU|¿/s¤í‰=Ïj’W%œÖÒä>.g·E;\¼/6µiQyP|-4ÓÚ²ÅC^dRÒ‚ØòHc8ã4qŽ†Sÿ» e̼\á˜1inIøÏ[ÜÃã¼9¶ (¦D +Ö);¢n‹¬?¶MÐB´ wx:™Ä‘IPÿFRÌ߈3çÔðFùÒ;&,±bàÈÂù c÷̱ÑZÂEªæW̪x•µq^Y[=ÒdÛT öÞwÐ6Ñ
aP|9‚d}ÙÔÉaÊò¡i ÿ ý×°Òfu·mÚõì-ƒ./ \Fs€[¨Ä¡0oûdô¼9x‚EVÃÕ«¢ëˆ£ÜÒÂýŠ\ iäyd‘fu·2.,:Ú +7/p PÖ¸1LÂ㪨wx'$b$!‡ÖOöGÌHýó¸ÙæƒtáæR+&¹9»9”p\ÇÅäâš)p7ÏÅ—ì“2'ÁÓ'lÞ$d Ta´Ú‰ÒŽUÌ?Ì® "¹ÂÂÍÔM!Ý)TIÂažÿÖ®·×W_®0òHD5N#¥³ÜEùáêãg m`
Ó.‰î=ç!Òf ½¬Š~»ú…ÊëY”YR11¨(‚jzžˆ
ýõç|ÙÑ`hÏ“F:±6VÛ$RLMLrIŽfN±'l¯óaøt©X6¿ã·Ò¾[-7¡¢¡búÊø˱ì‹@ª‰”åyÓn²:/hNᇠä¿@ºmËšòú:IÀOÎ<>/o«‚ò¡¯sG)ÿnÀ ž6 +8…2pè†,¶ßd Õ`$ÄcHµC£²ÄÈèL“çY¨ôo°–r¼BÓ–‹Ö3 +@oðÒÖ†˜òn ¿º%˜6À>`Žðá„ €Âõ€F0 lÀÀt÷!ÛÕeÜÝb]á¸üç…åÅ’ô“ñÉ —ee/Ê@Pé/™?Ö×åRŸ:qQ˜õQ8úå —'Ž„¶³ÖcjxÂœÄ?%ÍÍi¥¥!)™rÂ,žú…öXõaZ<¤8œ×…š)Wžåüæ¦ÏÊš|\s=‚u
9\Gd Hèzƒß9ïwÈàý9ÎüŽA:s ±µškp +ùÈ0ø!«Êª(i¶ +pê‘ |Ø×ÁéÀâÕã
ju( +õ‡Eùä9 + ^céq1‡£EPh±Ñ‚ñT=‹áܳ*H@Áf¦[:/e2IÎ’Íì8Ê5ÿýÂtÙŒ`ò7·Ålø?ž Lís#>|OŽêÿa+wg]]wÌsÈåœJu9Ô=˜RúòdúŸ +íC‹ +*Á¦ DÌé³FÕIS“a¸é«Å‘–)gÁr’qy¡FA„êѱ^£iz<¸€ù÷ZBßËÃÿQOxÈé<h"Í¿8O‚sŒ +endstream +endobj +620 0 obj << +/Type /Page +/Contents 621 0 R +/Resources 619 0 R +/MediaBox [0 0 342 504] +/Parent 594 0 R +>> endobj +622 0 obj << +/D [620 0 R /XYZ 9 484.913 null] +>> endobj +619 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F27 593 0 R /F24 494 0 R /F19 213 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +625 0 obj << +/Length 823 +/Filter /FlateDecode +>> +stream +xÚUÛnÔ0}߯ð£#5®¯±#ž +j¡P©\VHxHwÝÝÐ\J’vÕ¿gÆNÊ"ÄËÚž ϜϙådG8y½z¹^^hG„`¹1’¬o‰ÑLd†h—3©-YoÉWúéýù«Ë³«$UÖÐõ›óëI®é—x¾¾ˆëÇó«³$Wt}ùùrý%ù¾~{z!̱k™Y&d‘ƒWe´â#’Ê\3« IUƸË#ê¬OR© ýñ°Ýù-î-½íÚ:â8€ãL;ù·ÄApæÄ3äüeŠ{ ƒlª6–nø¹‹¶²Aëe³‹öC9ìã—çëˆð“rÀãÓQ‘K¦œœh<.1Ÿ ñ]jZôˆ„qË8W$šim"æ¹B&‚Ü8 €ó·¾óÍƧ7`¤¹}Jœ…°S! +´“M9nˆÆQGıŠHÀAm.¶Pá™:†§ÒIˆ9h†˜%W2Ï' ô€TS‹$ÕZÒ¾ýa_ ñTÝÎwqjcIjAˆ8îÐ4ÞB½ÿù€ªT ®å0ëv(Û(¹t ;› +ANZe£œ ÊÉ¡œ´²t†DHÝv>~è«0íÕSü2ì‹&î{ßDLÈ,ïdŸeôïÆhEÕ·†¦€¼²©¥þsVjþˆøüÁͼ©s=î«"¸‚””Ìbú¸¹/ºw6”-˜®M1 EÙ7•ˆª¬KsC˜õhø›¬£an²Ù_Ø´‚~Ý/¹ +endstream +endobj +624 0 obj << +/Type /Page +/Contents 625 0 R +/Resources 623 0 R +/MediaBox [0 0 342 504] +/Parent 594 0 R +>> endobj +626 0 obj << +/D [624 0 R /XYZ 9 484.913 null] +>> endobj +623 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F27 593 0 R /F24 494 0 R /F19 213 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +632 0 obj << +/Length 1633 +/Filter /FlateDecode +>> +stream +xÚ•WKsÛ6¾ûWðHM#” +e´ªs¤Âg‹¥Ì2ÿå¾ûQè“¢ä| Ê’üþl‚&"4 Ò¡áãÑ‹Dœù;¼gßõ´Õõ¦º_p}DºÝ“¨êˆé, !E|ŠEs¤Uü} €i@qˆ§6!63ö‚gwø4‘Úª àéΕÈilØ ˆ_µ°ùaWªq@¹¼mòzßUƒ¦iw$F, Z@ bÌ0¨žt(+›Rè ¢ pVÖ} ElÚTÕ1èr¤ÈWp +¾2£pã /ÃsFz(ð.‘>Ô +»‚Œ¤µ–Œ"[ãKMôß›6æT}oË2*›†D÷¥#reL¥¶*…L“SŸAM°èmWM舚EE¾¬(™h pÜÀµÑ5XɵÅ#ñúÖý[ë‘·ËÖU£zÇèŽ]ε#†àãCÄœY<Ì¿:™ÈKX–ÜNfKyâÁf$Ì
+ Œ_0 ŒÄlÀí*Ï[ãÒK$㙼 EM‹µ:1Ä +šö3ðy˜±L;ýI„‹ê¾Ì<"f1œ, “'Þ3Îc|ÃIìùì‚Aö 6;X·õs–,³–»¼õÂ,É¢É?Ì[ò<!’éc_b„!Žp- ÒÈrµGR·Õ ¸Ô'€»i÷Ƙƒ;Z’9hGùŠ\ÈWÈåþr®4sYžij@@û€z×Í;U²ÓÔû”3Ã0}Ò™|O,Gbøô9û‡,N)0çHÉ„HþÓ…|ra5LaÚìܘ¦, äÅ›§Ú!
“, DþÏS¦zè-NÂN‹ÂÅÄÙU”ªn"§© +áæ‡ö®WÕ|R +° ¿øV˜}$oXžc +ÿWZÁ¼ÉéýsêR–ÈSZ~7«„³$æçÌUgƒ +šÀ"°Š¾ m¿•É¨¨Á*’A»MœU©åà^39²a(nJÓfÜÄ‹\ÛÊà‡Ÿ+CżÌM›Ú™8õ;¤¿j<0qºB »Fo´qŸQ°a»M&ÎÓêÍ…gðí]4—‹°†Ïìllð€òáAíø„‰bJD*ååÇÁ(~C´î¿t +endstream +endobj +631 0 obj << +/Type /Page +/Contents 632 0 R +/Resources 630 0 R +/MediaBox [0 0 342 504] +/Parent 636 0 R +/Annots [ 627 0 R 628 0 R ] +>> endobj +627 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [40.382 273.698 96.534 283.993] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +628 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [254.138 227.372 310.832 241.319] +/Subtype /Link +/A << /S /GoTo /D (section*.52) >> +>> endobj +633 0 obj << +/D [631 0 R /XYZ 9 484.913 null] +>> endobj +310 0 obj << +/D [631 0 R /XYZ 9 465.114 null] +>> endobj +78 0 obj << +/D [631 0 R /XYZ 9 465.114 null] +>> endobj +634 0 obj << +/D [631 0 R /XYZ 9 441.319 null] +>> endobj +635 0 obj << +/D [631 0 R /XYZ 9 404.707 null] +>> endobj +630 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +641 0 obj << +/Length 1891 +/Filter /FlateDecode +>> +stream +xÚXÝÛ6ß¿B2.fEŠ_êápHÉu‹ +ßß–d£R¨ÈòuIŠeFN Y™Ñ<²<úÈ» VÅ´˜BÿK¦²Åûa¸L¯_°ÉÌÅpd‚<È8³g¡ys!¼Zãµm°®Ê6.úþ‰– 1âÖC8íÚ¡Þº¾ —¤Ÿ† ¯ ær›&HiƒO÷Žìâ<³¸dRj2ë® ¼Ìœû)—ˆ +ŸV–§lµ–¹JoÛé;bvÀv"«—.Lr¦ XÏâô[àT‰a…É82j¦á ÉŠ<X-݆fœC>ÎØ^Î5}ž&ã‚Rà+@Þ i…¨`žÁk‡üSQl¸ä\¦ èº H¡Rî~;ön–SY²ÌL¹|-&yn¯ÆÄ>&ÂÇ‚F!˜US‘.ÅC2!ìŸR¨ÎÖmpÜõH‡vO V¨‚Y.ܾ(Þ Ï#Ëoô…3çbÐ3GÖܤ‡ò ËÓ ™xBÝ0+¨>+ _’‡d‡Å/—½¿e™ê}wêÇ=ÝÕÂ@[’y ÞBŸùåГïW*K» ÿºvü «;OG¿/Ûá¾ë³:»¾Î§lb¥ä+4Ñ3¯nÛatåö@ˆ\o&/á)†‰Œÿ!¢ªKDµ"¯`*.ñ¥
õ¾3:7úÒ¤5d“,ÇÚÍãØðr³×›˜xæàBfíÿµ‘aÞnn nxˆ5×9³&€< n®:Ü|þ5K¶pö}’1 #ãç<$¹»…U“|ºùÍM~Q +"V,LbÙ6Á™ÔÚ;i¢“Š‹VZ( ýü$ÄU3! tfv^ÄÄfe"ÌXyÐ\…ð3”Rpl“œI%‰I,yˆ
ÕÏCuõ×åÂF^ÈÿiPx³$¨`²0 ƒ‡,Am–‡ûÞ×&8€†Ì ôþ ºÄ‘æÈv; Õ¦cG§>ËâëÝN±p‘Xn·5 ¸Œ ã¯~pl:/³¤Ò˜vž#] :„Ué¶î]…ß‹DJYyÛºÝÑV’Už&$¢QH‹D „ O7ñ«‡“bÅNÆ„ÆÚv+?ú +GRC}Ig¹ @Æ@tz 9·x‰½ f•#Ú$ŒN‡î
—q’Cb 8R‡îàˆêžø"›†ÁÀíeŒÁƒ²¡OŽþJCè†WK¶
†“¦ ãÊù´€%½+¸*iÓ†O¶Ýé.|S†ê)ìëq `Ωý`/¨2‘º`òR‘ú4æþÝR¹¾ÅzÙ†ô¡RxÎ °Ô4TÔ GðŒ +endstream +endobj +640 0 obj << +/Type /Page +/Contents 641 0 R +/Resources 639 0 R +/MediaBox [0 0 342 504] +/Parent 636 0 R +/Annots [ 629 0 R 637 0 R 638 0 R ] +>> endobj +629 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [202.254 449.838 258.216 462.457] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +637 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [130.652 302.519 150.525 316.467] +/Subtype /Link +/A << /S /GoTo /D (AMS.62) >> +>> endobj +638 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [122.426 72.466 154.441 86.414] +/Subtype /Link +/A << /S /GoTo /D (figure.0.3) >> +>> endobj +642 0 obj << +/D [640 0 R /XYZ 9 484.913 null] +>> endobj +643 0 obj << +/D [640 0 R /XYZ 201.436 441.775 null] +>> endobj +644 0 obj << +/D [640 0 R /XYZ 201.436 441.775 null] +>> endobj +645 0 obj << +/D [640 0 R /XYZ 207.749 290.603 null] +>> endobj +646 0 obj << +/D [640 0 R /XYZ 207.749 290.603 null] +>> endobj +639 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F63 238 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +657 0 obj << +/Length 2184 +/Filter /FlateDecode +>> +stream +xÚµYßoã6~Ï_¡·“qk®HŠ"õЇ-n·È]õAí^ [N„µ¥Trâ¤ý}ádÉQœì-"j8Î/~3¤“è&J¢ .¾¿ºxÿ)u‘”"7FEW›H*'´2Qêr¡R]£ÏñO ü°ÈÓøêò—Ë«_¿_ýýý'i&ŸåJäY©þíˆé" ëDK-•PyŠA&—3W±=,” ú÷´q·XêTÆûâ QÊðz·-V%
“øPíoÏmɃ®Ø…ÑÃB¹¸Ü6‹%>^U{–êuUr¬«’ãA×ódzêa³t`áu3 · “@³;ÿ «=Oìz¦^1È‹–J'Â* -e*ÒÔ° mõÇ}µžs ²ÂæY¿à»Å2Õ*>Ü–$ObÙe*ƒÕ4Øû=Èe W]xÖôLâ]³¯šši¬;QÛrS¶e½ +2Hc"7ÚY V9cU®½?٫늂’&x§•“,®›½X,3kâ+¯H>x§qðS͆ŸÛêæ–È{~mKØSñwLñºa™}/48΋Ú{¾š(ºÿ +ŽráȲ=ª§Îi2úbÏ ¯EÛÓ½E÷ ¿}©z=ÔïæT% –Zeñ!¬D㶄‰ †õchŠŒ¡çÈ›,gìM/¬á™Aè`ƒðÚa?쇉Š—^ZîS‹ž«mYÀOZ'S„É£úy|[Ðþ{Qx9|p×6×[J× ¿CqF‡$’QKAƒŸ€Ÿý‡?—+Î_zùår +%ÌRÜU`¦,9…çlÙ4>HZ#<ÈVkúle N¼lÈŒ§.ÌölwE»ç‘O¡ñT[TŽ9Ÿh ÂTP®‹úË®¬98ã<p@»Hã#Žäu¯šeÓ®a¡Œ‹} uOÝ bg +ÂSóL<³å +ˆn9j£Thí˜+™Å[ ‰–#6ÂÜD†½ õþ“È´.¶Û§…SýdP™ vCn‘]ª$.WS Œ}™ö;ƒàKŒ¼/ÇS»¢æçÔöË‚pý†iŶé‡Ã½Ÿ)¦ÈlïèÁã
ôñêB† —ç‘rR›E«ÝÅ ‚è2ãgÇc?Ù¤ðÂûËŽþÖ\ü ýÔ—#‰Ü^$QŽÖ@e>8Ƨu¤Œ2 Žÿ_r„²1k&ÒÜö‘„ :ÖbbËiP—2Ó(”ÈEfB v ‰ ؇[™ ZU÷˜ šÇ§ûø‚©-»rÌÑ1&Q±KL|¹aê + ú¦s¦8aé9 G>/(~ÛüOë£eRN÷Ò¿Ÿ[?‡ÍÙ™õÙ»&.V+ƒ7áµãgˆ¯‰(¶Õ¶¬µ-ê…mWô¥²·Ûå ŸkŽR ÿˆZÈyý'N
z´ÔäúR¯»ÀÙ„g/kS¬ö¾ :|dö²–s-ϸ ÂAù±•™scÄ–óaL¨7 ±ËUµ¦Ž˜ã·°RoŽ}Hsß26ñ¼žjÄõR¨%rÍ%æ›bíXÃI¼“׬צmv¬©÷-‘0hÚ§~ÛСÉL Êø®{`è¡…k•Nm(d}¼hPÜ´e¹;ÂHU¸«z]–kÿâÂQª}bžòqF˜Qâ>Gg#̉‹S‹&CK¹:®:+„‰]ÓRù¸*·Û&Ë¢»o5;f¼½ƒEýŽ+ÂLy;Öª<’8…™TS5úü{A†âBç.:x¦ .&§žbýŒjæ«–2ä'%ò åO‡ á@7ÉÐqÅ‚/,¸"“Y_Øþ,‹{8.³èAïëþà'G eJ'O¡xR°G„ùnF Vµ;9ÏNeÀ Épœýëœ ´MfÐã!ä¿ k* ìCÄ“ÔõùÔÌb;4õ¹1pw©tÂ&ó,'ÉœÞÚ÷T™°éHÐ4ÈÒbûA²$G!ŽçB ]ói¤§^èe%è>lˆuÍŠSÂHØ`ŸšñP
ý“l%éà/ý6!¹
ÚMœÿÛr&Xš +´Çg ;ˆ;ö0 q´óÈ5 ôòwY1R=ÒÐ…ƒ$Ú=C7:ð¡’À_þ®-7mÑŸ#
ŸÛèÉhˆA8óHê-±9âzFudà‹?¼vùþk ìL¸÷‹ív83Ôe×
ËÎÄáQÒŽ¼ÿ@·Gìi ´Ì=kŽº—œOnB{&Þ‘(i.EöêQÔ§¹…ðÙóäž„i©©?×tÜ‘B÷þöƒŽ¯;œpÊ5¿…¨ÄÆ’ŽQt-âëKà¥óM¶%ßô½X›‰ûX›§Ùœa¹ÓÊ<VÛÐœ-Ì$½ª'×NΟÛnÏ/á"’†¡ ÍÁ("ëÒ³xžŽoú¾#êE» +endstream +endobj +656 0 obj << +/Type /Page +/Contents 657 0 R +/Resources 655 0 R +/MediaBox [0 0 342 504] +/Parent 636 0 R +/Annots [ 648 0 R 650 0 R 651 0 R 653 0 R 652 0 R ] +>> endobj +649 0 obj << +/Type /XObject +/Subtype /Form +/FormType 1 +/PTEX.FileName (./images/040.pdf) +/PTEX.PageNumber 1 +/PTEX.InfoDict 660 0 R +/BBox [-2 -2 220 37] +/Resources << +/ProcSet [ /PDF /Text ] +/ExtGState << +/R7 661 0 R +>>/Font << /R8 663 0 R >> +>> +/Length 664 0 R +/Filter /FlateDecode +>> +stream +xœµ1O1 …wÿ +°Û9Ç— Ub£Í†˜ŠZ†ÞP*•¿Í•SUfdENÞûô¬øˆL‚œuéÛ ÖŽû85gÁ/`\Å1ª,Vq•ÊÄeQ° _UâmWþ¯’~I‰)dm Ê5•qQ攬Ï=¸„9”kœCñÀ¹P 2ôoÀÂh(US¹É9Àî ³?–/¬Wp™ï—¶ð±Çn3”š™bßÁ¼sA“—ó +SÇ>ÁëÝù>÷7ÖöÖŸÁ”Æ ‚É[«Ø߃èA¸ñ$ž:¼D} ¸[è +endstream +endobj +660 0 obj +<< +/Producer (GPL Ghostscript 8.62) +/CreationDate (D:20110511102833-04'00') +/ModDate (D:20110511102833-04'00') +>> +endobj +661 0 obj +<< +/Type /ExtGState +/OPM 1 +>> +endobj +663 0 obj +<< +/Type /Font +/FirstChar 84 +/LastChar 118 +/Widths [ 574 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 473] +/Subtype /Type1 +/FontDescriptor 536 0 R +/BaseFont 543 0 R +/Encoding 662 0 R +>> +endobj +664 0 obj +213 +endobj +662 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +648 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.882 377.608 282.877 390.228] +/Subtype /Link +/A << /S /GoTo /D (section*.37) >> +>> endobj +650 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.787 194.636 75.66 208.583] +/Subtype /Link +/A << /S /GoTo /D (AMS.62) >> +>> endobj +651 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [91.845 194.636 112.439 208.583] +/Subtype /Link +/A << /S /GoTo /D (AMS.64) >> +>> endobj +653 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [190.041 165.744 210.634 180.2] +/Subtype /Link +/A << /S /GoTo /D (AMS.64) >> +>> endobj +652 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [171.509 73.028 189.307 84.983] +/Subtype /Link +/A << /S /GoTo /D (AMS.64) >> +>> endobj +658 0 obj << +/D [656 0 R /XYZ 9 484.913 null] +>> endobj +659 0 obj << +/D [656 0 R /XYZ 9 306.874 null] +>> endobj +647 0 obj << +/D [656 0 R /XYZ 155.833 269.123 null] +>> endobj +655 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F63 238 0 R /F25 463 0 R /F40 208 0 R /F16 210 0 R /F19 213 0 R /F7 232 0 R /F11 420 0 R /F27 593 0 R /F24 494 0 R >> +/XObject << /Im3 649 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +667 0 obj << +/Length 1082 +/Filter /FlateDecode +>> +stream +xÚ}VßoÛ8 ~ï_áGX<˱üã±;´· z·C/8`Øö Øj"À‘YîÖûëGŠRš +[ s²Ýæ¤?Z‡¹aþ#ÃhÍ>¤W\'¶# +¥ŽJCaòÒ«cB=˜0ß7Ÿ6à`±˜ËM§Fàð‹Žo¨-¡_«m¨’Žñ$¨©È…ô0hUˆ_Upvš!ú+™ ½½w6ä?¼yÔ½ ÉÍHŽïbÍ@ KTìÎKmÔ@”¸ƒÅ-d2OHË"ŽXOÒyÝÃr¤‡÷ùz +CÄBIM´!ãÈŽk¨žäXÄQî‚hdœ¼›{¬à*qL‹#ÒÓ´HТ¹×®ŸÐ;w@ÍÙ!R ûL£Î…’
„žŠgõ$àS¬Òhªpü(9ù%T}ÔFOœàe e͆õÈrÓó”(ž"nøÞ|K¦~¤‡®ß؆2ž¤ö +{ µ“£žÒl‘È
Â!€q¥¡€|mø+é,²xP±hÎo‚Ç ø†)™H‚FÆ7½áÄ#ô$ 5ÉåÈŠŽi,¢²›õèó«OuZï¶7?Y”þ +endstream +endobj +666 0 obj << +/Type /Page +/Contents 667 0 R +/Resources 665 0 R +/MediaBox [0 0 342 504] +/Parent 636 0 R +/Annots [ 654 0 R ] +>> endobj +654 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [129.356 434.727 149.949 448.675] +/Subtype /Link +/A << /S /GoTo /D (AMS.64) >> +>> endobj +668 0 obj << +/D [666 0 R /XYZ 9 484.913 null] +>> endobj +665 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +671 0 obj << +/Length 1843 +/Filter /FlateDecode +>> +stream +xÚµXK“Û6 ¾çWø(ÏجH‘zä–t6鶙ٙÔÉ4Óö •i›-¹zìÆùõȲ\mv/½˜$ ðáA‡³í,œ½òøvõê‡w:I-" «Ùj3“ƈ4LfÚDBšt¶ZÏ~~»ý<ÿsõ3ñJ‘ãy—22"–³¥Š…J5ñ®~º™/£Ä?Ý|úxûëêöGZ~žKe‚7 >ñöÝ;Ïü0¹û8Ï¢à˙ΜÉ0*‹á0-´Žé7 ÞÌ3 ¬n?ß®¾°náå=–RfBg(§„Œú‰YšË‹Dp×P‚I<S[箜/U–Õ†Æv7—AÕmws ¢õ<íÎÒdSSm·•+·D9æ[Ûдșý †$àOìѵÕ>s]ûë.Y—Ñuñ¨(5tN6Õ~_¡.þ,$ ò²´¨€˜/c©‚›¯G:©v¶,ø»]ÞÐdÇ‘ÈêJtQ•s•®h LQ§p¬M»ËÛÅ|iÂ4 +¶è K krq:öÂãÎȳÃÈPU×v¥5É‹"H•ÇIa›Æƒ$¢Ì#8ª«-‚Òèà¶ì¿tÍYfi Ƭ=øì$ÖìÑ”U‹ÍØ#"%0 ¾Ï÷no SGˆ[`²ÒÁ}×òlíþeÙ4òojÈôgû ²KáCXÅÁÁ’YòÒÍ‚h¨ÀD’‘J‹ppò‡9ÆC¿¶l¿Q|´~=Š —J ù'QC˜“ÛT$²séåT¶òÆ0fC\ø\nÌUº v0]Bq⌉&Jû +E—:y ¬ù›’„8¬ÓG_*ªÚgÕ[Ü:æu;åZ ™2$qFh†b² +Î\?6OÃûì)FˆdG¸«h•Ó0TDMhB¢ý +hߟ8
ôųÉ\]Q*×ÜEDq²°Í×OzI÷Ý“N‚æ˜vé ‰ßx˜CÎk—ßïŸ*Ÿ¡È¤~¶|ªï–¾DDÙóå3yFTŒï–O#²D¾\ÉB™Š( J˜ z VµÛB·±'û]t ˆ,„w•»¡9‡S +E™Èô¹tÿ2™çC‘Õ}AUo^ #×ÜuW0½´4¹t:®Ÿuº’PDL|åteÀ~Y³Ïáíñ{3œÒ]‰$[\°Mº^‹Ir«Ó°¹zÉiñKN3&¹Òè4ÂÑÿq·vâ4-”Jž=
’¤*D`A·×?Ü)oD”Sôžþ4ð°‰ôðFzyÜ‘bÙËÌ F&ÔÛÜÛ¡zø ¿hï€D‰ ¸¨ŽôdÎÎKŽ©´‚ÓÆYv¨|Ë[ß›à„Œà+¬|%Ri6ìcïBAƒ¯oÞ=ä[xukÿú&ÇãÖõݱ_Þó‹·?p"ë^Vr_ŒÇµ[PWpçKuÊJ +Þð¿E˵¸" ¾Gêïá+÷è øoŽû†Óû dјx„Ârm±ß;s +endstream +endobj +670 0 obj << +/Type /Page +/Contents 671 0 R +/Resources 669 0 R +/MediaBox [0 0 342 504] +/Parent 636 0 R +>> endobj +672 0 obj << +/D [670 0 R /XYZ 9 484.913 null] +>> endobj +347 0 obj << +/D [670 0 R /XYZ 9 465.114 null] +>> endobj +82 0 obj << +/D [670 0 R /XYZ 9 465.114 null] +>> endobj +673 0 obj << +/D [670 0 R /XYZ 9 441.319 null] +>> endobj +674 0 obj << +/D [670 0 R /XYZ 9 404.707 null] +>> endobj +669 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +677 0 obj << +/Length 500 +/Filter /FlateDecode +>> +stream +xÚmSËnÛ0¼û+t¤€J‘hRcRØ )¡@PäÀHTD@&’²š¿/W+· à‹÷5;šÝ¥³è5Ê¢o›»fs³gU”çiÍ9š>â,Í ±ªN)+£¦‹~“ÇŸ»¯‡ÛcœlKNšï»û‡¸fä ãû=Ú‡Ýñ6®·¤9ü:4OñsóãfŸóÔ´(ÓœÖáË +Ë´ÉV-Q²ÍiJkœ"ͪQ~Æ¾Ç 2òLIdkNÒ[…sÌ9ã$^F‰™ANV9¯Ú§:Ì+6ÐbÅIaÛ8ÐXèÅ«ÔÒŠ4}IÎRÆ8j4ÌA+*bz°5ÑÂOV¦qR” z, +¬]È– +äa~Y ÷qn:½Áç ¢Ö`—;ÞAOBdœÆaÃr‘3p®øu[á;WDuʽYó¿¥ WãeFŽÒÃcÎÉäÐjƒò—@þ'cC0bÅþ»-VºiôK7Eñ …÷Ò^]Ïú¼·´C@ ÜN…´…µLȳÒ-¨üø‡¹Ø]³ù -üþ¨ +endstream +endobj +676 0 obj << +/Type /Page +/Contents 677 0 R +/Resources 675 0 R +/MediaBox [0 0 342 504] +/Parent 636 0 R +>> endobj +678 0 obj << +/D [676 0 R /XYZ 9 484.913 null] +>> endobj +675 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +681 0 obj << +/Length 1651 +/Filter /FlateDecode +>> +stream +xÚuWK“Û6 ¾ï¯Ð‘ž‰UQ%jrj;›4´™&îk’ ¸ms¢‡#Éël'?¾xPò#ʉ +öðsû•f@º; û'O_y ¯·°µ-GÐA+ª§Ö4® xÆ´•W=¬É¬èÆ Ð Wë<Râî.3´q°L~ˆdjëj`Î<î´ Ira4 ðP?yY
¢Ñö¶bž<†«ÀÍ•+¿c
¹:Î3ºZ ˆð ÓR<ÎÄl‹÷G%çG²‰)hè>²…ƒkµ£»T,![æÝ-8¬]°gûc9 {ûŒ1–%—SiÅñŒ±Ð†KHŒ£PÁ~Ñ +L´½{\©TÄPÌÅéÚPÀ‡g˜†ñë‰ÁJgPrmÙ5Óvæ:OC•iŲÀoM‡^±Ì€G,]?šO¿’/µò¾Ôg_zGÂîX’õäC `½Çwyà<èyî²àS×VÖç P|8°*ÐcxÃ…h‰ÒbÛ!º×î˜ç£aŃœ×!¼¨|ÆK,B„["6°–õµ¸LÔEüùôL¢”#©9=Í>CQLnB½ ¯A(GŽã ó¿™/'tŒëõkÀ_ô¿YËŸ£ÄÐ-Yr¨ÍqpµEÔSå²:ù=ˆŒœaÌžð€îXWÌî
žþˆB¯ïƒ–»³-ĶæØ&”¥=Œ¶šté¦K†q”WºaD(%ì#Ý´eÎm½ô zä<×̡ƹ½©˜¨ •õLm¿ã±µŸŽ¬çªV²¥´»+2&ÎÄ–2‡— {JÉ@æ¡RÅubü\›a ć KDcK\²7-ÕNõhG¸±Ãqv£_åkî\].4¶uÖÂÔ±¤ðps¸´È_’™BãÑW¸9¾Úµ^~rãž)‚ Ø@q˜¡$8ÏJ¼ö€'ɽKuñõ²_ +œPY‹XŒ»þ¦6Xr]ë;©éG¬\”fî\„CF#–!?9î§ÎLŽÔTÉ—åTa΀ çU»¶~úNòò#bªÌmÉT ¨) \Å\ÓQ³ACt.ÈpžöŽaÀì¼%[^{,ºÑY¿;U Ü7 1©Äò²$íBÎâq©M¬'¥«;‚ø›Z-œjT<0¾
ä“T`ä–@XÔ‘GLŸw¸ºËTÔ@›nCˆÛQšrUhñ7†Ü^9ÝgÑþœmÔØH{p…‡]ïl[z9w¶D ǯ°g®÷É’)"^»¥tŠB£ïœEf¸ÙŸ?Ëß螶ò¹¢çXT3†%lÞ³ÞlÅU q›î™'¥A^©‘‡Ürÿ+/ꎌ/êBŸJH9î@Œ ¦Ž¹)Ü~‚Ö›O“ó%YÒ ¶fø½àQ{î³(X. ‡Þ”ð²Ø6£ C SçH +1ìéØ8ÑŒC”Í/-³@ŒyÐqê"Kæ‡Ñô‹ŽlŠóž¦4À¥0â]Óh®fpeâ)þ)B›_6Hû¶Æ +sŸM¥WŽnŸÛþ¡kzÿ¢t®¯ 7õ)ôÝz#ÕùéëTß<ê½ Ÿ ŸÌ£É»›
šâ,Jø·‘;GSÝ¢Ìçe [*E±† ”š*Q³øuJC Ÿ¬Ë¯SŒo} sQwí£Ž² whjüq6=ˆæ»råçGЧvþà ¼zh÷ˆ”3e¤Â ^Û ê¤¸°µÒD:Œ´¾®§E +ÐJ•‡QZes÷þcT0î Á‰40'Ô1.«ƒwwðGùÆi¹„·w åP«ââÈÛ›¡J°>F;Që96ýÁ¿i R
ŽP`Bâ?Õi|µ.õ?Áo I +endstream +endobj +680 0 obj << +/Type /Page +/Contents 681 0 R +/Resources 679 0 R +/MediaBox [0 0 342 504] +/Parent 685 0 R +>> endobj +682 0 obj << +/D [680 0 R /XYZ 9 484.913 null] +>> endobj +348 0 obj << +/D [680 0 R /XYZ 9 465.114 null] +>> endobj +86 0 obj << +/D [680 0 R /XYZ 9 465.114 null] +>> endobj +683 0 obj << +/D [680 0 R /XYZ 9 441.319 null] +>> endobj +684 0 obj << +/D [680 0 R /XYZ 9 419.153 null] +>> endobj +679 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +688 0 obj << +/Length 1918 +/Filter /FlateDecode +>> +stream +xÚXK“ä4¾÷¯ðÑ;%¬‡%›=130°Ð± Ü.u——Ýc»º™¿_*å»ÇÛ4 'ë‘Je~ù”³ä.É’/¯^__}öÖ‰”¢Ìs•\ß&¹Òæ‰)J¡ŒK®ÉÏéß½ù×»/¾ÙíµËÓë¯Þ|ûý®4éO<ÿö-¿óÍ»R§×ïþóîú§Ý¯×_öVæKÖÊ:!U‰›W£‰è*‹²${-•P¥ÁÀŠ¬(™êæ<¿²éÍN¹ô§£§Kýï÷ƒ ǦïøB%—Ê<Ú–É Œ]™3ÃS e+'J—I¦Ê‰ZL¦‚po®¯Þ_IÈ—%àl¬ÈsPiP[“Ô§«ŸÍ’6¿N2aÀà1ž“ «†mòÃÕ¿gåV²]˜)¾tظ4/D.M +œ~îR…uv}éÚfR‹|¶®ŒÐ™%%貋¥~ɲl_-d.A›µ‡
lmØþh‹LHG‚mŸÓRf¢Pò ´k±ÀÌ–eb²\hcùÒ-«ç"ƒLZ˜Ü,${ÊÎ ‹Q sÑ…>ßòî½, c‘'{7VLy}lÆÝ^+O
óêþ~è«šœúè#MÓý’IÓ5Stõ@÷‚Ë«¢ +d Y¾fìãü)=Iî
è ¯ûî@©ûñØp_Á{m5N[IžÑ%²wÛwž‡`26 àÐeÁ¹ŸÖÁclêªåéÉ3ÿªkêµ +-· ´I]Õ@ +è¡ …6)H>ín +²½ ¶WÔ ˜pðïÏÍÀœ5ª«Lû ï +ß F>tusp€d»ODÁS +›§?ª‘6°
^ˆG°#ÿê·Èþ–¿Í4nv*ãèYÖ&x'µ!Í]×ÖUWÇ¤à‰‚kÃS°\s‰=n–žznbc§Å0Uì3¼ËŸÛ‰©¹íÎ;Úº#” °–ç1Htù’"WÉPth¥ŠáãvxC¾”:(©\H7ýðÇA |5›‡ÙwÃÚ1<i0h)¦iÐĸkí‡n^fGSnN*3Åý~ ö貌= C† úë×Ôüï$w³ã‚´:°k°½ÖÇIvB‰Åw—У½û#çH$›™˜íafjº7œyâ óáüŒbӻܤ1<5|ª
É÷qäY´·çîP¢”Á©Èý–îPûW V èÚ¹BÌ·W¼ˆXÅ®Ùåg7…Ù.ôþ4¼D/Æ!éÙL4 æÅš¹Ý`Ž‡Øs¦4ÑHådÊY¬jawÆ´˜š-œpv)HðÈÑÌ%S<ýñM… 2ê´ \Ó-ÎÂq ‹¯§7tAQVéíÜP¦¯?ðÚÉWݸ>]€ #i¹¿ˆ¤øÞÿµ£§3Öqö"º‡9c1jç YômÔL +endstream +endobj +687 0 obj << +/Type /Page +/Contents 688 0 R +/Resources 686 0 R +/MediaBox [0 0 342 504] +/Parent 685 0 R +>> endobj +689 0 obj << +/D [687 0 R /XYZ 9 484.913 null] +>> endobj +686 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R /F27 593 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +692 0 obj << +/Length 1782 +/Filter /FlateDecode +>> +stream +xÚÍXK“Ô6¾ï¯påä©0ÂzKÜ +(rH2•ªpðz4;?Û³Ëæק[’gìÁ Pá“õhI¯»¿n9Kn’,yyõlsõø…0 ¥ÄJÉ’Í.¡ÌÎd"Œ%Lèd³MÞ¤<ýteEºyõ׫Íß«w›_ ¿ r¶Ì2b•…]ý!Pè*‹ç$kfÑ\&k®HflÚìÝ +LzÛ•MQÞV¾«Óv†;WåCyW+¦Ó‡0×¹‡²s}öù0¶ââ*Géû0:îtœ-Úfª%kª‰”¾‚!ƒB½ëîVR¤pj»¢ik¨
›À×5®»yí~ß ªmhïÛ±Õ´C\ÒTQð¾ ö¡Õ¹ë\S¸Ð ÚðÍçhƒ^YÔHÚn[6ù€k œúЮø3:Åß("ìþ_M”CÍ(òhµ™L¯CØ:¯ú6´¢Æ5îoWk@ÓQjˆ2îAvÝCè‚òGE=¸VNõü*_Vžƒ«Iy¦<ø &Vgt¢» œ› •-]QÊàÔ‰Øý¾,PU¼‘biÙÇ/šVq>tû!@ Íà1<=4å®íê0X·àÍT€¥C—7=ú'Lø;KMØüÆÑ=T +¢'S%keI&ÎLé1|fwš¶4%«µ¤"}…hI†ñ†§XýÖxµUÞ÷e‘WA°vÁNySý# ³1jAöu ã÷ùg)H¼)ÐZy4³ÁÒlŒ|غ¢UoBo—CÛEÑæLÔïWžöÚum Zmãf +Œ¼q8:S#z¾ío S9PÃÞuįžQO¼Ã3Ï p€³C3ð¢\ßæÝÑšU”ìË:0¦…·®ó +¤Tù-ÿ¬ª'3ŸÂrH%×~—Ö$ìåÇjÏ]ÀGé鴯 +(B#1¬+ÆܶÀ +ŒZ¢å1èï–x“é”Ò™¶SÊÃóòë¾í®û¸ÚNHUkb4ó¤2]&U;’jË#ãqRBÌñÊëöŒ¨ŠhøÆì¹pQËÜØx‹ç š¢Ô”hË/пyL¤|dÃÙÁþЈ”>Q«Ë·åHÐEƒµ‡¨z +Hqlå}<(|0ìÁ屨x´ä»åÐ:–.°1”ZË{·
S×£2Ðö÷ÀïɆ ö¢’¥Á ŒfÕe³©ÏÍvõ|sõñŠ‚²Y Ld "KŠúêÍ»,ÙÂ$܇m’{/Z'BÅÑQªäÏ«ßCõ +®9Uí¸$LËb^8R.¤)£„rzéPŽ—UóCÏ’ó¸YF‰Éä,”˜˜;¨ÌŽEÚÛ,Ëáå„J +²Ú³ÐŸb"Ré°…[šŒPŠAñmÅ¥[bÁè´sµ`3%&…pU™‡ šI’Nœ)&šo§9ÀN ¦#bO–BzM•ÍÀ‹œ}
‹ Ýÿ˜õpHú°fc8á€ûé§ +&nbÝüÚ[ í˜0q|‡Å®‰ôCÙ¸¡,¾üx8Ƙ¤±@4Æcb²u—ú$ 6ÛÐûžÍü þQ„ò‡a1§¶cÀcÞrÑ(óða’…÷:™åmÆ
hÀ×)Ú‡Ÿ‰õbéÊ Õèô?/z<¼ a‰ÇG8sy(W)Óþ ùê’Ës¹èò:#–+‚‡…üçs×sׂAV?E@ËñÈü gØ~ùÜIb^â +endstream +endobj +691 0 obj << +/Type /Page +/Contents 692 0 R +/Resources 690 0 R +/MediaBox [0 0 342 504] +/Parent 685 0 R +>> endobj +693 0 obj << +/D [691 0 R /XYZ 9 484.913 null] +>> endobj +690 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R /F27 593 0 R /F24 494 0 R /F7 232 0 R /F11 420 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +697 0 obj << +/Length 2037 +/Filter /FlateDecode +>> +stream +xÚXKs䶾ëWðÈ©x°x@rÚ¤´±\®rb«’rÙ>P ŽDg†THŽdýût£9¢”uOx5~~MžÝg<ûûÕ_o¯>|Ò.‚ycdv»ÏŒf¢0™vžIm³Û]öSþÃ?®ÿvóñÛÍVY“ß~}ýÝ÷¯ó iýÝ'¿¿þöãÆ«üöæ_7·?n~¹ýæÃ'aæ¬ea™ n\µA¢+ eùðIÚ9õV ɤ×ÙVjVI ýÌ¥$ÞRÌ© sÙVÌ™(óqMàè|‘øÓ# ñÀÃ1î ‘]GN>³Ì[.躔´ÌzET<<æúöê¿W.à™È´b…Q™6œÙÂfÕñê§_x¶ƒ³o2δuÙs <fB1å LÙWÿ$³,ÅÒ†ià¡•gÆFÁªÁ ãÊeŠiåJÚZèÖ2«E&+¸žôªÞИÕþBµÝFÚü©iïÁòŠçÏÍø@³ñ¡¦ÉRÔ‡n³…±jF\¾¬ª[ &¥K&yZ“¡¶ˆl³ÕÚæ_×mïzwѼ*[š e¸òÏHò›=í–È ã=SB€gq°PAŒï‚¬$ñîè½ÉÇò?ù@ËÓ#á Ý©E‚‘ÖݞƺûûõçzÁ Ÿ ó–k¯]ëR)šY%³ÕWðT!ÑQºfŒb7 ÎØ”Z Ëa 5Hn˜äx×Ì©š¶êërO.<h%X"œÓ³aoöìÕ +á˜Ö1†Âãl‘´`ÂóÜùyNbüU‚(Š¹ž`•ôd&V%
ÃË0ÖGšÓ‘™éÎå»ðHÜ¥ +³CoÛ¥kËqM,½Ðçç +<žV÷t²¸£,ËÅaÄ0è"ÉP·»xÜaô ¥m¡æü{ãDÞ7#> À«W$ª{ìëa ‚OìÃ-2™v"ë0oÚxâйÅ/ŽëÕ² +endstream +endobj +696 0 obj << +/Type /Page +/Contents 697 0 R +/Resources 695 0 R +/MediaBox [0 0 342 504] +/Parent 685 0 R +>> endobj +698 0 obj << +/D [696 0 R /XYZ 9 484.913 null] +>> endobj +695 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F27 593 0 R /F21 427 0 R /F19 213 0 R /F24 494 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +701 0 obj << +/Length 864 +/Filter /FlateDecode +>> +stream +xÚuUË®Û6Ý߯ЮP+"õä2r‹[¤EŠ4X‰¶‰H”AÒvó÷áP7v£®† ÎœyªÌŽY™ýüôÓþéÍsÝgœ²iD¶?d\ôE%š¬îe!ê.ÛÙ'öáÝû·¹¬ÙþåãËþüóþ—7ϼyx&E![ VヺEÐS™üd;!뢫šlWµEÙKB½×!߉¦c³&©Æ1 PôìÏ’×VM¤szVî —Ã ®c‡‹ Õ¬m.:V¼Uáât‘ïj.Øþ”\øË°CnÙŽwEÓHuQ×
1´÷𠪢” âá9ïSN +½|Ýýªþ¹áIO ¹×îìtP9gÁ,öјžôÜ2«£ÕÁ ‘G™´Ä@
ô¬ê%S!I£ñAÙAÓÍi™‚ éfâ“žO‘7€=}û"žÃ2{$Õ°D²WæÆ-áW5&À¡K ¯èP3»„d¢™ÓŠû>A=éŒEÎT«—KRS”+6yR$ ÌÝ&%Š½n8ôESÚ%àE¤¼_sѳeºÆQ,a_Ë2ëÑ(÷•´x¹Ì`‡:VôTnP„˜Ç3¥Ž¾fƒÖoúûÄ"dÏ&…<nt‰] +òèe;( [R4ìí0,nŒ|–$c§Ê Ò½·äô&®›ù1DÛôGÈd×}륶£$·qbPÜõÜn&œè½ãáJ½½Ä «íø É œÌñ„Ñ®–§84 >™S_¢ ÿ@¸Y{ }qÉΓÒ1Úær³o@ýOÓÁi:øÃt R”l9<ÐqûíF"ï,urÍM×ÇŽB±q/™ÿ—ªŽê†à”õ³ñžÊßÈ +6’ñ"‡r³°–ιèêÄFti1¡ê +endstream +endobj +700 0 obj << +/Type /Page +/Contents 701 0 R +/Resources 699 0 R +/MediaBox [0 0 342 504] +/Parent 685 0 R +/Annots [ 694 0 R ] +>> endobj +694 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [104.114 305.379 142.156 317.999] +/Subtype /Link +/A << /S /GoTo /D (section*.77) >> +>> endobj +702 0 obj << +/D [700 0 R /XYZ 9 484.913 null] +>> endobj +699 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +706 0 obj << +/Length 1548 +/Filter /FlateDecode +>> +stream +xÚuWK“›F¾ûW航,›á”ÚØr¢”_µQ9vÅ9Ì"S…@aÀ»ë_Ÿ¯§„d|¢§ 3ßôkou\y«ß_xöûÛþÅ/o"±ò#7Œ’`µ/W~ »ÂKWQ º~,VûÃê çó§ÝúßýŸ¬ë»Y Ý +7 +lK@—ƒ5¡|q©Ð²Ö-S7»³Þ0¾7¡…<DÝiVxàû¨æ8. ;˸†Z"óƒi{š@Høá%-<gÇÂYš3£Bí5z¬¾eªçN2N½Œç‡ ô"!}¨ Í‹Á~û–¿gT¯¢#
Ó¤;™|õü°0Qf¥ÖÜê0ä¦>Á2õ87©Õ±âŠZ„%sVÆa2|K“æDñN pvôdÎÁõÒi„&Ž(# mt"îŠz¨
B¬egÛ‡^ªf´VÍR™IÓÞ¨Cçnß ¹¥¡##|uÁôI¢ñt`…°80×v¶ìÊCXª^”èÄÆ °© /ö>Å>üi Š†ùV–aãhJ9§yƒ[7ܵ‰,™ìAŽvò±b’;%oV"ÑLYÚÃ@õU«M5ú— +!O-1¾™‡éÒãÇÊSyFõ^©ØÚÕŠKôÖjÚÌU‚]Ådg’“›–œåôFÛ–'8ž
ÓÜEÅEhÃhv]-f“ð˜×_½Ø“6]'i°|/ò3Îሦ ò¡7& +j~<Ø ñø=‹ÆQ…<˜‡˜y;ö¸Æ:O³`¹#qÅâ&¥C|ØšÅæ
ÄEÿ҂ɵDÚ +D—; +endstream +endobj +705 0 obj << +/Type /Page +/Contents 706 0 R +/Resources 704 0 R +/MediaBox [0 0 342 504] +/Parent 685 0 R +>> endobj +707 0 obj << +/D [705 0 R /XYZ 9 484.913 null] +>> endobj +349 0 obj << +/D [705 0 R /XYZ 9 465.114 null] +>> endobj +90 0 obj << +/D [705 0 R /XYZ 9 465.114 null] +>> endobj +708 0 obj << +/D [705 0 R /XYZ 9 441.319 null] +>> endobj +709 0 obj << +/D [705 0 R /XYZ 9 404.707 null] +>> endobj +704 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +712 0 obj << +/Length 1827 +/Filter /FlateDecode +>> +stream +xÚuXIÛ6¾ûWè¨ÆŠDQÛ1’tŠôÐÖ(P¤9p$Ú&¢e*J™™¢?¾o!eÙÕ\¬Gò‘|Ë÷:NA |Þ}8ìÞ}’e$Q•e"8 ƒD”Q*²@–U$d šàkøÛÇ/ïï* þx8üy÷íðó»OIvµQ•Wp*m%2íbwO°O‰J‘GqY1רUk¦;Q„¯wûT”átÖŽjM+~r!†QO¦V-O<Ýíáw°Ö<8ÈÜ%¡¶¸T…ÓÀ,v®ñü3TÏ_ý2é ç§{”dÜ'2’2c¹¦³‚»E^…ýÀß…H‘G$È«§ñPG¹]ÿeø‹zyÆ[tÛò‚ê&¾€" +*…*v»*Ú8U ç;Wy IŒ«N ˜ZP„¦H]uqk\w€ ÊVýæíy +£É‹DƒpÎë¹]zZå<°\LÍEƒ®ïCèž8¿¤°ØÉ _ΫŽ¶Ì7Ó6,×@ ÒV‰ðäbGäÝ*
U]3W žàTI…ÇŒLöjšGHÒû<•á'ôÊàV¬!â>Ò»g|˜ê¸(oU¯#·FCïº-kN®[‚šÉi×µ]Z{*,DãýM«¶Î$n“úöó Ðö[ø´“™æ‰k w^Lxpðˆ™Z!ìÚ4ä9«FÃu8¾´ +› ^ó¨Çe¬Â€ã̼À]fÞÊLÏ=£êOÜÎÆÐRŽ\ð²Ø·´ñR +&ü®—ã7" úhN±–RãÐkß²¦7—ÒC & ¹¶Žä2ó[ÀW€ +2¿ÙÔÔ" ¥X%xx)£·þV àC S%~$Õ>ò¶p%®y……Ë Âw¢Â§ÆÑ/¯^8l¸Ç`'Al þ¶Ó¨Ý~.*tÒËæcàæMˆ+ÂϳiÐG¢H–†
é'ˆ‘ÖÑ:´ÍóóÖ®°T¢@…`m`ý‡ÑÏ÷È#Ÿ"žz 1ËúѲ~ˆ<ìþÞ%@ÆATAÎÍgÝí¾~‹ƒfA‘(Êà™x:ˆ·*Ê` mðûîWþÇ r\Œ?èrE$á-‘UQ!ªëÀ̓*ªr‘#˜¦€Ç”'VtE§áICç‡*g±tõnŸ`=KÐ@8‹ +#« JìýJ^Ã9Ìß–ñ/œlÍwê^ZÇÄQÏ”fÖ%2Û¥u¨ ÿì9×°ŒKJ]›¦\¥Ó5‚pU,7ÒgMux¦á¤]¾NÓË£èÓHU¢”#ÃW€èÊe·_pá‚âº: +endstream +endobj +711 0 obj << +/Type /Page +/Contents 712 0 R +/Resources 710 0 R +/MediaBox [0 0 342 504] +/Parent 714 0 R +>> endobj +713 0 obj << +/D [711 0 R /XYZ 9 484.913 null] +>> endobj +710 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +719 0 obj << +/Length 2054 +/Filter /FlateDecode +>> +stream +xÚ•XY“ܶ~ß_ÁGN•‡ÆÅëÑNœM”Ø‘¦|”ìŠÄîÀá#ÔzýëÓ0—(¹òÄF£ t7¿þ Hž‘|w÷íîîëW¦J¤Ìê<WÉî1ÉM&‹<1U)S&».y—¾ýáþoß¼Þlu™§»¿ßÿfS›ô ÿŠŸoî_³©uº{øña÷Ëæ·Ý?¾~%óË¥UQfRÕ°3jj4ºÁ—d«¥ÊTm@(2QÕlõ¼QeÚL°‡¬ÓyoYøUHã§J¤óÈJ7 íìaÏniíÍ[{œ9ÒôÚÉMa…}3ßØ ?»¶·açv ¶è.¸º•&3&g÷¦ÙÍËì†'XÔTüº2uj{Û‚'«í ¼©õÎeeÖ°2»Ý´³72 X%;ç-šýøxåOÁþ F¶Ð`áx1a“É~XxsÍo󌑃†ßü +¹i€ùæ0.ì ù=ôŠrÇKŸ2£t¦‹™y[¤ïáy‰*Ò£ ÃwðhÔô¨.éSâtºÄÌy;M¸!J•WˆRU&ë:‘5 +š6™Ö¡,ÔJ”¥È*‰Žé¬ªå—¢”`©äu”×n©RfÚ$ºVYƒlW Ë3¡«Dg&7ŽÝ欀y
î—¦ÙfkDîöˆÑ‰?5W'c Ah à®2£¤®*‘ªòôyïZ|qC“rE›tgžÿ 6X J‘1š÷½eíû
ñ…å†ðýÂï…ºeyšƒk›8õx†]WŠnZŽÇÞUTìÆOps`é|pó>ª©â@bŠYúÆó¸oБg „B«ªsAã:±Âp´¸âÍ{¦Ú\XŸÄ–Û¡6`W`êÉ[òEa=ÚÖM¼ØDê +ñ7-ýå‰äDòôqôv ûŽW8sÆÅjáaµç¼½;öÌ3 M<r€ +8" üx˨ä†H»õ}æÙ Žs8” +ì) ô¹áÙðc°OX’O aRȘ¿µXøáÍýYàBÅôÖMiƒ.ÞWV ;bÅ+WØÌwÀN*ÇÓÏ<c œqÐá¡¥h‰pL‡cx†³4¤¤ ±1¢Îc½µŽ"¾´
Ùé*èUžÂ ? +æ€'Od(ÂýY`f±ƒøŒÏ ÿŽù£©iZÜ|D¸.¶«H™þ yã¦ð¾ß¾†rbúç>,øÄæ{î±0A9@UÃ㓧Ûs<Ƴr“RpW©L/\ÿ\»ˆàÅGžLðh
× @²¢(>‰ Y^júï@mMêÓOúÆ/¬ëF~r¯ +endstream +endobj +718 0 obj << +/Type /Page +/Contents 719 0 R +/Resources 717 0 R +/MediaBox [0 0 342 504] +/Parent 714 0 R +/Annots [ 715 0 R 716 0 R ] +>> endobj +715 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [115.879 292.481 180.651 305.1] +/Subtype /Link +/A << /S /GoTo /D (section*.58) >> +>> endobj +716 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [138.96 191.36 190.109 203.979] +/Subtype /Link +/A << /S /GoTo /D (section*.34) >> +>> endobj +720 0 obj << +/D [718 0 R /XYZ 9 484.913 null] +>> endobj +717 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F27 593 0 R /F24 494 0 R /F21 427 0 R /F19 213 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +724 0 obj << +/Length 2038 +/Filter /FlateDecode +>> +stream +xÚX[¯Û6~ϯ0ú²23"%êÒ·HŠÓ +l‹Í>ðØ´-D–\‰Nr‚þøåËÑiè>‘ ÉáÌ72]ìéâûWß_½yŸW UmY¬w m*•»È«Z™¼\¬·‹'ÿ|÷ÓÛe'ë‡ß ÖÿZþgýÛ÷ÚÞ,«ª‹v¥6E¦W©œ³XeÚ(SçÐ)TZÕÌ5>Á Ç%‹¤ï<w>¤¼úÍ{£¯(S•§6žð㬩ªtY`#Í[núaðãi¹2%œ³mº=ÓCÏãæä†ÐlÎx<D¨~Çí±MßáÙ‹U¥•1Ùb¥s•ç–Ïlð6•NN‡%œõ46׶OL;wÍïg¯–«"M“õYM’ÛÀ,Ÿq•“=šGÁ§Á¿}yãG"‘P©ˆS°8ƒß»î;£PkT^®P«t9Y•+lâ· 9õòäsõì7ÂÅJ¶¬d›€üUò„<UÒ‡ƒ_ê$àexöCš <“¦‹R…½½ÚxrR¦’_ºå*Oa#Ø:)m<0íàºíkèê:1mÓ¯zT ™ù#g´dŠJYSÞ© <¤Tu™ê+Øå*Ë*æJç”Y* ê^]± {´Ü'±ÏTR¨:Ó÷6l]h>!§G‹À ètFÔ¶Öá!¹Òõä!7?øiSh3€ÙŒ D ŽÈ +Ф±¸õ†}…œcy«t©³Ûû‘ÑLVL¶Wh“"Y/a«ž§y‹ÉÊˉY!ð¸×‚ÎÊÿf¯úOìeUa ÛKØÜÞ5 bžeò,Ò³| ›~ÐY ©«íÐìÂ7|]huäkûìmö‚um¡liÿ÷2ª¬íͽ$RÂÑDd6s;CÝ2îŒ|Ç>òlúã ZðaR@k nóy”=ÍÇÁ@ªtU݆Í+ Öàç“Äê‘€$Æf úV(·jž98”Zièþ}ÿ½Ò›°!RM–ü†fÈ7QzÁ¾û~ýi%ÜH4@ Nˆ®rUÞÃá7 Á<OúóžÂ¾ ];bLÍ%¶erY$‚ÕÎG2ÌÜ¡ (!®=ÁCÚ;¼Æ>„Èn;—Gv=¢›3¥ÀÜö˜B‘š£gûü‡TgýF¦cêDò‰#?d®fä¹âÚîÀ¹õ$gO82’Ÿ
% ˆÎ§0ΉF×1,œrPOt5 ú/p–ï62¤,Ž +£!¨ÛúV¢ÜÚZ©h¬ k£Æ¡sì)qB¯ëƒ{lŸóÂ9ÝœF?‹#y +\$¶ 1 ‡©0) +Óu=1W6¦ð +àh´þËÆ{ü,!¥£ ájzLú¬ô‚iG :?÷CëeM´#ø!×àÄ8'ÿyA”½M‘Ê¿—Â-#äB°uÔ…P©½ªãp(æBß©ç °œÛÙ2ÿওåcDb%醛Ö3&ñ+n¬„¨‚¥Ÿ˜2ùî î¾bf¯‰ûg‡9n:¿Ÿ
P×ï˜Ò +dÿÀdY¨ %s KV}búäW-¼ÈÙJ)°^>ÓðI‚u[•%?õ1™~e®ÞDï›ðõ{èG+äB›s|+ñžÄ>ø p ãAzd¤bƒÿ€±X,.…DQò›Nþ‰¦oÕؾ[¿ú/[4¦Š +endstream +endobj +723 0 obj << +/Type /Page +/Contents 724 0 R +/Resources 722 0 R +/MediaBox [0 0 342 504] +/Parent 714 0 R +>> endobj +725 0 obj << +/D [723 0 R /XYZ 9 484.913 null] +>> endobj +722 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +728 0 obj << +/Length 1341 +/Filter /FlateDecode +>> +stream +xÚuWQoÜ6 ~ϯ8ìIô®–-Ÿ}ØSZ$k† Úð¢Ùƒbëb
¶•YòÚüû‘"íø’ËË™")Š¢È¼du¿JV¿]¼;\¼½VåJÊí>ÏÓÕá¸ÊÕVîò•*÷ÛT«C½ú.¾þqõþæòãz“¹8|¸úüe½Wâ?_Ó÷ËÕÇËõ>‡›?oßÖ ~{-ó¥étWleº‡“£Õ\¢ÒE¾¬6™L·é^±Û&åž´B£Ãz£d”AB‰Îëzbºã3áÝz“ÂÅßú‘xƒiu°ÿÓR°Vp϶Ý&YÖR4f ÆÃÀ6ÆÊxRÖè/øº‘j«TNþUà ¨…AWäU¦’èU¦$™Gâ¹Wȳ¬<+Õv0³ÉF¾î\ä“r"tçF:ùÄ« y÷¦ yW.½&9clOëF ˆòãm"w•5´‹˜+²Õ=ÐÎÞë`ˆyt¯LîÙ1àÔldfØœóËôUT+éöxˆí˜Óºøijbé)nðCÏ·…§€Û¿_ô`½c+?lhØ^Ãæjë«Ñ{¼õGlÏÉ—¬äjÀ Dâ ¤áwH¿R|…\˜ ÖÝDOnNS–t} ü[<iSÒ"¥[áÛâ8¸n’bù ûšbê,?fÄç[jq6žnÀd’;Ú_NuÐËBc=QÞµ#ßi±B'±0Ž¯·«ÆviàÒÚOÚ¬:Øûfòõð8g\|7F…TбSQ +cáÀÖÿ3‘yºc¼o´sLzG_?V˜úͤHöÔ¬¨ißÌ”ç +¬n[6}Ô\>Wã€O]ÿB’Û$OÆÞþ; ä9+·qx£Xï*UÂ?ú`:¢#ˆ¦9ÃZUiO°Œ¢†õ9úO`ÊÐ ·Iq$rV0ܼ ¶6`0-÷ê
î¯#¢ É!LK€*Ý¡ŽP”·ԃ=†h±á@R ±ï‘æ't°<óŒá§€Ril…j¼Œ)PÀÅMçz0 q6`Ú”¹ø@ï^L…ÊsK +endstream +endobj +727 0 obj << +/Type /Page +/Contents 728 0 R +/Resources 726 0 R +/MediaBox [0 0 342 504] +/Parent 714 0 R +/Annots [ 721 0 R ] +>> endobj +721 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [22.153 392.054 83.155 404.674] +/Subtype /Link +/A << /S /GoTo /D (section*.55) >> +>> endobj +729 0 obj << +/D [727 0 R /XYZ 9 484.913 null] +>> endobj +726 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +732 0 obj << +/Length 1893 +/Filter /FlateDecode +>> +stream +xÚµX_sÜ6ϧØñKµ3‘*R¤(MŸÒ»¤ã¶I:µÛ»™Ë=0+Úˉþx$]çÓ HYÚ•»™æîeI‚ +vîöä _ßZ, ±’Až;¨œñ¨×D™=òI¬û X|ì-f"ùø|’k„lO¿ÏƒuuA´ +‘¾já_a¤üÚbL%¤¿ Q?éSF$ð®¸ÇÁG…ÈæÝ¥º"4[Ä?¥•3x +ólª ÇõŒÊùô1رEh«¡ö+!áÊâæoGHNÍ FIK£o3`Ç…5u=t~F{'ÍÊwþ Û¨žFÏ$ò"¦ŸWNé}š 46º
ý³_l¾R@Ð9@c{A,ËäAÐ][÷‘âLF5#µÑøöî±£ÿ´…—©¡g +=LN@chËp¾#ø/¥ïªòˆ^dž¿+ä§ÆJž- ¸(çñ¦Èg +±l3ãz¦+Q§Í3E¦ø¢²OœéÊ/,2ÿÚT‘ ?¹6zYgµA)•çsm +÷÷Ì`+ +¡–3€ZªúĬˆË¢½ÆÅýŒ‚ÿé96ŸJMKK½£+øºã‚ç0Œ]ãJ •„Àˆÿ~™[ݲê4*Ñ”oÉó2ôÖ@ñHŽSíIš†Pÿ äPQÓ_Í&Á;bY@(d %_0½¾~ñ'K覇 +endstream +endobj +731 0 obj << +/Type /Page +/Contents 732 0 R +/Resources 730 0 R +/MediaBox [0 0 342 504] +/Parent 714 0 R +>> endobj +733 0 obj << +/D [731 0 R /XYZ 9 484.913 null] +>> endobj +350 0 obj << +/D [731 0 R /XYZ 9 465.114 null] +>> endobj +94 0 obj << +/D [731 0 R /XYZ 9 465.114 null] +>> endobj +734 0 obj << +/D [731 0 R /XYZ 9 441.319 null] +>> endobj +735 0 obj << +/D [731 0 R /XYZ 9 419.153 null] +>> endobj +730 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +739 0 obj << +/Length 1913 +/Filter /FlateDecode +>> +stream +xÚXÝÛ6ß¿Bè“ ÄªH‘"Uà ÒCÒË5E¿Œ Š¦h%íZ¨mm%y·¹¿þ~Ã!eÉQ6yè‹E“ÃùüÍpÈ4ºÒè››¯w7_¾V6")´–Ñî.Ò*¹Ž”-©L´«£ßâŸxõÏ7/ßn¶™Ññî_¯¾ÿiS¨øWþÿýkþþôêíËM‘Å»7¿¼Ùýºù}÷ï/_ =g-s“Y@²ãª3"ºI½.Ñ62‘… OR[0UÕ6ÒÄc‹Ïç#¤©<núê¸>7<;ÿÝ7LqWVc˜*ýLÜ÷aO<ßm5¼ÀŒNãÛÍ3Í]×7W|ʈëG¢oXÒo…J”Ò¬ewGÄæ² ƒ®Ï“a±oåØ>¶`8:ù+b' í±aª‡CÉ‹$±:¸¥º}—Š¬éƒ"¼vªyõèu70s»P2g%ëæ<Õ¹ŒûÿnT‘ÆÝ¡!eL—/TÝñ¡ìø÷ÔŽ{ o%¦†‡²jí¶ëëöTŽÍl¶Z‰øçXhWÓr +n.˜àÛ7åЬ FOÎL±/ Ó ÎÆMã·µÓöiÇmë¹8Ðä + —¡j\J.Z@ŒÌØÊL'Úš¥5Îz8VJ#-ÝÞnhÇ–`@kݴ批ºžôÄäØ]6ñÜlÏð~›ã´a%¯á«‹ø?+e6 ?`…‰=ôÍ0pvX<€gb„hä©æÏsÉÊÑ<£ WBüMyhMK¨Ë +x Zx^_eÜVš»UE¢çw¨®ÐøFŸkƒõ¼2fªpe¶óC.VÍÊŒ›wM¯:èbÖ&W~‘kFdi†²bÿŽ³À¥i~bú6—+²ôCÆ¡Õhæ÷‹çB»âT|ù®|'‹cµÔ¤È®ÉšoW¬!˜ûIs J‡Z˜SóÉÛ ¬À©YËÐoß7§Æ —4ù¸q[;ì_ø(ØÇÇF]ýO{×Á›Ð@™) ]3 ¨PTýŠg{Ô59ÉRs©C¤~Ìù `Ô7w^!oSša>h××˃¾œß®©’¢È‰w熖½kO•ÐñçÞµ¹kmÜM =Ó0–Ðé ^à¶$'¼Ù o4qmšÌµ7Vxãö
’ý,Û.©}Þ6•ä2P@Ôùàœ+| /ÙCÁŸ›Có.V"ÄJL±óXYŽ•p D]ÿY±É¢bÚå-à£ËŠ¿#$N´e•p±Lã¯ÏH'©ýµ•0½š•H×hjßÖjמþpͬ«$à í ÝÓ¾h~Ïd®á¥‹,ýὸ" ý=«wÎ"œ +±vCWá2kÖ<®½ÏÝÃqö á¯Ùó]—·°(ø-„}Õ)g*[ÔRYé6-±·9úðž:Ú 9á^ ¬ïáG!›‡× þƒÖ=™`ˆÃžîânÏÉïÙ:~@²¾•%IoßTݽKHwõéîùB‰Ü_B¡Üt«™®4´Ì‰ëoë¿$ØÙKO»+íœÛǯŽÔ^ž›\öÿjiœ¥Š,¦L!ÊcGWUÑ…ÖÇÆ9 1ÂNㇾó‰Ôm3x–îâ€ã–kzaç ®¯øQ+õúáê¶o <PºÓ7TŽÐæâ6ZùàÁe‚×üM1|ÑUý ¸(A½ +endstream +endobj +738 0 obj << +/Type /Page +/Contents 739 0 R +/Resources 737 0 R +/MediaBox [0 0 342 504] +/Parent 714 0 R +>> endobj +740 0 obj << +/D [738 0 R /XYZ 9 484.913 null] +>> endobj +737 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F25 463 0 R /F24 494 0 R /F19 213 0 R /F27 593 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +744 0 obj << +/Length 1638 +/Filter /FlateDecode +>> +stream +xÚWÛŽÛ6}߯Ð[e «ˆ"u{L‹¤Ø¢ÚÔmQlR€+Ѷ°²äè’Íþ}ÏÌP^;Pƒ¾XÃápf8—Ãq ìƒ8øñæûíÍëw¦”ŠÊ4M‚í.PIé$
LQF‰Éƒm ܇ïßþüfSšp{÷çÝöïÍÇíO¯ß©ôêX™DeVB+ H
ÝÄÞNp«U%¥‘EqQŠÔÛ¹j›ÚÙns«Mî]tÓÐT¶%FŽ'[¹È›+ƒ<*óX±5“G¹Ö‰´öºÔªW1Ä’àöBî®ÝýP»AìN½°öÍçM’‡N¸õì„}úcÓ¹®rd"¸Ui™,a"cRQK:’¬ §C3U„ƒkíÔôÝxhN¯À*âðГþ'6SEèÞQÄ+È0©8Òþ<N‹šS‹(,Úpçq¦ 1¯9zfÕß²‡±w-×pÓ¦³““ +ÊHã—µž¸XÞno>Ý(XŠ$8‘%y`´ŽŠ2ªãÍýÇ8¨±‰ F&/‚'=*TJçÚà÷›ß¤¦¯Mž•%&J2_Ó â8^»/ʾ,–ûªµd‘Òj‘€µY ¥å9°ÕjdÑqœ,2(³Â—#_T6œ^Ä’ ‹¢<ER~ "’¥ùuŽÿ踚“<¥UßÕÍ„¼Pr¥e¾„r¢$æ@²µ\™£¬Fî¸{nº½W ¯³vGÛÕãj¡í RÞˆqr)W5¶ÅZEú¥`°\NJÏ|†Ï¾ÌÀ³ã8s…—9 + ñ#A»»~8âj+Þ4(O“–áÓ¡©HÝA–ì Ü7D¡oÎ=ÂŒ“„ãy”¥ûb«©}þêüh—óÃ?SÆaßÒ:‹áñš?|Pgt÷Áy’ŽÈüÒ‰1ÚܦÐónS$¨†£ma ê¼XLçwý<ÅÇP¯áÊQU? Χ…sÊ¼Ü „J{W‰á]¹¸ +òÒUáP¬éà ¯ÀÃû3Ý +74ª ïäp¥ ÈÃê*•Ñ‹ªuvÒ <w²âÆÈ—jÑõÝíK4v‘;Øiµ@,U{¢CKŸ„šetŸfÆyfpQ&ztpN3 +ôY¸;NŒðm6CÉJ:V‡œb<v‚û«÷îÕ×F’I_P6 ïg€¥Êoï- ¢ZhLçÆQ¤9`w½|ò¬b爲pv„ï‚ *Ò´¼v`ëk*U¤HáF÷±„tx$Ci V¬Ü‹çl¹ [yYÁì;.-p0>oRÚý¼<¥+®t½„RÍ)ÐÆxå`4Ç3FÂ
“ç£è„B™?4óısy¶ˆþ¥é i)9 ªE +¦¯‡Pbì]çBiqN hö’Ô‘×æÛ8.½Lz‰O^œÝÍ]m9wr!ØYC9\œ£”Ô9 ZÓú…£ }‰hß1Dìú¶íiòxb¨'ÖÉî =ÚÄ2¨ôs럤-‡ƒ…S'oôÀHé aé{jj #ÕeR”áΰ?½Ù ÕL£ì·=¿:`UmOPGéI®ÒVpÚ¾EL¼ ½ ¯¦îç‡iu j¥eÒXù!VY5ã:í$,N +¾¶ª¼˜T$^G¦ŸÙ\焇vü²ôiCÐQŸ›ˆ÷_ðhý‘zàÚÂ76]åA½ñ,º +}»~’ΑS–‹,“É€ØW)à +ÂZÄéec?XzˆËæG©Y}4.£+×¢¯ ž‰d´Ãw¦ dDWÖž/C€òuìäs ‹.©\V·“¯k–Òó+» 'ˆ"_è/ï€zéJÏå®$šÍäêë)ÏÏFIx'rã/®ˆÚIX'¼œn b +endstream +endobj +743 0 obj << +/Type /Page +/Contents 744 0 R +/Resources 742 0 R +/MediaBox [0 0 342 504] +/Parent 746 0 R +/Annots [ 741 0 R 736 0 R ] +>> endobj +741 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [283.224 160.921 320.487 173.54] +/Subtype /Link +/A << /S /GoTo /D (section*.77) >> +>> endobj +736 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.822 28.542 281.949 42.49] +/Subtype /Link +/A << /S /GoTo /D (section*.163) >> +>> endobj +745 0 obj << +/D [743 0 R /XYZ 9 484.913 null] +>> endobj +742 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F21 427 0 R /F24 494 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +749 0 obj << +/Length 1459 +/Filter /FlateDecode +>> +stream +xÚ•W_oÛ6ϧ0ö$1'R¤Dí-ëÜÎC™Q¬hö@ÛtÌU–\IŽ×o¿; %Ë©2 /"y$ï~÷ŸŠ'O“xòá*ã¯Ë«ŸßK=á\ÉÉr;á‰d1Ï'R%Œ+=Yn&_¢ûi.£›‡ižDËé,ÉT´€Ã÷ïå ij\) f<Ž™Rùd&R&´$ËßçtóÃünþpsK ~ôl?Óúã{ æ·7(s¹ø´X~>K‘,‘©—¹bZë giœ“¿>u¸f‰x
Lå* StñÏûù»Eêæî·¨÷‹»w‹ûÛy¸OrÎ2 L%“2%^£Øã!vÀ3™'€A0žfÁB;K‡¹NÀ±wùC+Ó˜b:“"Žµ+×îPØkXKvn=Y´£íÎMƒ µÀ›.¹g¤W--«-í›"0Ž5Qµ}vÕ”GÇÆ+: 8.T]Weã6¶6ƒâÈù@°Ò^°W*M†JqÆZ5‡©Š#‹ŸµýÆ̃ײîB¯;Iñj¨<ªmP +oF6H\!Ãì†H&È2 m|‰3” +Çd2p|¬£Û kòîy¸P7(BaâŠQ2Ó‘SÏJF;ƒ‹çi€”mm¿ -™ð +QÅ£'Z +³;®¤{gÞUQTìämî÷üÒWà1{a6cð`(„Û åšU ª<.M—›öÖjƒiç×ÿ€+ÝcÌ¥YöÖwý‰,ÇÈ5N¢ cU Épêˆ+5)ÓYØðKa_ )Äðlð)Í9ë}G+ׄ±¤±3;Îû€ö1‡ Z?vÌ^Ę˜]ʇçKÓ7hÛ—×Õ¸¶ð€x‹¶cþ£Þé¸ÞÙ+z§½Y([šéôRÇÆ£Œ_ÕUÀ+M¾Ñ³ž!8L~´=>Ò +ÿ#š f|«¡/…*€LuÔØšìÕжiÎçCaŽyz™p!Éüwƒ™“†® +w7¶µë– +=,«:Œýv³®Ýªß§J “€v¤^R#¥§cAù¸ MŽ€f¨övÂõð=„äý ÌU;ÿøɲÐ,5Ô3ôöž½ôŠ?GÉ0Úõà 8; Ù!³ôÜ÷´N£›†vMQ[ƒüü‰à88æUQ ;¡ GiL!ªŠí ›púz Àêˆ-rÒ…ñÜÜqUVaBj!B,‚U¹¥öˆ['‡u g¤BÏd¶ÞÑ•=>êþþþPÁîl9CÕœ iö2Xd ¼C ßžaû~û( `cè¹”#žyñ\Õ"ºþ C =ÉãÄ §ÜþÕðŠó )ü^ÚYxPRùâÒ¸@ë: % ÈÎA щðD!/Ê?Wö2ƒG{Ê2 ÂY©‹CóåÕ«Ü. +endstream +endobj +748 0 obj << +/Type /Page +/Contents 749 0 R +/Resources 747 0 R +/MediaBox [0 0 342 504] +/Parent 746 0 R +>> endobj +750 0 obj << +/D [748 0 R /XYZ 9 484.913 null] +>> endobj +703 0 obj << +/D [748 0 R /XYZ 9 465.114 null] +>> endobj +98 0 obj << +/D [748 0 R /XYZ 9 465.114 null] +>> endobj +751 0 obj << +/D [748 0 R /XYZ 9 441.319 null] +>> endobj +752 0 obj << +/D [748 0 R /XYZ 9 419.153 null] +>> endobj +351 0 obj << +/D [748 0 R /XYZ 9 407.197 null] +>> endobj +102 0 obj << +/D [748 0 R /XYZ 9 407.197 null] +>> endobj +753 0 obj << +/D [748 0 R /XYZ 9 377.426 null] +>> endobj +754 0 obj << +/D [748 0 R /XYZ 9 340.813 null] +>> endobj +747 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +757 0 obj << +/Length 1963 +/Filter /FlateDecode +>> +stream +xÚXMÛ6¾çW9É@ÌŠ)‰í©š"í ¼@±mQ´=p%z-¬,9’¼›ý÷R–72Ú +¥‹Í]½ù#ùùûÿ}»µ:¹ûð뇻߷ÝýøÕ{i®–Y%lnaWZ`rœô&
çlvÊjQdf³Ër‘––gÝ üv—™<9
MW5§6tŸ·ªH¨]$‡L öŸfaž ] †Ïcõ{þvý]ûÂsŽ®é¶ªL&øŽ,šnB
7;Yc,|µÐÚ°^óù:…ÅØyáŽe>ž]Û†>Ol[îUØ;ôÛ |ú1¬Ÿ¡Q¹ahÜCèõëaÄÕ÷®ƒ# ¾ÃÞÄCn$UÓ dÎJögØB-ƒßûÁw•ßÝóÑô[¿ðè¾Óè$lÔ~¬†æ45}Ǽ:üº.˜Š ÿ„W6ë¢?S“.¶kÆwx’L¦`ò»55¼qY$£o÷;ÿÔÔž}›I±ÝéL%ÿGKpÎÐ Ü„Þ÷aÔ£ ¦°Ý3:Zû¾m{Üòyü÷“É„‚œa´¢XA×}nÝD÷_FG”ɃïüàZî´äýç‘{„1øvn:aºçõ/A‡ú{Dœ¯¹· úãš.þÓ‰®Ï
:î4Syr Q§íM÷€íˆwEx¿Š0¥…µ_²p¼5:Œƒ5Ï–Áª6B¨ºµpÎEYÌ3ÐUׇý±Ó±‹Þa½fø>‚l_Uð
Æ7qZªäÝ«t!S‘ç_`Mu½_·FÊ/²fpMKèq¬.¬ùg«$[E)OKŒa% +¡”Œözñ Ö.EIQäq£ÿæ±GϹÍuM‡†?m)l)¯1ÍÛ•yÜ;†wá<zú“{pœ‰Pg´ÍòĪ}¥òb äöNMòäªs¿f¨†Ê£²+÷Ó!‡XVÊ$èã?¹j¢Ü ´$ •²¢ÔúÚÂÑ éÆ2Î%ÐR¤ J +€Z<AQª¹÷Ü0¡Åq ç›"K~éÚæ1òŸå¤?S©‡qBO–•”gâÓ„¼hàî8AIÝ]A3°ªEU +<¢ šU0C]IgïÓsˆÛ‰!‹ðü¨PճƱŠƒbœ“BZ + A+iÉ,¬<ɸ¤X%y÷—ÕãØ[–¹®ü +o•“·‘¢Õ‘Ä
ÍÓÖèÄÝ·ëéÆ.£Âæ`©V’9ñÊ5×—z†<20• µÖ®Ò +‚ª ()@ ;ð4Ëæ‚¢|óŠEv¼„æS9Û\÷0í ÃÒ— ’&˜KñDÒšçÈÓ‘3Òùi1Ј™Ù?®»®(¹Ÿ92…¿GïØÑixk0fOÔ·_qÂY ÏèK =ÏBæw¯ eáõtÁ/r8s5mÉV_XÑ«Ü ïŒ¹µdhí2ÀÖS*V³¬Ç¸+Ä +j)L®Vbsó’¸9-¦l·ç/W™–;cÚ™+‡‚MÏ”Wð4BN¥SËÎt!ñ û! BûÂp¬=Ÿ½b•eâm ÈÐ Uñ ¨üÂz|3Ø"æF–žZG4^Ë –pdÆa¢< Hß<;ÆiwÃ'ÅnM©ñ|Œ¶Òò 6´<š…Mÿ©1ÆÄ“cÑM~ºâkU¤¼0«U?á,|Ñ{Ï·×
©É¾ÎŒÈ³WaJÀ³üàmJ¾ð ÏL5¹ÇVrËsã×6o\X@À ,aŸPæ ¡i"˜2 +
fˆµÇê„OH¸¼o1Û‰5ÿ-GùýÄrJh „ÏZnSjÆÁñ pÈ«&”;þ˜›xâàý%«Ô, 0À}Úvzö8ŽZÜw¤0 #¦²†C"Äqwœà}ƒ›‹1H܈m©’ßøÞ@HÈYEbÈR?ýŽ2+¬”ÿ”3Œ4 Rž.ýšÞÆmàï!váÉÜ#pÁðüTŠYÀWJovLRùµi3×ÊpÞP€ÉæHJ,e © x +`¸»BÙä; jœDo˜äê $]¿,œ$Õ_tè +…öý<»£” È«ÔS{ƒV¯i¤Ð©ýOpšæWx<ôç– ¯Ï ˆŽ‡&þßÄ7 ¥Œ:’ˆ@lTdžÐ‚Š>Òÿ%ÆÆèSü?Ìòy ¿ßß½ùDç]Æ +endstream +endobj +756 0 obj << +/Type /Page +/Contents 757 0 R +/Resources 755 0 R +/MediaBox [0 0 342 504] +/Parent 746 0 R +>> endobj +758 0 obj << +/D [756 0 R /XYZ 9 484.913 null] +>> endobj +755 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +761 0 obj << +/Length 1948 +/Filter /FlateDecode +>> +stream +xÚ…XK“Û6¾ûW¨öDU_›“S5v¼ëlª¼ªT¥â 0FBL‘Z€œYÿûí@QcŽ÷" +™ÞdA—Í.2•‚I™fuÃ\þ4LÝŽ(eò°ÝÉ*1¸‰ù¯nÇî+1ÿ™ìÓ¶(Ý™~ L#3+"ÅRQ©Êò¨È?×”E*Ô¬ëãàø ñ´¬DâÏš:=Ú¡ç‡GþØëqÚ¡àÍNÔYZ(¸—P©RKtºÆL%FÏþ—Mrq®ŸìÁ ˜a<é1Î Þ7ƒk:Ã$Ûó¨™îG=†/ ]«Ìo| ë´RM¼×Ô[ºÅ.ϳÄm‹ î?íh;ÛÓT;¾DÜÈ—(y»îAG•I?ô;Ú>ŒÚ}EZ™œ²Êšm¥J 1ÛÿÙ‚UwJ4‰3þÂ>náÊJf¯8°Vi^ªïû/KkQG– AZYBtt|XÒžrP
ð['k<SÙzpmѤeSÜ^Û™GãLߢ¥ÉDaÊÒø@ÂÑ™£vìLäõ<¾×íŒÕ}d +wWu*R'ÝJö'C +e·š@̃ï;{°–#HÅa˜•xQž\œí[{éÂ2~wƒ÷É^÷–É3ÎIQXhï§3‡"Hí»Àà ÁøUÕ^¿Ò ºV$ú8<4‘,'Huž¿~Ίl-’E“§ª¨¢‡MzLWAG¦U>s§ügp
ÞïmdâyØE¿—©hÔí•B–7›¯))í`y°Ÿ3‘ãu#ö +'3 \%}mµLÈgQ¥Eñ[Ð^&-Ø l1:íG¦`š6œÐŒH‰¶Cê³õ§[¾©?@4 Vx(ïkà9…mŸE®Ž¦7Ž
º¬è´0R±4Þ^ëoLdɪ€¨îº|æ0S¦ÏXI8`þ!R‰ä-Á|™1óqß˳5 TUZgÍÿÊ9AîÖ¤i]¾¬–²ØTiSeb!P9e;[ÍÅ´jÊÍnÁQ$úئ8ULuÁ"᪮–U Ù 'pB6Fæƒñ³NPü‚®ÁËðìÒªNE&_¸ôdúálzÈd ŠhÃu½¾ÖuBG>&1Xh‹ø-/ nèr€¬PÊÍÊ6nÍ—g a8¯ÝNNÙd1Õ ®ÆŸ”‡‘KmÊEî'ÄÕ… +ïÍFĹæáL6 ƒ(¡ö¢Â‚fàâ…(Bí©í´ zÏ‹ç“mQÚ),-eh5Û¶…ÐYÓÆ`ÿ6 GÇ -!ç¨æuü·¥>ƒ£{Oœ3‡ ¦6†~5‡~HŽú6#ËÇ®ÉR}Ó à·4¯âa°‚A×ÕEò¸
+¡2¬ñ¡ì_™!G×Qƒ‡¤……óZ5 ¤< +õü]?²¥`2Îz Ë—qz Y + ê^Ƙո xä#¹ÐL.2Ç]~4—™ ó ù ©ó/ø–õ#{µrȸ8¾,ˆ"Á$†Fž’9—rPÁžçÍTÈhr¹èØs`c†4€ÌÑÌÂ~èVªª‡uÑÔ‹˜3Þ¨©Ø,HšŽGCæ¤ÆEôHÉ +Ä\¸ÒªGŠ4µPÉG3ò¦É‡sÏúˆ¯Ÿí†ÉyÓÍ*Øœî=”`‡':J‚>Ç C¾<:kúÈÅuZm;y€Øjç,àÕ
¹H’l CGX¹®#€Gºé€‘T4É„î ¯>\£'È2y$uïmè€dijÎá‘ÏïÈ.´†+©É‘&]MÛN}í–óÐâæW¾h^qÃœó['Ø9ÛjU5ï¶càãŠH(ÔP¬ŽžÕ¡ÏD|ÓÀ# LÄE +\˜#>Åá³á±Õá>b¹ØeX¨:@dÍ/D<!àžƒ4£¨Õ +endstream +endobj +760 0 obj << +/Type /Page +/Contents 761 0 R +/Resources 759 0 R +/MediaBox [0 0 342 504] +/Parent 746 0 R +>> endobj +762 0 obj << +/D [760 0 R /XYZ 9 484.913 null] +>> endobj +759 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F63 238 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +765 0 obj << +/Length 1062 +/Filter /FlateDecode +>> +stream +xÚmVKÛ6¾ï¯ÐQÖŠ ¤% ³@lÑSa(Š h‰¶™¥Iƒ”âæßw ”wêb¿‘3ß<è2;eeöíéeÿôé«è²ª*z)ël̪º+šZf¢ë‹Z´Ù~ÌþÎÿøòûçM/òý럯û¿6ÿìûôµ’ŸõuÑïz8•> =•éžl[÷¢h™m›]Qv=[½ 7[ÑÊ|:kvùÅoª|2ÞñÖ?êe>¨Œ:¥‰læü¦îòo”ÏÊôÈ€qˆLžwŠ?uÞmÑÃl[µ…”=¬¢B²_³3G .hZ‚OèÐóf+Ë6W‘AP£PÁéqRnÐ 6u›ÿdY±Áu³Ì£â†?:@ˆÇÙ²V]¯Ö j ¹ÄÑ29´c‡ˆ€¦ªóCPotJ|F€¨q(5ï6)< óUÁUÍ'6A>Ñ"™6 øDXÿËÎê`4„ÙF±rða»æZÐ1…èFãN£—Í/awp&Ç ªï:¼±,'ègc±ÙvÒž²-k8zRa¤<‚1çeÈüŠ+yÓqÂ/ê¶ÃÌÓJá¢pÑ^Õœ[Æ òY¡æ8bü X…tÕmŸL<ýŽyAmÐòöƒ²‘îñï÷¸·1Šºì ¬ì A›Ê~2¸äØuÅì þ¿` +e©ûE®¹cx(GÆÌtokÚ–r‹gLÈÔ%}SÖXm”cÜ* 2+~ܳرB´@= %º…8€q Ýç˜ ’q¾˜¾H BKê0o¸zקä‡~уš#u1?q¸b?@³Ô}“ž †ZSkCEøTÐÚZp EjøcÍFЈñÞȨù>;Èõ0ÍA¯uUgÓæ§ îíß´4ò›.£Š yCíºCôvž4ï®gzñbjŽy„ôLé D`¹ã{ \ü*UéµmdIu× éºô²á7 +endstream +endobj +764 0 obj << +/Type /Page +/Contents 765 0 R +/Resources 763 0 R +/MediaBox [0 0 342 504] +/Parent 746 0 R +>> endobj +766 0 obj << +/D [764 0 R /XYZ 9 484.913 null] +>> endobj +763 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +769 0 obj << +/Length 1627 +/Filter /FlateDecode +>> +stream +xÚ}WKÛ6¾çW=É@ìêAÉr/ÅMÒ-Ò(Œ6@ÓW¢m6²¤’R¶òãûÍ åµ³JOš‡Ãy+^ ñâí‹8|_í^|ûF•‹D3U¤‹Ý~‘äùºŒ7 •gë$/»zñgôþþýò¯ÝO"›¬·yβ«2Y«¬\¬Òb–Jdw?¾^®²M ½ýín™¤yôûýn¹UÑÝr›E»û_¹{'ü7÷¯ßý j“üFm‘¯³b µé:)6¢öC’©`C|m/¬Í3<†…î÷sú’j&‘Çeº‰ ,(·Qo+Â>ÛÆÑØ U ꇮ5ê¶Öp43`a º—Ë•Š‹èñ¸LËè,ܺ[®è>%Œï^7MÐØ‘ÅxªZÇI¶XáeJb*n#•ytpÝØÖß³\›$ÚMäѺP·^ æ‡Zù èŸÑøÁv`Ö·\å»5‰^™JÞ°-ñd³Ê¶+ÂWƒÓÕ`jA èÚ³Àb0 +dÄQ–"ªø\¦~VPÁ׆Ë1— J2É$&º‹¢åÎœSÀ µåL‘ö ‘'‹À|+:]Ï¥¶!j*y˜“‹ +endstream +endobj +768 0 obj << +/Type /Page +/Contents 769 0 R +/Resources 767 0 R +/MediaBox [0 0 342 504] +/Parent 746 0 R +>> endobj +770 0 obj << +/D [768 0 R /XYZ 9 484.913 null] +>> endobj +352 0 obj << +/D [768 0 R /XYZ 9 465.114 null] +>> endobj +106 0 obj << +/D [768 0 R /XYZ 9 465.114 null] +>> endobj +771 0 obj << +/D [768 0 R /XYZ 9 441.319 null] +>> endobj +772 0 obj << +/D [768 0 R /XYZ 9 419.153 null] +>> endobj +767 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F40 208 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +775 0 obj << +/Length 1629 +/Filter /FlateDecode +>> +stream +xÚuWMã6 ½Ï¯z©L¼þ¿ºèaØ)¦(z(‚EÛƒÆV&ÂÆöÔv&3ÿ¾¤œ8Yï%’hŠ¢ÈÇ'&\=¯ÂÕ/wŸ·w t±Š¢ LÓxµÝ¢¸’8]é¢ b¯¶õêoõÇ—ß>K¶>nÿZÿ»ýõÃC”^m+ã ÌJXå
YHJw¡?gµI¢8ˆKI„E)ZkÝ°·Ãzç¥2UÕõëHÕ®}ÉØù/4ê¿£HjûOéö¼>˜u\¨Ó=VE¡Œ·xZǹò/=S•µµ˜Û™~ÜÛž …“›HZ§â˜i¡“ú¬ƒEªä ²ièçÝ«ô]#ßÇ=¼·2·´1Xo²°Të"VgîØËÆö§s-EÖíDéÕ‘©Ód×
W^f>|Ö´ÃO8#MÔvƒu’r$rxɋ环ä·í[Ž+‰GQÎ((â…íGGy ¯äÃL Vz¶ùêF3º®5‡%g( ö@¡-#…;ñ8¼˜ÊÊ´!Ça”Õ“œJ‹˜Ó ÙäÉÎVãá]dWyƺk-å¸,ÎGt}Mù¡)àÓËÞÿKe©zûÒÛÁNA'_”&µk$Gº§È(4~›ê¢zr@ÀÅa³èi90yèñg8Š"@™2#²ï^Ïè
}¼Á52dé(W£ìtƒ¨
]c©ŸP Ü×™
2 +$0:Ì0ߘ~_NmJÍgɼæu@_ñ6x–ˆ!Ž‚ø¢%AñQ}?° ‰d*ÐúX #R÷ù Z¹Ï;„nôJ®ilíŒ0A®Zëž÷tk¯c¿ïÎ7,TÍÜÄiP„úºèk'èùˆ +… +Pèyçý%.TUF¦UÝÓP1èqöEÌèÏ&´à î=A m³/¼!‡ÏÖMd€›ÝîmÀ‚½ãÒ Ïµï….ÁÛñ² :”7j™Mé#WbVNÚøŠ|y+¾é5`åßSæËL: öGƒ¹ÛÁCu’òëŸh´"ÎrùCňP +h‡}3ÒxPØR$ŒŠ
Œ•/i[ÊÀ|«?~VéËeä§õìQ“Åò ›¥hª“)˜|JõÕTÇn)ø:
ôØáùÙŽîé-C ‚ñå$Üë]fHBObßÁ™D¤ò–Ð ]Ò(3J ÜßHph’æKňy0 k72 ©—‚:È;\Q‡ãŸSp3D‰¦ÄùWÝ?9¾¡Ÿ,í;.R¾Ë÷”HýBU QœIÞî—`_Q)'avé@iaߨ) øÄÒy #Cí(>¶?7$Üu}s-5‚Éî&MˆWfDÏU.äH$·äg‡v£öTóý§ëýg’?Lü`Ò{«¿ÛÓˆ²ÔƒÎÿ +Hkz^›NxŒ5Nžîh¾Š”Þ‘ŽNò@Çèš²@‡Ñ¥)ôe]ÙK÷³ ôME/ÙçÃÌ0°ã6Ö×ÿ9ñ_3½à6Œ©…§3t‡s:žÙŽ®J¨ Ò"›v}\2Œ{¥Až_ß%Óûpøþ·Š=¿UηúA>: j#KÁ«éÁ)àäAº’wLÜRŠDÒ1;ÆT‹] ¿+ƒ4-n[<)¢4 ÕãNÚnÊ97MˆÙeŒr2&•9<ó=;™ž?OñÞ\ý¹ŸÆ/Û»ÿLFC= +endstream +endobj +774 0 obj << +/Type /Page +/Contents 775 0 R +/Resources 773 0 R +/MediaBox [0 0 342 504] +/Parent 777 0 R +>> endobj +776 0 obj << +/D [774 0 R /XYZ 9 484.913 null] +>> endobj +773 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F24 494 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +780 0 obj << +/Length 1452 +/Filter /FlateDecode +>> +stream +xÚÍWA¯Û6 ¾çW=)À¢J²dËoØ¡ÞëÞP´Xl(Ú ü %1êØí4Í¿ )ÊŽ“º;ïQ-‘ ÉOŠˆv‘ˆ^-^®Ï ´¤ä™1*Zo#qkãHÛŒ+FëMô½ºsÿîÅëå*N
[ÿ~ÿöÝ2Óì=Íß>Ðøîþõ‹e³õãßë÷ËOë?ž?H3ÝZ¥’k)ád¿k"Ñh!‚/Ñ*–Š«Lƒpa3²ê˦þNP ;-UÊ ÉýÞÕ(¥lŸ/•eßh
6Œ2ž%q´R‡M> +# –V±¦- Lär¥RË~£Ww-mSö9ž˜W´ù!ï:oïÃQzŽ– dÊul†ƒ„š Ä!r<°¬ÑãÞÕ]ÙãÉg:°ÙŽñ‘b×.%ËÑöÚ·v‘ÚU›‰{òêH+¸5v8ó×9· +uÞ [/CèëÕ*ôÚ¦$Gf¿FO쥥¼w™iϼòÈøT!g“Ð!lºü$ê\{.€ù®$Þ®Ãt>ã°2Ž€ +;ÿ匘yPI¡Ì8,-›k>ÜÓ]ì&Ý +endstream +endobj +779 0 obj << +/Type /Page +/Contents 780 0 R +/Resources 778 0 R +/MediaBox [0 0 342 504] +/Parent 777 0 R +>> endobj +781 0 obj << +/D [779 0 R /XYZ 9 484.913 null] +>> endobj +778 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F24 494 0 R /F21 427 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +784 0 obj << +/Length 1644 +/Filter /FlateDecode +>> +stream +xÚuÉŽÛ6ôž¯0r’XÕjK§ÂA'“)’™tâ¤)š 8mÑâ’R<úñ}=ö@¹ˆäÛøøvE³Ý,š]¿ˆd}½yñË›¬˜ÅY˜fËd¶ÙÎ⼋8™eyÂ~¶©g_¾ÌÿÙüΤqXæ9‘.â( ‹´˜-’e˜ÓnÞ^Íé*®þø´~w³ù‹Owox½¹½ºŸ—Y°¹Y¿cÈúö7”>[dYXÆ9ˆÍÂ,[²´ëûõ<Nòàó͹Öó2Ö»[Ïü~ýñ£ˆñë¬÷ó4®?½¿ºÝ0äÍ<M‚»{º,NB¸â⪓â×W £¿àÃÝÇͧwkRùêò)÷pŽÁÝ|Ƨ²•¢sƒ.àª<.ÁHI/W|ןšIá¹gMÊ0.À1DbZµ3žƒYò@á’²; æ‹dôv0}Ç~Ë«nÃ<)‚ |tUéW°]Ïr¶Ê2Ò궟ƒœïøÑ5ûÕ¸°ÍÖö-\X”u¼U]Í›~Øk+°ÃÁêʨ‡F3 UÎi÷'å2öj`ð‘.äý^‰ +…‡<àèmoç1ÃÊ`t¤]t©ÞG/x{
ºG§Ë.Òè£(¨ú®6h#Çg«ÿ …—Òé9ðþIJ ;¸µVî=¨†á
©y¼Ð"g-ÈôI\«Æ4Ú„óÅ +ô¿šÆ1nèx'ÎsÎÙóZá%û^©.Ä+‘bõV[ÝUz1e™Aßߘ6ð¨=*…»ƒ²#ñ¡€áí×(ÈS½mj8įм6Ìwñ! ìy=î
¿@¤“#{°§ac:¾ Â`Be« †GºÄ¸TÀA{u‚y, lÄŽO²èùÚžs÷D”£>g׶UøãGdLè7v,ØâRP§LªÈ¦™Ü¾ÏãU°vžÊûèÉ …ø#
=0ïèx5`)Ÿ÷xVSj ƒL?R¦0l›"A+éA ÛŽI/V¢ªåãÑ {Áw¼öNcƱc-MçL……“Ɉ¹u£Öìh¾$ÍKÌT¬F‡FÂâl9óÍ ØUÈÑUM#![³Å´N×K´êGㆩ\¤Ï²Hb<KK~—< +s*á[ÍDdª‡§rå(0íMët³e?wn°`W'WÀ‹z›ž2É×(ÎÅì“'I±ZbU³Gƒé&‰”ž$\cv{ +Dò'â("ÀárT;È ÆÅž/¹¸…QGÓ4Œ«Ôè&Uƒ"Å’sx(´=¨¦ É LA¥>ÊÖN€{¡®´áXC!TE᧨ ¹ñ®Â</ŸuÞ9.ÙQl›ÖÔu#{nmgÈÆÔ?Áœ¥ )2²Pö¨…I?Úvc`Û âD[Liç‹ñ7 Œs°3Š8Ø^ ®Ã D[®¯UHÚ‰
™—¯qšq]Ð`À—LHE—%’|3, ã§Æù³šŸW{Í)_R‚òÚb[´FÖ
ƒÐݸŽ+:ï… +ð ÆFêG™pFν+µ£äÚ$P`a2à":l••Ñ$0¿ùp¯°åïõ)œûæI"M|Ê…yt‘Ç'TǸ§xa ?Ÿo&\0 $¼ +ï—ܶ%çŸÚ¯”L +Ä«ªÒ q +.9U€qø±øL¾ 3¡3±N™ÔþÌód«ç})µ³ÕÉÉfX Ê‚3¶ø jÌ"Ñâï€0
ꛟ=áé+DÓc ü‘87/äÓãpDÔŠ~ `KŠÁʃ1l½“ñ(‘p>’À‘GØ@CßóŽ,JwyÓ£@…M‹î)¬O¿áðÓ½ ãl¿ÀQ˜¦•Ëä‚èjó⯪ Á +endstream +endobj +783 0 obj << +/Type /Page +/Contents 784 0 R +/Resources 782 0 R +/MediaBox [0 0 342 504] +/Parent 777 0 R +>> endobj +785 0 obj << +/D [783 0 R /XYZ 9 484.913 null] +>> endobj +353 0 obj << +/D [783 0 R /XYZ 9 465.114 null] +>> endobj +110 0 obj << +/D [783 0 R /XYZ 9 465.114 null] +>> endobj +786 0 obj << +/D [783 0 R /XYZ 9 441.319 null] +>> endobj +787 0 obj << +/D [783 0 R /XYZ 9 390.261 null] +>> endobj +782 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +790 0 obj << +/Length 1847 +/Filter /FlateDecode +>> +stream +xÚuÉŽÛ6ôž¯0z’ر$jCE +L’ ‚00ZM ‹¶ˆhqE)Îäëû6ÚÒT¹˜| Ÿ ßNïV§ÕnõþÕïûWoÞ©|†Û"I¢Õþ¸RÅ6Ïã•Ê‹m¤²Õ¾\ý ¼¿ûãîñí§õ&Î’`ÿáîáq]¨à3Ãïx}¼ûôv]ÄÁþþÏûýçõ?ûoÞ…ÉTt”…[†ðe’šÆÈôj'º¬6qm£BÁ&Ýîò‚¹Žc]ÃTÔ¦=
ﻖס2¼ù² “n½‰² ë·ëý>ɺ+¯œrƒnKÛž„þRÖa åAeÜ0§›ïT”Ý„j«T +êÃP?G± °qº‘Ýe
*i(<ÚÉÚ"åºÖ C½„N_E>^z¹\Ã`wœQ«nt",3U2e%»±G/ÅÑýP’L÷($‹Òh½©&9€ÔŒ{âÏÒoù̸Ke¨w5?~îÍ7 ŠÔÂVé’è*ˆ +ä%/ãwmÇkݵ'Ó£à\CN½n]c‡Á”Kú x>‰àK9¸»!G#äQ€ú¦àضdŽc׿<Ôƒ-Iù$¥g’ØœˆÍa§Ïç¾ÓÞ¶,NNã{ÑÁèËÔqšN̓àÅRê¤ a®&6%#Àý`ïok6bšíÑ’¨`ï%wë0xr¦gÎEmøJ +
Ì#„ :áCGqÿͶƒ˜¢¢q¦>rÁHãiÁµ-²ÜŒ¡Òpw [⌕ìúÁËà*1ƒT4ÊŒý :üã£Þÿ‰YJÝE“,JÆ4÷V-Ä
(¤g +ÛýÊ‘oó‚ t}ÑÏnÊ_Üø¥TÀ®Ñ§Öci^/š.o¾¡ã8¾ZŒ¼8V,0ŽçW# }8í_d©–a tdàÚŠb¢ø³æ;ŸèmcÚa©¨ÇÑn›©«¶lÖxoC(á³+<šú™ª.¦:¥¬œ/°ù +y ‘q©My2Âsœ–ØœzÍÑ3—uÍhðŠ2uéd§E¦ xå*ìÄåÙ6I^¨VZwÃTPQL WœˆjÛÁpË@Й~ >B%P*»q6ºý‰ŒI[Ard©üT¨ìˆ7(0_0<¢‚½…6 •õè,æc+<”!È噸BÍŽMê&àu/x{£™ä½YRsâ‚XE7Ä*œ5 q¦ÜLJf#UIaµ<é¾ä=Å%ˆ è°—C½}8zcѺІ)bs_Mã<¾Õ|DŸÇ ?jªt¹óœ› À
ùªÀÔ£sQ$džǽš‘þKÓ + L%—g#gÛnX2ÛQ×õkÌ„Û"ä· L»…ðF±-š"Iƒ#}‘šVdUœ;T‘¥.{Šä6F81 Ù-Ç µH (¨Ùu_´-¯BƒÆ–e-¼Ü™C Ü0zmË—DážµíÄ甡ïηfíc g1 Oz¤m’‹3©m°Úí'ü!šBd\Áh4ÿŽ†úÑ +›/a¬ÞëbØêEUÜY Ì/Ü[0_z~á…T +lizƒïXÝ ID˜aÓb¨åØðÅÚ8ÇØ[ã +ý 2š¿ C?y¼èX³Û+Î9\1ùÁ°Y‘á[Ã0ºÒ·êÍ™ X9 BNÝôyÁL§¾éQ‰ +tÈiÍ8zÀytÍb=˜ø Bj¡MŸ8|·7<ˆ¢jäPz +endstream +endobj +789 0 obj << +/Type /Page +/Contents 790 0 R +/Resources 788 0 R +/MediaBox [0 0 342 504] +/Parent 777 0 R +>> endobj +791 0 obj << +/D [789 0 R /XYZ 9 484.913 null] +>> endobj +788 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +794 0 obj << +/Length 1765 +/Filter /FlateDecode +>> +stream +xÚuXKã6 ¾Ï¯öä +´A¢Ûƒ&Qí:vêÇÌæß—/ÙNÆs‰)R¢(ŠüH%Z WÑêóÃ/Û‡ºXÅqX¦©Zm«Xa¢Ò•.ÊPé|µÝ¯þ þøôÛÏëRÛ§¿ž¶¯ÿÝþúñ1No–•*,³´Ò‚L㤇HöYm’X…ªÔ@daT”<ËÕk•½m/íMïšz½Qe´¶ë;$³€YYП,‡¡Þ›³…•EЛŠ™—¶¹ +2`b>÷Q9ºa@I¾a’Ñ@è'™¾7; øYWP<áçú®Ì# Ÿ‚ ïÐZÑcy uÑb¦ÅìЀ )dývØn¨zÆUÆd- ‚Ô«cHÖó Ÿ!÷«ìr¿R š÷ã +Hfyé¾1qhZáÔ<«¹¸“|Áº†IÕÓq ìÌ +ùg!¡;¡ëï)yŒ/8Ê ;Ù¸ÞfDÙÛ Þ &tÌ5üYr5KÀ;Ù‰’1Êރ텢–èrŠi*)£K ƒ@ùom‡ +œë¬LyöåU‹7“4¢4ö÷€cŠi™°`Ôx+?Á4 @ÎÔ8 +öjÑÊ5Þ4³x ΘÇÚõÃ^8´MTNSÆ`@.IGÀ˜0h)h»ÑäY2o “8Ì¡Œ¼W×pJsëUn–ºÊ° 8ÑØ~' Š·Á—÷Áðb&*ø½¾[Þ +ŽËMüJÎOÀ±•i–I[7ÃñÄ4íŽ<@ Äîd2oÄüiÁ ²c>å®ÿ*Œç êº\æ^OÎWKjÌ=ÄtÜ–ó…)ìoFpÁyt¡sùTi”\·J&éÌ=8\vÏ;à¢â0‹•Ç‡ñ±²ÑðØzSò$,òrŽ)Zb÷ø¡? +(ÒŸG(ƒÏæ¼”R (ûÝœ/•Ì¼ð…œð¥LC]ÆwUº¢<õýPô8Hr|òL1•KLå>¦€¸´®Þaè_*{;¥µÁËì5!‡Yr©øi*j¼yçs¨%€Õ;ü± ¼)®KÞÔ€›é-B'¾õbzw&Ò{&É$ ßYš$£‚é*qÄe6Q E™¼+Fܽéõ™E1Ä7£·ž¾¿¢þüÂgÌæ¹7°¿4ÃÒè^HǵÖŽ97híónì°Õ»`$. ß}S<bеÍKc&!]>`>¶ñcŠk¹sù÷Dz÷؉oÚ{ Žg‡¹ ~´½Ð¿ÿz0\žŽ–º ~µó%7Ô5J#àÝG ʦڂ3®ŽþT¡bx–ZÙö†ÿ b>7ù Ïç wü'É?m þ¦rìµ +endstream +endobj +793 0 obj << +/Type /Page +/Contents 794 0 R +/Resources 792 0 R +/MediaBox [0 0 342 504] +/Parent 777 0 R +>> endobj +795 0 obj << +/D [793 0 R /XYZ 9 484.913 null] +>> endobj +792 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +799 0 obj << +/Length 1842 +/Filter /FlateDecode +>> +stream +xÚuWKÛ6¾çW=É@ìèEYê-vilݤAÒ-qmfõpI)›ý÷)Ûöb‘3Ãáp ߌãÅa/Þ¾x³{ñê6/I²®„H»ûE^Ë2[äeµNóÍb×,¾Dooþ¸¹{ý~¹Ê6"Ú½»ùp·¬òè3ï?Üò÷îæýëe•E»íÇíîóòŸÝo¯nq©:Ý$ë<IàfÒZz;[«,I×i•Ã¢XÇeÅRãQþ,Z¹L7ѣň†{¦ ‘¿ëQŽzè×ËU.ªhÛ3÷´\sÐ=ÊŒ×'ïe=¾Äeáï‘}²£ê@SíÎOÆNzD;ÁÆU’¯ó\°]¤¦ŠÝYX T¯Œly£%yååŒjA/؉¦<1í(-/ìt:µZ5ÏTâ“K~2 +Áyû5Nr»4¨`ƒö³âä¨k÷°yIDZÚ¼UÀoÔý`sNf ŸÕJ5º?0ñ^ÐhÀ[y¼‰ŽY…zÕwúNÀ -ˆ§yÔ¡ÈdGÞÑ1izÜ ¶ÉFÉF^˃Խ——,Øi[}Nø +æØépP®†·îù;à‹×äi:,„Æ3,<S&Ñkæ‘«Ê+W!Ù¹Š7ꇶ£Å58e0LäGÀ¢“}è~}ýØ"ªÑT0 +Ó/qÔ({Ò£º’”Ÿ,? å83c³#-Kôíĺyw6 DÐÜ°s°|Á¨a5¹ ‰°áZX&?Ú¢2ƒQ!aºe° + N”"úc âd.§¯;}8ú⃒V·Oî‚é´ +U–+Z 3÷ú<;;šÂ x‹%†_ÉbVÿ”öÏb™EÚºS-»ƒÿd™7ôm0•8À¯n‹ì×’Í:‹+kòtZBP¥Á_Õ!$›ÒŸz…•XUѧe™¢çò$¿ô nek1È &î ˜ˆ¾Á$ 3ê MÓ*k™EN!E/Y +OVÌW'bUÉ©‚tÙX!¼1ê Š’dÅ1®5OÌ=W +î(Ç‘Mód¹”Y ˜þ"μÌÏ$梨\WÅ3÷Ï^Í P [pý¨Ç#¯æWðv ø«GìtYíŽÚñß¹Àºwâ’½cfrºÀ2J6ä÷Pï¹7Úbï,Òh?ai Á5C+V,0S94‚ÓIÿN„t¸´\èªÖ¬šv(imƒMW[Ê ¾qa§à G×G«÷bt~ j]ÀKÌ Ÿç9‚4®‰ô2¸S'§TY%›3h/ߦæ@ Ö÷f@8…"×^lÄ<VL ´ $ŸÓT#Kßâa¡°9óòk,b îA”YÐ\-j£x# s¾/!L²×:Óšt@b Q]+ò•æUT ¢Ä4côGª„÷œ ì!¬£|<ºœDaÆs\Is˜:$ˆ9Ì +4lÎÁ¾†i„ÇŒUÈ.À¤¹ ³êÜ‚`½7ÄPZòXaò¸1¤aÂ<qàÆ
ƒÕÅ@›“ANãñYÑTlbW£ž("IU²qÚ¢a +¨â18^$ ƒ³0.î` þB‚ªš‡ ÜüýqK·¥DÝ^Ð_¢5KmÝe °¯•á…\ŸÂOÞ®@Þ {«ŒòàJÈWœfÒÊÍ)iGêËÊÄZ£åA±¬úáJÝh,#ËTɢߔy`ÂE\¼ˆe²
:ËÔRÐ\Ud~t‚ĺ–Îs!‰½‘ô0ú +endstream +endobj +798 0 obj << +/Type /Page +/Contents 799 0 R +/Resources 797 0 R +/MediaBox [0 0 342 504] +/Parent 777 0 R +/Annots [ 796 0 R ] +>> endobj +796 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [111.256 189.813 185.45 202.432] +/Subtype /Link +/A << /S /GoTo /D (section*.80) >> +>> endobj +800 0 obj << +/D [798 0 R /XYZ 9 484.913 null] +>> endobj +797 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +803 0 obj << +/Length 234 +/Filter /FlateDecode +>> +stream +xÚUOÁN!¼ïWOpX +,lá¨Ikj<bbŒ¬Ä•M(«éß ¥5éiæ½™y ì÷ÝîV[.¥X Á€þ +endstream +endobj +802 0 obj << +/Type /Page +/Contents 803 0 R +/Resources 801 0 R +/MediaBox [0 0 342 504] +/Parent 805 0 R +>> endobj +804 0 obj << +/D [802 0 R /XYZ 9 484.913 null] +>> endobj +801 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +808 0 obj << +/Length 1648 +/Filter /FlateDecode +>> +stream +xÚ•]sÛ6콿·'énÖD‘ÔÇ^ziæ,ÞÚd»K{ë 8™¶u‘ÄL’›ë¿ @²œ:ííEAÄ7 x¶›Å³__Ån}³~õÓ•ÈgLD\¤Él½1)£<ÎfBòˆÉ|¶ÞÌþ +>|X†¯#ZRZÚ9ãE”År6OÒ(É/oÂ9Ïdp}"XÓîn±úcq¹^ÑîânAÀú:œ³Àm®Bž·ïo~ 9 èòòöf…Oƒ\Qœd𤈄Hé¥Û+ºwùöbµZ^^¼¥í»ÅåõÅÍòÒ¿ü,àÉ×× Ë2áQ‹S–(äÒ3ÂÛ;ãã)ƒ»Å[”ÚIøçrýÑò“,hŒ)¿÷7+G¶º +YÒ n—kÇ÷µ3k<uÁ¼H£Œç`Õ$biFŒî5‘29õ@’EyV€/-Í^…I|ÆIy¨º Y Õæ íûA
zã`M”ª 1Tî ¸WAeú¾*=M£K¼´®ªÊÞ*>wbœhOu²c"0‡€mg‚†½v(S×y>UíŽPµÕãéçp.’"x"w• +F~MÓ™•$›Jr–(ãîm Õé~ˆÀ¼’÷ažx¶@Þ:çVuo² +là +!eŸ³s§‘x,' ³!Ž«V£º £´Áhâ"¸ówrº“Œw\r!8Zþ•—θ#)xçÉ÷Ü‘¦žK‹5.³(Éi18ƚȕ°¶f +¥î ÁÎÕV~ØÀŒÐûžŸrº-f4Ô5íõà[-ì½&îÏìïRZQ€˜…y¶ÓÉ~§ +<&t²WûÛ +,ù0¦' ·8€u“üþ?ÄV«Ü €%U +œ5ê»}°Pd®Ò9
ñßÅ]·ÿíãÿ>üE§ð-â•DN³¢ÅúÕô)ð +endstream +endobj +807 0 obj << +/Type /Page +/Contents 808 0 R +/Resources 806 0 R +/MediaBox [0 0 342 504] +/Parent 805 0 R +>> endobj +809 0 obj << +/D [807 0 R /XYZ 9 484.913 null] +>> endobj +354 0 obj << +/D [807 0 R /XYZ 9 465.114 null] +>> endobj +114 0 obj << +/D [807 0 R /XYZ 9 465.114 null] +>> endobj +810 0 obj << +/D [807 0 R /XYZ 9 441.319 null] +>> endobj +811 0 obj << +/D [807 0 R /XYZ 9 375.815 null] +>> endobj +806 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +814 0 obj << +/Length 1879 +/Filter /FlateDecode +>> +stream +xÚuX[ë¸
~Ÿ_áG8ñÚòýq8§Ho@ÛAbw 4Ž’¨µYË9éüû~$e'™uŸDQEóò‰r£4úÃËO¯/?|+š(Ë’¶,UôzŠ2Õ$¹*£¢iUÔÑë1ú9þû×?ÿ¸k‹øõðÏÃë¿v¿¾þñ‡oYù´UI[µÐʪ†„^ÒpN´Ï3•¨¶ +éføçpËíb{? -ºU¨ "Kñ#Lñ²ß|‘ˆŒÂ;Èà/š2‡ÈÉ Ú†Õ{YmYÂN(ª4>"¯ôl=A +y ˜@
‹àŽt]È|º‡¸äÀÖó<Y`~pY`yŽ³Åfa|¹àP1Ú2ü‘ *'³`-- ˆç¶0«“²lŸÍüqÔ½;K°tý4™ÜW-ËÈY)'!q¾ïJ„‚gàž ,š„Ö2LF÷aó 5t½FAî%ߟ, +EÛ‘‚¼(âÁt‡‹ mç…õKZ¦ b 91 +Ê6a„öï’e]”À/núš}Uä°±GŠ|·ìªèÌ‚¬“ñF0t^QlƒµÄ’üXbËÎr© +
+8e·LüµëŒý)ìÜ)$øׄFÿE/IL³Étî<JÛIR|ß?8 öu¸X'B}bó¥ &Иî5 &±Bö.ûƒðï…òÿx¨®ø¦Ïë’Áìžzéò‰âò¯ïåO,¾™øš©×ž_–Þ{Ý-:–´LGsÛì]´·ðã¾Dwtà²l—’n—ŽÔýLÎ.N–Îøž„|#´ +»Ô
ªN2jÞ/Œ:^> +ŒÇ‹ÓíF •žoÐo=·G§—À8ÈŒfÒ½ÌñÀ;û¾ÈK‹U}¾ +Ø¢Šð…K‹àUnÎràßu´/Ôæñsî Q ÿÒ³¤ +endstream +endobj +813 0 obj << +/Type /Page +/Contents 814 0 R +/Resources 812 0 R +/MediaBox [0 0 342 504] +/Parent 805 0 R +>> endobj +815 0 obj << +/D [813 0 R /XYZ 9 484.913 null] +>> endobj +812 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +819 0 obj << +/Length 1778 +/Filter /FlateDecode +>> +stream +xÚX[“Ó6~çWdúäÌ×’%_ ɶ˜%Sè@ D¢ìzêØ_Xöß÷;:²CK§/ÑñÑ‘Îý¢D‹ÛE´xþ(òëÓÍ£Ÿ¯T¶*ŒU"›ýBhê4]( ‡Bg‹Ínñ!xÿþz¹ŠEp½üsó Ÿa®µ;±R‡Y¾XÉ$”™âO@ŸêàjýŽëWWë›õ«gë·~ãf‰û^ÿÆ_›kž¯_ož¼$6 …2‰q½ +•JøÚ77ׯž]¿yéÉ__ñz³~ùd™«`sýûõæ/dt®Ö*I!0d”¡HR¾lsg™Tès}bF±‚} Ѷ®ÚbgÓ€Àb×{:+‚Å¢!SpóüÑâƒÛk·KЦÿÞÓ³Õ=U{W/eÜ3Mwgº²DÁÀ·dì±)ª•³ËÊ 81̶8–8&“ˆ¤[I-!ôç¢#.¼wì»–¡¾eª¢âoã °¤AÝ,=¡ºš)a„â3Ýåù ›š©mÓ¶2ïضÐw"æmcèåìé”ËÒàc$”-wô‘8‰ix9öPäaÜZ7¶+¶ÃÁƒ©`£p¹JD¼´ cI7ZÛþ¸š“bPÒ>& öuCÒÇ`Ýv¦Ú2^{ŸÐÆý¨w üU
~“‰doº=š]uÅÁ±ÚÖ}ÓÚŸ1r1{ä\2Í’U¦ëÙå`D5dü,ØÚ–tJUp™ÚšíÎÞh {{yŠÆÞšf×ò L +™ÃNœâ1…Š)·}鸃`‚!~ 6 {ÅģrÀÕ¼RFV;†Ou +¤Ý]Ñ2zȃjÎ/c KR¥pFá(&Œ9z3™¦uÉ&\øÒVkI*‚öM}ð伌N^} —>—i¦R_8 ô4£ßÑéÂ8Ι*š³>š[’-Vgdœ4)’ÆÕc™Cq1ÕŸŒ¤´ÚnmIÁ`w„ˆ&)@î#"}F¡â0Jó Ý4Í‚§}Ç÷¶%ËÁÜgê/íõש#Ðù³<&û¥h©uĹî‹îŽ¡Æ¶ÞÛŽ1.~hå0É©äÜ3pòYìP (^s „ö "0;ÑXB)å?ú4s>;ãS¦4
œ‘! +Ò ›¥Eß÷íV¦2Ìb}™}ÃL@û–T”cŠf
‡+—Ørݧ4ÒC“Öy$›vD O Ä2YèžÌÒÎÖgw™L.-Ôvý®°;WV"
µÎ§g¯–| +mï¢céû×°¾@ªjÁ¡•`êo½…)yàL¨©»¥¼ðÎ?Q2ÿD‰ôé•çAý©sï‚
/<*D4$µ}Ùyº=¯û¾Ú™Á ®^‰˜#¿éNåwN¦{7ëÊD=å4få¦y`tÝwŒó:D;B¢¾ÝC™hÏÿ` +ÿ¢ÓüxÆËËŒOmÍrY·wNæp.¯Þ±ÑOÝj˜¥¸Uñê¢ ÀùëÈøz ξU7ã4”JÿÀ0é"ÌýÐĉ¥ñœEécü7Äÿ»±Êq¥ÀkEEÈQ ‚I>!Zo ý
Rć +endstream +endobj +818 0 obj << +/Type /Page +/Contents 819 0 R +/Resources 817 0 R +/MediaBox [0 0 342 504] +/Parent 805 0 R +/Annots [ 816 0 R ] +>> endobj +816 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [129.696 386.94 190.264 401.06] +/Subtype /Link +/A << /S /GoTo /D (section*.86) >> +>> endobj +820 0 obj << +/D [818 0 R /XYZ 9 484.913 null] +>> endobj +355 0 obj << +/D [818 0 R /XYZ 9 465.114 null] +>> endobj +118 0 obj << +/D [818 0 R /XYZ 9 465.114 null] +>> endobj +821 0 obj << +/D [818 0 R /XYZ 9 441.319 null] +>> endobj +822 0 obj << +/D [818 0 R /XYZ 9 404.707 null] +>> endobj +817 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F63 238 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +826 0 obj << +/Length 2157 +/Filter /FlateDecode +>> +stream +xÚuXK“¤6¾÷¯àHEtaâµ·±ÃãhÛ{ØqÅFlŒ}PƒªJ±<jôÿÞù¢Šjã ¤R))Éüò!âàÄÁOß ¾û¬Ë@©¨Ê²$8 •”Qšd.«(ÑEph‚¯á— ý´«txxúïÓá»??÷Yew˪$ªò +v¥EŒB±œìS•DI¥È£¸¬Xªu§ó.)Âi·O:ï$œFÓûÎM“mxb´õäZ×[3¶ïÌzuÓY¤Ï–Y/¸•m‡Ý Þµ›pøκ&jk’åQ•.ªÖ[Ÿ“EqZ.Ñn¯S >‰šµéùdkü û$‡¥yì•Ž´Îx™#]Ó8|&,üy@Å^{ Ng³Sd +ï~i8lèOv$½cQ8g…
èYV¡ûßvAš ¨*_϶gÞ뎿 ézè½k`S9YÅ.ÂU£=Ú‚ídŸi`ú,$L]ÛÖŽûM½*_Á¡gë' þ g±ì]Ãæv–.CF@³é{•¼«lqí/"“ET±"‘8*Uè(T¼‘$*`ŸýJ ÔQ„•8ü¼+¶CÇzNgòP¯è2+ 3ôu;7ö‘wÏÓ{=Á +D´4HpXÒ†œÑ6Â3Ý +H?´3º¡ÍÒ4½žÝ5d`È=UÁÆ·&_oµ\àn½—»ÅÐ Ùöò«Uç¨<Rq¶n½ÕVeØ«ªŒ2Ðq¯Ê¨(õªIË÷ +¸^ÖÝÃ×?â .¸î¤eðJ2] ø– +?´Áoÿá¿4ECœ`X@œ$póKƒBGªÈîã$ª¨Ê“œ i¸ ¦Q®Dè{ôv’…øAaÝ ò¦%@qF:„œ« ±.ça ý»œ?ÊÊ•Œ ø8'F1lî—F¥aÖ³ü¸ÀEæEUš¢ ?¬îÏx$1Duþ0tôS ¥%©jù…€Œ/o r ̱KÖs…̕Сq.‚ª(Ò¿áÏR´vvrÔ¤Yz;Á¾¹Uš.I››áTnØøæE@4ú· ÿ`Qb¿Š¨»K +bžFÇt¨¶Ð
‹^/EÅ*ŸKóéy +endstream +endobj +825 0 obj << +/Type /Page +/Contents 826 0 R +/Resources 824 0 R +/MediaBox [0 0 342 504] +/Parent 805 0 R +/Annots [ 823 0 R ] +>> endobj +823 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [186.363 30.111 245.364 43.163] +/Subtype /Link +/A << /S /GoTo /D (section*.168) >> +>> endobj +827 0 obj << +/D [825 0 R /XYZ 9 484.913 null] +>> endobj +824 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F63 238 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +830 0 obj << +/Length 1820 +/Filter /FlateDecode +>> +stream +xÚXKÛ6¾ï¯ðQbGO[FElÒm$F‹ é+Ñ6= QÎfÿ}ç›iRô¤yq8ä<©pq\„‹77¯ö7Ï_§ù"ŠÖ»,‹ûÃ"Ýó<Y¤ùn §Ûž\ü¼¹}wûáå¯ËU²Í‚ýÏ·ï?,wiðIð÷¯åûáö×—Ë]ìßþþvÿiù×þ—篣ìZu¼ÖiÑάuAè&T[«$Š×ñ.%`³óHÝŸ\±Œ·Ái¹Ši—{ÀVà“YÆyðíŠbªÎšòACg¿^lv_)³Ûu¶|Fhž…iš¶VQW«^¤K.Í +v’«(]§i&vU®v½-éìaD6dØÜ•®—•y ¬—«”à—ƒâÒ‘P˜þÒY!µYÜ^ãjHú'6]È…YFA£"
Ž¨7_pV°se +;±u3Ü¡ÅÒÝ.èOV +÷Êq®¯ö ´?¹æ À„@£Dãõ+Ÿ¢m<;½°"ÉöÊbO>Oò^ѼØf gª9ÃH°íèBÒD¼‚og+8¢wßO3Ù4¥ +þ?ÍsŽ§½T¥„æ @ +_%»F¾¼5€òâ{„c”¯.ýµÐ†öŶÕx Yè¼Jy‘³dÔYoUç ÷ÙÀ£üB !›Æ!\TT—Ò +]< ºÜ‘&nQ!½.("câÆ&Žˆ‡4µ3)«žìBd8/Íc Z¶µqÊ’PI[ÍmÊØ)&ÿr¬Ã © ò±ªÒ$%È·sWSµÍQ +§ÄpvûÈ¥¸«ê[ ÛÒùÎ MW*ù¤|×|£Œc_Á” +C7Å™< í´8µU‰¥ñ&à|Gî±v"œ©„´µmŒ ŸÃ,”¿I®K|”Äëm’ %Þ®ëÙNó$¤ØNR:Ò IXEÉv †»© 'xœåœfq¶£^à…Ð z;€w\Ùì€Rä±vÛ”ð·HhÐcáYkU£=cT(;HäAÃQÌÛ®³ì‰u² üW|‚&ñ.€¶‰‚IÌ+›c ð)ä… {˜‹zן:©©ðî~XOĽÉ&8ÚÆvØ;I¶ãÞ`°oˆvµ7ºD (§ÉŽ +ÿDGÅ9zïe-œ1EÕxä1ÄT]d ‚IÀ*Ù£•«-…x9s" §])ˆEãÖ±Ö½˜êšlæŠ+—óH“ÐH#' ”Ì]UÅñ&â”Ê”£Â\[AÆ!Žà/ÍÐÿã4 òƒèÃö‚=V'`Ã0ø±RÚÎ}É–¦½ãߌ‘‡®ÅÀG^\,HŽôqÉô"&5 + nHÔÊÓ»ræ…€:hä\Œr©ƒq®£ÁÈÞ»ïQéY”Þz•N³\†–v¾§´èq.3wœ5´‚(©G7ÔFÍ9g8ybLòká«JEdÎ>]ÉoUÌ’ÔtÐ
ç¢]ÞM)ÆrñhRPN)|]ÍS7½³ß1‰ž¹Æqﻤ„vÃã5áúÇðÆB ÄTUÛËØ›f£öáÝ;WÐOòHÕ"³§ý‘ÿ[xªfW‚œ~ýI
ÙH'ž·•Â:z¹±yBîÒ; À"é=;ÍàQ8ôÔáÒÇh½úô™M²F>µ6u¼Ojj^4íz7üYP|Z™{¢Dò×5™P7[P+Õ5™®7ÓäØL’c£,(›2ß6ÃÃVÇûÝÔKü°Óá|îö ÍBµó^î +endstream +endobj +829 0 obj << +/Type /Page +/Contents 830 0 R +/Resources 828 0 R +/MediaBox [0 0 342 504] +/Parent 805 0 R +>> endobj +831 0 obj << +/D [829 0 R /XYZ 9 484.913 null] +>> endobj +828 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +835 0 obj << +/Length 1880 +/Filter /FlateDecode +>> +stream +xÚËrÛ6ðî¯àôDÍX | Û™4㶗¶š¦4˜‚,L(ÒáÃŽÿ¾û"%¹LÚv pß»`=Diôîæ‡ÝÍ› M)•TÖêhwˆ”.“LÛÈ”U¢Míöчø··¿|¿©L¼»ûãn÷×æãî§7?*{u¬ÒI•Wp+ (42ݤòh›)èÊ +oÔ(ϱ µ_ó/´1†ßceÚ² \" !Än¹çÙe!¯LRv®ã!ñÉZ¹×i¢™¹óáIAX/S ÐËš€) ÑdìE4
L@?²…•MRýÊÄWÃVY|‡ªÕÒMÆ¡ÏÙ€ÁaZdÌñÂâ3Luâ¼õUó‘M´º´I¦Ò$+‹Ù(? Š¤*RE]2MJUF&É2iéšu!úU¢S Š—IQJV<²X܇Ð>€€y»Vò‘O¡Ý3Dî‡õÔaÞb
,¨hµL–â4 ( ÷ŠJ0 + +—…O–+![ë+H^úJv½ˆb¥Áõic¡.@˜õAR âxd¤÷[Ø×#Ÿáž!Õ‚A^k@PIæ<©.Œ£aØQ§dNµ:<©ÄÂUÛ ¾ •àBŬŒÃÇA¬Ø¹°r Í +}a ?‡¦¹fœG„÷ µ„!«v*4t›d]¶R×8Ž€Ñj‘¨¼àRÄ_ÇNe“*û¿ÙP~#ttRTöÊ8˜ø00}_×]¿çT +ÔíÞ¥Kƒ®2i³¥9¢ˆÈ˜ÅHx=³þ;€‘¼¸‘rL8ñ &Ý{Õ´W¢ ù½… ׫ “/á‚Á“ƒîÁ"#T@I Q5Ìõ a +¥É;šn€Dò"°f Ÿåѵk™|¶MQ,Óï~ªi¤ýÐò–Ì@y¥Åíš_H%,Öœ{Š…1”&€F¤ù~äÖaÅ˸wì gÉ¥xt£ 3D
6=‰L{ ¼Šãòj^ |9)ž“ Å*8ˆŸ1Çlò-ì úîÄÐE34ë±b®bÅh+xzÁ¤–ÔØ× +Ð Ýwâ„ôÒ<„:¡‹à¾e^ MØ—©ø2=·ü(¸8ç`œ?L
ÓN®…¤LÖd¢÷N$rnd»ÏŸÆ v˜¯n¼ë™ö1¶Y†+Iœn:¶—¡ÁsÐ({P¹§y—•ú–3…£¼>cÀ¡yi=>ì ½s¥‡*¬ÃÔŸº‰^rÊɸ¾›äð>€ ózjFŽašþ¶¦°,/ [‹ŠEÜàÓÕ ²÷ØF¢À6óà +’‡ÐÙV”„í¾J3«â;¹…&väj™½ ýØQ+C •bö«cjÞnþÞðé÷¨Þ²ñy +ó» + J²ªŒž‰ç)
+ð4j¢ßo~å8E”C[ÅþýR'fú,OŠL_O yT%U®sdÑ höI®òyä Wg4’¦éäí3׌Œ~i Az †°ÀSK*Q&=5“þˆÀ> õ4ÿýà+B+v@Åû±Àoïn¢tìw˜Ã–KÿüóúÎ +endstream +endobj +834 0 obj << +/Type /Page +/Contents 835 0 R +/Resources 833 0 R +/MediaBox [0 0 342 504] +/Parent 837 0 R +/Annots [ 832 0 R ] +>> endobj +832 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [263.214 28.533 315.02 42.481] +/Subtype /Link +/A << /S /GoTo /D (section*.86) >> +>> endobj +836 0 obj << +/D [834 0 R /XYZ 9 484.913 null] +>> endobj +833 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +840 0 obj << +/Length 1737 +/Filter /FlateDecode +>> +stream +xÚ]sœ6ð=¿‚Gn&GÓ';q7=ã8m:M dÐÝiÂÁE;þ÷ÝÕŠ3\™8éËiµ»’ö{—‹ƒmo_Ä~=¿}ñÓ^ŒG)Ï“àv` pð,XV·uðWøéÓåj²øýûö:Ç¢2Ëܹµ(£„‹`äQRp:w~ñîlÅ’,üýòúã
Yxý†ÖW¿^¿zÿ೫×xg°ÎxTò`
òpžÓ ¿]œ}øxsyõv}³®_û3×Wþ,-D¼]• 0ðs 'ˆr~ýi ŸÇ—K£".çOÝ\¼¹¸¹¸zuጧ†Y3VF%*˜D,tâ¶;eV¹mG‡X6µŠ +F 6÷÷Ä ‰¿êÚ^} T[©—h¢îè{bغ±Nù™`Ù“`%^¡J+I«,ì› ¿ÇêmÀ5}O”ÑFÖ(i÷Š, ϧ… V,Üé +Q;’=±?¸›èŠ/m‡»¢8g/ØÍÙ µî½ÿ+F㌠†T”q£¡¾E‚<¡î‰q#
qúèÔ ]Laû¡Õ{ ›`‹-`—Ds1‘Àij ÈF¡“¨i̽‹<Geq³Ó[´m0¢<´“þÔh'ĵWõ#áín¼¯VUÙŸ—äºðNqÅtY745aGo¹xG„ôìšp +¨éÖ~/›fI¸ª‘zÑP@ⶴRò%¤8ØÐj eBPÚý›µðÕÀe<ã†Vy×[#+ŸÕÞ° ÄqLD•RDYVÎÓäŒ%|»ao¥±vŸc–(·”7 +N)ÆyêR ×~8 ‡ Âá$÷ ª;ð€·"G‡€7Œ›‰¿£Ç“°W`äÚ;9 ‹“Vpt pLó›ÑÅ®Ô.¨\¦Q~š#I°bvTX0,¦~bŽ—ì’D¢Ì‚õ„ÍMÉ¬Þ j“N¨'1ìÄ©ˆ±CÅÚ7^ò=GÙÑàg?‹(I“ rg•ùóÞoò$/±]bÉ7®H"è*QI%ì‚8ŒzD¾ÄâžÆéS;Ç6°ÃÎH,{¹…™j1ëaä.yú?x Ò¹F¡}m"±µWnìŽM<*Š“pBg F>ˆâص Ø Ù*+mª¡Á) éµî+g„|æq 8O«žM
[×a€G[O§>¿ØoƧ1)|¸ãüƒ{¦'¸ò‘ú $çYK„î®Wæþ8Bp ÍΟ÷g{m}LÂFUî*$ ~J4ËC5&/cãôJvXòsnNžwsñ¬›E$â|ægšxÁ +Ê0 ¦´£AÙ9·`õÊS&þq •õ =Ç1Ë—| k¯¢¤x)h.FÖT«aþ®µQnÃhàÌW LÃ"Óa4y +R¤Í>Ø”?ï>-€S¶´*œÈ°‰U– ñBØ@Þ«%}Š|Ž³øÉ«›aKŸˆ™¨Œ¶wôUá¿ý—Ð<~DæãgüÚ‘þ‹ §h\¡tyÈ•³ÅQtRÜ\±Ä8î<H0ì†âá-&Åü& V‘å«€9¤ãù`O…˜+—¤Ç¿[‚u–‚f0«òBÓ§‡HgL·/þ󥇒 +endstream +endobj +839 0 obj << +/Type /Page +/Contents 840 0 R +/Resources 838 0 R +/MediaBox [0 0 342 504] +/Parent 837 0 R +>> endobj +841 0 obj << +/D [839 0 R /XYZ 9 484.913 null] +>> endobj +356 0 obj << +/D [839 0 R /XYZ 9 465.114 null] +>> endobj +122 0 obj << +/D [839 0 R /XYZ 9 465.114 null] +>> endobj +842 0 obj << +/D [839 0 R /XYZ 9 441.319 null] +>> endobj +843 0 obj << +/D [839 0 R /XYZ 9 390.261 null] +>> endobj +838 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +847 0 obj << +/Length 1954 +/Filter /FlateDecode +>> +stream +xÚ}X[¯ã4~﯈x!GÚf ;Wñ€ VPqѲiâ¶aӤ블#ñã™[Ú¦xiìñx<žùæâª` ¨àíê«Íêõ7IÄqT¦©6» ÖEdt$Eé$6Mð.üéëïß<•I¸yþåyóûÓûÍ·¯¿‰ÓÙ¶RGeV‚TÚ'È´RrN°6±Žt™À ‹TQ2—?اu¢ã°iÇG:<VOº_xâì¾r
³ Úñ‘·JÅ gwÖÙ¾¶ëíÓZçá +hŒ$q”A •¹Š1oèÒD¤$2F²B¼˜_TT(¬ïø¾:óµÖF%Q–¦óØ !â@amJv7†íh ;Ë1eK׳]‹Þã¸N¶™b= Tº-IÝñG¨¸è" š²Ær<7 x¨\÷ ‚ÜQžóg·Å‰Âè„<dòœÃ9ãì…+ Ï·<¤X¢ ®Ý PÏÓËÁö"Nn×ÿ qfu$üÀM „–6ù½%Š°#_x…LÄÇ3±®zæº ©–ŽÈ{ËÙæ 9âNjq—·´cØƀѾ{á‘ýûv쪶 ™ÀÁq`uˆ7[ÌÃÑWN6Ôƒs@`¡Ñ… + + s@¿H @Ú ›Y UKí‡3-ñáÑÌ‹_ð꿤Ÿûã +endstream +endobj +846 0 obj << +/Type /Page +/Contents 847 0 R +/Resources 845 0 R +/MediaBox [0 0 342 504] +/Parent 837 0 R +/Annots [ 844 0 R ] +>> endobj +844 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [133.827 74.246 195.817 86.865] +/Subtype /Link +/A << /S /GoTo /D (section*.55) >> +>> endobj +848 0 obj << +/D [846 0 R /XYZ 9 484.913 null] +>> endobj +845 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F21 427 0 R /F25 463 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +852 0 obj << +/Length 2031 +/Filter /FlateDecode +>> +stream +xÚ•XKÛ6¾ï¯ÐQbE©W R`“n_AS£h‘ôÀµd›$nH)Ûý÷ጼ²«=ôb
?Éá¼é4:Fiôîæ»ÝÍë·ªŠ„Hê<Ï¢Ý!RuRU2RUdªŒvMô1~wûËí‡7?m¶²ÌãÝ÷·ï?ljÿIã÷oéûáö§7›ZÆ»»ßïvnþÚýðúÈ—[g¥H”prص̑é&eY¢Y’Õ +ˆ"I«š¸öÝl³2Þoàç3 UTñ¡*n7"öˆÔ± iFÓÐé±%à!,n]¯‡vÀ-Æî‰f<l ãÇM˜'l<év +ƒ…€ùÞÜw«æ
wŸƒ°ñ¨Ãõ`ˆé6¯ø kÜ`¼ªaÖGÎIfFB:ǘOŒÒ¦áS\êů,Y öÊ° ±³2Âéáˆj˸< Š*#„ŽgŒ‹ÄžçFK3A0(ÃPÑižCiù¡u!v÷”†¯%|ƒ|hÇÞ„pÃAc@AÄßÈ9 +Á„3€'ÄŒ¾íD?ž`Ž(ŽF¤õ8¶ýÃH’À‡‡Ž÷Ĉ_‘©Õ®3Xô”Ê®¬…Þ
¿ 3:/ˆ ÕÓ̲âŒaN?ÍÚÇ‘¦æ ÜRÄ÷ÓHØ Ÿeé‹ž·fMãÑ)²‚ v>ZëaÎæ08h¶q40¤2æcÇäËƆ+‘QD™äy}?Cj= +ßF‚¸s*å¬,¢† `²Ë)06ä?€Î," à íZ½;Käsø1¹jðûe²C‡Æ<î°5PÐß‘C –r7Iívÿ\ì ¥À[°Ñ•(æ(:eHŸ+‘¼æ* +Êx¡Ã ¢í3T ¦¹¾ ƒèiåŠ#d"¥ÊÐ÷ôÕ„è]ëì‚6Sðë‰ó»)-³èõ¨V‘Æ3Æ.ÜH"Û=7‡)ù£L¡ƒÀ„§Û«ú"£WÛ”°`êñ—Ó–[ód%á¡{öÒO©«¾,‘ ÍßRã+×öu’Šlæüfm3 ž~æju™uõ¼ËV%}Šõ=Ež”R.‚MÎ
”„h ÿl@ÆÖîHÿVÈ8ô—êáÿ D •I]¦‚.ž'ŽR ôü,ñÚùu"JˆÞôœØÚÓÉôþÄ&frØß-³øíîæËà:PGE™deíû›¥Q(˜6‘ ÇÀÓG"«“<h§‹~»ù•þˆ*£„ÆÃ!;e ä˜(¯“2«/….@ҺȊ`úD•Ñ4-8¦v'g§ãÉ¢ÚòBqAÌ l |ž;M'çNé“æN°šÌV¸pò-#>ê™^Ôk bÇ3Øá¹½«%& \ÌY|àGjA28†j<_J,.U‚?«ë¼¼¼5ì á½üg÷ /ÌLÛûP4Ïï¨bàM™âšNÜ|S¤¡qx†?`‡Ž)íýÔ3½‡²´”CxwSFZ´ô…ë/øÆ¿ÙG] +endstream +endobj +851 0 obj << +/Type /Page +/Contents 852 0 R +/Resources 850 0 R +/MediaBox [0 0 342 504] +/Parent 837 0 R +/Annots [ 849 0 R ] +>> endobj +849 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 175.367 68.906 187.986] +/Subtype /Link +/A << /S /GoTo /D (section*.55) >> +>> endobj +853 0 obj << +/D [851 0 R /XYZ 9 484.913 null] +>> endobj +850 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F11 420 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +856 0 obj << +/Length 1306 +/Filter /FlateDecode +>> +stream +xÚVKÛ6¾ûWè(1CŠzñØ›vÛ^Ú-Š$ZæÚBµÒF¢v³ýõ©ØŽäÄáp8 Î|ü829%2ùióã~óö]^'J SY²HTV I^‘åU²?&ïÓ?î~ûakòtÿ×ýþŸíÇý/oß©âj›É„)
x¥
U‰FÎIvZe"39¥µa«‡aÜîò2O-Ezl§†/ç¶ÙfUzæi;;φ£›|0l}°ÝÓv—Õ©Ûª´ †~à`3ul¦•¹ŠÁþºz!)jUE“7àΘԟc$žU¥n´¾ ztì²\‰º¨“ÊEž¼ó¯1ÌÝ‘=¼¶Ä•˜ÊR¥Žç}ZF¥…ÔKTî³m|÷º³Tlw¦€q€pÐÓ8àÉÏ[ÌÈÃÇR‚ä3¾É0µx“`9<ð•*#ÊpŸ’ϼ››®=:Ûƒ¡VéÉ
ί8“icû~ð¼r èÎ Å0Éd9ÆÁCûÏoèly}nOXÉ +›¹ŽM3Ì ªEa®#ÙŸqï<áçY1 ¡0Ì# O£{nÈ\4i†¾éæ‰Y +K¡]= ;ã$À´õŒ@‚ÐZ$¥V@~O9vDE`TX8„ž&
DìŽl@ ݧ"CøT²ô~»rá¥ÑÙ.BŠÈõ¸ÿË9ão@3û/¯]–/2S.Ói>øŽ>2Øð”3ÔÁHu#/ÓËU@Oì¡ -ƒ\š,Ÿ4‘ÿü y §… úUKÚu©)íô+<¹0¨¯»†žÔ=/Lgþ‹@„š?!gÃ$ P$‡–®ƒJêÝPÉ=Jmÿí/°ø0t õ$/ Øá õÓyWýâÝ~óiƒý™LTb’¢„V´HšÇÍû29‚NÚÔÉ Ù<B×jDa:»äÏÍïÜت21Дf%§Iò:ÏÐÐ"!duø›Q€îqî<áÙ|½;K¦°°„F2››K˜×ékôšðJ;CKªÔEtYn„®õmGzyh %$ai ù¾ )Jù•k
ß‘©tM¹ªÊ-JÐ-W·‚)‘ɪ[ˆ¢ZžÖšû-`Ðᶴ\Z/-›!“l‹2µm7ÁÔuÑoG +endstream +endobj +855 0 obj << +/Type /Page +/Contents 856 0 R +/Resources 854 0 R +/MediaBox [0 0 342 504] +/Parent 837 0 R +>> endobj +857 0 obj << +/D [855 0 R /XYZ 9 484.913 null] +>> endobj +854 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F16 210 0 R /F11 420 0 R /F13 858 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +861 0 obj << +/Length 1605 +/Filter /FlateDecode +>> +stream +xÚ}WK“Û6 ¾çWxr’gbUÔÛÇ4I;ÛI7§ÉLÓWâZlôpEªÞüûâ%É»c÷b‚ +†G^5,é>èôøЊÈë…´ŽWw®Yu˜¼{^ Ç¡ßÆEàE.–;Ò
wâų+ÞA<öeP鞉£ñL€±Ž)Åeðƒ7Co˜8mwÀ , ý,äÕ7è/Q|"‡Õ\±˜óWƒÄ+ ÇÑs_ ä`œ%ÁI;gû#o*¹7Ÿ†Éµ¢Æ·@Š §“/ ³”|C™æå›JÒÞØcƒæ دi„Ͻ^l½¹æ î!5qZ£áÛíÙIH¥§q ieœc™fÁ·(‹Z=
ŠY|£nuÃ…Ì.™µqo€ÎÓ`…ÀŠ % +不{zFƒÃXÓÉmsŠã¢Žû ¤„¨Ù! Eí†ìl}CŠó´U©&¿Æÿ=u'¾¾H¨Ê´ÈÝáZ ` sà>L 0HŸmÛ²¢>>*«½™%¾aÊMß"•WÖ,fÕ=ö˜…+>œe]&„‘2
:¼á6WÃÒ¹*‘þ¿ÂA9ȵC‹×l«À>²¬‘Ø«.öOI&BX,ù05×Û +Ë)Üîò$ +¾lK¸Ÿ2O-çÄ„`VayŠ…Ñ/PUTphR€Œ¥áF.tÅÉÚ¸j´”ú$–& ÝB|ỄØjÇrÍ[Ât¹`z급AÏͲmú#ö,,÷I +z@
¤wvèqÖ”9Ïà/ +Ël¡kõ”Ô^åÁ—=F…;^œ–²AE8ýƒÙz;`øŠ :È}$|ƒ›˜Ðã#èÅJrˆ< F@T³LB(f´™Mƒ 8ëìÁÓ2{@>w«[áIöY`úÚ15¬‰[
Y: ü°4F€Å éÍ“gªÕ ’²àz‚Xzä>âäÌ\dH_i÷· ŒÖ§C¢"JsÝÀ ‰Z´—Œ 0æ¼õ“ šÙˆz´ +àÙP¯ìTB1¼YVvnd1ôRÂj) â[KÃ:ÜyÆ$È„ß/“3—føÍ +Â¥+ì\¨° + .\`‰/Hí–³¬3{Él{µÈ •t"øÕD%’]•RyŒÎã=µB + +.¥-"ŠdÊÒkœ\ I‰/bf,1¤YLï .»jûyl³¡|njq¾^ýÖ¼¾ÃF‰j ^ßš·ÒQíüŸ$üLí饇{ib8ÍæÚ.w xÞ LÎ9BZÐ…Ãr‚?
ó{owÍ·åÝŠø3ä?ôt½¼p‡ùÅD +endstream +endobj +860 0 obj << +/Type /Page +/Contents 861 0 R +/Resources 859 0 R +/MediaBox [0 0 342 504] +/Parent 837 0 R +>> endobj +862 0 obj << +/D [860 0 R /XYZ 9 484.913 null] +>> endobj +357 0 obj << +/D [860 0 R /XYZ 9 465.114 null] +>> endobj +126 0 obj << +/D [860 0 R /XYZ 9 465.114 null] +>> endobj +863 0 obj << +/D [860 0 R /XYZ 9 441.319 null] +>> endobj +864 0 obj << +/D [860 0 R /XYZ 9 404.707 null] +>> endobj +859 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +867 0 obj << +/Length 1768 +/Filter /FlateDecode +>> +stream +xÚ}XKsã6 ¾çWxr’gb¯^–¥c·³ÛI§§Ž§N·F¢cvõp)iÓüûâ ÙN•½X ’ ðáA‡«çU¸úéîãáîÃç4_EѶØíâÕḊâ|›Ä»UšÛ8ݯÕêÏà×O¿ü°.ÒàðøÛãáõ_‡Ÿ?|Žv7ËŠx[díÊ ö9„îB=gµI¢x)Ù6Ì ‘2ëMRäAÙùÖú‡õ&öÁp²°‡u¼^ðÓ £w•íAAwT™“âØ~8ÉdÿÏh¼ò•(S¦z•qm\õ +º!¨L"GùÞÔy0¸‚Žœ*Ô•¾ßJ´>êRÎD,ká\PäG†§¸A +Ÿ8¥ï%Dd§½$¼ý%IñèlzžÎ¤ ¨Eeî…“siãý NGß5BI‡’LQi=é¬ +”¸Å’=»Ù6ÆS¬UlºBÕ¬˜Ð¾'†ç½ð¤2ÄSÚ˜ÄÆóÜlO% +ñm:)š^@Eõ}l«I‰…Ò‡7HÌìã(8œl¯«Þ@# $ÜBCD±ûB€hê”ÂNÄ®`cüHβ½3:Wvº¿k Aý½H]ú×OBr?Ð/ä
.¡±ìBÊáÉÔ©&ÿ;¾H®FÿÚ¶¹—¤9.u õà¬N¡Í ©Áýœ°žÞºœ g7m*B™|×ø’kÁ›CãýJ‡ÔG}=EØW>Ñ#\—D‰ìi qìêZà< k¹«Ü—0JK#Å—Å|Û-&ÕoJnï×·«žaº ‚- @œ_SòUÙ=·’ ‹©vÆ·O^™ÿdZ®÷ƒ0©ïì„š{ JÃMvpxyqÙ{¾H©û^ÐX&ñc]Ép>ƒ±E;B½u\0Yvi°0ÝŸ¨±Pr<kÍïu’o» $’Õ¯ò!r> JJRB¹—ù9“çÚÙ¢j4Ý8½y0¦œ¦Çz8”»])¼l>˵%uAR©¸-™Ê6“‰Ì0z«MýÜQRð,w?s€#PÕ˜^zûR¸W™«._Ú~ô;üJ’!Z &˃§qXR©íx«lÚ" f'žO¨´¤vØgœZ!pÝVS^ò¥y‹›n¦ˆïè…˜#’Ö±sr)V4%m9Þƒ#—¿‰¥–Ýw£Ö DThOÓÉtIaI™˜ <¦Ùª4qÕB€-¯jpÈ·‚wuúÕ4C? £ +endstream +endobj +866 0 obj << +/Type /Page +/Contents 867 0 R +/Resources 865 0 R +/MediaBox [0 0 342 504] +/Parent 869 0 R +>> endobj +868 0 obj << +/D [866 0 R /XYZ 9 484.913 null] +>> endobj +865 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +873 0 obj << +/Length 2082 +/Filter /FlateDecode +>> +stream +xÚuXKä6¾÷¯0öäº Ë–_ØÃ"YôLf‘lI!AÉA]VW)ñ£"ÙSÓ@~ü’"årÍxO¢(Ê¢øú(§Ñ)J£·ß ¾z#ëHˆ¤)Š,:¼D²Iê:dÝ$™¬¢Cý¿}úïÓû¯¿Ûíóªˆß>ýð~×ÈøWšÿð†Æ÷Oß}½kòøðîçw‡_w¿ þóÕQ¬?U"‘BÀÉþ«UƒB)ëís‘%Y#(“´nHj|Ïge<5U<©çNOº¨¡}¤Éõ¬V.HŽåÇáîe<Γ¶´vQv"f;Ò8ŒS‚jE¢JŠ¢‰öB&R¤Ë/f:ƒXQÆV¿ÀiÃ?Y€N#±ÇÙÑ™iêxÑÂ"œÕº¿[ý!rÐ- yeaœ3‘h§‡ !b÷·Wb§EIZÐEÒ,î•%S¤yì:õL\ãˆ3Œ4ïÆáäï <E¬§ùØ™V«¦G0Öøaž{´hZÅ`[ÚvÝeuÌ)«½jé½Rªsxžàsa\ÎÚ 4’ê@\À$u<âMw{ &ã=%$¹ „Ø\f8Ñüßà-½lQ@ñ†ã¸ -L[3¨I»-ýZcõqê^wûBTñÕ;²5jd,1•ÁP*Ê2vÆ{™^cDób4¡)>¢˜Æs“¤>n9ª–Àš»È´‰é›š&GeÁØÀ i²Û—µŒ¿™'b±VHNëDª@ŒÈ Ë`3GôõlŽ¨îyÓkÖ{UbØ“{Í +†<Ô4à 7|*í 3˜iük6“w +n€«·´€9B(Zæk²HòL5‰N6ÁV$U]) Rðù»Ór05@!_Ź„Ì+‰hÚ1ŒDµLÊJܧ'ÇÃYᮊ*çuR–Ù¢±·f,
%EõšXWõºu—ºLʦû6³1ø¤lë'\§‘»*`ÄÀ«{‰Ï«]+kÕ½û •PTâg_‰R0šèñ¶JÄÇ]ÁŠ ï8k°nKt€j¤1? ÿ$!,ò0Np Hë÷«v+z=¾Ê¥Þç²Æ€ s_hlõx‡®õ©$67ˆª9,ÒÞ°a£XúM¾RÈúÿåÒI½ž¬9ªä +`COÇj˜ ,¡Õ§qv$8m¢+Ý2Oc*N@´Ú yö
‡Ç4àÝÀ܇-,`ýÏ}L¼ßë _È¡½r(Øb Ÿ'ã &îZZ»•GXöxˆgxœ†-pãZŽq“€ÝÈÊK“/y<èÍdÏ“²XŒ$-‘!×`S{³"s hœà"¤Ð¢’óbÙJÛ-u'rÁ£| ‹}#à½PÜ;C¾à‰ŒêŽè•;š‰u…Ø“ÎhU$Ùu4éUË”¿¥—„¾È.uv~ý¬ÝfÈÞ™%/›Ï0Øý[¨Ï `ù<Ò?ÑWT€>gR¹Wn‘M>Í( A|ñ1m +\F:Z9YècºW~{Øg3Ye_ÿµ¥Ã¾æÖ '9 r!éÛqg|:5ᡧ;§ ]–Ô*²Uš>ö}‡a!¸ 7{Ô¶rÚR˜Ý:x“ ¡Â„Þ:>ó÷G + GSj#qssÏ:°ñr¬ã`¡iÍ´ú<ÄêFö®:)‰ÖExðµð•>~°æd0”"BÙAZ,ÎÚðn¢*iªTxˆo2 +°ðlvÐ`{x—€ Ðý1´ÔÑó@Êð,ER‚zç}È™@ëþQŸYŒ + Î^°ZŽ=Mk¬¿r†AŽPxé´{¤Î:ÀŒ_…wÕþ.ó? ¡ü¶ÿCM +endstream +endobj +872 0 obj << +/Type /Page +/Contents 873 0 R +/Resources 871 0 R +/MediaBox [0 0 342 504] +/Parent 869 0 R +>> endobj +874 0 obj << +/D [872 0 R /XYZ 9 484.913 null] +>> endobj +871 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +877 0 obj << +/Length 1141 +/Filter /FlateDecode +>> +stream +xÚuVKÛ6¾ûWè(‘"‘z ÛblÑK7Fb“-Ñ6ItI)‹ý÷åµ7îE‡óüfÈ,:FYôyóûnóñSÑDyž¶e)¢Ý!ÊE“JQFEÓ¦¢¨£] =ÇOý¶m‹x÷øõq÷ÏöÇîÏŸòòæX+Ò¶jA+ h2ÚdÁN”È\¤¢-€¨Ò¬iYj>©y›ÈL +Û(¯dÚ@Uºqóü#‹z`CÀ©l›è…„F(r›–°Î¢!ú²ù›qWQ 5ÖÔ”"ZÉ 2Óq›y /^#!(XdPzqPݼ²Ô̼° e] ìIN6,òx€ óø胸eiÅˇ¥L¯ÕÄÜd± ~M¼,#³Á‘µ¢ÇZNƒQ†ÌH¶Ð’G +r£êÃñ3Ÿ˜çÌÑôÌt–2 +Ð ²NS£\«…Ó3œNîÕa ëÍŸÌPV”ü3ú€0òH˜T Þ'„SgîO†ßÀå¬Ä[k‹)%šBPøy
šì;‹< éŒ%½«º»³õÉèà”Ô XHJ '¸#¹ +-–àô<D¬†|)OvJnºéÈ4iU‰µê;îE݈¬Ó¼× Ú]R…®™™2+jêPóË,¥·Hó ò ÓÈ1ÛE†÷Ô‘wÕÑ2ËÛcÏkN&HÀé™ +endstream +endobj +876 0 obj << +/Type /Page +/Contents 877 0 R +/Resources 875 0 R +/MediaBox [0 0 342 504] +/Parent 869 0 R +/Annots [ 870 0 R ] +>> endobj +870 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [237.636 434.727 311.47 448.675] +/Subtype /Link +/A << /S /GoTo /D (section*.95) >> +>> endobj +878 0 obj << +/D [876 0 R /XYZ 9 484.913 null] +>> endobj +875 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F16 210 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +883 0 obj << +/Length 1652 +/Filter /FlateDecode +>> +stream +xÚXKoã6¾ûW=É@¤%)’¢=d»»AzØ¢»n»@·Æ–m¡zl%9®ÿ}g8”,JŠE€pf8’Ão 4 îVÌo7«7 ¤ ¸Œ©E°Ù\‰8åY Use‚Í.ø=üòå×õ › I—Ç™RN7JEÌ2DBÇÂHÒ½»]'<üåóçûÛë(IUøÃOÑOŸÞݼ]g2ܼÿìM±é²QÊc-$˜1×)™º]‹,Ün›vWÔúŠ«é ‹³TÂQœzßÀzœ…wöÔu7HË°_óðXtÈðpÛTka‡¢Îw¤jk[^úbkËß‘ê¾Ë›*ï#\7ˆüJlYJMëµôÔIXÁÒ"
w9²2lö$>‚½÷î¸þ觿µÍC™W$ÝÚšˆg«ض- ×ÈïhÖö45) 1Ü›ïiß”eƒßiYÅÃ3²ÿ]ÖF„ñ:2pÀßÆÅ”‹Ê À'¤nIÖ]ºÞmDî8 ³íCÑ·¶½x{ji‹ ñ_™b]ë
Z„ŸîVOwú¡8ÀVÃCé¿ LÂâ8%Â]ë6~®I³ñ£ó$Îw§vo·¹ŸÝ“ÐݹWè-xÖÑŒ…›cÞyñqàé]Þ‡Úö‹þ´ áNð)î@#UÉ€»Ó4u¬Ù^#ºº +q©µš2t;9ÑE½HõžËíçŽÄ¹ÃÁG¯ˆz +ut•Ûº›+ZjÔ:U Æ‚ÇöIGT´9»¼”š ½×)•¿^ƒ×»à‚ Hc^tqbÔ ò=XM³ß,YY¬²ôõÖnU:o.XU r‰~½ÕÄ[ms"&(DÖ… 8hÁH0gLÏ‘³+졵xUB{›÷΄»í aÌ2c ^v5¦d–¼ìë n#™ C¤&ädüçH+ñz£‚ŒŽ°Ú%ÕS×7$7 «D<‰)<¾@?~e\ÖEŸ—’”¶=äDzÜâÿ 4á²<ŒcºL„¢‚`ªoˆ·eIZ.`< ‹1š€…šÒæÝ7g¢!ÿ¬ÞoVܧ+n²€gI¬ n«Õ_+káä•rÃþ@ðæ¾’Á»fõ3ü
SZ‹&æ¨ê2t¯ÚÁ_ªØ$IÀus>æG'z¢ þ”×@Áš$¡Œ—n/PÂѨ` +_µË©ms: ‘Ñ“ +ˆœV¿Ô’ϨíâC£Å¯žC¦©=á# ÞÙ0·`p<=,
›» ^à~lסߙ¿Ó ©Y?ïÃi.u¦æ=rvù€ l +$`Caê:yvä†2ê‹EÇŒóAÅoÙÔ‡Ž » +½dþèa¥±’Éüì9¶y +réÄï€6’a#†£ó´‚„:zÚÍîIø ´+è#Û’C€”öÀÐ}M¢²øÓû ¹ÊÖ5¦~¤ÏùµgÆzcCÏʳgœ' ”Òt¬zËÀL¶ +ˆg´œ çS\&(]²ÙÓÙîh}xºþ,
ï{š¸¾ŸºÅtÄwX"×^à +¿b{’È®Ë ó© ±O/m¡öŸ =0OÓÊÑÜ]cV€,¼ +‘úœ‚±rqƒ
wi¶®{ÆnPö½<pH°Ð vOØ6‘ûí +endstream +endobj +882 0 obj << +/Type /Page +/Contents 883 0 R +/Resources 881 0 R +/MediaBox [0 0 342 504] +/Parent 869 0 R +/Annots [ 879 0 R ] +>> endobj +880 0 obj << +/Type /XObject +/Subtype /Form +/FormType 1 +/PTEX.FileName (./images/087.pdf) +/PTEX.PageNumber 1 +/PTEX.InfoDict 889 0 R +/BBox [-2 -2 207 127] +/Resources << +/ProcSet [ /PDF /Text ] +/ExtGState << +/R7 890 0 R +>>/Font << /R10 893 0 R /R8 895 0 R >> +>> +/Length 896 0 R +/Filter /FlateDecode +>> +stream +xœÝ™;$Ç„ýùmòŒmÖûaÈ %Þ'È:¤Á5(AÒßב5Ë(z"›©é®ÊÊŒŒŒÌýáJw¾’þ?ÿ~z}|ù~^ßþý1ï=S¾þõH×W^î’Ó¾JŸ÷hýz}ôz—VÊUV¹÷Ø×÷ÞîµÓ¸jš÷š]+óνԫÖr×UYéª}ÜúqÔ»U «+±·6ónm—«¥z÷®gf¹SͬÞÉC+l9+mß9éÎ_úÍ|×¢…}§Å»Þy5v¿Wíûê¹ÝÃ+™rÉW¯úI/åœî]ÛÕ±n´ì•}—~u˜d^.ëNóê{Þ¥z—:ïº×5ò”™Ziü–ó5jÜ1ãžÚ5z¿G÷9cÝeñÄlw[Z˜ûî¼<6~Ü~dg¹öš9ßyë䂹¸àšEW“J w<Ó0wêÂo™ '~Ý]¾f_wâà³¢ËuöÙó\²à4î´ðLj~dõ{çvš¼Ý÷šdF¿VëÇÀÊá‹p®‘ï^¦V*ßæ¸ÙXßš®Ä\d. SǸۜð°?XYõ^ì¿ ÆÙ”Æ9Šì&&9Ë–F&—Üì—ŠWê"Ƽ5Š/ + –?7§'ÛÒø4ʾö’C…¶Çøç”d>`Áõ‹¯ÂƒˆÖö0Û²®÷€08Ñц2»qK0—n‡`¤tÏ©Œñ9£ß7§Yq…VðÐÌi‘2n€q¹DõÛq8I†Àø˜Õæd +ÁÔµ›Vʈq )ÂQ¹ + +BœœÝ ¾‰¿7ž
“>Ì»©5³/Ó6+ +X›xlš ¡Ó‹»…vî
Œ–v”ð–ó¦ÐoQIuË 5§j– ºH}Z9h… 9¿ +¼Ïûzr_G@W{k¥§o><–‚¨àu' +Ü1¤H +õÌòy*ZE߉qˆ2S/Rð
'›P>§©†µmS·‚NÚ–N¨•ì†K”=Ý6WSvšAdoÑ>P vz¶ºn#IÑ[TV•ÒÓMhêoa ”F‚šûå@jJ R@Vb® <Ã/¡úùÙ±¬rj7ËuÒ]¢äí ÊDgTª|ôlÌTpÍ<C\SÓ={§ +5W1J„)iÈÕuq§ FI©ÿ>Y3ˆé¹ ™§j¬ÐK´Fm‹Kü-õ9Z<*Eš£…B›ÉgåìÔþª `©¼æÀVQ ™›mƒ»4¡DõZçR/‘ט!:p2]ž‘6Ïtœ6Îl¢Øy4úæH~·ƒÕMl[3[?¸ g83UUMBCc(õ +%úžÏ¶ÍG¨ i£{»±FƒVP»äÖÃGi°¢6`¨>Ê¡*eê{Ô¯›LÔz¨’
P½ëœÅÉ« Ù¡ÁiTòvGç F”¨Žó›è@D¬Ÿo—¸U†SIš®¸UX•R]æÙšeùŽ^Sòô>*VÀQz%Ê p§ËDnE+ß͈’˜%~Ù*;= ›dÒ† +s?Ý>y LšZ{ûF½Í ,6©ŸPaUõÙ n÷MÊ/I@å–µÇÆMa¢ùH³ )hV&Û3$ªÀs(MþS~ÎVþuv?ÀÙdfMÒ¬oÚÈ´ÚÛiCQwY÷«jªS´M >˜7¨Þ£YB§éY`’6’ì>‚J݈$>žÝG’óÄJmPgEºý’bîÉ?¸(ê”z3Ö«óJò•t Î^Ž›'CÁ]xjº“šÂ²Óh¹Ú±’ïöìÁ¥<ѦíLhT4"ËI+OX¡h
Q=¨2V†&‚Uû¨'pfÁLš#ê†ÂmÚçâvS²¿xNçžÍ¯L{·D_× ÿa"°ûdÉ~ÌÜ»Ÿ)ëÒünm7!ª—:à &3Ç +Áû¬ätdm‡Ä× ›-÷‡l3 Åwb£ÐÞ…^
É0)1>ΞÃÙšN÷häE㺴ç`¡`¬X¼¼
¤ DÑé¾Ä”“FErû?Üßx f{ +ÄFU·¥=køF +åE “>òÛÿëQå? U¤Zûõ¢¾ +²øMÕ8¨Íú™ƒ^²„')ÿ¢UÒ¯ÿó¨a=mûåQõ³Gµ§ûjùœ÷4,&`ã¡?]ýôœ¼~Í9ÿÅw„iK€gQÀø-ÕŸ dªùúño³üR +endstream +endobj +889 0 obj +<< +/Producer (GPL Ghostscript 8.62) +/CreationDate (D:20110512123704-04'00') +/ModDate (D:20110512123704-04'00') +>> +endobj +890 0 obj +<< +/Type /ExtGState +/OPM 1 +>> +endobj +893 0 obj +<< +/Type /Font +/FirstChar 49 +/LastChar 61 +/Widths [ 490 490 490 0 0 0 0 0 0 0 0 0 762] +/Subtype /Type1 +/FontDescriptor 891 0 R +/BaseFont 897 0 R +/Encoding 892 0 R +>> +endobj +895 0 obj +<< +/Type /Font +/FirstChar 80 +/LastChar 118 +/Widths [ 631 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 557 473] +/Subtype /Type1 +/FontDescriptor 536 0 R +/BaseFont 543 0 R +/Encoding 894 0 R +>> +endobj +896 0 obj +3423 +endobj +894 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +892 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +879 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 357.384 40.405 371.332] +/Subtype /Link +/A << /S /GoTo /D (figure.0.4) >> +>> endobj +884 0 obj << +/D [882 0 R /XYZ 9 484.913 null] +>> endobj +358 0 obj << +/D [882 0 R /XYZ 9 465.114 null] +>> endobj +130 0 obj << +/D [882 0 R /XYZ 9 465.114 null] +>> endobj +885 0 obj << +/D [882 0 R /XYZ 9 441.319 null] +>> endobj +886 0 obj << +/D [882 0 R /XYZ 9 419.153 null] +>> endobj +887 0 obj << +/D [882 0 R /XYZ 189 282.399 null] +>> endobj +888 0 obj << +/D [882 0 R /XYZ 245.833 181.065 null] +>> endobj +881 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F16 210 0 R >> +/XObject << /Im4 880 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +900 0 obj << +/Length 1885 +/Filter /FlateDecode +>> +stream +xÚ½YK㸾ϯðQÆŽ¸|‰w±‡$˜ÙL°‡ pÙ ÔÛ`KIîÁüûT±(µä¡Ûž=äbñQ,‹ ¿*Ò|sØðͯïþ¼{÷ãG]n„`®(äf÷¼²dJ]:&µÝìêͲ|øíO[§³Ý§}Úý{ûßÝß~ü(ŠÕ0'™3´†¥D¡w<γɕL:
ÃxéHj<úm.Ì>ÃÇf]Óná3’~)–úµc¢“ú¿'MLñYtÕq‘ÕMuè«3µ «aÕ-³_«ËVdÐ +?MÅ8~ßå]_7m5ú!e˜T‚q^LÓ^R–9æJ5Iü‚k-3õ>¥-W\2ðz.4Óº /ÉÕrÆ ±Pª”ÈÛæ…âÙî :²ƒÆ¢ÌZß Ž[YfO0s™u—¾iØeƒßKò{™Éõ #˜‚{ÓóŠéÙU[§ýÄ„*¯Ô +,ÓªxÛ›¼é”yÛ† aЛ³XÚ +¡ïA^0#Ý”"pý¬ghmóü¨$øΤïcm8W§‘˜ +¥Š>§f OZ\Öw†ë÷Ôõ4ùž´´Qa÷L_Ú +2§¥ù?ÀnJ9I_Ím™y¥¨[«(Ö«¯"pwšÓ¤c…1ß 3N>jÜKÚÅWñ0©
xQÉ•‹oDMÙñƒE1Çÿ ®ìÀ³ ±diÁ6ùÇvþÿ4¼9]OܬÒÊS— @Ž—ÚNÔàñfìq¤îÚSçCýx ÀoEý”îúþÙïÇÓטN0¸^sxíçBÃL8ÄYsHtSÎT–¤°øf–E¥õýT¹ÐóáxIçm¼,,l ÀïŽÑÜ…—Ú xYˆÁ¨ £z N©ïœNÞˆù絛rùï Õ[€üvÊÚç1øs¸'C ¿¤=gH‚`ìtu°fŠ¹1Ú5p#Ñ—‚!°âB{ïOÕؼLÓÆx +‚8"µð¢d¯”Iǘy7òý¥'õé½áP`9ÍJ®Ö‹½Ì…~<É@2ˆ+I +Ϋ H‡ŽÚ¯Ö }c7ˆ
¯×;h
>\öŽÕÓÉc^âTöq[Š¬‹9/Y¶Þ. ¤¥ÎöÕJE` lY0 VgÉõKÅ@hž¥fƒò® šÚ‡\ëÏ]&ù*•¡}¸ìO ^!u ¼wÒT4ãòþÐ J( î3¨§\\D”ˆÉ'Ð@¹(hÙ!Ÿ²Í°%¢Ìž.ãÊ 3ݪOxõ0e|IÁ›t M\p×{Ô³fŒB}£†¡y:y’Fs°«î+Jý£¶4„Á8Zw1,“FÅ70lð|y—T]J/½ ”p¸Œ½Êöž¹$Ÿs•UãXÍ! ÚS—µõpÄ·‚[ +WÐ5\^U¨¼¸Œ÷·(9 «‘z¿„k"•á¾—§öò3nåuÂýS:/s@×W‹¼—rÛÇRnûpÊ};I6w'\$ÉöñLj;)£},e´«'”딑sV +|!‚ŒUÆ”ñŸ-ìMîuHBXÄ3–cÔ;îôó"´]»ï</8Ù󢘵ÅãIÈ·zCÒf]6Œ}^ ãÓ.=ÃqcÖ(Ã× jâ90S`„ÂàÛ!áÃwI“P=øîìG¸ —2d,él’š¯T"›Œ4åû)_L ›ºÙ_èùDGƒ¯Ÿ7Ö:ÐÝc´<û+fÿ${Œ…pïmÐF¬žs‰á°ÇÇI*Ãáý “Ò+;þRõ0"¨Q„<ð¾óB(ù4R²/~÷'öb12Dñzù.–˜8ol$§@¡…ÕàÕ=a¹ k+1Æ…å@‰¾\…”}¡»‹Oç €[†Ì/> 5 #'ŽDÒ4‰=èhfOƒ¯Öó?
Ó÷ÃîÝÿ +endstream +endobj +899 0 obj << +/Type /Page +/Contents 900 0 R +/Resources 898 0 R +/MediaBox [0 0 342 504] +/Parent 869 0 R +>> endobj +901 0 obj << +/D [899 0 R /XYZ 9 484.913 null] +>> endobj +898 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +904 0 obj << +/Length 1944 +/Filter /FlateDecode +>> +stream +xÚÍY[ܶ~ϯœ'R«ÖÕv‹>¤À&݃â¤H-Š¦ÎX;ãÖc|Évÿý!EÙkÏ(ÛlÓ}™¢$Š"ù‘œd³ß$›WϾ¾yöùK•m8g¹Öbss»Q9Ë2¹QY΄J77åæçèÕÕÿ®Þ¼øvËTG7ß\½~³ÍUô}¿~I¿o®¾}±ÍetsýÃõÍOÛ_nþûùK®—[‹”3Å9œìvÍ$2=K¼,›XrÁD®``X’åÄÕÞâöy4 ,
ú±»-vþc×6}UÚΖŸ!3{?î¶"‹ôUÐOS cg§ýŠÁS·"Æ£íª]Q#)‹ÞoµŠŠ:FA¸˜+¦”&FÛoc•¤QY½M¸„eÍ VÁF¶»§é¾®ö¤ õ=Íßví‘æl±Ã™}µp·ŽX +iEß·ÛxvU1Ø’ˆwÕpX‰dH¤Æú£Þ¹%íH2Ia¢Q*wÉ¡'â[.P` bž@™ì?n[ž2óõÞ߃R©è¶èPÅʽDJTzV1T0"ÆC[—~IÛ[AßÀí¤ aÆñHd÷dÀ5àƒÝáTK„rË£ŠÞ ‰v´p:œË¶±1*úz PM’LE%"zUŒ}_
‘v8NK"ìhF8µe‘_TœNue=KQã3 yh=%ô +y2[ä¼åHܵ x“ŸjÊ c8Õ +…q¸~ð0ð‘ÕÖõð¨´Û¨Æú)Ê\ 7N.ݸï!eBðijX+<âÜûÊÞ!N$ _© Ú©³:qõ ©;ºZDÀ,£ÿ"¤}•2 W×._XÞÒõa…«R,—æ‘°&¡%¾ÁÌöUÐvƒ‡™ž| 8O3“ +5Êm Ü)a¾Yð•¡È¦R÷sJÅX%!°åŠ?r-ÐDÆX3>åøÏᄘ¸ÏdJ™áên§×ÒˆO½¾¼Ýùv†¥ õ?±Û#JYp=÷gªÕ€ÁÌEÌÛ$áÛ˜›t …‚ÀM2«ñyP?¸¹xš¦•úk5f;;:s6ǵ´£/C7‡¸ ÁÑ3òË(ÃF— c Jãc±oªa,m8H^ÈÔ\ûÙ¹cç&]cº;Þ;æU \šùÞ'}8 €©'ÀÄï%ÖCéKxŠ©'~.Ñõ¬¯bTשXä)Å®°ˆ‚“O„Í”¡sY:!Ãa¯L5‘ã£ê‡Mu +ç`¬éCBð d,y΄ÁLQÀ +ÏJ‚hæ¡/
—ë.-[r¹‡ÍÖ…4Ì£¾qÚ·6„y(É1}éö@é«ã©¾]<͘äücQÔ|Šª§¢è Æ+yŽ{¯ž{ ŠÂü©rˆ¿GñT9ä¿D ê19.aD®äø" # +,DfküÆ.Žw +'¨=…Õ´îà9±Zç ö‘zÙµ +DËÈLRÑ'3 +“ú·j߹ܫ×q*Ôä)ýê/ƒé÷êæÙÿ¨‰v +endstream +endobj +903 0 obj << +/Type /Page +/Contents 904 0 R +/Resources 902 0 R +/MediaBox [0 0 342 504] +/Parent 869 0 R +>> endobj +905 0 obj << +/D [903 0 R /XYZ 9 484.913 null] +>> endobj +902 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R /F25 463 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +908 0 obj << +/Length 1326 +/Filter /FlateDecode +>> +stream +xÚ}WKoã6¾çW{’X+‰¢,õÖÙmŠž +£EÑôÀH´ÍV]‘Jšþú΃ô#z±†Ã™á<¾ÒÙê°ÊV_ï¾ÛÝ}þRÖ«<O)‹Õn¿Ê‹:…\•u“åvµëV¿'??üôíº)“Ýã/»ßÖì~üü%—7jM‘6UVI¡.Qè. ç¬6"/Ò¢)¨Ò¬nXÊŒëhšÄ 5r²û›:Ôô܇M׫çE1 ÔYJ ½]oŠ-ïyý²–2Q“QÞØý 7y™–¥d¿Øê6ñz8‘ªž”Ÿ'®7U¹MvÑ'Ø_ç ŠÔQ„ãïiR7ppÿƌ֎Ϋq
+žmì-˜˜˜V7ÎTìŒ@ Ž¨drR“Gª"‘Cq#Sr¾n9näù#ž3»¸Ò¬sÐvÐ~2”Üyæ +Å_Œ§‡,86qZ;°_fc&\Tâ¢Ia3ÂBõƒu~ ? —Ëê,mzþÚù +Zç1goëºH +½Û9ë@7,yÕé§,/GÝá ÞÉ æ€ˆ{ã%mkb¶Ê¬:ÅŸë¤m“™pñÙL8g#U3“ç‘5(_l 64\‚ÕvHÅi#К8ž¾¡q¦¼#Wy†t%ßWDö1 +v±Yê ‡UÃD‰n4nÕ2‰ßÎŽ:pFþº¹Å#Ž¼Rü¡R*r}åÁ§<ïÛ‘o>¤‚½†*UØf ‰º öîqï M¹Íöº³ E¨ƒ†YÆé +endstream +endobj +907 0 obj << +/Type /Page +/Contents 908 0 R +/Resources 906 0 R +/MediaBox [0 0 342 504] +/Parent 910 0 R +>> endobj +909 0 obj << +/D [907 0 R /XYZ 9 484.913 null] +>> endobj +906 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +914 0 obj << +/Length 1780 +/Filter /FlateDecode +>> +stream +xÚµXYsÛ6~ϯÐô‰š Y àõè:rªÖ9ÆV®Iú@‹… —¤ì(“ ßo± E)ô$i_`w±X,¾=(wv;sgÏŸ¸fümõä× ‘Ì<á"òg«
¦©{ÁL„ã…Él•Ï>Zïß¿]ÎÿZýÁž“†¡¶=Ïw<ߟÙ~äø‰`éÕ Ä¡uýzž +ël xÖùÂ^-_úù«—«åË7o^ðòÕ´‡Ì¼È‰tÂ*!"Öyýzq¾<» _]‘êÇ +®ðp X«åÛåêƒÖg,NŽÂ†ëå³ÅÕâï=»6#‹7ç—`Ÿ½<µ˜½àŽ]f'dàø"ŠYý;É’^8ö— ;¾—ÀõZ&käÜöϪ깟X¼P
®u‡!¶êVuª6œ®æqS7%mÜYg4•5ët-ù%[wÅÞìؾʥÑ[oØ7Ƥ#ß¼PÕç9J?sÏjÉŸ1QOÉ &nÕšø[P"¢`žµ¼¨+:™f÷ó0´²Ûì ªÊÕöæý’Ì +áøþH@ 6œËN6¥ªLdà²)!ÃDHó‡§à@‰œä4Ãèl§h¿e×CšSƒ¾È刋̳Òäµ:HAýž”£¢„ŠrùÉõDxN@ân«ã¸U„` +uáë ˆ€R0
*ï +Éó2«*ÙР¤; oDFÖYEƒ¸/SÅ˜æ› @v5m7•)”»c·U-ÏnØYüûÑ(d/()RXVšI“U}íXØÔ¥Q[‘QDÒÒDÖTö É-•~^8Á‡w 4\‚‹/„E6’P©‹Ç=ÕŒê–Y»Jqò*u]…“0‰÷Ilɼþ4®]g=}<±‘%ÿÞetÛ–—ä;þ% +$Ãå«áƒðn8¸ÌØODÖà¡ +˜@vT9%½}ÅcÉÈðÈ>‚벞™„$¬›¬%Çî 3—â:iÎM®yùnÝ_ˆvë÷ë·O˜qRÄÂðPÄ0×X +£qK¨ˆéD>Þ6gIUÞ]¶²àhoÚžõpŒD ‡ž@2÷$ 6DƒLô!
’ü‚úÖ¶ŒO¬µc€†ÏnZ}!ØWx’¾óN¼à¦?Çl.2î`´ÊGJ"½©z|ÆL€m…ºÝ’{:^êw#>òOÆ¡š ”D®%÷'^ì„aúÓݽ4¼£W¡)<Øq4è‰{D'Œh’1ˆ.‡@ z‰E»Ù›”<aû `S÷£:p‰4$@Ì‘ms2Më¦Ôƒ¤r©ó ˜;º=µBà¡Õl˜ÚñÅ8e»’ÚµqŸÈÕ§ž†ntTkZÊ;±iÛˆk°¬E˜rÚ3GܽÑøp(n´T†=(û®ÄLv‡‚“PÁ¡ã<Î|±;î߈ü ½µå°ÞÇgÇÒ:ÍÅÜîc9ÂË Ò¢}£;_Nûù~ªæ¨µ^2´'NU}»: +ÒI"HúdizA¦ ÷i ä +ù8`lOöR^ê;" š˜|²›Âçc „?ècD ZöhµKjƒ–ÉŽ +Qᧃ-: yƒbÛ|4…ž¶ûcL™€j?:Ø0Ù’y® ý'¢+B¢§Ñ#ÜC‘$ƒ\_C‡ÈÔ±©Yã.Û jºž?h¹tØQà„±8) [à„‡÷ßÝõ¡$™bòžÒZ×NlÀßw·Â;ň–æêÇû¥&?¶'Âí¸ÓÔéÑÇוž)/ã»<ŒOQ燳
3zûè ¤,æN~¬;1à`Ä&‘9‰ÿ >OÏ#xþwç%é)’OÏsCñÿܯ›:Oƒöß GÕ% UÅOJ˜2åÒ1¾#Êì¶RÝ.—ý£'÷ìLÛì +j
‹ã|œ +endstream +endobj +913 0 obj << +/Type /Page +/Contents 914 0 R +/Resources 912 0 R +/MediaBox [0 0 342 504] +/Parent 910 0 R +/Annots [ 911 0 R ] +>> endobj +911 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [261.023 358.048 330.745 370.668] +/Subtype /Link +/A << /S /GoTo /D (section*.74) >> +>> endobj +915 0 obj << +/D [913 0 R /XYZ 9 484.913 null] +>> endobj +359 0 obj << +/D [913 0 R /XYZ 9 465.114 null] +>> endobj +134 0 obj << +/D [913 0 R /XYZ 9 465.114 null] +>> endobj +916 0 obj << +/D [913 0 R /XYZ 9 441.319 null] +>> endobj +917 0 obj << +/D [913 0 R /XYZ 9 390.261 null] +>> endobj +912 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +920 0 obj << +/Length 1779 +/Filter /FlateDecode +>> +stream +xÚÍXÝoÛ6Ï_!ôIÆ*VüÕaÝÐú²ÍØ04}P,9Ñ K®$'uÐ?~w$¥H“¸hºîŢǻãñ>~d \qðöäçåÉ‹7B”’TJ,×ešp&¡SÂD,óà}øûëw¯©—§ž.ÿ^|Xþúâ
•³e)#©JAªY 2ÄNOqÊK ‰uj¹úËbq¦ÂUSçe_6µ I“˜¢d•ÅÁ ¹[F-£S"A ÕÄ$–1ÿ䑆$F^ÊÝî˜oC á`f4aûÁ§†‰¢Ã¶ó½_!ÂS*d£Â¿ÂXrB& VxÇñ=:a8è\yTJsíÓ8“£H‘5Õ˜÷>ûcÂé£þÒf“Sa?ymgD°Ñö!"€òPDÄ «0~“AÎӇ̡EŒ}/ƒnü „Ô±ýcn¾ÁØ;z3m"‰Í´½ô LÄ° êYÄ( Y—¶ Òðj!e˜U%ÔÄK½¥6 ®í° 8ß5mQ/˜û7Ófu·nÚMfÊ©¡qeU5(ëºs´¶Ùà(Ye‡6Mˆ”`Dé ?Tf²ˆ—á_ ÍB£< WYmËwñiÛ]gÿyf>s”u3*i¥,‡Â¿É.ê²ßå…Ï™šë¹òÎW0(‘p0èuu\ÅP_\1îë!ê¸üS_ßCØ7Ò÷H QÇ¥³zºtVÇ¥³:ª…¨ã²Õ±ýèÏVž*æx}Y®0¦/!¢…ÏÓaQ5õEg)}ã¾&òñDzüŸlå²)i¸5‹›²F®ÞoÖn=æ +ÖÍ®òrSÔ äcV™¤]º:û»-ˆŽz`ZD€š0}ÌÒ¨Ûí6ÏQBYx‰¹‰ F:ºlXÕG@õÙ¹¿PLì «*ÇZTŪ/rŸg±ŒßB骊2«á]DRÈ°-ÖT*°Í:ª1¿yYtPWhœÒðtœ +=¥±ÀØUÛ +öã;:Æ%Qr,ÆŸ|禀cDJÏ}RRH„³îý2(O ”¡&بæÆ'DB\ÒC!âÐ
¿<uáµ5øùõòäã ®Œð˜ Ì)'ùjsòþC ä0 Ç@D¢ƒkú ¨$Tâº*øãä7 óç +Ga± +5ð‹´±ÿTÿÆÚøL›¸O›k3Ý<×䳪k,"hÎû¬¬œà¦:ìªÞ2ô—Yï½ÝA´²c‘€zR$ ŽAw"Î9F‘T<Þ°![Å +u^køª¯ƒ¬$%T«Ç±€~ ¨‡± +š€˜ÃK‰‘* +endstream +endobj +919 0 obj << +/Type /Page +/Contents 920 0 R +/Resources 918 0 R +/MediaBox [0 0 342 504] +/Parent 910 0 R +>> endobj +921 0 obj << +/D [919 0 R /XYZ 9 484.913 null] +>> endobj +918 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F21 427 0 R /F24 494 0 R /F25 463 0 R /F7 232 0 R /F16 210 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +928 0 obj << +/Length 1638 +/Filter /FlateDecode +>> +stream +xÚ…WÝsÛ6 Ï_áGú.òôA}=¦™Û¹×%»Ôíe×î‘›«,y¤”Ìÿý +øb ¤yÈÖ(·A‹!ÚbŒQOê„á}pµðKâ˜= c-¡ìy$KX#ÐöëÒªkM/Ú +\;¼¡òB€‹XC°TSÎâf ŬQ›ù nš• {7ô(HFé½ÿL_tž>Øûø8™=4ƒ¾"±‘Ô˜Ôn§$ +Îî*ÒÙè×ZÀùElÝLÂc¡óp¬a¿VÜzÊ9ak¨ô‰@oÌÐx&ìÞz³ ZYç7(Ðã j éâ•‘irÃ&8§çÌéLGî˜`P* ¶Cz0îK4¶ ª}âÕ’€,m› +ä‰mɲÁÃxÌl € mÆÈÖ#†$¶y+”µ l¸ãUõ[’ZŒó¿Rh¹"¦j¸µ¶ëþö&¾“$|C ý© A Oñ¿c¸ÃD¼F½Ø ¢¡Ù˜&ˆx ‰ÄU²èÆ•ÓµÅÐàÓÆ3·ñt¡›¸Ã)€jØ/ó”C–Uí§Ç”j‰Zå/ºŽr¦r‘é$ôÃãL'Õõ”;cªñ£i°Žäý0ªíhéiÊþÄ쾸 +DEÕ’Ü ™ŸeØbˆD®VüèË}ÏÀ^îʤÀF€žÂÄMÓ‹çŽÅWCŒ%öà2"C¥OT×æ_RãäØ£U- eNí +ú\ XŠÉÂíZ‰þ +§×Vh¡<‰®žN `·RöÑΨ8Ë €Oå¾ib™#Âí øjwñ +endstream +endobj +927 0 obj << +/Type /Page +/Contents 928 0 R +/Resources 926 0 R +/MediaBox [0 0 342 504] +/Parent 910 0 R +/Annots [ 922 0 R 923 0 R 924 0 R ] +>> endobj +922 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [217.145 343.603 291.555 356.222] +/Subtype /Link +/A << /S /GoTo /D (section*.104) >> +>> endobj +923 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [150.308 300.265 216.074 312.884] +/Subtype /Link +/A << /S /GoTo /D (section*.89) >> +>> endobj +924 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [21.735 228.036 95.642 240.655] +/Subtype /Link +/A << /S /GoTo /D (section*.95) >> +>> endobj +929 0 obj << +/D [927 0 R /XYZ 9 484.913 null] +>> endobj +360 0 obj << +/D [927 0 R /XYZ 9 465.114 null] +>> endobj +138 0 obj << +/D [927 0 R /XYZ 9 465.114 null] +>> endobj +930 0 obj << +/D [927 0 R /XYZ 9 441.319 null] +>> endobj +931 0 obj << +/D [927 0 R /XYZ 9 390.261 null] +>> endobj +926 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +936 0 obj << +/Length 1983 +/Filter /FlateDecode +>> +stream +xÚ½XMä6½Ï¯(ääº K–¿°‡ÅH‚^d/I!;‹™=xÊî*#e»#Ùéé >R®²k<Øndv.¶HQ%‘¤¢Íqm~|óÝþÍ·?˜|£TX$‰Þì 6Jça¬“É‹P›l³¯6ï‚Ÿ¿ÿé ÛÂûû_ï÷ÿÙþwÿÏoPÉbX¡Ã"-hV çzùu6»XéP†iå…H¹fhún»‹³8(»JCÓÖÒª[ †óó6×A¸Ý%Yü2 ¶:N"ð´ÕYP:?îä‡ÕÎÕÝÁýþ&¶*Có¾TJŒÃx 0Å3”%EwÊ„Æ$¢ÜS3`O§æ +¬×æ²ÞŠ5?ŽÖ»†c'ÐÞ+ôÕ„ó‹ 7ÝQú¼Çè·r˼”ZCô7t—BV56×5ꢼQc⎴´Q†Â…,Oƒ=ƒ!zJkËîX·õ„•`V½ìÅÉd| àãsx4S]]WkJ0¸$j:!x»ôw×0Ȧè÷[Ã!žZéî$Ñ5–—!btƒP¶>b;¶Z³oMq#z?}*âøöýõ°âÕ«bE :›¯Æ©í{]߈{ê, +u¢–<÷uIM|Ì¿U—|;Q_ +ßÁ«sJ‚-\5§ÃuƒÏTÀ/…ÛÒyÙ9
¨Û´ <©AÑ*;¯ ‰¤:+È¥Uð ͶDŽk¥ì=îX¿çX%ŸÖ +$:‚F€ùox !U‘ÅX[»G¾¾#µ‰u&G<=ÿùL3€{‰ywRõLć‹Á@|ÂV@ÕW5(‹Ç®Ù!H\Ÿ‡¦‡œ›Î×7
ItSäyüÔ„g%ôM/K踩©{lñåÁ}÷Ùë4*
\‰:ÐòBzyæãY01„ñlI|© ®“±üjEÿ «[i¯©5õL÷’á^„¹þšÕ^Ö³h¥n&&c|¦.Am—ÐíK.O½>@Q?…ÕáRÖ:áùç©ÐIš*I”‘Ü^Wȧ2FŸjcðXy5|È ø OÃà˦^)œåS:f°vðùtéOuÉy5¿i¦”$Ž¦Çm¼hÜn˜x¥@„Ä_n¬tÑÂÓimù½P³±œ<Ñ‘ù e}³¡õÚù’ÔÀ†"53>¥¯ˆ¦õðúí‹-N9¨ˆª?>Z<ÍWžÝ-j§,x(ò K§—šËòôÿ~ÿæO7û<ß +endstream +endobj +935 0 obj << +/Type /Page +/Contents 936 0 R +/Resources 934 0 R +/MediaBox [0 0 342 504] +/Parent 910 0 R +/Annots [ 925 0 R 932 0 R 933 0 R ] +>> endobj +925 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [183.919 437.716 257.752 448.011] +/Subtype /Link +/A << /S /GoTo /D (section*.95) >> +>> endobj +932 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [213.705 423.27 242.023 433.565] +/Subtype /Link +/A << /S /GoTo /D (section*.101) >> +>> endobj +933 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [270.533 423.27 303.074 433.565] +/Subtype /Link +/A << /S /GoTo /D (section*.104) >> +>> endobj +937 0 obj << +/D [935 0 R /XYZ 9 484.913 null] +>> endobj +934 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +940 0 obj << +/Length 1619 +/Filter /FlateDecode +>> +stream +xÚ½XKÜ6 ¾ï¯˜£ˆ ÛòKíiLÒ-‚X m[³vêÇÖ’³™ R”gí©7»¹ä2¢)J$%ò#5ÁænlÞ]½Ù_½~ç›0ôE’D›ýq ?Ïù&Î… ÅÙf_nþbïvìn¯ßo=ž%lÿÛîÃíVÄì}xKãíîýõVp¶¿ùófÿiûÏþ÷×oÃd¾u”…~ † Ùîš º +œ-‡‘ ‰ˆÔrARfeìzЇ¬©;¥‰|¨êb嬢ÏAÝJ«…
±L¥ˆh{S÷[× /fï· lÓ× îfœ|Á±ÿ¶!•Æõh0ë…± Ç XIÔ÷p·0`’†{9˜º ëd…LŸ´Q-M[#`,z¯ JP2iÉ}Ù& “
h}E…‹ƒŒ?ƒƒrùÕ ¶Ød¾È‚ER?Y/´rV*\»’ØÏx´™IêK?¦-zJ‰6‘=§/´ñŸê[üBmp• £ƒÆãAfŠb'%™¢oÛ¾ó·^’ìúhÆIš³VšqPD¶u©iв(nSÁUÒ2Á ê¦!‰² ¦QZ/"Öi•e[ +4SICah£=Ä$’Mm“îDz,ð«¢iÕýHi¢M<´ÐÔfœ¢—ÌÃïš±daFÙ¬£¾€s]¡–IáRÈÔòô½œ¦»é\€~¨Må( ÎÄ€À µJ-üƒ¬¬Ðø“®‹u{´,l ˆhߊ„™Ÿ@,ä>V ãÅy|Ö÷Hî«TºêCÝÝÑ·=$ˆF—q”8$xõj¨Á6ËD`ʘÓl$-¬q 4¨âc¡(O™éqÌp[ü<ÂÙíÊñP3Š ê&à @Èþž Â9{ %Éw½©¬/8Ñöä©’ ñпµ+v1“M1à ó–Ôš¨ W-ÏÝ1ÎN`:Ðú ±!üÝU‘Ü㾊ˆ³sÞšiR: K 2HƪØG¤ñ¶Âˆè_ ¹ŒÉÖ€¢WàL©À£ +}Òý‚`ÑP‰œG]I +\k—çlšž '`'ݱÃlÑЌͯ©]Z‰™EXȺÏcW)È m¢È!²&““Édœµq“g©EÀ¸…Ç‹ èÊUt³ ¢9KÓ1ûÅäY, +¿ Ãϵ +†$NônÕ¢b€S ^aM˜’®A}"P¡y˜—/ôÌ–¦)kJâ€Å ÖBp' +Øb* È Mù¹m¶˜ E^Oá½Ò ]èõZ—r?8÷f«Ý)÷ÃäÜœ¾YÛFø±H' lxÌn:o€¨ °ì µ®¥˜f8uýŠÚ t.§àà©kYèY +×#Íg¡y¦·ÐmœaÁ\vqq¿âýcåXë@l–‰05!4T0;ÇïÝHX°ÝX4 ++'4!ÁYVSÍGøca#æâoUú‹i¦q·¿ú/¶º +endstream +endobj +939 0 obj << +/Type /Page +/Contents 940 0 R +/Resources 938 0 R +/MediaBox [0 0 342 504] +/Parent 910 0 R +>> endobj +941 0 obj << +/D [939 0 R /XYZ 9 484.913 null] +>> endobj +938 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +945 0 obj << +/Length 1888 +/Filter /FlateDecode +>> +stream +xÚ½XKsÛF ¾ûWhr¢f"–ûâ£=¹Çuë&WMÜIz ©µÅ Eª$íXùõÅcI“2ãGÛéEÜÅbìø€U0»š³ãƒÀ}\ |÷ZÇ3¡}¥C9[^ÂPùÒè™6Ê&ž-W³Þùùû“ùB %üþ¹ü™7 +?1†6.„P~©ÙB†¾Œ5ï<:?œÃ¾WKØï5NÞžýúûéá<ÑÞòäí^xûš¿ËŸŽxp|ôæèìð5Ítä‡a´¯uÈ‚ß¼yuòîôh¼ÿ쨓üþdù‡³3 pF`3X)}F,ìƒeNa†'‚s$*‹"ž´¶ó…4‘WVsy_x’—ø½”§[øD^Õäm^¹•¶â¥Ún‹4s2Úµlk’v“7°!-˜xYÕ¤^)ÉÁ;X8kF—P]â©8…Þ•-mbºó2Ë·…[ë˜k‹boòv.coÇ´«üÚ’YsÒ a77«1Vppv|0ûHì¿ÙŒˆÌçó…ð0>@@÷Ë»9ÈÜž V‡g ƧHQP¨={›f-÷nÀŸ/ŒŽ½% ³[†‘Á“×sáYž]7võRÞ'¡ôaQ0ÿ˜{·ÊmÃTºøÖör1e—m™¹ÈbÊø±Ò]dü2<"ðcw,/§¤D¾”{2¤j¢Í tÁïÄL†© a<Øð + Mm›ù4T ¼Dûë\mŒ—àl¸Ž–ép£<àP‚ÁÊ6YoŸPÁ=_ò°LÛk 3 +LÈ'
éÎWgØ‚íÚ–ÕÆ–˜2ô>&`—Æ}PÓº +¼fë˜3nÑRUïxLÞ‚m´A Àe¡× Wó†I.0Þy ˆtÍ8è +ÀË ² ¨íšŽÎ²&RƒqG€¶äQî¾Ù„k/¤‘œœÃ¥®òÑÄÞ¶ +6LþFµ›2N„_‘·ýpDÓ¿»˜BMì`Œ óG ¼± +¼ ÜZ²ÿF¦vPÆ}ó¯% i÷K ,-™‘“ßæÜ)àê÷ʱõù¬év ·Xä™k·œž‰6rÿï…ú"o¹Cû ƒ½æúZ˜öšËÅTC7£DDäNÙ=Ž¥ìŸR`úêÓWˆÐ×a²Ðɽ¼]p’b.1}‘’³×7b[<O—üWºÄ3µ©ÿñdú‰ºÀ‘ªoz ¶uâÛÝE"=þ+£iyÆ- Ž*¤÷- Rú–fb_ 7ÛÒýÁcק$ô§ÌæŒtúÇkü§š0 +endstream +endobj +944 0 obj << +/Type /Page +/Contents 945 0 R +/Resources 943 0 R +/MediaBox [0 0 342 504] +/Parent 949 0 R +/Annots [ 942 0 R ] +>> endobj +942 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [242.703 372.494 317.138 385.114] +/Subtype /Link +/A << /S /GoTo /D (section*.80) >> +>> endobj +946 0 obj << +/D [944 0 R /XYZ 9 484.913 null] +>> endobj +361 0 obj << +/D [944 0 R /XYZ 9 465.114 null] +>> endobj +142 0 obj << +/D [944 0 R /XYZ 9 465.114 null] +>> endobj +947 0 obj << +/D [944 0 R /XYZ 9 441.319 null] +>> endobj +948 0 obj << +/D [944 0 R /XYZ 9 404.707 null] +>> endobj +943 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F63 238 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +954 0 obj << +/Length 1823 +/Filter /FlateDecode +>> +stream +xÚXÝoÛ6Ï_aôIjUÔ·¶§®H² Å +dÆÖ¢Ý#16Q™ D¹iö×ï>H[v”¢/Ññx$Çßýîœd±Y$‹ë‹ßÖo®òz!DÜEºXß/ò&®ël‘×MœæÕbÝ->G×—^Þ¾}¿\eU¿üp»lòè?\ñ÷öòýÛe“E뛿oÖŸ–ÿ®ÿxs%ŠéÖi%â\8™vm]$Þ—Å*iœ69eœÔ
[©oË´ŠÔð´\¥U ƒ4îÞ;9ꥈ¬aõ—¤HŒ y`M ¬·Š…÷vP7ÿ{¾5°\°¾µÃ +Ý—V"ó¼`7å Ð6ï \Xˆh´øMøRàž÷ã {Ïzk+®åÞùÅ]Ù¡ÓFŽ~Î=¹QíxRƒ«5î?u¤dG$\s«†˜æDEsjp§æ¢Ž )n,wÊéä&1l,Êvò&£å¯Ý,|Ynûn5êzåm¶ƒR«pOkdON¬æ¼ø¦Õ#\&©9 + .Öfã^ûPm•aupåV’²ŠZTnå ÛQ
Ú©°ƒ:E ©Þ>ìü³úͶš—ÎENcè³:º£wTà
÷¦SÆ )«`fŸxŠOá Œ$J¸7)u§$KtÇ©ýL 6˜ÂÄjÎ'‹¸Îr¿C^Îz@ä7=/`N:ž»·}oQÿè~©êhMçÁ"‡¶šÍéÐŸÚ ÌBþ ÐaZJ!†;~¯e¯{¥¥áagwRxWJø2›&¼(€Lš:$¼ŽU<Ç ¢‰3 oηÖù£5•ÂóÂý ӌ±<³$>
ÜK®(Àjqî‘QK ÷%¹ê; ¨ïÚ.†¨¦MtcBbd@j1ª=f¶ ù|[1ÄÈ·¨{š{x§&68!mJzã´©¢³•4‡o‡sBÊ 1 ï\Äu%~"Þå1Þ’ôFw/ûÀL +“n$Ê:úUF;K‘á°—È ?C9¥G>IO>!óÈY ·ø„øê†ÇãVŽlá󪈮!“ ƒ¦—”l:ØïF’gí ÚÙ$ u¯’À{Y‘…ÛLûÁ¹Ë
8Œä)àÔQu¯ü‰$E°‚‘¯šiɱr DêEŸ€ôö=ìôÄêy²×ã Ïûô|§†QRf”
Ô
TÍ ëÜ~³QŽj"b#çsÉjk÷˜(€Yô•ê’Ü!ì^fúIÈÍí‘xÌ{†TQÂNEÀ ±fuÜg²U q0!Ñ´ògÊÞYÈå¦j¢·Þñ&›3TgTÄ^ +–ÝÐÙáïé èˆøA_B +¦a‡p "3>òŽG#÷&(J¢{T¸ý‘G„ï,ØBúÕžÎP<‰ÚjÈ>¡8 ÐÁ>ò5it¹o{¬ò†‡ƒõO6ŒZ>ø«²º´wlÊ ›á¥àIàža*¸“çL‹:€Ü &Å8«*| Ÿð¥ÀÀ—C», +ÈÀÞ›þ²G @oâÖr0Ùì¬G¨ÓÀUÔµ3¾ÆÌÞ#ÇV®ç[Ñ;}u<© Ob~²¤¡õÅžº¥Vu¬ .™IRT¨¼ÆØ×¹Ïè¯^V —šàRV”ËeÅ$(CT–¡Ü - ¶¸êÉé–¢šNáÁ&ôø¥.†¦Øï;)r¥)0ØÉn6x 4æíˆ?X²$ ÐKDhvÑÐp#øÐÖ\.1´8¹•^¸#ŸY&TÀŠ Øm ¼®XÕ©
´õ³Ýé=3ÌC?\ô ”ÉCÛ˜rË‚¬@QN}‹€Â×<K–G”¥åaÓs”‰èåZw… ´øä¨}[–X¯¤#àKˆÏ, ú|!XQ•¨OxMˆUPØ;Õ!qöb¶Þñ²2§ûÓ?,µ=UJÑQœå £(í,#wàãFëMÀ; NPI +@¥c×ÃOaòÒd?[7&øÃ~s:·=€7£OúqÒ.4üŒ)lKýÒ\É®‹¸Jͼ¤²—E½¾›m2³<nÄ¡bwûî´w‚™ƒß}•¦I\æÙémÞòÈkìNúB~ÒQâ»]!¨OÍ‹O¡!4“Æç
°¨ÓI tn¼Ñ$ü~ƒaP›ÙvrßK|¢¬¬]>6y
»•á_ Åÿ3•Ì) q +2/ô±ÿ`ø5[Oòô{
-õNn´ñ‡)ùòOდÞâask!òïªóù>²¥ô¤pÒèò¶Æ†ÅL“ÓþyïVcñ£23í(Â÷r}ñ?/äO +endstream +endobj +953 0 obj << +/Type /Page +/Contents 954 0 R +/Resources 952 0 R +/MediaBox [0 0 342 504] +/Parent 949 0 R +/Annots [ 950 0 R 951 0 R ] +>> endobj +950 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [154.849 218.04 174.392 231.988] +/Subtype /Link +/A << /S /GoTo /D (section*.86) >> +>> endobj +951 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [199.063 218.04 231.926 231.988] +/Subtype /Link +/A << /S /GoTo /D (section*.95) >> +>> endobj +955 0 obj << +/D [953 0 R /XYZ 9 484.913 null] +>> endobj +952 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +958 0 obj << +/Length 1232 +/Filter /FlateDecode +>> +stream +xÚ}VMÛ6½ï¯0r’•¢O[BO-° RôT‚n´DÛÌJ¤CJ»Ýß7 Êko•\ìù"ùfæ
©tu\¥«Ïw¿íî>~*ëU–%MUå«Ýa•åuRäÕª¬›$/·«]·ú;úóá_×Mí¾üõe÷uýÏî÷Ÿ²êfY“'ͦÁ®~A“SÐ]ÎYÅE–'ySBØ$iÝpÔî$\ÇEº‰ÚÞ¬ã|µkü<96:1*wxeÅè>HãIΦyµÑ•Ñ÷гb|û˜¥•bEÒG÷ð[œ•IYVŒçå¤üù'@©‹HXIB™½“ö™<²c—S©S? +-ÍäÙæ¢û&Z©×y lù_‚d|L«Té°å+`ÈnmY§ Ó¬v —e ,Ò0+R̘Ë2 Q{2¿²Yh¶)ÝጬÔj”}ð¹Aô=»Å`&MËÆd ojwRn 6:¶ê¨PŽ¢J#+ÒJÝÊxï“äT»×uGÔ’js][Z1¨ã)T‡Tq>[s¶J0,2ñN’•QÚµ_@"P§¡½3ŠÁôýäžî?À Ú*ÇATê¢Î)`›ÒH~ŸÔóºBçúKÛ|¨a¿`õ³˜œS¨æ’ƒ™lÜ©Aj& +*é–¨ Ê!36¸W7JêÝÖ“¡ŽNÆIͺ°{5ZaUïK‡&Ôu…&€Í ¾£ë `;éXõI’@¥ ùˆÍ´£˜é×pj8[y"ü{TAº°“psÈ/̓"”Ù6zQã‰%< ¾d,¶DÛërÀv)dåÞ¥ùÀÐöžªÐ'ýmrñR-FRv~€Àåí°Îó}€jå(™ÚÊ„a0vñqœD*ŒŒë_h ;9º¸Š¦]ÂrÕrªÜ¶æ +n›ÈœÏ< Î_$ðŒ†=Ü-2€@lºVBh¢¾†ì+Ç„ígÆ;˜Evò›2 +T`…*žoªhD•GœçaA÷€áüçSo»'
”Õ ÇÈ+dt 0cž{ÖÞáü9™‹4ç‘MÁ½‘ÿt©Ç³ÀTç¡à)Å¿yµXXM÷P +¾…ÐÞèc +Áá©È/Z@éŠ]ðà8ÕIæ}Ê
&û/ÂŒ¦yƒöì<°æˆ³3C¡ãúÓ:÷’·ò|ƒ™ò] ;ùò _ø »MÊëÈ^AHþ‚g¿¸}–X€à,zbì-½$¼]ÀP&ÏX¿—››S]*ÔMúÊ#ÂSÃ×IŒ•R'Íú×À3¸(3æG]BÜÔbÚ\Çqþò†;ƒŸyÿ. sò¢?š‡¢Ùrü)M õ‚xõâX£Pæo²òô£(ÞRì6Äú;kp²ç!6Æâ‰Û\×.<7ãâåA/4O‹„4Ïu‘oM>ÒÌŸ'£Zyø›øí³mRUÍíž‚†÷ˆ‚úÉ÷ZRŸÏ2Ù7³Ý9¼žˆ?.È?^¶»”’V½Ñ™| ÌotŽo -‘ºÊ£ž¹Sa¶U³È‹i~±¸ðó¢A3 ß|{|·À¬†ëÛ˜,?¹:©°W ¿”{fÛ<#sÿAê@^~=(hîÍ Ï$I3`È'¿ñó•ÅI©y¥Ø¿µ…o½äæÛzþØÝýŒ-c +endstream +endobj +957 0 obj << +/Type /Page +/Contents 958 0 R +/Resources 956 0 R +/MediaBox [0 0 342 504] +/Parent 949 0 R +>> endobj +959 0 obj << +/D [957 0 R /XYZ 9 484.913 null] +>> endobj +956 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +962 0 obj << +/Length 1730 +/Filter /FlateDecode +>> +stream +xÚXKsÛ6¾çWhz"g" +!ð<ÝÆÄpHD)W¦¥õ¦t´X7UÕÄ2öøcVD-«ŠM ìZóÕ6}8µljgá²²³°z D%£AÎÞÂiïŒ È‰76% +úê¥í¼ˆê†žë¾]A^"x´²_¸È–},¢ªCæg¢Ûš˜ûÄ»®¬W¶~$’7y¶¦ÛÀphåh«Ó‘ÏÇÿTŸ¥Ë,œ†3®©z4‹ÈÍúl{×6he¶ô>0<¶d˜í¼S˜—%r–¦E˜’À?b-½é¢ˆÀ€¶Ã¥Ž°7!êºm¶D,éqânâñbŽ"º*+‹®2¶ «f[Úú-åG– ç‡, ¸Ä2æÒ<—3º å%*ÜNkz¦Ñ~c—±Ôц^1–&p8zúHÖ÷• }UVD(ƒV¬è½5ìEVîlè"ŒÆD,Ñ ƒ ŠÎ¯A…ziæ>BN<“±RœÔŒ,X¡’Á'¿LÖgZè…Åó,UÑCq ‘ òÛúÊA-0R¸¿5%Øžfu ù8oQ%iJõ¢8˳3ø€G¦,ZVdÀ<a%jpºí6´=ZKàª)3•bׯ›©˜LFOXG×?Að@Õ}M¯”£¸"|‰nç1KÌDŒiØmÚç`^ª™Vgæ¡{d‚ÁÂÈc¼m¨w-"D–4‹*ûä“`o!nšhïuM^׃ב®ÕÑ‘( %]vfõ mmaÝZ¯ 0ì(5 ‰áѹ '1‚Š?Cý:PÀ»õþ vûÚ®›v[=ƒ ÒmÀ×µ¥}ÜxAá>[÷2TÜd†JL¡¶ñ1Žž>à´×ml Ž…ÉCµ +«âDó€¥2#,E JzL@)’=”ŽNB€d †ª çÕ$H–#J|á)÷õ4ˆUÑú–]öUÙùÉÖ+`PÃ,8g˜ðN 9ö>ͱ'·5-©¾òbCÁw;Ø uý9Cƒª5à Ô‘ïDO'»¸¨\3UàC7]·ÆTÏóPÚ4Y +îŒAÁë&?" aa¼ Ò±nºÉ&,àKcÌY¨&çSè"•¡Ë‡o 9Îô0•ÁŒ_º/ö0VŽ ™P¦Oôf +endstream +endobj +961 0 obj << +/Type /Page +/Contents 962 0 R +/Resources 960 0 R +/MediaBox [0 0 342 504] +/Parent 949 0 R +>> endobj +963 0 obj << +/D [961 0 R /XYZ 9 484.913 null] +>> endobj +362 0 obj << +/D [961 0 R /XYZ 9 465.114 null] +>> endobj +146 0 obj << +/D [961 0 R /XYZ 9 465.114 null] +>> endobj +964 0 obj << +/D [961 0 R /XYZ 9 441.319 null] +>> endobj +965 0 obj << +/D [961 0 R /XYZ 9 390.261 null] +>> endobj +960 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +970 0 obj << +/Length 1620 +/Filter /FlateDecode +>> +stream +xÚÛ’›6ô}¿‚G<CßÚ™dg;}J=v’>hA¶™åâ"œÿ¾ç"aã°M_àÜ$ »’à$ÁãÃ/»‡÷ U—Y&ƒÝ>²ˆS™ª(c©¶Á®>‡Ÿ>üöó¦Táîé§Ý_›¿w¿¾ÿ(²Å²RÆe^®´ T(ô¸s‚(2–¥ “¢d©éh6QšÉð°á¨7r~m&=5C¯[æ|I„2mÍGJ±8RdqšKäãšZp‡Ty‰w¸e¾ › +:"*ÂW„µe¤6có ¦æó÷ãÐ1kVöQ·MkÝãA$¤Š³2@ÅJe|”=m"Ü¥jè"iVÚ†lÓÚ ÃÏx–ƒ§Q÷v?Œ €iÃÞñŽnq5DÃX7½žŒ7‘ÊE¸;6–TIœ9ëðÌ* ]‡ó„r‚4ü‹BÖ¹…ÍjÇ뙧ù×ÒÚWðÚ.Q·¶»ÝJ·lÅ,‹£}Ýd +MMKÓ° ˜×‹ÖÔ̈÷)ÂãÀ‡RòÅ‘:š½M_™ˆï5з¾°Ø—$Kº¡mÏö@ÁKί…l¼RÜn%øÙVcs"C¯èÒiï™{;"²
+¼âq°¦i¡ØÆYV.W“CèÎ-Yä•O쇉 2CP5 +à<]y+ˆ{ÂÓƒ™² »î*‰‹mæ…½÷`É‘äÎ!àp“pà`ŸsÀq9÷ÎÅ÷6‹,[^Ñ6à .¥Û°‹
ýn¥Ë`8 ?÷5zÁjèm˜xØ„ŒT:uᯙ¼È§[‡¹|{iúÓ2ä w’*„4¡s$dÏÀT¥UjF‡óäøtXCæ%ÅêÌ
ûÈW!ÞxÏü»û®Åe†œØ†vjÚAŒå@‹s3ÆQ?ž'M¡*0—ˆå4j¬³‰íùÏÑ,®iÊ -ÿ÷XzM)í•'ÑràwŽ[™ +(V=sì#ÂêQ© +> ëÆZÚAIÏæ΢×R
’b;KPÍY ö9Reî@r’’ètô8V$%¾÷+Hp5¶K´Í ™îµ±†)(k÷võ"I¬’»ì¼ ã<äÌìDužmÄ!œƒN@k ‚Ù-… 㻾-EœlÍ~l²ÔäyÝdBüÐdO¨ZF. ©ár—Á?¹ÕfÀ¡“PÓ@qL¤¹.
a0tš‰ù\r€<Sô¦õÐ!سd=5j d² +”=[fbÇmÀ ‘Ÿ)n¦&×Â;È,œqýD@Óƒs2l•†£Ó©²zcŽI¯o^×ß«` æ‘\Ì›‚mV³>žNã@—p¤¡¼·ÆÍu·ï + ´ô‹ëþ´®Õt˜¡})€
L¡NB/=7Îþ:=fýèmVg Õ3¹6}É,]L_ˆS‡qý #,uÙw«c'DQ®æI²‰M¼þê‹EVx©ÛÇ á Îth;#;jâF Ó3ð â&Ù$}k,~îD`?êÎœ3/½{‡9Ö0^–âkm0R0ê=õ~¿tRˆlBý—ç$›'?„9f ÷zU…Šf‚½Þ½s¦!EW@º¶ + ppø!€Š‘{ý¸³n/»¯>gã«¥ñ5ß >y´C”:€‚ZÔmÏ à!BE9òk •CðmݵðìN\Ä5·i/ÑÚ¼ÞñôéúEŽå^Þw#‹ó·]¶ÿÿ°{ø;€Yú +endstream +endobj +969 0 obj << +/Type /Page +/Contents 970 0 R +/Resources 968 0 R +/MediaBox [0 0 342 504] +/Parent 949 0 R +/Annots [ 966 0 R 972 0 R ] +>> endobj +966 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [311.193 239.626 333.996 252.245] +/Subtype /Link +/A << /S /GoTo /D (section*.68) >> +>> endobj +972 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [54.828 225.18 98.883 237.799] +/Subtype /Link +/A << /S /GoTo /D (section*.68) >> +>> endobj +971 0 obj << +/D [969 0 R /XYZ 9 484.913 null] +>> endobj +968 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +975 0 obj << +/Length 1783 +/Filter /FlateDecode +>> +stream +xÚuXYÛ6~ß_¡·Ê@ìè>§Ø¤[ °5Úi ¸m‘%—¤öø÷K²jŸ< ‡Ã9¾9 +öA|¼ùu{óöCVq¼©ó< ¶» «7U•YUo’¬ ¶mð=üxûùöþý§Õ:-ópûÛí—ûU…ßxýåÿÞß~z¿ªÓp{÷çÝöÛêŸíïo?Äù¥ê¤Œ7Y ÃͤµÎQè&[‚uRg›2̓uZl¢ªf©íAƒþ,
ýAö…éa‡¿Y¸·j•Tá£ñÊ›¡çÍV[ó¸JÊP·Ì0=KûƒqÌyÂm:úÂ[;; çk˜Øë~ë¸Üäy
¿Ù&Ër6K[Õ\ž…§Õ”
Îòx6ÏÙ>سxÌÃû^˜§ŸÝ9¦ûÁ31ôÝ %cc¼È<~FVò¸E'í,FFb^ÁæY} PüÑô{ƒ‡ò»€hõN7xmR‡Ê{Õ ÜÔÄáž¹~`ɦSΙ† +ì£nÐcÕ›Æ1ëé`ø8 `·º%ƒ ì0î¸OW—ó%¹bós )¢ ,f÷ ßIü°#
Â_¿Þ]§Ð÷ð ke÷°>bÀ/^¢íÉj/N)ÏNÑÇ“±f½d¹¼¿;…*žøä +ÕM‡o–lR{¸Ê‰ÙW R\gTùÿŒO9–”ªbcþÛN;·¡ —êñŽ ¡0D“éfèÿŽâ¬—¥?€“„V§SvLoŒØQ-Á$i›H +‚yÌh”±§ƒ¶z&Ä|¢ÎC
l´Ow->º÷¨žÙRó̵záµ-ůÆ8\Iq6Ÿß®~¼Y³8•4«_ƒˆ‹ÐdQ Ó!‘RöiÇL‘ƒœ'ã,éÃA"4Aº eèÑÈh†õ`[Ó£ù^xîÅy}\4ˆU'©\Ø
¤¾1Þ=°qi3,•ÕL¸#›ŸàÇð[90ëd£”K¹â$Á‚]3B¡_‹Dòè4G=SÃWFh P–R¡áƒl±"hït²äÕgs”üEL|ÖO~èZŒ™$e•„›ÕºÊc莨jÄûŠII‘Ty€º™I‰Œ´A6–œ+8é¥y up¡zöÎ¥)Rpàdoèy–¯„¬'|º©®¹2”\ȯbɃ’{)_€!Øl9$íØÈ+ð9K G6 @€Œ£WUX» +í®¥P‘Ø
–´Á.V8²À5VIA¾T‘?C–#ùÖ¨cs泋-‚Rßà{{x$ÚY…¾š°c3ýöçú²NÓ €gì Ç,V΄p€ W€pÐs좛ð½I)¢I Ž5Ϋ¾ÑÌ^~¶ 8nBjBUdM)´éŒ«(íëM3‚^xÅ——¯…: +~`Ip¤Â†U¯%Žp-ö*æj×(¹ì•‚æ~絓 ˆg†âªÃÃ硇{¢Œ0’I!% @C º~¹cÊÕ!Œ`ðªââ%I±°Ó¤ƒ+„.P2YÔóˆÂÛñwè…A¯uœ°Î¡Å¬Jâð}³~½c6Ô1ö(ÉCbãÿâ„;£ %OB8 |rzíùÄeç’c0ö-ïJ3 +rç16?O• –ÁdoNÔ:™ Õç‘v.?â`Iàƒl~R€ÑÝÀ¡AZÆ_°FξÕÉyOÊöÕò+/Ë/‹¥ü*.¿Š{)Íi‡Lžûmás×jj{¸$‹ÓésøçcT(˜ ð…½Å Œ‚1|l¦Î•^7ú4 ¬Î3<rÞ¹$ðÐœÆRXì¡—z–™;¨ +endstream +endobj +974 0 obj << +/Type /Page +/Contents 975 0 R +/Resources 973 0 R +/MediaBox [0 0 342 504] +/Parent 949 0 R +/Annots [ 967 0 R ] +>> endobj +967 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [106.913 406.5 171.665 419.119] +/Subtype /Link +/A << /S /GoTo /D (section*.89) >> +>> endobj +976 0 obj << +/D [974 0 R /XYZ 9 484.913 null] +>> endobj +973 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +980 0 obj << +/Length 1868 +/Filter /FlateDecode +>> +stream +xÚ}XYãD~Ÿ_áGGÚ»}kŸ´ A ŒÐÂCÇî$Öú¶3³óïùêpŽÁËKºªººººn'ô^èýððíÓÃ7ß'…EA™¦Æ{Ú{‘)‚ؤ^R”Irï©ö>ù¿}üéæLü§Ç? ŸþÜüýôã7ßGéݱÒeVB* (3bzõ oG&0e ¢®jèÿ +£dì\½ÙÆeêï‡Q +QÅ”1˜då À»&×ÓÕËNÓ¹ +BûZ\NG‡7‡qר0¨¼¢Þ½iM†ØÞÏan’’u§õh'v|©st+À4eª™(µP8IˆY‚€ÄP¥g×WNåtð4âsE-+&®IDÚ•…†„ñû +&9H-ÞÀ/Є󋵎W³PÈBtL#Ôø”á8ò…ò„pÈ'½lw^N}- y?÷ÇZðã€P;òIË*eäu” ñ±ÐrØDVÕ#—ЂënO½H²l_ÿWÀŠ‘u /i,±š.AAg[AºÌ‡¸O£LR’¨È~DB{^N\K 0)ƒ)E*$È +— õ¥‘ÏÚ¿>:i'A’˜êR‰‡¢L×Ó½<;V¨÷GÁ*ׯ±›â’ãrJÄ Õ¬Î éªpf|Xõ<² °ÏÙ¢¦³ š‚, Tñ›^`+‡÷d—7¬¨Æ/*ùET›BObtÐ b7–»€U¬6Bûªñ|A`©ëx^îœíU’Ü‚ŠG}ÍNšB»0Z¬"› mßT$!1ènÙq‚XéeŸb ò(È”wæÛËzäÆ$Žphr*R +xÎœø–ŽZðÛ@i›ynÝZ^žÆagw
¤ë©oæO âm{ t ÐÑ ¡vÏÍÄfÃ)êPü>ÀýâNçQõŸÐÜHŸ(Ò´¼·Ù/½ Úôcg'q¥ö“¥qáàz7Š˜:Œ¯÷œ£kQøž//Œ|ž.Bi8`Ñ”ç^jìvM+í6Ùr7€kÒ!\ù>"j£{ôÒi0_r/íT€ŽNž'å¦ÎêÐ &;6íjÉjJ)q™‹á>* +R$ŒßÙ¾—”¦ýÁ:³£€þ·o¼‡UÂry&XÄÄË\-ÕÇ,Üj ס-Ë—æ·Ó +¡b©üí´’_"%ÓFq9±P¹)Q3glêD3Ý uIé•P¯ÝLý—º•Hi}TRÕ`_Ç<£E’W óÒeÌ3—‚9 ÈPGÅtV‰‹¸Û¡nšbJzO3G(
4ãÅü¡‡†FˆÊr¨…jXòv£çn‚•æK]µÐbå®rE][Ú*2Í#¬Ò* +LAT õìËH|KùNh²8·³À·…*ÓÄÃ:ÍcSÍ\6ˆÚë}‡Ñ¹î̧†²òfÿzeùp²£Î³ûqèd4Õ +–/˜¦'å:ZÝ:â27²õpäv.-’·±Àð kg?K!þj]‘†`|Ìl¤¾r€¡võ¹¢M‚‹Î&I–‘1½T<‚oÌK<¶îd.M%’±Þ~ùðiŒ÷oæJÍ–ËWPZ¾5ï»Û”ãLbÊòµ„Je?J’( +ÑŠGzá,èȽêu¦ÛKµx„þAxž·ë
2Ô¢ $qÈ3ªkkB"¾’ˆ,‰¨³ïô›·ôò ÌÈ?yã(HãÜK‚8.Dl´úi QyÛ>n’t‡•êfBi¬®aË›¢H´(ú×Y›:—DF¹)î_×b !Ó„©¦|¢öÓtN‘]V\._6`8ëo@ N6—™=F¡·ÊX
²‚û0Mª0ùÚ¼|ý¨Ê©HȽ‡–>'D]`Ò;òUeP0rða„¶Ì‡™¦|®ó$Í ¶ ÃY…i»ý#âãÓÃ?ÀЋ¼ÒKMP˜Ì«º‡O‡^
*ôÈÞ ót^dÊ z÷ûïòIîeˆræÞ3&H²ØKÒÀÉ}d^”äƒ
–Ƚm dÑ2¬HrPŽÓkâä::Ʊÿ±& ÍÜÇ€ÊP€æ·qþF7\%}ñ#uÿ +Óð»} O¦7Ž}ìo?<xŸø܇“†¼ðED=2á‘›äãý?7Ÿü +endstream +endobj +979 0 obj << +/Type /Page +/Contents 980 0 R +/Resources 978 0 R +/MediaBox [0 0 342 504] +/Parent 982 0 R +/Annots [ 977 0 R ] +>> endobj +977 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [240.715 37.085 299.716 51.033] +/Subtype /Link +/A << /S /GoTo /D (section*.168) >> +>> endobj +981 0 obj << +/D [979 0 R /XYZ 9 484.913 null] +>> endobj +978 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +985 0 obj << +/Length 317 +/Filter /FlateDecode +>> +stream +xÚm_kÂ0Åßû)ò˜<4ö&i“<:¨Î!$ dÛCµq–µ
´•á·_jª8ØÓý“Ã}¡-£'ÍB! +endstream +endobj +984 0 obj << +/Type /Page +/Contents 985 0 R +/Resources 983 0 R +/MediaBox [0 0 342 504] +/Parent 982 0 R +>> endobj +986 0 obj << +/D [984 0 R /XYZ 9 484.913 null] +>> endobj +983 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +990 0 obj << +/Length 1622 +/Filter /FlateDecode +>> +stream +xÚuWKsÜ6 ¾ûWèVíLWI=sÛ&v² ×NíMãN’£¥WœèáˆÚl<Ó _€€öáÙ^DÀ +’TE"-‚Õ:ø¾Ÿ•I¸¸›•*\Íæ*OÃ% bÿý²úƒìˆ¨LS‰væ"Î")U0—0 z}{s¿|sy·@ƒ«%ÌÈÜí
«w—D|¸Yþ}ywϳ‹-p§@H©\ÀI”$Yþøîöúò +>ÞÞ¡î? ">† Tg9€‘€Ñë,žfY êa–eáHj"=ÆžÞÍ˜Ä ‡¾4e ŽµA" ×ös,²jÛŒ3™‡Ï´º¶®Ú:gÖ4µ š†ì +î¼£¹e· LóÌ2µu¯Î¡Z iÉèxâžteˆü §±ö¥ +,’ƒÄ¾¯pÓ.<iõO øËrÛú.QøÃ>ƒ»ŽPt/À¸Oq 1§°ÿWÆ'+púíÈ•‡/¥5ëðSH(ß—‰:ñXL®±J{šOâ%û?q“ÙþV“»žœèµmmg >$dŽè÷ÄK W}Yê¦ñiÍ"tÿ€a& £î*ãXÄ2Ÿ V/«o[a<0"ðôƇå6ÐXæ8 ® œcâm,6´Ž¦Þ93íÓh;h«˜ã±ð9î Tpƒ ''·Ñ¹Pm÷Ý
‹™nîÌßÜþ‚MÃÖ¿u;ø|DízZ$ +endstream +endobj +989 0 obj << +/Type /Page +/Contents 990 0 R +/Resources 988 0 R +/MediaBox [0 0 342 504] +/Parent 982 0 R +/Annots [ 987 0 R ] +>> endobj +987 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [221.795 310.38 287.374 324.501] +/Subtype /Link +/A << /S /GoTo /D (section*.89) >> +>> endobj +991 0 obj << +/D [989 0 R /XYZ 9 484.913 null] +>> endobj +992 0 obj << +/D [989 0 R /XYZ 9 465.114 null] +>> endobj +150 0 obj << +/D [989 0 R /XYZ 9 465.114 null] +>> endobj +993 0 obj << +/D [989 0 R /XYZ 9 441.319 null] +>> endobj +994 0 obj << +/D [989 0 R /XYZ 9 404.707 null] +>> endobj +388 0 obj << +/D [989 0 R /XYZ 9 394.532 null] +>> endobj +154 0 obj << +/D [989 0 R /XYZ 9 394.532 null] +>> endobj +995 0 obj << +/D [989 0 R /XYZ 9 364.76 null] +>> endobj +996 0 obj << +/D [989 0 R /XYZ 9 328.147 null] +>> endobj +988 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F19 213 0 R /F7 232 0 R /F41 211 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +999 0 obj << +/Length 2174 +/Filter /FlateDecode +>> +stream +xÚµXK“Û¸¾Ï¯`岜ª—ÀŽyØÙÉÁ®x&Îaw’˜âCKVùߧ €Dé©ä"ÐèÇ×ÝJ£C”F¿ûËóÝïUeY¢ó\DÏûH‰Dè<R•N„*£ç&ú9þëÇO{÷éÏ÷ZÅÏ0»ßÉ2?~àïóOïxð¯Ÿß}zzwÿëó?~|ŸåëƒEY%Zk¸—ÎÔ™îR/I´Z%¥Ì£,’´ÒÌõ|lÝýN(×ãPÛÓÜŽÎe èí࿳³ÝžÇÃ83Ó—{QÆvúÊdgæÖíM=@©DœÜïTZų?Áñ&7·]ǤÎ:‡bF»¬Lò\ÃW%Jå,ÜÍy;™©ø¶Á…µYœeJ;󷳦q8”ñ<2i>zžÉº¥›Ñ̯–»öp¼Uìé¶oçÙ6$Vê*X |.ŠR¥~; Ül&¼¹Êb34L3yÔMû¥mÓ}Ã=î¿9Év™üä+L{îd·Ä9±6&ÿá’î+ëàdœk‡OÆeæØY?8û%ÍÔÐΖçîdjû€ã" ¬7íZ¥49/ÓàyðµRÛùH7ªLÄ×cpfÝ ‡õØ“|8öb݃JÀr‚=ì¶'‡D.<—G#hÌŸ8‚Gäyü [ÏnKÒ±Êã7 »EŸÔiü´ÔxçWUl˜i¥ öhÉn°¶ íÊNäy@9ããÒ5Ìî]“× N>X¿ÚÛt&öå±ÇM¢ˆ“i‚ aå…¬töˆ…:,qÛ³ÑGÂë¸uGÛ$tÕV4=‚ e¡ãqjȬeÊf’uµ9]äÇ…c +s<iÚÎö½y`¿|²†N€n9 àôR˜ÞÑtX³Ûˆmÿú•]o^©ÈRøý`Ïó8üàxÖ|ÛîVEFX„Ôó±
æÃ)Æ~Áç—Þú èJæñ~œ˜t˜,Ð6LÑ´– +-áZ˜ƒÇ` Ü7ò÷Dïݶ±: A €$¹W‰öÞQ…XÕñ@ðî ½gšáimÙý…Ž?úõš´ÃLäÒ~|Z&Æã6Ûè$Ô + +ÐL‚põý + K°4õ\!%’O¤”Ü7„QpSþ¦,UR‚<ƒwûÇýç9jÆ´¾^cViÜ (‹] –b2)êô[‰²B&JäáÆ_R)˜«ŒŠD—²B¦<Éò ^š(í šnˆ^&*/¢g–“/7U)ÂÕ„ +Ø‹Û\Šb_œÍè½R]»Ï–•ôˆ +ß
„ *{ܲx©“Jÿþ8S¿Çâêm‹çk Æóý} Â?bZß @ÑoxDsí™mW£í¼ 3Ô£ºU#ÿw6Vòª×5ñâE—ŠþÜP—íàEœ¤¹Ù¬äe%´^0äLRQº†©
æq7·)! 6ùÔ_ñ¿NÌæ =äë"QUæÿHùÖ®äI[v-E’¦Õÿ¬yR +ì&äÚ¬¯òt–TBF¤4ø¼‘«ƒù×™z} ¤Uå:)`×÷#J&¾¤ +2ÓºÀXfÿÿ´™o +%V.^A
ù`3A‰¾bJàk¤õ5@ÐÀ7]¼Jÿ¬á#ƒÜ]*E•]©|…à +Úˆ”û}. •ÈblÎ –ÇN»A$Ýüǃ„õntÿ©EdÅ Ã%Ì'Ó´Ëf}SI&.5ŧí<V‰êEz Œ:[Àøàÿ_XUÈ+üãªÐ×'7õåë/øñ¢ó! +endstream +endobj +998 0 obj << +/Type /Page +/Contents 999 0 R +/Resources 997 0 R +/MediaBox [0 0 342 504] +/Parent 982 0 R +>> endobj +1000 0 obj << +/D [998 0 R /XYZ 9 484.913 null] +>> endobj +997 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F16 210 0 R /F11 420 0 R /F7 232 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1003 0 obj << +/Length 292 +/Filter /FlateDecode +>> +stream +xÚU1OÃ0…÷ü +ö×vÄH-*B ÈBBˆ!4N +ve»Šø÷8¹´R¦Ü{÷îò:!† ³möR!Îi]éq¡èVHªš +Y!Ý¢üº{¾'µÄúðvÐïäS?mö¼X©Šr^¦ó +endstream +endobj +1002 0 obj << +/Type /Page +/Contents 1003 0 R +/Resources 1001 0 R +/MediaBox [0 0 342 504] +/Parent 982 0 R +>> endobj +1004 0 obj << +/D [1002 0 R /XYZ 9 484.913 null] +>> endobj +1001 0 obj << +/Font << /F48 218 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1008 0 obj << +/Length 1759 +/Filter /FlateDecode +>> +stream +xÚ}WKÛ6¾ï¯0r’XE=ÛSñ&.‚Mu‚Ù h‰k•)G”²Ùüú΃òc£öb‘Ãáp8üæ›q4Û΢Ùë«È¯×W¿Ý$ÅL$¡L²x¶~€aæBÎ’T†"-fëzö5øüùójþ÷ú/Va™¦¤¼qÆY2[ÄY k¯ß,ç ™§Áûwww«ëÕÛÕú ÞÝð÷OþÜ ™Ü¬nWëå /¿}Ń/Ë5ž7KÓPfœ“„I’±yÜõñöúÝÇÛWËW~ãÇÛէ击¥w2:¿Ñ"a!rð1E–³‘ë¡g]‘ž_H‚j ¡! w˜/â<ÐÕШ޴ÖÁ´ÌƒÖò·ßi ë»a.‚ª :/i .Tò`°æû muÎKTãZ í[\å"ðÛ¥Ë/Ø›‹ËLZR¦²-ØïxR›NWèd8_À½ƒõÎkÕš-7ía¯-žÔóúˆ_ÛÚÅr¨SkeY´Õ r º<»Ýë¾{˜ˆ Ñ5â oYÀWøÑnA_x…‚š¬!‚Uõ/aXH©ž… WÊò–J¹žG5¸ 6ý¤_¨
wÄèM3yñ¦IÄ?ª±÷‘HÀ?mµsSÈD(ËlÔ'ïÁx;t<pU¡Ÿàî£éwíг¼j÷Ænyl8Ð-«U-ž™šÊkâ6~à2
“t|ᔤ0ɼ…F Ïè¹r¼d;lwã;â" /!€"@Ã4Ñ?<v;£må
ÞGiôÁè½²Â/K¼ÑÍ~×6ýOXáTlG„Ø$èi7¦LwÊÖŸ
$ªé´ªŸx²áó5¾M’=,õ„X3–¿µî•iüfë):´g°“0tCwPΩMƒ÷Ê¢ *S› aþÄ’
zåÇÇ;Â4-ù ”¿GÖØJu8ºb9O2hŒM¯¹¥•c嘓 +
|Õ—Ä«b>’<ÕS å°(…99’ÁÍ ‚ÖvÞ‚ŽÆèàlFivrf•2á7¤"$ŽzŒÍ \n°i ȱßáXQŒ ÒÇÑÉêúÉ[Û8Ý ƒ€K-/ìÔa2=»XN Ô¦/ÜÉé†
ùÌ9æÛ™’éxxF&¨ªÏ±Œ ˆ^°Ì¸ão¬i±ÍàŒ¯—¾AÖ6ÈÌ +ê ‰Ü·˜Øñd¯joj8\îüÇ¥áOÈØÍ…zÄ1ðè‰MïƆZ„iþ¬¤QÌÚfØ£?±¤6 + t©Û"2pñ$u™«VððAËjkNlËボ ¬ð`ôÇL<r#ÍËhšlPIƒ|#h5: +ô^cÑ}É&¼“•h›WD30Ù3s¥%—‰Êë«G–{*ƒÁØs–ö,a²üŒ)yÄ` ¥ÜÃÄ¢4<çM˜nGÒœ wŠ²<1{yÆð>™ôìN*ô„PÓ*òÀòß%q’ðØØÚ|7õ@iÍ¢£M6¥¢ +endstream +endobj +1007 0 obj << +/Type /Page +/Contents 1008 0 R +/Resources 1006 0 R +/MediaBox [0 0 342 504] +/Parent 982 0 R +/Annots [ 1005 0 R ] +>> endobj +1005 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [200.358 170.253 272.864 182.872] +/Subtype /Link +/A << /S /GoTo /D (section*.98) >> +>> endobj +1009 0 obj << +/D [1007 0 R /XYZ 9 484.913 null] +>> endobj +389 0 obj << +/D [1007 0 R /XYZ 9 465.114 null] +>> endobj +158 0 obj << +/D [1007 0 R /XYZ 9 465.114 null] +>> endobj +1010 0 obj << +/D [1007 0 R /XYZ 9 441.319 null] +>> endobj +1011 0 obj << +/D [1007 0 R /XYZ 9 404.707 null] +>> endobj +1006 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1014 0 obj << +/Length 1702 +/Filter /FlateDecode +>> +stream +xÚ…XKÛ6¾ï¯0r’µ¢·¨S‘ +ð×XÇâÙhpŒv®§Xë®a‹ ¬ ëzØ3Ï‚o¦öOÂñ™çIó]×¾}½s¥`Wð"‰*§DåóåQMG¡Nz•3¬;ýÜŠïY×½O_ð˜YÀdI‚ÀàÕÐüz´ûiñØÙÝšo¼‹Ï"fì‹®:÷²…Ûjo)0i¾{Ó@ø»¯Ûq°¼\w˜}s¼—?ÉæsÈo'Å4»â% †»ÈãàÃvn‹‡Ö®!‡+EaVs˜UÀx‘UÏgŽÚ5,³/0y4ýÙx÷Êjr†7øVÜø–H)8ÏSåÂþ¦4e“Ÿ€2J©[ú¸L:øÄÕpÍvy„ú/ˆœÑ ¦øär Ÿâ4kìàuW›w?AΦ&Æ+ÏÖºëzÏrÓ󈙲áç‚à8ÖÛÃ4?Ö~·öÚ¼9_pÏ,eØad÷ h ï´=ž¶€˜X·¶3(–Ó! ¼Ú¶e©öÚvw{Ô£ãPȲë x6<at•G’&ÁâOΘ]4Õ
€‘L-Èâ k3Øc§½¬¥PàÈÃ.çY¬«[ð…Ø´H—lšT*ŒÕD¦6„t^ãÜ*¬Šr²Òt‹]ÃRàíû7aÚî†hƒ¯‹„Ê¢‚0d 3 ‹ ¡ 2Sg½èï¿ZÓ ýéàƒ|#K@C‚°  À”«ÚqgÁxáñ7£Pæ° 9¿ø‹©=ãPf+ì‹4¦ªà«=ÛV;à•R[¤Ê +¡•"7ý +1¶ˆx&pV̆S“h€LÅ‚‹×r?|a2Ù¬7¹À^È\ȪE™HzaQãF#djÍ’P;ªæ²ú
;iÛØw&¸«¸1F ×àB¸jÅ‚]a¬p@øÊà.3êÂêÂVÒY¢(|‚%<ÏÄ P™³H^$jžƒýáõx^Eè +P:KLï:eøæê¹±òøäÇZYI™PQ0húm *ª’мâ™ø2 +áS”Ækå§ £¢šŒÄ‡ëܪá1Ärà‡í#ü
ÒÒŽå|?¨PÔÊâþšSa‹ªº½n†^ž9þ,a~.ƒß:6œ(L¤Ü!@83ÿÔC¶ecùµNÊe\þa?í þ†_wü +endstream +endobj +1013 0 obj << +/Type /Page +/Contents 1014 0 R +/Resources 1012 0 R +/MediaBox [0 0 342 504] +/Parent 1016 0 R +>> endobj +1015 0 obj << +/D [1013 0 R /XYZ 9 484.913 null] +>> endobj +1012 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1019 0 obj << +/Length 1773 +/Filter /FlateDecode +>> +stream +xÚ¥ËnÛFðî¯ |¢€h³/¾PôÐ4N› ’ÖQ{‰s`È•D€" >b8_ßyìÊ’B·@{âìÌìì¼g$í"ýrõjsõòÍ#¥D‘$:Úl#«….’Èæ…Ð6‹6uô1þùý»o_ßÜþ´*l¼y §ÕÚdIüþ 7¿Þ0ðç»·ÝÜ~¸Y}ÚüöòJNëÌeSx—d*iëJzU¢µ‘©°V +™Ìö°ÒYÜÏm
è4¾“Êv ÞöY<훑QC95=ƒÓÞ1õë*Iâ² +¥Õ©RJ§"³¼™ˆDñ“wÒ¨%”¦êÿˆ ‘2"EZä©aÂØtþ¡ììr*Lšà ßÑrQ')$<´N„ʽÐ\u³¹úr¥@Á…Ü +ð¦5F$Qu¸úøIF5P~‹¤°Y =ß!*„”¨u}¸úƒ~ñœ¤µ0Ê«v»h‚ZÚH+ÿd‚ZP-)D†¥HMöOÊA²Ik/´»ð[& +«#«raóäß=gÙqúyÇe)Ä ¬ÌÉžÿå;/Ë™€ÌüoÎûNh +©˜Gk)rã ðæƒ ;á[«Œ5°y¿4‰ÅÌ- ùòºåj3‡²mÝÀ(ËEBÇi_vËNÀ%:Hz®RÀYàysÅ刢ëjظÁu•Ç|ÆOìšn ÷„C?x¨ê»±©×TskeÀ‰`¹‚¼µÞr7”Ÿ[o™ûÒ—&Þ
®œÐD<P€ï‘:”u3ÒÆýö‚X5CÕz*šqýá¾ š±÷ç‡fÚ“JÒ+“²2,$×á…G&©HÓc/¼] vf )"½lß)c¹9m½ ï÷àRq½Z§Rů ™ùàÊndö§ûäTεØ-;vjù‰Mç{;Ò,&éMU¶xÌO62½*;¦ÔÜ}h:Ï ÈŸ\
HÒ$¥(5£æ®ùŠ¦¸atK½“‰<³÷0Š2«ˆ \Íc×áIÆû +y‡>" vZÊæÚ¹œg5å»çxhC×ã×ÆmßíÜÀ8 r&SàzÏßÚ B'¿çñKB"•¨«±á=.!o +«‰|<É5<ž‡Ýsâ€Ä®ŸeÜÌUÛÔŽ{Ø¥cîÛ²ãN‘ùBj¼ˆ ï&,îc:àÛÃÛI=àq ¶eåøú›ï6 ™Š1Ûð0¶Íni4fAµíÐ x{)yw¹o É ©pBA+Î)Çg,ž46ßx"À¤IrQß›=:ëÒšŒSÌø¢Eàhåúh ¢Ïª >’YÜ6_©‰#ÌÉ8"¬.8ÂM¾…/hCf$*¸©P¯= Ù* +îË{ŒZŽé„S†aÐ ¦hÌËAô +endstream +endobj +1018 0 obj << +/Type /Page +/Contents 1019 0 R +/Resources 1017 0 R +/MediaBox [0 0 342 504] +/Parent 1016 0 R +>> endobj +1020 0 obj << +/D [1018 0 R /XYZ 9 484.913 null] +>> endobj +1017 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F27 593 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1023 0 obj << +/Length 2129 +/Filter /FlateDecode +>> +stream +xÚµÙŽä¸í}¾¢ÐO. Kk ¾Á˜ :ÈÓl'‹ “·®R¶Êîñ±½¯/¹ŽñÌ&yEQIQ<”nö›tó§w||÷ÃGWn´VU–™ÍãóF›RY“m\Y)ãŠÍc»ùGòéÃ_Þo+—<>üíáñïÛ>þù‡:»ÚVJë ¸Ò:¤z—ÊA›Msåœ WiY1Y³5ErèCã·;SæÉ¡ (’0 ð¯y«€u2>§Ú5õúNèdœÂá¹n¦ˆª§{ +—ô¨s‡”“œ Š_Š™³˜¶[8½F-ù/søe›9`èa™Lj»ËL•<a{â=ñpD’˜ 5œ FæZïb¹Hš04óéìÑÁÅ‘3}é V—ªÊMt†fÍav‘èJ<Ëi›Ô<àIGÏðÔóH®ÀP·a ×Î×&SyQÄó‡U‡MUfËHÒz¹—®îlè[ιUYe¾ËŽŽëà~ÎfÉÓ<1Ïç~@ÀDõöpGt(OåÂf²éfgÒL¹´øÊ@k +[åÎʬŠU©<](èîA2ôd ùjmžŒõÉ3ŠdE€\qí³?"’œã’ÃgmÝ+z\? Û ?›»ßÁšKé‘Ð& DI«RÐíJÇW< Zx’;krámÞÅo^"M`¥>SÊÃfÉ ëMßSÍOB0ó + †I È‹t£]à{~ Ì +4œz!Ý'Ï ƒW(ÁÃH¯ ì±¾iïõ$% +Ù?¢G9ð¨…yW£3 òç;ºµœ+”)ªsA’¥xS+¶3Fi{¶p¼Zä^s¾ˆþ ¢ #®Q±Aá!”™¾–ðÇù%>ôH„Ñ®·PmÞ¯<;Âq#ƒ˜€q §ÁO1ø|W¨¨ð„‡Ç•#ò ƒo°B‚çüðë|c'¨Û›ÜŽ1¯€*¥kyõT?#
¤e$ñ%È×Kh„eÚ s¤§{É$pÀAŠ€ä»^4šR+þVSÙå_Ã$GÖâÌ•†bâ¦`‚G… +'ù’qA‚1‚dÑ’31P_fNýHU·‘ve¾}¯£Z pJ'±©´Éu5†K(+Ž ææZŒÙuw =¿Úè2S©5ß5œÎTa–0ü{¬ÅòÄ^ƒV®ÔW‰ üzy—)Zèl(E—Wéþ›)ZÈ Ïà%±¥ç ÕÉ 1ïbYý‚»‰càØÑæ›fèg²ï»2¬–ÖŒÎGW=R
M™åMpG(ÒŠùج›O§ð2óµ &#°ÓOsP¦Ð5ð¼F)"¨y˨y%ØVF·…Ë7º7§ò¼øï›Ê¥*ùM»»sbcé1Õ@ã(± ¡{|NáƒÃq’yÍéþ5œð®fÙqîZizQ(ãTr6ÀÐn_ã¢v¦,±D‡sÆ07í$×Í÷Øóšûj$â^€q +Õ7ÔeÒDÔÝEbºAüß`E0ÏÔð×ÇÚ' +~àØ4y/Å¢±gƉ® XRĺ Ä” +¬ê°?ÄÍ€‘JÁWÌ€çþ0hèz’½’éc'Éìêab˹â¦z`\‹ºH ݯÖÍÏu¼¡²’Z€3¶JãÉ%&S é÷ +5FÔûš>:€ˆ~Ö*ÎlÿJ4ýÌfòÃnM¦k[¢§—)ûA‰50w_\P\oC_cÿÚµl_¨çEU˜5}ש™/›,½.îWÄ›†ú\Úç¾I'-ÞH%y6Å@ÐSǸ‹bW¤^Þå%w戣D +endstream +endobj +1022 0 obj << +/Type /Page +/Contents 1023 0 R +/Resources 1021 0 R +/MediaBox [0 0 342 504] +/Parent 1016 0 R +>> endobj +1024 0 obj << +/D [1022 0 R /XYZ 9 484.913 null] +>> endobj +1021 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1028 0 obj << +/Length 1274 +/Filter /FlateDecode +>> +stream +xÚ}VKsÛ6¾ûWpr¢f,†O‘ìÍiíÖ=83¶ÚñLÜCB¦$¡`lÿûì‹zd”ž +¡Ÿ²J{Ýé v€xQ +q"løY€Q· +BRÙåžs»ÂÕ=D‘„ ز±²‡îfà™¤¸ Ov^ÛI»]óµW—âÚX3€K°6‡ +P)ŠÙ +&½øˆƒc =ÎÙ5”†ÆÎ; NÎ1I0¢=àwr| +Ó:ãP@ÊÑÂdhÆ‘6‚9'*;*Ožu\òÍ*º¥ ><“e õ¶çÒµP Z!ë~T–á¦ÁÔ$ùÜ @$ó +7Aä«V : +é§Æj¤fM²Iöd &×1²VäL»äH•èRhŸ°1d™Ü '[Èp'©–sÆ eVõ×ß°êªPt\\ÊrsA«ÙÚ T89È—Ñåb+C}ŠõÃ`ãNƶñg§¶ð%d >,…¦m}#ÎÑUÜF³™ý`DmFAÝ °¡•r"ºüÿ£Ü`…ó?{ø_ñ;?Ú8H‹ßZœ<Âßö éŸgãóóóùÿ—mˆ¿“
½tyß¹C*.óx»¾úߪ# +endstream +endobj +1027 0 obj << +/Type /Page +/Contents 1028 0 R +/Resources 1026 0 R +/MediaBox [0 0 342 504] +/Parent 1016 0 R +/Annots [ 1025 0 R ] +>> endobj +1025 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [127.34 189.813 196.629 202.432] +/Subtype /Link +/A << /S /GoTo /D (section*.119) >> +>> endobj +1029 0 obj << +/D [1027 0 R /XYZ 9 484.913 null] +>> endobj +1026 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1033 0 obj << +/Length 1699 +/Filter /FlateDecode +>> +stream +xÚmWK“Û6 ¾çWøHͬU‰zXêm“n’íd²Ó$Óö K´ÍYYrIj ÿûâAiíNA€ +=C§ŸÉ c=§ïÚ3SzËJ£¿ÈÛT“Ü`˜ + kV¼œJ}% ˈuÒ1੨”† Í¿Eþª°Ãá_Q¦Àò´ï[uôÞòÖ„ ÀsF¡§DŽ‡NEÇXæ]ò½’QbLefYy]œSØ3p¬S
¾e–]¬|!€•;²ŽF=ëžÞØ
½v=XKñF•!‰²ßÙä£Gø+|Üö„~x0š)}Nt T€™;¸àÒЃˆÆ²LÕ5LÔ-oP½=YÖÔ^JwÿDq6`ù6¼³A±3Ó;ÄÝ,»j áá^¦ÉJÀ9©j{Ãm2O.Ûd^† ¾MêP…sÍTÆÐå‹Qjlx8C2ÐÖÐŒ(¢iÂàˆ;SOYÚ÷xAdëÎU-g岌 ‹ÊŸqæ À(¸H^kßý˜‰¹Ž_õª¡Qž¹÷ƒ`¯¼ÑíTû¸C¾½ˆ¦p +õÐŽ}šNÞÀgÎwU¶•'‚ÔÍyÀ@&, sG3%3ŽYm™u]˜Èá0¢ A/p0Hø…´Tª™P0ÁýVNÍ.I8
Ý”âÈšÊ èCe-õQÐRü¶ ¯x’±ÿ’è®Ón@¤óœQ„óí]8çÚ„²E)cãã%´¨ LŽ¼€~5ƒ3EeŒìÀ5jW™Æ/°Ð,[H4õ Àö« ÎæF³hK +–Ç +P[à Â)ù™pÇÂ[ší4\ûô^×xÊž%´?Lð ’ÊŒ'Õƒakèü×ٹƒ! ~šW–N&Îb‘D1OéÈ<½ØÆ¥ï[IEÉ<õQ“8 ¨Zót† .LÚš ‡ÚªS¿"`e4ib>ùaÀ¶ÅÆ÷4öëdlÒ@}<¶tQXPÌj¿Ãyà +#ë„쇶aö‹W¨‡hB¥¡äÃqç¡üÉ È™éoÃ?½”ðë˜Fa’øTŠ£üJênýæa®F +endstream +endobj +1032 0 obj << +/Type /Page +/Contents 1033 0 R +/Resources 1031 0 R +/MediaBox [0 0 342 504] +/Parent 1016 0 R +>> endobj +1034 0 obj << +/D [1032 0 R /XYZ 9 484.913 null] +>> endobj +390 0 obj << +/D [1032 0 R /XYZ 9 465.114 null] +>> endobj +162 0 obj << +/D [1032 0 R /XYZ 9 465.114 null] +>> endobj +1035 0 obj << +/D [1032 0 R /XYZ 9 441.319 null] +>> endobj +1036 0 obj << +/D [1032 0 R /XYZ 9 404.707 null] +>> endobj +1031 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1039 0 obj << +/Length 1497 +/Filter /FlateDecode +>> +stream +xÚ}WKoÜ6¾ûW=i/ç -zhR'u jo‹ +Ç`† +Q£ X1yŽa&ãÊÝq¡à^" ÚãVÿÙöx Ë DhùL!™îPÔ5-Ř9@Œ…á‰Pݳ»lSÚ˵ +Æ„’6/ª 8%8X4˜åž<ßÄ×7ç=ŠÊHx®·„xc*¶dØv¹Ú H:!£‡ºïˆðý¾eQ—C]„Ô†k*W}8üF~80”ÉguD庾u÷–áj]¸‡c{¨ƒ¡[¥E0mêÙpæåˆý`Þ¶”ÊfWÑ ÁêšÈ;nø±¥ƒ¶®Ýi»'< +Œ€P†”ѸsnBP6 ñÆ·4Ö–2‰7ƒVC7.Ó šˆ«Ãve ]ˆž¡Id ÓGW
£ŽSÑR $T+ëY °€¶—k#"Õ,ËÌØü ³lu¢ +&… ¥&ÕÏ& +„Š;w8Õ–ÖPÅMhÞ„] ¥,O¹ðÓ•sfÀÍ ³Ãƒd
âŒéTGÛ™XpÖç.µ=ߗĘUhÅ©(íSøßSÑtë³v.¶ˆõdž3.—0MEÃ'THú²íãî¢í£ÉrR»f Îl1Ç®v_/D˜}9ø@eQy¸øô™Gpo¦€õäe‘93@ó¨Žn/þ¢wd%€/â©)™ö)Í™Véà$ÊYžÈÄ¿6_xð±D„@¾Ýd +endstream +endobj +1038 0 obj << +/Type /Page +/Contents 1039 0 R +/Resources 1037 0 R +/MediaBox [0 0 342 504] +/Parent 1016 0 R +/Annots [ 1030 0 R ] +>> endobj +1030 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [240.953 406.5 310.242 419.119] +/Subtype /Link +/A << /S /GoTo /D (section*.119) >> +>> endobj +1040 0 obj << +/D [1038 0 R /XYZ 9 484.913 null] +>> endobj +1037 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F19 213 0 R /F7 232 0 R /F16 210 0 R /F11 420 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1048 0 obj << +/Length 1595 +/Filter /FlateDecode +>> +stream +xÚÍWKoÛF¾ûWð¸ÂÍ>Ée \ÄNÕ&v` mÐ$š¢%ét ÿûÌì.)R¦l'i^Dqw9óÍ7ÏeÁ*`Áë#柿-Ž^ž*pE¥ŠD°¸¸àT$:PZR®M°X Èñ»w'g¯æïg¡Œ5™Ï>-þxyÊuÀ9M´¶ß…QLM¢‚Ph*ÿîrþöÝ›øJDäÕÉÅü¯g† ÏŒ ‹ùù™Û8?ÅgL¿û“oÎ/NÎÿ b™B.©V‰»¸8>»<Á7çowÒ,*ÅÎhÂná åJ€±ö×·77›|›—í,ŠIZÏ¢ˆÜ£U†´ + +ÅçÕ â„TíÚ½ö&ÊÄ»—×Û´ôtmîݱ¬*Jo<‡ðbrÏøb™S„ÎÈ ØZ8V…æä¦Î”“Öídà¡´ÉÝË÷žÌRÿí²øÝ¢—#@NuñèV '°ò[(±n÷v…[÷,ó0µ‡Y•
®‹r…fIò‘qU7-¾R•ÎZIr;Ž‚ÆÝ‹ W×î5s÷Õ¦²¤eé¦h\ +endstream +endobj +1047 0 obj << +/Type /Page +/Contents 1048 0 R +/Resources 1046 0 R +/MediaBox [0 0 342 504] +/Parent 1058 0 R +/Annots [ 1041 0 R 1042 0 R 1043 0 R 1044 0 R ] +>> endobj +1041 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [251.929 410.498 313.915 423.399] +/Subtype /Link +/A << /S /GoTo /D (section*.52) >> +>> endobj +1042 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [54.568 374.287 87.157 386.907] +/Subtype /Link +/A << /S /GoTo /D (figure.0.2) >> +>> endobj +1043 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [261.003 88.194 277.953 102.141] +/Subtype /Link +/A << /S /GoTo /D (AMS.132) >> +>> endobj +1044 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [44.552 73.748 61.503 87.696] +/Subtype /Link +/A << /S /GoTo /D (AMS.134) >> +>> endobj +1049 0 obj << +/D [1047 0 R /XYZ 9 484.913 null] +>> endobj +391 0 obj << +/D [1047 0 R /XYZ 9 465.114 null] +>> endobj +166 0 obj << +/D [1047 0 R /XYZ 9 465.114 null] +>> endobj +1050 0 obj << +/D [1047 0 R /XYZ 9 441.319 null] +>> endobj +1051 0 obj << +/D [1047 0 R /XYZ 9 403.773 null] +>> endobj +1052 0 obj << +/D [1047 0 R /XYZ 198.69 209.24 null] +>> endobj +1053 0 obj << +/D [1047 0 R /XYZ 198.69 209.24 null] +>> endobj +1054 0 obj << +/D [1047 0 R /XYZ 201.485 133.026 null] +>> endobj +1055 0 obj << +/D [1047 0 R /XYZ 201.485 133.026 null] +>> endobj +1056 0 obj << +/D [1047 0 R /XYZ 224.716 65.778 null] +>> endobj +1057 0 obj << +/D [1047 0 R /XYZ 224.716 65.778 null] +>> endobj +1046 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F40 208 0 R /F21 427 0 R /F25 463 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1064 0 obj << +/Length 1552 +/Filter /FlateDecode +>> +stream +xÚX[¯›F~÷¯à«ñfï—DyhÔ¤J*Ui{¤V:É|ŒŠápOòï;» Ø`À>U_ìewØÝùæòÍ€ƒ‡ + ‰$ˆrĘöBx +8 6gb àÀp ÎàH‹˜8rˆ Eʈё‚ ³aÇX|°X(>9XýÌ¿ûá×cAÓ´ uvÈò¨òÖ·³$`=j2xðÓà±î?Ï öÎïýcYó}wBB/‹íó¾³Â /UöPÉ·ªxæaæYÓØhNü\”—~™µ.ƒ"}€{9¯™ŒrJÂ|ìÙC8½[‰Mô-«m\)jáR.8¼„‹l›Èæw¿}ë{”$ÍH-@-É,\N†@&Së‘9·äHœ.³ä•†©é½²ûa.^%¹É%—Ïë]²ó‘M•ßL# +°²¯œÚVñÎRôíSÃýYÏ +剾†©Í€W0e†9r§æ Ó‹«ilm!Á-¼¯§ Û-]¼Ã!zÑžþÁÏËŽûa쳎]ó)¶˜ OB9Ä ¥Vcjn!t¹@°"=ÁÊ%ÓR8¬·E4YÉ[ ðçYu7¯½Ó +Àœ—Å97ÿ¿^ý|dm,Õ3ûÖ’4´-ƒŽº@s‹%3þÈAÖ`á(›sv¢u1AëÅ´Ëð®5uþ…IXïËcžøq³·Žw´U4Æá>:q_·žú¥ºÌ®ÊtÓŽVìÿ±òËU¹ÍÓƒÍÔX†Ùnð6‚±µÁ'/ÓhbNEÕ4¡œZ¬9î6æTng8Lž#|XÚÆCðwQÚç§7šËðnŸÖíR•ÖǼñã]U üÈéÏ]úç¹½oÐ5… ‡@@ß ëö=ÖXï1]ÁB»º„Ú‰ìÁ§
jí3¡¾Vî+G«Û/qÚk¢]ShI¶=¡§/:v"˜iÛèê©·2tƒ“ÑB]»©O6·z/öÆ·ø…ÍŠî²ißÙSì©Ô¨iì?©øt\úl aCÂ63ÛCUÝ´¹{× ´É|·g>»´_ÄEe{ùíì#ô˜gº£Ø3‰yOp©b®»c@n`ˆ*×ÁD ©tüD ‡Q…H—€],Ûôä9s6¯8tÿpµ qµÌ +endstream +endobj +1063 0 obj << +/Type /Page +/Contents 1064 0 R +/Resources 1062 0 R +/MediaBox [0 0 342 504] +/Parent 1058 0 R +/Annots [ 1045 0 R 1059 0 R 1060 0 R 1061 0 R ] +>> endobj +1045 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [22.2 434.727 39.15 448.675] +/Subtype /Link +/A << /S /GoTo /D (AMS.136) >> +>> endobj +1059 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.396 341.985 243.347 355.932] +/Subtype /Link +/A << /S /GoTo /D (AMS.136) >> +>> endobj +1060 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [270.585 341.985 287.535 355.932] +/Subtype /Link +/A << /S /GoTo /D (AMS.138) >> +>> endobj +1061 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [205.184 62.73 222.135 76.678] +/Subtype /Link +/A << /S /GoTo /D (AMS.140) >> +>> endobj +1065 0 obj << +/D [1063 0 R /XYZ 9 484.913 null] +>> endobj +1066 0 obj << +/D [1063 0 R /XYZ 226.255 380.929 null] +>> endobj +1067 0 obj << +/D [1063 0 R /XYZ 226.255 380.929 null] +>> endobj +1068 0 obj << +/D [1063 0 R /XYZ 214.76 174.191 null] +>> endobj +1069 0 obj << +/D [1063 0 R /XYZ 214.76 174.191 null] +>> endobj +1062 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F24 494 0 R /F25 463 0 R /F27 593 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1076 0 obj << +/Length 1956 +/Filter /FlateDecode +>> +stream +xÚËnÛFðî¯ z¢€h³Oî²E
i{i*(’ Ö-±•H‡¤lçï;³³¤D…’í&i Ã÷“'ë„'¿\½^\½|«]"Ë‘Éâ&Ò1%M¢]Τ¶Éb•|Hß¿ùýçY®ÓÅ»¿Þ-þž}Züúò0£ÏœeBdðjø@ŽPW<"JæÒ9æœLæ*cÜåöîf6—&OïgÒ¥—~»% R cЖå™ëÜM‘3áDÑmâƒwáñm
;—.Ë·_"Þ²ÛÄÕf&Òr9“6'Ã÷5Ü4庬âöfŠ:á43fàÿ·c Úr@8sÂ%š)ÙçSL“MæG`eK˜w5’~WVküDj
ˆ$OæB3
7ÅÖwå 2ô+™¥]=E°oe~Bï‰N‘`Ûƒ¼ ×-ˆDST´Ùx¼!aO!´3Üþ›_Ô¢æa¯&…X' ÉØõ2˜Û›ÅÕç+´ +q[®+t˜)±èŒ9¥ ‹\
*ó-¡ •©lG*#3ThÆù眑Ɍ”*{+ +îê üÔtÐ~i»bײð¾°Qó±’ÞÎœL÷
º÷®n +‰V’ „0ŸÞ6eµ,o·a+B<Ž¤Äà]Wø%¢ß- ì[î6¾‹ï‚ (@MPòÏ~µF_ÑVSœœz©A>Ï›
’ر&ÝbØÖh—¸
ì + +«]áÛ=°¾ž7$÷}p¿)‰GÚ–‘ ‡Švcv<>%Ú~\‘?h©áì¦hŠjYÐÅ´3%YžÛïà
¹ÆÞ°C½í{†„…›âÁ/»í"”§”4q…f ˆî#£@£µcæ· +ý ª¬`øF +Æõ9 É™Êå£LÛÿ"9Ái€O¤t\M)]A8R:nËÈ(˜øWšñÓdKZW`ò'å#:פºc_)û’ic@j( )ª©W˜£q×Õ„ª-"ÎML>t»‰§ãTÞÒaO€Â8‹8ä"u’‹FJ¢Tô| …¬ErU€Eän ýmL$ 9†Œ þïÊ‚âøŠög
L8fTþ¼¢„=d x¼®ÐApÕŸ÷åi¤. ûcû(¤Ã`'måoA¨@²HQºu÷C´!¨S•9q¢3ù¥åžÜŨ`y¬©"Ø9™A›ió ‘ýD¶ÙmʘÀµª˜0Ða/Q\½Îp‚ÂDø²j‹&~áéèÖ7]‰µlCÒ³lyZšõµý\9}F–j*3PÝM1=ö!ã`Qו»ËoB¨Ô3„…5Ú ŸÅBf쀻`k6© €’ñ`¥=ôÐ6d)‡ø‘ñ ó¿Õ.rD +ÃՓćÁ²ÔÓå7øPÀUT}i˜'ú£¾‰Ê›Ø5…þ8¶à ¹ÐM±Ctt[ÄΪ½ÐZ…G¦Z«¯ N0h´€Î j\õxÌËUvÁí²0Õ™ Mwä’i9øœ˜l‚AbÐ< 5¦mÑ€Rg_‡x< }¶B<ôÏÂé§Ex÷H„ÏFA†"| ƒ+͇`ë1Žâ¢-ÀÃ}hœÊë~¾¤£ŠfU¶Ç +*6¼r…›ÐGÎÅ$oÌóíÉkPä +eíRAqÿ~9ú©° Ì”¥Áª1[l¦ å@¥ßcî•Aß–¤n€ÈðCÖÚP1HÇG²Ç˲ê v@/³ Ý7äo£AÁÂ|UÔá-8¾ÝÔ]½nüí†ö×Cërä«#E +
•´Ì1ùCÍú|5žÎ½r«Fs/ tY(V]bbÎå ¡X—@Yƒµ c.°}yÊŸÂÆÅäÇC.˔Ɖ›Dž s…á±:N@ö̘«çõ ³%p8Òª/âá +endstream +endobj +1075 0 obj << +/Type /Page +/Contents 1076 0 R +/Resources 1074 0 R +/MediaBox [0 0 342 504] +/Parent 1058 0 R +/Annots [ 1070 0 R 1071 0 R 1072 0 R ] +>> endobj +1070 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [284.693 373.379 301.643 387.327] +/Subtype /Link +/A << /S /GoTo /D (AMS.140) >> +>> endobj +1071 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [202.258 185.583 219.208 199.531] +/Subtype /Link +/A << /S /GoTo /D (AMS.140) >> +>> endobj +1072 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [169.171 29.129 186.121 43.076] +/Subtype /Link +/A << /S /GoTo /D (AMS.140) >> +>> endobj +1077 0 obj << +/D [1075 0 R /XYZ 9 484.913 null] +>> endobj +1078 0 obj << +/D [1075 0 R /XYZ 189.746 421.71 null] +>> endobj +1079 0 obj << +/D [1075 0 R /XYZ 189.746 421.71 null] +>> endobj +1080 0 obj << +/D [1075 0 R /XYZ 192.971 91.906 null] +>> endobj +1081 0 obj << +/D [1075 0 R /XYZ 192.971 91.906 null] +>> endobj +1074 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1091 0 obj << +/Length 1764 +/Filter /FlateDecode +>> +stream +xÚÍYKoÛF¾ëWðHÕfß-Ð Iá´(ÒƇ +j¢á IœˆîӔÚ0¦³YGìç䪜HÐ ·¥ˆ"¦+b M¬ŠšÎ(ç©5ÁðlÖdQŸìK)Ö,xF)Mš%¨¶ oãz®·(I„ˆBÞ¨Éë“É— ‹QbV%@ŠÂÎί&§ i6‡—o3J¤±Ù½Ê%–ãwËìýäï|«¬!T«L‚ÔE Ï–)BÁ&A¤ ˆ«ý{Έ¦²ÝX‘ÜJŒãý½½™ +ÁŒYN lË v:æñ›©åùf}5I%óúrQ…d¦ÁÌÄñùzu>eùòf^6bE GÓž8!òë)di¾†D†Ÿ:*ƒ2‰ß•) ¸b·‡ö2{˜´˜ÚQbVÜ7v«9Š£SŠ8†;!¡Zu¬ÊëbSÔå JL©üúo£-~0_Tu±:O,ü`ánÊeQ/n›ÅoÖIó©!¶•òGd ƒ˜Ý涊ëÜ-–ËƶYØq|Ø”ˆ/å +íE냇ÌNEßCÜZDšõÍ&ÀHµ*®«Ëu ¦[a <†Aë1ªePçÌi.̵eLYÊUGŒRƒ8í@ }é}¤÷"9Àă0ˆºƒ@ˆ ‚Bv +9 Ø.2!9áÜ>…œ"\¼0ã¾1 +‰þî&A¼Ruꀚ ú$ FþAõ±P$‚2b‡ ÷êáJ˜ü" Œî„Á貨 V`¹ +U±˜Ã1-uÄ +œëÃØV[Tq…`qSÕ[…ˆ Þ0fˆR®_¼‹y,ñÅy±<‚âd2¿,Q»» +9ÔŒÂ%l í.ÆhŠ_â )þåZè}§-LÁCùå¦X†!@ã¨Í SRä +».{AÁ0¥%ØS¹ X$ +endstream +endobj +1090 0 obj << +/Type /Page +/Contents 1091 0 R +/Resources 1089 0 R +/MediaBox [0 0 342 504] +/Parent 1058 0 R +/Annots [ 1073 0 R 1082 0 R 1083 0 R 1084 0 R 1085 0 R 1086 0 R 1087 0 R ] +>> endobj +1073 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [53.007 449.173 69.957 463.121] +/Subtype /Link +/A << /S /GoTo /D (AMS.142) >> +>> endobj +1082 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [124.084 292.839 141.034 306.787] +/Subtype /Link +/A << /S /GoTo /D (AMS.144) >> +>> endobj +1083 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [268.308 292.839 291.403 306.787] +/Subtype /Link +/A << /S /GoTo /D (AMS.146) >> +>> endobj +1084 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [101.411 222.708 118.361 236.655] +/Subtype /Link +/A << /S /GoTo /D (AMS.142) >> +>> endobj +1085 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [142.402 222.708 164.329 236.655] +/Subtype /Link +/A << /S /GoTo /D (AMS.148) >> +>> endobj +1086 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [239.52 208.262 256.47 222.209] +/Subtype /Link +/A << /S /GoTo /D (AMS.140) >> +>> endobj +1087 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [240.628 194.48 296.589 207.099] +/Subtype /Link +/A << /S /GoTo /D (section*.52) >> +>> endobj +1092 0 obj << +/D [1090 0 R /XYZ 9 484.913 null] +>> endobj +1093 0 obj << +/D [1090 0 R /XYZ 220.804 353.685 null] +>> endobj +1094 0 obj << +/D [1090 0 R /XYZ 220.804 353.685 null] +>> endobj +1095 0 obj << +/D [1090 0 R /XYZ 203.971 280.036 null] +>> endobj +1096 0 obj << +/D [1090 0 R /XYZ 203.971 280.036 null] +>> endobj +1097 0 obj << +/D [1090 0 R /XYZ 217.138 148.006 null] +>> endobj +1098 0 obj << +/D [1090 0 R /XYZ 217.138 148.006 null] +>> endobj +1099 0 obj << +/D [1090 0 R /XYZ 227.522 47.559 null] +>> endobj +1100 0 obj << +/D [1090 0 R /XYZ 227.522 47.559 null] +>> endobj +1089 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F27 593 0 R /F24 494 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1112 0 obj << +/Length 1717 +/Filter /FlateDecode +>> +stream +xÚíXKÛ6¾ûWè(£k†oQ rh´Ø¶—¦F‹"ÉAk˶R[Ú•ä}ùñ!)Ù²iï¦H‚¢ÈÅ&©çýÍŒh´ŒhôÓè‡éèÙÒDŒ‘T) Mㆮ"iRÂeMçÑ›øõ«_¿ §2ž^þq9ýkünúó³ ™¼f˜†[í Œq¤QÏ(špcˆ1<šM¨I Ùt•'R¦q~ßæeST%nM\-Üq»*·ªóf»n/`“Àqå‹r¶ÞÎs÷N~;æIœ—øÛú·îÆ,^3<Zù³¿-JMXB”Já_)•“ézÍàJ¡D\mÛ¦˜ûM»Êâœí+ž2"yÒé} ²&žb’Ý
è!4Q9ËçªÍŠ2Ÿ»Ý +øàÖuŽOŠr‰[ç7Û¬ÀP·/XT£‘qñ,ýÆR¾¥ŠøanH
¡I§±v"e%ræ:n¶××ë|ãmè¸Â1h¾ÁU‚¢+>Gßáã:_gm'Ñ¡y˜¤$‘ÀKB!Ò,ÃO©¢„¤ eÎHL$‘$©ð1GÃ¦Ä ›ì‘½ råàÕ™ Öñ çrC1n]/…t ò(X1+~š<úÉò|€PTñsO˜ ¢‰È
žª™#î|x”pBÎ7§àIÙÓ´{RÂEsŽ£=Í%æ˜a]n +YîÌ|Ôá£;tsîÖ
ø¶Y<tïøÓëñÈ«¦Ý‚ïswMÚ}¢ÄD›•³‡ãç( F¡Kßueožm—LØ7ñ],W64A´Ø7ˆ„¦¢³qZ +aâÛl¶Bö“ ÑÚt䋪v,jg‡æãÁqV_mÕ^ÌyQç3Ì„ .b ü8PóÊY®µxD c)Ro58i šò-EàΔ÷*þ @פ'±™ýélD>`3HF‰a²CˆôLvp’¤ +³£'#ãI’(À}{ Ϧ;ÉÙ&ïUnª!87« +éïJ=EÙ#”¥Eµ†‚è½óè• +ùj:º1_F™äàñì)¢Ùfôæ æð P‹ÈÄDw–ri!Ž ×Ñï£ß\?uX +ºõ›-ô)swÚϼ«T@²ÎluÛëÀÓÏ팆îÚÕŠϨtçÐý½ß–³ÉéI«õó Öש®?ÑÇ &œ¹±°›8n±GÄqzJ;âÛP-Iôge³)š¦gæŠïaûi_€ + wÕ ×¨ ‡ëo¶y㤵«j»ž»u?OÚ ?fÛ½ßΗ¹§³
A°æcÍzj³ežÖly²EÙÍœ(q8õY ƒö<ïê8ú` +)ñ‹”>¨Jg5D, ö +endstream +endobj +1111 0 obj << +/Type /Page +/Contents 1112 0 R +/Resources 1110 0 R +/MediaBox [0 0 342 504] +/Parent 1058 0 R +/Annots [ 1088 0 R 1101 0 R 1102 0 R ] +>> endobj +1088 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [317.046 434.727 333.996 448.675] +/Subtype /Link +/A << /S /GoTo /D (AMS.150) >> +>> endobj +1101 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [133.036 66.642 161.984 80.59] +/Subtype /Link +/A << /S /GoTo /D (AMS.158) >> +>> endobj +1102 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [32.066 52.196 54.869 66.144] +/Subtype /Link +/A << /S /GoTo /D (AMS.156) >> +>> endobj +1113 0 obj << +/D [1111 0 R /XYZ 9 484.913 null] +>> endobj +1114 0 obj << +/D [1111 0 R /XYZ 195.439 405.848 null] +>> endobj +1115 0 obj << +/D [1111 0 R /XYZ 195.439 405.848 null] +>> endobj +1116 0 obj << +/D [1111 0 R /XYZ 230.992 231.552 null] +>> endobj +1117 0 obj << +/D [1111 0 R /XYZ 230.992 231.552 null] +>> endobj +1118 0 obj << +/D [1111 0 R /XYZ 235.586 104.566 null] +>> endobj +1119 0 obj << +/D [1111 0 R /XYZ 235.586 104.566 null] +>> endobj +1120 0 obj << +/D [1111 0 R /XYZ 288.32 47.559 null] +>> endobj +1121 0 obj << +/D [1111 0 R /XYZ 288.32 47.559 null] +>> endobj +1110 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F27 593 0 R /F63 238 0 R /F19 213 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1127 0 obj << +/Length 1885 +/Filter /FlateDecode +>> +stream +xÚÍYK“›F¾ï¯àˆ*Öx À€S>8;µyº’Jªì 0-Tl +6 ûÛ¶#»òº\Ñj
Ö
¯K©ýº¨ðèZ"‚åðŒý.7Sö‰0f"Ò½ú›i£pçÄezS´ÏË€þ5*²bÁ•:f])Ày,s—#ÇL‘"ös°5EÂÇݾ±9! :C©É¸rpÕs½ÄcǾ`pÐ$ñÏ;Ô¦ýÂi5i[”·´n©hÕå©ãCÇXÒucÈuwîM“Víºn6»ð–g!$'2"“–VC¢üxÛ÷\¦%‚ùûTþ æSÁÇ·`Ãdì"Å4 å¯Á[B'ú±–î”)>?««lª BíCè€ ]V¯çµ\Ïד X”|f=¡‚´Z¶ ™ØícîK +Ú(##ª\ jľԳ2…f!`Þ@ä…•ìW¤È ÑF…fi¹jLëX ö?à¯Û#P g]‹/º¶ßLïÖ>$»°veÙ'÷áQ¨€¢1¥ßÕøT`ú’B€ÄKS™&-‹Ö¬0dP‡¿|À |,êm‹P‚;ŠŽ˜‹ÖýÅp'-‰t`°s½®‡¥7¦oë©ŠŠƒ +ïëåÇzš%è ±ˆ½€)Ÿª;
ÊÁ{l{gNü c—×RûKE%Ü!1RÀä[gsã6µW„®¶Ã¥àµÒ”ngMAÐ ÓÑ“;Ôê•ž9v X¬ôèØÀ‰çv,ŒÊݶåÚ‹‚Œ‚¨Ø²Ç UíÞš¶O]+|ç:Žê;Žê«²¬›2ˆ·ÍnË
F/–F¹×€B Ý8œBÓƒö Y"ä6bRëA`¯ +rQAß/6W¥¡5vÁ0´G3|×Xß×-ýt9+7BÙ5e=.>ô¢,z8‘]³Íº~¿Ô¼³eˆÎÑ°°O¬6 ,@qhD? o±pcÝÔ'…ZSk"üUT«–¸(ùƦ 5ÓÀ¾Ý1ª]'VC£±¬a+•[ozmí·¸ahÑ'àr +3ÂJ®v°µ½iÎ +X]mcQ^;С‡Q ™„gÄ”ÕM3ÒïüàŒ«»d؈ڧM`X@£+ÓÌlpbrÑÒm&³..·eÚ µ.ëfUTЈ£½m;4a†kœ¶e§ô¨Ì5.t¿Ë©°qUØ :Ô?€4¼_ե㬈±¶È’vEÙÎO?¥À^Í,¾C£Cß +~_0YZ¹…õ6À†ý¯u¯) +ñu7k ¼ÍÆ0&]XXµ<n3Χ$ÄŽŒ/ËF³ó5Q¯QŒq ÛmWtÛÎý`.š©áÓ
J® r wª… +úç닳 +endstream +endobj +1126 0 obj << +/Type /Page +/Contents 1127 0 R +/Resources 1125 0 R +/MediaBox [0 0 342 504] +/Parent 1058 0 R +/Annots [ 1103 0 R 1104 0 R 1105 0 R 1106 0 R 1107 0 R 1108 0 R 1109 0 R 1122 0 R 1123 0 R 1124 0 R ] +>> endobj +1103 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [105.416 449.173 128.511 463.121] +/Subtype /Link +/A << /S /GoTo /D (AMS.152) >> +>> endobj +1104 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [129.922 420.282 152.725 434.229] +/Subtype /Link +/A << /S /GoTo /D (AMS.160) >> +>> endobj +1105 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [224.783 420.282 247.587 434.229] +/Subtype /Link +/A << /S /GoTo /D (AMS.160) >> +>> endobj +1106 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [22.298 405.836 45.393 419.784] +/Subtype /Link +/A << /S /GoTo /D (AMS.152) >> +>> endobj +1107 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [71.988 405.836 88.939 419.784] +/Subtype /Link +/A << /S /GoTo /D (AMS.154) >> +>> endobj +1108 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [191.239 405.836 208.189 419.784] +/Subtype /Link +/A << /S /GoTo /D (AMS.150) >> +>> endobj +1109 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [234.784 405.836 251.735 419.784] +/Subtype /Link +/A << /S /GoTo /D (AMS.154) >> +>> endobj +1122 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [251.827 376.944 268.778 390.892] +/Subtype /Link +/A << /S /GoTo /D (AMS.150) >> +>> endobj +1123 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [293.963 376.944 310.913 390.892] +/Subtype /Link +/A << /S /GoTo /D (AMS.154) >> +>> endobj +1124 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [166.56 93.009 195.508 106.957] +/Subtype /Link +/A << /S /GoTo /D (AMS.162) >> +>> endobj +1128 0 obj << +/D [1126 0 R /XYZ 9 484.913 null] +>> endobj +1129 0 obj << +/D [1126 0 R /XYZ 278.601 166.732 null] +>> endobj +1130 0 obj << +/D [1126 0 R /XYZ 278.601 166.732 null] +>> endobj +1125 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1136 0 obj << +/Length 1756 +/Filter /FlateDecode +>> +stream +xÚÕXKsÛ6¾ûWpr)5µ¼A$ÓƒÛ8 åᤱ[gÆΡè˜ItH*¶ûë» €i3ŽìØ™éE +çqĪá4Ҭɫ¢Îýhsê:&~UVù•ÒüfªtQŸ”Õ<õ˜Q¨nŠÙÌOÏAÞ÷êb>F €ÍŸ<ÜRjþÙ ”Ã'Ø&ñ9 ’û~áO¬Jø4ñt™å^Ö£Byú©X¤Õ¥¿(—Ý‹2à ç6ÍX NsÊÜ=Øú²Å‚ú™e„Á¼H áÂFÙ|ëè¦0ù"¢Dš$:w¢óˆ)°V\7‹ö·þò†}åÈv3cˆ¦Á2)¥Ca ·Iûl膨Ĵ°M+ĺBŠP¥VÏÙ Ä81l%S,¼ÏfiôXž ]‡eƒ;KÐð +á6¬ŽÓ:¼R1ÏW/¯‰æíÓ+/þu¤$8H‘~'›åd4–BÇ““mïÛ4ËÊjš.+ºè9HÍ©ÿhN‹:È·†ã×ÖyÕ Ý‰!gP4‘”y$áj4n
õÎM4¬3b¬ì=Q_@dJD ©ß†O%’ëVOOWþÀƒ3 ‘BmEx)~3±1d& ÿ0 q_x€\¤¼†<åVpäàÈ8vWßæ ÀSTÄ-'‰Ò?Èíf 'Zòïs†½‘3 &±ïS†5fMO‡£l¢ KXßSÒÅ^HQdõb–VÈÞRÚ wÔŒ p[ (òvÉeÝäó!<œJÂä*&½ 2ªóÈvf€o„´:¨ :ŒÈ 1` Q ƒÅ +ÓWp×× ¢Ú•åð 5766$iÃ,6]hØ +UG“×Û¾UÑa¥”퓶Ã>‘™†gU ¤Cj€h,UG ìJaèß:äÅmˆiCD(¥Ê6`xA ç_–.¯MI)ûiúá(á.i×9v O tUåüÛõ,J÷Ÿª gÿHº}è¬Ë9?„ïut>˜?X,‚̆–*o «±ÀdS' ÉÝ +'"}^¡Ò ?-¼Á”þËÁÇÎ:›pŸh4nþJ¥ vpm~9@Ö`ÑÛ«NçùPÜwUNŒY_maëWB§>se v½Ú°^rÖ:hx*q÷ýŽêÄuâ½^ +¢7w¤¶‡ÎƒKš;ìÐiâ!NŪJd<i¼¢‹ðÓeм³
³r4褾6¦¢p>ä²½wEoÀBVÒPð‹Oð)‚Ïbë ØwJtHq½ÁX•ÏÀº¾
æ%þ6[BêB‡z4è@¬À$w úëU–Ѳ«©ŽïøÛ[A´•ýÛ¯ÙI* ƒ±.«t† "ž9c?¯ýT±ð£!ƒçÞOÜK¨ÝXZ÷„Dë8×eï!M\q·[$"wõ¦ä=ùÃœ&6:-„Ž²~üØWá žgY§`€‹X_G2}åšåryUE¨ƒ¦8¶Žà8ï^;€ þjŠ»îµ
_`öjïvÞMÿPœkûÓ^;!–‹‡xíûº›Üð4H9dˆ|èÚRÅXs»d
B%Ú€›,«Ùô‘Ÿ_¥{0ÿºX|vÓžH>톧e?/‘V`&Ɉ !qeLö„v¶þ¹àØõ +endstream +endobj +1135 0 obj << +/Type /Page +/Contents 1136 0 R +/Resources 1134 0 R +/MediaBox [0 0 342 504] +/Parent 1142 0 R +/Annots [ 1131 0 R 1132 0 R 1133 0 R ] +>> endobj +1131 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [185.548 410.498 261.155 423.399] +/Subtype /Link +/A << /S /GoTo /D (section*.74) >> +>> endobj +1132 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [8.004 156.116 36.952 170.064] +/Subtype /Link +/A << /S /GoTo /D (AMS.162) >> +>> endobj +1133 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [97.4 141.671 120.203 155.618] +/Subtype /Link +/A << /S /GoTo /D (AMS.167) >> +>> endobj +1137 0 obj << +/D [1135 0 R /XYZ 9 484.913 null] +>> endobj +392 0 obj << +/D [1135 0 R /XYZ 9 465.114 null] +>> endobj +170 0 obj << +/D [1135 0 R /XYZ 9 465.114 null] +>> endobj +1138 0 obj << +/D [1135 0 R /XYZ 9 441.319 null] +>> endobj +1139 0 obj << +/D [1135 0 R /XYZ 9 403.773 null] +>> endobj +1140 0 obj << +/D [1135 0 R /XYZ 283.349 215.394 null] +>> endobj +1141 0 obj << +/D [1135 0 R /XYZ 283.349 215.394 null] +>> endobj +1134 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F40 208 0 R /F24 494 0 R /F21 427 0 R /F19 213 0 R /F25 463 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1146 0 obj << +/Length 1160 +/Filter /FlateDecode +>> +stream +xÚ½WÝoã6 ï_aôeVë,É ò{ØG;t؆Ã`îö 9J"\bu²³^öו îymºëöbÉ$%þDR™'«$O¾»øz~ñê¦P ç¬)K‘Ì— SJ%…j˜(êd¾HÞ¦_½ysýÓ··¿Î2Y—é- ¾¿Í¿uÃËÑj¥XYJØ<¬ã¼D©‹<êK2™W¬(8L*–«†Äô¦w³¬u:¿5 škîf™¨Sg» CfþÄÑÐßHð —Å=’ß,²+TéÀ.gY]©ôf¦DêÝö£µk}GºL—!j@œñЖ„Òv+ØB4 +f4koL¶°[ÓõÖÆNoˆÓßéÖ\ò"½[#¨}oÛž˜¿“–ÖmM ddª#Ë4†soìn¨"@Ú|°ý`ºÖ +û}ŸMÌ6zNK7SðÓ›)jÖTüp1?D‘2rs”¨X¢“2^˸oN„@mÍDSÄû=¥©`µ‰À’z=ËxUOê„eª©Ÿ§T¼ˆÒêyJåT¶C¥òT)EºáÞkš ob¯·qæ¼]ÙîêÈï¦NÄ‹šUõä±Ï12ÞÕ šñò¥áˆOƒóÂhÎsrô›öÑ›ÛA²£t%*Åj¡ÆÇÚmÝÊtÆíz|m —îºv€Ì~9&ª)ÿˆq) q„žŽ˜qV?é^™œHMÚS1Ù¨çi{Ä{çhkž§Mž©-+Ê:½_ã Ób^“•!ýS!€)³'b¯Û/÷ñir¨IäÃÇ&ºÙü±Óè´ÉXT\ºŸÿ©˜ldõÏ1) ëƒiDŒ«@ƒXUxÄÓ
«Tb5îÿùdd¹Î{ +^ +QžÌòÄ}ñfV2šG¬U3 •rvrÌóÝú q„!^†x ù(Œ©—þÆSh3Q€‚wrŽ—¹¬ÊPü¹Õž~î-ä +x®©SÉžxlWpò3ô,oƒÖU\„~ÔÑ«ä°/
PÚßmÌ•¹Î0¨Fx™§¿`uÈEÚb‡|oVÚ/¦ªº m÷>T×ø¹” †§ï1µ}SYÊÓ + È¡GrèJªL–ÎoCí,¬½u×…:´¤Öc$ù Ο€u¬¦±Yi¨Ù¡¾D¥2ìVC£ý>¶Kvkˆ•m,kÑ¢¯±ËQ”j‘ýC({c÷×d¹ëuׇC…” ^ÕÖyoúØ.v‹ø¸Ž¸š~Ñ\Þ
aÙ%qBŸ€’¨ž6:¢›ê¡?VÛÿ¾Ý:FÐa¼ž_ü
iÆ[ +endstream +endobj +1145 0 obj << +/Type /Page +/Contents 1146 0 R +/Resources 1144 0 R +/MediaBox [0 0 342 504] +/Parent 1142 0 R +/Annots [ 1143 0 R ] +>> endobj +1143 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [110.531 280.805 133.334 294.752] +/Subtype /Link +/A << /S /GoTo /D (AMS.167) >> +>> endobj +1147 0 obj << +/D [1145 0 R /XYZ 9 484.913 null] +>> endobj +1144 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1150 0 obj << +/Length 1631 +/Filter /FlateDecode +>> +stream +xÚuWYÛ6~ϯ0ú$kG¢(YBŸ6©7Ý"Ù
F› éWâÚ,t”´Ç¿ï\òUåE$‡Ãá gFál; gŸÞ…2~ؼ{£³Y¤—±NÕló4‹`žÅéL'ñ2J²Ù¦œý \ýº¾ûíöÛ|¯’à†ˆ¾ +¾ÿlþx%pp™' ÉXdÑR+=[¨dg"cóûO¤ÁúÛ×õÃí—õÝfžEÁõg¦~¼¿»¹}ør´Ííý SïoxÄÃpÑ,ÁÑlÅËDç,÷Óúný0J¾ûñýüüÃú³HþóvóuÖá©Ý‹$YfJÎj¥+–}ãçJm=e¤VKµÒàFâ4|O÷Öõ¶6½+p½ +úm½Åe˜Šiûù¾kæÈÀçÚ'Þ{vÀh_®xõ‚ –9jƒ‹7^¸Úl]cÉ% QdÆh²:p/) +ö¾¥ë +ÛuL¡«`´Ï(°†ÞµÍù–‘µ÷낇eW8Û"¸oy|$ñB4<-ÛÆ& Ò3<×° @ •$ª„;®)‡µ[ÎÄnЙÎÊ9ã-³£!BöØRv›ò’íuïá +`8Õ&am Z¬ã Ûµ¾çiÑÖ{CNÓ:0ì÷âkÙ<¡‘×`4<TÆo-ŸjP±¡Ffq“çñXèž]9€‡§\ôØYÿ<Oàz@:¢“ð7<r”aòÔúúH`m
GŽÑJE +ŸWÈ«°¼cŒï˜kk +h² ÛÊ4…ñYи³Sz¢Á®2òäRÅñ‚Á“Â@Îý#M–ÃFazSµÛÁ‚_
·gº£@®B†&dƒ“†·´ÍO¨{0ið¶z›Bÿé;Gì°{¬ß{×Á½x"Z-“$?7æÀWf)Gf¹-Hf˜Ûì S ÇTÔ¦eZm
Á;#ì¢W½)¬ˆeLfˆÕ¶²±”þ¦4c~D_Ñ#ZOͯQâßà«ç±«/pnQ † Á‡ÉYÔb*`û`,^bü8« +‹Ÿ|ܯà20 +7{Wù=—'Á§Áq Ó'ȇS)(%¼u45‰Á@s;Že׻Ɍ¼5=ªœ7p’æ+†@Fè˜b˜‰»&‘îIzŽ($pY +0R'Óñãà*él†=Ž a‹†Vo—ågìœjØdVî.ËæIq{šÒŒ¨ ³$ΡÞOú‡J烎 ýk×.P † +endstream +endobj +1149 0 obj << +/Type /Page +/Contents 1150 0 R +/Resources 1148 0 R +/MediaBox [0 0 342 504] +/Parent 1142 0 R +>> endobj +1151 0 obj << +/D [1149 0 R /XYZ 9 484.913 null] +>> endobj +255 0 obj << +/D [1149 0 R /XYZ 9 465.114 null] +>> endobj +174 0 obj << +/D [1149 0 R /XYZ 9 465.114 null] +>> endobj +1152 0 obj << +/D [1149 0 R /XYZ 9 441.319 null] +>> endobj +1153 0 obj << +/D [1149 0 R /XYZ 9 406.5 null] +>> endobj +1148 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F40 208 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1156 0 obj << +/Length 1699 +/Filter /FlateDecode +>> +stream +xÚ}XKÛ8 ¾Ï¯Èm `âÆŠŸÇ.Ú.º@‹ è»{ÐØJ"À¶²’3iþýòeÇ™q{‰IŠ¢(‰üHe»:¬¶«? ~zx÷)-WIWY¦VOûU¢Ò8©òUZV±J‹ÕS³ú;zÿíÛǯ >ÿµÞìŠ,ú Ÿ„~üþûôç»OIvg£J`nKÐì$)Pëa+«®6»m §iD oËŠÕ†£YoÒ´DÂyks^«2º2ó¼Þ +¦ëìp7 ôÖI4Úmì?Û$¯Ï(
7I +Îeìè¤}[M³(œëµ*¢#s
ÚjÎõ`] Xd{þ^Žv®I#wrÁ7ÈNÉ"z´3ž¹½wJ#£ÅÚÜ¿œýs`ÂÇëM–åÑ{´“‘F7ò<2?4 Ì#ÞHYXë`XÍíù{0½ñºåaØ,5oÂÀÃ6ðˆÆ—u–FÚ¶ú¹5Ó„·xËÛ4:yGól_“dÇËÂȳu;\×e¡‡Û’F¦É ´¿ØÞê›Üù+ÓlewÓmÌ .dZwÚ,yÔÞj+™®¢p‚ЀY5_|–hC:Øeѳ„]Tã²``ðçánï<æ‡
ƒ=ÓÖðJ øÕqå»ÛsÙ"Èf;£M”´ Pà0+)̀勂 À
7b¢ŸÌ2qDKWÞ4†NàI´ØOýRyAf;hò
øÁë>t6>%Ñ#ºþïl=9 +1‘q–U÷iö}]*LkU€i¸g–è }…›ðÌÛ> š +9\¿{í7~ÌÛ Pª"}ðÆÜ. ŸùÎ]xHe¾˜Íwù 2A†Î>…Ìä M9µ‹)µqhbŒ øýj.ƒãˆF¥ÎÈõ¶M÷‹ +f–JЙw {Ðè FA5B (ã.,£Ó îÄ( +qGŽ mL8ÙÁü<æ‹-Ö½;Óö€«$ +¦- —á;ÍÙƒ¾ ã’2„:„sw 6b«7g3zp—ÔÔZpRCÁ-+h„0Ë-œ4u @í]Û:ªòöœ%å¸8Žºm™ÔM˜ +endstream +endobj +1155 0 obj << +/Type /Page +/Contents 1156 0 R +/Resources 1154 0 R +/MediaBox [0 0 342 504] +/Parent 1142 0 R +>> endobj +1157 0 obj << +/D [1155 0 R /XYZ 9 484.913 null] +>> endobj +1158 0 obj << +/D [1155 0 R /XYZ 9 165.695 null] +>> endobj +393 0 obj << +/D [1155 0 R /XYZ 9 165.695 null] +>> endobj +1154 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F40 208 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1161 0 obj << +/Length 1872 +/Filter /FlateDecode +>> +stream +xÚX_Û6 ¿OáGkTI–ÿuO-Ð
݆ۂCÛ£»hsìÌrî®C?üHQv윆í)4EQ$EþH…'÷ O¾¿y³»yùª!Xç2ÙÝ%BV,“y¢ªšIU&»}ò1ýåíO¯7µJwï~{·û}óy÷ÃËïD¾ÚV•Lˆ´ú
BT(uÃÃAÉ6ãSJ +fn…s2íØãñ¸AÐéý¹õ‡ÊÔ¶mieÔΖ‰ôÔêÆŒ
[ݹAq51ºëÌ4€´ÜéÞºQwÍÚ¬‚Ìrçn Çt6eJ¦æé`oíèð @—R3Xï<(jHêa“ç© ¬©û˜9OoÏ#íB[QŠB…T£™xÐÝ6fÏ}‹ëU–îk{ëÏ5{âÝnÀš/D“" ZÛêÞvv#R¼2ü߈Ð]P0{ZÉt ìErŠªv"KæP€hVAîäünèøU^d¦…À|mÚÞ7†Å¡Ç3žìÑŽ“ ó +—É Àê¯sŽ4Vt +˜ 0¤ùœV‚=qö’;ÃÔÀ¯`(PYÁ©è 0KV—\øšS5SU™(–e¡ `{+OÅÊ,K¶ I¶ÙªZ¤;ºß|º¥ÒþŽ8ã´Ôak“ƒ½]?zG·"WLʵ»° ï3¯Óô¡éÇÇÕäUÚwŠ1+Ê“°lÃV2åûóà“åï¢=†U¶-íË+Xª¸t>ÅÊ\ã9 +#ÊËR<#Å\.A•ûV…‹>y5á_%Ò°—šŠ‘c 1›Zðžµî[Aé!ô²G¦ƒÞÛ³ûÏ6Nß°z ^ÔS屃D®ÀœVC'™àºÂ)ài$ê4ØöÔ05zsèªRˆ@Ã` A|m‹R^A+ÅDGo 2šþ<bæÁãR{¦›FÞ¤„p—>ögšˆ¢Öz-ÞqYL +|QʌɢJ¶’³ªÊHü¿$AAQ$Ì\ñ¥ +D¬æ7ÁJ>oŸx&B©
§d¼¨}» º²˜ªE¯ b:¢«`²r!$ýÀøvwó× +”…XT ~ù +¬.HS=Civ{G\ÿn(D˜ÆÀ†d4dÉY)c¥³v=«!‰W5McŽ˜Æ 8íÖ¡‘ÓWw &ø8Â8p ÂJsvcÔ¾æbÖs:xTp¶qÕùóሪhÂi?ë>„· â ¢ã¯ÊzF GŸãн€-ÿ=ýHSßö]EMÓòô{Á>:ÂO
+æŸçoTä¢Møûlj˜×ÄB…¯xu…L?œ‡i«;·#ÑG}ðÏ—:/¯ÜòóºRêòNÃx<Œ8½!±RñEÚ·FœÁÜ+8²ËÙ Ç ‰ìbžø×ÏØŠ^™‘’Îÿª˜€²Ú'³òÉ z`fò)‹+>6À™ECÊw +endstream +endobj +1160 0 obj << +/Type /Page +/Contents 1161 0 R +/Resources 1159 0 R +/MediaBox [0 0 342 504] +/Parent 1142 0 R +>> endobj +1162 0 obj << +/D [1160 0 R /XYZ 9 484.913 null] +>> endobj +1159 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F25 463 0 R /F21 427 0 R /F19 213 0 R /F24 494 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1166 0 obj << +/Length 1871 +/Filter /FlateDecode +>> +stream +xÚ…WKÜ6¾Ï¯ÐQ¸Q¢^G/b³ÈÉf°0àäÀ–ØÓLô˜P’Ûòãó‹T÷$ +ö"‹E²TõÕƒiô ¥Ñ·ÿzzøú½¬#!’¦(²èé ‰L&¢)#Y7I&«è©‹>ÆoøáÝ÷ß<~8 óªˆ 1÷Íðýåéß_¿Å«3½®p»…hHê!õ·FÇ<-)ˆ2Ië†Å¬þ}5VÏtI/µU2žg§E-fy6_¦µïXF
Ó: 2ûÝ2çõY·ÓØùc¦³ßd[Ò : …„>ëñr8â mé/eÜj>wµ_ˆQÄ烈'ËôrÑ,õÒ«Q/LÿGÛ–¤k¿!NŸÖÅïü©ÛÆ ”? gàh 3ó jÞkW²vÓJâiÏS¯ )âù˼èÙÆm1¨g:Î,k§ýŽ`0Ð'þÉp”?gP}Ï,o~0ÍÂœ+™Á °£Õ¨[=ÏÊšž¬”•±ž[õ²Ý¡Ó‹nÉy‰GLUIS¥ÂFIŽLò¼ö ÙÖQdUR–뤪%K>².¼ß&p@<rµ¬Ëø¬ÚÎ(2«y±Ó8
ÚμvQ‡¬Ž? XWÚu˜:&Ù$æ\Æ,=Á½d…£¨’¢hþâ!‚W)ãïõuqXÝMl‹™§ã´01¯?§¢l5Ï j1¶ªo×^-}ñćžfmY׎™ÃäC‚v! + +×ÉiOR_Qyâó|y¢ ééÎøå)kªWå©Îb‚Dö}rz`y@-¼ +i‘QGkîžÆŒ=¼kZò"Mhk¿0}³åì7M{æRœüÏÀ–Kú·² î4ö^GÚ)ÒD¢Í@¥KDåÌi¿ÌïÓ¾LˆHCàì†2b“p0vB2½ªYÈ ô>÷\¨¨·¦à;ó|Y˜uú£âá[«u<3u(KçL2-¿7škãߊVÖ$¥³D”ÕV´¸%‚†‘¥¾ˆˆÿ¢9úˆÌQÇ?mºÉ*þðáÑEÚãë6Š%
¼ëòWJ63á«» yªz«U÷…'ƒ¦Hv¾ôP$.<P‘Ç +iѺ¤¿§-eîASfñ³ µua.•FG;xa´• W2œC 7F:IåET€e™mûz8ÂG/M¯¦ïY + (¼ÙOs®—•ÅM1ÖŠXÞk¾È Á5ƒá ‹®7[_ ÛR!#tá_WdÊWá¨ý쫨‚Øp>$¸ï.[ÒÔÌ<¾XˆAý_SWÒúf#šø#wlDlo#ªÛÈtoç°gG·†òŒý–gy0c&âVÞ0ãz=§¼5¼Ø²Y«]ÂNå)Å +ïoºC!MoÖØë-\w—߀C“¶Ÿf×¾e¾½ËÝ}.ZÝÊÃèç’óúÎ$é*¾ÿLo½;&þd7 €®âp‡`»ùŸ+-ò1ÂíUŒ¼ˆßSTº× V|¿3ˆ4Ñ®{ƒ”¯Š)¦ôëÚçûí¢y ý¹ —>5UŠÂw'n¹8Q0¥‚)œr´ª£˜7Ìñu· q "”C«)Ä֊VÔøÜ{’ÏÎ`:jâB¢åÛBÊÄ} +G®Â£8¿‘ïez<²×Uˆ5¿„gÓ–»ß==üþ |ÖÇKH$iµÃÃÇ_Ò¨öHÐÆFW'2àUÞ$æiÔG?=üÈ÷ +e¯©èÁ
³D¢h–yR¤ÕëT5ISf%WR<é9ê‘GûÙ'Óݛà Ò2Ðëž$Up"xèý¦¶·.–ÿw@:d›¯3/s¢äîßé¡£«ŠíQ_ÄáI¯úaš—mCxT5yŽÑY–õt/@•·5¶íÉ¿^§÷é kƒúÍõ¿3O]Ë\¢æM”c‰ãú¸²u…æîI‰~rfhÝ£K†6’ˆ[“‹—€BL¼¢n)àNM¼NZ3‡Wîæî¿ŽpÿŸ7À“Ö +endstream +endobj +1165 0 obj << +/Type /Page +/Contents 1166 0 R +/Resources 1164 0 R +/MediaBox [0 0 342 504] +/Parent 1142 0 R +/Annots [ 1163 0 R ] +>> endobj +1163 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [22.888 194.254 92.429 206.874] +/Subtype /Link +/A << /S /GoTo /D (section*.92) >> +>> endobj +1167 0 obj << +/D [1165 0 R /XYZ 9 484.913 null] +>> endobj +1168 0 obj << +/D [1165 0 R /XYZ 9 209.032 null] +>> endobj +394 0 obj << +/D [1165 0 R /XYZ 9 209.032 null] +>> endobj +1164 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F19 213 0 R /F63 238 0 R /F40 208 0 R /F21 427 0 R /F7 232 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1172 0 obj << +/Length 1851 +/Filter /FlateDecode +>> +stream +xÚXKÛ6¾ï¯z© Ä _¥=$HRlQHc(’ ¸2m ÑÃÑ#îþûÎpH?¶JR{09 ’Ùof>-Oö O~¹{¹¹{þF‰¬Ì2™lv‰S2KtQ2©M²Ù&ïÓ?^ÿöbUêtsÿçýæ¯ÕÇͯÏ߈ìf[a˜9œê7ÉQ뎇‹’µâ9ÓZÀ g¼(IͶýܤI§ÕZÉ<z:[Š›³¹„:Y ÃT‘ÓÖ\¨EC8+´ŠvüŒ*‰P,‡# ¸¸ö-Ý“±";ïüiépÅd&¢†!›GWõÝvĉIû íPù÷¿ÞÜ}¾Ã <«TÆJ^$ZÌä"©Ú»÷ y²…Å_δ)’“Wm“’3Éq_“¼»{KqzòN“3¡D¢¥a™‘Ñ)|ùe‚ £Àò[K¡çàg©Xi2R½‡Ð +¨4¥‰iÊàJ¥[Â|.™(%T¯Œ)ܳñ˜ÓàÖÁs3ÑØnÛz +rt †x dpîþ>RB uë žÆ1d¨2¹qò1Àâ•eåm$¢«3‘§³ÝˆCB?Š¼÷Qp<ôS¿ ìñPCT$ ܾ –Ô‡} á ';`J”Ra t„±Å 0°÷¶¢ÄUM} M<ÂˈFx¬µ„.E}×<.åâàìˆ6i®ÒÓ!¼QsžVT6p¡Åñ<NA
g¶žHo×$¶4F¢äl$Ê!P ÕÉc‚_fø›§î Ç
4
©ˆD.Œ<äaÕN-8» DË÷–ºÈÀÑCßí|kºM3·ug'Ì+\ŽÁƱ¿µšz
廡o/KwA¿SÎ¥6N
B¬UiÒ±žfº :g’_tçîÇ »Çj±zÑÃUZ{T©Çú¡q +W)_¥•«¼i*KGâsÏÀÉè O.¬°=¨²è õŒl¶”öh=gxôPÆåmm!9Z°+“"½ß‘îSfW ”…öEs©YÊ ê¹Ë¿[*†e5|™õ'¼G³®ÇÖYxÿŒŽhÎ3J:K à} ¡H16þ€C]¡Þ¦ÔÉ4 €½‡Ú 3¦óü‰ÛlCN3)l]=9’äÜÉžY¨x3û{ ®c` + ˜,§À„ƒè7ø A²^ +Ùà¨/.xR…TgNø*x²÷•Ø
h”̬‰Ì”ꆙÝú[3£ J_´ÀJ—©Eüjö£ƒÎ‡ÞÇGé3vtÄ +0ðDâ!¯Dç '(:qoÌ6T êÔëãþWP¡O'¨ò&¦ò?ÆÔkåê6ÓÔ%k滸¶,Îù苽>üD$äé zÓä‹>,QfT.4è\ÁËômµ8âXc‘Ò¸ +éìË#´ŸÇ:Ì‹P¦9:Ú×?ÜÓPˆ(„N¤W=·ÀØ×ÐRP…:‘`ô!³À!îñ|ÅC‘¨ ¢CEt€ ;*q†%E)áy‰Ï”uA·ìú¦éñ'*± ¢þL€¸cz6÷ur{‘,éø
tÛQè{„Ó~ Äm{_Œ¶¤EDõ¼ n…5& 1*‘ ƒ-#ÍYjhÈ S÷õ #|{š‘Þ™(…oïögÈx²ó6ÿ©GJFkžòØÙAa´û Ó"óÁÐÈóì'_»:ŸqD‡‰œ ~½»;6b"÷¨GÛVƒÂ…ºÅ¯'_Ç ´¤Oáƒl!5å<ÿ^2Š’5;'# »s'´=eÎa¤9¶ûÚÁ¤¿
¦(B Xî‹ èûþà?ä`vª§b]çÚö¿\Ým퀨0â*b˜"ñãͯ\»i$™Çž¥gƒ¼÷ÉZ +endstream +endobj +1171 0 obj << +/Type /Page +/Contents 1172 0 R +/Resources 1170 0 R +/MediaBox [0 0 342 504] +/Parent 1176 0 R +>> endobj +1169 0 obj << +/Type /XObject +/Subtype /Form +/FormType 1 +/PTEX.FileName (./images/127.pdf) +/PTEX.PageNumber 1 +/PTEX.InfoDict 1177 0 R +/BBox [-2 -2 97 210] +/Resources << +/ProcSet [ /PDF /ImageB /Text ] +/ExtGState << +/R7 1178 0 R +>>/Font << /R14 1181 0 R /R12 1183 0 R /R10 1186 0 R /R8 1188 0 R >> +>> +/Length 1189 0 R +/Filter /FlateDecode +>> +stream +xœÝ[Ë®dÇq´¶ý½ä,nO½ [J„LLÎ +Æ,‘³JaºxƒñÆi 7ˆ¶¡³ªÞ½àšJÊÓ}s|©}üX´>1²Ä°¶Ìü,u5ì˯‚ŸÃì~}bã‘.¦»¾ ˜½öåØ9¨aïž}b`!iTl.l}¹R†ÛÓà—ƒçìÕ·6?1²ªú›y±ªŸaÀ <ÃÖÄß6?1°ZÒB+·±ð ÚÁåá<s™Ãæá'–÷3¤ÀJÈS¦×ƒ…8Èmö)„5Ö‘Õt^0¬5]‹óâ¹èXˆ² îîbÝ1°?dë¹qöÄÚu^œ´²e|´u``õ óâ “U]ѽ¯¾+«Â d‹u`duWq±p ²Æ† +SÈÈ)±UáÜÇùÓ㻟qìï%®ª$¡oÎ8¤c(æì^gðMÒ3ÂV©|aYŠ‰Îg–Š8Ê €•.ÓRIH2®‘ôùÏ"¤PJx ¾I% ç> ÷àgš[Pët Þ›’EñD:~ ÆU«Œ‹\ _9 + Ù ‚½žæ\³l7~‰é0!TDjn7 5jÂÿüwq:Ê Ò“Î} nÂÏ7ö÷"¾±R¤Ì¿¬Ô~%>Ö 4'rmS +òcÊË&ÈòÓ/[:1²ÜôµAaUmCMSe»·L¼,üÄÈÒäkž¡,*Ó²<ˆ¬ ]µÝóNŒ¬™
Ôa…-¤Þ"^Í&[A³ƒÓVœä»D” ni²0O™Á£NŒ¬ ¹fÆ6eá\]1AͶ{ì<1²šÄ_‹¹Ê*¢3ûê0³¸Çóý3¿½â¿~ëg~©3Wù,ý¶=½ r4»”•Ï<3N]É‹—UÚç{Ò;1² +Tt[ÉRYX²%U½€ íÉøÄÈ +ê¯3‰+Ëir™ÉžW Zjì"áÄÈÒð?µ…’ªX©i’ŠT»v91²`储æQVÔáÔ.^šXwIubdÍoSŠ)Ë©ŽT{8–›Ò;1¶¬á¾P)S + ÎDá<eä€^¶ËÏ# åB¹ÉVeå©#UÝ’•&ëÒÄ'FV”)L%$îÑÜC +AÞg¿àĆ¥tvÓi™ŸÍÝ™n¦:¨m«2l˜Ð¨íjï™ ©ÕÄú”,l÷b¤;6–ü!²b±ª$öŽ§§N!ÅKÍjôÀÆe¼®±F¡‰·ŠdfÒP^å%Di7ÑgØXb±"áÙ½·‰ÊÊŽ¾ßÅheI`Nx`Ã4,oeJ]TO#–@&°“6h,Y]K– ( vV’ø“Êt6áyqb2Ý>%ëkÙÞƒ™ò¿"ƒª‰Ï +@òVܱ±ª
^©±3¯ˆV%ìÖ÷j†ˆ^ }ø « +Bà¼ÂÁ¬–ˆ9µYQUöÔÌõl¬âŒÈ +ž³†«X¾ÆƒYæp¶6VÉX™ìm?giIÌXZ~V€‹uÇƪd‰,±>+^ÞçOÉ1«b"Ù<ôÀƪ°‰Ø»V‰W¶ÿÂV»XñUñÑ+ª«3@,ä¶uˆ\oOݱ±:DVäŸ ‹š½tA®N‹Swh¬þb¢böQÓ&£súië»Øç±ú4ÆW†öslÜ«´Íæ€Æê Ù”$M&[êÕ›Ú·èÄÆêiÙÖ +K[_vW·l?¸«Ëfç,íÆ™]\]¼ÝžNl¬îŸÙ¡°f“Ðìõj.îv~bc5%Í?”¥ÍKó£«é¹û߉
k•N¯Î짚s_}Ø=(œØXý[ &Ê’6¯Åœ«;¼Çª««l1NYÚ}¶Xxu÷zbcu»gèU’6Å-B_Íô=ªŸØXMxËÊj3Çä™®¬¡¿'™ërÀr“°æ%‚å°ëòaO}'6Ö¥…¥Leé冥ÖëRdOÉ'6ÖeŠ¥re饋¥üë²f— +'6Ö%I eée)‘ëiW0'6ÖåÓ>JÒ;*ÓG×ÝÖ.«Nl¬;1“cÊÒ»3“m×Û®öNl¬«:S‰ÂšWz¦&¯«À]„žØ°DÓ®J’{F“¸ërrWÆ4Ö•¦ j%éÕ§éîëÊt—ë'6ÖU«É|e镬•ÛUîUD и.€g顤yQ<K”í‚y+mNl\ÓZ)iÞ_ÏÂi»÷Þê×}ù¬Ó”5ïÕ}XïÌ»÷<±qÝãÏúQYó¾ß¯hjïlõé‰ëý‚Y×*k¾‡0ëßíí…n>±q½õ0ëmcÉÛ³.ßÞªØÊù×˳
¬ùÒÆll/{lm†×K"³=a,y™d¶1¶—P¶öljëåíšIßqÑÞÊøì=²ô¯oýøááõïùϧñüòããý·|»aÖòñ»‡¾÷ïŸXh£×òíTzñÇñøÝ Þ½ácnÙ÷þû¿y¼!!¯§ç[cO çûñ }õŽo–Èùêãã)néwûKÉŠxW%jI14!-ŠÄÝúû&ƒÀª
“;Æûµ}¶ñ?=‚té„©#À<ß¹Ò.•þýéaO_ßÚ|í×Çü?=¾|÷¹ªû«ã þFƒðîY‚±õHãÑ|ñ«w ÿ |ü\ÿÏ À›¶0 i3þÜ]O›9†‡o:¾Ñ x͈ üÍa=5Ç5la]‹?2,¯Wrù.ì+úéÃúû°|Wí×ñ—¡—'œâŒrûc~'½¹AcúÉê_¿xG £
›öaßx£Écy+2 É¿{ã2jÊËÙ~xâÜ ûäoÔÔoÌ»Yü
¡¼S»0Å5¹jˆ0„Oãñå×÷_ÿËó?ÿü_ÿöxÿÛ§¼ÿgþß—ÿúKüóõ¯žÿôøêëç7Ó îSýI;-ùb„9ìÀ_×r¾øßù§šÄO^YBª
ÌwP‘Uãßem”äªü/(èi²¶ÿùü¨¾yü „$vO +endstream +endobj +1177 0 obj +<< +/Producer (GPL Ghostscript 8.62) +/CreationDate (D:20110511111341-04'00') +/ModDate (D:20110511111341-04'00') +>> +endobj +1178 0 obj +<< +/Type /ExtGState +/OPM 1 +>> +endobj +1181 0 obj +<< +/Type /Font +/FirstChar 122 +/LastChar 125 +/Widths [ 450 450 450 450] +/Subtype /Type1 +/FontDescriptor 1179 0 R +/BaseFont 1190 0 R +/Encoding 1180 0 R +>> +endobj +1183 0 obj +<< +/Type /Font +/FirstChar 1 +/LastChar 1 +/Widths [ 816] +/Subtype /Type1 +/FontDescriptor 891 0 R +/BaseFont 897 0 R +/Encoding 1182 0 R +>> +endobj +1186 0 obj +<< +/Type /Font +/FirstChar 49 +/LastChar 50 +/Widths [ 531 531] +/Subtype /Type1 +/FontDescriptor 1184 0 R +/BaseFont 1191 0 R +/Encoding 1185 0 R +>> +endobj +1188 0 obj +<< +/Type /Font +/FirstChar 68 +/LastChar 83 +/Widths [ 813 725 0 0 0 0 0 0 0 0 0 0 0 0 0 602] +/Subtype /Type1 +/FontDescriptor 536 0 R +/BaseFont 543 0 R +/Encoding 1187 0 R +>> +endobj +1189 0 obj +4233 +endobj +1187 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +1185 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +1182 0 obj << +/Type /Encoding +/Differences [1/Delta 32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +1180 0 obj << +/Type /Encoding +/Differences [32/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quotesingle/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/grave/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/bracehtipdownleft/bracehtipdownright/bracehtipupleft/bracehtipupright/asciitilde/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark/scaron/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +>> endobj +1173 0 obj << +/D [1171 0 R /XYZ 9 484.913 null] +>> endobj +1174 0 obj << +/D [1171 0 R /XYZ 9 347.273 null] +>> endobj +1175 0 obj << +/D [1171 0 R /XYZ 29.833 180.633 null] +>> endobj +1170 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F40 208 0 R /F16 210 0 R /F19 213 0 R /F63 238 0 R >> +/XObject << /Im5 1169 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1195 0 obj << +/Length 1792 +/Filter /FlateDecode +>> +stream +xÚÍYY“Ü4~ß_á7¼#túà- U„@–‚*ƒÇÖì|,’'!þ;ÝjyvfãÉUCŠ—±Ôju·¾¾¤ž\'<ùêâþÕÅçt‘ÁJcdrµI„ÔL”Y¢‹’I'WMòKzïÉ“‡¿üúçË•ÊMú5|Dø•ðûëÕ7Ÿ?æHF)`¯a·¹.xÔš¬Ï˜ÖãEIl7ö SétÚZÔ—"µÃ¥ÌÓÉEÒ¸¹ÃãwÃ3nNTºFÞ—´P
ñÛ;Q¤S::gýÍå +XÇ¡i‡ë(q¼• æ‚©+¡ÁLCæUÃugé´R žVqf²l>ì3.Ô&93°-2± `%a§,¢šŒ–~º,dŠG3<¡u™¶Ccדmh Åï6.ÿ0Ò±á§êˆôt ç«[;Í +yU¡Óÿ²F]Û±¯ÁTW†jÚ…0@f7î|ˆXXGœqLnŽxŒÏ`VHöqÁßÆš¿`’ýc×ÞØA‡è@iAäHûçÌÐ"ÌþÕžŽk,æ2Àðû®‚SüÕv˜šh
Ïâ™QlÜDVÃŽÖw¸¸tˆ°Ö<}âÚ¡n£r"¡HqD”{¸¡ÆWAÒ¼S ê
ÌžãÌ[qy–ßµSÕŸxšö#È\À¨¶…ƒ†LÔ%zd^® ¾a2Â:OKhÞëË4€€Êò`œ& l«~&@Éëm׶/«+mãÇ!â¨E)Ñ
IãŒjG3U¨ãBã›í8×®ºÙú¸¸¡o@ ~ìª(ÀÖ]{ãí’!ah–%†¸eúmEÑðFÐBÍ/!ír!Ò« øí ¿)Ù‰Ò´¾vö¦gb!)ßu( ‘o h5b½`¥œ½Pk±†ä1$´)?Ù.œ'GP á„ŽÄåfçB À1úr–1ƒ&wct.8!Œs¥¿©\뱚áüH§Ê©ðX‘"†lÈ©Àgc_Ð`‹\»¡q¶™H€BG,u&DN¥}Ûumo'‡M“HãнÄ~‚õP¢c‚LO‹Xgœ&šUu½sUý’f/B#ˆŒƒ÷•‹k]„öÕïˆÙ)D¥j~Ûù©-<ŠsXi\@¾˜[÷°ã˜D†Pd‘6 =€bO–â”cÐP%3ÜÙ: æpYX{P¿/ +Hëmå¡Äö‘H½y©ç]‘£ó4 ì¡xš‡; |c$dG"éàH1…v=¹þ€ #‹Ä`5Ъ74ßíàz Î]ih8 ²Ìoªz +B4\Îúj¬Ã|ÔyÌG…Þ®¡‹^ï(ça#Fl¼íM=Q…•œ 6Ò(:Ê놖¨¸K yÅÌ :ªš&ÕL\hìóëfh QÜ]ù~ªœ'ÖQ€dÁ½Þ ' “ì}u¼
‘îO0ð6ú¢
KÒ¢c^ëºCà] ŽjÝÙC` ÿE g\ïVîy\’Yw= ”ÛïF~ÍŠ<;Æ6ªÏÒ§pfŠ½ ¯…:3¹&®Góñ=WPù[¸X¯£ùáEs…F •¬r¦E´é¯pÿ~xuñÇÞAy"¸Þ¢L„Ìp•ÔýÒuÆDâ˜V&q6Ù\|O„c BV–f¿;(ùçÕëZÌùP5¥d¥’Çjþ^º]á mðô(±~w¦X•I ì£1æ¹,ÏÁЂ峆§!°ÞmÃ$œá-`K¡XfôÂ
øJ‰·£-1rJñj\žÿ%Ú+‘•L0`<¾û„ˆÀêC &g +(ûWçK–Àµ,f&¾ô:3¡jæøbI†bð Ø¿UË%cTβL~tc¤Ä—¶)ÒO¥ePF¤|³eø>)³âŒaŠë·ŠÛ?b¹Œ¯X#™Èî<c
>;¤>e9”6iÞˆ,E~Êr*Þ;‹S‹§!43óѬ³Ec8æ"®<ƒ1{ŸjuëS ` µ*}VŸBÚŸÓ§‚c®dÙé\1¢|wq…:k®äú
¹¢Î›+ü¼¸ÊWq\9?+®Eþ\³óÆëyqåú¬ñjò³âªùŒkÁ8ˆ:ÂUðÿQÃæº%/O»%Ù{ˆ+ÏêeÎêõ¦–+Ïî¥9k¸ædËÕ «ËÝ–ÈüÔryyôçÈü…‹ý¿¶g,û +endstream +endobj +1194 0 obj << +/Type /Page +/Contents 1195 0 R +/Resources 1193 0 R +/MediaBox [0 0 342 504] +/Parent 1176 0 R +>> endobj +1196 0 obj << +/D [1194 0 R /XYZ 9 484.913 null] +>> endobj +1193 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F27 593 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1200 0 obj << +/Length 1994 +/Filter /FlateDecode +>> +stream +xÚÍXKsã6¾ûWps¢ªF Þ +‘qc·»¨ð™4¤Ú¼…‚Þ/¥ÊÓwà¢Þï@X¹ô—_nKaSúuø )ô½G©I üo] Âæ£ÿGUE‡5X·éiNÛuцƒ:BŠ° žmµ
b>CX“Ñ«úûˆ£›å–qo{–9î`4)]Àbó&Ëaåå +R™<sÎLÄZÁB@në’|N•–ûÝ¡mŽÞþD7‡³íH"¸ØiÁÓ^W »hªpDµUÄ&NS âÎ뉸ac6€ñ)8LI˜–ÝY¼› +_>¤i ñ¨£&ëC[K3þ®Læ¬í|¹¹àî6ç Ê}³ßByRE÷À¦Œöiâ7)„ +ÂÝ0•ÞÞÏÊ»œÛLØH0 H¨=¿KŽxTW$ÌáûèçÎXSJ¤éк@:=nÞ¿½ÜM8ðmaÖ}M×1*¹äS}œoÔúÅDíÉ£@ w¾q¼·UØQ/øKEÅâ‹ +À\ ¢õ¤–Íæ™ÕúšÁ^uáHÉ€7cþ‚ ó±}èé6pR‡Ë!- —tÏâôÙ£J¹½6³|Æ_ŒyÄT.^¡- `ÖÉkå^0† iGúšfØQSÅu>ñ7„3ÇÈa&á|K‚¥géÐËÑ~4ì(Îzt¶ªQ/exº GûH!>¢µÝ“$½HÏ# q~ì©ï ¢¼¬æžžbúhÃ{Z÷*-L7ÔæovÝó] +û[ᇠ+endstream +endobj +1199 0 obj << +/Type /Page +/Contents 1200 0 R +/Resources 1198 0 R +/MediaBox [0 0 342 504] +/Parent 1176 0 R +/Annots [ 1192 0 R 1197 0 R ] +>> endobj +1192 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [22.898 427.671 96.998 440.754] +/Subtype /Link +/A << /S /GoTo /D (section*.95) >> +>> endobj +1197 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [160.247 220.412 220.756 233.032] +/Subtype /Link +/A << /S /GoTo /D (section*.55) >> +>> endobj +1201 0 obj << +/D [1199 0 R /XYZ 9 484.913 null] +>> endobj +1202 0 obj << +/D [1199 0 R /XYZ 9 442.449 null] +>> endobj +395 0 obj << +/D [1199 0 R /XYZ 9 442.449 null] +>> endobj +1198 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F40 208 0 R /F21 427 0 R /F25 463 0 R /F19 213 0 R /F27 593 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1205 0 obj << +/Length 1763 +/Filter /FlateDecode +>> +stream +xÚ…XÏ“ã´¾Ï_aN8ÅF+ɲ-QÅ +–Z(¶xõæðªX G“ {Öv6ðß¿¯Õr&ΘáKV«»õõE&ûD&?Þ}w÷ö±‰RÂå¹Nî ¥P®HŒuB›2¹ß%¿¥ßþúë ¾ÿ¿Í6+óô=>*üjüþ~ÿÓÛw*_Èp +{s v+׌§¾}Wd×ìÛLÂ…A!¤u¼«^¬ ×R”6›eO=¬MÏ]¦ýðç›ÍÖH“Ö}76;?ø /w~_MÍgbòíß«ÓÈx>45QÌw¤ñiœxö°ÙÒš¸ô‰'Ãc? !ª%Û¨ÌV³J}É¥aÕhpꚉFyÚ?2åX#ª}Õtã´Ø‘§µï6Ú¦ÓÐ<žöUË«8·ŽëM<¢ `bÜÛdÔ¥ˆîªndÅûŒÊmÚÄïãÐ yÄNÄ rŽÍÔD"•<uÛ®àµ?#SwÃ4ôÜÝíy¶kÆzU»ž0TÄm$s¶;ÎÃáÏ Eô†×@똮>2 *šð=3z´Z@3SÂJ‚šJ)Öã£ÌŠU KÀØÎPû&Ê3ËpF3ËG)åê©Rg t[æü"žç’R¸ +«¥²‰YC@¯É2¢Ìt²½bVdå¢ÀàVÖÝ÷wŸîÔ• „–™p…K2+Eá\R ï~û]&;,⪄)mr¬ÇDëtmòß»ÿpÞ¸ñ•…'2“d…¹zE•c|¡™éë5Ïo•µÂÁ÷[mE©#^ÞQÜ2j +6Š}OYE©˜s”Ä9Ê ¡"€úÔVµ§ ¤ÌsÞ}ô‘;fÕ à#ÿ×ÓàÇ‘s*x,™' 5”.^Zf׸ ip%{¢¼uÄ555•íl¨zÓpª9}kçÒsÓƵ}Ï:šæ»†e¨,„‡jò#¯ŸC~%"ÊÁ ô Ó9¢.ÊÄ‹})yªº:H,\t
-ßÒ ŽüƒgJøW .$| +§òô>ø“ˆpæ©gÌ´ª W+àçMŽ*Û6;.÷¬ƒ‘y,¶Ž»Xù®?¼ª5¾Uç£ >C(º œ=H ÿ\÷Âr3 VëÞu9 MrqHD ¶œËmd‘þqÚíCWƒ"Øfkhy®Øq¡µÕ4‘ÊYÔ4|;^«xº ¸p6¤ßP¡¿YS‹âÁ·;¶`®ÐÑÓ IpšHêJéçD¹^v‘›õ¥ê¾‰uÝwµ¿if¼Ú°–Ú, u昜}9‡,d–v~:5AÄštï;?T-Ç0E'Fƒè5{íµ@ž=„´°Ùªøu¸ŽP½NÔ Žý@I$×!‰ØÔó¾H[‰½ëðë‹ÈÕÄ8v×
,-0]êÍ‘jì}†°e†£°ùË+Ë D}r ëý%g²ë .a$îÿ@B„MþèçØ"Òòbz^> Ö°÷íFçiÇâ⌠Æ~x†SŸËDrÀÈö٠& rLl*:†a“K¸ ?ŸN€Øß,ƒ|z`Ž&ÊØùí?‡ÄSÒ!!“yeÁ
q9{¥,™ƒÂ#„ó<.x + ‰˜ªk4ÑÖçxOG
ib>hºrC1y“äÝê{jaODÜ=×>òŸý’©Øƒ\u<ç+ Ês| Sc
NÃ#¡ªý ž <‡ì+.ö]”àG™M¢»H‹pRîêÉòØ ý9[ Þ#ÓÛŽiQC»´4>{”‹–Z¶tŽÏÎr0«c ùöóÖ-ŸšŽ3±½.¯ÚñúÌŸØm~”¹$|Ó8øØr©ŒŠiz¯Ä¶š< öÍÖíê1 Èe¡†i*Áð £’Xسwq Bú*š«Ñzw™‰üß²:šäì¹I^L‘Kõo)'ІÌL?sõÔB*~_ņ½¦g:Í< o£WZ[ˆËKóZs« +Êj“õòö⠉ί ©.
.µWÃê àÎ’PãÜ•/„C syš„N¨téžúîË0‹-auéÊÊØcaå¦ä¿¡°Ð»ÝêK4àÅåo—_VÕ‹ÌoÕáVçñŸ ×Dè^þš¿¸¶ÿ.¡™ +endstream +endobj +1204 0 obj << +/Type /Page +/Contents 1205 0 R +/Resources 1203 0 R +/MediaBox [0 0 342 504] +/Parent 1176 0 R +>> endobj +1206 0 obj << +/D [1204 0 R /XYZ 9 484.913 null] +>> endobj +1203 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F21 427 0 R /F24 494 0 R /F19 213 0 R /F27 593 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1209 0 obj << +/Length 1904 +/Filter /FlateDecode +>> +stream +xÚXO¯Ü6¿¿Oá£È¸’-[ò.öÐ +„[#VtA“„Œ&á€LÅ9žvÃ`´óý+ð.S¢>ÚeB·ùû]ÃL£‡#ߊ2Odö0 (dK~鼨U
[x!b@>²RÆðn3Y´’qd ©0²ˆ‘E‰âZ¢,*ˆì+®GÆØêÑa˜’% úðf÷ðû2Ë€½bA½J*8½Éºã￱l‹`h!¤Ê^ë1«xÑ4˜{cöá។Õw +^@vV,ê¶ùÿl½Kø¶Pe•µEÛ +bûÛª¥UÑ +Î,D
(× h‹|\ªŠ8ð~Eÿ¶†£þ”úeQKñMõÛ¶`òÎU.D7Ø^ª +î²Dþ—5Ïl¹u³m) +%£ÒoBNE¸ÀZ¦W8’ÒWiE;ŽÊ„£5»ìq ÏN0:Ÿ¦O(áKP}ËÁ¸¢›ôÖ!à7<%<h2Ž¤Jb»øH?#zd8ã8XÚÛÇÍÒšd) Hõ›Z³ Ítð=ÖÁòï×ðûeögË-l¨ÂaPZæ »eÔ „!œ¯òÉz"ðÚy žFy"oÔ
¥Ì†¶‘ÚWKú_}Ú:½àæR”An)x~0“ 0“É@50Ž8@÷ +—UÁ™L;ÝšlUuæÀëDÑ 'Š¿© `*kèMy{#ïðÊEô|5Þ³€ò‹ßDäß3G‡Áì¥7t?Ó‘¼'d¬6¸d ¯ ~Ý| f?¿¢ò¬§ýJˆ×—rXñTá9vf¾TT\B±åÐÉÌÞÙÉ ÑI¡à#ÍÅ}î#Ö2"P™‡ÑÁ™tÌ &Ôwk·kas“Âׇ ¼Ì8ö§:§®(oXz ¡yˆ"¨K©.ëWWUST¦åµÖ%Æ~ c?5-0ˆà$E>x¢PvÕ€QpD™é56bGߣÐÓ0Å䬱yºbG±‘€î\½-o¦ÎÀ•ˆ¦É†01ADÕä?8ç2Ä@Xx
{s¤…GV³×všÀ§0äh€M£‰ B‚l©b3VÜšN1àô¶Í ÑâL™3zâBP¾· `ˆ¢ñûæ¢'„XoöwÜ Hû«¦ù™HÃYà6ךcòZ›w_B„Mö@:â ÒE±¼×(øSj¥a5Ô›=ÏrBŠáõ_#ãõú%Ê`¦ÇUÿ íŒ m•à2(gƒ³Zh!íòäA-ÁYn# ´!dÏu â ½EÞ +ºB³: æ»ðRÉ |Aƒ m?Bu]wà°&iƒ×ƒÓÇFføö‘ÑžR| I +i¸[;Ñ|ˆB:;ÍÀ-\YØû|¶ I)xR丮ê÷&$ûú™59¸‡‰ó«‚=½`Ü«#áÃGسÓÓ!ÖGà1˜,ûÿÝ5»X,’‚ݼn–#ØÄAgœqz/K¤8CžÐtë ½A W¡àz¼¡C Åů‚a»þ +0ßî±O« 6Ž9 +¿LÐu2•’ñ/” +endstream +endobj +1208 0 obj << +/Type /Page +/Contents 1209 0 R +/Resources 1207 0 R +/MediaBox [0 0 342 504] +/Parent 1176 0 R +>> endobj +1210 0 obj << +/D [1208 0 R /XYZ 9 484.913 null] +>> endobj +1207 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F21 427 0 R /F19 213 0 R /F24 494 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1213 0 obj << +/Length 750 +/Filter /FlateDecode +>> +stream +xÚuT;oÛ0Þó+„N4P+"%êÑA’"Ò õP é X´M@¦ ’Šã©½w<ÊSwïÍïî;*KÖI–|¹¸Z\\ÞuÂyÚH)’Å*á¢HyS&Eݤ¢¨’E—üdŸ o ®ï~Ìæy%Ù <||-î/o¹<©ÑpÈ•pEÈæBbÔEoMæyV¦EÁA(Ó¬n(ìÑÎæ¢b¿g’Wl\f=›¢`²$´}¿V[5ãLeÈöMõ×/ÚÿžMÆZï括V (à)“a,ó·…ÌÒº¬&Œ×ZA|Þ°‡Öv¯Ý “’ù6ç –ì”qËM»ò€âLû²NE-¦Ê qN%ƒ™4A¬ØÃ’-—ѹKÉ#Eö aHv?öztäý¾³Ú¬•ÁWÊöÚ@_<%ŒE–V"ËÈØ ÊyH(Kœ ê +րȶèŃõL¸<`ðžžìÝ@È ©fð$¨Wí<!Š +òWþ@fÍ +endstream +endobj +1212 0 obj << +/Type /Page +/Contents 1213 0 R +/Resources 1211 0 R +/MediaBox [0 0 342 504] +/Parent 1176 0 R +>> endobj +1214 0 obj << +/D [1212 0 R /XYZ 9 484.913 null] +>> endobj +1211 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1217 0 obj << +/Length 1066 +/Filter /FlateDecode +>> +stream +xÚVßsâ6~Ï_ÁÓ<ª~[ê[`¡åH&йé´}p°45rÆv’Ëýõ]I&1 mya¥Õ.ÚýöÛ•Éàq@³ ÒÉñúâ§+¡T`.¬ ”(̸ É1•z°Î ñ|¼˜ßÌî.o¯OþZÿ(6R§‘Ö˜ +:1pÖ":}M8E7w¿®’O%š/£œ.g‹ùê:nnöÊùrµ†ŸÏñúzzs—öבþu”œ*×1LU¯›»¶NCUþ¼i«:Q)z‹ÎŠ ÄJ©Á2;ð^o‹d$ŒBW \_=»<km寄ýC<œZ×´…u %}n¢Ò»J‚ªúíÐxV{uöbÛðW1*û±0M1á j‚ø9¥’¡iýjƒ9„($62… + ¡¢ÙU¢ª ˆ±´›„¥h J‰þ$’´uæš2^”÷Þà-®¯q”‹NŽëª)À‹&JzXf;ïsßýæì ÑÃ0në¢i†P/¦5Œà“hs‰)õ`,ž«§€ÌÆÿìŠ*”¹Ü/R´¶»Nͤrm±{ŠG´·¸Ý¾5vÓœD–S¬”î!K •èKUÛö{ô^Eì†ý §Fa)ýWnè;®Ü°€«×-pÜ áª &eV.ß{ï±D£›oUOA܃õ°”Ä©†0y +MÊzæ©x‹Íʸí6!Ø~¢$—¦uûT†Ìöê»P8ûíüTL9íÁ¯yŠ¦ +l8n·ž¡ë¾)¹B‹Ê=ŸÃh3«‹ÂE·OQLª3}î@žýaæ÷¾ä^žQr˜ýZ› ‚ÇQãÃ[Ùò>Á¢¨ÃÅñøK¶ÙÙ²Ì΋|ÅAq#Y
9œ*£8G¤6p‡³U™G«ÀaÐþB ÖTð^BFªX[¢q'¿Ú² \µçT¬lª0aGcd LP´ ’ Eñj›á©D¡»ù’·‘›Þ5¥è2a튺ۮ~<¬Û&î>yÁ`ØÙÂu÷Tñ”ÀŒ¼Kà“½øž¬Ê.Þo勵»—‰,Íy—îÞÚÑ’ÊNO0%dÿ2Áf…+ê3'˜I±<úˆµí^ŒÖç{‰Aÿ…v÷Šã¡àu}ö{cO¯?ç)ç >}ú×]zì˜@« 9šæ9Lƒ¶rûéÑÓ#¯Ê¢h=ò¯¾ë³ý;ãç€ {àE›ãîíö±ËZ˜m§‡‘w½ðAÄð¥æç½ÐØ(Ó=3L XM×ÿ +endstream +endobj +1216 0 obj << +/Type /Page +/Contents 1217 0 R +/Resources 1215 0 R +/MediaBox [0 0 342 504] +/Parent 1226 0 R +>> endobj +1218 0 obj << +/D [1216 0 R /XYZ 9 484.913 null] +>> endobj +1219 0 obj << +/D [1216 0 R /XYZ 9 465.114 null] +>> endobj +178 0 obj << +/D [1216 0 R /XYZ 9 465.114 null] +>> endobj +396 0 obj << +/D [1216 0 R /XYZ 9 465.114 null] +>> endobj +1220 0 obj << +/D [1216 0 R /XYZ 9 465.114 null] +>> endobj +182 0 obj << +/D [1216 0 R /XYZ 9 465.114 null] +>> endobj +1221 0 obj << +/D [1216 0 R /XYZ 9 441.319 null] +>> endobj +1222 0 obj << +/D [1216 0 R /XYZ 9 419.153 null] +>> endobj +1223 0 obj << +/D [1216 0 R /XYZ 9 396.986 null] +>> endobj +1224 0 obj << +/D [1216 0 R /XYZ 9 259.46 null] +>> endobj +1225 0 obj << +/D [1216 0 R /XYZ 9 81.087 null] +>> endobj +1215 0 obj << +/Font << /F48 218 0 R /F40 208 0 R /F63 238 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1229 0 obj << +/Length 1289 +/Filter /FlateDecode +>> +stream +xÚWKoÛ8¾çWø´K1Ã7Åî)Móh4EâÅb±Ýƒb« [J%ÅHúëw†¤l)UÚ`O¤†3||ß¼Ä&w69Ý{?ß;8QÙ„sê´“ùW˜š>Q™£BÙÉ|9ù‡¼ÿøþâãÕéõá糿§ÿÎÏN¸ ¹Œê ¶ Ú\XTÚc锃#ûÚ3É UŠÃÄP–¹huUNgR1rì˦-|9匑ßJGæ÷ÅT3RÕÏQ©úå§5ŠóoóÖWi‡¼\Ɖo“ùaÓŪ¬Ö~LVQå¨*gxÙ‰Ô”ól2ã +®¦ã•špè·Ç¢ 6E3övå(gÛ·¿›Îlû…í…#Ë"Ž7¾m‹z?ÚÑ°`oug‰†ZOa”ä:\û9IwïHË7~.è()ž$¶;ïÇ›¬žž6>èOfBKªX÷hõ ÂÕ
1ÎK¸ãæ( Ö>iDMX×SNôkÊ/µå~üEKÇ +×̧à.Ï«ªŽ +¿EË\ªórá›ý$YEunÚæI~Q•KŒæ_Æì½V8§[Mªó˜p’ /Vþ¡Ikèÿ(®½’Ëüd +iwiHÃÕ6n*ÉÇò ãz›ï†»uÔŽäË„Ü. ‡ Ç wߎ©q¶ y +~^2Õƾ!H†‰2ýSš¦è±D¼ˆ gR…øP,Š5†Í-\(#Eý+ÆêAŒz âa•ÒÒº([”ª€6®Æ¬˜X´õã:®^øjyPˆ‰ dm·áñ·G¿ÉW»@áÙóë]B8¢ûÆ7îvé +üÜY ÒvŠœ†žñ‘gŠÕrÔÏ¡Á€&Cô×ÎƵë3ŽÒã(ø)ãP‹læþ/ã²[Æå Æ…Û¦@@ædo§÷‡jcLWmTJ\JÉ·Uˆ¦A72 i ýMm?ÍÌôUGP†A|›Ôþ,ý&õLH¨°/°ù\M³«¢{¨bƒ˜…)øÌ Ò G ®š +ílFŽîó¨xMüòå«¥™!3˜ÒŒíÅ‚„ }™ƒ®Š]‹‹•¢ß VèŽ@~¼êâÂ/0…ÅØ;‡½îÊ¢õÍz4¡fxû.¤s¤ÝJlž¶Ý¥¶bˆÔy‘—Mê ÓLµ÷ÑCŠ¥GAÆÁSR×XÈ ¨Y¶¯ +Ÿàb[£ ¯},6y½„÷ DN0Dêû[t2É)ü {ùz:øÇêÆãùÞ´ R +endstream +endobj +1228 0 obj << +/Type /Page +/Contents 1229 0 R +/Resources 1227 0 R +/MediaBox [0 0 342 504] +/Parent 1226 0 R +>> endobj +1230 0 obj << +/D [1228 0 R /XYZ 9 484.913 null] +>> endobj +1231 0 obj << +/D [1228 0 R /XYZ 9 153.407 null] +>> endobj +1227 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F63 238 0 R /F40 208 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1329 0 obj << +/Length 1190 +/Filter /FlateDecode +>> +stream +xÚYMs£6¾ûWhz‚™Â"ø8nÜìN÷Ðé‡ÉîAÙV (•`·™öÇW \› i½‡âHÞ÷y¿å @Þo¢éy·Û¼y‡r +€pBœƒ] ¼ úáþwÿÓîÛw00 +‹¨€Ãê +5Ĩ8I.ž \Î÷úIý +ÔÉÒâ‘u‚ˆg(ûGÙ±® l#
2ë2¾•à-oXIêÉuÈ`_IÈhR;èÁ 6™::H×ÿ›ñÆÄtŒ`S“w¢ïŽÚ+UÔ@#êf C˜@yGÊÂ#mL0ñzj»#’É—±Œ<åä\˜m<¯B„ º£¬=|g2rìÊx4gG ø² +ˆ\L³‹”yCzkIZŒ»¯,LëY[ëP =èOcœ9*CGê2äº;Š”»š?/nrè⊂^=Ï+\Õ‡‘³¯Ås‡8=ïw›¿6pZ3Uz‹”ÍæáS*õù…¨ÈÁ—qU£~P”‡)Ì@
~Ûü2ŸHçÅfEX¤)@q¦Í Z
jôäÏÆl´àÍ8Œ'À-WóÒÕ˜‰¼F¥LSI“yì=±Â%³-±ARIÅg § 9É‹ÎcqK…Ý ìZŸ +´&Õ¤%kžúZšjã+PŒ©GîJ µc±×CdÏ:ÛY(Ï `{S']/ +²Ì†Ïû¾¬YEIû{¿¬pÍ‹® +æ©…ïíy/‚Š5´•*,Híx`µ˜;Ô‹¥ô¿ÒR_éÞò6°³¯³¹SVá*ŸHIƒŽé¶Ò$C|3ù+µð²î.ºKw”:ø Nl@‡Œñesn
}í(oÏsÞ8 +.ž\15ý&TPUÇŒ·_ØB•3à Ó0\IG½RkÒ%Œ‹õ„Ú©dz8’ÆXô¡Ù^§f*‚ŸG«1±wBëòª>c ×ÒÃPo‰¢UDÁ›†Ö¬½UáþÔ9ôbìœàÔ9D^ÍÇ‘ » è:«@•ÐlârÌ#Æ©gÝ?”–L‘E•t+Ám.ô‹uêžVHËtê¹ ÉðýC% /æ^Üea +endstream +endobj +1328 0 obj << +/Type /Page +/Contents 1329 0 R +/Resources 1327 0 R +/MediaBox [0 0 342 504] +/Parent 1226 0 R +/Annots [ 1232 0 R 1233 0 R 1234 0 R 1235 0 R 1236 0 R 1237 0 R 1238 0 R 1239 0 R 1240 0 R 1241 0 R 1242 0 R 1243 0 R 1244 0 R 1245 0 R 1246 0 R 1247 0 R 1248 0 R 1249 0 R 1250 0 R 1251 0 R 1252 0 R 1253 0 R 1254 0 R 1255 0 R 1256 0 R 1257 0 R 1258 0 R 1259 0 R 1260 0 R 1261 0 R 1262 0 R 1263 0 R 1264 0 R 1265 0 R 1266 0 R 1267 0 R 1268 0 R 1269 0 R 1270 0 R 1271 0 R 1272 0 R 1273 0 R 1274 0 R 1275 0 R 1276 0 R 1277 0 R 1278 0 R 1279 0 R 1280 0 R 1281 0 R 1282 0 R 1283 0 R 1284 0 R 1285 0 R 1286 0 R 1287 0 R 1288 0 R 1289 0 R 1290 0 R 1291 0 R 1292 0 R 1293 0 R 1294 0 R 1295 0 R 1296 0 R 1297 0 R 1298 0 R 1299 0 R 1300 0 R 1301 0 R 1302 0 R 1303 0 R 1304 0 R 1305 0 R 1306 0 R 1307 0 R 1308 0 R 1309 0 R 1310 0 R 1311 0 R 1312 0 R 1313 0 R 1314 0 R 1315 0 R 1316 0 R 1317 0 R 1318 0 R 1319 0 R 1320 0 R 1321 0 R ] +>> endobj +1232 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [66.852 424.537 79.754 436.226] +/Subtype /Link +/A << /S /GoTo /D (page.47) >> +>> endobj +1233 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [114.186 410.987 127.087 422.677] +/Subtype /Link +/A << /S /GoTo /D (page.44) >> +>> endobj +1234 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [73.792 397.438 86.693 409.128] +/Subtype /Link +/A << /S /GoTo /D (page.60) >> +>> endobj +1235 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [91.367 397.438 104.269 409.128] +/Subtype /Link +/A << /S /GoTo /D (page.62) >> +>> endobj +1236 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [108.943 397.438 121.845 409.128] +/Subtype /Link +/A << /S /GoTo /D (page.65) >> +>> endobj +1237 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [111.398 383.889 124.299 395.578] +/Subtype /Link +/A << /S /GoTo /D (page.46) >> +>> endobj +1238 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [116.246 370.34 129.148 382.029] +/Subtype /Link +/A << /S /GoTo /D (page.15) >> +>> endobj +1239 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [133.822 370.34 146.724 382.029] +/Subtype /Link +/A << /S /GoTo /D (page.36) >> +>> endobj +1240 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [90.186 356.791 103.087 368.48] +/Subtype /Link +/A << /S /GoTo /D (page.83) >> +>> endobj +1241 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [47.125 343.241 60.027 354.931] +/Subtype /Link +/A << /S /GoTo /D (page.50) >> +>> endobj +1242 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [53.792 329.692 66.693 341.382] +/Subtype /Link +/A << /S /GoTo /D (page.50) >> +>> endobj +1243 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [125.246 316.143 138.148 327.832] +/Subtype /Link +/A << /S /GoTo /D (page.90) >> +>> endobj +1244 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [97.792 302.594 110.693 314.283] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1245 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [66.277 289.045 73.724 300.613] +/Subtype /Link +/A << /S /GoTo /D (page.6) >> +>> endobj +1246 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [78.398 289.045 91.299 300.613] +/Subtype /Link +/A << /S /GoTo /D (page.95) >> +>> endobj +1247 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [50.489 275.495 57.936 287.064] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1248 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [62.61 275.495 80.966 287.064] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1249 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [66.519 261.946 73.966 273.636] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1250 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [52.398 240.816 70.754 252.505] +/Subtype /Link +/A << /S /GoTo /D (page.124) >> +>> endobj +1251 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [85.277 227.266 98.178 238.956] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1252 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [52.701 213.717 65.602 225.407] +/Subtype /Link +/A << /S /GoTo /D (page.62) >> +>> endobj +1253 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [70.277 213.717 88.633 225.407] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1254 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [44.538 200.168 57.439 211.857] +/Subtype /Link +/A << /S /GoTo /D (page.48) >> +>> endobj +1255 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [49.67 186.619 68.027 198.308] +/Subtype /Link +/A << /S /GoTo /D (page.117) >> +>> endobj +1256 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [102.225 151.939 109.672 163.628] +/Subtype /Link +/A << /S /GoTo /D (page.6) >> +>> endobj +1257 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [114.346 151.939 127.248 163.628] +/Subtype /Link +/A << /S /GoTo /D (page.78) >> +>> endobj +1258 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [131.922 151.939 150.278 163.628] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1259 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [78.095 138.39 90.996 150.079] +/Subtype /Link +/A << /S /GoTo /D (page.48) >> +>> endobj +1260 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [107.216 124.84 120.118 136.53] +/Subtype /Link +/A << /S /GoTo /D (page.98) >> +>> endobj +1261 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [94.428 111.291 107.33 122.981] +/Subtype /Link +/A << /S /GoTo /D (page.73) >> +>> endobj +1262 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [112.004 111.291 130.36 122.981] +/Subtype /Link +/A << /S /GoTo /D (page.123) >> +>> endobj +1263 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [42.004 97.742 54.905 109.432] +/Subtype /Link +/A << /S /GoTo /D (page.62) >> +>> endobj +1264 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [107.883 84.193 115.33 95.882] +/Subtype /Link +/A << /S /GoTo /D (page.8) >> +>> endobj +1265 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [120.004 84.193 132.905 95.882] +/Subtype /Link +/A << /S /GoTo /D (page.12) >> +>> endobj +1266 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [137.58 84.193 150.481 95.882] +/Subtype /Link +/A << /S /GoTo /D (page.15) >> +>> endobj +1267 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 70.644 50.793 81.788] +/Subtype /Link +/A << /S /GoTo /D (page.28) >> +>> endobj +1268 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 70.644 68.369 81.788] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1269 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [73.043 70.644 85.945 81.788] +/Subtype /Link +/A << /S /GoTo /D (page.67) >> +>> endobj +1270 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [90.619 70.644 103.521 81.788] +/Subtype /Link +/A << /S /GoTo /D (page.95) >> +>> endobj +1271 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [108.195 70.644 121.096 81.788] +/Subtype /Link +/A << /S /GoTo /D (page.96) >> +>> endobj +1272 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [125.771 70.644 144.127 81.788] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1273 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [66.519 57.094 79.421 68.784] +/Subtype /Link +/A << /S /GoTo /D (page.12) >> +>> endobj +1274 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [45.943 43.545 53.39 55.235] +/Subtype /Link +/A << /S /GoTo /D (page.9) >> +>> endobj +1275 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [58.064 43.545 70.966 55.235] +/Subtype /Link +/A << /S /GoTo /D (page.21) >> +>> endobj +1276 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [75.64 43.545 88.542 55.235] +/Subtype /Link +/A << /S /GoTo /D (page.74) >> +>> endobj +1277 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [93.216 43.545 106.118 55.235] +/Subtype /Link +/A << /S /GoTo /D (page.75) >> +>> endobj +1278 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [110.792 43.545 123.693 55.235] +/Subtype /Link +/A << /S /GoTo /D (page.87) >> +>> endobj +1279 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [128.367 43.545 141.269 55.235] +/Subtype /Link +/A << /S /GoTo /D (page.89) >> +>> endobj +1280 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 29.996 50.793 41.14] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1281 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [54.255 29.996 67.157 41.14] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1282 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [71.831 29.996 90.187 41.14] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1283 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [94.861 29.996 113.218 41.14] +/Subtype /Link +/A << /S /GoTo /D (page.122) >> +>> endobj +1284 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [231.425 424.537 249.781 436.226] +/Subtype /Link +/A << /S /GoTo /D (page.122) >> +>> endobj +1285 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [278.788 409.297 291.69 420.986] +/Subtype /Link +/A << /S /GoTo /D (page.43) >> +>> endobj +1286 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [238.122 394.057 245.569 405.457] +/Subtype /Link +/A << /S /GoTo /D (page.5) >> +>> endobj +1287 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [294.243 378.818 307.145 390.507] +/Subtype /Link +/A << /S /GoTo /D (page.43) >> +>> endobj +1288 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [311.819 378.818 324.72 390.507] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1289 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [236.607 363.578 249.508 375.267] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1290 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [223.334 348.338 236.235 359.482] +/Subtype /Link +/A << /S /GoTo /D (page.43) >> +>> endobj +1291 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [240.91 348.338 253.811 359.482] +/Subtype /Link +/A << /S /GoTo /D (page.45) >> +>> endobj +1292 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [235.637 333.099 248.538 344.667] +/Subtype /Link +/A << /S /GoTo /D (page.88) >> +>> endobj +1293 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [238.97 317.859 251.872 329.427] +/Subtype /Link +/A << /S /GoTo /D (page.52) >> +>> endobj +1294 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [256.546 317.859 269.448 329.427] +/Subtype /Link +/A << /S /GoTo /D (page.77) >> +>> endobj +1295 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [247 302.619 259.902 314.309] +/Subtype /Link +/A << /S /GoTo /D (page.78) >> +>> endobj +1296 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [264.576 302.619 277.478 314.309] +/Subtype /Link +/A << /S /GoTo /D (page.79) >> +>> endobj +1297 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [282.152 302.619 295.054 314.309] +/Subtype /Link +/A << /S /GoTo /D (page.82) >> +>> endobj +1298 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [299.728 302.619 312.629 314.309] +/Subtype /Link +/A << /S /GoTo /D (page.86) >> +>> endobj +1299 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [279.364 287.38 292.266 299.069] +/Subtype /Link +/A << /S /GoTo /D (page.83) >> +>> endobj +1300 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [296.94 287.38 309.842 299.069] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1301 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.516 287.38 327.417 299.069] +/Subtype /Link +/A << /S /GoTo /D (page.87) >> +>> endobj +1302 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 275.952 227.214 284.975] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1303 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [268.213 258.591 281.114 270.28] +/Subtype /Link +/A << /S /GoTo /D (page.79) >> +>> endobj +1304 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [285.788 258.591 298.69 270.28] +/Subtype /Link +/A << /S /GoTo /D (page.84) >> +>> endobj +1305 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [250.546 243.351 263.448 254.751] +/Subtype /Link +/A << /S /GoTo /D (page.72) >> +>> endobj +1306 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [268.122 243.351 281.023 254.751] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1307 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [284.485 243.351 297.387 254.751] +/Subtype /Link +/A << /S /GoTo /D (page.89) >> +>> endobj +1308 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [284.516 228.112 297.417 239.801] +/Subtype /Link +/A << /S /GoTo /D (page.53) >> +>> endobj +1309 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [277.213 212.872 290.114 224.561] +/Subtype /Link +/A << /S /GoTo /D (page.87) >> +>> endobj +1310 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [249.667 182.393 262.569 194.082] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1311 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [255.425 167.153 268.326 178.842] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1312 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [229.94 151.913 242.841 163.603] +/Subtype /Link +/A << /S /GoTo /D (page.29) >> +>> endobj +1313 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [242.607 136.674 260.963 148.363] +/Subtype /Link +/A << /S /GoTo /D (page.121) >> +>> endobj +1314 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [253.394 121.434 271.751 133.002] +/Subtype /Link +/A << /S /GoTo /D (page.104) >> +>> endobj +1315 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [235.97 106.194 248.872 117.763] +/Subtype /Link +/A << /S /GoTo /D (page.40) >> +>> endobj +1316 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [238.394 90.955 256.751 102.644] +/Subtype /Link +/A << /S /GoTo /D (page.121) >> +>> endobj +1317 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [294.486 75.715 307.388 87.405] +/Subtype /Link +/A << /S /GoTo /D (page.96) >> +>> endobj +1318 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [312.036 75.715 330.392 87.405] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1319 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [225.697 60.475 244.054 71.619] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1320 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [276.304 45.236 289.205 56.925] +/Subtype /Link +/A << /S /GoTo /D (page.69) >> +>> endobj +1321 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [263.879 29.996 282.235 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.124) >> +>> endobj +1330 0 obj << +/D [1328 0 R /XYZ 9 484.913 null] +>> endobj +397 0 obj << +/D [1328 0 R /XYZ 9 465.114 null] +>> endobj +1331 0 obj << +/D [1328 0 R /XYZ 9 465.114 null] +>> endobj +186 0 obj << +/D [1328 0 R /XYZ 9 465.114 null] +>> endobj +1332 0 obj << +/D [1328 0 R /XYZ 9 441.319 null] +>> endobj +1327 0 obj << +/Font << /F48 218 0 R /F16 210 0 R /F11 420 0 R /F15 231 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1442 0 obj << +/Length 1248 +/Filter /FlateDecode +>> +stream +xÚ½YMsÛ6½ëWà(ÍT A€$píDö4‡Î´ñ¡3N ۘᇠ‚qœöÇ AY’%‚k¹=ıh± oß¾…CtBt½øõfñáŠ2„qÀã8B7wSÄ #ÊxÑÝèvùÛï 7¾Þ|úp…ãƒÓI°ØØêáˆÛC‹Ð™7§„À‡Æ 9½&aPŠÍ7I2>|êc¦žd-³zµ&„,õƒhÔóŠ‘å/ÎXˆ0RÖ¢ýæÏëºíbœ Üf¾¬1 vW[~—EÛÔ>S>m*q¦DÑåZ~·…u“7WxÙt÷«(]ê·ºº³¯Œñ8YfZ6õpAs7ä£ìÃxj'¯ Kyn¬}–Z å±åK¬l·e–‹JÔÖ5}èo»]mšr²Ò… kqÞÿˆŒ±þŠØÝÀ ¸õb!: +½gußqÕ¹KÅ—0gkY÷5j(Aiþ{î# ÿLu€ñ¤³ÏïgºŽŠ éK0 A â©9”þ3Tfû`qõÜÊ|µÆËEr@›P[%ô®Qˆžçn:ÙîN%Jcó»ÔýÕ#¤=–#O[7Ûm)” JÉ:—ægŸ·étó5Ý·Ò!Ø Yµð^Žâ 4$Ü›Ûä¥Ü¶bÌä·µë«çt䛢õ½öï}š©7¥% ™uô‘tŽÁ¦ç´â¹Î*™·^ ¡AAÛpà
4ºˆPR<ƒ]]¦ªì¾Ú¶.hšŸƒýa—>Y¦ æz?‹}¥ˆùœâÖï—=G÷lN0Âau 8º¬²¶í,R;Åa1ZK”^Àz[Àp„ ý´Þ í„ñ´Íj+Õ‹É™"ǧ£6uÞtã˜x™ò½Ãv”¬µ¬„µpåycºF!Ì +ÊzêOUæ%40•èóâ©~ë<Ü qÊž$ˆÆ$À1; ö9´ÓÿGäuÉ\‡¦cǃIµ¢ðU?:cÊmÝ› n•RÒrp€ú;ö¤2L—ý+K*™ÊŠÌ))êzÐ&>3Çø¯¤þy-ÌYøì„ ;?DPÌ>k?EÖùöê Õ£|†£ÄxÐñ¶Œà8 J<v™ÏûÛƒÁŒn*/òÉ$ö®³R–BzùvÒE—²º½kTÕ¯Œ>®„r>I.Râ4¼'fL•Ë÷ŽiŸ[-ªÝ³Îy½´n”Ùó2íÕá8OF(/Ï sáQJÁ3úúÃbà
='³ªÜµí»ë*¨«lzèõNî8b§ ùûì^9ìBÆ +endstream +endobj +1441 0 obj << +/Type /Page +/Contents 1442 0 R +/Resources 1440 0 R +/MediaBox [0 0 342 504] +/Parent 1226 0 R +/Annots [ 1322 0 R 1323 0 R 1324 0 R 1325 0 R 1326 0 R 1333 0 R 1334 0 R 1335 0 R 1336 0 R 1337 0 R 1338 0 R 1339 0 R 1340 0 R 1341 0 R 1342 0 R 1343 0 R 1344 0 R 1345 0 R 1346 0 R 1347 0 R 1348 0 R 1349 0 R 1350 0 R 1351 0 R 1352 0 R 1353 0 R 1354 0 R 1355 0 R 1356 0 R 1357 0 R 1358 0 R 1359 0 R 1360 0 R 1361 0 R 1362 0 R 1363 0 R 1364 0 R 1365 0 R 1366 0 R 1367 0 R 1368 0 R 1369 0 R 1370 0 R 1371 0 R 1372 0 R 1373 0 R 1374 0 R 1375 0 R 1376 0 R 1377 0 R 1378 0 R 1379 0 R 1380 0 R 1381 0 R 1382 0 R 1383 0 R 1384 0 R 1385 0 R 1386 0 R 1387 0 R 1388 0 R 1389 0 R 1390 0 R 1391 0 R 1392 0 R 1393 0 R 1394 0 R 1395 0 R 1396 0 R 1397 0 R 1398 0 R 1399 0 R 1400 0 R 1401 0 R 1402 0 R 1403 0 R 1404 0 R 1405 0 R 1406 0 R 1407 0 R 1408 0 R 1409 0 R 1410 0 R 1411 0 R 1412 0 R 1413 0 R 1414 0 R 1415 0 R 1416 0 R 1417 0 R 1418 0 R 1419 0 R 1420 0 R 1421 0 R 1422 0 R 1423 0 R 1424 0 R 1425 0 R 1426 0 R 1427 0 R 1428 0 R 1429 0 R 1430 0 R 1431 0 R 1432 0 R 1433 0 R 1434 0 R 1435 0 R 1436 0 R ] +>> endobj +1322 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [97.61 450.041 115.966 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1323 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [58.822 436.405 77.178 448.095] +/Subtype /Link +/A << /S /GoTo /D (page.121) >> +>> endobj +1324 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [103.307 422.769 121.663 434.459] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1325 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [100.974 409.134 113.875 420.823] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1326 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [58.186 395.498 71.087 407.066] +/Subtype /Link +/A << /S /GoTo /D (page.16) >> +>> endobj +1333 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 368.313 50.793 379.457] +/Subtype /Link +/A << /S /GoTo /D (page.96) >> +>> endobj +1334 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 368.313 73.824 379.457] +/Subtype /Link +/A << /S /GoTo /D (page.122) >> +>> endobj +1335 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [124.307 354.071 131.754 366.973] +/Subtype /Link +/A << /S /GoTo /D (page.3) >> +>> endobj +1336 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [136.428 354.071 143.875 366.973] +/Subtype /Link +/A << /S /GoTo /D (page.4) >> +>> endobj +1337 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [148.549 354.071 155.996 366.973] +/Subtype /Link +/A << /S /GoTo /D (page.7) >> +>> endobj +1338 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 341.128 50.793 352.272] +/Subtype /Link +/A << /S /GoTo /D (page.26) >> +>> endobj +1339 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 341.128 68.369 352.272] +/Subtype /Link +/A << /S /GoTo /D (page.78) >> +>> endobj +1340 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [73.043 341.128 85.945 352.272] +/Subtype /Link +/A << /S /GoTo /D (page.82) >> +>> endobj +1341 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [90.619 341.128 108.975 352.272] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1342 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [149.337 327.492 156.784 339.182] +/Subtype /Link +/A << /S /GoTo /D (page.4) >> +>> endobj +1343 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [85.004 313.857 97.905 325.546] +/Subtype /Link +/A << /S /GoTo /D (page.26) >> +>> endobj +1344 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [97.61 300.221 110.512 311.91] +/Subtype /Link +/A << /S /GoTo /D (page.47) >> +>> endobj +1345 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [74.67 286.585 87.572 298.275] +/Subtype /Link +/A << /S /GoTo /D (page.16) >> +>> endobj +1346 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [82.549 261.544 95.451 273.234] +/Subtype /Link +/A << /S /GoTo /D (page.16) >> +>> endobj +1347 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [64.519 247.908 77.421 259.598] +/Subtype /Link +/A << /S /GoTo /D (page.96) >> +>> endobj +1348 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [82.095 247.908 100.451 259.598] +/Subtype /Link +/A << /S /GoTo /D (page.121) >> +>> endobj +1349 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [63.034 234.273 75.936 245.962] +/Subtype /Link +/A << /S /GoTo /D (page.71) >> +>> endobj +1350 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [93.701 220.637 106.602 232.326] +/Subtype /Link +/A << /S /GoTo /D (page.12) >> +>> endobj +1351 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [111.277 220.637 124.178 232.326] +/Subtype /Link +/A << /S /GoTo /D (page.18) >> +>> endobj +1352 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [128.852 220.637 141.754 232.326] +/Subtype /Link +/A << /S /GoTo /D (page.39) >> +>> endobj +1353 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [146.428 220.637 159.33 232.326] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1354 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 209.209 50.793 218.232] +/Subtype /Link +/A << /S /GoTo /D (page.71) >> +>> endobj +1355 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [125.186 193.452 138.087 205.141] +/Subtype /Link +/A << /S /GoTo /D (page.47) >> +>> endobj +1356 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [56.549 179.816 69.451 190.96] +/Subtype /Link +/A << /S /GoTo /D (page.59) >> +>> endobj +1357 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [54.852 166.18 67.754 177.87] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1358 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [72.428 166.18 85.33 177.87] +/Subtype /Link +/A << /S /GoTo /D (page.48) >> +>> endobj +1359 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [120.034 152.545 132.936 164.234] +/Subtype /Link +/A << /S /GoTo /D (page.48) >> +>> endobj +1360 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [79.216 138.909 92.118 150.598] +/Subtype /Link +/A << /S /GoTo /D (page.71) >> +>> endobj +1361 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [87.004 125.273 105.36 136.963] +/Subtype /Link +/A << /S /GoTo /D (page.105) >> +>> endobj +1362 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [84.913 111.637 103.269 123.327] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1363 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [102.74 83.846 115.642 96.748] +/Subtype /Link +/A << /S /GoTo /D (page.89) >> +>> endobj +1364 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [65.428 70.817 78.33 82.506] +/Subtype /Link +/A << /S /GoTo /D (page.13) >> +>> endobj +1365 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [108.186 57.181 115.633 68.871] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1366 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [120.307 57.181 127.754 68.871] +/Subtype /Link +/A << /S /GoTo /D (page.2) >> +>> endobj +1367 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [132.428 57.181 145.33 68.871] +/Subtype /Link +/A << /S /GoTo /D (page.54) >> +>> endobj +1368 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 43.632 50.793 54.776] +/Subtype /Link +/A << /S /GoTo /D (page.76) >> +>> endobj +1369 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 43.632 68.369 54.776] +/Subtype /Link +/A << /S /GoTo /D (page.79) >> +>> endobj +1370 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [73.043 43.632 85.945 54.776] +/Subtype /Link +/A << /S /GoTo /D (page.82) >> +>> endobj +1371 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [90.619 43.632 108.975 54.776] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1372 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [113.649 43.632 132.005 54.776] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1373 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [136.68 43.632 155.036 54.776] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1374 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [99.671 29.996 107.118 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.3) >> +>> endobj +1375 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [111.792 29.996 119.239 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.7) >> +>> endobj +1376 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [261.607 450.041 274.508 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.54) >> +>> endobj +1377 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [279.182 450.041 292.084 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.79) >> +>> endobj +1378 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [296.758 450.041 315.114 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1379 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [228.91 436.364 247.266 448.054] +/Subtype /Link +/A << /S /GoTo /D (page.124) >> +>> endobj +1380 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [237.94 422.687 250.841 434.255] +/Subtype /Link +/A << /S /GoTo /D (page.47) >> +>> endobj +1381 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [255.516 422.687 268.417 434.255] +/Subtype /Link +/A << /S /GoTo /D (page.56) >> +>> endobj +1382 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [223.091 396.92 235.993 408.609] +/Subtype /Link +/A << /S /GoTo /D (page.46) >> +>> endobj +1383 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [240.667 396.92 253.569 408.609] +/Subtype /Link +/A << /S /GoTo /D (page.59) >> +>> endobj +1384 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [237.107 383.243 250.008 394.932] +/Subtype /Link +/A << /S /GoTo /D (page.50) >> +>> endobj +1385 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [238.667 369.566 251.569 381.255] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1386 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [217 355.889 229.902 367.457] +/Subtype /Link +/A << /S /GoTo /D (page.37) >> +>> endobj +1387 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [234.576 355.889 247.478 367.457] +/Subtype /Link +/A << /S /GoTo /D (page.47) >> +>> endobj +1388 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [252.152 355.889 265.054 367.457] +/Subtype /Link +/A << /S /GoTo /D (page.49) >> +>> endobj +1389 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [265.667 342.212 278.569 353.902] +/Subtype /Link +/A << /S /GoTo /D (page.37) >> +>> endobj +1390 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [274.607 328.535 292.963 340.225] +/Subtype /Link +/A << /S /GoTo /D (page.123) >> +>> endobj +1391 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [216.622 302.768 229.523 314.457] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1392 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [270.91 289.091 283.811 300.78] +/Subtype /Link +/A << /S /GoTo /D (page.31) >> +>> endobj +1393 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [288.485 289.091 301.387 300.78] +/Subtype /Link +/A << /S /GoTo /D (page.34) >> +>> endobj +1394 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [306.061 289.091 318.963 300.78] +/Subtype /Link +/A << /S /GoTo /D (page.36) >> +>> endobj +1395 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 275.542 221.76 286.686] +/Subtype /Link +/A << /S /GoTo /D (page.40) >> +>> endobj +1396 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.434 275.542 239.335 286.686] +/Subtype /Link +/A << /S /GoTo /D (page.49) >> +>> endobj +1397 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [273.191 248.315 286.093 260.005] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1398 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [290.767 248.315 303.669 260.005] +/Subtype /Link +/A << /S /GoTo /D (page.11) >> +>> endobj +1399 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [308.343 248.315 321.245 260.005] +/Subtype /Link +/A << /S /GoTo /D (page.13) >> +>> endobj +1400 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 234.766 221.76 245.91] +/Subtype /Link +/A << /S /GoTo /D (page.44) >> +>> endobj +1401 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.434 234.766 239.335 245.91] +/Subtype /Link +/A << /S /GoTo /D (page.73) >> +>> endobj +1402 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [244.01 234.766 256.911 245.91] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1403 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [261.585 234.766 274.487 245.91] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1404 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [279.161 234.766 292.063 245.91] +/Subtype /Link +/A << /S /GoTo /D (page.93) >> +>> endobj +1405 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [214.319 221.089 227.22 232.658] +/Subtype /Link +/A << /S /GoTo /D (page.79) >> +>> endobj +1406 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [231.894 221.089 244.796 232.658] +/Subtype /Link +/A << /S /GoTo /D (page.81) >> +>> endobj +1407 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [249.47 221.089 262.372 232.658] +/Subtype /Link +/A << /S /GoTo /D (page.84) >> +>> endobj +1408 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [290.167 207.412 303.069 219.102] +/Subtype /Link +/A << /S /GoTo /D (page.81) >> +>> endobj +1409 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [306.531 207.412 319.432 219.102] +/Subtype /Link +/A << /S /GoTo /D (page.84) >> +>> endobj +1410 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 195.984 221.76 205.007] +/Subtype /Link +/A << /S /GoTo /D (page.88) >> +>> endobj +1411 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [225.222 195.984 238.123 205.007] +/Subtype /Link +/A << /S /GoTo /D (page.93) >> +>> endobj +1412 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 168.758 221.76 177.781] +/Subtype /Link +/A << /S /GoTo /D (page.55) >> +>> endobj +1413 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [225.222 168.758 238.123 177.781] +/Subtype /Link +/A << /S /GoTo /D (page.97) >> +>> endobj +1414 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [270.652 152.96 278.099 164.65] +/Subtype /Link +/A << /S /GoTo /D (page.2) >> +>> endobj +1415 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [282.773 152.96 290.22 164.65] +/Subtype /Link +/A << /S /GoTo /D (page.3) >> +>> endobj +1416 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [258.213 139.283 265.66 150.683] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1417 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [237.485 125.607 244.932 137.296] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1418 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [248.394 125.607 255.842 137.296] +/Subtype /Link +/A << /S /GoTo /D (page.3) >> +>> endobj +1419 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [240.894 111.93 253.796 123.498] +/Subtype /Link +/A << /S /GoTo /D (page.59) >> +>> endobj +1420 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [258.47 111.93 271.372 123.498] +/Subtype /Link +/A << /S /GoTo /D (page.65) >> +>> endobj +1421 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [276.046 111.93 288.948 123.498] +/Subtype /Link +/A << /S /GoTo /D (page.72) >> +>> endobj +1422 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [293.622 111.93 306.523 123.498] +/Subtype /Link +/A << /S /GoTo /D (page.95) >> +>> endobj +1423 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [273.016 98.253 285.917 109.942] +/Subtype /Link +/A << /S /GoTo /D (page.59) >> +>> endobj +1424 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [290.591 98.253 303.493 109.942] +/Subtype /Link +/A << /S /GoTo /D (page.63) >> +>> endobj +1425 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [308.167 98.253 321.069 109.942] +/Subtype /Link +/A << /S /GoTo /D (page.69) >> +>> endobj +1426 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 84.704 221.76 95.848] +/Subtype /Link +/A << /S /GoTo /D (page.72) >> +>> endobj +1427 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.434 84.704 239.335 95.848] +/Subtype /Link +/A << /S /GoTo /D (page.87) >> +>> endobj +1428 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [244.01 84.704 256.911 95.848] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1429 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [261.585 84.704 274.487 95.848] +/Subtype /Link +/A << /S /GoTo /D (page.93) >> +>> endobj +1430 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [279.161 84.704 297.517 95.848] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1431 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [255.031 71.027 273.387 82.716] +/Subtype /Link +/A << /S /GoTo /D (page.123) >> +>> endobj +1432 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [276.167 57.35 289.069 69.039] +/Subtype /Link +/A << /S /GoTo /D (page.61) >> +>> endobj +1433 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [293.743 57.35 306.645 69.039] +/Subtype /Link +/A << /S /GoTo /D (page.64) >> +>> endobj +1434 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [311.319 57.35 324.22 69.039] +/Subtype /Link +/A << /S /GoTo /D (page.95) >> +>> endobj +1435 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [214.531 43.673 232.887 55.362] +/Subtype /Link +/A << /S /GoTo /D (page.124) >> +>> endobj +1436 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [292.319 29.996 305.22 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.98) >> +>> endobj +1443 0 obj << +/D [1441 0 R /XYZ 9 484.913 null] +>> endobj +1440 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1558 0 obj << +/Length 1277 +/Filter /FlateDecode +>> +stream +xÚ½XKsÛ6¾ëWàVr¦d°@Ç´ã8N Ï4Ñd¦ãä@KÄ vÒæÇ|9¢, @d÷ “–°,v¿ýFç³?泯(G +Žî»U™úPÒ¢X„Rôaö׃ªnàœ‚ DÂaˆ(#>°%ÞÅ‹#6Dœ)ŠîkÂîe‚"‚Qãz‹ +ê8ô@j„Fež¬ŠA‹š£'(O…ß¾
^I—#÷=¨y[< Î=8&Ý£i²n ñÂH±Éh×|µÏÙ ]OÊÓïý¯7]oê;Ô2‘:ZÓ캮µ¼|!žêøvß7ÎT‡M›[дéñŒ*pÕäË8Ú\?¶QG~m:ôÖŽEô$pà0RüŒ¿Œ+ÅvG§$;•ùºÞh¼Œ4ÕÖP,É+‡ÄÓíÚv@±ßÀ– G¶ Eì—Îm¸_àÖóyîÛÀö¡uOÄFéZ.šÒdrª™g·¢‹ò&y(“ÿÛ‡wIß eZiÈ }Ä*SPÐØÍ¿¸]ëèFñ/‰Îv`cÛ6¹¬Y#€¦‘e*M’ŠYßžhâZ˜\°ÙÖ7cF‰ü¤TÁš“Óæ«àÄ aƒ+ˆð +endstream +endobj +1557 0 obj << +/Type /Page +/Contents 1558 0 R +/Resources 1556 0 R +/MediaBox [0 0 342 504] +/Parent 1226 0 R +/Annots [ 1437 0 R 1438 0 R 1439 0 R 1444 0 R 1445 0 R 1446 0 R 1447 0 R 1448 0 R 1449 0 R 1450 0 R 1451 0 R 1452 0 R 1453 0 R 1454 0 R 1455 0 R 1456 0 R 1457 0 R 1458 0 R 1459 0 R 1460 0 R 1461 0 R 1462 0 R 1463 0 R 1464 0 R 1465 0 R 1466 0 R 1467 0 R 1468 0 R 1469 0 R 1470 0 R 1471 0 R 1472 0 R 1473 0 R 1474 0 R 1475 0 R 1476 0 R 1477 0 R 1478 0 R 1479 0 R 1480 0 R 1481 0 R 1482 0 R 1483 0 R 1484 0 R 1485 0 R 1486 0 R 1487 0 R 1488 0 R 1489 0 R 1490 0 R 1491 0 R 1492 0 R 1493 0 R 1494 0 R 1495 0 R 1496 0 R 1497 0 R 1498 0 R 1499 0 R 1500 0 R 1501 0 R 1502 0 R 1503 0 R 1504 0 R 1505 0 R 1506 0 R 1507 0 R 1508 0 R 1509 0 R 1510 0 R 1511 0 R 1512 0 R 1513 0 R 1514 0 R 1515 0 R 1516 0 R 1517 0 R 1518 0 R 1519 0 R 1520 0 R 1521 0 R 1522 0 R 1523 0 R 1524 0 R 1525 0 R 1526 0 R 1527 0 R 1528 0 R 1529 0 R 1530 0 R 1531 0 R 1532 0 R 1533 0 R 1534 0 R 1535 0 R 1536 0 R 1537 0 R 1538 0 R 1539 0 R 1540 0 R 1541 0 R 1542 0 R 1543 0 R 1544 0 R 1545 0 R 1546 0 R ] +>> endobj +1437 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [63.458 450.041 81.815 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1438 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [144.186 436.154 157.087 447.843] +/Subtype /Link +/A << /S /GoTo /D (page.40) >> +>> endobj +1439 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [60.428 406.672 78.784 418.362] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1444 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [46.519 392.785 59.421 404.354] +/Subtype /Link +/A << /S /GoTo /D (page.61) >> +>> endobj +1445 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [76.337 378.898 89.239 390.588] +/Subtype /Link +/A << /S /GoTo /D (page.45) >> +>> endobj +1446 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [93.913 378.898 106.815 390.588] +/Subtype /Link +/A << /S /GoTo /D (page.60) >> +>> endobj +1447 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [111.489 378.898 124.39 390.588] +/Subtype /Link +/A << /S /GoTo /D (page.64) >> +>> endobj +1448 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [129.064 378.898 141.966 390.588] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1449 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [146.64 378.898 159.542 390.588] +/Subtype /Link +/A << /S /GoTo /D (page.95) >> +>> endobj +1450 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [94.983 350.856 113.339 363.758] +/Subtype /Link +/A << /S /GoTo /D (page.110) >> +>> endobj +1451 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 326.147 50.793 335.17] +/Subtype /Link +/A << /S /GoTo /D (page.99) >> +>> endobj +1452 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [56.489 310.139 74.845 321.707] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1453 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [34.428 296.251 47.33 307.82] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1454 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [46.216 266.77 64.572 278.46] +/Subtype /Link +/A << /S /GoTo /D (page.118) >> +>> endobj +1455 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [83.186 252.883 96.087 264.451] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1456 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [100.761 252.883 113.663 264.451] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1457 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [48.155 223.402 66.511 234.97] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1458 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [81.519 209.515 94.421 221.204] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1459 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [99.095 209.515 111.996 221.204] +/Subtype /Link +/A << /S /GoTo /D (page.56) >> +>> endobj +1460 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [116.67 209.515 129.572 221.204] +/Subtype /Link +/A << /S /GoTo /D (page.57) >> +>> endobj +1461 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [134.246 209.515 147.148 221.204] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1462 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [126.171 195.628 139.072 207.317] +/Subtype /Link +/A << /S /GoTo /D (page.11) >> +>> endobj +1463 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [74.701 181.74 87.602 193.43] +/Subtype /Link +/A << /S /GoTo /D (page.55) >> +>> endobj +1464 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [92.277 181.74 105.178 193.43] +/Subtype /Link +/A << /S /GoTo /D (page.67) >> +>> endobj +1465 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [109.852 181.74 122.754 193.43] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1466 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [57.337 167.853 70.239 179.422] +/Subtype /Link +/A << /S /GoTo /D (page.96) >> +>> endobj +1467 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [74.913 167.853 93.269 179.422] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1468 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [70.943 153.966 83.845 165.656] +/Subtype /Link +/A << /S /GoTo /D (page.32) >> +>> endobj +1469 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [88.519 153.966 106.875 165.656] +/Subtype /Link +/A << /S /GoTo /D (page.108) >> +>> endobj +1470 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [111.549 153.966 129.905 165.656] +/Subtype /Link +/A << /S /GoTo /D (page.112) >> +>> endobj +1471 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [83.428 140.079 96.33 151.769] +/Subtype /Link +/A << /S /GoTo /D (page.32) >> +>> endobj +1472 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [112.573 125.586 125.475 138.488] +/Subtype /Link +/A << /S /GoTo /D (page.34) >> +>> endobj +1473 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [130.149 125.586 143.051 138.488] +/Subtype /Link +/A << /S /GoTo /D (page.35) >> +>> endobj +1474 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [78.549 112.305 91.451 123.994] +/Subtype /Link +/A << /S /GoTo /D (page.99) >> +>> endobj +1475 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [83.64 98.418 96.542 109.986] +/Subtype /Link +/A << /S /GoTo /D (page.18) >> +>> endobj +1476 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [101.216 98.418 114.118 109.986] +/Subtype /Link +/A << /S /GoTo /D (page.39) >> +>> endobj +1477 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [118.792 98.418 131.693 109.986] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1478 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 86.99 50.793 96.013] +/Subtype /Link +/A << /S /GoTo /D (page.47) >> +>> endobj +1479 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [54.255 86.99 67.157 96.013] +/Subtype /Link +/A << /S /GoTo /D (page.50) >> +>> endobj +1480 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [99.943 70.982 112.845 82.671] +/Subtype /Link +/A << /S /GoTo /D (page.31) >> +>> endobj +1481 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [117.519 70.982 130.421 82.671] +/Subtype /Link +/A << /S /GoTo /D (page.37) >> +>> endobj +1482 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [135.095 70.982 147.996 82.671] +/Subtype /Link +/A << /S /GoTo /D (page.40) >> +>> endobj +1483 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 57.432 50.793 68.576] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1484 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 57.432 68.369 68.576] +/Subtype /Link +/A << /S /GoTo /D (page.90) >> +>> endobj +1485 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [73.043 57.432 85.945 68.576] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1486 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [90.619 57.432 108.975 68.576] +/Subtype /Link +/A << /S /GoTo /D (page.108) >> +>> endobj +1487 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [113.649 57.432 132.005 68.576] +/Subtype /Link +/A << /S /GoTo /D (page.111) >> +>> endobj +1488 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [136.68 57.432 155.036 68.576] +/Subtype /Link +/A << /S /GoTo /D (page.113) >> +>> endobj +1489 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 46.004 56.248 55.027] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1490 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [104.458 29.39 122.815 42.292] +/Subtype /Link +/A << /S /GoTo /D (page.113) >> +>> endobj +1491 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [228.819 450.041 241.72 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.68) >> +>> endobj +1492 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [253.213 436.07 266.114 447.759] +/Subtype /Link +/A << /S /GoTo /D (page.59) >> +>> endobj +1493 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [300.97 408.128 319.326 419.817] +/Subtype /Link +/A << /S /GoTo /D (page.125) >> +>> endobj +1494 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [218.697 394.157 231.599 405.725] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1495 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [225.334 380.186 238.235 391.875] +/Subtype /Link +/A << /S /GoTo /D (page.39) >> +>> endobj +1496 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [242.91 380.186 255.811 391.875] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1497 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [260.485 380.186 273.387 391.875] +/Subtype /Link +/A << /S /GoTo /D (page.46) >> +>> endobj +1498 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [276.849 380.186 289.751 391.875] +/Subtype /Link +/A << /S /GoTo /D (page.49) >> +>> endobj +1499 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [308.425 366.215 321.326 377.904] +/Subtype /Link +/A << /S /GoTo /D (page.44) >> +>> endobj +1500 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 354.787 221.76 363.809] +/Subtype /Link +/A << /S /GoTo /D (page.71) >> +>> endobj +1501 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [295.122 338.694 308.023 350.384] +/Subtype /Link +/A << /S /GoTo /D (page.78) >> +>> endobj +1502 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [254.849 324.723 262.296 336.413] +/Subtype /Link +/A << /S /GoTo /D (page.4) >> +>> endobj +1503 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [266.97 324.723 274.417 336.413] +/Subtype /Link +/A << /S /GoTo /D (page.5) >> +>> endobj +1504 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [279.091 324.723 291.993 336.413] +/Subtype /Link +/A << /S /GoTo /D (page.26) >> +>> endobj +1505 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [296.667 324.723 309.569 336.413] +/Subtype /Link +/A << /S /GoTo /D (page.74) >> +>> endobj +1506 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [314.243 324.723 327.145 336.413] +/Subtype /Link +/A << /S /GoTo /D (page.75) >> +>> endobj +1507 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 311.174 221.76 322.318] +/Subtype /Link +/A << /S /GoTo /D (page.87) >> +>> endobj +1508 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.434 311.174 239.335 322.318] +/Subtype /Link +/A << /S /GoTo /D (page.93) >> +>> endobj +1509 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [244.01 311.174 256.911 322.318] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1510 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [261.585 311.174 279.942 322.318] +/Subtype /Link +/A << /S /GoTo /D (page.104) >> +>> endobj +1511 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [284.616 311.174 302.972 322.318] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1512 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [307.646 311.174 326.002 322.318] +/Subtype /Link +/A << /S /GoTo /D (page.110) >> +>> endobj +1513 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [224.788 297.203 237.69 308.771] +/Subtype /Link +/A << /S /GoTo /D (page.96) >> +>> endobj +1514 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [242.364 297.203 260.72 308.771] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1515 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [235.667 283.232 248.569 294.921] +/Subtype /Link +/A << /S /GoTo /D (page.96) >> +>> endobj +1516 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [253.243 283.232 271.599 294.921] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1517 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [232.97 269.261 245.872 280.95] +/Subtype /Link +/A << /S /GoTo /D (page.50) >> +>> endobj +1518 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [249.334 269.261 262.235 280.95] +/Subtype /Link +/A << /S /GoTo /D (page.51) >> +>> endobj +1519 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [236.304 255.29 249.205 266.979] +/Subtype /Link +/A << /S /GoTo /D (page.52) >> +>> endobj +1520 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [252.667 255.29 265.569 266.979] +/Subtype /Link +/A << /S /GoTo /D (page.54) >> +>> endobj +1521 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [270.243 255.29 283.145 266.979] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1522 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [287.819 255.29 306.175 266.979] +/Subtype /Link +/A << /S /GoTo /D (page.115) >> +>> endobj +1523 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [218.091 241.319 230.993 253.008] +/Subtype /Link +/A << /S /GoTo /D (page.50) >> +>> endobj +1524 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [235.667 241.319 248.569 253.008] +/Subtype /Link +/A << /S /GoTo /D (page.51) >> +>> endobj +1525 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [219.879 227.348 232.781 238.916] +/Subtype /Link +/A << /S /GoTo /D (page.13) >> +>> endobj +1526 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [237.455 227.348 250.357 238.916] +/Subtype /Link +/A << /S /GoTo /D (page.55) >> +>> endobj +1527 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [287.819 213.377 300.72 225.066] +/Subtype /Link +/A << /S /GoTo /D (page.11) >> +>> endobj +1528 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [305.394 213.377 318.296 225.066] +/Subtype /Link +/A << /S /GoTo /D (page.13) >> +>> endobj +1529 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 199.828 221.76 210.972] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1530 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.434 199.828 239.335 210.972] +/Subtype /Link +/A << /S /GoTo /D (page.95) >> +>> endobj +1531 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [244.01 199.828 262.366 210.972] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1532 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [231.394 168.863 249.751 180.552] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1533 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [222.303 154.892 235.205 166.46] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1534 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [239.879 154.892 252.781 166.46] +/Subtype /Link +/A << /S /GoTo /D (page.68) >> +>> endobj +1535 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [257.455 154.892 270.357 166.46] +/Subtype /Link +/A << /S /GoTo /D (page.95) >> +>> endobj +1536 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [275.031 154.892 287.932 166.46] +/Subtype /Link +/A << /S /GoTo /D (page.98) >> +>> endobj +1537 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [292.607 154.892 310.963 166.46] +/Subtype /Link +/A << /S /GoTo /D (page.117) >> +>> endobj +1538 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [308.758 126.95 327.114 138.639] +/Subtype /Link +/A << /S /GoTo /D (page.123) >> +>> endobj +1539 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [284.455 112.979 297.357 124.668] +/Subtype /Link +/A << /S /GoTo /D (page.46) >> +>> endobj +1540 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [302.031 112.979 314.932 124.668] +/Subtype /Link +/A << /S /GoTo /D (page.74) >> +>> endobj +1541 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 99.429 221.76 110.574] +/Subtype /Link +/A << /S /GoTo /D (page.99) >> +>> endobj +1542 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [226.434 99.429 244.79 110.574] +/Subtype /Link +/A << /S /GoTo /D (page.117) >> +>> endobj +1543 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [265.637 85.458 278.538 97.148] +/Subtype /Link +/A << /S /GoTo /D (page.60) >> +>> endobj +1544 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [302.485 71.487 320.842 83.177] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1545 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 46.088 221.76 55.111] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1546 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [283.243 29.996 296.145 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.58) >> +>> endobj +1559 0 obj << +/D [1557 0 R /XYZ 9 484.913 null] +>> endobj +1556 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F16 210 0 R /F11 420 0 R /F41 211 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1658 0 obj << +/Length 1247 +/Filter /FlateDecode +>> +stream +xÚµXKoÜ6¾ï¯ÐQ,E|H¢®E š:^ +890½KT+)¤Ö†Óüø’zÖzÍGÝ â69 Î|ß73Lƒ] 6¿ÜlÞ½Ç$ +Ý1a#0ñŒSYš¯ÂÚùc£ + Ó +}ߌˆ1¬söe+Ö/ÓCæqU¬çl5;1q eyHž|ã—!'7æ2ëö~PB—ˆ
{ÁX\ókå8ìX%»¸:VчñùÀÙø+Ï'ÏÉÓ?½JU]܉š·t`¶G4o¬¾=ák¡~bÜò‚¶ÌNÞuâq=þŸ(—©9û^᡽~‡]{÷–¾ïeš¥UKðËæÁ¡Ýp’zyw.Ç›y° ’ÉÜÇnßZߟ,…b`Í“¼{ÌÇnâÖï»¡Û Úï¥ÕOK ߃”Š,ÏC-ó{4 ½ufµ14÷X½1háô£ ØaÍ`gMBÞ +endstream +endobj +1657 0 obj << +/Type /Page +/Contents 1658 0 R +/Resources 1656 0 R +/MediaBox [0 0 342 504] +/Parent 1226 0 R +/Annots [ 1547 0 R 1548 0 R 1549 0 R 1550 0 R 1551 0 R 1552 0 R 1553 0 R 1554 0 R 1555 0 R 1560 0 R 1561 0 R 1562 0 R 1563 0 R 1564 0 R 1565 0 R 1566 0 R 1567 0 R 1568 0 R 1569 0 R 1570 0 R 1571 0 R 1572 0 R 1573 0 R 1574 0 R 1575 0 R 1576 0 R 1577 0 R 1578 0 R 1579 0 R 1580 0 R 1581 0 R 1582 0 R 1583 0 R 1584 0 R 1585 0 R 1586 0 R 1587 0 R 1588 0 R 1589 0 R 1590 0 R 1591 0 R 1592 0 R 1593 0 R 1594 0 R 1595 0 R 1596 0 R 1597 0 R 1598 0 R 1599 0 R 1600 0 R 1601 0 R 1602 0 R 1603 0 R 1604 0 R 1605 0 R 1606 0 R 1607 0 R 1608 0 R 1609 0 R 1610 0 R 1611 0 R 1612 0 R 1613 0 R 1614 0 R 1615 0 R 1616 0 R 1617 0 R 1618 0 R 1619 0 R 1620 0 R 1621 0 R 1622 0 R 1623 0 R 1624 0 R 1625 0 R 1626 0 R 1627 0 R 1628 0 R 1629 0 R 1630 0 R 1631 0 R 1632 0 R 1633 0 R 1634 0 R 1635 0 R 1636 0 R 1637 0 R 1638 0 R 1639 0 R 1640 0 R 1641 0 R 1642 0 R 1643 0 R 1644 0 R 1645 0 R 1646 0 R 1647 0 R 1648 0 R ] +>> endobj +1547 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [45.64 450.041 58.542 461.609] +/Subtype /Link +/A << /S /GoTo /D (page.12) >> +>> endobj +1548 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [63.216 450.041 76.118 461.609] +/Subtype /Link +/A << /S /GoTo /D (page.18) >> +>> endobj +1549 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [80.792 450.041 93.693 461.609] +/Subtype /Link +/A << /S /GoTo /D (page.42) >> +>> endobj +1550 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [108.034 436.492 120.936 448.181] +/Subtype /Link +/A << /S /GoTo /D (page.13) >> +>> endobj +1551 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [57.276 413.903 64.724 425.593] +/Subtype /Link +/A << /S /GoTo /D (page.8) >> +>> endobj +1552 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [69.398 413.903 76.845 425.593] +/Subtype /Link +/A << /S /GoTo /D (page.9) >> +>> endobj +1553 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [66.67 400.354 74.118 412.043] +/Subtype /Link +/A << /S /GoTo /D (page.9) >> +>> endobj +1554 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [117.64 386.805 135.996 398.494] +/Subtype /Link +/A << /S /GoTo /D (page.117) >> +>> endobj +1555 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [139.458 386.805 157.815 398.494] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1560 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [50.095 373.256 57.542 384.945] +/Subtype /Link +/A << /S /GoTo /D (page.6) >> +>> endobj +1561 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [104.458 359.706 111.905 371.396] +/Subtype /Link +/A << /S /GoTo /D (page.6) >> +>> endobj +1562 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [102.458 346.157 109.905 357.847] +/Subtype /Link +/A << /S /GoTo /D (page.4) >> +>> endobj +1563 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [114.58 346.157 122.027 357.847] +/Subtype /Link +/A << /S /GoTo /D (page.5) >> +>> endobj +1564 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [41.489 332.608 48.936 344.297] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1565 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [53.61 332.608 71.966 344.297] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1566 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.761 319.059 74.118 330.748] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1567 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [40.276 305.51 47.724 317.078] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1568 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [117.398 291.96 130.299 303.65] +/Subtype /Link +/A << /S /GoTo /D (page.43) >> +>> endobj +1569 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [53.367 278.411 60.814 289.979] +/Subtype /Link +/A << /S /GoTo /D (page.8) >> +>> endobj +1570 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [115.792 264.862 128.693 276.551] +/Subtype /Link +/A << /S /GoTo /D (page.12) >> +>> endobj +1571 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [132.155 264.862 145.057 276.551] +/Subtype /Link +/A << /S /GoTo /D (page.14) >> +>> endobj +1572 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 251.313 50.793 262.457] +/Subtype /Link +/A << /S /GoTo /D (page.18) >> +>> endobj +1573 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 251.313 68.369 262.457] +/Subtype /Link +/A << /S /GoTo /D (page.55) >> +>> endobj +1574 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [108.701 237.764 121.602 249.453] +/Subtype /Link +/A << /S /GoTo /D (page.40) >> +>> endobj +1575 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [110.61 224.214 123.512 235.904] +/Subtype /Link +/A << /S /GoTo /D (page.16) >> +>> endobj +1576 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [126.974 224.214 139.875 235.904] +/Subtype /Link +/A << /S /GoTo /D (page.18) >> +>> endobj +1577 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [144.549 224.214 157.451 235.904] +/Subtype /Link +/A << /S /GoTo /D (page.29) >> +>> endobj +1578 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 210.665 50.793 221.809] +/Subtype /Link +/A << /S /GoTo /D (page.85) >> +>> endobj +1579 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 210.665 73.824 221.809] +/Subtype /Link +/A << /S /GoTo /D (page.112) >> +>> endobj +1580 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [130.519 197.116 143.421 208.805] +/Subtype /Link +/A << /S /GoTo /D (page.69) >> +>> endobj +1581 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [68.913 183.567 81.815 195.256] +/Subtype /Link +/A << /S /GoTo /D (page.37) >> +>> endobj +1582 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [134.974 160.978 153.33 172.668] +/Subtype /Link +/A << /S /GoTo /D (page.107) >> +>> endobj +1583 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [130.064 147.429 148.421 159.119] +/Subtype /Link +/A << /S /GoTo /D (page.107) >> +>> endobj +1584 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [61.489 124.84 74.39 136.53] +/Subtype /Link +/A << /S /GoTo /D (page.44) >> +>> endobj +1585 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [124.701 111.291 137.602 122.981] +/Subtype /Link +/A << /S /GoTo /D (page.48) >> +>> endobj +1586 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [87.277 97.742 94.724 109.432] +/Subtype /Link +/A << /S /GoTo /D (page.4) >> +>> endobj +1587 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [99.398 97.742 106.845 109.432] +/Subtype /Link +/A << /S /GoTo /D (page.6) >> +>> endobj +1588 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [111.519 97.742 118.966 109.432] +/Subtype /Link +/A << /S /GoTo /D (page.8) >> +>> endobj +1589 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [122.428 97.742 135.33 109.432] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1590 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [140.004 97.742 152.905 109.432] +/Subtype /Link +/A << /S /GoTo /D (page.16) >> +>> endobj +1591 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [37.892 84.193 50.793 95.337] +/Subtype /Link +/A << /S /GoTo /D (page.21) >> +>> endobj +1592 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [55.467 84.193 68.369 95.337] +/Subtype /Link +/A << /S /GoTo /D (page.23) >> +>> endobj +1593 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [73.043 84.193 85.945 95.337] +/Subtype /Link +/A << /S /GoTo /D (page.24) >> +>> endobj +1594 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [90.619 84.193 103.521 95.337] +/Subtype /Link +/A << /S /GoTo /D (page.35) >> +>> endobj +1595 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [108.195 84.193 121.096 95.337] +/Subtype /Link +/A << /S /GoTo /D (page.55) >> +>> endobj +1596 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [67.428 70.644 80.33 82.043] +/Subtype /Link +/A << /S /GoTo /D (page.73) >> +>> endobj +1597 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [100.974 57.094 113.875 68.784] +/Subtype /Link +/A << /S /GoTo /D (page.92) >> +>> endobj +1598 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [117.337 57.094 130.239 68.784] +/Subtype /Link +/A << /S /GoTo /D (page.94) >> +>> endobj +1599 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [67.155 29.996 74.602 41.396] +/Subtype /Link +/A << /S /GoTo /D (page.3) >> +>> endobj +1600 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [235.94 450.041 254.296 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.110) >> +>> endobj +1601 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [207.061 435.455 219.963 447.023] +/Subtype /Link +/A << /S /GoTo /D (page.13) >> +>> endobj +1602 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [228.213 420.868 241.114 432.436] +/Subtype /Link +/A << /S /GoTo /D (page.80) >> +>> endobj +1603 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [245.788 420.868 264.145 432.436] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1604 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [268.819 420.868 287.175 432.436] +/Subtype /Link +/A << /S /GoTo /D (page.104) >> +>> endobj +1605 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [227.607 406.282 240.508 417.85] +/Subtype /Link +/A << /S /GoTo /D (page.74) >> +>> endobj +1606 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [245.182 406.282 263.538 417.85] +/Subtype /Link +/A << /S /GoTo /D (page.115) >> +>> endobj +1607 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [251.182 364.446 269.538 376.136] +/Subtype /Link +/A << /S /GoTo /D (page.124) >> +>> endobj +1608 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [250.849 349.86 263.751 361.549] +/Subtype /Link +/A << /S /GoTo /D (page.34) >> +>> endobj +1609 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [222.031 335.273 234.932 346.963] +/Subtype /Link +/A << /S /GoTo /D (page.98) >> +>> endobj +1610 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [239.607 335.273 252.508 346.963] +/Subtype /Link +/A << /S /GoTo /D (page.99) >> +>> endobj +1611 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [245.031 320.687 257.932 332.376] +/Subtype /Link +/A << /S /GoTo /D (page.19) >> +>> endobj +1612 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [262.607 320.687 275.508 332.376] +/Subtype /Link +/A << /S /GoTo /D (page.21) >> +>> endobj +1613 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [278.97 320.687 291.872 332.376] +/Subtype /Link +/A << /S /GoTo /D (page.24) >> +>> endobj +1614 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [296.546 320.687 309.448 332.376] +/Subtype /Link +/A << /S /GoTo /D (page.75) >> +>> endobj +1615 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [255.97 306.1 268.872 317.79] +/Subtype /Link +/A << /S /GoTo /D (page.24) >> +>> endobj +1616 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [248.758 291.514 261.66 303.204] +/Subtype /Link +/A << /S /GoTo /D (page.84) >> +>> endobj +1617 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [244.516 276.928 257.417 288.617] +/Subtype /Link +/A << /S /GoTo /D (page.70) >> +>> endobj +1618 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [262.091 276.928 280.448 288.617] +/Subtype /Link +/A << /S /GoTo /D (page.120) >> +>> endobj +1619 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [212.91 262.341 220.357 273.91] +/Subtype /Link +/A << /S /GoTo /D (page.8) >> +>> endobj +1620 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [225.031 262.341 237.932 273.91] +/Subtype /Link +/A << /S /GoTo /D (page.49) >> +>> endobj +1621 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [242.607 262.341 255.508 273.91] +/Subtype /Link +/A << /S /GoTo /D (page.52) >> +>> endobj +1622 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [260.182 262.341 273.084 273.91] +/Subtype /Link +/A << /S /GoTo /D (page.98) >> +>> endobj +1623 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [263.516 247.755 276.417 259.444] +/Subtype /Link +/A << /S /GoTo /D (page.18) >> +>> endobj +1624 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [239.607 233.168 252.508 244.858] +/Subtype /Link +/A << /S /GoTo /D (page.28) >> +>> endobj +1625 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [257.182 233.168 270.084 244.858] +/Subtype /Link +/A << /S /GoTo /D (page.53) >> +>> endobj +1626 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [228.667 218.582 241.569 229.982] +/Subtype /Link +/A << /S /GoTo /D (page.92) >> +>> endobj +1627 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [284.516 203.996 302.872 215.685] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1628 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [277.213 189.409 295.569 201.099] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1629 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [274.213 174.823 287.114 186.512] +/Subtype /Link +/A << /S /GoTo /D (page.52) >> +>> endobj +1630 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [291.788 174.823 304.69 186.512] +/Subtype /Link +/A << /S /GoTo /D (page.75) >> +>> endobj +1631 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [309.364 174.823 322.266 186.512] +/Subtype /Link +/A << /S /GoTo /D (page.92) >> +>> endobj +1632 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 148.808 216.305 157.831] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1633 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [219.767 148.808 232.669 157.831] +/Subtype /Link +/A << /S /GoTo /D (page.54) >> +>> endobj +1634 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [225.697 117.514 244.054 128.659] +/Subtype /Link +/A << /S /GoTo /D (page.104) >> +>> endobj +1635 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [248.728 117.514 267.084 128.659] +/Subtype /Link +/A << /S /GoTo /D (page.105) >> +>> endobj +1636 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [233.303 102.928 251.66 114.618] +/Subtype /Link +/A << /S /GoTo /D (page.102) >> +>> endobj +1637 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [225.788 88.342 244.145 100.031] +/Subtype /Link +/A << /S /GoTo /D (page.124) >> +>> endobj +1638 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [259.091 73.755 271.993 85.445] +/Subtype /Link +/A << /S /GoTo /D (page.98) >> +>> endobj +1639 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [259.061 59.169 277.417 70.858] +/Subtype /Link +/A << /S /GoTo /D (page.120) >> +>> endobj +1640 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [244.758 44.582 252.205 56.272] +/Subtype /Link +/A << /S /GoTo /D (page.1) >> +>> endobj +1641 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [255.667 44.582 263.114 56.272] +/Subtype /Link +/A << /S /GoTo /D (page.3) >> +>> endobj +1642 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [267.788 44.582 275.235 56.272] +/Subtype /Link +/A << /S /GoTo /D (page.8) >> +>> endobj +1643 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [279.91 44.582 292.811 56.272] +/Subtype /Link +/A << /S /GoTo /D (page.76) >> +>> endobj +1644 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [297.485 44.582 310.387 56.272] +/Subtype /Link +/A << /S /GoTo /D (page.82) >> +>> endobj +1645 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [315.061 44.582 333.417 56.272] +/Subtype /Link +/A << /S /GoTo /D (page.102) >> +>> endobj +1646 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [293.667 29.996 301.114 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.4) >> +>> endobj +1647 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [305.788 29.996 313.235 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.8) >> +>> endobj +1648 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [317.91 29.996 330.811 41.686] +/Subtype /Link +/A << /S /GoTo /D (page.10) >> +>> endobj +1659 0 obj << +/D [1657 0 R /XYZ 9 484.913 null] +>> endobj +1656 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F16 210 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1701 0 obj << +/Length 828 +/Filter /FlateDecode +>> +stream +xÚV[o›0~ϯ°öR¡>¾€ý¸ImÕi[ÇZmi q&™n“öãg.ICÅ ö!Ä!Çß¹ø;ß1F£«Ù‡hv~Éð%çEKDø”pÄ„ô Q´@sçæâÓ{W2'º¾½Ž¾»ÑÇóKàƒm"ôƒÚn +½Õ€'¶6–¨Â`êÜ +è1éSzP§6•®GB'iN4ÚÙ»?Õ¨“¥«1“lê4†`ê†pbB<zÃQ~Á¶®ŠíÀ7ÇéÕëÝ]‹µ÷³ÈTܼyJsU¶ZgI<8zã +éž—¦Ÿ'Þ„G´'y› Öa+{ÃQáé¨+ÕXÐntX[i X+Újªb œÿ¥Ö±í B‡ :ü6ï?TH2ž +endstream +endobj +1700 0 obj << +/Type /Page +/Contents 1701 0 R +/Resources 1699 0 R +/MediaBox [0 0 342 504] +/Parent 1703 0 R +/Annots [ 1649 0 R 1650 0 R 1651 0 R 1652 0 R 1653 0 R 1654 0 R 1655 0 R 1660 0 R 1661 0 R 1662 0 R 1663 0 R 1664 0 R 1665 0 R 1666 0 R 1667 0 R 1668 0 R 1669 0 R 1670 0 R 1671 0 R 1672 0 R 1673 0 R 1674 0 R 1675 0 R 1676 0 R 1677 0 R 1678 0 R 1679 0 R 1680 0 R 1681 0 R 1682 0 R 1683 0 R 1684 0 R 1685 0 R 1686 0 R 1687 0 R 1688 0 R 1689 0 R 1690 0 R 1691 0 R 1692 0 R 1693 0 R 1694 0 R 1695 0 R 1696 0 R 1697 0 R 1698 0 R ] +>> endobj +1649 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [93.367 450.041 106.269 461.73] +/Subtype /Link +/A << /S /GoTo /D (page.14) >> +>> endobj +1650 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [48.034 436.37 66.39 448.059] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1651 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [66.519 422.699 84.875 434.388] +/Subtype /Link +/A << /S /GoTo /D (page.116) >> +>> endobj +1652 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [102.64 409.027 115.542 420.717] +/Subtype /Link +/A << /S /GoTo /D (page.52) >> +>> endobj +1653 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [92.549 381.685 105.451 393.374] +/Subtype /Link +/A << /S /GoTo /D (page.18) >> +>> endobj +1654 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [110.125 381.685 123.027 393.374] +/Subtype /Link +/A << /S /GoTo /D (page.49) >> +>> endobj +1655 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [127.701 381.685 140.602 393.374] +/Subtype /Link +/A << /S /GoTo /D (page.98) >> +>> endobj +1660 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [82.58 368.014 95.481 379.703] +/Subtype /Link +/A << /S /GoTo /D (page.52) >> +>> endobj +1661 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [100.155 368.014 113.057 379.703] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1662 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [77.367 354.343 90.269 366.032] +/Subtype /Link +/A << /S /GoTo /D (page.19) >> +>> endobj +1663 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [94.943 354.343 107.845 366.032] +/Subtype /Link +/A << /S /GoTo /D (page.91) >> +>> endobj +1664 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [112.519 354.343 130.875 366.032] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1665 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [81.943 340.671 94.845 352.361] +/Subtype /Link +/A << /S /GoTo /D (page.21) >> +>> endobj +1666 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [99.519 340.671 112.421 352.361] +/Subtype /Link +/A << /S /GoTo /D (page.24) >> +>> endobj +1667 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [78.943 327 91.845 338.69] +/Subtype /Link +/A << /S /GoTo /D (page.28) >> +>> endobj +1668 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [96.519 327 109.421 338.69] +/Subtype /Link +/A << /S /GoTo /D (page.53) >> +>> endobj +1669 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [63.822 313.329 71.269 324.897] +/Subtype /Link +/A << /S /GoTo /D (page.9) >> +>> endobj +1670 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [53.186 299.658 60.633 311.347] +/Subtype /Link +/A << /S /GoTo /D (page.2) >> +>> endobj +1671 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [109.337 273.991 122.239 285.68] +/Subtype /Link +/A << /S /GoTo /D (page.11) >> +>> endobj +1672 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [126.913 273.991 139.815 285.68] +/Subtype /Link +/A << /S /GoTo /D (page.55) >> +>> endobj +1673 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [69.822 246.648 88.178 258.338] +/Subtype /Link +/A << /S /GoTo /D (page.105) >> +>> endobj +1674 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [92.852 246.648 111.209 258.338] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1675 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [76.034 232.977 94.39 244.667] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1676 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [99.064 232.977 117.421 244.667] +/Subtype /Link +/A << /S /GoTo /D (page.103) >> +>> endobj +1677 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 452.162 227.214 461.185] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1678 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [242.091 436.312 260.448 448.001] +/Subtype /Link +/A << /S /GoTo /D (page.103) >> +>> endobj +1679 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [265.122 436.312 283.478 448.001] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1680 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 409.033 227.214 420.177] +/Subtype /Link +/A << /S /GoTo /D (page.101) >> +>> endobj +1681 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [231.888 409.033 250.245 420.177] +/Subtype /Link +/A << /S /GoTo /D (page.106) >> +>> endobj +1682 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [277.819 395.304 296.175 406.994] +/Subtype /Link +/A << /S /GoTo /D (page.103) >> +>> endobj +1683 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [234.974 368.613 247.876 380.302] +/Subtype /Link +/A << /S /GoTo /D (page.76) >> +>> endobj +1684 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [252.55 368.613 270.906 380.302] +/Subtype /Link +/A << /S /GoTo /D (page.102) >> +>> endobj +1685 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [261.697 354.884 269.145 366.573] +/Subtype /Link +/A << /S /GoTo /D (page.9) >> +>> endobj +1686 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [273.819 354.884 286.72 366.573] +/Subtype /Link +/A << /S /GoTo /D (page.16) >> +>> endobj +1687 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [291.394 354.884 304.296 366.573] +/Subtype /Link +/A << /S /GoTo /D (page.17) >> +>> endobj +1688 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [308.97 354.884 321.872 366.573] +/Subtype /Link +/A << /S /GoTo /D (page.70) >> +>> endobj +1689 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [208.858 343.456 227.214 352.479] +/Subtype /Link +/A << /S /GoTo /D (page.112) >> +>> endobj +1690 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [213.879 327.605 232.235 339.174] +/Subtype /Link +/A << /S /GoTo /D (page.119) >> +>> endobj +1691 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [275.758 300.308 288.66 313.21] +/Subtype /Link +/A << /S /GoTo /D (page.61) >> +>> endobj +1692 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [214.758 287.185 227.66 298.874] +/Subtype /Link +/A << /S /GoTo /D (page.52) >> +>> endobj +1693 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [232.334 287.185 250.69 298.874] +/Subtype /Link +/A << /S /GoTo /D (page.102) >> +>> endobj +1694 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [255.364 287.185 273.72 298.874] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1695 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [228.667 273.456 247.023 284.855] +/Subtype /Link +/A << /S /GoTo /D (page.114) >> +>> endobj +1696 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [233 259.727 251.357 271.416] +/Subtype /Link +/A << /S /GoTo /D (page.104) >> +>> endobj +1697 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [234.213 245.997 252.569 257.687] +/Subtype /Link +/A << /S /GoTo /D (page.103) >> +>> endobj +1698 0 obj << +/Type /Annot +/Border[0 0 0]/H/I/C[1 0 0] +/Rect [222.607 219.306 235.508 230.874] +/Subtype /Link +/A << /S /GoTo /D (page.39) >> +>> endobj +1702 0 obj << +/D [1700 0 R /XYZ 9 484.913 null] +>> endobj +1699 0 obj << +/Font << /F48 218 0 R /F15 231 0 R /F16 210 0 R /F11 420 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1706 0 obj << +/Length 144 +/Filter /FlateDecode +>> +stream +xÚuŽ»!D{¾â–lòÆ[Jã²±0ÆÎèÿÿ®TÆXM29s2ž ñ'C#«Dð ½Ð æÖ"(ƒ|íÞÕ ®ôXsiq ˜¶††Ëpk{`¹CLJn¬ïà4ךOséä¦|&–¦ B¯yÊ‹i1Ásß‚8æÎuPHÓn¡~.ÇF^;Â.Ë +endstream +endobj +1705 0 obj << +/Type /Page +/Contents 1706 0 R +/Resources 1704 0 R +/MediaBox [0 0 342 504] +/Parent 1703 0 R +>> endobj +1707 0 obj << +/D [1705 0 R /XYZ 9 484.913 null] +>> endobj +1704 0 obj << +/Font << /F19 213 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1710 0 obj << +/Length 1508 +/Filter /FlateDecode +>> +stream +xÚXQsâ6~ϯ ÷”܃!!$oIŽä¸Ë„ qÚÉ´}¶0jŒä‘d(ýõ]!ŒšéÜÜ ŸÝO»ß~»º~'ïô;'wÉIïáb܉ãèúòrÐI–x8Œâ‹Açb|
.®:IÖùýôiz?y~>?žý™ü8é»ÝíßÞC<î\E×WýØXêƃ‹½©îpõÇ×ÖÔ„ggÝËa|*–öW¯¨]¼HñMµ}x¬4å *sû8¹âãpßàt~ŸÒ‚h¶azwcß%h뵤)#…} ÖåàTÃøÎ +*¥öDHÁµ8ôéJ~.DbžØBé‚ã|Õò0åšJN ¼[™®ÀcAˆÑø`¯ +¼•YMš1Í?Ê·¤eARÚrTJº©©"8ívý;Q´M ³Í'ãg_
Q¨´î%‰áy ÄVÈ$«k‡¬Z,µëL¬ („C̸ uM .õŠ¸O¸€†cºnqñ™õ|ÕT÷:åN²|å¬Z,(ÊUÒV +~¨sû¨D똢â(f>ã’Žûr߉ê—}¾Âk -aȘҒ-@â 8íJyïÆâ<`nð|[¦AÖt V%•k¦„¹å·Ø¤Ok+VRìH¡4 +Š9î†Í†"+Яó€k…üÓ«ÃÈ µÙl +%ã b#| C2x¤À F[$vcPûÀ㇓‘T¬Mk+r 3æc[¶´óµ¯©f® c¹àS¢vX‰ïŸšJÑvyÐz^ôÇà”ÈÂKöÍJ–B…fBU¥+ _\ ö½ +Ü…07(ÎŒŠºË ¯(ø_ “ää_Ž³G +endstream +endobj +1709 0 obj << +/Type /Page +/Contents 1710 0 R +/Resources 1708 0 R +/MediaBox [0 0 342 504] +/Parent 1703 0 R +>> endobj +1711 0 obj << +/D [1709 0 R /XYZ 9 484.913 null] +>> endobj +1712 0 obj << +/D [1709 0 R /XYZ 9 465.114 null] +>> endobj +190 0 obj << +/D [1709 0 R /XYZ 9 465.114 null] +>> endobj +1708 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1715 0 obj << +/Length 1582 +/Filter /FlateDecode +>> +stream +xÚ¥XMoã6½çW99@âµ”MŽ»é&H¤A×=m´DÉl$R )ú÷ Š ê‹JÖÝ“-Qgæͼ7Ãõ"_¬'_7'Ÿ ®nQ´º»¾Ž›l]^®¢«xqu{·Š¯>/6éâ¯åóÓý·—ïO/gÿl~=Y»·?=D·‹Ï«»ÏëȼyÅWí«×W«u ÙW¿ÓD3ÁÏ.®/£e´:»ˆÖ7ñò‘r*Iaïn¨,•ý+2ó/ÿPgÑ’Úÿ„§vñwš2¥%ÛÂZÏíú+\Jñ/ìc {¬5å[*ó ]{ÁÖ‹ÛÕÝó…ð¤œ%öñƒo +Ÿ‹ÀËØ>¾ ¹_»•4V‘Ôm
æJ{¿VŒÃRŽ7v¹"R÷ýŠ–zÇœ§¯?iò¹ýÛˆÚþa<e Ñ÷!zôÀŽìÝ¢Üë5O©TBìn\Rü†è›rcMñ`$¡•Ûƒn‹ïN!×!DÊ^,¡<„1ãšà.,éÚ&H¼¬LÜEE¥nÑù{}½Ö’¤´$òíSÒ>ÚH–ï4¬D=·JÊ5"úä¬òáI…ýåB‡"aomYênm]FؼŸj>ý,ðvá,k¥íI›sŠb¦™ 声IªkÉûI Q(Ñ„@D¼Q1:2n>1Û;áòqØy'œ •PŠ*õ¿ + +á á+Äá"_ˆi_â#>çεAÏ5…ïút®³±d¢ +ÓX"™jà;_w)v Cð]VRV5½Ë3¬a¨ý½!Šå˜Æg=“«@Žnc7šñÓ |çn@¡23s‡,OViF³"Xã—öwaüb{¸Þ‡‚Ó˸-™t>J žÇ+ád5Joèö@xBˆ×B\*ýYŠ=M‘‰~Ë°vk©è +À]Ø;¾qü;3Î64O™¯!¨ ‘~›9±€X”ž’ƤÒöŒ +endstream +endobj +1714 0 obj << +/Type /Page +/Contents 1715 0 R +/Resources 1713 0 R +/MediaBox [0 0 342 504] +/Parent 1703 0 R +>> endobj +1716 0 obj << +/D [1714 0 R /XYZ 9 484.913 null] +>> endobj +1713 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1719 0 obj << +/Length 1470 +/Filter /FlateDecode +>> +stream +xÚ½XMoã6½çW{r +–ž„Ós:p)ïuªDИ ˜Q# ,-BY,®YÓ¸¢i3U·KQZ/BÙ÷håÄn¶µvçZ'ºìÔ̵ž`eg0ãÁ©¶ÌwϦ²{¡7°N’³Ì5P;M}C +©™—Dîu«Ð'XÀÔÚºb"ig¿¸àNÃò +uì¨ç +;c:WF éá9Æ«ŸVo•xqŠ òÀõ—]%òöó· +œ6qôH¾Žç¢>TV¸(Ã^5 { +‰Ÿ•"rižüh†Ù”ΓÁ÷@ü}Ø\|)™¥à +endstream +endobj +1718 0 obj << +/Type /Page +/Contents 1719 0 R +/Resources 1717 0 R +/MediaBox [0 0 342 504] +/Parent 1703 0 R +>> endobj +1720 0 obj << +/D [1718 0 R /XYZ 9 484.913 null] +>> endobj +1717 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1723 0 obj << +/Length 1648 +/Filter /FlateDecode +>> +stream +xÚXÛŽÛ6}߯0(àl%ïÅ~LÓÝt‹ šE¢íMRITIi ý}‡"‡ºÑ›í“M]Èá™3sµY ›Å»‹ Ÿ/® ov‹8Žö··Éâ9]ÄÛmß$‹›Ý>JnîÏlñÇòýÓÛ‡Ÿž>¼»úëù—‹{ûú1Þ-î£ýý&6o®ãä¦{u½½‹6»½}5Ž ¢»èj oî’åï²¹ZßnãeAZó'YÒ«x)Ë®j{£–ö:)™½À„®•84ð\Íí½:ÚÞ<IõÙþ¥ý%ekÿ DIT»2C°ë]´¿»³QYTŠkÍÙ +ƒQŸ¹[®©ÜÅR–•’•¼†¥a*»¶Tö¶»g¢ò÷R CU¬ìH”4‡qÃDyt{‚!„7¶Áü´Bs¯Ä~¹¬ +±? •ü›SÛ;x£<pu\×ÅÙ,õÛ î5YgÜm¶ÎH@éòcNp‚ßH)òÜMóæÓÛ§§Ë1`ƒé†«43Ás„4¨$·^`È•2L%uSÉñTžÔÏóutøÁþÑ¡þss»9NÑ Ž`[ñò×ãU U/«F׎¸ãRöäcLÔ° ŒJÿtÊù˜ßüKÅKmp5''{$‘sÕˆ_ÁŠ«ÚÕ(ó'å„K°¢Tµg>qýÁÔ”{»îü,òPIƳtÜm±¾Çét*þOÃ=8™ßìœÁ¢Ö’0©%Òæò#Œ‘© 0ÕT=’5Y¾¡ç+¼nÊÓýí(;GoXìo°½‘¼æª$Ș!Ç
0Xš7˜OtCó&wÑ9aˆüL€Ÿ]£õ‡ó^P`fÛÁ¯+NE*¦ÅUEŽŠT™ -ˆ#œ3éØn{•¸ÇMþ$‘º.(šu-øÈ‘ÊCÎv›õ6—ÌÁOÀ‡•—“*'mw!PÕ\$ûÇ
qfÍØwFØ&¤ «=_î&ÉXñ °ÉŒ?ë +endstream +endobj +1722 0 obj << +/Type /Page +/Contents 1723 0 R +/Resources 1721 0 R +/MediaBox [0 0 342 504] +/Parent 1703 0 R +>> endobj +1724 0 obj << +/D [1722 0 R /XYZ 9 484.913 null] +>> endobj +1721 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1727 0 obj << +/Length 1799 +/Filter /FlateDecode +>> +stream +xÚ•XAwâ6¾çWðr"ïC’MŽpK 5f·ym ÆX®l'Ë¿ïid v¶=Ù’GÒÌ73ߌÜkm[½Öäê9¸ú2¾{lYV÷éþ¾ß +6-k0èZwýÖÝãS·÷µD?Ú3wèxK×›ÜüürÕÓ«¿ŒÇÖ×îÓמ%WÞZ½> ¬Öíà¡Û{|RK#–å‚‹œñäæö~`µùF=‚ÿMÃ\
&EN“5ÛÛ«ïåd¿ýÁÅ ³®<¶uÛ·º–ÜÞ‚3}µ½ÕuºOÝ8û¡ßvõÎ^è
˜\¾Sƒœ«¯áŽˆ-UïD=6T¹PO£uU®AeÐW*ØkÝ>vŸ 4f4IÁ*ñ£1•C¶‚i)”é©D© I6*h¢Î©Øk¡|G´ FÕ{FóS… ”B.òZÆ\ÎôFd+(Ýà +„V{_dúX¾Î .LA–eƧ8ÿ!XÎ’FUð} kŽjä;ú®j8c`/5²E¸cïzÙ˜IDÊÈ"I¤^^8™Æ5^™&šÓùGBEÕú[¿½ +ôîV•yDËŠ“Ÿês¶Œ$ÆkM¡ÇÂD"ÍX‡l ØèõôŸ‚¥² 52W “h澸3Rë¾Û¾o{Á«¶bä.‡3Û}q|5žõ¼ýbOœ¥Üª‡ó#¤iI»güíƒöG¿_ªÅ§iLÂcõ¬¢áÓ
ðü5zUñTT%˜”¨½$Õ !M tØæÒ‘ÿ»VJk4yBG´+{†æ"X{þÃÙùçåP²Ò†5RI± +öcR”¢LŠm%'þ +ºó‚=tóuì$aø¦ +b¦êY¿Yr8÷ß :M :‹ + ôÈy±ý_µ9ß=Ç× lo„/¯†© +NÜ2@¸€V£#@Ç,æKðËÒU‘w*Ôo/Wð âêR)¥Dc•ÔVßLƒª¾³˜ÙÃß ª¾3^¡·o•6g×Ó#á…ü ¹ˆÔ¨©Z¦K[ó󃔖ê!ý ²S‚‡ÊLCy`ïšbúmvBFM(ê5Á%›êB°I—¯¡Šìy‚ 埽ûž<xƒâ +endstream +endobj +1726 0 obj << +/Type /Page +/Contents 1727 0 R +/Resources 1725 0 R +/MediaBox [0 0 342 504] +/Parent 1729 0 R +>> endobj +1728 0 obj << +/D [1726 0 R /XYZ 9 484.913 null] +>> endobj +1725 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1732 0 obj << +/Length 1672 +/Filter /FlateDecode +>> +stream +xÚX]Wã6}çWämÃ9Iˆ `aßØ%캅À!Þn÷´}Pìq¢bK>’ “ß‘%ù;Ðö…HþîܹsGf>ڎ棯'Ÿý“³»ó«‘ãÌ®/.Ü‘ œÅb朻£ó«ë™{þq䇣?Æ÷Þ—åjí¾žþåÿr27oŸÝ9W£³ësG½9uÜóòÕéâr6¿ºÖ¯ò4å"ËÍ(œ:cy:½X¸ãŒ«_g ÑW=Èv ©à›’™Ú w™:¸ÁÂÕk9³»ÙùìtêÌ/Ýñò5€43ËpÑZÆ Ç¸Mh¡¾!èv—é[<2— I€ÏAÌÞéÐCQÎpê©„z¯lgÑ]Í®/
G”™ +jÍa@U a‡œ=s¬5c´xCJ PRFsÕú +L‚œØšÆ>Q':†-1‹E +ƒ2!ö£ +»ÜЉ²Ê…úB ¬::Fy–‹.1藍sãå™CŸ‰>·' "˜mröÝ¾Ï Ãðo‰T,ÔF}2/ª~%¬æ˜sÄ`ßAœ5ÈòûPUoÓ94g†Eg½ó·R3pP7z‡ý ÑÖRf˜ÙeYúéì¬(ŠYºI4ãbûvÛUo-juëNóFËý?©hþ·Ïþ.ý“ +endstream +endobj +1731 0 obj << +/Type /Page +/Contents 1732 0 R +/Resources 1730 0 R +/MediaBox [0 0 342 504] +/Parent 1729 0 R +>> endobj +1733 0 obj << +/D [1731 0 R /XYZ 9 484.913 null] +>> endobj +1730 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1736 0 obj << +/Length 1519 +/Filter /FlateDecode +>> +stream +xÚ¥XÛrÛ6}÷Wè!3µg,š¤îyjâÛ¨I”N$ Ú>@$(¢&¨_ß…€¯î¤ÓÛ¼»{ÎÙ í#ôxñqwqó0]Ž‚À[Ífáh—Œ‚ÉÄ ¦áhº\yát1ÚÅ£ß.?¯oï7ÛõæñêÝ/¾]}ó,G oµð½r „ÓóÒñdîùË•Yú * Å×kaÝ8€%“Ð<Ý¥ôj<›—¿Jñ'”¹x¬å{*æò3STy2W d”²W»Ìí~\r}+¼d¥yDÌ nN +)¦Ð‰¥·šÛàf~ð»?ó#øs>™è³†ÆUtöÀþ™Ù?²Ðæ¤ êüžÂÙß46—à•æT™ +òÊ. ™8QZvÈ*Á_ \î;¡R)ªC*Ð +èŸÂf¨¦Ò•F{“Zûû +$IËòÇ‘êkoé¯ÌÓ*5§ÁÌ÷ÍÙ3-•…aK2ëágòbÍÜ2uº65åign-§A0·Kt>.Ïùi3r¶šƒå¢YØe4'ì\fûÀ`t?C.ê:šè\D îaUH©H0Í2tvX©ŠvfÄ®ÒâÒ>,Œ'BæÄ‹PR{L+ܶÕÛª>Ò½•CãÖ¿sc€íXÄËqA´m¦Y¢4&C ö€U˜Ä1;7³!´šQ—ïÏ…,‚– .‹ %=¬S íÍ
=BÁè;~›2j;ÙýwA©|¥ f ®ö 8ì¹ÞW“¯ûp è çÞreŽ-l㨚º&Ñ%‘ì]šÝ$ÿ¯xÏÿKñ hØÂXåX× +8bŒJªÂEð&¹À†_A£FÃG¦ê‚r„–;4p’»QQí3áFE¥ c* †+"#½2™ëáÅMKÉ`–Eà„î« ô›C +‰•@¥˜:Í,îC’HJ3NÌJÓàq?4—`˜[?5„ĵ^6ëSA媛rg3¤”C… +endstream +endobj +1735 0 obj << +/Type /Page +/Contents 1736 0 R +/Resources 1734 0 R +/MediaBox [0 0 342 504] +/Parent 1729 0 R +>> endobj +1737 0 obj << +/D [1735 0 R /XYZ 9 484.913 null] +>> endobj +1734 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1740 0 obj << +/Length 1151 +/Filter /FlateDecode +>> +stream +xÚWMsÛ6½ûWè(ÏX´HùCò-ib×$ã+ÓC'\Š¨A€fõï» °)±iNˆ¯Ý÷Þ>@ËÙ~¶œ=]|Ü^\?Þ¬gišlno³Ù¶˜¥«U’Þd³›õ&ÉnîgÛ|ö×üËóoŸ¿½>{ºü±ýãbW_?¦ëÙ}²¹_¦~å"Ínº¥‹Õ]²\oÂR¶gB5örq»JçŒs¨PûÐuªÑRpa/Ó9äþ[6ϵbصB«&|)°ktÕcW›8&TØ©q¼Œ-Ë,4¡Ý–ÚŒÁ.ÖÉæî.FT×F3šïh®°ñ‹. +0ñ«Õá×Ge!¡ÝRÌzµ +Û=+ GE\ Ӱ‡Ji0a¯½Á|RNÊC ãØõÐ@~&íœ
Cm\Å™R:ÂX±7˜JL T lÌ‚kÅ1Æ wËþ‰
Ìú‰”ù [" +ŸÆH÷ …BÈ‘ÊY€ÂW€«0àˆ v‹ØÄÍ9-;4´—.ï•ÐaÓDÍi%…Êý0PŸ + ‹yVH]ÅŽÓ>ì´³?ÁÂVá H 4Z >Áo«Í[3-=£ ä˜óUð’AŒ†$ÿ;3ñXÑœ(S±˜0§šŒ2Üß» +Žéz5 b?g +ÿú¤ÆY,>±3Ì ÆcƒÌƒ7úd) Fôk'£gï¼G³6€É¦óhlMé%äO‰²w\4.¬zâï‘R·¥06†v +¿ÙàrðWÀ9NI¬ŸÊ\׬‹2‚ƒ¡à0. `l“Š¶¥£dZ ;¹_NŒq<‰¤žCòPŸCOÙp]ÕR0EqŒÔL j0N'™¡~M:ˆpOê૦çR
²¿ëÈ3¨û+1ÞXXnþÅacºÊJvj3GZ^žH(ÌÐü‚q!…=<tñei’Þ§c—‹Fݶm² PçÙ~ÍbjѶ$¶ú; Fö0Ÿø6ûß¾š`ñäÂ+u;~Ùuo©©WMø¥7ÃL£óÑó +ó µSywÊÕÄS‚¬©XuîH^=× +Ú¡(¯N.è¸_æ÷;/ÆínÄÆgö›ÊBöç4¬%Å ã#9‰Aesïõ]\ÉèŸý~Þ^ü ±Ž€° +endstream +endobj +1739 0 obj << +/Type /Page +/Contents 1740 0 R +/Resources 1738 0 R +/MediaBox [0 0 342 504] +/Parent 1729 0 R +>> endobj +1741 0 obj << +/D [1739 0 R /XYZ 9 484.913 null] +>> endobj +1738 0 obj << +/Font << /F48 218 0 R /F18 201 0 R >> +/ProcSet [ /PDF /Text ] +>> endobj +1742 0 obj +[329.4] +endobj +1743 0 obj +[597.2 597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 791.7 791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450] +endobj +1744 0 obj +[777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 761.9 689.7 1200.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 500 500 611.1 500 277.8 833.3] +endobj +1745 0 obj +[531.3 531.3 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 1062.5 826.4 826.4 1062.5 1062.5 531.3 531.3 1062.5 1062.5 1062.5 826.4 1062.5 1062.5 649.3 649.3 1062.5 1062.5 1062.5 826.4 288.2] +endobj +1746 0 obj +[622.8 552.8 507.9 433.7 395.4 427.7 483.1 456.3 346.1 563.7 571.2 589.1 483.8 427.7 555.4 505 556.5 425.2 527.8 579.5 613.4 636.6 609.7 458.2 577.1 808.9 505 354.2 641.4 979.2 979.2 979.2 979.2 272 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 761.6 489.6 761.6 489.6 516.9 734 743.9 700.5 813 724.8 633.8 772.4 811.3 431.9 541.2 833 666.2 947.3 784.1 748.3 631.1 775.5 745.3 602.2 573.9 665 570.8 924.4 812.6 568.1 670.2 380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 508.8 453.8 482.6 468.9 563.7 334 405.1 509.3 291.7 856.5 584.5 470.7 491.4 434.1 441.3 461.2 353.6 557.3 473.4 699.9 556.4 477.4 454.9] +endobj +1747 0 obj +[565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.6 494 437.5 570 517 571.4 437.2 540.3 595.8 625.7 651.4 622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 750 758.5 714.7 827.9 738.2 643.1 786.3 831.3 439.6 554.5 849.3 680.6 970.1 803.5 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9] +endobj +1748 0 obj +[550 575 862.5 875 300 325 500 500 500 500 500 814.8 450 525 700 700 500 863.4 963.4 750 250 300 500 800 755.2 800 750 300 400 400 500 750 300 350 300 500 500 500 500 500 500 500 500 500 500 500 300 300 300 750 500 500 750 726.9 688.4 700 738.4 663.4 638.4 756.7 726.9 376.9 513.4 751.9 613.4 876.9 726.9 750 663.4 750 713.4 550 700 726.9 726.9 976.9 726.9 726.9 600 300 500 300 500 300 300 500 450 450 500 450 300 450 500 300 300 450 250 800 550 500 500 450 412.5 400 325 525 450 650 450 475 400 500 1000] +endobj +1749 0 obj +[569.5 569.5 569.5 569.5 569.5 569.5 569.5 569.5] +endobj +1750 0 obj +[816 761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 707.2 571.2 544 544 816 816 272 299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 761.6 272 272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 979.2 489.6 489.6 489.6] +endobj +1751 0 obj +[869.4 818.1 830.6 881.9 755.5 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4] +endobj +1752 0 obj +[885.5] +endobj +1753 0 obj +[581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625] +endobj +1754 0 obj +[413.2 413.2 531.3 826.4 295.1 354.2 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 722.6 693.1 833.5 795.8 382.6 545.5 825.4 663.6 972.9 795.8 826.4 722.6 826.4 781.6 590.3 767.4 795.8 795.8 1091 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 531.3 590.3 472.2 590.3 472.2 324.7 531.3 590.3 295.1 324.7 560.8 295.1 885.4 590.3 531.3 590.3 560.8 414.1] +endobj +1755 0 obj +[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] +endobj +1756 0 obj +[613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1] +endobj +1757 0 obj +[583.3 555.6 555.6 833.3 833.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 277.8 277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000] +endobj +1758 0 obj +[319.4 436.1 436.1 552.8 844.4 319.4 377.8 319.4 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 319.4 319.4 844.4 844.4 844.4 523.6 844.4 813.9 770.8 786.1 829.2 741.7 712.5 851.4 813.9 405.5 566.7 843 683.3 988.9 813.9 844.4 741.7 844.4 800 611.1 786.1 813.9 813.9 1105.5 813.9 813.9 669.4 319.4 552.8 319.4 552.8 319.4 319.4 613.3 580 591.1 624.4 557.8 535.6 641.1 613.3 302.2 424.4 635.6 513.3 746.7 613.3 635.6 557.8 635.6 602.2 457.8 591.1 613.3 613.3 835.6 613.3 613.3] +endobj +1759 0 obj +[531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3] +endobj +1760 0 obj << +/Length1 924 +/Length2 3648 +/Length3 0 +/Length 4253 +/Filter /FlateDecode +>> +stream +xÚ’y<ÔkûÇEc-[‘|²Á"c+…cßéXØaf,“%ÍØÉ–È ŠÈ¾ïIv)¥Å’}_²/Y{¦ÎsN¯ßyþý½¾÷ ÷ûº¯ûº>ßÏu ðéŠÃ 0vM /•€* +PÃ"lñH ZÝP +0øy p¬ÂA …H{<`‡pB¢ÁŸš´ÐŽ@ƒ§ûßG^,Ž, +ú%S ‹tÀ QÀá†èbÈÝd-ÿ ²þ]\Ó…ÒµuûYþ—Sÿsnë†Dþ›qs÷Ä#°€ÆEÿ;Õñ—8U êÚhámQH{8Ú … +!qšH „ƒ oï 8Ú¢pˆ_qÚáßÈÆý +@tùÞ ÿÐUI +¨¬ /#ëÿ2í=±Xÿë]“ø7;"ÉãF |öà¡Ï{Å —¤êü +ìÔ ÆzóÌŸ¶§¯w,gé ©ÍÓ|å£xeéUù*5HVÎL3e \.(ÍgÀòØ#?L&tÔ›%!þôè;R€K(mèȦÑóìA퓇'w(öíA‘‘8®°/xzÆáoÜ׉þuã•râò°ÖéŒùÂÌêüª·:bî–Y‹ Ñ#M5 ïº]«ËÓõ•¦ÕG»_p_ëm±%Æ*ušìj>é='^:œ´é𑶉ƒxÆÐÝõ (¥| ~—ÃQØ÷ÃàVÖ®ŒJ¿©¾?¦²ÏøÃ4rwA¶KÌœ49Ûy}ìzNÏl‡ ê¥Z5f¦ÖÉ¿d5+>LõÍIÙ6wóÝ"·‘)]BÚÖ`V–ЖD¤5c |cN÷Ša[&x™âY{…B"óÑbWM:&8ð E´tDx,ÈçõÎ1WBaí´[\WTèXéµ¹7ãTë'33…¼ÇÓmðy+9{S—#sZîæ:ž>ßÄÌ´Õ®”
Ì +Wè +Õw,ˆ\P›ºÇã½éb$T[öš¨:†èíÒ½%ù-££Ã©ê.é=¦I3Î Ð5/É–ÉÌnI-ÛÙVSÖ]ë´¹þXr™Ö& +y\G]×wofs_üÌ•*^0}5;‡Ÿ}Xº3ã¾³¶ÿ(ZDÀ‰ˆŸ›¦|ûœ³ÁjC»]ÞAÿtüeÙ|Iù’;[Çè!Öã4ëeæØý)ÏÆ„•e_ý€°Ý³®òDÅû!«üFÓçvÞ˜r=b£+KyŽôxb±½%\ñòü½ :!°ÆÈ¢›ïEf~æ[;yqö¬j?-'vM6~üŒ4+J C½ˆ8¹:“é¹B{mái|ðSËÛ3¥ÛÝ c@’dº`²Õøë +ǽ¼-ÛýLQFÑ#מ¼óÕfײ¤S ®2ÄÞ´Yà1ºzsPƒõmº˜kíN‹ÃÉ;ûz7«¨Gïd#hHÑŒÆÊAà%Q¦7&Dñ…t"Bû¦:öqÝŠI¬‰6—ã‘ +Ò‘W= žmgòv.P F±IRÂn gßlð×,öËVD´+6d†½U ˆª—´9_Äccu熷…SGJ =*èÈì=¬7«n•¼Pü@ßìÛìdÍèõY¨^ÉtÖj@CÞ"Á¼õóŸÖbÝ.ápVéñ¬ƒ žêÞÙªcMŒoŒf<œB¿ý”‰©\Ð^¼f$•åñög×öŠÚ„ÄEÃ+ÊItKžÒàSX&/uvé½ÚEª ¸Ò‘óxê'uæÉ“SqϪ«|·ð œŸ¦3Ç+|+׫NÏ[9`\Ÿz¨<™—pÝå +ã —œ8¦†iÊ^ælu~ƒ¸ñ.«žiƒŸù‰?çm¯krxÎe7…væPNØýl'¹é¯ÒúiÃ…Jç˜ÁGœE`aýÜ•‰ ™YHþÔÄôÝòˆ o®Ý1Ñ.ºYp 7 “zÑ3[fèèäü†Ö×mT‰:«í^h´ij#¿´Œ& ~âuêÙ[P¥sµU¤Hð,çð6aýtIV®ú ¥
LµÒ—UI¢–wLc¦å©Ëcú\Ÿµà1*Ë’&É~H“é’ÐÔô!ê%l»ñ\ÐoC/õLçhPü!² rõiq_ÉÇ‹P-^Éú7Ä•9Š7<:Îs…žNUÏœª˜LÚ–ð‡ ŠIC—ç RÊ9Àï?ôôž8LÌäò}°½™þac/
^¾'êÉuíËϨ¹w ådÇg3Hr‰Ó>{Éð
CGÕÿ±Á%¯d«Z’ö"ÛT”uS@k¦×ÈçxÝË´žéðÓ¤G¨©Äîºt’|xQ´£Å,;žÝàó]ð%¼§ +×…ªìIvÖ‚>eF&½Ýæè±ìp úÁ¬2«ˆËÕ÷ +2}'6öëÅ@ŠÂM¦—plj€Œ”«£Xq[LÿÅéËé— ÖìÛy¤ÃÄŽú”ªúØ÷úµ¿«íŽÏJ•Vpš
R¯OäbDT´÷ †ÖÏF”5vê~¾õ„öîÑèÜèa +'á{]Ä¿˜—j¬HÜwËH\u q ^N ]ž
ÕãiŸß1 4ÔÅ#¯ÓØkœªªÀr‹ÒÉ‘¾ßQÍÄ/»R·Ÿèiõ¡°vW÷;L\èe9ÊW8þ˜¤6ÝEw»Úʸ~›x È §Sy9B¸w͆2tÞ +ÖZSç,ÿ\< l?Ýk«u*Øﾆå¢FZ¤a÷ÅPZS”¢& ûM_ÌÓÉ ³TW m.³Ê¢W*L‹ Œý÷l.µxÙSîq‡´ÕŽ|ù&ÄbPcû]‘-²µÌˆêõlo}Øj 3ül²Áþ¸WÎ~*äŠ5Ð'sŽ1ˆIV†«}ÛF¹E„žmL¥©Œ´¶»Ö{…Ný]hÂZÝ°¬ÜëŠÜ Ñ ûåw ÷@Ì',½Þ½
àÝŒ÷Ï;QÏY°«è÷æé#
;Ä”Zž/ï·zÑψ°–
Ô˜.vB4ÿfQ~Â&ÓK— ¦Ê
fëQ&)V9ö} øEûa…:¢c1} +g}î8Raàû|üQÞ&ƒ“ö®‹þ85;k²«£ÈÌÎ)/?ëØŽãö8|r¹ô’¢ã }ÑÚÍTôy³?5·‚Ø‚“²Añ=û±Ö(o÷%¸|Ö2×Ò +úæI,MCE±©_pBá`Òâ…—|ÇçÆyPø“æ¬ç}yÑ©
«¡/›ÄÌÁçHº<%‡Šdf1áñl‰R(ÀëDÚ´2íë +o;4õäá‡^·<±\Mt!î?O?A +endstream +endobj +1761 0 obj << +/Type /FontDescriptor +/FontName /EPEQML+CMBX10 +/Flags 4 +/FontBBox [-301 -250 1164 946] +/Ascent 694 +/CapHeight 686 +/Descent -194 +/ItalicAngle 0 +/StemV 114 +/XHeight 444 +/CharSet (/A/B/E/I/L/N/O/P/R/S/T/U/X/Y) +/FontFile 1760 0 R +>> endobj +1762 0 obj << +/Length1 1354 +/Length2 6967 +/Length3 0 +/Length 7774 +/Filter /FlateDecode +>> +stream +xÚ”eXÔÝú¶ ‘”IiéîºAºd„!d˜¡ iî®I¥D¤;¤[ºQxçyöÞÇÞÿ¯ï1_æ¼Ö½îëZë·ÖbfÐyÁ%g{V‚Aݹø¸ùÄ@Myc>~ +`C…d "ÚÀ Àl‹Ç£CyQIþ„úßæJpD äôWû¿wéÿŒƒœ ˆWÀœœáî`W€&Ìì +ýßR#ð¿ÂÉà ÿÇFÕ q°–ƒÚAÀ +Þüwk±ü·,„šà†:¿ÿ0*˜»½+ü·ò/‹¼<ì— +Á3>Ê] +¶tv¦;5õà™èÉ`Å?eŸ}SéÜbª·^+}¬xoÛF̨Ã4± Â¥ºX;½×Ÿ8# ؉',eŒqQ0$>”\µÂU$ wl«)VŒ'ÖB=9] Ô”/q§Þi { ûŸ×”ªF) +Ó\-ÑW°ž ñÙ©K³°Ã¤1ùiÌ
,˜ŒÂÃ6¹øló;§dkJªX‡ä øœ®ŒB¥r4ç˜ …Ü‘‹ÜÚ\ZQøÀ‡úC¾‚Ô4sÒ,ží ZeÆÁ§YG8À[ ¢ìŸ3h‘¶ÖñÓ§òŠ\S¿òeÙNùÓ4®>æ¦Ç÷$½£^sÉæÅ¿5¶=œœµì´¤ f«Ç>Èg ÷U±ÙNï©"Žô7?.-»†(Yoñ[ØIn‡×G¿ ÈöÍc)1:ô’öÑò^% «ß}Ä+ÔIY4s-¨"Hö§hu> ¢œ%½ŸF’£ïÛ‹óiM=’±-¼dÅ— ð-ü5š8p-oçJK‚3=}ëÂçÈM¹’ëö\˜•8 ©ÔÏOøee3Àð0ŒÛµÎå±P°/Ý3oø&»3]üDK›5Á¼¯V¢«À îÅzŸ³ä»ø ')„nA2] Ì%Š eq'šçëd\»yÁѹ–6£eþÊì.AAºyŠ çÅÌÛ¥QJ¼•wü“ˆ=ÖÒ²à.1‚ âguVûï¥"ììE¶w‘kÏ‹NÀ@ñ"ÚŽO‡[á,üP—ž ˜ñ¹>”“Öþg %l,§¡Â÷²¥b +Œc!aÜ€2} =½"P{?€¶ W+¦œ¶ Ï›øßû_ÆRRªSÕ8‚Ym«©œÙ˜’àÿèõéqÕž8Ø !hµ'Uƒðyûs³†Ïõ8C ÛMŽWl›d7O!µ§_;È€KεKž¾µžV£F‰Æ¡ªÇ†ÑYS.ç^DÑ $Ô·¤Þ´IžÓ¨VÓÃß–æÐÜ:× V™*ùGS"1gÔð˜ÛŠ.„~ »ÀÇÆ3RŽ7‘¹jö â0nc‡;[–&DçÂ:Èxà¬/¥©Ät-ÓW¬Ë'‹_¶æº‰»—ba= +7ôLÁ-(åÊ4 ”~%»ð²>ÑHè&¤{ÉãS¢Ç +›H+õG½a陫ÔùËô¸¹“LéËÓ'mînèÄ8+ôžºÍÐ[ªËŒ–ÑO
/a狇5U9r_Ç«Ûɽ¥cÀß ±]WL0*y.†1¸Õó´ÆP¸Yøa½ª¡¥Ô2(å’‰Ò¾Tjr +˜Àw²þ)ŠÞXh§à¶øe²³9ìKËxB”ÔçÄgÕqØ{-:n˜) $Ââ)°G¥òØënÂÏ÷VÊÃBö¯ö5Òýã"ÛÑå Ö²Þ“/G<TeŸ £:µ>|'ÎÀêñ5Öåg>\ƒ6§mV[:[ÈZ6
pþLt‡Ò)媼tQ"AÔgyŽ 0çÂ,Y|Á5?"îº1h_ÅÃÒû˜h߸tâ—ýò× +ñ1µ¡ÐKm 9
‘)ÜœøwK§ËÓŠtìÏÔEDL€M‹O–y
×Òü’/Y§TB?È®0>›:ê0òT +¤ñ¡Ø¶Td/^L‘¾ I9•¬Ø Ï2 ¿þÂúuÂ.A`’Z’M¢køúèÝ¥MzbþKLÏa{®…ç9®%_®'§çà Í+UrÎÅÙ +Hç À€ ”:#nÛʇGFZ̯6Ù,8 +ÛúM5TX˜¸rr]›"BïlÜ)CL\æÓzsÊõÏ÷µ4!”×
F7zÇEìø´ž§…® éú·-§ ýÎ sì»Ö6d¦cŠhMÝÙ + ´;k7óIïsõ. +—´ïø²Â´§!½P$¦’$²wš ž‘©5LJnÄaLúµ)õÂ(»‡i~¥G„é¬*aߨ½¹Í!s (SÎóû¬Äc1Ÿú©Êàå1Aýȯ(•wLû=Ofû@*)IÉi1ÆW`ï)0 +4dý£pá[CM>³È¸%ÛcæŽØ‹<*Ŧ´ÒÏG‰Ò%ÇqÝS©à‘é@“]¿?Ÿ y`ëÌ‹:ÃËýô¿ƒü%–à⪣nÁý±r_½²·qBÜ„U»Êg™ÊÉV• 7e¯ÃSæ‚ç”AÓŸöçÂå<6¸šSß9õ&e>°?öÜœ[‘ÓÛü¢®;¾8¶~¹Ýîl~W1ÃÁ>¹áôœÉ¿¡?l0ÿt*±— ©É0úg +†m\^ˆh—ÞÑé–Äù lJdúQhëyÑö[/amúzÄ#ê¼lfÏhŠæ ŽBÜYµ¯cEañº§%8¢ôÉÞ Ïvìkù×Ô˜'ö³ž“:ÒnÓ'Ì,úLiRÏè[(öv¸ÀAã·Î= íuIDF‘÷nûº$©=×ZžŠëH&NcJ¿X¸ÊÌY >ï4§ø³@on å4àâºþ‘<Šºê¹*FrëþPÇpš]VÔ |1é=›”À ü20‚eâ7¾·D¶>Cfý܃*>„$$Ã;f[§ª£"Ýý ¿²\U? +rÅ—ÒþdàÏfs +Ó¯™ñàMÎT‘‡u†7žµ˜³ÌŽ/íÚ}Ð#ú@kºûø§Lu0WŸ6ZÁèÄ$ã:+úÔPuÇG è Ã’—l–ùNÜ݇dÂl)—çWyÜObc&-Ò•X =ÛgÄR éB 5-Elý’^V®H*í‡@úJ›h’d@ã›"ÒòøGeY¡ Ûp7Nöj$Å‚|5q’BŠ§E[v¾Z â6PÀFÝæl»ïvíºE˜"<ç½mô¯êºÝ´ +UsØnb/¤§—þ–þ6wß3Ç$¥D|û܈ÒT/$ÿ"À
ù•ãsFk1¼9ºòuˆUk¥âIZ¬¥í²”&‹°ð”¯‘×dn±I¬¾¸±TJ@Œ]ÁÕtM#(i'j”ò‡Ÿ¸ZyÕ(˜![½q8?¨àÅNµ= Â6,;®0¶ߡHœ_'p‘ÿ(œ]úâö<ËÔéqÚ²µ¡Š ÃZT¿mR0{oJVPƒŸ¯O`ÞÅø‰ã´Gc¯ EÅý¶& mòßuz7mÕdÚró„óÌË™©Cút¯¶TnÌÓõ¼±L€ä?,ƒÄ·¢®™ØÜÇøŒM<K?¾ñSNby§.;¹Ï´ ë¸ínò«¶î ÈågAïl8k¢•J–L€ùä
g¹CG¹ýÂUB§ +Ç3b±[ÙršºÝ—.ð
;úØÏm Ñ@€ZÝ.¬ /~á’Í}÷“œÛy{™4t^²ûJÅÖý÷©kîâ7|ýu®b"^~¡:8ÈþçÊ>G‹Ö~\Ç“5¢ïHÜ.¯òõ©Ûá«Däs×9¹PnlÎ ÝáÊqÚ)æOÉ0°GcÖ|èÿØ2‰¨,nmþ¸ñr¿{ŠÃvW«(2ÖºòFú«ØÝfÙ1v>i½sX•w?®pç“)š»÷É–üf¸û7W°‡¶~²³@¸£Ù"·‰ƒcÖ®“
d ™ +ͱ 3PBU å’ÊÀD’E)kM~Š»Â%݃wK'Õ¹l@U½Ô.š½ñßP¢dAÖ•7jëó¬ÞV Å[¤dŽŒþ8Nh„”–Âé.ñ¢Ä2?kÔ¦3Øx4” Xyu±³uJØ;ªNß"³ì*Ñ/9¤2ž°msf“ÉùâÂœêa¾ÄÊ‚FúŸ§ ®õÊ»À=]@ßCÌß~GÓí»ø5 ;9+à`h7ût÷ÉÉ gÇ´þÖ3JÓŒ;£ÝCÚ .Uõ±g¸Ä¿Ù œÀ +Xr”ë0,Ý!pg3פ&i‘\.9ÿ/åëhœ™Î‡O~yƹ ~úTVU2æžñ‹?u ñèƒôø¬e/t_HÄŇ€d€DHT3ôiëCl)®Ü +s®ãÆ KÖð &øx›i»‹mNÐ÷»–3éœî}6T‘§2Þx¯#¿áŸ ½àWeôºi›øáÚ™Nx ývßµ¾ërñYNTcÜhD$ö6¯…¦Z ~e>Ôxràò=ãGEËG#H:‚•ÎÖßç%ññПê…}Ï<Kõrz æóÊt?x ¿•t¬ÆÿÔc“O#Ðõñé›F&<«ŽTû÷@V?ºêèå>XoŸé3±‘fL…^Lijç‡Ñ[È,›Lõ‡ ׇ+™ôJb.Ô®;HêLuiö£EÕ²pÚ¡dv>ÏÛÄÃ÷]ÓgUMLc&¹“†¡ÑÚÑØx ø¯Ì#»ª^¯‰Ò™/<¼V¸»1ÇaÞÀ{{ßbN\+}S 1µŽ2mEñ?
µ¶wñö÷I¯dÊiê¸$yªÁ¥Ñ¤nõæ9Ò¾Õ° j]¿3Y‚g).¿TÇ;‡m¼t)ë$Ï ¡É³ :Y%7¬=x6œÒ3¼VÚRu÷î±çë8x-c†ÎKß/ñ*£ƒ& ~H2øX_ÿÏ~›ŠÎžù„C ô2è÷\kx¸‹:˜ãY žFÎ8ZZï"N´ÇØ÷ øÌ]ÂäëÎÔç[¢!
å±þœ/±O3cצ~7Óþº\T¦=î 4»“kFÜàÝE>&yÿVO¬ŠD×€ÏrZ)ÐxIÄL$/V gj•5õiÂY˦sñ^³2Ð>\&Õœlx–?;¢±±6åe_ßÈWÀlÜžý-Ý)3ØKÒ5I©Ê1øPþüê üyÜ@11шãä+®©ƒÊ«¸àB‚ž»Û¹T™üì“'JÃøº’·™Ù”Á¢£üˆqÊۥݷíihý#¶W“Í›¤yeáºÄ¡›œJiKñU }<rÃëÙPËËx²Lâ±?FmŠþ¤fË<çg*h 6Ýç1ßþ¸ÃÓL ¨ýAšùb›niåRÚ-T4Š\襳¤>HvÞɬø\)òÝ/¹$Ë!F-&–‡*U8ªV!îØZ åé“n¢°Fg<2É‘8! KYi8 ³öaŽ¼ˆTn`ŽÍãݽ»t¤ ÛpÐÊ úÐÓø˜Aâ}Vž}fl…7
+>óçt–B}Ÿ* æ+ÿVŽk&Çn7 ôfiÜÒ¾ ÂŇç,nQ—"ý[±ØWܸ[<¦|² ¶nUÁ¹üåÏ@«Ô~¿|g4/³â/å()~”}*™ä®&œï°0 z÷-ÉÔR?¢«ÏÆ_äq•B
<¾›(¶šô±PPæv Ý* ÃØ .Ç5š]`.#!FaÃw£ïc#õ †Q£hÎ]Ý @}o„b60?à™rmÌ YYTCûläª6—yD:Mt/¡ÚÃ!ã©/C:ßVI2AÔu!Ç—Üý&äb¬LE<oˆ ¿da¦½nÓ¦Â:¢wýLfàÉùDˆEÛ BÉ;v¾jG¥ò@ (ýYh‘zdáHàã»Æj3ÑÖ¯%8üï•Cs'mý"ϘJ~fzž²ú&ªŽÛ$ YT»$°ZÈøÂÂR^šïMNé¦á~á ¨ W×ÀÒ9þf[’ùA †äňïìâ¹I|Sž_f”W™¼ª¤‚–å¨f9zqÄÞ)ûMeÕT¶ô±—…ÝÍŒ\°DôÃÑfYwÑ+é_66nbx©S®â +#kÃAŒ3×ÀË-’n=•Þ!tÖ¬{VØ:RCè’*|q,C3å•2w¤¸¥Ùýä©œlÏeÎòÛ6Ívß`›‘ª yb n9R¬×‚d#Âw;9Gi¸—·m4ÚýübæÒ^Ž=L¤Öhü0vk™Ò–ô¿ðÝ©š>¥ûê6Z§_„îØæQlÀ9£_7Œã?–yIÔÞnØ“¿Àa¶B…eÙ‰âûÏ!\wObÄ&Ü ÒuÇ”ÎÞ¦^y]ŽCÕ‘´iŽ‚_Ý*£´óRÊûé‰[ÁÑ£fXÅâs‚J‡,ªÃ׎VZZ©ón‰l‘OWÃé»OËEŽ"ß>‹N#Á .c{‡Luýi^@¨r<Ù ‡•Uó‡%±@Ñ‘Uç%>KÌÖ¤=g¼¨Ç]ã}l¤d¨`ÄlðóÊ Ûbî«ŒÁðd(om𤥠æ
‹AfæÊðs‡è@ý·ºU6$"î£ôAd°tCHž,2Û7ãÈœ±Ï¼OA€#KÁ¼™xá©¡³˜`¿‘þ‰öÝÊÏFwúBAˆ¹fã×á:2Ò®þǦZu_b™¥¡Ø yk¯Ö/cùO¿ñüIÙŸª‰ˆ·ìÉ*Š}fãé!*P0º +endstream +endobj +1763 0 obj << +/Type /FontDescriptor +/FontName /FTCQQA+CMBX12 +/Flags 4 +/FontBBox [-53 -251 1139 750] +/Ascent 694 +/CapHeight 686 +/Descent -194 +/ItalicAngle 0 +/StemV 109 +/XHeight 444 +/CharSet (/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/ampersand/c/comma/h/hyphen/parenleft/parenright/period/question/quotedblleft/quotedblright/quoteright/six/three) +/FontFile 1762 0 R +>> endobj +1764 0 obj << +/Length1 756 +/Length2 1245 +/Length3 0 +/Length 1777 +/Filter /FlateDecode +>> +stream +xÚ’iTS×ÇQ¦ ˆ‘JËAæÒŒ$ ”™ÅDÀ"‹¡\’ ÜÜCD&0Dk‘IJi *”*N¨ }<¡(“ ‚‹Eßëëzúõûåî½ÿgïßùïcf Lråb1°†ŠI42ÜÙn»B|hT@#S ffî"#ê‰a 98ЀkR Ùš ‹a˲ÁEÀ JEH\¼Xº[-‹ì€« +Ì
DÄœx ñá•<Œr?äÀÝ[¡ xlغÝú¿‹])B*‘ +a@ý[¿ÓþŽq›DH +§’©T.Ä¿÷‘ ŒóD9Aã +á7ÁK„oã憥¤’è€Dgâ½év `Çd¤ÿ“$Á¨xå½àž¼cÜFN9„þ^Œã˜Í;Ö˜{6óüNµºU¢¡¢*»£5çœÂ‘<5è¨{OÔÔ 1§“£ÃCj>•OûÕR¸±ÌG®i7Rƒ)9}:7Öm°*= ¬ùŒ3µº½äzÛzÁÉýcýF£Â&ëg&Ê!I«zÿÍ®Ì`ú€ÚÙû½Kó ™úµŠ¹&å„È’fÿoá¯Ç‡ +n/>õÆʱþÊvbÄq¥Þ›~ƒ¶‡= Ö) –°Uüö ã‡ÀLƒE—Ž)8šW64²'®¸ a Rl¬Ö2–<™6ÉDú|ÌÔÇC¿e‹4[{
y®”·ÓoõêžÒHf¶t…ÁJ9wÓiòm…ΗõŽ7ퟆYd ¦Õ˜a®5k™3zâôªïÍlƒF™RÿÑÕoè6:KvÞÞgsMÉõZ‡´ÇÊì÷¾,i‰…櫤 +Ùì ;¶²÷ÑÇ {ûEF¿0"þ}.+wîùw×{ÑfÎç½Þ¼À¸Šï*ͪ¾ªÔκ|çµ ©Á?ÌçFp# ¬i‚¦ +|¾ìtjå1»6Çη°ó¯Ä[t¹AUªôì ¿ýCfï ^æ&‹…» to(,½ù º–s40.þURjßç ½¦N(5gÚ1§4ù‘‡ròæ{ór;Í5 :ö¼éxÆ1
‘MlÔ~¡£ R{ÕãÆ$·¨8àå.{<¨1åå/){»JuSóèA;I»y| Öß™I–9EOÕ˜ô'„/íð5 6;;“¦ŽbÛj~*YPrk"^Ôñ\Æ‘%‡]9gŽøê t:-c‘ܵZÝû2‰1†uA¯wCŽ@5Ët{㌔t‹¸å’MQ›ü’UÙƒkk¶žÚ–?¥z²5,aÕd'ó¾ê^œ˜œýu`”8ÞO2É|30gúÚ›±#~§ûŒ‡Óeµ yèú0¼g½M¹‡a ãwk‡>.í7\øÄ!Ì-(]W¢Á\czs›!&/Êû¹ýCmú‰±"gúˆÑ‹_ðöž¼»¿ âæ\£•Þù¥ ¶¡.%Jb~uÚ±+QuÉ)]ªã *3«ïl‘u{]š‰ºwÏgÍC¯{”º•wÚ4‡‰²±¶#óæû5gµÃT{ 2ó_=¸¨Ygïl»{±|¸Ìv÷ákD4È¿ÞóL®£Ü98éþUïðÁ¼‘ὂãÌKê˜æs· · ÍÍltúÃóù·® "Ó4ó,Š¥çˆË9jö¯F/®Ù "E)Í£3W¢›‹ÕçéenO]¥4áa CŸ=»îX—t 8Gºº²|<M¿~&&Ü,ªw—ó壴—-“·]•Ñ¦ÏšòÕìçÿ QQFÝúÑ/Í°ïÅàЂ¹é«TÖ5ñ¤(ú…6ûÓ“Ø\Ç]cQÒôÐt_<?|špϾÊî€ðÏ˵òó¤bïIý —ÚO9Ç-ísÜi”…¯NÖ³8Üê“RõÏS¯6T¿ œçŠŽx5×~#,_ÜÝ– u¶ >æ[T•!G-~<ß½xÜrKlUeBgdúéÝ ·¶çùŒ{N”ôý\ÒP¾úbšîDF*¡}ÕÛ, ¥ÅD[‡]»Ö©Ëœ@ÝTìm,¿ ‰Ö™ïÁMѯ[¿VQq©WË»-` úU;t茯NÞ»çûÐù8ßEŒc4c9 +Ï‘k~"ÿ• Y +endstream +endobj +1765 0 obj << +/Type /FontDescriptor +/FontName /DONXWO+CMBXTI10 +/Flags 4 +/FontBBox [-29 -250 1274 754] +/Ascent 694 +/CapHeight 686 +/Descent -194 +/ItalicAngle -14 +/StemV 107 +/XHeight 444 +/CharSet (/ampersand) +/FontFile 1764 0 R +>> endobj +1766 0 obj << +/Length1 1438 +/Length2 8414 +/Length3 0 +/Length 9233 +/Filter /FlateDecode +>> +stream +xÚ–e\›[³öÑR(P¬¸w÷âÅÝ +âèà°Z£±«@`Z@˜“ÿ ¦þ»¸¬›ƒƒŠ9ø¯òÿ ÓÿI0ƒ ¼þ_ +ìäæ +„”!V@¨ã§êÿq§ ´¹ÿ{UÁÕÜd)áhã +ähàâå˜C¡æ^h°Û#^€' +¿ ¦§ô›`zÊ¿ ¦§ò›`zªÿ’ +:ºþýjƒðØx Ðh‰¶8± +±Kk+ñ—)˜,Eft!Í(íËbÛ_™…6NhÉÏ°C±í@eX©‡ŠìVÖ¼kD
¾ƒ>šì¡ ؃xŒ 25QŽ-÷L†òz^‚s"w)¶œ™¿Q_®ºw W)íqòç F!•|8÷·[[|‘nE½Šfœ×ª”Ôù±š0r{ )€,
e^â>.õ,OÛ/adFç)#ÎeˆÜ£r0zZ¯¡qì»#$ñ'`NÔ¢uõ¾—a@R¥³ÿà³>˜•|;0//Òßù3¼mÔcmê•¢IÊ&œ3DÜl–l´À•ˆ(:Ÿti¨¨ªÁÄðU\y^"„ÌáE<™îb/m%=/aË"›Nä%Gd;]lÑ–íH\Y©¢çƒŸ<Nz‘e¯ŸšR„ y‚·™oQÅ-ÑVcÐzü\hs÷¨!Ž5Ч²KÍ}ôì“”ÛóÔl (“y0B W®ŠLÌÓþ2Ú£¸:ˆ¥]Vtf ðuJ€8÷¤xÀÏìÊ~Dçß¡i«@ +¯È‡¿;Ù")›&$ +*&?ÝEùEn<4¬6‚¿àÄJ§3‰·Èî>þB£ìû;¬MéÖóÂ>p¦XRž8ÇŒ©×fà/}(O\ôÁ½R«ÒãýOÏŠŒ,Ñ{•$¤:.nÂR-(6óÆ$2¤ÑŸû–‚~<Dgí%Q†…å/Òê€çÂ/%Þ#!ímûÉæàg‚…õÎ;œ‚¤eÑî×5ìLŠ î}VQr§¤‡„±êñÙ ˜‡\ +Âq</àðG¢5%ýÀy„|Ž~©x)vtÞ©ÀaÓÏ‹þ¨©}¢RžôÄÔÄGÓ£†ãŸ/R¿ÛÒÁ˜üJ
i`:ƒkÔ½ÄÝv™Î +½eŸè +_¬]AhSL³-‚HÙùZà pŠf¡ºÖ‰ªWëó ç± #—‰i·Äд²ÄÙôHóÙÄŠàƒðB ƒì]6îƒYN°©;uµ ½fÕ"\¿£‹Ñ[€›uÆ`=>B©Þ”aJJ öen{Œ)Ñ[ïg¦¼FÔ´fÆ<(ÎÎóònâÏ*×ð†µˆ¡ä/
2@®³h<
6’|¿ª-‡DäP”:CÓ4èÊ“M‹Óͺ‡–ƒûb#…U$ ×|c¼ žCõü¥ý²ªVÖý|Èܪl“ɾKwqMp¿3FÒÔ@f^¯Ðú–Yv%V
béveU›¡_ê©Hb}þDƒ {—Òaþ( ·ý3«ØÎÛV¯#„êó§Û*œ +#žñ ª8j\ «û]¦Rbz–› +Sˆ6{½Wz‘</tb03}˜uOÂëcd¶/k¼t˜ÐóçûþcT#ÇB¶¡•Âv`1 +V‡ný7?Ù²¡SáÚ¦}4á÷`½Q÷Ð[¨éÒfy³úª;G HJÒžºÉK7S*N¤ÎŒ±b´§ÝN¹Ïe@læÍËûÀF¹«ó…¯ æ•huœԉ9/XÕùi¢ÑTt©&7{,j? Ò v,Ü|äIX² ¡Ó¨J(`dsž²¦ë¢%8ž¯l3šm‹:W óÖÍšl j£S8öWõ¦B7HÊtŸ©™hWo1IQYq)\Ó–@ƒ‘QPOïDœºj*‘œ.@× çôò/l4ì•"@S„rä-ðU±çΘEÔºe¿ WŽÖuºE>ùÏlz–w+âBy7ˆˆ
9kg9Ìའù1ë碥’„áV¼¦ rGŠù׋ͩ3†F_÷R5Õèd†NÑ™Ä鄸νIW ’o\\¿ò¥>pQ ©'Ôç(ä—bQú«@Ÿu„Õ-Çhj8ìõ»ª'|ú9$|³Nœ±ÉR¿Ç*Õ/XX=)Ä’Äv«… ·6e°'X‰…g_ª¾=ÍÉ‚§\×½ 0ÏDÏpˆL±L=lȆKv™Óð{‡â>]6KIË,556D ¡úH gÿtO k^³‹Ô¡l{ïç\Š
Á½ºÊéÌÙ\žQ»ºÂq˜©u‘ø:ýª™£oN¶[½ œ:ÄQ:rðµ +vUAï2˨ ö—pÆaÍ® ¢»‹)lôÌ‘pû,AVïꉪãü ŠÌ_ËuŸù÷œœxìMówº°E^÷Éz?=ô,/Ü€‘Êi#‚Ògªkzu±'5Aû
Umþ
¦`Ux«¨·B+¥Ì¡zV* "ë’ãÍc ±Ó¹Ò®€×§Æ(Ò@›Þõ£ij«eÜ8éV–ôÒÀt³þ‚@Ä3¥SÌÕˬ › &ÅÒ%¼ø}áðèî«û²r‚å4•Ø$ÅåÈ%”åÂzA%ÿžzÛÓàS¢±›iôÔ‡8¹‡í» ·Ï~Ö +#Ñb¡Þ¶ª÷å'Ɖ G +³–w¥ôEb$—ÝOêÈF梾vª÷)!.Þµª+eˆ]ST…ï'‰ 3¨xå;\ŒhÛ†®ê±üÓWzZòŽªW ¤N:ÞS ±ï ºó~ìY¯˜QyAÊðy9±jŽTŽBó¬ÆM_ÓøÄ)ÌA¹Nü¬?p¸ëë×]ß à±#D|6W éÆ”£™žd –)# "ÑëÙo¿‚œko½„Q{î´xÕª2µvíˆÜ/ +&"ÌS\3ý,Ì—iý5'éq&ø-ê×± µïØ—E KXy08‡ê°â×ɹä2#Šä ódÑfWꨮ‚ww1\TŠŸ½wE4Ó‚ô7m¯%c¬Å ‚çÊ(uûÏàéJ¢€3ŒBÂÛ_ +‰}ëI'Q~Ju‘Ô¨cbŒT zˆgëpùðÄc˜Y6’Ø.-()/ÐëR«±PbFÒóê?ëÞ´ªËmF. ¿ÄÂÑÖ5YÉi¥
¥dç:m'0‡#'þð¼rÓoGk;€LÑôrÖ†Å[b©ò»ù«v•c1°ŽXøÛõ«lá ÎŒiF ¡(Ȧ<å TÿùbšVìRêÑæ*¿ô•º ˜ ®fn)}&ú6>¬@ñžBl§‘:×C=úΑ|ôUW7/.ÆŽÞ«ÊÝ"]eÙÛ ¬Z\%Ÿ™ õç†oÑ£xwè²û4OM}ACƒ~= +‡° 8ò•{N[=-Â/òY3›£Ä´4E¨ê°:çŠ#Ws lB‚™ àêŽ_,\?>ÒTE^þ & ¨ÉQ£tÁ¾«±BBuò:»HAÂÃ-¸p¹•’åQÍýЈôð€]‰“bW!ÀBÂVžfÓA/Ö R’eºhN”© ~¦wõýW}WQŽvôþ§Fìwd·Q€ná\ªµ©óר/9)L“_<sïmyKÑÄÞÖÔÞ;©ã ï»ûá½Ä€ïR}ÜÀáRÿØ÷õp³¡fµœÑËú:nü°¸$ÙÖzô‘bV‹×â3úz’®LíÒì'^?i.&RÅÈm×}c½ðás6uÂMÎ$>é +ýk%w±ýs4öˆˆ±›©§f×’l•¹VþË…xVuâã·¢ª wqqƒ½Û™ƒ\> NìÛ²G«µ¤ Wôµ.«¥JŠsº«Â´Ð"Tü Ÿô0}5 Ðåœ?KhÉ Ë”!1o_Á›È¢ºûü†£plmëg‘5‚•q#’4ô"Á–„`çgq›~{4<‘îŸ=7¨åóñØ>¨XR/úÌ’áûß[r»^Ç\¸ª`0³9t÷|÷"aÇÄf'¼ÙÖ‹r$Ù¾Ú^ VB’œ¢½gÒ´}4Nåkæ œdç^uÆÁÞIËÛC¤y÷éįqâU0³&Ý×Úyß w$PÞß ™‰—¸·yw¨‰\iÌÚãÐ{˜kÊA4/H¹&Žõ5ìE¢¥{jçÑê0•> WÎ)Ké±4|_ §Œ‰y)„é9¿ø¬S 1;T5 …ç±Ô7mΦVü† 4^Ÿ0v„!–XJ,. dmÔƈ æ¹Ä©‚×F¦³n 8ÖÇßHÉëï%ó‚÷®XéÄÔ</Ùºþ–¹÷e¨KeáTÅ ŠmÛ‡¢Ÿ¶^…AÇÈÉÏ[¤ìm“ÊýŸ®ë•Ïïú+É'Njårs úv°i…U û˸ÚÓ6Ûâ"˺ ó)8gt
=S-Ððæ•™€Éàé# Ò)Ãňç».÷§ LŸ4†à}c–["ÛjÕy]þ-ý7‚BT®·/P¢,…_ÖT¯P¸'›m”„ºxÓ¾ÂãÊ°J„ä&FZæ +U¼Éx â6ËG•m(l×´ÐYËïù +A“¶ V 7Y¶® …êÍ×B\¾™ià;–Ý ¯k'£l¼áò\ ù6ݯ±qS ^UŸˆ&-s¹bNBS–l‹Ó¶´´âA +úòh›¶LúŪku[–U:æ:R³FÄ+ôØB»½6\"Äàúæ&”Z€sS–³Åã¬V°K2
ñŽyC<‘0-6‰jJ¼ðñÕm +é§\ɦ_š2üÀÂ}PçâÿÊ&%_õJ‡Ù¹LÊԣÔWCeÒF 7 HÒÑÐǯ =+‘"tݨ[Š +§(ÊÚyu%UÔ¹Òñ«öÄŽ_Œf›X ‚/Óé) Ωv¡#Ú½·¤ÅÏØÎ!˜ì]^P),>—5Ž> ÚÌöË” ÄÝÜÚ[ë<ê—éIä«êvÄ‘¦ÔâÏ +má™Ð=?t»û[S•BF wÒïílnI
uû;4@‚ÖJ¡mÏc 'BŽÓI,’p²K¦)Q;O6¡geïÄ…ï D0ñì\¬tÛ¹z~ +)½ÚÉwD4êyL§_9•ç+š]ïã'ñU–ÃüQW +*¿ ½y4é91ân8öwH¼³b²°£õÏßo•R(?-WB…ãõ¿yvú=Ƀ#~ +¢UMœ§&ŒÒ4Ô¾©-®Ê†i¹òÍ¢»á†«Î “dèKáåƒGp®¾Æëh6,3¤†›d!к '¨0d®K6_þ¹ºîzfzîZN&ÚµÇHòCǺÙá’ià§&‹“•HÂ,Ö¶jÔÇÄÏ—(Ï
öLÇ×?îÒ¥§Ì÷G`¸Èl¸¹[oÂHäÎh8+d§ ±¦gÌ4ÄËÁÓ|3p–ˤù.7ÒòyÅ ·Öeaæ¶ËPrÒeüêíú §k +.¶·èB|_¥œµ ¥.{ÞÛ¦iüÊ å©Oa`â¶_¡ˆ
-ß µšP?UÙ~Sé‚<s½uM™†G.O1ãW&¤LÉ’¡<kæŽêSÇãíÛÊëcf,Zü߉:ö’ŠEÔã(‰:=_N+ÞN ë=Dú«}ë÷„ýºiI qkæð.îÉN cÔ<{ + øÕ92ævQkûÚH㥠$ÈÕn÷ÿŽ‚—9Oö ÷5ÇÛ[xÜ.9=Égø…,{xƒg/‘£iäw¡½azË ©s.,Ҷ侒”Xp3È C«
L4´ó&b»rcšõÇ„‘œŒ/¹ïßw†Ž?yA>
^@kÜqÅiÅlÖÃГʎ…I4ñž6ÆpQ'ˆM| g»ÅE7pÕR3¯tQW¬J¦YµÍdž3Ø€Bö“^k‚cT( õæßœôGÞùß%… î_fp.×™^Q3ç +áও{w$}‘šBëJ«æéjç󣕔ö(”waÏ;#qù·„¾œ’"½&@Ñ¢{0üb •Ôƒ-~Ýú@ Íå3>î«/3Íë{ß\”²¾²Þlè^ÄBÛ¾µ(ŠY¹"Ç“nŽˆŠìjî¡^¯gB)ˆ¨ ºªºqÔ üRŸd®Ã‡AyL@êàU‡"¡0³K‰h•:"éÅU‡‹ù°Rö)/×:†§÷ŒÊ=D<ù“ò²
žšñ÷è,ŒýÙ–ŒÍÞú¢K«Alí(hq=Pìëar¿O-›‚É Pô'íãB.Á¸Icê“ Nš3‡è`=‹kñ›’½PÉîZ^a‘œ8”_Ñ>Ú«ÆÊ®ë!¨íƒdȇF:Ãf ²:yÙ_O¾™?.bÇBHXJwhþ›4ï‹ +endstream +endobj +1767 0 obj << +/Type /FontDescriptor +/FontName /XGXXWD+CMCSC10 +/Flags 4 +/FontBBox [14 -250 1077 750] +/Ascent 514 +/CapHeight 683 +/Descent 0 +/ItalicAngle 0 +/StemV 72 +/XHeight 431 +/CharSet (/A/B/C/D/E/F/G/H/I/L/M/N/O/P/R/S/T/U/V/W/X/a/b/bracketleft/bracketright/c/comma/d/e/f/g/h/i/l/m/n/o/p/quoteright/r/s/t/u/v/w/x/y) +/FontFile 1766 0 R +>> endobj +1768 0 obj << +/Length1 1126 +/Length2 2916 +/Length3 0 +/Length 3580 +/Filter /FlateDecode +>> +stream +xÚ“y<”ûÇ͵ĸ¶HYâ‘Hdûžd_&dMÛ˜yfLÆ cÆ6ÝD¶É’ÝP–HöˆI !]eOÙ®’]’¥ßT·_Ëïßßëùçùž÷ù|Ïç9ç<R6'å¡n O’‡)À´ãÖÆÎ0% +P @a‘$À
Ä`ñPÅ/–Ìñh ñ-Œ"{}G¾ чa +ùâò0Àðˆ"àq +DCáF1aåÿáê÷ËMÈ8 áùåú¯}ú ŽðÄâþÍ xz‘I °& @"þ÷T'ð›9k…%{þNÍI y Á€Ò·ÖÇë¢l°$¤;€Fà|À¯qúÝ£s_-(ÚYZ˜ÙšÉý;Ó¯ÐÅ“ì¼þ{í—ì¯gØ3£?D¬?àªÄè/Œ‘Èx¾¿ù˜1 I@añ@YM @‰ˆ +x‰!Mù @ˆÐ/UW݈$ÈHc€¯1˜ò÷ ; ë…"øáq šôVù
ó®ú'{ý&Vûþ*U…ý ¿†
±Ì‘šÖÏÈí‡Fý'õC¢ñ3!yý0¡(z!ˆà×ïbTù4n?—‡iüK¾;ûA´~&¿Š`ŒF¨/kîö³¦úsüøß 24$øSäÝ”WÖRg UUMÐÐPþë—L$™È¨Múú‹2Vñûe,.c¨ úr€€Ô ½Z ^xÉ8·«ˆUbˆ©‰ƒW6ö>ä¼2ÁÝî°ô– pþTœÎÏ=Í:-î·%âsµþ¢m§ÉB°w gÚ÷ütz`ˆórºuÀ”×õ+ïx T÷ΩANôŒ>-Lr¹õ8c±õÝM#û™]ÃLM®¾÷š®‡ªk8›¤ã "Â*¤U$ìxiÞ…‘ª#~¼I ,#ϯ\ºÁ~_nh‰POÞý)—=;qçôÚýŽÖü†ª®¾S|ŸËd'„xGwÂö'u],i–\9 $vSd$?!hEÙ%|»¼x¬=ÖÒ`†F•è·cǼë0jttZ Ž×§(±äL¨P°;õÆÔöaÏÆR§KqGY»ú
Ù³ïÉ´©.)5©Ü =ÐЮ•S·b_žá}m‘¶b:¾ªe5
/©2wÂSYàvo\\Ÿ öxfDËó˜£áÉû/ +ëí¥¶1·± +#ûÿcùTbª&Ò1 `Qˆ=‚²s¿JÊ¿_Êq¿Ð_WòlÓ[ Gi‘k•°oãQ˜+¾©r°š¢"¹Žx»J—| aeåÁ&/"#ns¬Ë –eÎÇzÅwp¡Î%Ò2íúÄ1t9xÜE¤±»â–‹,Ð +Á$t¿ÄäÞ¬žC,2Ö(ÂýŠÍl©
iÞÌìè›’æ˜èúkz•2ü#ý•ÇÊÒÑá:M‹Ô(š™6r«Å¹k²~zû +÷%Žò!Z ²ÆDs+K"/ÚÝ4S8쀣׋#S%œ~k…I ^œçx–6‚Zõ·Ç%ƒÕ-2€f!Ú]Ùq´o³›€pQnrçÔ|\`¿Š ¸¼yŒfžšöìïö¢3Rv(«^¨~Hrdì&
:ò¢®åÔü|çç@Ó‚Xì U¦“´`S 6×ò ×?óð±,‹QæwŽƒƒý5ú‹ðÒ ãÔ‹¥>}#Æ£BèÜûR¢Ìá‚VjΗG¤9Ú¹Sº‹ÃE\H±´Þûá…¥3ûÅWdTMPÚK1Ï0‚|CŠgôó/ͨö4 HnøL‡rÆ”Š Ñ•FXw7=š®#gž7,ßN8Ǧ~ì{Ù@ØñG%ÍIï˶ÁXïK´ +ãuŒqÁ¬æ—+nÞeÖkG‹´6ä{Ô4rÄ<ˆŸ q|›è µ%8 òÞû}¸˜ûáGtöÝœoR_éZàì4¼‘˜Ú%aÀ ¹šmuøT›A6í¶¯wH Öc$aè¶ j^søQÑ!5ù™ºèŸ›XÔEG)ö:Lùßm/’ÏŠÝYœrY®=a;Tpȵ<B—;@ÉkÝÚ3ü +uBo NÙþF»šfÔɛɓ¬(Ì¡ïœÀG&É+·Š N.ŒÍªùξ#¶Ñ5d$#±)eܼ§omÇÇÚ D®;ª·Ý]è§ÐÇO…¶Y~”˜›AWÕ&àÃË¢ÍÙŠ K.â%Þ7MRø¨»›‡&âW†ê9•æ¢5”¦v)nO†©ÇÏÕVº"sŽSy +asJ‘
`è³Çµ[ƒGy# ìÁ䊳”:•jˆÃŸ“á üGg Utb.¼Þô¢“Ђ 7ʤÑg|ØâôÐ}}12Ãm‰° ñ/ôhT^Ý÷c\ö=aˆPGö¦zøάü>qå¸À ¹jÏ+L¼Å³C¼Þññ: kªÜ^®Ohñ´Y ˆõÍXžn6'”‡ýY‹~MËu¥e!³
ðìb;½ÊHV»mŸvÇûá‰üÍ \Îªï‹ ? ]T@¶`Ò ƒ f¹2%Ö‡'%ö½òXoý¸ Õcš A?™”¼oŒµâô›ŽÉ7#Ê#ÖÖWí N[Œ/G+p^f“‰Ê”¬º~›f;-‡ÿTàÊÈãÐá7*ë’›=_-îéÕ_åô›ò®B;*½üŒÚî^QÅßM-@ˆåbx>ø|P'ù;•Í'®uóµåú©–ð– ¸ pâ0}²x·¾eì(›žc¯«$󇋫ÊÆΆáh¹É ’Hò+‘ Ó†½^ˆŠ<ñ춈¼±O×Ʋ*†ûpÅ_,ª
?È[¡Â’Ü·¥•°Çæzæ«öWáSÞÖôÞZtÙŠ÷Ò‚ÉÝN £{–cù]•Tm\hYÎœõ©Z7 N>írƒµYB§âÌ9 ˆÂ¢võ +<è 7bå1û +)ŸÓòc¬ G‹HÖ S±d_ÿ<Ë$A“‰:ö(X«3h¢„º ¹çÀÀÑU1yÙ`'’žìÅ7hn±“0çkÐ],5‚%¼*øZøƒö¤]1<ÔL—0Í@m?ý̪› q“µ¬ô j! }çÆ®×ÄnA—aÝ%ˆSòú>ŽQ {}–û!A¶Ï]l“ûâFrO›‡7s½¥Üº:0ÙdisAªüˆùYÁ‚*,ÿ±É¾µ³ u궕—VسrÚxODïò#þÙ3?€[r“ÔZnØX‹+žïÞØÈRð-»rÖû®ùž\Ý2º³ñ»Í'y‘Ây‘õ«tk£ Î ÐP<äfNV¾·ðÞZ•Ï?â¡'øB +gCQM Yóx5þPµ»<K3åNä v-ù
§îŒ6Œ)Î^[¯¼¼vcY?òü2-f1ö¾×¤iámuÞ Çz3U. æ“KNÖyÌ5«¼^ÃW˜ OLT€é69ÒTòã—m o‘ººÓù.èhÍU[fèYËÔð«æm'ŒwÖÒ_N½µ<:uNÇdu‡Ýªü™Ð=çWK™ÇFS@{¸Õ6ç[îÍŽ•eÄl®®êþQÑI )òŽ°TÖ£ÝÂΰ?ý(a=óÊ¡›¯ÖÓÒ™¦ø–CUž*ÆÅìŸ/¯æ *5Ùƒ¹£ø°Jì9°E¸þA0~•kí–ôkò*¤Õö¢‚¦wE±»_‹¾íö\ rÅqÀ) +endstream +endobj +1190 0 obj +/RKJHQH+CMEX10 +endobj +1179 0 obj << +/Type /FontDescriptor +/FontName /RKJHQH+CMEX10 +/Flags 4 +/FontBBox [-24 -2960 1454 772] +/ItalicAngle 0 +/StemV 47 +/CharSet (/braceex/bracehtipdownleft/bracehtipdownright/bracehtipupleft/bracehtipupright/bracerightBigg/bracerightbt/bracerightmid/bracerighttp/parenleftBig/parenleftbigg/parenrightBig/parenrightbigg/radicalbig/radicalbigg) +/FontFile 1768 0 R +>> endobj +1769 0 obj << +/Length1 1037 +/Length2 5287 +/Length3 0 +/Length 5971 +/Filter /FlateDecode +>> +stream +xÚ—eX”í¶Ç)锺™¡é. a`b‡¡¤K$”îAº ¥¤%•’P:”8óº÷~Ýç=_Ïõ|y~kû¿þ׺×óááb30R‚"íaêHZHDXD ¢««)`ÞA ".. ‚†#ª4L K´¼Ü + ‹„ÂPˆ–šÃþeN…{¹ÿ3«‰†¸Á ”Nn0€ˆ¸0Hü_q¸§:Ü5€£ œŽ7OØï8 ý§Ìü~û +ø+òÔ=í* ÔQb…¡Y)`Àß9K1p‡š¯ Óøö‡ ë‡8ïóú{ÈÜsžnα®y¼ø1Ïq²ìý¯F盈T!Ã^ nùÌôÕQkðÈÊ q:”c=•È&¯M'f¶µœ8ôs÷>²9WòžÎ:ó„êzŽ¡gqÂuáN86O÷ÖT†Ü%!ˆÏ×qu„H$Ë•uÎ"¬e,CÀ$9i–ŸÀº+Ç–a!ßÚ¢ûàë8 ø+[É„fX`ª†¹¦é)cE¥C9£›ÜýlXme§»<¢;jÖ0ŒÒµvLT.YÄãu +—‘ÝÅ×!g î±Í¯_Kg7± ? üÙ°è«q̤³¼yvø†A xŸ¢Ø @œ“6ÑJ +KÄŠ±ýî£ +«çº +í=búÂß[´]ßVBÖÚézB¾Ì¨¸Ä?!øÇÁŒ8óS["âÕÙ¯`µÇ©A7§³÷½ˆ)ÔZ†æ›‹ Vàà¯á Å^ rUÜò 5=AZA·ÇòjÃMO·Ñë Z´ˆÊáËGžBö³duyWû¡xÁTS„âJ™ý÷‡Ê˜ÏôÕDpÚæÙ«·ÚÚƒˆ†:úï`&ß ÖOÚ‰= •Ïzi1¥/ý<æ=@Ól +çù¾ ÂದôóásŽ“ÝÉWbq
äŸuª)Ä ?ŸËBj€?x©žGoïíPjQuyŽáÓ8òã¾È¯’ØòFjºº®âHGÆ¡lr¢AƳÏò·¸~¦àU˜wxì&¥ŸDNùëV3P‘¿[XÓ7e%x"ö‰–~¯^…Êl* epK¡ýo{»‚ðÞéDH6[J)üGšyÅšÎq„”Ž¢‡ /‰=ìD‹––)eþ9i•ð8-ïvqÚ‘KzX /m›Ø;5½ó‘œ×ÃÜ‚nÙn3§âî™ÇÖ¸âLÒ¦öŽõŒ®Î-]G={=Þv‰Ṏ¡q"t]½Ÿ’Çb{5^5ÏRˆJ¬¢Bñ›ŽIз½˜,šÌ@]%Úh–s
¨Ý@p¿¯&OþbΞBwÖ½
Ž_Jî|j¬WB9"Dý‚rVÐÒ¢ã†WbìÉ™\_ (Î}8#è§9½šBÛÖv¢¦³‚hÇ7Y C¿®Ü-Ž~@DõÕêÒèî@šd%u«i”‹¸`L >Ë¿8¼‹Ÿë™ûÀCˆ»®ðàê5ш·™Ü±Å³IFc¿¤y9øžua½x–;” Χo€XîLÚ½-Á‡ƒs\k<¨äVRwëZ'ì'Ž¯=Éæ´`+`B®Â6åÆK¯¸¥ª‚3ÜåÖ½Pfz/ªÈ¢:–§/.Ïe›„Œ·ùß#8Ì#ë¾$Ć÷W^> {©í±~çy>Ü~´’»Ÿ¬¾F×a¾äH„ÞÜ I!{†0ú+³ ;ОDê’ª½CO·"¯¡e–y—àÑ,‘Þ;àcÒÆ>ÙÞÆ·0÷"
’-Û”W;cÝP"iÙâ,¶ô©_—øÏ"ÛL ò¸f¿Ém®ë(x•e˜ÜKI£;1õ.Ÿ{§Rý0+‘Nsu?Š}…*©Wa‹¬Ý7¸E ;¿Õø¢ÎÁ¿b!]ZþUʶôû#>fiO +‡lïußÚyï»Ï¼nQ#zÏŽ•.có79ÍÇ{å|¤ÎÕK üj©¯jfü9š3´¿‚ü +ËE7A÷Í@ûôÑ»oö·²9 ò”²2tÅ(”MI¹„ãšÇ`¢ò¯ÇÒ®åÓO;:nîN|FìX+éìÏá î)>Óh"õ¼WóÝ\â^ uøüÅŒ¬qO îÂDn Ç£¹àsò:,ÕÂoi5*UA§ÍÆcvÛÃiIØýIå4,cÂbÒ²#È¡‘(ÏÂë׸¢C)OybÔd9nÌQ]™P«ôlóÀCNŠåÂJ·&Å((%m¢©
ßPwÏï‘F'<`"hÿÂ’DŽóbHÅóqgÀÔ9ýË +EÚv,6o¼S ®@ã
äÃ~ëÚ3®Ï/õÞyOUÜ^çÉåû28½ÂÕ¢öÜÉCã(Ì>îââšV¦D#y™ê”—‘]µdîI‚û3ÒÛú¢ÉŸ_%ÕãvÖRä°$ôÏJö .«˜©Ú#,ÄÞø iˆ ¶=¦è§MʾÇ]xº¼ê^ZYgK‚o,òmò>YN/+›ÜN¬ûÖ<Š ÇDì:kÒ2ÊJÙŒÇÏëÜ +[ã[‹ÀørfG"˸!á íoù[½gk`ؽ ø·ß¬Ñ‡¡¶WÝÉ,™äYž 4rgvâ¼»(¢g² "šg&øR&ÓJRpéW˜ƒ¢¹'9ÌýË¥ãç90‚k{˜ >\‘ÏH[¥ÏÙê`/‹\ ‘Ñ$HÏP%¶*[nýØÁ%&¼ƒO'€¦¬ç+™¸ôƒ9î¥ü
õåxXÅuçã9/²æÕ…lG»©Õ éJžÕ£¹Åô¾V©§rè›>½I®ùœB„w§#sï2PL¨Ñ-âÃ]{Ú~±dIÞ;>úXúÓµâ“Ö‰óB¸ $!qÜ Ÿ†â¦s㧠Þéúéov§˜øNMçŒ9y‡òá®]¤[‡m¸ÿvê* !Ø™……ñtÜ‹)ç¼SyxýåÞëL³Ç<&G³æž•Ç›B +æúy…×ót]V¶6O¥ðrÞ)™´dÌ
³W镶ˆåù”nŇhå=¤}l%Éôz )“ITEBñÌ>H`3 _éf/˜ w$}B`¨iÞ¾3x-ÉS%¦.RñmXuÁçœ^4‚Äåh¨ÿê:)–1É41©çù÷÷P;ɕ£\½J:)DÉâ¾Â`'Ÿ˜ž[¬éõ
:úÛAu¬#”²â¸×hgHìì^0lV Iît ’ß×ÙQn~º}°ìÓ{50D…׸lA6?ìsxñj$MÍrrÄ~k÷þͦ,l5MäSCÁÚrÑV·ñ"±³õŽÆ–l˜£NX™V.CÎŒeÃY¦ˆ°³l ûUK¯ wd¯õÑÙóÖ¡UôÝó×oWr²Õ²À¯¨cPø\ñ°þ+ŠõÈ®ÉȮѽ£KÂD}2ç,ÏîiœMY”f³Ï…EŸØÉÎq×@>¿»”© ÌIåx‡%ÍÛ°(¯ZP…P‡½¹ 2ÝH¾r©!ZϾ÷5™Îî»cBÕ¦æÁÞÌ›
èÜ} ™àÇ)ob³•˜¾vJh›='T¦h¦ÓåNBä²µ£«…Xó«X2ù°ºoŽü]ŽüÎV|DÒœmì$èo²eË#[9ªD)´\ˆ d‡Ž€Se;‰7S¥pÄÏÇŒ§µÂ¹ëáéñmc%¤ ëø*ðg‚ ¼Õ$Œ`o|D}ØR !÷”¯°.ŸAñj$ÉgIÒ¦Ã+D/^`'˜—#1_†#³Â”
ß ºsHµu’‘5tÿµ‰A8ÅÓ˜öZãa¡šK”¶Ý/ËËxBë¦bº;ô QðþÈ".fNE¦”Eº÷[
L=æÞŒ«ýÁ/٢ú¸y%ÊçÄ}sJŽ}7 [;Ô“LóI¥!8žˆZ’ÜkÚmwÚ›‡§¹î6¬WÂÏ„øºêÝÁ#*&n‘u³èÒ–VK–WÒÎB‹oמ"Ç{Sñà+ªu½•A‚á/²÷P¥ôœ ´þ>á&“‚Ê^gêû;ËMTò°±¹Œ˜Æ¨&6e³Þuú7| ÓÃöcíã3(¨OÒÈx¿t¸¾<®è˜[-‚/1¾¥^:‡Ä r̼1/ºV~$fÓ(ÌÁÛ¦E>Ä568ÎyQÄì½ñ‚cŸ«FE3ýÉnYêYLð øÒ\-Qk6ßÜÄdç‚jÒÇ°ªæxjšõÑÉ=.€öz=i™æaWSB õ¯½òœUóx}+:—îûE¨knüæ:™ûn/'w^‡`54{ˆ¤©—=*ðH£šA§-»L¦Ê„ ¯ê öÓ}uå{íÆEàØ@ ¦ècôØíõ‰ñø² ¡ËCg4/5Šï–ø´økLyÕcŒòíYŒ ;Œ@–ÐÁMu¯Óí=Ç5´ø (©g@‘f¨Íêe¯ÊtozØmµ¤$Í)EAPÇfnàá˜/‚üÙm$ X/ âÑËÿ\Ž\wBðù²i€÷|¶ÚÝÚM¬²¼Z½¦Øm7¸škÕ.37qµ¯¿—>f»ƒû XS¼Yð–;]wIs׫¡¬ùš„Ö— +endstream +endobj +1770 0 obj << +/Type /FontDescriptor +/FontName /KWIDCE+CMMI10 +/Flags 4 +/FontBBox [-32 -250 1048 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 72 +/XHeight 431 +/CharSet (/A/B/C/E/F/K/R/V/W/beta/c/comma/kappa/m/n/period/pi/rho/v/w) +/FontFile 1769 0 R +>> endobj +1771 0 obj << +/Length1 1373 +/Length2 10483 +/Length3 0 +/Length 11300 +/Filter /FlateDecode +>> +stream +xÚ”cx]ïÖîãÆvƒÛvc[¹š¬$+¶m6¶§±m£a“Fml«áÉþï÷ÝíÙçë¹æ—ù¼Ç˜Ï3©ÈTÔ™DÍíLRv¶ÎLlÌlü +4gFdc˜ƒÌœ¦@ -"Ë¿4ÉÚ~²ðüÛlîbÿ¿.W £Ó›( +ÈÙÌðÉÄÆ ø hkþßJÞö÷9YM)
†ÿù´ÿ8UL@¶Î ö@ +²¾©4ÿ ß +ºÍ—íÌ‚R›BË|% ¿•ÃÒ9¥—Ot…4¤ 0 `Î;6Ok +¢An»B2Pk#~üáXÚ®Ðn¹hO?ãëe™ omÖz%/*Wz±ô\Oº:ùŒ¶lÐde5mÀûFM’˜à€Û¶éGˆ ¹Üska™/ÞÉ/† Ìéå»*ž0º!Òò„“š6O7èþyuÐÏZ"ç]‚rWŽ… N Ž I£è
ÆÞ©ÛÂwo$Œ_•šèÄe®• ÄÓ™ví~W¨•9ñHô×ÇÞ4‚…,E½bv·¢
,J–fú‰+AÚ<Z~ÕÁã=*î«óÛ¨T×;ÕR}œÓ:ôDûW9ïó늒¸´x¶q}¿*¦.ž—¦7ˆ‡ýzNägç.ns†å,Bo°×GÄ1÷|¼ÚáìfGY¶P7ËÜÎbñÈO 7;KõòGÎnl +ë I®´¯þUI#Þˆj”CÒo’‚7°ØJáþ{í¦¿àtïèÝ™o©÷ñ/ןcïàáT¦–l Þ/Mí2=&!R^-tÙÌëOœô8û•ˆÀg9< .¤3?Ïn±Áp½~è 5¿PÅ—¥¡ûC²:A}¶)\ê¥+¥èà{ÈéQòr3;a§uå0Éï$+ù–8 +å Ž°¢Ãæ‡/×ð¤NÍ}w¨
¨ÉÞ7Õ Ñ±âHÞ
ce´Î¡²î_j³ÎF ÚíÙ™È]®B¼ ^ÔàT mDö¥jÉ×=žº8Iõ«žR&j_…Vé°lÔ½×ÅÒÝœÊÈl¼_Ò¬§uÐØQsVå „Ñt‚ÖM¨ +YÕ¨(((?ý"oj÷ÞÒ(<›$Õ™XŒ‡¨ƒ½]Ðár{«ˆòK3cÃ:-´ä¼Ýý“¨d„Ëÿ‘“±¾+ŸÏvtÂB·¦ÞXaNX•ëê³¼x«úì±VØ'ª³ŠK“ÕÑT7ä½ =lTàà6É
éæÂÅ=NÖÚãK\&©|!Wqâ)Üõ£¥\ „Þ³ +…ôG==mñ{•â8¶lk/gǨÁÆÄJô
r‚‚U³plÆR¾(æ4åë_øÄ X RHÈ:ó]Ò)± ƶåsæ‰p À
#9B~*åTð{R¿å€É…Â^K¹"<&ƒHÝ9³W¾í8yå‹1Éó÷9…Ù¾±¼‚Ò~Üêa'ÆÇÏ¢Äþ…½äi»Ä´Pdâá?uƒX-ád}o(¥) +¼ ˜ÕïºSÐÚ?°áf¸Míº~wu––d=Õëš=ºÿè[D½Î,¢( +|²Ú*ž÷«4ËB ÆyÓU/mÛ»¥¾æFî™À§‘›Ý±ó†wûè]:cmÁZ·ý¡xhðÇ“\Ð’$¦ð6ušs&áÛ‰´-j‹»Þ} …'—u2ÆtÝc;"]œ^; TrÕs“ýÊkž..Ü.…Ùs?ú–ûÅŸòž† ^>h)škÝfÀ”¹´¯ðGQìu%rCb†àê4SÎyé'qr^ãBž +[¤ #Ôðå S|ƒs)•F ·G2<s©´NfÏ-z½F +žNä +ØeqvN&™7ã‡pHDAÎŒ”:SC}âñ[XÚßޞ̅ |ôÔˆG¸8•!×í ÷;M¯Þ3L¬`aò ®vøsÑ¿Òf”:eÁ–ÔÃ5I¾\`Éäƒ&WÊhg›i¨qnœarC ¨ w„”HÀ*ŠríJ%mCùb»‘OÕlS7Zå@Óò>kúùœ tUé®>‹Á8ÅÆ+…-«£C²5¸ÓîÝš¥r#« Yd÷"5 -ž·mY.I •jôÂqT<&†Öêõ.ˆÅ„2/d«:»³o~\&]Þ£D“wO L…s6Œ_žÎD +43½B ˆSn'’XŸ¾7UÐ+åA ÕpÆÄ6qÞŠFÊø Ž‡XeYR û}@gë}PÀ”æ,̈©p\/æì ÿè;¼~qãLRÄJOgê“rÓ)7:°„鯃œ`ù8°©“ÃKc-Ãâ%Ìíû@’×Züå¥Ä'"u3®åÓpÍ÷–å<·‚z>ç1ê‹Y¦½guPÔ“ /5±E¤“>øT”xøÌ"È2šEÐëSc*brôp›4&x%Ù.ßç ãý$sjkâßmØ“\~œ2uJ´#¨—77¶îN©„:prv䥉Œ¢
2µ¸w¶˜ ?×VP*k†¨p\A°iŸÒ´ÅaÚ|;ÓžÚ¸re ËMý¢0Tõ©úkSÑöŠFœ ¢ùéþ§º5RBB^<Êîø䪘™Œñ¢Ó 6:fq9¶‰a
DÚoŒô°Üû¦0 :n¢þBI´Iëø ªÙŒW}Õ¸Rp²Õ#N´=d½>ÿîb×»¹ßzÍ>%vøcTÉnòCÛ,
¿ùÇ»‚¢ÍS¹uï4 ˜³,DUÛ’ö¤_…ûQX__g xtƒÌ >¯Â¾I* d†»ãw åY|ñb±²;$ÖVHùìŠòiU'(3<üŠtâ<tËt ™¨àµ+?ýfÖae? ÈPµà°y4o?6‰°)tðÌ5Þíváà+ï ™4 Jê“7HJRz?ñ`±e'*Ô÷îûüvÃ ç „Ô¼R¯•Q3$E8³ePoÆ•ÇïPÚÆÎç ëÝ(K—B¢´<fúML7tìoöTŸ0aòUƒRÇß ïso.#ìcƒèí¯¨¦è~Aôþ*G=— ¬–)FÖ%Û<*‘Ê’>Ò4Ü\ƒ£±KeDÕ±0 >oQSNËŸžECõD KÔyLºCiÍR#†Ž;Ù»59P¸"Ð ¤Åx ¡ø¨éR>VÖ :ǬŽ/ÔΡö /\fÀ}E ‰‰ËºŒowkºÜƒkÛ¬f ©:¶×é’/ÃsæÄ´•ßnÄÌúØdªë7Ò;ÆëjðnªÊDœ (F<7¼£ò3ÇÙ êžXR7p± „¬ûý E}ñsTnxiÓ€7£ÆÉB‹£+Š¶ ¯wÿ±Ì9åÞ å´1hu«¶œf¦@®(6«©ó¼~j®P«W½š"fððÜé ä¦â k^%÷”Š0s»j3 “óFõï¿,¨ê®û´æB!Fåâ©i‰\ÙÅIy;õl¸ Üj8óry¯m£"—êèØã7¤•.9o¦"¢Eh9]’Jí:ÔÊ/Òòn*/yÜ + 7Ë݇õå6ü Í{$÷eúïqýæ¨Ùœâæ!ΙÈ~¥²¯k +îƒÜ?˜×DhÒÐè÷—˜éü‹Ù 44ϱ¡»j‚÷мøˆƒÂí¾µ4[‰ ~ðFÆ:Ñ.-E™©Oú×3Du +lÕ¢’¨Ù^½Á„çªíõš\XjÏ€œáÐlC‘£«¤ãG«ðØ™ý
NÕýèù î÷5¶ªsU +-`ý,Ð`üÂïèHq+í`õ¬Ðçq°ù ̾p*ö’i™)E¹"¡ s/TÄÔ¸$Oç>7mìàíæ8óÆì”3}²åûw[ܨB1^¶"Ì3²ó»¨Ä€ã!5¿3ËÈ_Z”,– +²vY° Åך ÌìCûsxñfÃp8˜’|«¨±«Éös>i
9ÿ «§úR õvÍ€¦°ä9Òyø^ }j Ö&•ƒÍ8©Ô›øè—¥¤Oä‡3‘LÑÞ±„`6í±çÑO‡ë%W$¾VÖ³NÕÓ´ÙüûÝbd¬¡/ß+Ù„nÝÑ-î¬çÒ/ÝŸ¿€ð ûUUQ_¼¦…RÌO° Ɉ¸™ƒaggÖ2¥^>>·ÑðnOv]~íOaBŽõ¾ûl†^ùŽ+³Â”¢G'Çí>§^í`ôŒÓ™ ®ŠëRåi4þ4-!y‡%ÅV‚Þu3æâÚò5Q i4˜{ÏW‘%žzô$ôž>]¢I¥É‚Ó +“yT›Ù,¨
š†ˆÌc1Ðð SL±~ÀèªÄ2d¦„#Þ’ë³kãM=øÚç…—UÏJ* [™±a„o&KáS?W,c„ÞZ
˜"}S¥9½cÊ…‡„˜Ð×WªpºÁ¬t"rË'Õ¸e…ÅÛTi +ŽÈ^¼-–À†À 5é3i#Ä ÆÇ…Ùéê6½¹Ïç_³7ÏÙŠ@}² +Ê9†\f.~†°N¼·kXkÎ绚½¢Dðë€@@‰u…è0R&ªñ(¯mË–Æ>f¤Ú ²²K1(Üé#FŽÓ.ÛÁ+B]Ï1O!B8GqÊ_o ÚoB‚ÑñÑÞ”FÊ,ZhO¯sL¶Ìþ¨¶2 ‘ÐIN’Ÿ'/»ë2ßÎ^ êي؃%šl…wʉÅw oòmÝ‹¢'Ä´ëH¡M >ãˆ]ÌÖXD(mæ>ÌŠ}òцÙbÅcš·ž|ò³×¥Ž¾îhYìT=¢a¨²IÐå]Ɉ~Õ>c2
e7e;À"†ñ@½lÇê ÿ’Ê2 ‡¾í ǃº( ³…K!hçgCÿ çÁëùë7Äy
»Ò…ºoÈBxµ¶á ”D²¡ô^o
ýš ç/b!1·®*˜‚*ÓºÉÚd]¬Î…–VÿY¨ ¨Mx# uÕSŠ]’\Ýx"'Ãë²àMµƒÎ£Ý‰ +-¾g7¶¯A``'Tþ¬U+%Vþe—ýäÀ/^ºÙÑÒo\Û•_>Š·R{ccY +Îiäv +…ë +ׄåÇ·"
q¯$OU(;[¸$£D‘ì>&‡ë_±ï.WY‘ì©Ÿ2~ØâÎ0ÒózÀÓ+À/߉ËÀ'$ˆ°^’êŒg^Zä"ÊdïFÚÙ¿xûµ?àentö§ðn-P¤¤"_«ö ƒÜs
¡¸Ùoæ–I²½ €¯^Ó]šlƒBQ9Ú£ ó²Ï§‘·V ‹É[ܸj¼½”«èñV˜K +¨¹ŸœàÇh×—N<Eµþ.ù8B ¨ Vèq»¸ämÓ¥Z
Z|]ͨ´R°=DÕöÊTœµ˜S;åG:† à ï£ÕÑ +¥˜ï<9€˜SÊMm©Á8n¯•8ý©–âK †”ÙØË@åöÔÖhüã+—Ð|Îø ©\ÈšÖ’]È( MÏ×grǽ ȼO—+sÉ J_Fì‹S‰@®¯ýÖäùþ9WMHXÓÆÏF슪’P†A>D&?”I¼r†²jOT©û9rí¶"´© Vn{8ç%…½÷EDwû’é‰ÙýœVÇ~ĞʅüŽî—ŸËBjW¶¬Ot?ºäùEò6aFUÖ”t>ð '<G!îú¦ ÈJšQÔ£DÍúå¡ ZΓ!§ªª—”XйKônGŠ¢Um)ãc)v‹TxuÔ½ô9IT³4¸ýëX‡ô •’ +v‚Æ2-èFÚHÒƒµaëÕ}äyÄîb‡c[ÓÓC§8ù—wšAÂÇ—^Î÷òù #òHñ{ºŽzcZÄk ™ÕœNVÀAƒ+./G•Ôià¨UÅëýü¸›òžü>
mc# ]¹<-Ð ÇOF‚Q}Žý OuvHÌ‘ùë…?‡8™²Û‡(QB=dûeÒ1]×ÙNy8ÿ* +Ò@t¼,~×)º''\qÅr{B¤=JQ¢˜J;Vè8/¡ e툌ûIwÐe×^2ÂbYqñ}OiyÅ[4tªð+8sä{Þ»`û¸¢¡5>´²ëÀï—rNï'2˜-Ævi}šÅÍ·”
ïÞïê°œd ¯ ÔUŽÐI8
êÅVÞ"§ q|ñÝî29F*€äE®ìVñ…ÚhÏð¡˜D7ÏÀCÖç™8˜‹Nfõ´=üȼ®Hþ@=rSeAÊhïBÈ S¢Tð++ % 8Vn(û²® á[ À…¸‘Ro³ãéÞx<sa¿×êî^nbÆq²¼žó!MnH¢×&z›à'}›¿pz…&HàÊRÙªÍ-“BÝÅoåT&uÕªóu¬ÅŒ…cr@ %rŸ»»oFgÀÅm°*¨ ½êå4%y˜b½²¦¿˜ðÏ€?R9¶k`ÓÛgÈÕâ0C¹æŽœ,¬Œ?”³û1]„uÌÚ×gùÒâ5Ç %kÆ‹œ‡³Ú Uf¼g¤_’¦T Åïç4ÍÒÀ4¾ê!_ ßžÂF‹ªI©™c FÊWÙªœ‡‚o}©0Å]”IYýAÉb ÷-¹MÏM³R,eŸ0?~®†ªBò1>£ƒMP‹ïƒ¸oúû95U1Þvÿ$ÈÇ|Âå\ÓŽ'Ðr½È¼•Ûuè›’ý’~²c/[ªÀKú".K(GÂô™ùk‹ªé +²²j^Ðnþ’¯‘KHÄXcøýî6Âî,yâ”»‹^"´ãÓ™ÐW·,tä á‹Eº' çl}ãF[S$ŸÖº“× æÔïOÍ.ãÞA E =tj0D&Êš¶bÛšjiव‰`I¹„ Ó KŒpö]§˜ìïÍ}Np±°œx<€jv9)m|^³hg]‰*É7pânAM ÿ-ö“ü;úœ£;+¿Ú$„<ñ:~ºÆô¥‘JÓo[ˆùë&âS‡u]UóoÖŽ?Q§ù_ÕÛ D +ÖåoI¸<ó·Íð{Ï*çæî_ÑüæC¸N¾áB6™ü_¾ …C_½~/-køvÄPi¨^c—ôÍ*<Œ§ñ—ö:}i„‰ÚÍÇŽúñ WL:[EVg¤íì9 +©¼Aa¸g¿Æ;~_w+‘eç7°i +î NkEð
·3;Uå¹½zX£±«™(µã÷ÁÖaTÄÖ-¾"ï”tºûVEì)-„ÅFx-”epMu~/ö)Z/|" IâvÄÁ¡úJ¤Œæº˜q¼ÇR¿e¡û¤®VÞ—w}þ +‰”Uv™Ž + +© +endstream +endobj +543 0 obj +/JIUHFT+CMMI12 +endobj +536 0 obj << +/Type /FontDescriptor +/FontName /JIUHFT+CMMI12 +/Flags 4 +/FontBBox [-30 -250 1026 750] +/ItalicAngle -14 +/StemV 65 +/CharSet (/A/B/C/D/E/F/G/K/M/P/R/S/T/W/a/alpha/b/beta/c/comma/d/e/g/lambda/m/mu/nu/omega/period/phi/pi/r/s/sigma/slash/t/u/v/w/x/y/z) +/FontFile 1771 0 R +>> endobj +1772 0 obj << +/Length1 2091 +/Length2 15520 +/Length3 0 +/Length 16641 +/Filter /FlateDecode +>> +stream +xÚµst ܶÿ4¶ÑضmÛv²cÛN5¶Æ6ÛIc§±Í7Ï9÷žöÜß¿ïÈ û3×Äw͹Ö^¤„ +Ê´‚&vF +0¡ƒfd$0±0v&0˜YØBÓÿ#IÒÖÔŽ€ýßfûÿ]r8:}Š" ø—LJ‚O‘&v¶Ö & +.áç +?ÿ1üsß8 8Ù8}þËÓØÅñs”Îÿzg?/Òÿ²©Åçë +¼^N ÜÕõ ½*¤¢ƒ¯fÔË“û½TþŒsüÅFE»®£?[=ÅâGV¢ªõü%$É…z†9PÓWu0 ÿ` …#[4·ó:ø([uŒ±X/¶ðã8 =7!ôðw‡¼™ôÄ3 „¢€úí– ¢xõAêipK•9B*{ò~À8ª¤â¦¶ (S>Ã[A£‹Gãïª ½Äà¹Xi¯˜Y-«·I +mÇ™WÞÝCãÉ’Ñã ‘XˆMö +µªßße™ „x
9™ÿK·íŠÑWU1æ= ĘîVnÓ¼E +£“láÖõ âóvZCDÎÇ'Îýûqšw˜h,ÙWi¯‚ ˜[•×b˜t>«F²Ù…F&¼íï³¹µzÊ -»[ˆfõð³ë456ŒD%ìÂÊ`ó´GƒM¨ñVo"›ˆ3"_NÎ>`P¥q2fi<”ŒÞ߇KÎ[æÂ"šc—¥ÀA] Ëç©Y%ï†J‰æKœßãä̹ΥŠHæ=¥öa–¾³M/|Ç,L&EàniÃç3ý¤·dæì¤4_ÊÜ#çšÞšXQTþÙýXhI$òÄ)%9Çù`|W"ˆÅCÉlE8^ƒAl¯u^ãÎn ¢‚ôÎöC×Y.€=< <lL» )X%Òï$÷ûoŠèu„c‚üŠÃÃG’vÃÂ\Ž Þâ-Nq†Ønñ‘¤€2nò"§ ]¶3à_×ÞuC ìe@„FþEú4MH^&”|UðEùÂwvÓn<ºØ¼&<¤„°“¤7ž +I‹û™ÕËY3«p¾•¢2(b²÷ ºóÄœ žûUböÁª=Àœ¶‡˜ƒl +uo¶dÚA4ï¶%GÉ€|’‘ +Y"×d +Ò ~lF ~)ŠY4EGÒ÷½ÿ™,YÙÂ5äpÇ€ƒf€Â!æuÛ¤I9³ä‹˜ÞfÜ›³M®ˆÎ9°¼ DãoA‹Sê¼í•éÂu~ÅŽ¹Î– Y7—e#ïjè,Äuä8f˜Ìâj©›KúdN›MÅãB‹`‡Y³ôõµ¼Ó¦C>h&ktXÊÐ`P¤^KG@|årP„ßK%¡ÊoGOFzúaj” ŒÊŽ›D вiÞuÖŸÚlè¬>“SÀ6ˆ>ûZF"»Ê#õ¸Y~¸‡] ù"}@à]œ·¶PC¼pH웑¬¿]S÷¢3oÕ +¹ó¢vcÆÊi‘± ¾àUUéjŠóO'¸ÎÝü'ÉL‡tø,ÍöþÛƒ}Y½þ/À4‰ˆ Ü™¯£Ôwr« Vd¬¸°ýÃAªþÞLˆ9Ènëí³Ä• —GÒ ™{*ÂH9NÊú /‹Ñ⵬^E¶¼±¶Cpæ‡* +÷ævã9ÿ˜ÐŒÅ´æbÄÞwÞ(Þžû Jì-ô"<ê´e –ÚAû… ³ž»®$“¥ !…×ronL¤ŸBËý-ÍKɃ¿2 ø¹÷Ë,µ ¾Ú8ÆW a'Öce5‚Õ‚;l¼C¥Pß|da±dQþ‰ 4c‚òÌfIE¸ãXÆ{õ5 Ä=´A¾•§ð`¬¬1Â9ßÁò¾Z-íƒÁßýík~^z.A¿‚ŽÄHmJÖÔÝyQ¥½(´³U=Ê"Ê~îóW y‰ )Hø\´ŽÓå» òB°«ñZ”5ó‰¥ @3¦‘oþŠYⶣõÞ篼‘€¸ íøA!‘G'%Dl`ƒ'åâcu©ÖÏyÖ+ÞRE˜çÊ |NØ}¼u–Ö‘%Ýy{¨}Ñ-×$Z·MufŽ$¨TÌìŒÆëï ¯úÓ(©¦t»».$ô÷Ü
Ú%>7”Œ¢£Ÿ¿"ËiÌÍït!‚§֫ÇjIÕïN#ÆÂ…S¹(^šÛ€>8Àj¾~ iŠ‹:Í#~ÑsZJfo/ÉSeзzÇ
°º µµxFQRx&³L¨OrP²ˆî Kàõè‘+¬@à£(BE‡GàÞsGO·K îò . ³5oƒ›äbIõÉOÞ +á’ÑÛ¥›P° +ivÇÛ´Öq2aÝ\㤠[ˆÀ%·óE•Z6‰ž¬(àú_•yÙ¢dvгù‘arK ¯üô§hF·ÞTH…ÐÂL‡ˆiÅÉ=áZŠ&8Ò®ôZ›+)ön™ëÙrÑ=zäJ
L嫇4?jŽ³È§Ä˜#XÑò’]ZXî8jeö÷WÂ÷R0—Þ Ð)ŸWîÜŒèjlÓZh~5ïHPÖ¾‰?ÁËë5¯ã Ô”"nñ? tô€ÂqHþÎŽã›fLõ;ÒNÙÂ>Xvd{Á\`YÓÜ}ɨµŒ¦á)Ýæ çXÑÃp0ëåÚøìþ’'Là5ŒÎ +÷ª"62«™ûYx=/]6í¬$É",‚|—öÙ v…°Oÿˆ½0jdRòÝ`« JVÞÁÀdxFδÍ*Ì þ‡@âJܺbz‡ŠaüÅÛU–_±I†$äüð€yôÑ«ÏHTØk- ½eáoV¦âÛFM'Ãn=w°Ë°†ú‡Ÿ†ÈèsxnÛ* + B~* +Sæä~4š›T•5dÜΘél0çoÇsÆ é +®|/b9ײàú^_‹K¹·êEÓ΃³@%¸0Œ‚ñ@žL# Æ¢þèUÍ@U^P®Å«h“Q0Ñ ô:^½~úZ¡Yß×ñq¾ëJ`—³§À}®j+±¼uöÔñÕF^Kç½cl›ÖÙ—"YóVÅ8ØœLm+™»¶Ç×°úzóµ¢" ôªÅ"Y(ˆV…<NÎÒÆ0Ù›_ôw ÜÃ%_nT`tSå²ËÏOŠNLF¢T„eL;=µY^2ä‘.1J¸…•+†éÂÁ9rÿ=‘ï©Ù¼“ÙƒV{Íjƒ«Ï]ÐISoýÅmmÞÞŒk¡ïÊ_ù6c‘§fsÌ9`6"½3ˆîÞ-éÅ! +‰)ÑŽ¥_‹œÁ¥y/LÝ´Jžž•&ø¼C £Z¼W…¯Z[È\—{Hýî*,D]ù)^Ù•n|²A¯Þ$* ;ŠhGP{Ìaö}´£‡0ã¬f§® Ÿ}+J
ÅpRˆµ×ë6¸eBŽ7à(º¬"Ý~Žñ£œ ðI8x‰ðÍÙ»\áÃùóñÙçŒôE»ð²®µù¥ôH¨
‰!·£©þ†Û ©ùMå{–äÝÁéÒ¡Õ¿Sþƒô·ýÜ4(Å1#ѾîW•nƒ„î+éÝçƒjuG£çô‰U ;góP{^9/ç‡kY+ e²PbN¨g¼FC(wÑÀ1ö²ª0š±¤œ9Að‘Éàå0X! +s"¤^ôÐZ uGäjÙku^ŒY¬¿¤ P¥µ“ÅiŽ|¡[øžËÏÍâŸv»ãc²‡:Û:ÝaÆRS7Ê»lG”«H…?ÒGi’vßä2’çÀ†#g"·Ž²n·%Mû H y ºr‚ì9î%ZÌ+Úˆ8"4õ=z”ßxÀÛœU±+p2<;rµŸ½“1Äû…'5üÒ5ZÆbœ?`ÅóŠ’CŒó§úÃõ騌`$±=ìæÙ¥/ñDñI”wó¯áøy…¸¼= ‡¤Û#
œ‘ç¹Õ +¡*tœ:=¢§yGܶ
àã†(ûšsÀtá#O@æ¾e±Â¼×¥´N*d¬|„$±NÐßÇn#1Ãdß[a?Òˆ#Ùz¯:FsÏ@# ¾:L1ºP¡åD^®ýim¶ ahÉSÒÀv”ˆæ]üLÍmRC랯B]Ê"Æ»6éŒj» _Ä¥Œ÷*6š Ð/4VU®y\BAÙÆRUÛ1 +Àä˜Z6 ê9mgµð.ô·Ý<üŠºk% ZØ÷ùR»Á找QÞÙÇîà
¶ÎÎgƒ›«¦÷Æm“Ïê~ `¦:Ã$µ;(Ö²a¬BU’uÐÜB SIn°bäpê´MR|^r'ÊW›RÎÄVU«ê‹Aôä³Ê××åk'VùÐÜ6 ÇðÄgŠÒUW5=4h˜W¦vOó²”\Á9>NH k¾Ø‘ZìÄšúÖ(PòÙkq(Ù‘‘‘ÖC < +‹DSVF¤Ø´€W-Å×ÄSNhqi¼÷#²2ö¦•ŽŸ9']¹8G"ªòN¿]Ó¡ƒ-0ù¨‰ËG'§cÌIÈ??I³»lè-|Ä g'X ÛyM,Ó‘æÞà»èܘ• ‘2! +ð{ͦ£’4Ù+5cRéú«ÊèúmzxÚòp l)¶P³ò`F êw1&=Ó Âp²Çõ.è|}÷ï$²¤¤°²þ_/šfì–&IöpAܳI[à7;^›î#ÆÁ¿ª i¨Ï®5ÑXJ80-Ù¿Èèþ¸´‰ˆ?:Û¾rqÔlBœƒ¥Í‚*Ñy§#{V†^}?¯$' sTåhš†\è!@Þz7Qµ…[ŠîöÿÚJæâ•«‚ò ‘øÂ'ýÄõ+¯K¸žŠÎAëÇO‘œ„ç³®’éЉÁØt¹’ Çõ.¬11<Ñê Faæu>G èh(Ç!ø¡64%gËœ¢¶êi=¼’JnPÆ+®TË3ø pÐ",û‹ám–p’»_‰ßצ +²KOñH…à@åO “x,à?£¤•<i]ŠÛê‡_VÔ/£º“ çf?Ò¯t+6½’‚ÁÔ½ S0ÒßÐS&¦[pj²c¡œ¯PÄÞšo‚÷qÓŽÍK³’æ lŽêã½_n óÛäÊB aJÁxàZnDB H‘ý c› ©ëHÞâ¶%-¢ÛÞ°ŸÔvSço§0õñ/ÿØ¡e!1ž0Á¼‰/ÀŒìQ-Ü M°ÃhÁ¼¬rj²×ó`}ˆ9ØÌ‘gØÇt "T;¯+ŒñHšÁP<¹‘¾ý +_‘ÉV;üem¹Bh
qÄúbì§ÇGCÖð¥U-Nn×þêÜó¼3 îc 3f›¤”ݾ۸^–æŽõ’†-ö°ŸyoE;`/¥¿äÚ¨û¡jãZ¹Ýã þ¤TŠd®©Çñ +ÞhF®¡Fêw”V _bèc@þ¤ ‘›@ *ˆ«iŠÖÁBŠñðjÀlG". Ê6¬¹†™(PöÑ÷–o¢¹Tð1»ø ÃøK€ +»¦ë…+š%³nò—äck¸†Qµ,镬Ùr»:lÈ‚„-:É«ý€“ìþÁW©˜3Wͺ‹™‡[ðŸ©vâá.Â7ó¾t±ŽtX£‡ìqÑ<sp0l¡ _hÞ2ÆwÚçû8ò7À ð}wQáÔÓ‰œìëóõ®ºL\_R¾?Sû¦äA æމ߇Çp‹˜ëÊKX*.[¤Ç—»èg ¾^¾@ –Æü+É¡Ïèr(åÍɆJE#ǽÔ$XÉÎm-¢0&¾ìÅL¥¶-w¡ý£§d縩 + ¼N7
ÜLÊ{¯ÞG[„–udyݼUkZ‡s'fÞ#¼$GÓ’£@É¡Ì L`‚¡Z’'¨–´XÅïUâ]ä/qº-½Ò1 ¶S֑ÂÞm®qfeY0ú–©µßcò3I~|7ÌzÑ se,ž"§¥„hXh³¸›dµg´ÇRÅÖ‡&¯³~"=)¤aýµNb*V콿$blÅÌÏ"i°Ü=ÝÿÀ$LãÖ[£Áhí©ß¶¹ÿäų)ýç²ÐîÊY%¿UtÀþ7©oóïú‡N?ÊêæöÓÛ_î´^ìԞݡ]ö9+¶ ju£( ýçC~g¶Ùí»7Mšš†æ¤»v"µŒ°- åð½k-EµôA×HñZ„ùÅx Ü4Î\f܇|?/¤ƒ +15«òzoÒPŽ¿œ8¬¾±ì¦´
ƧèæÞ$šlVçäõ†€‘êôüBFó’ †/ZâÅ žoT2t‡®^Od¯‹ŠgÓSu‰Í÷{÷¦«>—¥ºè\:€ +(ŒÙ^+üù$x²Œax7øòEi3@¦šRÝ’¿g$‡7&çÛϬ誾âÚΛŒA‘æÁïÚt•pF¿™¢ vÔJi;¦ÑÂ˲Vûkq†eú BÖÚœt“ý$xÔ²*ZB±À<«J€“UÕ*? +Ñuئµ
ñ“i©Ÿr´W*=»kçY7 +òy2D=~K+°2Á>ÜÍÊ'î_Ü–èuôݲؽiu&ˆà¬ŒìîÃDÄVIV®Õ×g°TsœÚ§à$ žNJ%QÐäÅ:™ÅÇJ>¾ë® Awïé£ácœ nw ¨T<[·e|b‹Yœ2ˆ= º–Mfy Ó7À +ˆm \ Ql%öAH¼ ²¶~¿tGi¨ü"´6&û
²^Ôcícîf + ‘•6†bl* +;F"ž™ t9ÿv!õ,2šHžl^]¹1v1ˆÄ1Úc ÆK±œ>Mû£ +«ß^»ù &û)Sëþ…›.8Ú)íôØ«ðRgÿѺ³/ (a=Qú .{€É}ÌîFÂïk,ðÆC¯Üò/é«5œî=˜Ã÷&ƒ oeícðìPžá °¶úîNÏ \/q¹s…q‘~£Îy©W5y@üÑS3eKWºÂC~L<¤ë,ivb;Ð¥®ßä¤xyÒ +µ3Óya®é²-Ä +î4ý
èÊm}ÉÇ=üΰ›fo q|. +ª¼&š¢€X€âJùŽ«o„*û„ÝpÐdv3tO<amôŠ¾Ù+å‚\öklÊ{°¿6°ÑeWUü DØŠ–Ø/±.å8#E ï–Ò-Ž¸’‘ ÂN :”ø8uf¨ð:¿¢Ã¬]ÄŒ £K/Ñ
}¡™² +3vJÕÇ`q<ý ãÄ Ë»“wŒþÀûý4[ÐU1 I5–Æ Kk™l…µ rsúvú|¹|S#Tñ+¦mÁ¦s~|¨Ê
I
²ßLzŠÑre¾õT¨?Þ<S…ú»¾`¡SÏ«ä 1ë:ûCï2Ë°Ü»°c?®q1ƒä 3M7½VqV®2uHq;%#Ø.1ÑØ+o¨üü„ÊS¹e# +2-Ã6‚¼Ä ÞˆD°5ð¿Ž~{µ@Zx>Iê 1„#Zlž¯ÎûÂÙ]ãÏÝ-ZA±zæY
Ò¬ã Õ‡L+›eæÝ+²/Û¤°–èþØýuQwrý8Z™ìf Þ‘
Œ ¼û}ÍÖÍ*ƽœ>T-~÷Ùº RレÖå»÷~Ò<ÄãB¡†€‘‹ +"ÜÀ.ã†{·`‡ŸÕ)Å+RÑðèׄhŒC3ðJV£FGÁž\VYU£äqD@Ž +€^8jЙ˜l†€MÇ >ÒsÃ.ªMÆ +©#´¸øEV Þˆ žZmM0–±KªOûá7YžÅ É d°Œ7»×†6E¬Ë/«bš_Uº¸/ln¾W Ö?k›ÄíˆYÓ6‰Æjâ“—ôi¯]æj¾ƒ '‘ µÅ&Ò‘U½¡¥€Š’+‘§úõæFÖúЈ:i{]‰˜u½#Ê9çP‡´‰U…šó~ì¦kGif²«]JCM_˜‹ÜJæ%ÛI[êy‚ué” …”YþUøëÖ$\5öu.Gl…¹²¹Š=ÓT*Nù¶ñ~×jÓŒsµÞv|)òí¨×=ÜhªÀæØö}]³U(ë¨=Í“EŒº™§-Þ!4%ýUænE.œ‚·ù7Þ®º¹ÖÑí¦Ù“T}ºðÖJm8M)y,Û¼'ЊôZìÜŠ±0*9ˆšd±Ø= ”É*ΔðÛÚi9 ®\ ÒrU–à‹ÕfÅ{Aš +äRœÃ.òÊú2‡õ[yºŒˆþé9¯p"ŠÙ-Éž¾eâ`†9®&*ªî—ù +ãº@ò@þ£°¨ÃŹռûÛ„,øùÍ » ðþ5ĶO¨¥lŸ oýMWe€ä^ûº#<ãò>HRceïí‰%Di²ÖO;NRÏ34ÓÛSýœCÑ õ€Òx±½sPTVö[Q$‹‡|ný·ÐØ Ÿ¤ú õh}£>£ÕVXØ »ª´-:æ¤ckbNh|lô¬O#ôÛxâëEÚ” ® ×Îs¨†EAWeê +7 +ä®yÔ¾6nÎœ5ÖË<0K‘|ž´×D ]¡‘¢…gËÖ0®,`IÑ~g’î°ÂrŶøñ¯K*o¼ÆYÚ0—
“óí{ +(Qü+ÌùmâèOêûbð… ˆŒvžÀæûä×À´¤öŠòx£‡¯Ð%ò&3J£ ÷î…ìiã\ÐFY¢ÄXè©ëOï›Uv¡jO§qðN>0ÆåY Ï^°vùüøø3²îò°§ù +<ªª½ö×{žœÓn¡–߇S› ]Û›.-ðèo¾ž&å +Ú+×èÙ|!Fä‹"ãÉ_ªP‡íuzy/z \ž©7Ô/Ó…"ÌŠÝ•g$tÌ‘Sˆ3z—É(oóDì&6ø
r#¿>Xêª7àâ‚|\;Â:6P3Eò³aÜ‘ýÅÜ, +A±×$Â
ÞºçÅð%uYzhO8ÛU5©R~y<%ã–Aû ç©Yœ×8÷Ñ[Àsð=¿) "Ø ¸„-Õh Xœý–íY ªž Oªv?õŒí»[šþÞ ã¸\ž q)ö6 õ#À- ‹9ùù€+ãRéÕŽâ7½ñxâ ®7‰ÿ–å&–ìGu:áƒpQ º&òÎ Û*
d +AA ’¬Ã…éÚæú&?žq9æCœÚ/þ;ÁA•OaT,(ŠÇ_]À†y’£ü… [âî{AÛÈð“îBEý¸æÜK# 2‘ Tn¯ÎJ‚ƒ/ÒC”¾Í&ü÷Lõ±>qçûèýá‚^Ðpæ!³ ÚÉHÙÞ3 Ñylòó‘02…Y8™óh®æÓ34 ûÛ0‡2Gp6ï+®d™¦J‹~_NA=ø¶i/´YΛýÇX+¹Ýþ¸ŽÔ÷J:6FcZQêªæìjBЪX–muOeØ7nªŸ–t¥ÛγÎ#ÓbÎC;«Óla·`à¶lÆÀ¡¿é*¬Î½;K æïÒ®®¤Í +š‘º 4+;»^)tŽzó ŒqoªåµMpmDýָ0ñ5½ßH—16sYûjë–@l*ãyÖèy¥RŲUAQ|ðݨ.@@öÒjŸ¡EÊë#ÊQÞVmì?Íü +]ßEº$¯áYfb°ÿR’ã0$| +T~
¤Xž*õ^ŠŸòöÚ”q3B\Õ"â‚û†Åà žé=g ËÅðókز÷è@ÅøÆóÅŒ +ÐV½bÝñqÔ(¾«]ÙbãÌ‘xðÚ¶6R + åR· ‡=ŠRø%¶]ñŸI˜{¥5a%?ug +E5³Ñ÷ÛBÚ&yYf)zá²°£'“ƒÍ3ߤ~„óiQYuÏ…PóßDK û§«” ”/î^œ‹‡Ë¹oŸñ!p©† äÇ`ì +/FMõ˲ÛIVΉÂã.#ìÔH3>yÆ1^*k¨+€È4Œ²5œ-{rÓ¥ÑÑÌ(¿ú´ð÷vÐ9+Q!_zªN°EVY„óŸ©ò…ôm•?mÜÁUmÖ5¿VÂðE€23÷/`W§4 +ô:†T /ѹ„þ¢ŽÇǨëk¸¹žÇ.Ë=¸êã &·£eêúQTIFÿ&ˆãÁb‡ã”H ‰¢ZÊîÙ„NÏüŒIï<¶Qü¶Æ¾dId¾¨ÅOǯ2Å Á ª@¾{¢Ñ÷2!y^
ÉLö2¼ _¾’ ¦(êçäù‰½…¼ +¶iÃÚ'(¼‡’¦Ýõ‰Tˆ}Ì_ø«¸p8RÒIo dÐ9bÎ-h ‘-—a`5ëŽï/í½fõ©pÓ»E“ @˜§4vç5# %€Ó%Ýà™Xœ‹Š4ÐÍxg…µØàd†ŠG9¿OgæŸÂ
Œ\UGkZÓƒãsж ¨¼dï¹9®¿Âã°™u:È]·÷xÌ07!¿{EÇA#œ”JÎŽû&h#åþš;$‰)œ¬6ÌzŽÎk¹©Š¦'/8Q÷á'.ˆ`¼›ÎwhÚdô2¼Oõ× ‹kÄØ5–tñËÁMIäc_©Šh½ ŠFcª”¤%ÿ¬`,³ãúÖw¨ßFî‘Ë£#(5‰^L5â8yᵦ¨’“SžmÀ¡â[Ì· .s̓C
âfo‹FÁÍ©†ˆIFœ"»ˆ’¼®åˆªî“@•XµMü5!&¦eX_E&TÔ[AÅ¢7!!Qb•ÐZ ç㳠ʦK P{ßYÈ +ä…ݯ÷õaµ5·÷'ô ´°ê‹£ b[îÄ;<Q…,ÑÆbÑC¡uObDŒEY‘c¥˜n aÜp…œƒ¸0¡=¶.¹k!¼5ʽà:!+«»—ÒëNw#ÐÆÜwfq)šh=•Iwö Ds¨º âõ|AÕ¤|²3p㲧nÏ©<ÊüB±\´:åªÜ“ш[¼ +®B.Üà Tý¡¾:B[’ü˜u¦Y¯m_Níü7¬ +š)lY^1rs=K¦wÑ5¥¹È8–LË«^¥N}¨ f“ëÂœO1žï¥÷®Ã˜áGÁ§ôVßÆ2fß-A‚z™÷}Ôwß½}oRGmøŸ#^Ò‘)ù }EAë÷Œ{þ§º©_6#èaj%³·9àô¡ d Ì%†}óx 4¯.Ùõ!OW˜W¢šë¹ +kòƒ6™£ÃCr”{]ˆ] gïžÅ³„!Å£Ÿ )àe&A‚zç;Év8ïÏDÇH°I¦ +Zîã2¦ R
#ÔFFCD (NI£T Y-÷Upxé5>“m–OƒLÖf—MqÔ0“ùÖ†Œ~eÒÝ|P¦l¸z [Aü4t€è°>~DUÿK6¯pdy ?fôÍ+Åzˆ|$±T9ŠL½Ï5§ø« –ZªPõÐmÁ,MU/ÕLAAÖ„V®,Щ¿=%¬áå‚8”©—ÂYÕ~èeç÷v¶3møt<§#¡E_²èÇƶª ’«U°]Ü¥„°µ1oœG¥`°4!©lšý¶Ÿâ®ªy d©çxöñ¬~ö[ž_’X™cë({Kêòç1åÖ*"u…&Þj=æFëMô´Jî‡çx¨áMÊ4¬ƒe jAA„]üç¸Ñö‡¹ÉÇ®÷ÏëN¾Í>aPÇ*¨ùéªeÿÎ^…†&\-õ°‚Ú&{T‰JʉšäY;NeÖÙŸ-9ˆÈ;Ï€„ŒG`{óŠÊ]ûå I`hL'¸Ùé&”¸ƒÅžç{ )+¥˜ +q‰È ¨´•§VÍ Õ‹÷6=-* +À|¼ñkº Í\å +endstream +endobj +1773 0 obj << +/Type /FontDescriptor +/FontName /QNCLRP+CMR10 +/Flags 4 +/FontBBox [-251 -250 1009 969] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle 0 +/StemV 69 +/XHeight 431 +/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/a/acute/ampersand/b/bracketleft/bracketright/c/comma/d/e/eight/emdash/endash/equal/f/ff/ffi/fi/five/fl/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/question/quotedblleft/quotedblright/quoteright/r/s/semicolon/seven/six/t/three/two/u/v/w/x/y/z/zero) +/FontFile 1772 0 R +>> endobj +1774 0 obj << +/Length1 2154 +/Length2 14699 +/Length3 0 +/Length 15857 +/Filter /FlateDecode +>> +stream +xÚµUX]²¶‹»»»»»»»[°‰»Cp×àîNpw Á!hpw‡à°ç×½V“^ÿé¾8á®Qò¼U5æ $UQg5w4H9:¸1²2±ò‘ˆ+ª±²‘°2±ÀQRŠ» +üô²œÀþ¸Y¹ + +„Æô*)H¿¾Gsv(·ŽT–fDX#;©J†ó×HŽˆ5O””$ˆµ©›˜vú•+Çnw´§b˜‚ä7ƒÛ£Y}¬œy.C‡ÉùE«{;+“˜XzâØâ/Ù /O59ÌÂÓìT s‚9É&\’íäIó£[x¾Í¹þLÁ«sac +žlLûå¹®«¸Jºý$E¿»²ï™®µÖ Z”N;u‚@«–Ù[|‹ fliTe•]aíïøW-º ÒZ"6ÒÄYý>™ ,ÃÄgÈ¢9’¯m²Ü7z®eBÄ æÔædbFn©L¼0Xœ%4ÃÒUBÇn™J²ëýbûýUe<µœGýÝå¸O?ÊÃÁì“ä`ŸUÿ¡%o<xP½o‡"í;¬Ÿî{¦ÉLêW™%_Ö`¢¤ÔR{Ò}ÑŒx ¬B '• øJâš]Üך Ü“i×–÷È…yÈa^Ÿn¬Rrƽ¯ jµçï³;†¦ŒÎ 3´;Òü²Ó&¦\ç>Ýë=uY¸Šàtn›ëºŒäϸzSyÈ%ƒM{5Ÿ ÑbÇFÄ/ @Ÿ5àÖFùO]È;ïbÀq¤®rZU(ü$w.ÃCáÃãpRy-;½O¶œE'Dð•–KPwȉÜ7²fëŒ(ç +?®MŽzPÄÌ€ Ì òa9KajDGüv×ýƒävÛc€=›µõ¸«ÞK ɶ‹ÛŤž¨#"ÝØÿ´Û:Eò¸Âbà ø™Ÿ²ÐÊ(.ÝŸb˺©o\,?ÅŸP‰&2¢]Íî¿·Õé°ÔËJ!!Ò³{G^©tà0eäyª áWÞx„ɇÏܺyE + ÛÈxÄ•VF ^™eÉ%Á®G+Óh[ô9Tèše'OŒÞeзÏGŽº+¢i»·UÏP¼MvJ®¼ðÉe+ÊRÀz6Að³D—aY|<E@©q°CÑj×ä8ȇœQºVŠ‹>„mEE|±öW/±£O¯ñ¡§Za‰×Á÷̉ijU[ø!÷j ôª=¢2Þ« ‹ëhííVþ áé®Èêöi™%}ò]ÙíÜÉŽ#ûG¯¯$L‘r»ô›*&ñï7Éüü2ˆ™¹EǨ ‚Îë0žiÙ %tmHôb§èøkÛÎÎ__¶§±ÞÚêøïp&š”=HU# +±î.Hü¨õÐw¸Ê‚²º%/|FY·úSÂ~=·[±Òˆ ¿S ›ÑøÛ8Fâí èzj×b0&GÐüfLcDºJP3·Ïé‚å&Í%Ór‘5{ù°ËÀûã¿Fg£4ÂÖøÿⶄÖv¸UAßDÒ毧¦l hC«?Æ?¬J¥@FÂ/bOÃ=(dúýy°ä*Ë@ï¨æÃ6‡gI ?7Nšæ)Ì30ò•™£›1¼~T÷B¼®å‘Ù +û*_ú á9¡y Š+ðH +LP s50ž¥ +qœdUÑ<eY?|úÑêéu^Ä–ƒ®#i®©®Fy 7éO87Ø×ű‰X)í7V¼Õ+ï*iÝ]EÑ„Ï'p"ìb^ì¤Ú1Ý„2ÂËôSÃ!剹„ê•ž&ãH
OUu +Üa¾ÐQ¶ËµY+ø†~|o´Y¹Ÿ•{K~g(š‚×b¾×Ë"N£
ù²§:ª$8%7\…à;#ê¥.…' ¿ S/P0ü¬Sû6 ƒ+mÓHx†=oÓŽŽµÍÝ¥*~"‡©
Å“ <ÃÇé‰Ð³êKÿ
~åÞÖtlµŸø‡ ëF™BDyÏ@®àS8¦ºØOoL¯bµ“ÙM[¿czGEדe‚ˆ¦^@¼Ï#÷ +†Çøž‰ä†MšºÖ#vW‹}<jbTK Žm(Z½}=ñ;ö°@(ôÓ;¼BpÚg–$Õݯ}
J5ãh7Pš8þ~:¥ý6¦êçèär“9%·/L dDÝßDAʾ’ƒèÃeî2Ú]Š(óO0ÉEKÑ™‰Ãº5 ™c^ÄqY C–„ã3À¡Pˆ+8£ W+Q}è‘\ã–ùB̽#râ†éaÞlO˜4 Rø+Irû ÷ŒF’œw¡÷ë> +c|}$è<Ħ# ²ÄÃE_î¿‹ö•r+¬åÞ "iƒD¥Ö A˜õ’Éa/Ý[{
l…k0‰¹¡I¿÷Ÿ|ÖáKP4©W½hŠ–[3%M7]Ô%bÚ‹€+ _ºUú´u£ÖqµD |òîÇÎØlµ¬éôKì q-4¬ó\ó×ùí C° +ìDgáòÀ "º°{¾ÄÉõŸx0—m6û0‰;°GI¿ÙšÐà ݻÛ]Òòu õûч(ðÚÏ<.êŸæ3U©ýp¥ FêŒx± «l5,|¸ï,*xƒIð·%o“FXªÝígÌR—1°|=(œRÛLr±ã;xhÍõÃ,;±Ì«,Sš› îj³X’æËéî uýxû™FÑ0‘Œ˜RÖ +Rn`ýÁ#o¾<ìs”#ð%kŒ¡ãV˜_œÎš’@ ¸˜\ öØßÇ„”õr)5¡@ºÃ›^4uÏG0˜…ÒÒ!¡Y¨C(¤p
¡%Ü.‰ò•Šc¥?HötÂÆZëaäÀEuubåóèn0ãôçN5–¶ñÊ-P¬k™º’&Ð
…¹Ä)#04g× ìkÀ²`ðþ`$ÐQä÷oV¼‚‚Íñ¡jº ä
ÚD +èÓ¦ò°ð´ÁξŸ9œ6´BD-¤ðàò©h…‹H+—ö4B +¤ì¾·€£@Ƥ$bd®áDN~cÇ0Õ¾ö•cWÑþ ÿíËL`¡ãèÑPéµØ-·ÌjG3ÖBy91¸\û°›ÀìØn¼?¶V}pp²ÇÌÁŸ¯§ÝkÓ‰¢çÄ]^ŠOî%3Ö¹˜R?S̾úÁhcÛVÍã‚Ž[\¦t ìqfÎj]ð⧤¥Ð0VÏ¡"ê|%¿ì 6l‰~AÑjÊ€ÓNpl lT‘Å» Öÿ.ïR¸±¦ŠõŠ}†HÄÂÀ²§Ÿð‰`ãaü—gÚnãrxZ§ÇÐ,Õ‰\è…<Zg¤l,l†ÈùTöÎ!b oä r´–>FŸ«á[Ð×Hiæt÷åyy_§øˆN$<Ã~"ïµÁY·¬¶ó5vø0fˆiøKÝpSÿGU&úrCr þ%…òvEÛ +íûö
ìBÈW•óú“kÉrCí™-G< XJ.•9 ´ÐÓxö§{ju’K§ ÕáÂñU¬ÝÞZé•©7@¦ $å#˜ ˜ifßâqºN†$ëZª+ªZ¹2÷®Šä]ÙÚ*‘¤þ#È'výs)´kòl-x²òÞõE¶Þj®-ÜQï6b…Þ5+?BÝ= Èöß7:Æfé01 +ì}¨Èpö*Éxˆ<#;¨ŽÜØý =½A.ñO[Tªb6Á´¡ôþÉõ÷œ$=†åóè*œŽ¶4!Œñ÷å~¤÷Uìߟ*H3- +‡´òÖ—ßX [ÚÓ9ÔP¥+£«ójb‡ ;úamª¤g-ªsAZjISûßÔ L?[eÖ—< „´8Ï»¬Yätá€Édª˜B»nÛ_wóœ)f +øeÖc5µL|_M¦&ñ?QœcÌ™¬ÐÏ7)OŸ7ˆ>Ga:LÒNR>Aåå±{0Xf¹ÿrÚŠ:1ÙŽ¢› ¯¼ð.áHfYø‰%ä"¢"ô¾ì5©9+ÄÒqa>µ›ì°í™g‡%F^Ú}%󽤊åÉ'î~ ¨X
+NÓb–èˆq7ÁÒu-£ µërQÊב
HõíC¤u.,G‚'6 vÐ:ïzÞÉg<PnVž?æâÇì´q1B%’Œaó—Rq„éÂØ¥Bûõ½FŽ~ie¯šl¯§Xärn‘rC¬, ¡ù‚|H¯z=G¸úÁSsjüÅrŠFEo-}=—ÒåFÛw3Ò;V'ºE`ÜÈW<ŒzË®¤;)ž| .hSyòè?+@S µÌ©5knN®Ôéž ñÆ8»Õa½éö +š%
íwÉŽÌÿ¡kP¶µà~•Þ©-ƒw¢d«§˜ÖÈ„ºk(ôƒ É t]‡áìžFh€Õau#Ó—HLt
JlZ zo´§ô¹ muŒä:‘! mÓ9»XAqð…M•ÀÍÔ‡`¹JòÚïþªß?µ[©
T?1-ªÔóX qÐòÉPú!îýe(mî*?zf›w{u¼ûžÛþüT¦pëó "{¼Ä‘qüꢷò’7v-VM¢Ì½â·|tÙÈ@9{?“ïvÏGN¤€—ôAveó²‰1tö/U‚°Rº±‘»÷Ã’Úúw`¥¤Úº°Ð’ŸïNS]¸ýÎDˆ F#ÍêKEW•Ž¬CÃ>9 &–4bô·ÒkáùIŽ—c˜U'@j…I©¤”(ÔoØpç1.] ú®“éˆu6IØÈÒ["\%ç~o{yóÄÊRè7ÍtœP0SŒáÃÑRšëôÒߎ}e‘õ¨>E’FžZ¤ª«idA³vuTmiלbÎÒé>{šÓï•ã_p =ö'0íÚbZO”ËÈåeÙ1 iDÿIœuúÜB¯ž-1ª'É"ß‚TçÇäMÍ.ážÎuÈ!ÕWßB ‡¥ÔZ +$•,`+ÎœüÿkãôÇRàç~(.ÜK4m¡L ТKÇ2æ%L‘Ã*Š‡9•) . ³Z~Õ½Ý1NøUýÆÙÑ¡|Là ‹‡WUÉDÔŠŽMB“c î}<§\ôxsÛa3Aø<“Ë~)D‹¼ÉÕZ>µ=Ádrwgøœ[Í+‰9ÊìëpEiØmÉ×Õƒi¯jy²Úã'ˆ^¤ao×ÉëóŽš _he*nð¬‡Á’—W+M4¡áµåú„°þRÄÉ_¥YÕ:ÚO&öGÊpîKogïTt@”<ÀüÄë/E‚=€£´çÇ–.ª|¿Æþá_“ú)e¢`Zê÷pk^@¤}bioy Wíù|¹½bã@s›˜'³¸¤†À¬×œÂhÜK#~ªÞ÷7‘sy+²Qx +¯Qx9 ô1…úÂ]á²ñ0$6„].hoökróZæ| +âm/„FOö$ªÝOŠ+ÐI¦ÂAvQ ä«á#FRðœƒÒ~2ùŸD÷:çžO»înraR]j°èóQnÁ¥$³¼j=X´·-žqñÏœi^׌±üeKZõ2—!Anœ6dIÍ<×JqÕµ/Ën±mÔ\ dŸe–³<ó†!/¢`à ¶†3„.ú
Ö°åï™à– Ù=Ssí«åøñˆÙ 7÷Àùí-Aç•œt‹8X«è›JÒ|ŒŸæ„Óm9däl ›-›B)Ï™ä³Ääç-à’VfdÐ ûܬ=À¢%¬'7nüúyE_ù®T +ÎbDùûm·›X©VÔÄqÍMaºi7Š–!ŠÏÞ-†ù ‚ƒ¼¤£ðjúOÞÈe §äµäïŸÇélX÷² •SJQgôÞ`qø2™QkÀo"Rßê"‹J¡âÂp-Èù.døW +¡èÖjû‹æÒâ²H8”äßl +h +¥¿¨² û&ø.‚m6й.l;«Ø#ágÓà‹Œ7Èãtt–à²×9Öá×½éTYµ•þ´Â‰ð|Ó3ॽt܈<n¥9-&-GÒUÞú½v7º‚^Ø"i¿ "¢¸"`?TÃœ Õž\î,j"´}\'pU B¡²õæÜ/þ‚sGápùØêÖ·ÓLWüy)§)ûFç&Ôó5ß6<âÇø¬7nÐl•ÑcÝXíUÕÑJdJ€"œ;ÚÔiL–_Gýù¼*1;öZ¯ Û9 VH|ÛOϱë >pôXËwBTbk6žd°²þ—¬ú‡âÇ‚^ã5¥¬‹yص¯¯„`„ÍŸ”i(u½]DîÿÐÀuNtb¨Ðü€Uœ €«ÂšvµYØè î°ªTEñ¾é-c¯$ˆí”#½'„¨¨ì°t 7G@C ×f”…ݦbr¬fç[L´wöå[9ôõm^ý!Sb†óf„+5%øêî@&Vj:VøSÝúsÎ|C]ŠÜ1¸`"h ³XBõû üÛ»¤€ ]'H÷U„` +7 + +&úŒHBu Fdtz¬‡‡•;ÆL’ÂbäÃÊN['ßdÉï/úX̹dÞÒ( +ÆâiQKW›„½É½ª^Pwhï¨îsö5綖R T塾]—ßDY
{®+@ͨë’ŒÎ2ο^(Eãš?ãXȇ>µ&!Ñ2ð[Ì7á(Mz•ÞŠ.Ðú}OSÛÆ1:¢ +¸Óßq2«:58–}J.Êù!ÁÔ«âŒâØh9,£–ZÉ +f&3‘ ½ÕÞ=0Eg’c»QkOË¿DÏgUÙyK +Œ®6}`ÀPSãöë®ÆçaX³ùJâ½-CûÒâWeÇ"UæZõxùÃÏŸÐ%ꬳCaåw6÷ôx• FX¨¿SÏÐñ !xÔS,}B> |ò.«Ì ßÞ ýµÏ@ûƒùî{Ž=éë }º€ƒFEWÚï!Äžî´âôfþ%0· 솵õnÕþ!,:Pžatk¹/'QPI͵ þ±wÍ2g¢EpY—P=‹Ù4ãÛg ‹`“†™XÃ1c Hdük~øXg‚²WlN…ó¿è–x#
ŠO±;б 嶒í +X6†±¾YC²—гÈé!c[wÎg£Íçÿiu™Gˆ8ž’”J?dŠ="‰†gGÚqLG‹ µÖ=…¯ô‚37>â8–ÍÌb¨@VÞLaDÉòÛþOûucs•c²w™ƒZÀ܃wÜ@Fk°ÐÚ5¾¬aíŽ)ëî{Ü[¯›ÿ€åbSÉ.RørNy })øÝc1''ÄÏ/ÞŠ²ˆ[¨ ä1Ó:ªß¿i´ä…fú”É(µ¨#·ª¾¸"owÃѲ½Í A _Óƒs¹-Å Õ‹ìb6Œ8 `^`KI.8þnËtT3,ª +£OõÈ# (”“°Én#ëüŒ•ˆÙ¥í²mrnkjÈZp8ÖžÊf1®zØs´)YaYýpo ZŠ8Ê4Žà6—¡8þlƒÿ¹ ùSN‰g_$«åë ƒäp #ûò›P~ŽÃx¿Í×…¥Y™ž¡I„#a*œu_ ›Àhª‘ýëпÉXô„T¹ÕQêøÓg¼9úØbmWðø:É”˜6Ù©?Ó ¦4Å<wM_Í^]eŸï•öôoŒÐMÏ*kÎüAu‡éïÖsBEve v 7Æ~ ° +é ñÒ—<±—× ßràßûmFû.ÖŸVT.@ +Åò: *¨ð
@á¼ê +ã ™@ ø$$õmCäÐCƒrYwô§a˜8îÄïd—nç#s›•‚xÞçn¦_[±Æ’P‹Lˆ®–“ùm‚rÝ‘,½–ÛQÁ1U3Kmø%…,·ÄÁL,øVœ÷ÀJ)Í¥–çÙaDœÎÛæMpÐ~ãˆÔYuJ
”iDã4²ÚóÙ9ö•Žâž¡&«‘‚?œH!6ÕÌk¸ +Ÿ¤qd¯Uþ£qP9Š²³¾,MQúÇ0J"|ZÎráÜ`SôQb` ù‹ ç·mèœ6$äp·ÐÈ#õû—V𦠵î +TYüËòß0ø†ÕCï7üoNg]a«ô98ä…§q%rä û4ªcØ>”¤°p‡¦£[°3w—íâh®We¡Óº}<<ß…†Çû•±È´´‡ÏÁïvõ¢ ºÕ–¢â¶…DÝ‚ß?ƒ¤Rð3 fÍ\_ |âì˜ ë§ šˆ»…Æp*õ«Â‘)xsñáÛnïuË…'áV(ÅŒ£í +”ˆêճònTQñW¤xQ‘à¬?.&Ý !”¹ßD ô×ÓÔ¿rOy¡¾Yì˜^õà1âS†&Ç*ß4¸üå.#ÿ;Á œ²ÆQkx£V*(é› WErãiPåd°"q߇ d‡¨Ø!1F·vXg_Ù/ÎOËÖ(y™¹h³x[!ݼ Š6Õ«Õs÷Ù{–ÕÄhº ‚Òçš·>×ñ5_¹¯îsts‹Ç™³áïf!õ}yÑI(õÍ
r†úÜñCZ4³Ý¯ê¥Ê 蜵Fè/¼ªÀaÃ+Ç"Ÿ8}¥ò¾gI†R0')}™
¾”á’ÌŒ˜~€;5x5ËíegnHô ÜE5|ÛŠ2 ëÝP+ÿ½aÒÛ¾ ÙmœWØÆHç râÞ›E¥ÔÌêïD˜;ÓÒ•êENÅå#~&Ë©œ#U×Ó ³;µx’Yãg §f¨é”]´pÿŽå}>ÈT46¯Ø$8Daô“¬rÌÿžb,GÍÓ –…Û/<þ ûRÀ6au´ÊôãßJ uWaqg+jÏŠ®w,è§.–ÐBpáÄß¼¬¤!Åešùø‘ÈCxž`Œºöl‰°aÇÞ£‡uw½MüåèÎÐ@šŸŠ:ˆ˜…XéÃâi~•¼K[±,¢"Á·"ÌD74 üáFkHå~Þ¨*‘«^²¨ßÚ´žŽ¶íÞ}Ÿ£ÃZ™du°Ê3t±m` 3µ³ž¨ Zç!Aôõ^NvOÒÆ„ ÿ»¾tPx.ܺú•9k¿ÿ—° uij¼Z !_vF„ 8)×ÞUª¤|æUr ; »†}I=Š¤´õg‚WJâîXÅŸ±! +kJËJN8E‰2 Y”Ù03¤š—•I ™®06ÇϨK.Zl=Ÿ Ë& ”ÇÎ1Ò·¼ .l_ùžgûÎZ¯®™‹–e?qTrt6â@YÄcë’JRâ3Úikàp“ôTìÚ§ÓÓ²ñvüöfË:è.xËË)~KÈ–‚gIº]Ïúé¾R
ÙgŠAlÅÝ +5@+¥Ù°Ðû%.”Ž¼zËîÌõ„/ +Zã [uäEË¢a˜Ê†p¿ý¥’Ÿ† ß8Û{ÀâvÚ¨_(ÊÅ°÷Ø] Ií S{Ì,J»š¥²Æú$ Ù€ëC]Òfº÷ðNïd?ó‘ `T–DîØ#û¦ÐdÜ·°¡âVKÞ¸…UºVÞ\>ž”<ÏŠlÄéÎÎ@ŽËŒWüHc¾ð
º?Wm¬E±[OD|ôë&õ{|—5{×æ¤SŒ™ÿ€NÄŒ>{d™Ö¢Þ‹Å`+-„m!¦–ƒ²$›S“ “Õ^Ù× 9…ÔáˆNsåÅ +å9®ú%ˆ ¢¡öS _0Åðår‹œ4±‚mP] +w>ߧ=¼;–6Mt±T[ ìÄ +»öx¤esß*éjN#ö7·Ê,ÁZð·+]¼(î ³ª¨ûs ·Ç¯ù»íKªžonAÂ>â˜cª¼m¢‚ ,’Äκ+j ”4kzâü~¼9Ç+Dϵ«@²¢æaFž(yA‰úBs>” º` %ƒ0i• Bs È(dˆ X·,©€öõ”žò‚Wý¢ØxÅ¿!`5MÆÚ¡Ç›*ê„ îëš kÎàú‚œU¿‹"iLòôlÄÂ6ÓÑÜä…Ï·ò“Ñ2`‹ZÌæË(+©kß“¶Ù‘u<Y˜ƒ˜ t}ô±qò~ÜJ.Ï3Ã4fáAD›~äïM«:q‹C`2µÆF¾´dÏP *ë¹`SOôh•Áçþª/ì´¸÷j¦»×*5LKÛ -°Øxy|‘Ý‹±kB€~œÜ +É‹’PzXN”öÔ Rpl ¹Ë¸<¶¯IXðYNþÌ´ºÍ°6Ù†\¥ï$£H½Ÿy1Ï?;Æ"Á;ÿ>ž‡2çH÷¶CÅL;ûΨ}°lµ³½¼ºërƦC+Š9JwI¸WÐuQ… 0Ï?j.²Q¯Î¯• -lé¨Es i
¶~<…‰T|h:eÜH ²_m¹ËÒ’!™¡M?0šÿø7>_y§AÉÎ Ó _Çb7:¸_ +¢£±}2Ôº ZoÂý”Q]•jŽý8> ’¦S7öq4/&;ZªŒœ±ŒÖ¡¸/»•*H‡¤l,Ç|õUíÝÀì_û¹µféÙ›s‹\_:Ê¿/1°¶?ÉHOÐ-fû1:ÃîèÝ`Û°ìe|Šh +—GÜ®~]Õéˆð£–¨ÄQ‚$ýµ0÷óg“Ÿ +I]W%xÅ|¼v†0¶Q…ï:¸Q*“ŒË¹4±Ad2Èt½Ý}Å1òµñc ‚
Ú3uç/-Îcoj0é ¢ÐÜãf˜¢a¸Å$hA`
¯Kò7 à4æsÐ8Ÿ VTØŠ6®‘—gZ?EVàæ JÎÝQ f£n•Nß}É‹òº'¼’$ï<ž¿8{–žØŒÎNØ ~ý ·µò‰sÇF¼ ®|ÖëÜ=¾Vá•ìëÍ(‘¥¾ŠÍr–þŸ}Cûï]Ï*‰[ +”iºX
RÔ¾žy¿FsákÆ@C=¾-$êÃ'+ ¶ç1cñ‹ç‰ŸÈ€³žõÃé¡;¬c¯x ä~Õ¨k©·[^«¶ /¦ÀX*²5Rpé¬5"' °O,áŸ25¾ö˜º5ºUÅ9çmýÉa–‚\úÕ²QnsLöÐMÛ¼ðB¢ƒTˆ\̹Û}Ç +ÍÅ«·úþŒ¦4ó¢ +§»ú;c k®çc°zqÑá`º€Uª½0Òüá®ÌOwEê™#¬
”»bðIš¨AŒžZµX¦-ÎoÑ/i¬l.~xtž +˜ÁÜ´ºáêÎâÐÎ8M»× Gâ¨C ¨
þ(-”±.–ÏÇDuÝyô·‹˜W[#˜OP9©¾“—¾õdB0Z‡-~9ŒìFjþ ¶fÉûòÌŠ±á„ž®²vÁK¼1h3•¨^kE,Û*°hÙ¡lÐ[‡f‹=6‰ _¨±™É*’@ΚI1O¶&åU<Q +HÑÿheòo¡ õãx‘"d‘þðüg9s0Àî¬=â@/K÷Ã×t(•Þ^ôÒ uÉž<Ù +×]ÝzÔ‰» MÝ¥ ¨sj_ :‹MƒÝqûR§t³Îv÷l9ø²¶â²»NQ,æÉHõÒlªÆ `L_Ô<8™crOí+ô| ò’]¿)êsbgO KÔÏê Tz!`K0M/!´UT1šìUËË% X(£!-Üx
ªƒíîØu
=ÌMœ€¢êŠ¥=7»)£d4:H°@TïÙEµO'z`Zíë¸àeD‰LçY‡;E$³„ £Ýi/8-ÆÄÍ6¨¡&òoY¶” +Ü>Õ ½øÆqÆêUˆ¼{?Œ¾Íq Ω“!\* ûc‘„þªþ +endstream +endobj +897 0 obj +/YSLVPG+CMR12 +endobj +891 0 obj << +/Type /FontDescriptor +/FontName /YSLVPG+CMR12 +/Flags 4 +/FontBBox [-34 -251 988 750] +/ItalicAngle 0 +/StemV 65 +/CharSet (/A/B/C/D/Delta/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/X/Y/Z/a/acute/ae/ampersand/b/c/circumflex/colon/comma/d/dieresis/e/eight/emdash/endash/equal/exclam/f/ff/ffi/fi/five/fl/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/question/quotedblleft/quotedblright/quoteright/r/s/semicolon/seven/six/slash/t/three/two/u/v/w/x/y/z/zero) +/FontFile 1774 0 R +>> endobj +1775 0 obj << +/Length1 804 +/Length2 1692 +/Length3 0 +/Length 2246 +/Filter /FlateDecode +>> +stream +xÚRy<”kŽ/cmÔG)^ûfÌ%22¶ì„6ÆÌ;¼ŒyÇÌk—u,}–$Rä'“£,ÐQ)!¢’(mô‘½¢#”%…3ôuÎ÷uþý~Ï?ÏuÝ×}?×ïzng·ÝØ$Âtd7Fc X:¸ =”ŠŠ%$!LßOB@c +L§EŠÒu„yo<'ÿS?'†ÒhŽ¤àõñ¼ŒþV%C´ÈÿÔá`F(2˜2é?K=ÁïÖ @ +üsÕ!Ñ ²ÝŸzß)ˆE„"@Š3„ +q :<¾„/~(—ݼÒzKmzÙê¹Íb£à q¿@§¤öâ÷ÆnÊRƺzY™âDm‡
» T 5Œæ$ŽF9dl+Ì›SkäpªËû§>É;[Æ× +¡9[º‹§¶èÜ-0¯k4Kˆ/n×À¥^²:Vw#òéµFb®Vòž3ªÖŠÞ[iæ`£÷Í@¤F«¶@ʽZÚ« Jß¾êe/»µY ñ=ÑYÀ>mvÁE`zŒ4 +Åu' ¹LìðP²Î + À†î\裷îi¼âùÜÄu 'QU<dø×HÀÕúU‰V–šøMõE æÒVó;W Ï楥Íùû¦”'È )°‹ùäd¦rð„Þ•% ‘*²Ý³†@o¦x)’cÐ-YYBÃIœu‰ƒé«Œ}õnII÷Ùkñ&¤"\{vq@Q;h¶(k¦ûú%¸ý ªW©%LÊV°ÒÐèî¢F]Í éèTˆlS××x0†[*·Y³§á‚wÝ’Ÿ)¾ÎÁüñ+}k•ð†.kMÛò½M›Ú„ö?RÅãÉ_긛s|ÒMâ9ÚCg‚6R »¢ÍÛ¯EP<È—‹Cㆠ+éÆÕ;Ù2Æ´Ò(Û3mœ•mè\ï%JÛîþ*N{“"W½]¢hê¤Pb^q*£)C• ä@ä êÍò0®ô I!¦‡f0Ø|qórÇ«&’†ë[õ%ÞtmB1:*f×$:³¶ Éî1ÄzÔÆðr»˜ÖAþùÌ¢™=~r ‡‚g#=%Eˆ.+y_¢åKtøß«ß ‹ cùPtæ +çûÄj7 > Â72¼ßà„“í{õ)Y÷æ Ë7w·Ïˆ.I• mJnh+ûø‹ÑJuª]É]Ž*^ù±CHß.Çž—¥ÑÛz·ä©8• çöº(C¥T—'¿·´q7ò ÓI03ÎA÷äökêûô¥°jíѪ6ÛÙ:®jYf·EXØÐG‡¯»^è#¨ôĨWËíª¿ï^AJòeS•Š!ÇmãÒŠŽ¨/ÏûU9‰ès”eŸ¹w4óÌ·äÜY™L7±Qf˜ÖÇýSʤqŸ°MªHNjÊ’¶¼À©”òÉ´Û—I²/›ÇløBvNœôv¤ ;3¤ö^ V<Èj³—Ùª2·V^µ«Ð/ïwMôšÖ³h« Ž1¥…¶û5 ƒå ×}nPäæ Äß$•,ñ™/γa ÞŠ9ÇaºÁñWr¥‹+ƒ MÛNþ2=Ir
-øËоű Ê#³Ý_[ó'ï(H¨bŸå×ÁøŒ° ¨lä|
aE+ö·Ùô8S)ÎÓZiû¬7ƒ,‡àM%2ùþfóüžÜKQåfüMÑó™ìônÅé¦å"vÿUÑN 2híµ5ø¤çEîðɉÙÓE‹¯Ïß+[ýÀ/°¸£Hd-íiL¼nLa'Œ5”¿'›`r),#ˆ eð×w•z.¨|M}Q¼¢>ø@ ùí(I=#nílrcí×Ôòó–©Êþáök33~¢ÂåñçT&¥<Ü›9 N6f7ÁmgZï涺À!TÍJxŸU‹@Úo¥õ¥«ø3Ê\êÏ2Üø0»•èó\<Õ”ý@ñaÌ2\Lî—®T7Çñc¸Eúf3ŒoþŽ…}ï—çiñ–¸¾ÓÛçì"&¡áI“;W½%t3? Æi¢«‚N¨¿ÓÀëY‹ÝUýp.dQó,A +endstream +endobj +1776 0 obj << +/Type /FontDescriptor +/FontName /XJZFWU+CMR7 +/Flags 4 +/FontBBox [-27 -250 1122 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle 0 +/StemV 79 +/XHeight 431 +/CharSet (/one/seven/three/two/zero) +/FontFile 1775 0 R +>> endobj +1777 0 obj << +/Length1 1262 +/Length2 6624 +/Length3 0 +/Length 7381 +/Filter /FlateDecode +>> +stream +xÚ—eX”k·ÇI )é@ZbènFj@z€†jènDT”îîFºDéi8³÷~ßÍ>û|=×óåùµîõÿßõ\×Ã@ûJ‹]ÊÂÁ "ï +ÄàT| „žÊ!ôT ¡§ö@=õ¿I¡÷ê +š„PÐz ^ +½«âDx¿ÐѸßP¹D6ùh Ë :ŦNÝýr3ýõÁ«žJïøƒªçOGºóà üÆšÉÓ]>dõñåÁÂÄ×¹Ýé‡=;Y¯˜eµ70i‘Ú
ܪÚ?†ð èÉ°Ó `ä¡Õ$Hu*Œà
_r'HŒG[
ö³ Ǭc[8rhr%¼ÊÁÌL¸3<Ý—4 M›â7‚LÍXOÛÛYƒ£¢Øxi¢sb>Ö7Ü\•¤qJŒñÔ0ƦÂ&ÅÒÀüruôñS«”>Ué~ A‹“¡ƒYî/Ö驃K¬ +ùÛHЂà]ê"qšO#®aӣ؄ÑSº½?gŠÄ ý&’)¾µŽ*Ù[¸…Kímcà]·òú,¶p ΀’½Hkˆð»L²s€ 8òŸoÑ,‹±|ôî÷» !× kºaßÌ,DV’ñ +dj'pt«aÕ‡Üäûrd5 1 +gË~õkÛŽce²Ë#0`A“D_j)‹ø~¨#Õ8Γâ%ë-Ÿ,ÊW8ƒ"ÚvíXh8^sô†¯Ó_q+_<¥Àô…!ã>ÑL¦y0ÿM±Êòwúåô +Eƒåëä(Lxξ%½¡{Lžù–Áò«ñ,‘h±šŸvÄ:é‚éŸa ÷ży®X=«Ì¥b´õ.ˆ 4â"ÉËJÝdƒÔ[ÞÐQ2pØ_ U‹`ø|ßÇ×{eXêÄÐÿ:‰6Û¼ø˜«Êáu⢩© /Áš5#ˆkö+š½¸³SûŽøoœ'/ê5è¦.W´ 4• WÅö3Ç—µiâƒr¤`ÖÞœ3ø 8±!š¢[b¨oâ
gTÑ„bº‘. 'c »ûpœØG×hGõ)‰â4 «¸þNZ]Aïb Š³Äß·¯]¤?Ts¬ƒÂ —??)’ ýà‹ w” M$²îTšÄ]²*#"( ?B&yŽo^LBd›Æ(ËÝSb„òI³ðL‰ž÷«ÝÞ” #Û”+hp9Qæ0:‡TO ×3`–Þ0_}ío×üÏÇD»#ZÙsÒjÛµæñm× j̉qQ!5³Ê_SMA1¶˜e‚ {àûÍ„R4›ï g¾-5tª-ZU—8Ñ” v³®ržB2¨âr>:
™bä7)‚ׇÏ?'ùoô>“ÓtŠ :ÒŠÁÉà¬Ðô<ŠÊ:.oâ 2ÅhÚ0Û²zÄý2á¼7ìë˜Å5‹šÄ'hv °CQc)BéÂÖŸÍ»
ÿ¹Mb}qÂQŸ,ÔáŽ1IÿdÙ<LÁûÉzôuAx§ïF•›å|ä· +k5þÜú*u³œÎ £ç!•Z†ÜëG¯V×ß ðŒ:ò å/âî« a'£Ãí¬|…_É¡á Å(,H„G³P”)ŠsØMƒŠªJ—44šÚôùúU)Š½…«‹ÍÕ¥¶m¾<áˆÌ0ýݳX„Iúr®Ä_T¸#T»">žà'—SV]©õGuîœ
ö rSß±;TAÖXDá”e#C¶ À¨wq® $\À/II¯š +òýîØñÈŠÂîÎÒ¨¡³gÛ"ð1¶0H{YîÞzÝTé½ß’D{ýò„Ť½ß T8 za¤àï¯pÓ,Ý 0¦ rG¶ì$··zy]Q÷•Á
ñí^Yltrz¬CÉö +1üâQ½K{:‘ñª,–ü…
Eqà|'¸6âtìž6›¡ŽïÈ׸IœÌÀ=0 \K½êM6ƒüß4–½Ú ÂZð¹»(î֧¿¸™×ºDtá})Ùq2\uW=ʪåÖ šÂÎQvV0OÌš#Âßµãÿ,q?C»X'3â:†3 Ma„SøšPÅñ G¤þ¨\bªp«¾^þ;XA 5´Û€xÄ97½t- +²°ŽPØ€$q+|•ïÁ^ÖÇîŽ
±ÁnæÒ2›^EZZÅŠJBÁÉ7Ìê}{pV® úµº2åàN b3ÈáF›žÎâPe¡éR}ïòRNh!ã%–@uu‰‰_ãQŸR&Á8TatãèFUpÔ]¼vŽ‘Îñ{æØ¡ð¦×?Žgw=?¸ÉJGÃä
88{ˆë2ýºZ>Gª‹ºËçgß =¥0AJÝX/Û]âwTbÈIíÑdYzv(ªPå·:}Ó¢D +‰X^æŽþü‹»˜ù––ßç˾úJ”*˜Ytæ9…–µµ¯9/¬,]«Mšš…ö½°4êy‰Û¬Ÿàkó·ÚÒ
ïi«3°´@þ«ò4O†k5¬X™÷å+eæ–elÈð3&! WDöhЉàGý²ÍØi̓$¶;&ƒð†ÝBŠ@/ûÒèÈNI²8æ`[N6íW‡öéî@š0Óœu¦¹Ý´ÊŸ+Á'hs¥¿Yy6ô³Ãï“è2µõ+a\¨5à,+Ê”±xƒØcÌ*ãOÙp +û-ªeªw#B 줗:ð:Ü‹•ÛÚÙ +½fyüÐ +d,ŽöeeZ;ð(ïlQxP„åéˆPç—ñN6Á¬
™kp `ùQÐ )ù‘äú»R1g°¯da4a·åù˜¢c!)þ«=ܱõ\ÍƼɧC¤ü!ÉùÞÏB‘XÄ?ßQ‘ú ¾a'Û§.‹Û¶&ÀÎ /Éù`Ú¨£;ýž“gi›³DRˆV|Ÿ4¤MÇ< ö½>`Õ¥G€6K¶“oKÊÅÞ<¦uÙ㶀þZ¤‡"åŽ+ïž>¹ïÓ +KÔAº WšÚ£É•ÌÁdŒ=n5äà0Q<¼¸[óÐãÒïDÝ|‘R+ADUÙ?5=¬3\dÐ×mDZÕØXHׂ”?oRЗsx“…z»-¬6[ 8KR‹¿à©^ÖkÈ~†
®åJ¥ƒD¤1½G¾ás¶á©¨Æ2W"™²VSLd kšqÂñdQ¥f…V#×Ê|jÞ§Ž|P¾¢¬.¤9E£j$©È …”—UÎKD¤ŒÉ͹QòæúTuGq N‚Þå°¨,E|ß©WMRD‡»Ç 5¼L+šˆ9öÚs-îôH‰—Km— =•›:
±\¢›K—@ß“"ȳ¥^ðÆÛÝ6Å¡Öím»Ÿšr–6A5YEUy ×D¯!†J ³¾ºd6[œMžÄcSg W…ýªu¿Ñ¬0š¿}Éh$yí6?°dã!qÀoñœÕºÅ«ç“][m*;:i#õê³yõ§–aÚyù¸ä<œ0sb6öé3¯sŽÆˆ*• ¡“Aß +´=J;_Ùf
\ö9ê ®–ôƒ4ÚÅ-_¦‚¦l›b +½=È…»e'E7Š³É +;þ`²1r‰Ÿ·ˆ9r í¼)–ÿ ÑÓƒg¼óö YŒý×oá?9Ø Ç™b¡’¤DZ¾bc`0$X%”R‹o×À†ù°l
´2íEòÖt bu¬ÍaÔ2#%[OO¢1= µ”§ ×5À%Ý™æs +=ö¢8³c/±ñR×Ðá¤à—›ÄvG÷A´b´O’©PgÅ ‰'ú4«uà˜MlˆÉåM2! ;ØBºÎë4¯ÿ"ò£^ÖQ9W‰úB°*›-@à B|ôÕAS6Vœ»§ãýÚ©
QË}N'ŸÁϱþ¹ÜÞ2ݦû(ËîcK‰ˆ_ +¿å><‹2— ü(sP÷FÒ‚ÍuØÒ:2‚Ú»Òy‰ò.!>Ò¸jЕNÉ®”ÄÊãFHë~Á¾b›öÆO$Çñy‘œHýTø,×tíGçsÁç+1ójE£=²Gi´k}i¸òe4‹»Usó2nW>HTWœ xÏ|©Ø:Æ,§ÝßLèS»‘P@S昸f c¤ÔϽØÓg{Ó/£bŽ•bñ&ÜðbÄgo²âÓ H«SgجWä%mLjt•QQKîÝ„ë؇P ’Oˆ$Lv>ÑéíJÿn‘^¾^“›H¤¼ O§óÄâù¼Î&+‚fÈ’/æO¹íªp\fQG¨ +ŒŠÛ\åþµÿxÅoûð›Q'O×DMe$#=ñ)ع’.ÙØ0z½–Š™¥ƒtTHêyBœ +©òÑ1!ŒY‡ç2Š+<cZ[~ü¦]çÓvoï’î«ñVu®w‘aòƒ
$óÙBžNßùt ]Nò/©k_òÍŸqáWqé:þ¶É Dxël_¾Ú_
3×3ùˆ–ÂøR›µC£H_]QýÂI¢ YŒ +Ýæ—\ ˜è±ä{*nÅ û”)E!R¡£âºJýžâìÜ9ý|«¤ØÊK›(¯%+9”séØIìÈ´8ŒVG<ל,棴W¢Ó-úÖUW+yÆ 8 HB+h:èýn•§®»þ04×ô„_ #;st|”\’!–“eÒ€D“ÏÐ>龜ïjÔqó-=Ûg¥¿9¹oWî“ûæIªˆ¯Ñlè> 2.mCíC‚;ñÅaìGô—†R™‘úŸï«rõu?¯0‡àH&ûüýªEÕÔõ[7g)`*w`èªécwÜâ +Ѭeía 8[¶‰L‡F‘±¨Óòa›jv”Üƒç ‚/¿¹2ÔV7%O¿ÇüÄ®§)B!ª^þj%¸+o’9ͯNÇ)‰ög 3>kVIï<[={¦[Ö“ÈÇýÝ‹èºÛi»PÒHÞDÕþû\åŒOV»cú´ß¹
Æ* +‰Ïl*—®÷Ä)nNyï¼4WÝß*I½JË’wU±ÿF'Â%ÔrõK³•íêÃQ×únå°†þ1D©ïîüùŒ¢‡§ñ3¯u?\²»Ýµ\qB¥ ¬¡¼€ê>3¹²¾ö×vª¨4grÍ%SÖHbsC‰âàœž7Çd½6•áã‹ÔUÆÇÁ>O©lX°ÇÆ{ôæp¹ÔZ±\`ÏCr3F—Ó›LEkµ¾ï˜²(Ç? d¼ +°ìm]–r ƒðµíÀ⧦å2£™=¥ˆœ82I³bêUçÖ›ì‘piKÐa‚ߊTI`Ѻ[´Kbþš 3:<÷ì¹or¨qzäõ %i©ŒHh’oˆžÃÇ©øˆœ‚ÆlKmÌnÂ<+÷Qª…g²ñomì 1qÖ-÷ˆÄ³»Ý¶0“g™g„õ"†óÉ ,qt* +,’²G¾mDØõè´=ïÕ©wöÇ×±UFÚz]CE Qáw´Þ*r‘O¾=)pAAòö ;Õž£³K“Gst<ÌúÂÐX„Ûq‰e˜nk&¤?ýšb í7¥Æy£Kmd€Û6ª¯“B÷ê²ÄuáÕŠñGai†Óúíu.ßÐ’¿†)qDÚ™€,ã‡mfSÈâyåÏ…Ý/U¨L¨m¯ÕÛ¢ªb†¥FÇ]@VBƒûš´´Dxèîc¹‘Œ]ë ÂRê¨[× ã‹È±v4ÔÙø`›—´ˆÞè†=sÿzŽ|âNZœŠ$_…™[*äšG<
8eÈê|j™žk-«ánÕU/ýÞŠ
Ï,ÏV»<$Ôåòãt%»Ã›"uÆV‰7O1ŸC~ ¡2ì-e•5jºÞÑ·áFsë/Îc–Òk$€Sª²Ö–T‡á”«Ó=–Õ{À›ÒïÈçºAññùØK á'N8<
`!€˜C¥POܯÙh+Û‡É9ÆŸ^OGž©|s%@ 5ˆž¬úaôvPœRPìñéÚL(¬úãù©Nùe€Ü$ dRë„ap°`¡?>™AçŽ:)Õ†îšd;VÖ¿ó^Ñ.gmÉÓ7dóq0ác®.P~?ðWõ<„+ØËö›«B'úúre´€P×müÏÆâß'¾RégBߥ۽Ì)ºXNO%m±Q¨Þªí{C9ó"çØg +]Ò§™éQ° ø‘…aJ°ö’•¯©4· Cc3?Ž® ɼhª+™–ü¨×:ñ?˜vRí +endstream +endobj +1191 0 obj +/NZSLPR+CMR8 +endobj +1184 0 obj << +/Type /FontDescriptor +/FontName /NZSLPR+CMR8 +/Flags 4 +/FontBBox [-36 -250 1070 750] +/ItalicAngle 0 +/StemV 76 +/CharSet (/A/B/C/D/E/F/G/H/I/L/M/N/O/P/R/S/T/U/V/Y/b/d/e/f/four/g/i/n/o/one/parenleft/parenright/r/three/two/zero) +/FontFile 1777 0 R +>> endobj +1778 0 obj << +/Length1 838 +/Length2 1082 +/Length3 0 +/Length 1655 +/Filter /FlateDecode +>> +stream +xÚUiTW‹ Á.Ö"‹¥>MSÌ2A’&¢6+a‰ +B£™IœÌÄÉB¢ìeQ*¢V-V +b)•ÖD@Z('zDK4E±¤‚k±––µRè€ZOéßžùó¾{ïû¾{î÷ÎÖüP9[‚1hIèÙÿ`ùzˆ ÁbùS(¬ÇH" +S†õ±¨†î¡„q '•ª7s€ÇAøø
Gu(eD‚ +#ísʈR:Úp§M.´E„$p3@Pƒ+#éY(íäÿ05¹yÇe°f¼ýDJÿáa
†›Ÿ)HÖ G)L"(EL–F OÍ£fÐLf¥zÇ”B£€
-á𼼟˜.3¡H(¦WÆŒëÐ %ÉVèø&Œp£äkÂ=Ÿíu‚ …1B¿Æ¬Eï…z¢†^ÔtJfÑ<ÑBú{~RLH(I#Ô€ï- + £I*’bŒ¯ÕË pé[düÓ…ÑÜÌ\
Ftÿ +¶&´4oCñÝù˶wrtß ‹.¸5JϽѴÕCöjåoóú;šm–æÞÀ%#uþ*ûF¡³ÌëDÛjö÷
©•Çr#•½Î]uÂ#›}鯀U ^u<{«×Ñ#`Ϭ£Ã$Ûœ× ßô³•£ÙõÞ;rþ ÷œ˜ÖuÓ>6·¸{¥ûTŸyâ»D‚3ûïºÛ^äÚÆ Ži¥7[ºBVþ12ÔŽ‰ÍŠz´éþI
U±Ö=Óç’m¹ÊrT”eN—î³µè?°KK°ñ|l˵Ãzrnd&Ê÷OW ¿&’eNmÌ|¨ãSÜÒð rjLõ©°ÎˆÄoö½_rÞwFWé_|6DÔ²ªù1¡ÇW,Ÿ é=R ×Jã>Ú˜|jSÉgk"Ëà ¡]½Â¦ììe«yÅ:×ö·
—à¸PÁ˜+Zm\2xbÝñ[΋_z¥órfÂ^÷)mÆ£†Ô®Â˜wfòƒŠ‘SåLÛ¦ÈêN·á± +ÅŠC×W4îm¨«N]:xm(ªP»»´Ýf*‘W¡è ´ƒ^ÿ/Æ|ÎDZRxeÓoÌ«±¤Ä׃Ù%Ò‹ÇSÞ1mÉ
¹zá¡_d·ú-ô$×;hkç\K]•á?7äðÅêÇÆ´ÔÖ,F 'løÉ7Òùð±¨o÷5®åª|ÝÓÀa±*•þ3ùnjÒ° %/ø*·' +endstream +endobj +1779 0 obj << +/Type /FontDescriptor +/FontName /EZSWTR+CMSY10 +/Flags 4 +/FontBBox [-29 -960 1116 775] +/Ascent 750 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 85 +/XHeight 431 +/CharSet (/arrowright/minus/multiply/periodcentered/radical) +/FontFile 1778 0 R +>> endobj +1780 0 obj << +/Length1 746 +/Length2 603 +/Length3 0 +/Length 1117 +/Filter /FlateDecode +>> +stream +xÚSU ÖuLÉOJuËÏ+Ñ5Ô3´Rpö
Ž4W0Ô3àRUu.JM,ÉÌÏsI,IµR0´´4Tp,MW04U00·22´25âRUpÎ/¨,ÊLÏ(QÐpÖ)2WpÌM-ÊLNÌSðM,ÉHÍš‘œ˜£œŸœ™ZR©§à˜“£ÒQ¬”ZœZT–š¢Çeh¨’™\¢”šž™Ç¥rg^Z¾‚9D8¥´ +@'¦äçåT*¤¤¦qéûåíJº„ŽB7Ü4'Ç/1d<(0¤s3s*¡ +òs JKR‹|óSR‹òЕ†§BÜ曚’Yš‹.ëY’˜“™ì˜—ž“ª kh¢g`l +‘È,vˬHM È,IÎPHKÌ)N‹§æ¥ ;z`‡èû{¹úûhCb,˜™WRYª`€P æ"øÀ0*ʬPˆ6Ð300*B+Í.×¼äü”̼t#S3…Ä¢¢ÄJ. QF¦¦ +Õ† +™y)© +©@ëëåå— +úE™@·…¹0½áä”_Q Lrº–¦† +†F¦F +æFµ( +“K‹ŠRóJÀ 0~Z&0 +m‘ìõë‰û²HxÍÖ®Ë"&4˜î×»,^ÙÜ5÷Ÿ¶ú+ÏÃ…a3æ´>’¶Ú_ôxV§²ÎÍ/Êõ'x楼pŠZ¼ïû½kÜBZA“´”¤Ìo®`¿Ë(&^y÷ù¥@O¹ý©+{æ?Úx¾·(ª@CÒ³ßëÿ3‹ÝË6*· ÿ¬½8àšÞ"‰«›üž :Äï|Öú/ïm‰èLÝjõ}Ç5ùÞßù©?õî뀂Œ{ÜÜÌßìxâüLp —ã 'æX Ì6Õ1q^Ÿ·&ŽçˆÒÜ7" †§:ùLœ£nW¿Èa_µÞT©íÕ“¢÷lg¶cx'´ñÄÓÏkå]–K†¯Õ9j;±ú/§r£hDÛ;³ ‡ïæU-z?çÓñú!ófÊ >$ø̯_Í6aiÝ|m÷Ç ÜÓ»Ö'·u½R½e"ìV]véƒ~ÃôK-r·ÒÊ‹¥²Î¿á^ý‘1‹c¶®ÊKǧÏS¦9mÕàUZ´ÐsÎÊ‚žOn×ܔ┓á—:'j9'<`Ú·1ÐôÌü×O‚~~;¦>koêßU‡$ž u*ì<¿)á…‘„xòœÄÑ’w'˜.9»%ÿŒc˜ñîI~G9æ}{˜íÉkßCDnofÒ57>ýZzý55Û¼Òœ–1(ysx'j‡–N[ +/ ³½Î.ù¥©Àòy¼ÂB…ö¦?û› æŠ4뼫 }›!ähªú;smãÝaÅ,rXn1hÝ<T±áôò‚çSdXÿ¯e”É:g¡6Ÿ. +endstream +endobj +1781 0 obj << +/Type /FontDescriptor +/FontName /NSJEOL+CMSY7 +/Flags 4 +/FontBBox [-15 -951 1252 782] +/Ascent 750 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 93 +/XHeight 431 +/CharSet (/prime) +/FontFile 1780 0 R +>> endobj +1782 0 obj << +/Length1 769 +/Length2 714 +/Length3 0 +/Length 1247 +/Filter /FlateDecode +>> +stream +xÚ’kPW†G© Ag¨¨ T9©J Ù
¹p³š€ —…€"7»Ù=„Åd7l6TQfT¼ÔoUq¨ŠZ‹Ãè”6"£PK±åR/€@Á Z-PttDÀbíê8Å¿ýsÎ÷¾çûžóžå{®Vû)ZÃiŠõC…hU©× +¨06ê¹ 8¦j'!k…Nâl'Œ !“
!EAâ,Ð@-IñD6 H*ò‰2a2¼•²!cä Àr)à šÒY +—Þ8ˆ(1QV©¯:®ÆHŠ· @Þ™Ç÷è»=—CšA2"D”3rßÛUê¤Y+)œ&HJ ÄRÀ³ð®•X*Q@R4hæ€EBŠf¹#€K&¤Ó Ïö¨¨ˆh¤4\¸µiãeI +Ü] óGê •/l@ÍE§ 7tM8, ^5ÊröÞš}n?팞õP™µëŽÕÊÊ>뎎=²øþÍè„î;Ž¤ýúã묋k¥©v]…·Kòš÷$¾ìñö°3÷o9Ó:OܔӀ혟m]6°¿Ôþφi};1Ë!?Á¹ëcÓ,T]j.?ÌÚlÌz¬¤¼¦gÄ|_í;Ô²éçÊ‘/j»Êtñsžº”·¯¸D*JSïÍr¯ bk´Ý¿å·DiÒ>U•?9^q¡JÊ+Æ–†hÒÚ»Önød©äSñ‰Ê}a]ïKE FõëâÄ3»Ëê§ëæc'ÏÞìöU~P|q¥OÂNÇÌGÕ©^Õ…âiÿ +endstream +endobj +542 0 obj +/XXSSMS+CMSY8 +endobj +533 0 obj << +/Type /FontDescriptor +/FontName /XXSSMS+CMSY8 +/Flags 4 +/FontBBox [-30 -955 1185 779] +/ItalicAngle -14 +/StemV 89 +/CharSet (/openbullet/prime) +/FontFile 1782 0 R +>> endobj +1783 0 obj << +/Length1 1343 +/Length2 9316 +/Length3 0 +/Length 10115 +/Filter /FlateDecode +>> +stream +xÚ—eT[ÝÖ¨q îÁŠ Å)nÅZ\‹ ¸»µHq)îÜ‹Kq·Bqw-îRäòžó}§½çþ½#ù±Ÿ5ç\óÉÜ{í1BO¤Ê*fjg –¶³uf±€Šj² ˆƒC @O/á6r†ØÙJ9ƒ€ ~~N 4Øøåâå+ÀÍ# +6°¿·{é~qùÿ¡õß›K»X[¿7²ùgûMêÿ‰Ù@¬=þ'ÃÎÆÞÅìT´3;Úþwª&øßrŠ`Sˆ‹ÍGe¬!&b¶æÖ` +ˆ‹ƒëßë'iˆ;ØT âlb43²vÿk lkúß&/óû—»†–ò{Iu–ÿ¹µÿ +*AlÕ<ìÁ@Ž?ÙÿbÐ ~’#Ä ¨Ëñ2eÐKâËç¯ôþ«™”‰)ÄÖ ÈÉÍ4rt4ò +ç?í_dœÝìþ +¿ø¸ü…/?Åõ/|±qûkn/.ž\^r=ÁŽÿÞìÿ=ââvî^¬ ž7@VΗ¶/š<@~ ~Ÿÿ+ÓÄÅÑlëü¯WÏËáú_6ƒ¼œG0Ø l˜Ÿ±3 ´Lª.ö•‚Ž— 29‘§Ž´Õ¦² ¬âN96Œ©)Ïq‚p,!¥Ø‰Gòåì¦fÜk$õbÞý^ªìAs8ýøL9©ªÈ'& õá²úº°l2Bw究ìXNh¯V]Û+öA¼¹$Gaų3¾V~£kóhɦ´Û‰ +x–"ütŠÐ*“»Ùú( +øw”ÆønŠoKÌ «[·éÄ„6ÚPìZœû8à]ZPúŸ¡’ª6}Ž®£ùA˜g½ ÿ£ùd G.´Éò–V)Q)áô`#åúÎÀ³öë•Ni e|™õž7
5“ÍìÓK³Ö=ë‡Ñ N&hNo=g>_ga˜\PþK€0:´H{f²RÇùPûù ña˜ý–êüà= +YGÂF ËŠVÍ–¦ú‘¹ oåÛ çSš4•bžir§È»å5Núª{úh‰D)Ck‚E
çͨ í¢z±Eêv~Åë52 #©ÕÊn
žÆ¸WiÒ³þ"A…3VNß0æÙÄ ˜A鸲ôÎS˜Û+U0pxR×5x5ÞôA Ûr^ª£ŽH{ÖHar*ô†•Æ÷ÓxÏÕÕÊêøDÁ:쎆°N-êÑÔ1=í¥5ïó–ädÉiýó˜h«z 1RœYàY£(w‹±©Ï—|¡Y»ô²ôË”sáˆGqâ@žo°h›Xñ áÛ½˜–Ø+H>í£;©+€Ñêg¨•‹,”aƒU‘£øèØÞƸґk§ŸbËN6PQƒ$%þ3ñ›‡‚w¤|Ç˵éBÍ“æ³äü(çdJ´Œ¹Ì¤Ã.ϺÎË_djäT>ô—Г&’ìi`˜’wx'_Á«¡aÄá µÏü¶"‘ïõUÅeé5N’+8QÉ’“¨²n~Ôý.õi Ý´ênkp[øU
Fxºæ`Úô6éÁPÿËîÞñ~ óø÷ùFñ¡´N†f±Wž¶ÙÝ(âÏôÝð7XdG Oï×’²dä¨wŒtöŸal–ãß#ã[’1‰D¬ó|:ÂŽºv“Rê½_vA»®¼øÑ2ÌÃZ«³[º3èE±E +[÷qÍ”Ù"WÜ%Íé8¿BÙ¿ HnÞ\w/}ë£Ôm 9Ü¢¾Íõ
ª¢†ßSkOh${Oz3ñ‚åôÒ¶pÑÔŒ¢}° ¬C1Q7g0B3fã2PR 3\`¸Ø«6Ï7ýσãÃÂüM£h™ï:{- +i&¬ ÉÐÒÔò¤}·wê¢ÿ9I)/¬+ÕF¿€ \E±XyðÕ× õ 7Z ~ÌÃCˆQÅñ¶Zßî³G0°ág‹ÅèÉÄFµWz¿‘\nw‰ÆÄ'U]b9ÿ5^`¬Dº½˜êºÝ{¤ü"°©×lçƒY‚Òbúõ{_ñ]é'…Bq9ó¸~Y^ªÄ)Ë…ODßÞˆÒò‚`—¯_w?xüÈö,ÓE¿}ì×èÏùIR…e’|ÑJ/DÝO±'A×®‹gô¦!~3ê(» +ÏKOeÚØI¹¾M;µœI}ùVÎÖ°¯ •ÇBe¨*œW}³ c‰Ï—ÙÞ¸ÞXDKeÀwe(1t +øõ÷¨@«à! (½ûë«Þ,¦XIŒ¬7ÙÏ61oðºEx}ö뾣غÔ_•µÎ!7'Þ!€uxS6ª¼¾J-)j¦ºR¾
WÒÿ‰ŽÝOP. T[Ø•zÈ[¢”t \PγO:m矓ÎÁ§Ý2 Ý ”¿ßJ©VËvÛÄË1ˆ×ôÝ+ôwg \CŽÕ«åjŒ¦Z¶8äL®Î0è2Z =6ßBÒe…o&ß BT…ÙzE¸¾\ë‰këÅÚý›¹zFu:—¡ +ö—Î$FQ1e˨TFk.‡Ï* GEæš„…ðX<È|î´½¸ÆÔ7zéÉJÆÐPÚë@¬z¢†Î]Ý°£aPÚQÙìP‡ÇMµ?ÅázìMwÑßùãݧ@ôF\úvË2A·5Ÿñ¼ù7À0çO"¢·ã×µqÚ² Ó§ìaœX kÆDë§×?’¹+(Ü„u1ïÁRŸfÛ…çËÇS'Í%ÊkÒ!Þz¢ËYè.ûÞÝ:b‡žŽU.WŸžûfŸwä-ï†1®@,Ï5î\°ƒ+ž4»=àFU/~Æ:6€âý‡=’ÌßaSÈbüF¶7O³*-û+!-1ŒÜ|È|ñ$MfÐVW=)ç
Ñ6lkÏS®ï´nÌŒ„5rz6i .CüÂÒ”-§ÂÀk3b ¦UpÃ’W³½±(Uóæ²?*ò‡'8±uPUš]]ž;á<ç+] ø€J‘…4åtj.2.«d¦t2½‹OoOöê[Û\ XyuCÓ( +[r &p¦1+1¶>²êñ£ÐLÊ…Ñ4ËÈ~™û³ý¿]€cª
-äíU ›`íÚ*ãfé
ƒ¢ƒW¬‡ãƒ'B+VŠŸËjÄ"ɘæ¹méHDij:K©T3þNßã\SŽ:hòk\YeA¹$Â>eðŠ#l™£!u ³Â\|cIýαê¹u5ða©Ç°q”éûÇ9+þí·ZôQþ*‘±RßpIfP†‚Bš‚~ÕˆMèIêDä!Û
¤m8WwxÖó³_»¸ˆ† 7”—é&‰Í2Ðc~çs…ÓâMØQ%Ž]‰Ï<ÁΟ7K @¶ÖUÁ‘•nó1Ó«öʯn)´˜ ÞùʃñÄþê´¶©w8Ê:Ç‹mñH¦õ°³2ˆ¬ÒÂ܆ޢpY+ËÓ⬠V Ÿ*™ÈÝláŽÑJb-¿v¨å,þ\üu'%#&÷‰+íuòM¯,‘~1O{• Ó¶È5„‡j‡´ÎHÐ +—´¹ ^’On›ÅO–ÆvJõb?ŒŸKxÏê +Ÿ¾T He`Óݯ» yèq·2OŠllŸ÷¤(ŒpÑ,ÖÇL9KÕ²,JEèúü´²›eeÓÐëBÚø¡& n! ˨ëM®D7Ì°ë{.º¨†ÁG°Ô¦—’Tö«ÏõÙҨŸBjj2ns«q”«àðÚê4¶88¼—8F+1™þ±úµ÷Œ;-Âõ¼xéË—_k\XžwC·pt»•ï¹}b½>~Æ"B†¶èþ˜«‘Œ" ¸mxçp6µ)S:ÐJŽÁd€Bg¾ÐÍUžéJPݺ7©á³Â +4¿ç {ˆ¿˜fE—¦œ€›¢¼Ï{Ïiá5…¤Áµ¨:¦Í®;ÙVñ G‹Qù*E^A>!ãf÷¡ë2ĉæJ`Ë“f2Ž\¢.ûµú]:‡Œ$:Ü3;‹`4òHÔÛÂàŸGëä ¸„|eGJ:HÁ- )n$íY=o ±ßmÏ
8È/%hÌþÒ6E”jëú¡€õ=ÞGBn3±i÷ñQÃŽ,b:Nl¿1íƒÿF‹¿» ¹o>mí¥¿Ê÷ |³¨ŒÆ3ïĬ“{ž®4À„Ñ6qBݧ g-»g‚ìÝ=[¼" ÊqÖ‡F!¦ÀÏ +AéÚÆ U¯J>Øâñã±7¯ØG~ u÷FÏĦ¾Ó(ÿ}cnÅú¾ ;ˆN&ÜL$¶Të“8Q?×ÏJÀÞ¤uX§ +\eÊ\<–ûèµÄ[‘Ï +<™¢ñÌز 0Žâï=?æŽ& ÝÎb `8Ò±7¨=KýÄòõ 6šïKà"AÄ.''‰2PZeND§Ã·qÊŸÑ…¾ýš±Š ¤7/òd ”±×Íû,W(©o@÷¾U/üÔ)ŸdÀRÞØa”o©œÉ‡ò{Z…m’ ðp”‰Gf–zRʹeR¹†Ù>šÛ¯Ì®mûé÷œ¼&gÿª¦fÁ/8Âgë·‹ ‡¸Dn…dx( ê_]G tWÄWz¨¢må M«²å0Mñ¨²v± »Uȹ J!ë1=K Çûª¢(™k™( —…ù€ Óu”ÔÒO äüèY¤Âå¸7ÛHV›Ö¿'ä¡ì¿ÍÁðZµÔøZ«î¶1 ² +Õ‰](;‘O`²—^‹]°‹Ó~7ËŠN~îâLšØD
ž’îÍÛ»ù€ój”KŽtœmûÚŸ&Ù¦kÊ7_ïËÍT µ9YüÚÇÜëo"EfbÀDÑ +¹´“G‹Ñùº—šœ5\…SXÊìŸaŒ›îqšÛ¤b˜M)CÑ®Ccsqk«ñsÌhܩ׼3Üsκ1TЉk|Øö¶'då÷ ì†pµì?Ì~óŠ¶Úæs¯ÁìÍ´
Äû»zCgá÷Úê=aÓ¦Û7ÑEßm†@Ÿ'r'ñ²ÇÅ©-åI1=š”aXcܸŸü‰j^ùý‚w 6À‰·zGË¥ƒÖxJnð9V=ÅeËÙ- +X*«Çë’J¨"úõ„a{¾¬ðh¥“ Üû*ÎÓØšSüÍt"或5QV;0HÅUps Ügê|øñšõÈ’pݺá¢+}fš¶Bû« óÎP7—cfÖGq² ©©ì5Ú²¦¨ö D½¹K$ ŽO&Øæ…üs§H*K>yÒ H3xjcÃÇo+-ô[¶×õ?8•ÐÊIU‰Ó`»Òü¨…]5©6Q?iw
€X¸é7Dȶ6tlDÔî¸'’ùîÞuŸ¦{ˆ£=©”pؽ +‚úÞ͹åqNs…zòhzí]—;pT§Ü¿ã9†bjê%¡#½)Ìç ߎšBÙj
ú’j=F6:¬’[¤mú%¹çþëiÚ ä矼ÿÇ•œ©`¢ì7ø”µ)uPø»’þ.ò +=û´òÌ\ðú k6ckÚ‘9òçL¸yiiv¦ŒÕŸj$]à-'–º ¬ª6áT  +Ý4ù'Ö …ÊÕˆ$X£Ÿ}ts#ÕåÍ [# é°œhêƒy¡ [%êQî£ÞJ=ÒWÁ—‡Î¿Þ£_1œ ø
óBª?ˆ 3¥"Üê¦ßä¶áÝ£·…€ ÇôQÈa2h,ÓŽô,ÝškQÎ@{o"håfÒV´íL„Ëõ§TÃL¼~ g@áPQ"GŽ°aä]wº»M$òL +3c‚àÌ~;†T_£ +‹¦àÕcg¸ãBvúÀ&ÞÏßæ‡á§·S¬_/’¢NöD˜ô¾‡÷ƒ§¦šØ`©?l>•¸UÎ7Myh%2ažv¾'Ž@¦*¨ Öc¹G&-:L³à„% Ñ#vÐûha§Â5±L ºãnmyùß>“]£ [h¬¢m3-RØü›QÉßJT¾ÉK<0ÊÃgÉ2‡iµ.nÒž idâZœ9Âc™ë †¾S:º ƒÕãà°! øLhxŒ¦ÊèzW¦ýŽWléaØr=I%îkáÙ¯lé©çKÂdI¶kÒoÃ@Õ÷1µLš²Y$$ ³GõÊ2?êØÀröp&¢Ê.÷˳ÊQü>¦3%pûòwJ +Äø¾ó
ÞÔñÖÝÑç=o°×õ7’§jèjÐ0_eC[…|ß ¢)n9Í£\Ï‘Wªkg´¶$;¹eE37V,VØŽb‡è±„KŸ¥“ܨ3‡}ûñýë‡ü¡ÝÓáÝ– — (”‘ºÜ&ѯ÷T~=ĉAïs>»/B/â, òªÅ>ÈL³"Á‡¦IZ{XZ+¼Ó(Ö\¦ô”©7†ù-Êû1*kì×=7Q Ϭà(;Î8‘
›úã&¢¢ÁD¾ãáZÉV™2ô¬ðNlü€÷wæ€ ³SºÔì Ψ.\ñõzS²8~‚¤ §Íéþ³_ˆ‰ 5²BUš~|PF*D¸45? ׇ†7 +ö á5Z¿N±€’áèké™Va݈ÌkßR ®PRQ2FG^9Ƀöí˜.âÚÛŸQKˆÂ«¾‡bJXžA¯¾wi$(Ô#èïo“0ZµèW·êLöÈ?âÃ(Ñ ì26\\,¥E“•h*e ~høBxÚ»—{ŽÀÏëžÝ·oNY"ºƒµˆ%jÊh®òþs‰XQàmz,%IÛž÷«‡]É£k’~";ÅmIΛ›–
ûß9£ÓÌLûÝÑlRÅÂÇ<y(| bÓòÐÝÜi&m¦·ÖÔD’+¹œ¹Ýôú7'
ÌSü‚Ü$+a”µÊì“ùÊ¡‚|ÌNžI
E¿\e®÷6SÕ—–J•›é+¹Š¶ÔôGK9äƒ*2C±7hÜ}’¢yf|Îùö%µ ›ØŸ© ÞÄ 6«ªßcÄ1œÜîZâv?û±ÄhDRÂøŒ®g=[&÷µb4 ++š?]¦AlB‹^&ØÆ›“ ïT· Cr®rW€ï1+ú°?\e ‰„ +Ža2JuýÞçŸgHû8ÐÛof«²óô·£Í©3¡>n×6ÈñÉ6‚{COôF}•ß= ¾éŒ$ yWŽ¯Å%Í•ã÷žµü@Òä] ßšŸÕÏÚ›OFÜUK»x`Ä?„Ú¶ªR¶:DëÞÚ&ÓâYU}uo€ÆÖ+ µgê{„åìk0¥I,ϼՖz’¤´²añáµN~ +¨¢ º +žÕçmõS;ˆN™ßzÈ<ãÔ•Òi´Õ³¯ØáËð5¼»œLyJè[˜½µ\m\=*§g`rÑ›í»ö´ÈÌg$¼
¦ò( +©ÍêžázXô®šŸðÙtšïïÿ@C V¯àeL:ÇÁ(ï÷$› ƒ=+…D‰â/P#ˆ¬³`Õ péVRJb„%Äk¶TÔvXV/ÐlóF|æê!aMZO6{*ú³Ê¨Ä€/ꩵ¥¿:?räm–zßzôµÔgmníþ^ÑSb¢ Is¦Ö…PùÁµ“.ð½¢rgtòhó±¬oZ¦Þå{RlçI’']Œ‘z&4½0 ~®ìî–þâòxfJÇ-¼÷ZY¤ñ»øWW ¶Ä¼N\V7—§óIÃÜ~ð÷{P s{M¤|d‰ +·ø F'µŠþ±™ â#úœÒåˆü>ãuáT‰*Y)~;û}Ëh]µ¼tú²h—“Ù^ÍÔSÞ(”ö‹ Ýôº )
n¨.C{í£UýçoåEvËŒÂæÌÕˆªw†u•-•õô5s(Ï›OŽ4‰P·ØhX¥mX…²üñî¼(–pˆq²ÿ[×á“&e^R2í,1 Û~t9«çÕö¥÷…
‘nà挰çÁ:‡¨8³žÒ´ ÄdaîS-á¸)„™Ï)^øÚR^Ç%ºl+MÕ(2 +ˆ*j¹Ï Í7,5}øˆ¨í´¨P½FIØØí&wÛös8QA4µ ýÔÓm
Øå6R¯M,›Ê¨äH2Ž2ú+]ÚàÝ
·#åë[ÌqxõôfíQôȵ ê®(Ìb,‘ÔÁk™Æct°€CQxå–Cp>-(cO+ÞõÍ’wÁïý 9ŸtÖWºÛKwj„+¼6zšm+¾Ëè„qLnÒdË0ŠÑjÆ– ¹ŸÁnÓS–àÌw>FMyAÅ–9 +/_1žÌø^RÁ·•ÄCðĸŽ¼Ód@¸F{Ý_qhB«Ó©()-'Ä+Tì}¨ç
ZEðýPYìÆ +¬X¬&wüÆ]jÜkxt,e÷Î1Û1ÃŒLL9wÊA…rJù ¯ay“Øu:ÁrŸÞ3¤¨8~ ’( 8²1 Çן©0’j08HS|øÊÊu‹5íªÔ + »êN3fì£ëLPj ¿µÓS è5õˆù6i$VŠ›-Ÿ0›t·xw)Ö»àsk ¸Š +[™,¥¤éQf°yº€q? ¶y#ö”$À˜¬£6ý}ìÚïFüúSøñwÏØrhÓ-Zò6¾TZíRä²0}ÛtkµÃs<Óö}ãp|b oäj«ºæ(µ ÖyØGÓ5»LöÐëþûÂ+ÊöV'}_6Nr\‰=y#/)
¤“ cõÚ]£æŸ ÖÌÌÄ<"ç®o$Oúx³™àÕ'ðK.‚ƒ©æ[n° )däÂ\{? |3õmMµÑMì´¤·Spx´4 ̾£&«ûT3/—„+0» sŸ™cãÈÏíÇÅLJ¸JwÖñ¤·U®½½øj7r[¼qÙ÷Š{FçWãÔ}FÑ—½Ë”0[ÑVWîWPeÜðl
‰EÍŠƒNÙ£_Hý^0ÊOÜ:»kÜÎNT¡ Srî2yË 2c7Y¢hÃòvÌÞb&ox¦@ñï6l¾¯á˜c£E%’äX˜¥3Ê-<·Y‡û²Rd嫇¿µK•Þ îßÅ\³¯nQÙ7R7„ e¿ÓòH tþ$—¨Wü渓Fü†öivÝ:ûY/º†ta#{\9œ81ÍÕpi ›Ú£8C-òwŠƒTæÉ ;Aê ¥<炲ŠójÉO°´G9_ðm]º+¬Év–nz¦’ïÏiO¸L{# ?øÞ'·†… ëW=SÏ2›2òbGb]-Q_SÐÛu$.Ð\c©£¦ +UaÑÒ +p$,ÛLN&ŽdLÈëGèí>š#X‰:/½Õ‹¹å ñ¾ËK÷0T-s¾¼-Z%qÞ[¢ªE¦î]糬æ!¤7
ÍÁJ
(¤“Îhó½ ïÍ}\„@‘O Ûïʶ¿¦ˆc£³;¦HóŸ6¥ÞCßC/… YU ;¾ÃµºçÜ´n¬X,g ”)ŠrïÐîéY”ºœ•ŽèR FÔŠmw§w¾4tÜÆfù&“fn>Ñ]^Oèï‚fãúDvþûÄhV– ˜ŠJÿ\¼/ƒN¬w"i…0ʬ×Y[ºÕi"¿Ò¼nñþÃþ|kôH]§I*i¼7w'Ô¤á‚CÉ ‘Xú?r‚Í— +endstream +endobj +1784 0 obj << +/Type /FontDescriptor +/FontName /VXQNDU+CMTI10 +/Flags 4 +/FontBBox [-163 -250 1146 969] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 68 +/XHeight 431 +/CharSet (/A/D/E/F/G/P/R/S/T/W/a/b/c/d/dieresis/e/f/ff/fi/g/h/hyphen/i/l/m/n/nine/o/one/p/period/r/s/t/two/u/v/w/z/zero) +/FontFile 1783 0 R +>> endobj +1785 0 obj << +/Length1 1631 +/Length2 12530 +/Length3 0 +/Length 13456 +/Filter /FlateDecode +>> +stream +xÚ·eX\ݲ® 4¸Cp.»»»CðÆÝ]Á5¸»»»î.ÁݵöÙ+ïYçïwõŸ¾GÕ¨zžsŽ«›ŒXA™NÐØÖ$fkãDÇHÏÈ–U‘dd0Ò3À‘‘ ;€ œÌmmD œ@\ +Sý+‰ h
r072°È8™¬?jX”mÌANîô + cd¡g`ùŸusG1s7±‚¹“‘ÀÄÀÊôïuñ+ù˜Þ¿u +éC‹â_úТô—>´(ÿ¥-*食úˆó£¦Ö_úˆü‡˜?´XÛ}¼ OÂr>V
ÿÒ‡B£ÿËG'#[kë¿5>ÿ?Tƒþ"Óǵ±£Ù?R>¬˜ü#åƒÌÿâ‡3«$°é?ð£ÞßR, c7s·3Ùü#ãcí å> [þ?Ìý³ú‡;ë¿Èøáåo)Ö6æ6ÿpóq× +s6+@¤«F³! {Íeœ»ÞÍë- +”‚4Û~óÔƒÀõˆ`Ì&*ê^9{i«gŒs¤KÂØÎVyo¼Ö)äe½ +è” BaÏg ±eOCâDý¶ˆë;Ù +®zƒÞh{,P—„ô > ~šqd•o4Ï'`ó;(Î +*´öm• ݾ7Êu=IôíöÝ[ðìÍÞ;.,D϶pbwºÛÏ7Ê7Þ k3ñt*¯ÕÔ†HJÉÙ€;›Õ:c´uv¹n Ó.ßNã–ØhÊiwêÁ‹KjŸ4—çÕ=øE¾ƒ3^üðö§‘Ê&ú¢þ‹ˆÅ;üg‘ÛeŠ1W¯ÄŠº©ÖµÑ-ÒgE÷–¦3-Þµqί˜U¿IŽT›nìÑ#l)ÜÃî·¢×5Ñ:S®¹Ö‘×”ÃÂø¾ý » Sq¤ÞËÂŽæ÷ÔX” +‚VÈdì;ú-´¨¥‹å„_{UC’væI%lŒ°£ã»f¸l™ M™±¶ós1 ïˆèKÃÅNóÃÆN¤,n^_ sϹÖý½?© ÁÝà-cÛDø°
ŠÍv‚Ü@®n#©
qnµÞ°…’?J¸'IÈBØÏù|^p×l£ìZxÙz ¬sµN.—nìýéfŸÏ[ è‚=h€G¯ß{¯åJÛ õ‰˜ôÀV©cºQX×.‚ÉTUd#Éòߢž“Q諬 ¡ÁªÇF± ;Q ëœ\‰HŸ¿ R--t†Ðš€žh‘wÄŽY“o%/ò?3ÿFŸu…ºã3žÀßß‚ê¾VÇôuTJG%T>*ëJ*Ÿ1?=Ò÷ÜmeÏ
+g´ËPI×-•âä†wXüÔïý&=0j×àBÍãN”ÐÉ©!Q¶I®ðá +ö˜ës^ué–·8×8R+P²òk²¼½ü‹¼,¼S7tàã,dŽeGã㪔”Vs%È C^9*LË´ùjOlu¤%OÝ}·Ûr©6Dp£Q¶UqMÊ {òt=|‹±eŸí'Gžvip„i>x anj1ú/O¬Ò™”qþÒª¡d!‹¢?ÓÕ™Ý5“ +u.$ XçÙÓ‡á Z_ðIžB‡Ý9|$«²~²Ý*lÊØ0œµÇ?ãXDôâ6%Qðnƒ¯É—™8Y•5ð·ÌØ#†tÀûÙµsª>Ñÿ<ë"x’QóÈ…k¿ÝqS1æS =¡Ú´ÈøÒÜäæ-w/DSú3±ÛQÊZˆ×þ>h;æ‰dÒ‚3¢ÈÐ߶w2‡Ç}È 9ju¸¿ÍHp¾-á¯!¹à>hî>ËØíØ žDƒƒ—x'¼†!žÈÒ¦wŽ®Ž¶•y>~$èA» @Ç°ì ^Ê—"TÜ®-¬TãÚ7êâu#ÅCìAæ=ÜC§oVœ#C:ˆ¼¡^
"›îç
új%÷WKDºE$/fÐMÅŠjè:!á.XóhÒχÄ}z+^ùÜ[Ð +¿kPÖÐk +S •e :ã8UIÔs5 ¡¥ÚŸƒìßç‘K_gÿxÔ¢|ÛÃÕiOèrønh§|nñó¡¶(àS‹G˜XbÊ¢'imWhˆ«±Rô+ +[HŒÐ7’´‹_*; †£¨øº`‚:WQÖGhî%%ÕžQµ™œâ/rìÌ?SF/õ×úh8G0¯‚ý£{p¿Ý`d˜ð&²ŒVpÂdé ¿ëକ <Ó€fÖ~é‡×ž}•Ø¦¦ÙÜ'Z)¦ãT#áXÜýu²<j‹šU‰$—{æ ¹ +q>I³‹(kIjc›ó#»CŽé¡2*h Kc´›'ÚR>!*"Îmuö´BÚ +˜µ¶Ðg=ñ‘×ê¬!²zâ¥g ;°4ߤðö†à4‰èfB€Œ’04‚oÙÛÞt$0}¿ `iõ9\•ÑoÓhõ¼òu” +Ì,éÝx"ê‰çO1Éõ4 ¶…Xìa<³vÁÖuºMo§ÖÒÖ:mY¾2ãž¾Õ˜zÓøŸhκióî£Q
&|“É»îÇŽÉaw‡ÿLd Ìþ=·.]ûHˆYî¾sŽÔ)µÿ‰
bìº cñÏSÚÄcŒçÈ zHW׶ÑõÀ|mXЙr; ï2H¼bÕaû÷ŽœÿÌ îÑ_ÈÊ ˜ƒ ìCÙBúïÛà)ÌËt,®;CbN6A[ ê,4&ÔÇSáRºq)’®pS6ݯ”̾mÛlÅu+©Sª,Ÿ•´‹çF>•½VW{ñd$ÊŽdÝÂzFµ²M†vä˜)û ¤{ À•Ž{i)s Ýmë 6@4¾«n¯Ïmá_8ûÆâ]Q@Ó–_Dó£™ü$>)c:º‡Uu ‘7¯-ôéK§à;$>î¼%ÒŸFûî*Âä ‹6½ØB&ýt\=)-k¦ÎÚj”¦¹Ký +“…•TþÖ”?ù`Õ€2”¹;û3ÇC¢kí¨©”D–Ÿ Ž´G]W—’³~÷¨Z þàŽÞFX?lmIÔpeI&k‘Áy»xYÉáW” +…Jꆰï É’÷Aù+±˜}‡A¦Ò‹øq¸ZÇ7ì +Ò织¿ðzBL‹±Ï™T,Ò£y&óFRïæã¯x»ä°»Êÿü8ql,Tà @— +»26<žOdgó ב“²v±ø ;ù5L‡ò.Èfàžï®z[ÔÃÖ9IuAH ÑÁú¥HQÄ™4åñA <µ vcŸƒ{È?@Àc _¾ƒõ +B=TK¼¡=£úpÕ%P;JH&ṗ í*“œDŽ”>õ.isqU ¸Òðéll!»ÇÕl²¸Îé^cY݉ÜãW®ÌT +-“V¤FWBa.eXÚ“ÀçJàF…i¸u†ƒáýBÏ8o‘y"q_U^’Ûys ž—kÿ¹Âû¾•ÔB4±Prà±C}ËèúîvÙú÷Öm‘Eý#£-;’¾tÁ3âç¼ê^,1e¯2*¸Ú$â—ê|†Ég‹ô°*gµ"Ì’)}ûîDƒÏ8çH|0pX Ý +Z"“dvñâ»-*Œ.Fí¯·9à OÎ+ ò2
s7”¤ýˆ(¿uë ï]Ðx½ûáâìc²±G³@äcßš”^39¬¨®%ó ;ð“Muå‡ A¿˜í¦È!ù«ˆ[óc¨bðçQݳ.¦êiŒ€0<eœ´Ô鎷[¹O Y•! «*ü ÌŠ.6Dü¶´)GCn)õ`–y‘6’ ýñ÷Õ2õÔ‡j½ùC.PϹÛtRú#à±9ôD‡fy¢}BŽk1pèQ¹>&„(SKodbà}‘ýš œ'Vˆ÷†%Ñ»‡˜ÊG³UêéJ]MÐbÁïë“ŠjöÎpÛØÍOxÑ9BÍ"÷–› +÷~ÜððÎZ«Ùí÷u›A;×Tdx‰àn;|-°Yç¢þŒ& +hÒ¦VÞj"æ€5Ï©ˆ=3º…‚3±àNCϱP®"8ú¯ªi3 žk”ÁTÂ
GW§UÐfçâÒVõÁÞš3ælÚRµum^S|a‚mõL~Vù²QrïLzHÖ‘0qã²åÜQ?¾'©si7,„,µpíIaŠá·ú-Í« µ!Ü•ú_¦3´mø(òÈdŒOSÿ0H™™«!*Z;î6EW:Vy +PôbNÖ]WäO› +&Éq~[Nྪ¶®¨3ÇH*W6läÚV6÷u‘ÄŽ*SÇ¡í$^¢:oÉCõ6+ 7 ½q>I‡Ô/§Ù’ç$Mb‡C—#P`âYkÜ›g—ÒÉßÆd¼³4ˆ\¯·xêÒá‘l,
Ä à‚‚·àº ¸ÏµŽà Ày W°„ªˆ.ÛÐ#w…@Q˜iœ{a2 ‡¾¤òÍ:jù9ï¢t¥\‚ûâxÂ͵tÛþ é¾ï8s8-æÆwi`zZþ®3è7ÐÀ¡ÿžTÜ“U]bFQ*¨CMŽw~»Å3.Ù ¾5H÷OÙû gÑ!E>ˆÝýë—1ºt?וS° YêÕÂ]}×Ò©ì³ ýº¿‰©ÀªzeZ äƒÍ‹Kßû&–x[™ÍVê<ýq-p^g(ý;ŠãVýÄl€=,zÝÇ ãz lCæM×Ù6>U%øÇŠñõ¬ža+m\H<$"¯CKâàñF¢Ïƒ´¬1 ѵ¾ÃXÃØ/‹¿«¬:$= +Ä£ögŸ¨õ60¿æ@»¼änÞØž\Š*‡\gäsÔC!_‘¯ù"8ë
ŽG‚Ó5Ö§ŒDÿÑY ¾Öîß„u
á¢Á4 (<kf˜pºSEÁ b왽Š±±DT«ùGÎ NüºWÅ7PÖq4ÆníÎÛù+®a ~×+„\Æ"À˜¹ ’Š2¡E²à³RIùnþqÀý/ÝãL]³=à¨?¿©Œ‚Ì É˜Àñ‰Î*û!©ºØ#êÏOf„T4Ж‰§3ð Â:j‡~d +ÊÙ)ë“WÏ£Jð,í+>~Ø¿F¡¤VÐU—!㋉eížìŠ>˜<Q’ÝÚs|VM˜ ö"C.‰N£*Ó1ïÄÁ¶O`RMìë³"çcYÉq¾¡mÐvŸèA?û-ÜNà_¥ö¾è™´ À¤j06×ú(+lꘈ‡àü +ù,·Œ<cÆÐûWeþ×çÈŽª4ÄÙ¯•‹%ªiŒÖ+^˜.¸™ÏÞÖ9çßö³¿lž3q›åe䊊š,WÁ²"_&½)¤ý– `rò+ †ØˆXÎaU 6Ñ;xzðæĈN³´‹ÍR˜{,Áñçv•X»Ù9| )oÂ1¥¼i=6 Gýž‡²-4=i;’ ³u‡:ñ$È +踿Ž?aõç”'c"s“È£ER¦f mE +K#§¦¥g-í€ðkèpá ÕÞüÍ¥<»þ`˨òE°õWcz¼˜#ÿ°¡ú +9Øl›`ßé)œ'oéÀÜø!ëXe“ÎÍ4§’¬BŽs×VÒårpÎ]«ç|BiÝ—dÀÕì*hY‚Ëp +©ûÉd7ÃI|± +XÂ
§ùþ#³.HÛ1çsòdÔ&- +϶*½yvòì°mÐäHŒle!魯¶Îg©ƒX±áuC +× w&À¯7±äö½sÚªçH\g—pRŒ«ÚüE_šuâd½É$ue bR‡H\Eø–šŠ¾Ý–™•û¾ªñÜ$ýc~:–q +‚aà¶XK°F©øQc¸U/}Áí÷Aè_JvjÛÀüÕ²Y' K·4;k¿s G®|ô‡Tw¯©ÝßÑ`~Uü*k̳"‰%ºkœâ]³smp<™##ž#rõÝ£±*ˬMÄ„ê ‘ü=—鬡—À¨7çlšÏߦ´£½;¹œŠ6#7êŽH9#O1ÿE4¹•2ÓY¹ö`oT +_ßêµÂÉsÙ9Fn$ͺyùXÐû¾†O¬æˆ‘ðç*£Bm ý ”ìL>:s×Z ÔªSZLöê0‰cÁn§+£D½Â*NÖÐÏÝσÖ>E$=KÀ±g—>7hê’+Úv=öYD´BüÓ
Õæ ýõ¬;°±:O(ÑC˜‘-S)xÑÌÖ÷·ËþùÄÛ†^fãpnŠÛ©W8 y°aõ-ùpaòÙ™CF×)–G9Ÿu&E1ÜM›ana^LéíMy“.¤V\6K ·t\‘ŽkŽ Ãå#É| ÚÏZø‹á²
ËNÍ»-{Mœ¼@%©È!Hµ;è-³öt?a5cs^÷[ˆýÝdŽÝŽ YVÅ„–®š‰…BÇ(C†ÞÓÇ”;¡?Ÿdo¢$ ý’À=RlØ+/³1B’À$Xü#×ÐQíc„® R:ñt `l™2Þ`–æ“ûŽ,‡÷7ÇQbƒÐµ&¹³ÛCêó¼é9«ø37W}dÛyIlqJï»Ëð»päl°ë~Üsv¹Œ~yß'™]•ÜõŸFÇ™ý™šuü2Xý«¶Ï51¡Ø1¹ü[±áÍr ]«™Í»¯#ac…Æ-i ÉWιN9m±)¬ïg d<ù*.›°KΗ7”ðÉw~ÿ¸E»†Œãˆ¶!Š<ñC™ñð€ÅìË iJ·Æy®Å1a¶ z]ÞÙ*ëm’*8¤ªÇæk²ÉÓú•/]m^/á èß"Ïš ªpÓFM ¿”ã•}ñÏ
èðlº=Êž¶Áés§ùDÁŒ¯þ^yuÍ6F|w_†B”šgã¶`„eÌ`Tßro‹ê(ò¨™²Æ´¶" +ü6¢ð Ø \²TŠaŠʆ=´ªðý† 0Ck¢ª‰Ú½\9”ž[HÏpÄ<éÎ (ÜÌ“y;æ"pÄÈ3Ýá"æ &2(2 Щôt3†&% èûüÀÕE_‹ï/6¦Ã~§–õ6ç^þ…Êrʤ[íÔzÃ9× +”S ìÊÚŠÖHç囡Â3]
ãOžu² “ö±‘J—eïVÉÐF]›ƒ {£ä¢Cbgð¬ó´©¦’]ý‰ÇcôÉè½%õ»M¹=®¡EE‰U¦õ¶þ ŽbIU;·W*ü\Ãy!vÓ¹`aÁÅàu)ßHŒ… Eøi—Aú4rüF¡ïí5?ßðíþVÎ_¬1òLÐÑeOë!Á¬sž>,ƒWIUÌ5g1éQÅ›ABŠeÒ›ÓÅNA@To®jt%;ÌñR@|t K“_&àmzOÊÀfûFuµ:¼´AÙ'‚ÊØ÷‹ÆÀWZܯv¼Ð ™uùùäº1Œ}#XlãMüõÝ|•pÙ *vlôaê¼® •—“ÈÞC½bïAŸËãGΓ’†:/x“§7ÝMJ®v=9&V®Ô‘Qï¥EŸž†ÌoµÃ‹î®eQ sh$ ûÔ„† +Lä¤t÷\Oß|W×<z(xÐ è.“
Ö-FΖ +×à™Y¯ƒ±U pËtü1¯!xrI!©L—† +Tl=Sð<„(EQ„~¹&wÐj° ˆýzBÈ + Ë)ù½~Øe ¼¦úX‡uh¾¡.w*½ø=÷ÉÕ†T0Ù ÍrŠ–tFËÚí€ûRª´¾iE²xh:AœzÄͪBÓô‰~¼úÖýâ<¯Qà¨JqãNy¸x(+ŸO ²õW +„=×Ú ®Œ&‹ëZ˜*ŠVû€1zÏ +¼ «Éís¬’oÝ)ÊT(»Ø3>InØHùÑècÍ’áþXZ¹´g‚dZQ{®´²Ý²Ó–Ÿòb}Æ^š iÈ vÅÊkÇøl<þC† Ž|\çŵÉÙ¿áT¤Ã9kLþu’nŽ·q©8¤mz†&Üö¼o1VÆql¶B“Dp
ê䥛¸–žú=ût4 ]e†êb6s·ÖœYå _ Ãgñ“@ê8¶¸t÷À[p‡PÅ·«ÉŸž&ƒ4%‡1fÂÓ¦°zjXÙÛDÕòædÕÙb'(åÑ#4P‡PcŽŠ6Ë,êy +U-éÓ¢Z¥“¶MOp¿y0Ck¿^Em.Pî<<îqºæ@Nò‰†‘¢ŒÜӴГ9D|ß+×Aøߌoš#SŸ¨Ìv x6ÂßF³§Õ›ºÈIömüú$JŽç9í‹Ž‹!‘Eп Æ€±
1Q™u¬N+ÖÖŸA +6³rŠ€x™bl‘yOXP,‰k£‹ûáÐO$] +.ÊP4ÿè:òm¨g„}Åîô@îñQ9Í…wíé±ï<j¢í†c{ÄŒ]`åêéúÏ+‘“³Ûþr‹õS)nÅ#_ékHá[@̯üY$¯Cù+®Á}%Û/*Y`Và#–&›EˆŸ)É{eâtOõoØ=IúS£ïTŸâùßð +%3-d —: ÑÊEçLûšáÅ;k÷ä§ +ØÙRǶ_ý –~Êù̉Xsmõ3êüQ ÂjøA·35JÊ3¡é:”À Ý,OìALdo\ ñ.
«åDr9ú ÉÇ~Å)[O<é>ZçÁåfA +SBtx}¤–‚Þ¦TøXÈ4î^Ô‰j·Ç
'…é$|Š™26e[Ø!U†ARÕ) ³Fì¹Ñ R¿k-¾?õ@ Íù0K‚ GXQIB@Y¼Q1TÓëe{s’î.SKWÔRóC„g›ÉÇ%ÈÎÚËîž?‘n>Õ¡ç’õC#ŒÜ'±ÂUù gGÑè7å K,[^D*¹^v[7S]£FS½h&ÏzÝfsõdŒÅ˜Ã£ÈIÁvN¾cË<5CɶØcÉ_íž„¯ˆDÅ*pEmî´ I°‘ä1xpóšMþìÐE`jÉqE¬ý>¬$ÅŠ Ÿ'u¢¬ÏQ¾zßóf8I01ŽØ$úÙN³ÅDÉHë,žc,Å]y@–xEî†_ý-/‰b:&Ä<õ£¹óO‹µ²&Ç ·ØÉÃçVð7áк´¡ÍÅÇBYµ:¥ Ëvð]œvd{§ùŸkì"=*0Ñ£¾ka_d_kë: +íñÏmt1b Kì(ª’Žž*¦ø47Is4£ÜeÀ¯j[‹Ê4Vý?SR912™¬]ÜúÆ°ÈCMÞMãíÇ^a;»õk +endstream +endobj +540 0 obj +/BRWAJK+CMTI12 +endobj +530 0 obj << +/Type /FontDescriptor +/FontName /BRWAJK+CMTI12 +/Flags 4 +/FontBBox [-36 -251 1103 750] +/ItalicAngle -14 +/StemV 63 +/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/W/Z/a/ampersand/b/c/comma/d/e/emdash/f/fi/fl/g/h/hyphen/i/k/l/m/n/nine/o/one/p/period/q/question/quoteright/r/s/t/two/u/v/w/x/y/z) +/FontFile 1785 0 R +>> endobj +1786 0 obj << +/Length1 994 +/Length2 4072 +/Length3 0 +/Length 4725 +/Filter /FlateDecode +>> +stream +xÚSw<\íÖE¢
¢ Ñ!ú¨£—èÑk½Ì`”™13ʈ‘„ $zïQ£÷$$D'A¢DK!¢ßIî½ï›ï½ÿ~¿sþ8kïµ×^g?ûáå26Q…"aZHVD ,.¨˜›‹‹â`115/¯:æ„…#NX˜< .''¨¢Ð€„4 .&/%A¼€:…CÃÝܱ +F ±ø + +~è._ÐLú¦Ñe¸uÉ:H·÷꣟l„j–gtU’{ ŸÉÎiGS &·P¹½] ¿óçlò~„ð s0u†ð@žýàTó VýìAywÁ…ÏìqÁ…Ò
²¥AÙ¬7‚\ëð'¸ÌPž’dmpÎ¥Jr7òv*ÚÒ·ºb3Æv4èXæí‡ò¸® @o mO0µR‚|ÐÊ"ƒ’šQ"£TOü„ë1:<¹Š¦Íâ°i/¹²L-¥Ú9„Æ\</žŒPìPu¿óvýâ]Ã#«ÉÏ=üù‹òÆçb¹x>DçŒ`hS@W +µ)mD¸?t\ vïɧK´”~]Vú ³œ—?n§ÓÃY¶»OlGÖÝ ææÎdt–|òRim‚Ñ
dpî¢Ð}§œgcùi¬þ„â3ðQ‚{îáÉ»ñKŒ‡ÍbFÅ89ð‡ÖÎ¥BlmΉ¼Òe"æ) Í;¥Týv,X΂3dl‡#/h„OS¯ƒ,uH/áiD+úq´é¶ž=n)ÊÑψÑ>êKæQ–_ä·}¢AkÓèÚK +‹Pž{›Q{Óéüú½+±ã~ŸÈ6 H*[é'ó%ó߰ч‹Ê‚Š8ÒýåR6GÝ¥Ù( ck¬ŠÝšqf‘ÒÓÒÉï‡ë†yØKŒ•$³ìÙJ˜}ú0ë^´E ù8«ÆÃ’"Fò’xbCŸŸ<ùèÁV +ÏññÓˆi856iØþr¹;m¿u’#Rûéh[À3®@è`|w˜ \€õ|ôœ5HR)öæUG ëö^¹Ð)͇]E‘~uÓWI—;Ô”·7"f9Æöm·ÓF£sÈ4Æ }U˜Ü[syȽÐÜöÕ #µl÷a™Rbø’:XdþÍ&,Z‘ÈéûZ£ kWŒÕÔ»ýõyº 6FªõcTÞÓm€lc`”#ªæ· +;”µ6cê¶&Y ô¶¶{4êp$=$þÌ.(ŠSV²•ë')÷— +áCz•6t“8·º´ì±ìÆ•G˜væÆñAÖVfóä·ÂÃWã+;!¦„´³Ke–ß«,³!2áìyÙšº ÓUrV1³Ëü:ý”Ç4%")C‚ºÓ•&wíMb¤% +‡7F®Sž‘Ù÷<þœ ß ü±!çé@h"¢µýÊœŽ¾êf¥ÕeÆ!Ühƒ_j!±ñ 1{žz6ã‚–/ºnÂj»gW1`4“Pâpp˜¼³ÈúbSê®Ô‰dŒyÆö˜b˹ì68±òaœ¥J¼ôO=òÉý'àr + §Sâ&ÖŽ7Ë3c³Ý‚DIvíWns>kr¼NášÕ5[Ô}÷ÖN¬¶¦·Ž8W(±Ì I½â4-†8øli@c1ú ãÉPbùÄÍܤÀ3‚éM61·¤{P€ìu0wÛ.˜ÄL} ¬Gß›˜ˆÅ¢Rå¿4Û¬Gwæ‚HãG”¶‹¯\¿Þ<a¿~wÂa'çûÞØ1x† ¡¦/ª +¨óuÝ €è¦Áö† Ân6”
(¹ø ½¥<¬¨ ³ú`3W„OsÏÕ§ò%h÷åhákØxÄOo(i™ÿ¶ô<ï
^q B7ÛÔV…‡i"i‡”L\Zïj>fûf2 ºñ.ÕF(ÑSýÈ¿‡®|†Ž- ˆžßãZ¿i=Ú+Xg÷I¸“ÿÛRTÚW½âsú&ñê–sê‚ÃÇ[<I¦}wxŒ‰ŒÈ[rGwãA´¹æÈÔ|º—Yó ½ŠÙõöy_:—¢Ê7P1žuB+^ R#_*ŸIh¨Ý<®ÀC…ì
Å +±ŽvØÊÉ\vñÝZ" šX<Uû¦ã¹‚R«¹q¿Åd…š¬™Š‡úUµ C#ó‰R®i1‚ž×z‹ 2%ª}ì&Œ’Ÿ‰¶O{ö}S)ë#=˜ì‰²ìzöLF>< ÷M˦Ýó ;sõ»Z’7È$õPØ“òC…Å ÉöÙ= $ú¼-ÈzÆ ê'IÕ°NaPªºÛ‡]c³FA³ûp5³‰y{;<äá z—üß<°Y),™
íÓ´O®S(!ëËÒ _V•¯g\§—[ì puJXdñ¹ñÓ;WR”jJ HOƒ7%ý˜æÉ èq’Ç/pÎe8¨yèpð ƒ*昀&ƒJ+©ÙÝ«å¡-BƒéÅÓ ŒÄn É1mF:ÍAç3û¬”ï/pZíx½4Q¥š~Lo»©¾dù«¿éLÚ•¢øU6OùüÙ§×þM‚##Ú
ŒÚìU•ùÛo0ïžX` WITW1¶¤\³dÍÏì×ÞzºwTËwT‘k7KôÖ(Á+¦¤¨G³ô +¤˜OVë]‰Ÿ~_Œ ÿÖ2¬Ï_SÕN¨ßOªîÔÚFÒ3€˜ò¯?Í}Y¹.E|$±íëvé%6û2$ºòZƒ½àºŠG´èóxi~÷—k 5lž÷ 2 K|HÖºð챪ÊvÚå¼óºˆŸ0¿ãÅï “ºãŸs>å"0%ϼóz^p]nNÐS²W™¯Kþî:“]x@÷ʨC‡`PëëѵCxºïæð¢y8‡¶û~yaÿ}–Ø’Q³*(öIämŽ=ÏòF»gÏë©iÝ2!X×3í¢S'ùTÝ|c7Å(RéÐÂ/Ý!ßA«Qø‰‚ß…¾³Xó uÿaÕ+ ‚OqÚ4´öÛú¬ +C ·[â¯-%|œ•-¯ +endstream +endobj +1787 0 obj << +/Type /FontDescriptor +/FontName /DPFJGJ+CMTT10 +/Flags 4 +/FontBBox [-4 -235 731 800] +/Ascent 611 +/CapHeight 611 +/Descent -222 +/ItalicAngle 0 +/StemV 69 +/XHeight 431 +/CharSet (/b/e/four/g/k/n/o/one/period/r/s/six/slash/t/three/u/w) +/FontFile 1786 0 R +>> endobj +1788 0 obj << +/Length1 1973 +/Length2 12685 +/Length3 0 +/Length 13766 +/Filter /FlateDecode +>> +stream +xÚµUXM¶p‹÷ಠ¸»ÜÝ!¸,ÜÝÝÝÝÝ-h€àÜ îîpÖ×½w'½ÿÛópèš5ç¨Yµê%'QT¡2±3ŠÛÙ:Ó330ó +lÿŒØØü‘bfõËä?È +Ú©‰µµ¡ã_ àŸ¤ àeÙ€®˜µ¡Í_k@{5ý³ajáúW’¦í\þ. +1û A¢æ´A§aîao´ý+4fñ‚´,ÿBPçþBP'¬ÿBP›þ’eµàOfvÐR[ Û?²¬ J¶.6Fÿ¼xf€ KF»?Ž œvbfíÑþÏ4¨†½¡#Ðö¿’ùFÿûYA +ö@Gc í_¡ ÿ³°3ù«¨iVzæàbç 41ú³WVîÿüï +ÌÌ à¿ÚÏ Ú£ÓŸüC@׿ÚÍ +w=Iÿ±:Y:™ÿ•$ø§ +3vq‰ó¿¾y çýÙÔô- +çj_$^ÑcM*¢z®?¸÷³ô-×K}Y5´%¡ÿÁóúV2Z/Í[ËŸ¹¨d íô½[u*78cØ^£º³|™œÌkyôceÄù‚IX—à,ùéÚ÷,«ŠÖK„fíarhÙQ 2lΛìfS¾\ k’¤ž×çÏA5®à:ö £61¥°ÂÝ´1¢ÏÔùÄØ9¹ž˜)÷ªFø× F”ùf¦» Ö#·J ³ã–”îΕJdˆbÕö¨È +±U½ëDj/®'~.P]Ç¿(Ï+>gPi@PžàÌ}g7Fp¿f_†i´°$@*öøZ$0Hƒü@ Àx‹È3‹Ûæ¼ÏÀïVcÖ ¥êY··. îê9•6Ŷ
.{áwAñܶB°ší,Ø!îFr˜dÿŠÞ½-%Ûù+‘ä"mfXc…òAXùã×$Zñ¹’w²ïLå)þ—У|†ÜýÑ_€&à8oNú(¥dËÜÛ¬1u(ÃÍý1Ñ—‚V¹¬I_I™¸µ{è¾I°Zº®xZ +"”Öjü¶eùÕ·a\Áî)_¨é-,‰ƒþFKjô¶Éˆ² ©üÉû +ÏpšpÁë«!ñ$Yê‚£Ù£7Þ>5 ÀëÃ’þØ|óè1`KûM÷ÎpÄY¦Z½K"é“z¹Þ¢¤Ý EéožŽcLUç—œuVCñ/t}ଠzå0>Ç÷w(N©ŸB}[z®7›‚3¶ÕK¬¾Â«Ž™dEò&ôxä}ÐAž´kJ4WªW%|*8|$êllUÀohל7´¦oÓ×wÚª¨ÎF8zºwÖ$Yê±k˜ÓûÞÔ¡/Á›Å¤ó›E/8™aÒ‘ÒŸÂBã×ãÏ9 pð×2ø"±KýPJ¬ß«$Ú/dŠ<=Ñ6hF*$½?·¦'H QSß·Gø]êzk\™¨Ù½¡6b(OÉ +tÁ6CN$™l“8#hS³n”SÕr NÞQñ¹m:‡E–¿óžJ-kr_¼§+êïUgu™IÛãI‘iaÓ˜¸Wÿz JP`Ww¹J²“¥¥ps ÅøÑF,c·‹D_¸Ðt1— ÝD`Ð0•öUîp¹ÎÀ:šPÿÃHUR-:¶¶ó…‘¸eG÷]LÚÑÍuÙìLlÙôçjn{º`qjš \×]G‹Å(¯ ‰C¥YÌB;ž~û›ùÖžþÏŽk±t 1«EøŸ‚b^ÇdŽg!dœÃ*#7uB r™ÞÏ¢èÜoIź(Ñ*-Äiþ_`Â'‚ .ž ÖÀj2¼ QÙÌí¹!:w{r'-S×)+E¯ÌäÑj[…ˆM®¥ËÍboÊô
cÛBë]>ú°´—šc”¼yrÀ…M„o´N%µ^añJ&C:„éâ»ñÇûÌ%ŸQrúF\“W} R$ +Ìè;0%ì‘Âࣟ)W}w¶#ú\ <Ñ Q )^Ï7¾1×ÏÙp¢m;oËV»Ýç±¼'Za{çù æx(^Qó(kÏù“ÈX^ 碥/HãWÀ|ª,Ó y< äˆÅúU{ûŸÚŒ³>1$|T ˆ«ƒÄ;M.>àdó;rÁo}’-csÅKn‰W¿ÈDÔLuòF/|,C 0ÉBPL6-°óƶÁåP + K‹+nõé×>¢k0úu‡)"ö +¢ï É’ÏÇ×'ÄGàÆÍBiš iMÜ6uÂ! öÿÒˆ€z”¦Fà.g/ÊÿY*vhö ÌYˆbßžO?ú$Y^7{3+ILVψ•@°Ö<lhZNxUÁèÂÛƒ8Sz3z5<)í +NÌ’ÄÐ11ä A
[ó‹Ñê-!VÐU$¢qn(çgN,°|)¯¶0„à +HËÏöÄçah™ äF šKŲAb Æ{¾QÕ¡9ÃX¼Ô)+»»æbÍã[Z¦„ö¼oµk{¤K‡ðˈ%ÙœáV÷³õû²*iG¹³ 2zû;¸HœUpò5%^}rš;]Ý‹gekžÿ-c×O^á³M_álT”ÿ ÛC¦Ã¬ ŽX+"uº°ìÁ1’qGÜ'§V„6b蘸†Œ.:‰£©ý® ›&¡YŸ
ÆL€Çúq©Ä,ùû`[$ {àìɾâÚeu €ÅÖT?ý©ý7LW5"ËÅMf3ï`â—Ø=Ùi]$/‘–Ó2«‘-> {ÿ\‡bXÛSåúÿ¾™ûŽóÅè”ßßQâÌ~ȱ۸˜„‡(z\)èy*Û[+ѱIzýxD ‚¾òß„UDs$~cÝj ¾ÄBd%_‚ ‹Š¶-£–6,ãEB"0†* B·ñ.³ÇJe~¥¨§WŠáúâ çèü<$Â9xçWß2=mŽŸ9MÒ_ðÉöÖ´kÕÝCÍ +NÎÓÕC?Ú,Åm,–Û ^4þLþeœmÁ dª1åN—ÈçoÐÝä›ü}©/š"~aícqbƒ&/ r + +œ{ì3K¥<Aê:H®!)|Á'8A—ÛªdÙŸk§³Â//¥qè µƒÚ° “ÅùéZ©Î¯6[mAY»^oÎq u-™É!CõBªÞ[©Èf‚}.ËÜëJÒ Œ‚4» ›ï»º˜¦”/°Þ¶ÔÑZh\A‡Æ‰1)ÀÖ`°ÿ +^]Q¥«j ÂiuÕ + +ï]ëe¾Sû3aÒ6žnF²ë—º•4dË nYFªQ–‹G|&”úòä‹m2θìvÒч …àS²+Û*¼&Îçcs¥¤iD_ >gËŸJL=¨Ë\bÏiê#!RÖ å /Ñ„„ð7B¦o)ÀMo‘< œâ¬zß–¦K•Í +*õD‚=ƒ‹¯ôðœ3*âžü>?% P,yÐ|#´+¦è„õ.öGÄÛ/5/ôˆåÞAÇŠáEzŽ”’üUü<MÏ«{õɽ,=¢‹uý¹Jšf¨_ñ# | ‘ÑW‘–”ÏØ~,¦îùzŸ¢¹ÞßGH¨íî} Ž:¨LœCÅkÒ!¤¦ ~ ^¤"$;pe¦'PFKª‡§ªrõ®ÓßÓ!Ê4bèîF5:ÕiÉ`%½…ÚA«âä~Lî8ƒÜ¾[¹ÆoôÇp¬[¸]3“†#8Ž 2‘Y·Ä¸|ïHÔ$Ó‡@‚ÌïÛÜ £u'µÝXQàšÂR?xHd°±: X’Œ¼â, .4ð.2¦¹@à +¦w³àü0%r_p ÄÌB Uäݯ<¬Øþùa—¶ì&íSëá« zãk«ÄøQDÐ5ÜBŒ @2÷iç
ŠðÓôíö°B”˜6ct@® À•Ûøpiñå»nþÒÑJq›&E_ñ
eŽž³,fvÔsZ·ƒXÚ6Úð±’=Òâ‹M¸ò‹|‡>‘ãÀéÅšêSô¯Â )° ^Š ê ƒÀ¯d&«Ò_Ÿö š
mU'[Bæ[0®² ƘÁ†Ò¡J{ecFŽ? ‘òÓ†?h"¨Ú‰1Oá¹%áB¯0´Òz3Pl‘Áéüî¹¥Ìr?‹†•ƒ¤;ß#ÆÏI‘Èv÷‡ßÝõÛº¨ýâá:ªè"Á m1Ñê"yÏxc÷íú3DzN¢ÓÆYŶµµ?@g!v†›Fk©4žç½ i–¨Oipm¼jkY“ôŽ_ÇûMë§2R=¾|é…ý®~øV#Íç™ÿ*Šq†¨ë9 lœ>:ž£yt[tà<Îê½2˜& ŸÅKÊÁŸ/!„l-Q+»ÙÛŠq1Ólª?b¾~ŸÊ2…€‘tDÌ:~Ù ‰ÒfÝÇçBˆåsÚÍQ\Vß¹LE4dFÕÜæ½,@qüåÇO ‘ ,àÿ‘óìiSdFD +ی؞g!«Ûº±±WjèNÙSê->õô=~E ÖcˇD,½éÊ ÀÌ+ÐAÜp÷‹ _ê2@㶪1ºá3ØQØØi 1—†}—l|`˜´3 ßΩ÷x~Û4Šsš/Q¹³äs
W±KÃHH;lƒ¶ W2nrüU®ò±Ê3EàzÍÎs7šGqHÛÙ&;ž„MË^\RšNtnÃ[»Øè +¼|XN‹®òv!„ŸÁ÷ò0]9– ¼<P&:C•„ +ÍÁÔß=äÃã@i4}Õ8Û›¡~ŸÞ´*r˜îUÛ¤$k@º»Ó䧇^)õ ]‘÷Ü5VÎe 'æi¬NmèÀwĉHqüý9š|ˇM(üèÃœ»æ®Ð' {ų⚤042Ë|ÎY « + Ãd˜UªÎ§»lu eö–HqÔø„á‰]3lð™jç+g†À¾J«ß¿ÄQp2D{~$ǧδFà<Äèu a›‹¦2*˜îc7Ë…x.IY7Ø! $Æùcv_«{•>ëÑa[§jš÷P8©9*a¬K±\rsý8êr–mN;GÀæ]
m«þn
žzð¹¯6¿ý-¬wR½–è0»ïJ¸ýŤää¹B}H£óh>}ÝGi>æLZ¡œïh9GÞ¸ð#ë'l2Ô~SÒß6ÏmBOhɇkV«ó/Du6ÝyÝ—¹ ¼¸‚ìÎH¬[:2×%í¹ö„¢ýå¸HÎتÂ^8¦T¹3P$ð¤ Ê-Å [Í1[JEB’J3Êxžç½D÷¥ 5ù™yÑOtÈž2á—)7|è9yqóZPÙ\Wàó&k$¬ƒáÆ›Õ(ïãAAùü!g<Í µã¡†^s¨“‚Ž8à^zïvÄ9ò¶5‘·åá“ÄR‡í®,z‘lrÝ%U.Fô×é2Y\»]{¾b󄞎(½[VjªNV´/`CR Œòûóמ{^³)óz‰>~¸ï…¶#Ž™]ý±Áõ)FŸ‹;d©MbN{ã~9¬ oý’kÝbæ‰Å_úTèÿ\Žy KŽÜå\p ˆ‹í-ñ‰Ÿå+ícæÃÏÁb“©©ëqM©ßN_7y÷X¡Óªü÷Žj&Ú:ÿî”õÙr/flSÒÐ'Tÿ¾mt
¢˜äׇɼx¼1Ù`°¿4ÏÐ\4m™èwm«¥"7´üö½W¬ a}¢{¨h¡³\÷xßÕÅñÑ×è¬óFºe\áûJK*0ƒïÿ +k öÂ_wµÕÉ!Üâl=È]R^L/leÄby»6ÇýkûNf&ë‘ÊÌ>!W¬hk(j§5îÅMÝ®ž{X(|ìK Ø6LÁ†½Îʺƒ§¼<%½m8…ß+Ä*‡¤UbímÈ÷ÄUãågëÐî™V= +Šôèí(¿ —i}œÊèØ÷€¢JŸÛåoÄüÓ•5Åý¿.Wp\Ý>V?~d$…îâp†¿’7ù +“¶#<ób/MÃñʬGïóÓ5„×Õ—€j/wõXYÑÕ+_â×ئC‡Ts2ä—€ñ"sá4×Êêv}±7l þ>÷ëZÒ<˜án!ö7µÇÄNV\³yõ8½RNæü³›ÕÜß2"Uˆå¢XI¼ßžüq˜‚K0W/oÖR( pøB æFÒ\ìyNª#ðßæHû`·Æ& RŽzç0Õ Öm²Â%aÔjU䈩1VÏÉ ßÄu5Èëw+×sönÿH
¿^ˆíú„Õ¸Cÿt6û~E%i#¦ŽmuˆSÄ+u&¼P®ËÕ¿Í-iós_4Œ¸& …k[{yšYV:!'U×à ÷¨æ%˜uŠ»ä¿Ñ„V·‹í ÂÜj¢.^þ*tó ’/+ZÍ&ÿ#N)
8;Ä™ã<ÐâÀ¥šl;Ôm3nfø&û€0´µÑ àÚÉ4?LîX"×aK +)c3NãhVñ¼-¹Å §8}÷¢KàZáš{wàíIà'¹¾>Ú˜¢³³0ò bM÷0yTÄz¢*ôÝÙL^D°ª ¹¸ýì–µÊ F~³QîmÓµ¦Ö6c´rMpÉBb·‡†ãÚ»@R[ +a>0£çóÆý²«:ýu£Ý 3ëê¹úÌX6ja,áï Øh‘¼A= +õÔpr¦±$ãÈò„g×i~QW”¥VÙWõÒì¶ÇëžÆ. Š¤'ÍAË6Ϥ{êÍgjG +Žò<LÀäI>)F °[‰óÕÃ[!¦÷ÚˆD·)ì[‡ å)é§]¡KÒÀ ·¹äñ>K©lÅXK2‘û?ÞžBüR£¼ßþÁIÅ&7¡É3ü‚{)Á²Ó4;Š«Å ]ÌW¨õµwB¸ç¾[Æ.º,žNà5/야Äí‡Ù2ëû!—#ââ;§Ñ[8ÿ½ƒÕ<ŠI䌒·ÛÛ_ŠÀÐ0«Pª„³òK›#wÓ¿a¢WW·€˜ŸÊ…ø¸òfkæŸ\uMçÎq+5·VV™MK·S®£¼'¾„vÃX1à·G)¤WD”`¾=AãN¡§6¦»ldu¸³ ‚ðVž¾= rørï˜nQ¶´Å¼™cœ(éZ‡Šòdi“9Äή‹V0´¿*kA°G¤Î>êøãÇ‘é€ÌKô3Ó|Tà»6Í(0ÖÍXl½ +q1hy)»ÖžÙÏKÆ MgŸŽï[hwÜl+¨õpDhÚÔKø6°ð¼ÞÕì*ã·å˜†ÒĈ4 ‡f“Xè¿«±úÀu…==(`4 +èªVö\°Ü+ñ‘I+CÌ+¾WÂ=W`÷cõ¡QÇÝX#š£J¿+臞MÞ +].þZ§4à+ ð’?zEì|¯Ä„C5ftg )ª€”þáÛøKD•-¶“Q+¿ ,¾† b–´RΣJžwª¬L÷û¤f mm¬Vƒò—Z „ ã!{·‘»3ªŒ¼Jeu3÷ªÝ]fnö§DøÔçÝû]š÷) We‰t×”›«è–Äöun³ŸŸå xMç>ÏŽÚeÍû•¦*ò³|]£€É×ípEýœ? ŽÖÙdy)Â9ð5*_?¼½ ²ä; A%üÀ|5{sz²nÕÏ“Wí=Y>ð¬ ìwŽ“}á„nd¾ŽÍÔ5¼¤ :sºðmd‘Bƒù“Ͳ›<u£ò4˳¡„Bpk¼ý¯![n‡–5dŸdw:ü a½1/ŸY´~.ÆóxJu DlHÙ#óžÎÿÔ!¢ÔÊÐó»½}Á] ©ÿ‚îsROI%¸ÉdYz%Ÿ¯ÈÒñ"c.+çŒ/~kpo¬Â Q + YSÑí£"iíB“Ä×oºo^ù9£¶ÂóùÌÊÙ6·QÙB«G¨ä™„œYx”| •ÛUè +mêH,îŠð˜ñÂì µIF}7«/0Ëß=Okà–ºÑJÓø! æZ¸>U¸Ìôdyë çïä ¼ïâ·{æŒUÿ²À:.€6d<û7<ág +ö+kÕŽ ”æÏ/ÛKtö£{[ßcÎ"›’¥G¿MÌÆ‚-†ý ª¸Ö”¹Í” •hëu¾æ“&øI,ìNÂô‡P
#<‡Ï¹÷-*ó«¼{Z 2L£xÜ
P¨ïÅY!UÁ)fÚ_¯—·
æÚŠ^çYÑ„Ñ´ÊC1Ì‘>_¼Ž ‚ÃÑ´-2ÓŽ þb%[ã™7,sâg‘àà ÚjÓMÌï„iÓ„Ov£e¦·¢£µÕ``[,(«vBGñÀäªÀ'7ÛÝswÊžZRÎ`äp~wPÿ‘²TFÎF‹ +?ÞgÕ¬'d´~¾™” õQ`Ñmk3üýd SLàLWB>&¯¬ú÷’Ö8´ÞUIÝvû9Œã9âY×Ë™=éF±ÙýæÛ¥%U•%
n~W +ÛŠ]üÙ±fEÌs…°Hñ›“AŒHõDó†Ô³“'-¦Îa;Õœ 4nï ϼ@ šçxÖBüä(¡¥úO» Ræf-¦p6½7‹=Vôì•‘Å\Ø +)µ$VÓm YGÑWÔaT²FŸ²e ûOÓv¥~~F¤þ¶ÒÓÄIÂv<ôãâÜ÷Pé•Æ¿…Á+±ôz«~ü8èÿ\”p·åžÊ]ä·×pÇó ŽZŒDX +ÐAaÈ84U)êRN&JNk°½â +B°Æ*`ć!-"ØTk“Æ‚ˆDàGËË áìFë”8™°û][2\[µ³ +šÇ1ßž%fê¦Y`vÐÖÛ
kÃ=ŒrV@Âê7áS?(²Ã”Á–@n–¨›ž¤¦vꊤšô\R…+ï +
rŸUS uù|È ~§ÕËË4þRrY´^Z˜…›Z8f_R œˆïP\ôàCâ‚«ª¹ ¯µf¿0;à¯Ï ÅLÜO»Þ΄2t>š‹I¯'Óvæ¼cûŽ”‘Gz%fÛSf¥ö&5ÖúßÓ³Žùw«âäÏa(:Çù†õ ¿8iÎ`´¡=ôD§è¯dl`Þ÷‰OªQÄ&Þ®®ÑʸM²:ñðwb*4÷æ<UG²Ðó`1 €q?>yd¶"]GUðjdrL)ùÁ{ ?RDä7—¯ó”?ÐÉ붦Ò{áQ’+¾SÙ³–1xR\½È
àÏß@ªK8Äpï·Ö‡—ºÃYÏåû£æ?“‚qänºM" !PôáÈXÊþR0~T£" Þ¢º+!+š¶®oÜ€¨‘Û›S‰-ù&
x³Ÿi‚—2 +ë˜~8\·3ð«Ñ2Ø ¥i»ìˆIC†2\°/zGÙ¼7è’ѶÝV¬=NÖl{ê{¶ŸŠ)–i +E]g’
™).U‡ëŸdH×à.¬„Ó `Þ¶Ìxqú]6¡¦¨Œi'¶iH-=ÖáT¾fÊ¿vÇ›öúcq›)#9ðÓ‡.p鹺ì—öùXÝ’Ì+1¬.×S”g2y!ŽSÚÍ3¿eŽÙ¹Ö¿€áX ñún˜mw ´ÚJÖzÃdíË‘XÊ“7ÖSi®éLYkÈŒMjks,Vº× +D!Ã{YXÉgxíDQ.'·"¿Å»R=öiìT\j«As¦W` Ħn_–¨µó£ˆ
e°¨›"`¸@ÿþ•!·•¢4á·ŸYQ¨lÌEï\fÃ8§¾áFq†¶»$Úþà¦;F)™§Þƒ––_Ñ/H¹–ßIZçY;ƒaÅ›uÐ÷°>Ê ®L3ãÊó–¥HdUB[xuŸæÊ]”Sÿ?fëöÒ +endstream +endobj +1789 0 obj << +/Type /FontDescriptor +/FontName /PJQATA+CMTT8 +/Flags 4 +/FontBBox [-5 -232 545 699] +/Ascent 611 +/CapHeight 611 +/Descent -222 +/ItalicAngle 0 +/StemV 76 +/XHeight 431 +/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/a/asterisk/at/b/bracketleft/bracketright/c/colon/comma/d/dollar/e/eight/exclam/f/five/four/g/h/hyphen/i/j/k/l/m/n/nine/numbersign/o/one/p/parenleft/parenright/percent/period/q/quotedbl/quoteright/r/s/seven/six/slash/t/three/two/u/v/w/x/y/z/zero) +/FontFile 1788 0 R +>> endobj +220 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /EPEQML+CMBX10 +/FontDescriptor 1761 0 R +/FirstChar 65 +/LastChar 89 +/Widths 1751 0 R +>> endobj +218 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /FTCQQA+CMBX12 +/FontDescriptor 1763 0 R +/FirstChar 34 +/LastChar 104 +/Widths 1753 0 R +>> endobj +219 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /DONXWO+CMBXTI10 +/FontDescriptor 1765 0 R +/FirstChar 38 +/LastChar 38 +/Widths 1752 0 R +>> endobj +208 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /XGXXWD+CMCSC10 +/FontDescriptor 1767 0 R +/FirstChar 39 +/LastChar 121 +/Widths 1758 0 R +>> endobj +593 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /RKJHQH+CMEX10 +/FontDescriptor 1179 0 R +/FirstChar 16 +/LastChar 125 +/Widths 1743 0 R +>> endobj +420 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /KWIDCE+CMMI10 +/FontDescriptor 1770 0 R +/FirstChar 12 +/LastChar 119 +/Widths 1747 0 R +>> endobj +427 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /JIUHFT+CMMI12 +/FontDescriptor 536 0 R +/FirstChar 11 +/LastChar 122 +/Widths 1746 0 R +>> endobj +210 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /QNCLRP+CMR10 +/FontDescriptor 1773 0 R +/FirstChar 11 +/LastChar 124 +/Widths 1757 0 R +>> endobj +231 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /YSLVPG+CMR12 +/FontDescriptor 891 0 R +/FirstChar 1 +/LastChar 127 +/Widths 1750 0 R +>> endobj +232 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /XJZFWU+CMR7 +/FontDescriptor 1776 0 R +/FirstChar 48 +/LastChar 55 +/Widths 1749 0 R +>> endobj +213 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /NZSLPR+CMR8 +/FontDescriptor 1184 0 R +/FirstChar 40 +/LastChar 114 +/Widths 1754 0 R +>> endobj +494 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /EZSWTR+CMSY10 +/FontDescriptor 1779 0 R +/FirstChar 0 +/LastChar 112 +/Widths 1744 0 R +>> endobj +858 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /NSJEOL+CMSY7 +/FontDescriptor 1781 0 R +/FirstChar 48 +/LastChar 48 +/Widths 1742 0 R +>> endobj +463 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /XXSSMS+CMSY8 +/FontDescriptor 533 0 R +/FirstChar 14 +/LastChar 48 +/Widths 1745 0 R +>> endobj +211 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /VXQNDU+CMTI10 +/FontDescriptor 1784 0 R +/FirstChar 11 +/LastChar 127 +/Widths 1756 0 R +>> endobj +238 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /BRWAJK+CMTI12 +/FontDescriptor 530 0 R +/FirstChar 12 +/LastChar 124 +/Widths 1748 0 R +>> endobj +212 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /DPFJGJ+CMTT10 +/FontDescriptor 1787 0 R +/FirstChar 46 +/LastChar 119 +/Widths 1755 0 R +>> endobj +201 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /PJQATA+CMTT8 +/FontDescriptor 1789 0 R +/FirstChar 33 +/LastChar 122 +/Widths 1759 0 R +>> endobj +202 0 obj << +/Type /Pages +/Count 6 +/Parent 1790 0 R +/Kids [194 0 R 204 0 R 215 0 R 222 0 R 226 0 R 234 0 R] +>> endobj +244 0 obj << +/Type /Pages +/Count 6 +/Parent 1790 0 R +/Kids [240 0 R 246 0 R 251 0 R 291 0 R 342 0 R 382 0 R] +>> endobj +402 0 obj << +/Type /Pages +/Count 6 +/Parent 1790 0 R +/Kids [399 0 R 404 0 R 413 0 R 417 0 R 422 0 R 429 0 R] +>> endobj +436 0 obj << +/Type /Pages +/Count 6 +/Parent 1790 0 R +/Kids [433 0 R 438 0 R 442 0 R 448 0 R 452 0 R 458 0 R] +>> endobj +468 0 obj << +/Type /Pages +/Count 6 +/Parent 1790 0 R +/Kids [465 0 R 470 0 R 474 0 R 478 0 R 484 0 R 491 0 R] +>> endobj +499 0 obj << +/Type /Pages +/Count 6 +/Parent 1790 0 R +/Kids [496 0 R 501 0 R 507 0 R 511 0 R 515 0 R 521 0 R] +>> endobj +549 0 obj << +/Type /Pages +/Count 6 +/Parent 1791 0 R +/Kids [546 0 R 553 0 R 560 0 R 566 0 R 575 0 R 583 0 R] +>> endobj +594 0 obj << +/Type /Pages +/Count 6 +/Parent 1791 0 R +/Kids [588 0 R 605 0 R 610 0 R 614 0 R 620 0 R 624 0 R] +>> endobj +636 0 obj << +/Type /Pages +/Count 6 +/Parent 1791 0 R +/Kids [631 0 R 640 0 R 656 0 R 666 0 R 670 0 R 676 0 R] +>> endobj +685 0 obj << +/Type /Pages +/Count 6 +/Parent 1791 0 R +/Kids [680 0 R 687 0 R 691 0 R 696 0 R 700 0 R 705 0 R] +>> endobj +714 0 obj << +/Type /Pages +/Count 6 +/Parent 1791 0 R +/Kids [711 0 R 718 0 R 723 0 R 727 0 R 731 0 R 738 0 R] +>> endobj +746 0 obj << +/Type /Pages +/Count 6 +/Parent 1791 0 R +/Kids [743 0 R 748 0 R 756 0 R 760 0 R 764 0 R 768 0 R] +>> endobj +777 0 obj << +/Type /Pages +/Count 6 +/Parent 1792 0 R +/Kids [774 0 R 779 0 R 783 0 R 789 0 R 793 0 R 798 0 R] +>> endobj +805 0 obj << +/Type /Pages +/Count 6 +/Parent 1792 0 R +/Kids [802 0 R 807 0 R 813 0 R 818 0 R 825 0 R 829 0 R] +>> endobj +837 0 obj << +/Type /Pages +/Count 6 +/Parent 1792 0 R +/Kids [834 0 R 839 0 R 846 0 R 851 0 R 855 0 R 860 0 R] +>> endobj +869 0 obj << +/Type /Pages +/Count 6 +/Parent 1792 0 R +/Kids [866 0 R 872 0 R 876 0 R 882 0 R 899 0 R 903 0 R] +>> endobj +910 0 obj << +/Type /Pages +/Count 6 +/Parent 1792 0 R +/Kids [907 0 R 913 0 R 919 0 R 927 0 R 935 0 R 939 0 R] +>> endobj +949 0 obj << +/Type /Pages +/Count 6 +/Parent 1792 0 R +/Kids [944 0 R 953 0 R 957 0 R 961 0 R 969 0 R 974 0 R] +>> endobj +982 0 obj << +/Type /Pages +/Count 6 +/Parent 1793 0 R +/Kids [979 0 R 984 0 R 989 0 R 998 0 R 1002 0 R 1007 0 R] +>> endobj +1016 0 obj << +/Type /Pages +/Count 6 +/Parent 1793 0 R +/Kids [1013 0 R 1018 0 R 1022 0 R 1027 0 R 1032 0 R 1038 0 R] +>> endobj +1058 0 obj << +/Type /Pages +/Count 6 +/Parent 1793 0 R +/Kids [1047 0 R 1063 0 R 1075 0 R 1090 0 R 1111 0 R 1126 0 R] +>> endobj +1142 0 obj << +/Type /Pages +/Count 6 +/Parent 1793 0 R +/Kids [1135 0 R 1145 0 R 1149 0 R 1155 0 R 1160 0 R 1165 0 R] +>> endobj +1176 0 obj << +/Type /Pages +/Count 6 +/Parent 1793 0 R +/Kids [1171 0 R 1194 0 R 1199 0 R 1204 0 R 1208 0 R 1212 0 R] +>> endobj +1226 0 obj << +/Type /Pages +/Count 6 +/Parent 1793 0 R +/Kids [1216 0 R 1228 0 R 1328 0 R 1441 0 R 1557 0 R 1657 0 R] +>> endobj +1703 0 obj << +/Type /Pages +/Count 6 +/Parent 1794 0 R +/Kids [1700 0 R 1705 0 R 1709 0 R 1714 0 R 1718 0 R 1722 0 R] +>> endobj +1729 0 obj << +/Type /Pages +/Count 4 +/Parent 1794 0 R +/Kids [1726 0 R 1731 0 R 1735 0 R 1739 0 R] +>> endobj +1790 0 obj << +/Type /Pages +/Count 36 +/Parent 1795 0 R +/Kids [202 0 R 244 0 R 402 0 R 436 0 R 468 0 R 499 0 R] +>> endobj +1791 0 obj << +/Type /Pages +/Count 36 +/Parent 1795 0 R +/Kids [549 0 R 594 0 R 636 0 R 685 0 R 714 0 R 746 0 R] +>> endobj +1792 0 obj << +/Type /Pages +/Count 36 +/Parent 1795 0 R +/Kids [777 0 R 805 0 R 837 0 R 869 0 R 910 0 R 949 0 R] +>> endobj +1793 0 obj << +/Type /Pages +/Count 36 +/Parent 1795 0 R +/Kids [982 0 R 1016 0 R 1058 0 R 1142 0 R 1176 0 R 1226 0 R] +>> endobj +1794 0 obj << +/Type /Pages +/Count 10 +/Parent 1795 0 R +/Kids [1703 0 R 1729 0 R] +>> endobj +1795 0 obj << +/Type /Pages +/Count 154 +/Kids [1790 0 R 1791 0 R 1792 0 R 1793 0 R 1794 0 R] +>> endobj +1796 0 obj << +/Type /Outlines +/First 7 0 R +/Last 179 0 R +/Count 5 +>> endobj +191 0 obj << +/Title 192 0 R +/A 189 0 R +/Parent 179 0 R +/Prev 187 0 R +>> endobj +187 0 obj << +/Title 188 0 R +/A 185 0 R +/Parent 179 0 R +/Prev 183 0 R +/Next 191 0 R +>> endobj +183 0 obj << +/Title 184 0 R +/A 181 0 R +/Parent 179 0 R +/Next 187 0 R +>> endobj +179 0 obj << +/Title 180 0 R +/A 177 0 R +/Parent 1796 0 R +/Prev 151 0 R +/First 183 0 R +/Last 191 0 R +/Count -3 +>> endobj +175 0 obj << +/Title 176 0 R +/A 173 0 R +/Parent 151 0 R +/Prev 171 0 R +>> endobj +171 0 obj << +/Title 172 0 R +/A 169 0 R +/Parent 151 0 R +/Prev 167 0 R +/Next 175 0 R +>> endobj +167 0 obj << +/Title 168 0 R +/A 165 0 R +/Parent 151 0 R +/Prev 163 0 R +/Next 171 0 R +>> endobj +163 0 obj << +/Title 164 0 R +/A 161 0 R +/Parent 151 0 R +/Prev 159 0 R +/Next 167 0 R +>> endobj +159 0 obj << +/Title 160 0 R +/A 157 0 R +/Parent 151 0 R +/Prev 155 0 R +/Next 163 0 R +>> endobj +155 0 obj << +/Title 156 0 R +/A 153 0 R +/Parent 151 0 R +/Next 159 0 R +>> endobj +151 0 obj << +/Title 152 0 R +/A 149 0 R +/Parent 1796 0 R +/Prev 99 0 R +/Next 179 0 R +/First 155 0 R +/Last 175 0 R +/Count -6 +>> endobj +147 0 obj << +/Title 148 0 R +/A 145 0 R +/Parent 99 0 R +/Prev 143 0 R +>> endobj +143 0 obj << +/Title 144 0 R +/A 141 0 R +/Parent 99 0 R +/Prev 139 0 R +/Next 147 0 R +>> endobj +139 0 obj << +/Title 140 0 R +/A 137 0 R +/Parent 99 0 R +/Prev 135 0 R +/Next 143 0 R +>> endobj +135 0 obj << +/Title 136 0 R +/A 133 0 R +/Parent 99 0 R +/Prev 131 0 R +/Next 139 0 R +>> endobj +131 0 obj << +/Title 132 0 R +/A 129 0 R +/Parent 99 0 R +/Prev 127 0 R +/Next 135 0 R +>> endobj +127 0 obj << +/Title 128 0 R +/A 125 0 R +/Parent 99 0 R +/Prev 123 0 R +/Next 131 0 R +>> endobj +123 0 obj << +/Title 124 0 R +/A 121 0 R +/Parent 99 0 R +/Prev 119 0 R +/Next 127 0 R +>> endobj +119 0 obj << +/Title 120 0 R +/A 117 0 R +/Parent 99 0 R +/Prev 115 0 R +/Next 123 0 R +>> endobj +115 0 obj << +/Title 116 0 R +/A 113 0 R +/Parent 99 0 R +/Prev 111 0 R +/Next 119 0 R +>> endobj +111 0 obj << +/Title 112 0 R +/A 109 0 R +/Parent 99 0 R +/Prev 107 0 R +/Next 115 0 R +>> endobj +107 0 obj << +/Title 108 0 R +/A 105 0 R +/Parent 99 0 R +/Prev 103 0 R +/Next 111 0 R +>> endobj +103 0 obj << +/Title 104 0 R +/A 101 0 R +/Parent 99 0 R +/Next 107 0 R +>> endobj +99 0 obj << +/Title 100 0 R +/A 97 0 R +/Parent 1796 0 R +/Prev 27 0 R +/Next 151 0 R +/First 103 0 R +/Last 147 0 R +/Count -12 +>> endobj +95 0 obj << +/Title 96 0 R +/A 93 0 R +/Parent 27 0 R +/Prev 91 0 R +>> endobj +91 0 obj << +/Title 92 0 R +/A 89 0 R +/Parent 27 0 R +/Prev 87 0 R +/Next 95 0 R +>> endobj +87 0 obj << +/Title 88 0 R +/A 85 0 R +/Parent 27 0 R +/Prev 83 0 R +/Next 91 0 R +>> endobj +83 0 obj << +/Title 84 0 R +/A 81 0 R +/Parent 27 0 R +/Prev 79 0 R +/Next 87 0 R +>> endobj +79 0 obj << +/Title 80 0 R +/A 77 0 R +/Parent 27 0 R +/Prev 75 0 R +/Next 83 0 R +>> endobj +75 0 obj << +/Title 76 0 R +/A 73 0 R +/Parent 27 0 R +/Prev 71 0 R +/Next 79 0 R +>> endobj +71 0 obj << +/Title 72 0 R +/A 69 0 R +/Parent 27 0 R +/Prev 67 0 R +/Next 75 0 R +>> endobj +67 0 obj << +/Title 68 0 R +/A 65 0 R +/Parent 27 0 R +/Prev 63 0 R +/Next 71 0 R +>> endobj +63 0 obj << +/Title 64 0 R +/A 61 0 R +/Parent 27 0 R +/Prev 59 0 R +/Next 67 0 R +>> endobj +59 0 obj << +/Title 60 0 R +/A 57 0 R +/Parent 27 0 R +/Prev 55 0 R +/Next 63 0 R +>> endobj +55 0 obj << +/Title 56 0 R +/A 53 0 R +/Parent 27 0 R +/Prev 51 0 R +/Next 59 0 R +>> endobj +51 0 obj << +/Title 52 0 R +/A 49 0 R +/Parent 27 0 R +/Prev 47 0 R +/Next 55 0 R +>> endobj +47 0 obj << +/Title 48 0 R +/A 45 0 R +/Parent 27 0 R +/Prev 43 0 R +/Next 51 0 R +>> endobj +43 0 obj << +/Title 44 0 R +/A 41 0 R +/Parent 27 0 R +/Prev 39 0 R +/Next 47 0 R +>> endobj +39 0 obj << +/Title 40 0 R +/A 37 0 R +/Parent 27 0 R +/Prev 35 0 R +/Next 43 0 R +>> endobj +35 0 obj << +/Title 36 0 R +/A 33 0 R +/Parent 27 0 R +/Prev 31 0 R +/Next 39 0 R +>> endobj +31 0 obj << +/Title 32 0 R +/A 29 0 R +/Parent 27 0 R +/Next 35 0 R +>> endobj +27 0 obj << +/Title 28 0 R +/A 25 0 R +/Parent 1796 0 R +/Prev 7 0 R +/Next 99 0 R +/First 31 0 R +/Last 95 0 R +/Count -17 +>> endobj +23 0 obj << +/Title 24 0 R +/A 21 0 R +/Parent 7 0 R +/Prev 19 0 R +>> endobj +19 0 obj << +/Title 20 0 R +/A 17 0 R +/Parent 7 0 R +/Prev 15 0 R +/Next 23 0 R +>> endobj +15 0 obj << +/Title 16 0 R +/A 13 0 R +/Parent 7 0 R +/Prev 11 0 R +/Next 19 0 R +>> endobj +11 0 obj << +/Title 12 0 R +/A 9 0 R +/Parent 7 0 R +/Next 15 0 R +>> endobj +7 0 obj << +/Title 8 0 R +/A 5 0 R +/Parent 1796 0 R +/Next 27 0 R +/First 11 0 R +/Last 23 0 R +/Count -4 +>> endobj +1797 0 obj << +/Names [(AMS.132) 1053 0 R (AMS.134) 1055 0 R (AMS.136) 1057 0 R (AMS.138) 1067 0 R (AMS.140) 1069 0 R (AMS.142) 1079 0 R] +/Limits [(AMS.132) (AMS.142)] +>> endobj +1798 0 obj << +/Names [(AMS.144) 1081 0 R (AMS.146) 1094 0 R (AMS.148) 1096 0 R (AMS.150) 1098 0 R (AMS.152) 1100 0 R (AMS.154) 1115 0 R] +/Limits [(AMS.144) (AMS.154)] +>> endobj +1799 0 obj << +/Names [(AMS.156) 1117 0 R (AMS.158) 1119 0 R (AMS.160) 1121 0 R (AMS.162) 1130 0 R (AMS.167) 1141 0 R (AMS.62) 644 0 R] +/Limits [(AMS.156) (AMS.62)] +>> endobj +1800 0 obj << +/Names [(AMS.64) 646 0 R (Appendix\040I.\040Simple\040Derivation\040of\040the\040Lorentz\040Transformation.0) 166 0 R (Appendix\040II.\040Minkowski's\040Four-dimensional\040Space\040\(``World''\).0) 170 0 R (Appendix\040III.\040The\040Experimental\040Confirmation\040of\040the\040General\040Theory\040of\040Relativity.0) 174 0 R (Back\040Matter.-1) 178 0 R (Bibliography.0) 182 0 R] +/Limits [(AMS.64) (Bibliography.0)] +>> endobj +1801 0 obj << +/Names [(Contents.0) 22 0 R (Doc-Start) 198 0 R (Front\040Matter.-1) 6 0 R (I.\040Physical\040Meaning\040of\040Geometrical\040Propositions.0) 30 0 R (II.\040The\040System\040of\040Co-ordinates.0) 34 0 R (III.\040Space\040and\040Time\040in\040Classical\040Mechanics.0) 38 0 R] +/Limits [(Contents.0) (III.\040Space\040and\040Time\040in\040Classical\040Mechanics.0)] +>> endobj +1802 0 obj << +/Names [(IV.\040The\040Galileian\040System\040of\040Co-ordinates.0) 42 0 R (IX.\040The\040Relativity\040of\040Simultaneity.0) 62 0 R (Index.0) 186 0 R (PG\040Boilerplate.0) 10 0 R (PG\040License.0) 190 0 R (Part\040I.\040The\040Special\040Theory\040of\040Relativity.-1) 26 0 R] +/Limits [(IV.\040The\040Galileian\040System\040of\040Co-ordinates.0) (Part\040I.\040The\040Special\040Theory\040of\040Relativity.-1)] +>> endobj +1803 0 obj << +/Names [(Part\040II.\040The\040General\040Theory\040of\040Relativity.-1) 98 0 R (Part\040III.\040Considerations\040on\040the\040Universe\040as\040a\040Whole.-1) 150 0 R (Preface.0) 18 0 R (Transcriber's\040Note.0) 14 0 R (V.\040The\040Principle\040of\040Relativity\040\(In\040the\040Restricted\040Sense\).0) 46 0 R (VI.\040The\040Theorem\040of\040the\040Addition\040of\040Velocities\040employed\040in\040Classical\040Mechanics.0) 50 0 R] +/Limits [(Part\040II.\040The\040General\040Theory\040of\040Relativity.-1) (VI.\040The\040Theorem\040of\040the\040Addition\040of\040Velocities\040employed\040in\040Classical\040Mechanics.0)] +>> endobj +1804 0 obj << +/Names [(VII.\040The\040Apparent\040Incompatibility\040of\040the\040Law\040of\040Propagation\040of\040Light\040with\040the\040Principle\040of\040Relativity.0) 54 0 R (VIII.\040On\040the\040Idea\040of\040Time\040in\040Physics.0) 58 0 R (X.\040On\040the\040Relativity\040of\040the\040Conception\040of\040Distance.0) 66 0 R (XI.\040The\040Lorentz\040Transformation.0) 70 0 R (XII.\040The\040Behaviour\040of\040Measuring-Rods\040and\040Clocks\040in\040Motion.0) 74 0 R (XIII.\040Theorem\040of\040the\040Addition\040of\040Velocities.\040The\040Experiment\040of\040Fizeau.0) 78 0 R] +/Limits [(VII.\040The\040Apparent\040Incompatibility\040of\040the\040Law\040of\040Propagation\040of\040Light\040with\040the\040Principle\040of\040Relativity.0) (XIII.\040Theorem\040of\040the\040Addition\040of\040Velocities.\040The\040Experiment\040of\040Fizeau.0)] +>> endobj +1805 0 obj << +/Names [(XIV.\040The\040Heuristic\040Value\040of\040the\040Theory\040of\040Relativity.0) 82 0 R (XIX.\040The\040Gravitational\040Field.0) 106 0 R (XV.\040General\040Results\040of\040the\040Theory.0) 86 0 R (XVI.\040Experience\040and\040the\040Special\040Theory\040of\040Relativity.0) 90 0 R (XVII.\040Minkowski's\040Four-dimensional\040Space.0) 94 0 R (XVIII.\040Special\040and\040General\040Principle\040of\040Relativity.0) 102 0 R] +/Limits [(XIV.\040The\040Heuristic\040Value\040of\040the\040Theory\040of\040Relativity.0) (XVIII.\040Special\040and\040General\040Principle\040of\040Relativity.0)] +>> endobj +1806 0 obj << +/Names [(XX.\040The\040Equality\040of\040Inertial\040and\040Gravitational\040Mass\040as\040an\040Argument\040for\040the\040General\040Postulate\040of\040Relativity.0) 110 0 R (XXI.\040In\040what\040Respects\040are\040the\040Foundations\040of\040Classical\040Mechanics\040and\040of\040the\040Special\040Theory\040of\040Relativity\040unsatisfactory?.0) 114 0 R (XXII.\040A\040Few\040Inferences\040from\040the\040General\040Principle\040of\040Relativity.0) 118 0 R (XXIII.\040Behaviour\040of\040Clocks\040and\040Measuring-Rods\040on\040a\040Rotating\040Body\040of\040Reference.0) 122 0 R (XXIV.\040Euclidean\040and\040Non-Euclidean\040Continuum.0) 126 0 R (XXIX.\040The\040Solution\040of\040the\040Problem\040of\040Gravitation\040on\040the\040Basis\040of\040the\040General\040Principle\040of\040Relativity.0) 146 0 R] +/Limits [(XX.\040The\040Equality\040of\040Inertial\040and\040Gravitational\040Mass\040as\040an\040Argument\040for\040the\040General\040Postulate\040of\040Relativity.0) (XXIX.\040The\040Solution\040of\040the\040Problem\040of\040Gravitation\040on\040the\040Basis\040of\040the\040General\040Principle\040of\040Relativity.0)] +>> endobj +1807 0 obj << +/Names [(XXV.\040Gaussian\040Co-ordinates.0) 130 0 R (XXVI.\040The\040Space-Time\040Continuum\040of\040the\040Special\040Theory\040of\040Relativity\040considered\040as\040a\040Euclidean\040Continuum.0) 134 0 R (XXVII.\040The\040Space-Time\040Continuum\040of\040the\040General\040Theory\040of\040Relativity\040is\040not\040a\040Euclidean\040Continuum.0) 138 0 R (XXVIII.\040Exact\040Formulation\040of\040the\040General\040Principle\040of\040Relativity.0) 142 0 R (XXX.\040Cosmological\040Difficulties\040of\040Newton's\040Theory.0) 154 0 R (XXXI.\040The\040Possibility\040of\040a\040``Finite''\040and\040yet\040``Unbounded''\040Universe.0) 158 0 R] +/Limits [(XXV.\040Gaussian\040Co-ordinates.0) (XXXI.\040The\040Possibility\040of\040a\040``Finite''\040and\040yet\040``Unbounded''\040Universe.0)] +>> endobj +1808 0 obj << +/Names [(XXXII.\040The\040Structure\040of\040Space\040according\040to\040the\040General\040Theory\040of\040Relativity.0) 162 0 R (chapter*.11) 295 0 R (figno.1) 526 0 R (figno.2) 591 0 R (figno.3) 659 0 R (figno.4) 887 0 R] +/Limits [(XXXII.\040The\040Structure\040of\040Space\040according\040to\040the\040General\040Theory\040of\040Relativity.0) (figno.4)] +>> endobj +1809 0 obj << +/Names [(figno.5) 1174 0 R (figure.0.1) 527 0 R (figure.0.2) 592 0 R (figure.0.3) 647 0 R (figure.0.4) 888 0 R (figure.0.5) 1175 0 R] +/Limits [(figno.5) (figure.0.5)] +>> endobj +1810 0 obj << +/Names [(page.1) 406 0 R (page.10) 454 0 R (page.100) 1004 0 R (page.101) 1009 0 R (page.102) 1015 0 R (page.103) 1020 0 R] +/Limits [(page.1) (page.103)] +>> endobj +1811 0 obj << +/Names [(page.104) 1024 0 R (page.105) 1029 0 R (page.106) 1034 0 R (page.107) 1040 0 R (page.108) 1049 0 R (page.109) 1065 0 R] +/Limits [(page.104) (page.109)] +>> endobj +1812 0 obj << +/Names [(page.11) 460 0 R (page.110) 1077 0 R (page.111) 1092 0 R (page.112) 1113 0 R (page.113) 1128 0 R (page.114) 1137 0 R] +/Limits [(page.11) (page.114)] +>> endobj +1813 0 obj << +/Names [(page.115) 1147 0 R (page.116) 1151 0 R (page.117) 1157 0 R (page.118) 1162 0 R (page.119) 1167 0 R (page.12) 467 0 R] +/Limits [(page.115) (page.12)] +>> endobj +1814 0 obj << +/Names [(page.120) 1173 0 R (page.121) 1196 0 R (page.122) 1201 0 R (page.123) 1206 0 R (page.124) 1210 0 R (page.125) 1214 0 R] +/Limits [(page.120) (page.125)] +>> endobj +1815 0 obj << +/Names [(page.126) 1218 0 R (page.127) 1230 0 R (page.128) 1330 0 R (page.129) 1443 0 R (page.13) 472 0 R (page.130) 1559 0 R] +/Limits [(page.126) (page.130)] +>> endobj +1816 0 obj << +/Names [(page.131) 1659 0 R (page.132) 1702 0 R (page.133) 1707 0 R (page.14) 476 0 R (page.15) 480 0 R (page.16) 486 0 R] +/Limits [(page.131) (page.16)] +>> endobj +1817 0 obj << +/Names [(page.17) 493 0 R (page.18) 498 0 R (page.19) 503 0 R (page.2) 415 0 R (page.20) 509 0 R (page.21) 513 0 R] +/Limits [(page.17) (page.21)] +>> endobj +1818 0 obj << +/Names [(page.22) 517 0 R (page.23) 523 0 R (page.24) 548 0 R (page.25) 555 0 R (page.26) 562 0 R (page.27) 568 0 R] +/Limits [(page.22) (page.27)] +>> endobj +1819 0 obj << +/Names [(page.28) 577 0 R (page.29) 585 0 R (page.3) 419 0 R (page.30) 590 0 R (page.31) 607 0 R (page.32) 612 0 R] +/Limits [(page.28) (page.32)] +>> endobj +1820 0 obj << +/Names [(page.33) 616 0 R (page.34) 622 0 R (page.35) 626 0 R (page.36) 633 0 R (page.37) 642 0 R (page.38) 658 0 R] +/Limits [(page.33) (page.38)] +>> endobj +1821 0 obj << +/Names [(page.39) 668 0 R (page.4) 424 0 R (page.40) 672 0 R (page.41) 678 0 R (page.42) 682 0 R (page.43) 689 0 R] +/Limits [(page.39) (page.43)] +>> endobj +1822 0 obj << +/Names [(page.44) 693 0 R (page.45) 698 0 R (page.46) 702 0 R (page.47) 707 0 R (page.48) 713 0 R (page.49) 720 0 R] +/Limits [(page.44) (page.49)] +>> endobj +1823 0 obj << +/Names [(page.5) 431 0 R (page.50) 725 0 R (page.51) 729 0 R (page.52) 733 0 R (page.53) 740 0 R (page.54) 745 0 R] +/Limits [(page.5) (page.54)] +>> endobj +1824 0 obj << +/Names [(page.55) 750 0 R (page.56) 758 0 R (page.57) 762 0 R (page.58) 766 0 R (page.59) 770 0 R (page.6) 435 0 R] +/Limits [(page.55) (page.6)] +>> endobj +1825 0 obj << +/Names [(page.60) 776 0 R (page.61) 781 0 R (page.62) 785 0 R (page.63) 791 0 R (page.64) 795 0 R (page.65) 800 0 R] +/Limits [(page.60) (page.65)] +>> endobj +1826 0 obj << +/Names [(page.66) 804 0 R (page.67) 809 0 R (page.68) 815 0 R (page.69) 820 0 R (page.7) 440 0 R (page.70) 827 0 R] +/Limits [(page.66) (page.70)] +>> endobj +1827 0 obj << +/Names [(page.71) 831 0 R (page.72) 836 0 R (page.73) 841 0 R (page.74) 848 0 R (page.75) 853 0 R (page.76) 857 0 R] +/Limits [(page.71) (page.76)] +>> endobj +1828 0 obj << +/Names [(page.77) 862 0 R (page.78) 868 0 R (page.79) 874 0 R (page.8) 444 0 R (page.80) 878 0 R (page.81) 884 0 R] +/Limits [(page.77) (page.81)] +>> endobj +1829 0 obj << +/Names [(page.82) 901 0 R (page.83) 905 0 R (page.84) 909 0 R (page.85) 915 0 R (page.86) 921 0 R (page.87) 929 0 R] +/Limits [(page.82) (page.87)] +>> endobj +1830 0 obj << +/Names [(page.88) 937 0 R (page.89) 941 0 R (page.9) 450 0 R (page.90) 946 0 R (page.91) 955 0 R (page.92) 959 0 R] +/Limits [(page.88) (page.92)] +>> endobj +1831 0 obj << +/Names [(page.93) 963 0 R (page.94) 971 0 R (page.95) 976 0 R (page.96) 981 0 R (page.97) 986 0 R (page.98) 991 0 R] +/Limits [(page.93) (page.98)] +>> endobj +1832 0 obj << +/Names [(page.99) 1000 0 R (page.A) 197 0 R (page.B) 206 0 R (page.I) 1711 0 R (page.II) 1716 0 R (page.III) 1720 0 R] +/Limits [(page.99) (page.III)] +>> endobj +1833 0 obj << +/Names [(page.IV) 1724 0 R (page.V) 1728 0 R (page.VI) 1733 0 R (page.VII) 1737 0 R (page.VIII) 1741 0 R (page.i) 217 0 R] +/Limits [(page.IV) (page.i)] +>> endobj +1834 0 obj << +/Names [(page.ii) 224 0 R (page.iii) 228 0 R (page.iv) 236 0 R (page.ix) 344 0 R (page.v) 242 0 R (page.vi) 248 0 R] +/Limits [(page.ii) (page.vi)] +>> endobj +1835 0 obj << +/Names [(page.vii) 253 0 R (page.viii) 293 0 R (page.x) 384 0 R (page.xi) 401 0 R (section*.1) 199 0 R (section*.10) 294 0 R] +/Limits [(page.vii) (section*.10)] +>> endobj +1836 0 obj << +/Names [(section*.100) 864 0 R (section*.101) 358 0 R (section*.102) 885 0 R (section*.103) 886 0 R (section*.104) 359 0 R (section*.105) 916 0 R] +/Limits [(section*.100) (section*.105)] +>> endobj +1837 0 obj << +/Names [(section*.106) 917 0 R (section*.107) 360 0 R (section*.108) 930 0 R (section*.109) 931 0 R (section*.110) 361 0 R (section*.111) 947 0 R] +/Limits [(section*.106) (section*.111)] +>> endobj +1838 0 obj << +/Names [(section*.112) 948 0 R (section*.113) 362 0 R (section*.114) 964 0 R (section*.115) 965 0 R (section*.116) 992 0 R (section*.117) 993 0 R] +/Limits [(section*.112) (section*.117)] +>> endobj +1839 0 obj << +/Names [(section*.118) 994 0 R (section*.119) 388 0 R (section*.12) 296 0 R (section*.120) 995 0 R (section*.121) 996 0 R (section*.122) 389 0 R] +/Limits [(section*.118) (section*.122)] +>> endobj +1840 0 obj << +/Names [(section*.123) 1010 0 R (section*.124) 1011 0 R (section*.125) 390 0 R (section*.126) 1035 0 R (section*.127) 1036 0 R (section*.128) 391 0 R] +/Limits [(section*.123) (section*.128)] +>> endobj +1841 0 obj << +/Names [(section*.129) 1050 0 R (section*.13) 297 0 R (section*.130) 1051 0 R (section*.131) 1052 0 R (section*.133) 1054 0 R (section*.135) 1056 0 R] +/Limits [(section*.129) (section*.135)] +>> endobj +1842 0 obj << +/Names [(section*.137) 1066 0 R (section*.139) 1068 0 R (section*.14) 345 0 R (section*.141) 1078 0 R (section*.143) 1080 0 R (section*.145) 1093 0 R] +/Limits [(section*.137) (section*.145)] +>> endobj +1843 0 obj << +/Names [(section*.147) 1095 0 R (section*.149) 1097 0 R (section*.15) 346 0 R (section*.151) 1099 0 R (section*.153) 1114 0 R (section*.155) 1116 0 R] +/Limits [(section*.147) (section*.155)] +>> endobj +1844 0 obj << +/Names [(section*.157) 1118 0 R (section*.159) 1120 0 R (section*.16) 385 0 R (section*.161) 1129 0 R (section*.163) 392 0 R (section*.164) 1138 0 R] +/Limits [(section*.157) (section*.164)] +>> endobj +1845 0 obj << +/Names [(section*.165) 1139 0 R (section*.166) 1140 0 R (section*.168) 255 0 R (section*.169) 1152 0 R (section*.17) 386 0 R (section*.170) 1153 0 R] +/Limits [(section*.165) (section*.170)] +>> endobj +1846 0 obj << +/Names [(section*.171) 1158 0 R (section*.172) 393 0 R (section*.173) 1168 0 R (section*.174) 394 0 R (section*.175) 1202 0 R (section*.176) 395 0 R] +/Limits [(section*.171) (section*.176)] +>> endobj +1847 0 obj << +/Names [(section*.177) 1219 0 R (section*.178) 396 0 R (section*.179) 1220 0 R (section*.18) 387 0 R (section*.180) 1221 0 R (section*.181) 1222 0 R] +/Limits [(section*.177) (section*.181)] +>> endobj +1848 0 obj << +/Names [(section*.182) 1223 0 R (section*.183) 1224 0 R (section*.184) 1225 0 R (section*.185) 1231 0 R (section*.186) 397 0 R (section*.187) 1331 0 R] +/Limits [(section*.182) (section*.187)] +>> endobj +1849 0 obj << +/Names [(section*.188) 1332 0 R (section*.189) 1712 0 R (section*.19) 407 0 R (section*.2) 200 0 R (section*.20) 408 0 R (section*.21) 409 0 R] +/Limits [(section*.188) (section*.21)] +>> endobj +1850 0 obj << +/Names [(section*.22) 298 0 R (section*.23) 410 0 R (section*.24) 411 0 R (section*.25) 299 0 R (section*.26) 425 0 R (section*.27) 426 0 R] +/Limits [(section*.22) (section*.27)] +>> endobj +1851 0 obj << +/Names [(section*.28) 300 0 R (section*.29) 445 0 R (section*.3) 207 0 R (section*.30) 446 0 R (section*.31) 301 0 R (section*.32) 455 0 R] +/Limits [(section*.28) (section*.32)] +>> endobj +1852 0 obj << +/Names [(section*.33) 456 0 R (section*.34) 302 0 R (section*.35) 461 0 R (section*.36) 462 0 R (section*.37) 303 0 R (section*.38) 481 0 R] +/Limits [(section*.33) (section*.38)] +>> endobj +1853 0 obj << +/Names [(section*.39) 482 0 R (section*.4) 209 0 R (section*.40) 304 0 R (section*.41) 487 0 R (section*.42) 488 0 R (section*.43) 305 0 R] +/Limits [(section*.39) (section*.43)] +>> endobj +1854 0 obj << +/Names [(section*.44) 504 0 R (section*.45) 505 0 R (section*.46) 306 0 R (section*.47) 524 0 R (section*.48) 525 0 R (section*.49) 307 0 R] +/Limits [(section*.44) (section*.49)] +>> endobj +1855 0 obj << +/Names [(section*.5) 229 0 R (section*.50) 563 0 R (section*.51) 564 0 R (section*.52) 308 0 R (section*.53) 578 0 R (section*.54) 579 0 R] +/Limits [(section*.5) (section*.54)] +>> endobj +1856 0 obj << +/Names [(section*.55) 309 0 R (section*.56) 617 0 R (section*.57) 618 0 R (section*.58) 310 0 R (section*.59) 634 0 R (section*.6) 230 0 R] +/Limits [(section*.55) (section*.6)] +>> endobj +1857 0 obj << +/Names [(section*.60) 635 0 R (section*.61) 643 0 R (section*.63) 645 0 R (section*.65) 347 0 R (section*.66) 673 0 R (section*.67) 674 0 R] +/Limits [(section*.60) (section*.67)] +>> endobj +1858 0 obj << +/Names [(section*.68) 348 0 R (section*.69) 683 0 R (section*.7) 237 0 R (section*.70) 684 0 R (section*.71) 349 0 R (section*.72) 708 0 R] +/Limits [(section*.68) (section*.72)] +>> endobj +1859 0 obj << +/Names [(section*.73) 709 0 R (section*.74) 350 0 R (section*.75) 734 0 R (section*.76) 735 0 R (section*.77) 703 0 R (section*.78) 751 0 R] +/Limits [(section*.73) (section*.78)] +>> endobj +1860 0 obj << +/Names [(section*.79) 752 0 R (section*.8) 243 0 R (section*.80) 351 0 R (section*.81) 753 0 R (section*.82) 754 0 R (section*.83) 352 0 R] +/Limits [(section*.79) (section*.83)] +>> endobj +1861 0 obj << +/Names [(section*.84) 771 0 R (section*.85) 772 0 R (section*.86) 353 0 R (section*.87) 786 0 R (section*.88) 787 0 R (section*.89) 354 0 R] +/Limits [(section*.84) (section*.89)] +>> endobj +1862 0 obj << +/Names [(section*.9) 254 0 R (section*.90) 810 0 R (section*.91) 811 0 R (section*.92) 355 0 R (section*.93) 821 0 R (section*.94) 822 0 R] +/Limits [(section*.9) (section*.94)] +>> endobj +1863 0 obj << +/Names [(section*.95) 356 0 R (section*.96) 842 0 R (section*.97) 843 0 R (section*.98) 357 0 R (section*.99) 863 0 R] +/Limits [(section*.95) (section*.99)] +>> endobj +1864 0 obj << +/Kids [1797 0 R 1798 0 R 1799 0 R 1800 0 R 1801 0 R 1802 0 R] +/Limits [(AMS.132) (Part\040I.\040The\040Special\040Theory\040of\040Relativity.-1)] +>> endobj +1865 0 obj << +/Kids [1803 0 R 1804 0 R 1805 0 R 1806 0 R 1807 0 R 1808 0 R] +/Limits [(Part\040II.\040The\040General\040Theory\040of\040Relativity.-1) (figno.4)] +>> endobj +1866 0 obj << +/Kids [1809 0 R 1810 0 R 1811 0 R 1812 0 R 1813 0 R 1814 0 R] +/Limits [(figno.5) (page.125)] +>> endobj +1867 0 obj << +/Kids [1815 0 R 1816 0 R 1817 0 R 1818 0 R 1819 0 R 1820 0 R] +/Limits [(page.126) (page.38)] +>> endobj +1868 0 obj << +/Kids [1821 0 R 1822 0 R 1823 0 R 1824 0 R 1825 0 R 1826 0 R] +/Limits [(page.39) (page.70)] +>> endobj +1869 0 obj << +/Kids [1827 0 R 1828 0 R 1829 0 R 1830 0 R 1831 0 R 1832 0 R] +/Limits [(page.71) (page.III)] +>> endobj +1870 0 obj << +/Kids [1833 0 R 1834 0 R 1835 0 R 1836 0 R 1837 0 R 1838 0 R] +/Limits [(page.IV) (section*.117)] +>> endobj +1871 0 obj << +/Kids [1839 0 R 1840 0 R 1841 0 R 1842 0 R 1843 0 R 1844 0 R] +/Limits [(section*.118) (section*.164)] +>> endobj +1872 0 obj << +/Kids [1845 0 R 1846 0 R 1847 0 R 1848 0 R 1849 0 R 1850 0 R] +/Limits [(section*.165) (section*.27)] +>> endobj +1873 0 obj << +/Kids [1851 0 R 1852 0 R 1853 0 R 1854 0 R 1855 0 R 1856 0 R] +/Limits [(section*.28) (section*.6)] +>> endobj +1874 0 obj << +/Kids [1857 0 R 1858 0 R 1859 0 R 1860 0 R 1861 0 R 1862 0 R] +/Limits [(section*.60) (section*.94)] +>> endobj +1875 0 obj << +/Kids [1863 0 R] +/Limits [(section*.95) (section*.99)] +>> endobj +1876 0 obj << +/Kids [1864 0 R 1865 0 R 1866 0 R 1867 0 R 1868 0 R 1869 0 R] +/Limits [(AMS.132) (page.III)] +>> endobj +1877 0 obj << +/Kids [1870 0 R 1871 0 R 1872 0 R 1873 0 R 1874 0 R 1875 0 R] +/Limits [(page.IV) (section*.99)] +>> endobj +1878 0 obj << +/Kids [1876 0 R 1877 0 R] +/Limits [(AMS.132) (section*.99)] +>> endobj +1879 0 obj << +/Dests 1878 0 R +>> endobj +1880 0 obj << +/Type /Catalog +/Pages 1795 0 R +/Outlines 1796 0 R +/Names 1879 0 R +/PageMode/UseNone/ViewerPreferences<</DisplayDocTitle true>>/PageLayout/SinglePage/PageLabels << /Nums [0 << /S /A >> 2 << /S /r >> 13 << /S /D >> 146 << /S /R >> ] >> +/OpenAction 193 0 R +>> endobj +1881 0 obj << +/Author(Albert Einstein)/Title(The Project Gutenberg eBook \04336114: Relativity)/Subject()/Creator(LaTeX with hyperref package)/Producer(pdfTeX-1.40.3)/Keywords(University of Toronto, The Internet Archive, Andrew D. Hwang) +/CreationDate (D:20110515153127-07'00') +/ModDate (D:20110515153127-07'00') +/Trapped /False +/PTEX.Fullbanner (This is pdfTeX using libpoppler, Version 3.141592-1.40.3-2.2 (Web2C 7.5.6) kpathsea version 3.5.6) +>> endobj +xref +0 1882 +0000000001 65535 f +0000000002 00000 f +0000000003 00000 f +0000000004 00000 f +0000000256 00000 f +0000000015 00000 n +0000009405 00000 n +0000607633 00000 n +0000000069 00000 n +0000000099 00000 n +0000009515 00000 n +0000607561 00000 n +0000000154 00000 n +0000000187 00000 n +0000010822 00000 n +0000607475 00000 n +0000000247 00000 n +0000000284 00000 n +0000015028 00000 n +0000607389 00000 n +0000000330 00000 n +0000000356 00000 n +0000025892 00000 n +0000607316 00000 n +0000000403 00000 n +0000000430 00000 n +0000036439 00000 n +0000607190 00000 n +0000000528 00000 n +0000000587 00000 n +0000036662 00000 n +0000607116 00000 n +0000000688 00000 n +0000000754 00000 n +0000043752 00000 n +0000607029 00000 n +0000000835 00000 n +0000000884 00000 n +0000051076 00000 n +0000606942 00000 n +0000000983 00000 n +0000001044 00000 n +0000055059 00000 n +0000606855 00000 n +0000001138 00000 n +0000001197 00000 n +0000057359 00000 n +0000606768 00000 n +0000001318 00000 n +0000001395 00000 n +0000065037 00000 n +0000606681 00000 n +0000001544 00000 n +0000001640 00000 n +0000067278 00000 n +0000606594 00000 n +0000001825 00000 n +0000001945 00000 n +0000073975 00000 n +0000606507 00000 n +0000002041 00000 n +0000002096 00000 n +0000089567 00000 n +0000606420 00000 n +0000002181 00000 n +0000002234 00000 n +0000097442 00000 n +0000606333 00000 n +0000002347 00000 n +0000002416 00000 n +0000101835 00000 n +0000606246 00000 n +0000002494 00000 n +0000002543 00000 n +0000118762 00000 n +0000606159 00000 n +0000002663 00000 n +0000002739 00000 n +0000124905 00000 n +0000606072 00000 n +0000002877 00000 n +0000002965 00000 n +0000138105 00000 n +0000605985 00000 n +0000003080 00000 n +0000003151 00000 n +0000141199 00000 n +0000605898 00000 n +0000003238 00000 n +0000003290 00000 n +0000151712 00000 n +0000605811 00000 n +0000003402 00000 n +0000003473 00000 n +0000163443 00000 n +0000605737 00000 n +0000003561 00000 n +0000003620 00000 n +0000170192 00000 n +0000605606 00000 n +0000003719 00000 n +0000003780 00000 n +0000170415 00000 n +0000605528 00000 n +0000003888 00000 n +0000003958 00000 n +0000178679 00000 n +0000605436 00000 n +0000004035 00000 n +0000004083 00000 n +0000184721 00000 n +0000605344 00000 n +0000004277 00000 n +0000004403 00000 n +0000194176 00000 n +0000605252 00000 n +0000004614 00000 n +0000004754 00000 n +0000199026 00000 n +0000605160 00000 n +0000004884 00000 n +0000004967 00000 n +0000208743 00000 n +0000605068 00000 n +0000005117 00000 n +0000005214 00000 n +0000217774 00000 n +0000604976 00000 n +0000005309 00000 n +0000005372 00000 n +0000234017 00000 n +0000604884 00000 n +0000005444 00000 n +0000005490 00000 n +0000242977 00000 n +0000604792 00000 n +0000005674 00000 n +0000005796 00000 n +0000247912 00000 n +0000604700 00000 n +0000005974 00000 n +0000006090 00000 n +0000255365 00000 n +0000604608 00000 n +0000006218 00000 n +0000006302 00000 n +0000261788 00000 n +0000604530 00000 n +0000006490 00000 n +0000006610 00000 n +0000271872 00000 n +0000604398 00000 n +0000006726 00000 n +0000006797 00000 n +0000272096 00000 n +0000604319 00000 n +0000006901 00000 n +0000006970 00000 n +0000277839 00000 n +0000604226 00000 n +0000007105 00000 n +0000007193 00000 n +0000288675 00000 n +0000604133 00000 n +0000007341 00000 n +0000007436 00000 n +0000293611 00000 n +0000604040 00000 n +0000007556 00000 n +0000007635 00000 n +0000313737 00000 n +0000603947 00000 n +0000007751 00000 n +0000007832 00000 n +0000317846 00000 n +0000603868 00000 n +0000007981 00000 n +0000008080 00000 n +0000351560 00000 n +0000603749 00000 n +0000008135 00000 n +0000008166 00000 n +0000351732 00000 n +0000603670 00000 n +0000008218 00000 n +0000008250 00000 n +0000369739 00000 n +0000603577 00000 n +0000008295 00000 n +0000008320 00000 n +0000435357 00000 n +0000603498 00000 n +0000008373 00000 n +0000008403 00000 n +0000009125 00000 n +0000009570 00000 n +0000008455 00000 n +0000009237 00000 n +0000009293 00000 n +0000009349 00000 n +0000009459 00000 n +0000599500 00000 n +0000599645 00000 n +0000010942 00000 n +0000010593 00000 n +0000009642 00000 n +0000010705 00000 n +0000010761 00000 n +0000597472 00000 n +0000010882 00000 n +0000598056 00000 n +0000599063 00000 n +0000599354 00000 n +0000598487 00000 n +0000011887 00000 n +0000011719 00000 n +0000011079 00000 n +0000011831 00000 n +0000597179 00000 n +0000597325 00000 n +0000597034 00000 n +0000012536 00000 n +0000012368 00000 n +0000012011 00000 n +0000012480 00000 n +0000015139 00000 n +0000014804 00000 n +0000012621 00000 n +0000014916 00000 n +0000014972 00000 n +0000015083 00000 n +0000598201 00000 n +0000598344 00000 n +0000016530 00000 n +0000016306 00000 n +0000015288 00000 n +0000016418 00000 n +0000016474 00000 n +0000599209 00000 n +0000018956 00000 n +0000018732 00000 n +0000016667 00000 n +0000018844 00000 n +0000018900 00000 n +0000599763 00000 n +0000020156 00000 n +0000019988 00000 n +0000019067 00000 n +0000020100 00000 n +0000022023 00000 n +0000022287 00000 n +0000021891 00000 n +0000020267 00000 n +0000022175 00000 n +0000022231 00000 n +0000317789 00000 n +0000000258 00000 f +0000023786 00000 n +0000000260 00000 f +0000023940 00000 n +0000000262 00000 f +0000024094 00000 n +0000000264 00000 f +0000024248 00000 n +0000000266 00000 f +0000024402 00000 n +0000000268 00000 f +0000024556 00000 n +0000000270 00000 f +0000024710 00000 n +0000000272 00000 f +0000024863 00000 n +0000000274 00000 f +0000025017 00000 n +0000000276 00000 f +0000025171 00000 n +0000000278 00000 f +0000025324 00000 n +0000000280 00000 f +0000025476 00000 n +0000000282 00000 f +0000025628 00000 n +0000000284 00000 f +0000027811 00000 n +0000000286 00000 f +0000027965 00000 n +0000000288 00000 f +0000028118 00000 n +0000000311 00000 f +0000028272 00000 n +0000026114 00000 n +0000023558 00000 n +0000022411 00000 n +0000025780 00000 n +0000025836 00000 n +0000025947 00000 n +0000026003 00000 n +0000026059 00000 n +0000036606 00000 n +0000043696 00000 n +0000051020 00000 n +0000055003 00000 n +0000057303 00000 n +0000064981 00000 n +0000067222 00000 n +0000073919 00000 n +0000089511 00000 n +0000097386 00000 n +0000101779 00000 n +0000118706 00000 n +0000124849 00000 n +0000000313 00000 f +0000028426 00000 n +0000000315 00000 f +0000028580 00000 n +0000000317 00000 f +0000028733 00000 n +0000000319 00000 f +0000028887 00000 n +0000000321 00000 f +0000029041 00000 n +0000000323 00000 f +0000029195 00000 n +0000000325 00000 f +0000029349 00000 n +0000000327 00000 f +0000029503 00000 n +0000000329 00000 f +0000029658 00000 n +0000000331 00000 f +0000029813 00000 n +0000000333 00000 f +0000029967 00000 n +0000000335 00000 f +0000030120 00000 n +0000000337 00000 f +0000031951 00000 n +0000000339 00000 f +0000032106 00000 n +0000000363 00000 f +0000032260 00000 n +0000030441 00000 n +0000027559 00000 n +0000026238 00000 n +0000030273 00000 n +0000030329 00000 n +0000030385 00000 n +0000138049 00000 n +0000141143 00000 n +0000151656 00000 n +0000163387 00000 n +0000170359 00000 n +0000178623 00000 n +0000184665 00000 n +0000194120 00000 n +0000198970 00000 n +0000208687 00000 n +0000217718 00000 n +0000233961 00000 n +0000242921 00000 n +0000247856 00000 n +0000255309 00000 n +0000261732 00000 n +0000000366 00000 f +0000032415 00000 n +0000032567 00000 n +0000000369 00000 f +0000032721 00000 n +0000032875 00000 n +0000000371 00000 f +0000033030 00000 n +0000000373 00000 f +0000033185 00000 n +0000000375 00000 f +0000033340 00000 n +0000000377 00000 f +0000033495 00000 n +0000000379 00000 f +0000033650 00000 n +0000000000 00000 f +0000033804 00000 n +0000034182 00000 n +0000031723 00000 n +0000030565 00000 n +0000033959 00000 n +0000034015 00000 n +0000034071 00000 n +0000034127 00000 n +0000272040 00000 n +0000277782 00000 n +0000288618 00000 n +0000293554 00000 n +0000313680 00000 n +0000320142 00000 n +0000324949 00000 n +0000344386 00000 n +0000351617 00000 n +0000369624 00000 n +0000034700 00000 n +0000034532 00000 n +0000034306 00000 n +0000034644 00000 n +0000599881 00000 n +0000036829 00000 n +0000036215 00000 n +0000034772 00000 n +0000036327 00000 n +0000036383 00000 n +0000036494 00000 n +0000036550 00000 n +0000036717 00000 n +0000036773 00000 n +0000038987 00000 n +0000038819 00000 n +0000036927 00000 n +0000038931 00000 n +0000041176 00000 n +0000041008 00000 n +0000039085 00000 n +0000041120 00000 n +0000597765 00000 n +0000043919 00000 n +0000043528 00000 n +0000041312 00000 n +0000043640 00000 n +0000043807 00000 n +0000043863 00000 n +0000597911 00000 n +0000046109 00000 n +0000045941 00000 n +0000044081 00000 n +0000046053 00000 n +0000048288 00000 n +0000048120 00000 n +0000046220 00000 n +0000048232 00000 n +0000599999 00000 n +0000049015 00000 n +0000048847 00000 n +0000048424 00000 n +0000048959 00000 n +0000051243 00000 n +0000050852 00000 n +0000049100 00000 n +0000050964 00000 n +0000051131 00000 n +0000051187 00000 n +0000053304 00000 n +0000053136 00000 n +0000051341 00000 n +0000053248 00000 n +0000055226 00000 n +0000054835 00000 n +0000053440 00000 n +0000054947 00000 n +0000055114 00000 n +0000055170 00000 n +0000057526 00000 n +0000057135 00000 n +0000055337 00000 n +0000057247 00000 n +0000057414 00000 n +0000057470 00000 n +0000598920 00000 n +0000059768 00000 n +0000059600 00000 n +0000057650 00000 n +0000059712 00000 n +0000600117 00000 n +0000062209 00000 n +0000062041 00000 n +0000059892 00000 n +0000062153 00000 n +0000063153 00000 n +0000062985 00000 n +0000062346 00000 n +0000063097 00000 n +0000065204 00000 n +0000064813 00000 n +0000063277 00000 n +0000064925 00000 n +0000065092 00000 n +0000065148 00000 n +0000067445 00000 n +0000067054 00000 n +0000065315 00000 n +0000067166 00000 n +0000067333 00000 n +0000067389 00000 n +0000069552 00000 n +0000069760 00000 n +0000069420 00000 n +0000067556 00000 n +0000069704 00000 n +0000598631 00000 n +0000071866 00000 n +0000071698 00000 n +0000069884 00000 n +0000071810 00000 n +0000600235 00000 n +0000074142 00000 n +0000073751 00000 n +0000071964 00000 n +0000073863 00000 n +0000074030 00000 n +0000074086 00000 n +0000076490 00000 n +0000076322 00000 n +0000074253 00000 n +0000076434 00000 n +0000079174 00000 n +0000079006 00000 n +0000076627 00000 n +0000079118 00000 n +0000080439 00000 n +0000080271 00000 n +0000079362 00000 n +0000080383 00000 n +0000089305 00000 n +0000082386 00000 n +0000089852 00000 n +0000082254 00000 n +0000080537 00000 n +0000089455 00000 n +0000089622 00000 n +0000089678 00000 n +0000089734 00000 n +0000089790 00000 n +0000083319 00000 n +0000083450 00000 n +0000577180 00000 n +0000087690 00000 n +0000083497 00000 n +0000552819 00000 n +0000086074 00000 n +0000083765 00000 n +0000503376 00000 n +0000084459 00000 n +0000083937 00000 n +0000084203 00000 n +0000577148 00000 n +0000084224 00000 n +0000552788 00000 n +0000503344 00000 n +0000094255 00000 n +0000092441 00000 n +0000092273 00000 n +0000090030 00000 n +0000092385 00000 n +0000600353 00000 n +0000094409 00000 n +0000094714 00000 n +0000094924 00000 n +0000094099 00000 n +0000092616 00000 n +0000094868 00000 n +0000094563 00000 n +0000097178 00000 n +0000098851 00000 n +0000097609 00000 n +0000097046 00000 n +0000095035 00000 n +0000097330 00000 n +0000097497 00000 n +0000097553 00000 n +0000099058 00000 n +0000098719 00000 n +0000097797 00000 n +0000099002 00000 n +0000100956 00000 n +0000101109 00000 n +0000101263 00000 n +0000101416 00000 n +0000101570 00000 n +0000102002 00000 n +0000100792 00000 n +0000099169 00000 n +0000101723 00000 n +0000101890 00000 n +0000101946 00000 n +0000104325 00000 n +0000106528 00000 n +0000104535 00000 n +0000104193 00000 n +0000102113 00000 n +0000104479 00000 n +0000111490 00000 n +0000111816 00000 n +0000106396 00000 n +0000104659 00000 n +0000111642 00000 n +0000111698 00000 n +0000111754 00000 n +0000597619 00000 n +0000600471 00000 n +0000107397 00000 n +0000107528 00000 n +0000109874 00000 n +0000107575 00000 n +0000108259 00000 n +0000107747 00000 n +0000108003 00000 n +0000108024 00000 n +0000113837 00000 n +0000114196 00000 n +0000113697 00000 n +0000112033 00000 n +0000114140 00000 n +0000113990 00000 n +0000116288 00000 n +0000116120 00000 n +0000114384 00000 n +0000116232 00000 n +0000118929 00000 n +0000118538 00000 n +0000116451 00000 n +0000118650 00000 n +0000118817 00000 n +0000118873 00000 n +0000121248 00000 n +0000121080 00000 n +0000119092 00000 n +0000121192 00000 n +0000122483 00000 n +0000122315 00000 n +0000121411 00000 n +0000122427 00000 n +0000124487 00000 n +0000124639 00000 n +0000127316 00000 n +0000125072 00000 n +0000124347 00000 n +0000122633 00000 n +0000124793 00000 n +0000124960 00000 n +0000125016 00000 n +0000600589 00000 n +0000127470 00000 n +0000127619 00000 n +0000128074 00000 n +0000127168 00000 n +0000125196 00000 n +0000127770 00000 n +0000127826 00000 n +0000127888 00000 n +0000127950 00000 n +0000128012 00000 n +0000134055 00000 n +0000133201 00000 n +0000130640 00000 n +0000133355 00000 n +0000133501 00000 n +0000133796 00000 n +0000133649 00000 n +0000135654 00000 n +0000134117 00000 n +0000130476 00000 n +0000128211 00000 n +0000133943 00000 n +0000133999 00000 n +0000131163 00000 n +0000131294 00000 n +0000131586 00000 n +0000131341 00000 n +0000131565 00000 n +0000135859 00000 n +0000135522 00000 n +0000134359 00000 n +0000135803 00000 n +0000138272 00000 n +0000137881 00000 n +0000135957 00000 n +0000137993 00000 n +0000138160 00000 n +0000138216 00000 n +0000139158 00000 n +0000138990 00000 n +0000138409 00000 n +0000139102 00000 n +0000141366 00000 n +0000140975 00000 n +0000139243 00000 n +0000141087 00000 n +0000141254 00000 n +0000141310 00000 n +0000600707 00000 n +0000143670 00000 n +0000143502 00000 n +0000141503 00000 n +0000143614 00000 n +0000145838 00000 n +0000145670 00000 n +0000143807 00000 n +0000145782 00000 n +0000149551 00000 n +0000148312 00000 n +0000148144 00000 n +0000146026 00000 n +0000148256 00000 n +0000149761 00000 n +0000149419 00000 n +0000148474 00000 n +0000149705 00000 n +0000170136 00000 n +0000151879 00000 n +0000151488 00000 n +0000149859 00000 n +0000151600 00000 n +0000151767 00000 n +0000151823 00000 n +0000154053 00000 n +0000153885 00000 n +0000151977 00000 n +0000153997 00000 n +0000600825 00000 n +0000156477 00000 n +0000156629 00000 n +0000156837 00000 n +0000156337 00000 n +0000154202 00000 n +0000156781 00000 n +0000160939 00000 n +0000159274 00000 n +0000159106 00000 n +0000156987 00000 n +0000159218 00000 n +0000161147 00000 n +0000160807 00000 n +0000159385 00000 n +0000161091 00000 n +0000163610 00000 n +0000163219 00000 n +0000161245 00000 n +0000163331 00000 n +0000163498 00000 n +0000163554 00000 n +0000168071 00000 n +0000165896 00000 n +0000165728 00000 n +0000163734 00000 n +0000165840 00000 n +0000167918 00000 n +0000168279 00000 n +0000167778 00000 n +0000166059 00000 n +0000168223 00000 n +0000600943 00000 n +0000170583 00000 n +0000169968 00000 n +0000168428 00000 n +0000170080 00000 n +0000170247 00000 n +0000170303 00000 n +0000170471 00000 n +0000170527 00000 n +0000172906 00000 n +0000172738 00000 n +0000170694 00000 n +0000172850 00000 n +0000175227 00000 n +0000175059 00000 n +0000173030 00000 n +0000175171 00000 n +0000176662 00000 n +0000176494 00000 n +0000175351 00000 n +0000176606 00000 n +0000178847 00000 n +0000178455 00000 n +0000176747 00000 n +0000178567 00000 n +0000178735 00000 n +0000178791 00000 n +0000180823 00000 n +0000180655 00000 n +0000178945 00000 n +0000180767 00000 n +0000601061 00000 n +0000182648 00000 n +0000182480 00000 n +0000180947 00000 n +0000182592 00000 n +0000184889 00000 n +0000184497 00000 n +0000182772 00000 n +0000184609 00000 n +0000184777 00000 n +0000184833 00000 n +0000187083 00000 n +0000186915 00000 n +0000184987 00000 n +0000187027 00000 n +0000189195 00000 n +0000189027 00000 n +0000187181 00000 n +0000189139 00000 n +0000191348 00000 n +0000191557 00000 n +0000191216 00000 n +0000189293 00000 n +0000191501 00000 n +0000192138 00000 n +0000191970 00000 n +0000191655 00000 n +0000192082 00000 n +0000601179 00000 n +0000194344 00000 n +0000193952 00000 n +0000192223 00000 n +0000194064 00000 n +0000194232 00000 n +0000194288 00000 n +0000196596 00000 n +0000196428 00000 n +0000194468 00000 n +0000196540 00000 n +0000198762 00000 n +0000199194 00000 n +0000198630 00000 n +0000196771 00000 n +0000198914 00000 n +0000199082 00000 n +0000199138 00000 n +0000201701 00000 n +0000201910 00000 n +0000201569 00000 n +0000199331 00000 n +0000201854 00000 n +0000204141 00000 n +0000203973 00000 n +0000202072 00000 n +0000204085 00000 n +0000206332 00000 n +0000206539 00000 n +0000206200 00000 n +0000204239 00000 n +0000206483 00000 n +0000601297 00000 n +0000208911 00000 n +0000208519 00000 n +0000206701 00000 n +0000208631 00000 n +0000208799 00000 n +0000208855 00000 n +0000211202 00000 n +0000211410 00000 n +0000211070 00000 n +0000209035 00000 n +0000211354 00000 n +0000213803 00000 n +0000214010 00000 n +0000213671 00000 n +0000211559 00000 n +0000213954 00000 n +0000215727 00000 n +0000215559 00000 n +0000214172 00000 n +0000215671 00000 n +0000598776 00000 n +0000217942 00000 n +0000217550 00000 n +0000215864 00000 n +0000217662 00000 n +0000217830 00000 n +0000217886 00000 n +0000220057 00000 n +0000219889 00000 n +0000218040 00000 n +0000220001 00000 n +0000601415 00000 n +0000223976 00000 n +0000222473 00000 n +0000222305 00000 n +0000220142 00000 n +0000222417 00000 n +0000224185 00000 n +0000223844 00000 n +0000222622 00000 n +0000224129 00000 n +0000233755 00000 n +0000226161 00000 n +0000234305 00000 n +0000226029 00000 n +0000224296 00000 n +0000233905 00000 n +0000234073 00000 n +0000234129 00000 n +0000234185 00000 n +0000234243 00000 n +0000229908 00000 n +0000230039 00000 n +0000536989 00000 n +0000232140 00000 n +0000230086 00000 n +0000230525 00000 n +0000230269 00000 n +0000230503 00000 n +0000536958 00000 n +0000236591 00000 n +0000236423 00000 n +0000234457 00000 n +0000236535 00000 n +0000238908 00000 n +0000238740 00000 n +0000236715 00000 n +0000238852 00000 n +0000240620 00000 n +0000240452 00000 n +0000239045 00000 n +0000240564 00000 n +0000601533 00000 n +0000242711 00000 n +0000243145 00000 n +0000242579 00000 n +0000240718 00000 n +0000242865 00000 n +0000243033 00000 n +0000243089 00000 n +0000245297 00000 n +0000245129 00000 n +0000243269 00000 n +0000245241 00000 n +0000247339 00000 n +0000247494 00000 n +0000247648 00000 n +0000250390 00000 n +0000248080 00000 n +0000247191 00000 n +0000245472 00000 n +0000247800 00000 n +0000247968 00000 n +0000248024 00000 n +0000250544 00000 n +0000250698 00000 n +0000250908 00000 n +0000250242 00000 n +0000248178 00000 n +0000250852 00000 n +0000252887 00000 n +0000252719 00000 n +0000251019 00000 n +0000252831 00000 n +0000255099 00000 n +0000255533 00000 n +0000254967 00000 n +0000252998 00000 n +0000255253 00000 n +0000255421 00000 n +0000255477 00000 n +0000601651 00000 n +0000257727 00000 n +0000257880 00000 n +0000258089 00000 n +0000257587 00000 n +0000255683 00000 n +0000258033 00000 n +0000259668 00000 n +0000259500 00000 n +0000258187 00000 n +0000259612 00000 n +0000261956 00000 n +0000261564 00000 n +0000259753 00000 n +0000261676 00000 n +0000261844 00000 n +0000261900 00000 n +0000263934 00000 n +0000266402 00000 n +0000264295 00000 n +0000263794 00000 n +0000262093 00000 n +0000264239 00000 n +0000264088 00000 n +0000266610 00000 n +0000266270 00000 n +0000264406 00000 n +0000266554 00000 n +0000268776 00000 n +0000268985 00000 n +0000268644 00000 n +0000266695 00000 n +0000268929 00000 n +0000601769 00000 n +0000269674 00000 n +0000269506 00000 n +0000269108 00000 n +0000269618 00000 n +0000271607 00000 n +0000272263 00000 n +0000271475 00000 n +0000269772 00000 n +0000271760 00000 n +0000271816 00000 n +0000271928 00000 n +0000271984 00000 n +0000272152 00000 n +0000272207 00000 n +0000274836 00000 n +0000274667 00000 n +0000272412 00000 n +0000274779 00000 n +0000275506 00000 n +0000275333 00000 n +0000274959 00000 n +0000275448 00000 n +0000277569 00000 n +0000278012 00000 n +0000277433 00000 n +0000275592 00000 n +0000277724 00000 n +0000277896 00000 n +0000277954 00000 n +0000280082 00000 n +0000279908 00000 n +0000278124 00000 n +0000280024 00000 n +0000601889 00000 n +0000282223 00000 n +0000282049 00000 n +0000280194 00000 n +0000282165 00000 n +0000284733 00000 n +0000284559 00000 n +0000282348 00000 n +0000284675 00000 n +0000286351 00000 n +0000286564 00000 n +0000286214 00000 n +0000284858 00000 n +0000286506 00000 n +0000290676 00000 n +0000288848 00000 n +0000288444 00000 n +0000286663 00000 n +0000288560 00000 n +0000288732 00000 n +0000288790 00000 n +0000290888 00000 n +0000290539 00000 n +0000288960 00000 n +0000290830 00000 n +0000292892 00000 n +0000293047 00000 n +0000293199 00000 n +0000293349 00000 n +0000296098 00000 n +0000294162 00000 n +0000292728 00000 n +0000291051 00000 n +0000293496 00000 n +0000293668 00000 n +0000293726 00000 n +0000293784 00000 n +0000293846 00000 n +0000293908 00000 n +0000293972 00000 n +0000294036 00000 n +0000294099 00000 n +0000602014 00000 n +0000296244 00000 n +0000296395 00000 n +0000296546 00000 n +0000297006 00000 n +0000295934 00000 n +0000294300 00000 n +0000296694 00000 n +0000296752 00000 n +0000296816 00000 n +0000296880 00000 n +0000296943 00000 n +0000299337 00000 n +0000299488 00000 n +0000299639 00000 n +0000302260 00000 n +0000300098 00000 n +0000299182 00000 n +0000297144 00000 n +0000299788 00000 n +0000299846 00000 n +0000299909 00000 n +0000299972 00000 n +0000300035 00000 n +0000302409 00000 n +0000302560 00000 n +0000302711 00000 n +0000302862 00000 n +0000303013 00000 n +0000303162 00000 n +0000305989 00000 n +0000303884 00000 n +0000302069 00000 n +0000300223 00000 n +0000303316 00000 n +0000303374 00000 n +0000303438 00000 n +0000303502 00000 n +0000303566 00000 n +0000303630 00000 n +0000303694 00000 n +0000303758 00000 n +0000303821 00000 n +0000306140 00000 n +0000306288 00000 n +0000309350 00000 n +0000309501 00000 n +0000309652 00000 n +0000309803 00000 n +0000309952 00000 n +0000310101 00000 n +0000310252 00000 n +0000307001 00000 n +0000305834 00000 n +0000304035 00000 n +0000306435 00000 n +0000306493 00000 n +0000306557 00000 n +0000306621 00000 n +0000306685 00000 n +0000306749 00000 n +0000306813 00000 n +0000306877 00000 n +0000306939 00000 n +0000310403 00000 n +0000310554 00000 n +0000310705 00000 n +0000311040 00000 n +0000309132 00000 n +0000307165 00000 n +0000310854 00000 n +0000310912 00000 n +0000310976 00000 n +0000313171 00000 n +0000313326 00000 n +0000313474 00000 n +0000314038 00000 n +0000313016 00000 n +0000311178 00000 n +0000313622 00000 n +0000313794 00000 n +0000313852 00000 n +0000313910 00000 n +0000313974 00000 n +0000602139 00000 n +0000315568 00000 n +0000315777 00000 n +0000315431 00000 n +0000314189 00000 n +0000315719 00000 n +0000318017 00000 n +0000317615 00000 n +0000315902 00000 n +0000317731 00000 n +0000317903 00000 n +0000317961 00000 n +0000320199 00000 n +0000319910 00000 n +0000318129 00000 n +0000320026 00000 n +0000320084 00000 n +0000322439 00000 n +0000322265 00000 n +0000320311 00000 n +0000322381 00000 n +0000324680 00000 n +0000325006 00000 n +0000324543 00000 n +0000322590 00000 n +0000324833 00000 n +0000324891 00000 n +0000327218 00000 n +0000339387 00000 n +0000327102 00000 n +0000325169 00000 n +0000339208 00000 n +0000339266 00000 n +0000339324 00000 n +0000602264 00000 n +0000331816 00000 n +0000331948 00000 n +0000485170 00000 n +0000337549 00000 n +0000331996 00000 n +0000335925 00000 n +0000332167 00000 n +0000547646 00000 n +0000334309 00000 n +0000332320 00000 n +0000332693 00000 n +0000332481 00000 n +0000332670 00000 n +0000485137 00000 n +0000547615 00000 n +0000343962 00000 n +0000341615 00000 n +0000341441 00000 n +0000339567 00000 n +0000341557 00000 n +0000344115 00000 n +0000344443 00000 n +0000343816 00000 n +0000341740 00000 n +0000344270 00000 n +0000344328 00000 n +0000346639 00000 n +0000346465 00000 n +0000344620 00000 n +0000346581 00000 n +0000348950 00000 n +0000348776 00000 n +0000346790 00000 n +0000348892 00000 n +0000350081 00000 n +0000349907 00000 n +0000349075 00000 n +0000350023 00000 n +0000352077 00000 n +0000351328 00000 n +0000350180 00000 n +0000351444 00000 n +0000351502 00000 n +0000351674 00000 n +0000351789 00000 n +0000351847 00000 n +0000351905 00000 n +0000351963 00000 n +0000352020 00000 n +0000602389 00000 n +0000353792 00000 n +0000353560 00000 n +0000352189 00000 n +0000353676 00000 n +0000353734 00000 n +0000356114 00000 n +0000356263 00000 n +0000356414 00000 n +0000356563 00000 n +0000356713 00000 n +0000356864 00000 n +0000357015 00000 n +0000357165 00000 n +0000357315 00000 n +0000357464 00000 n +0000357613 00000 n +0000357762 00000 n +0000357913 00000 n +0000358063 00000 n +0000358211 00000 n +0000358360 00000 n +0000358508 00000 n +0000358657 00000 n +0000358805 00000 n +0000358955 00000 n +0000359104 00000 n +0000359253 00000 n +0000359403 00000 n +0000359552 00000 n +0000359701 00000 n +0000359851 00000 n +0000360002 00000 n +0000360154 00000 n +0000360302 00000 n +0000360451 00000 n +0000360600 00000 n +0000360751 00000 n +0000360899 00000 n +0000361046 00000 n +0000361195 00000 n +0000361343 00000 n +0000361490 00000 n +0000361637 00000 n +0000361784 00000 n +0000361932 00000 n +0000362081 00000 n +0000362231 00000 n +0000362378 00000 n +0000362523 00000 n +0000362670 00000 n +0000362816 00000 n +0000362964 00000 n +0000363113 00000 n +0000363262 00000 n +0000363408 00000 n +0000363554 00000 n +0000363701 00000 n +0000363849 00000 n +0000364001 00000 n +0000364151 00000 n +0000364301 00000 n +0000364452 00000 n +0000364602 00000 n +0000364753 00000 n +0000364904 00000 n +0000365054 00000 n +0000365205 00000 n +0000365355 00000 n +0000365506 00000 n +0000365653 00000 n +0000365804 00000 n +0000365955 00000 n +0000366106 00000 n +0000366256 00000 n +0000366405 00000 n +0000366555 00000 n +0000366707 00000 n +0000366857 00000 n +0000367006 00000 n +0000367157 00000 n +0000367308 00000 n +0000367459 00000 n +0000367610 00000 n +0000367761 00000 n +0000367912 00000 n +0000368063 00000 n +0000368213 00000 n +0000368365 00000 n +0000368517 00000 n +0000368667 00000 n +0000368818 00000 n +0000368967 00000 n +0000369117 00000 n +0000369267 00000 n +0000369416 00000 n +0000372405 00000 n +0000372554 00000 n +0000372704 00000 n +0000372856 00000 n +0000373007 00000 n +0000369854 00000 n +0000355176 00000 n +0000353904 00000 n +0000369566 00000 n +0000369681 00000 n +0000369796 00000 n +0000373156 00000 n +0000373305 00000 n +0000373455 00000 n +0000373605 00000 n +0000373755 00000 n +0000373905 00000 n +0000374054 00000 n +0000374203 00000 n +0000374352 00000 n +0000374503 00000 n +0000374653 00000 n +0000374802 00000 n +0000374950 00000 n +0000375098 00000 n +0000375247 00000 n +0000375396 00000 n +0000375547 00000 n +0000375696 00000 n +0000375846 00000 n +0000375997 00000 n +0000376148 00000 n +0000376298 00000 n +0000376447 00000 n +0000376598 00000 n +0000376746 00000 n +0000376893 00000 n +0000377039 00000 n +0000377190 00000 n +0000377339 00000 n +0000377489 00000 n +0000377640 00000 n +0000377788 00000 n +0000377934 00000 n +0000378082 00000 n +0000378230 00000 n +0000378378 00000 n +0000378525 00000 n +0000378672 00000 n +0000378819 00000 n +0000378968 00000 n +0000379118 00000 n +0000379267 00000 n +0000379414 00000 n +0000379562 00000 n +0000379712 00000 n +0000379862 00000 n +0000380013 00000 n +0000380164 00000 n +0000380314 00000 n +0000380465 00000 n +0000380615 00000 n +0000380765 00000 n +0000380916 00000 n +0000381067 00000 n +0000381214 00000 n +0000381365 00000 n +0000381516 00000 n +0000381667 00000 n +0000381819 00000 n +0000381970 00000 n +0000382119 00000 n +0000382269 00000 n +0000382419 00000 n +0000382569 00000 n +0000382720 00000 n +0000382871 00000 n +0000383022 00000 n +0000383173 00000 n +0000383322 00000 n +0000383472 00000 n +0000383621 00000 n +0000383771 00000 n +0000383921 00000 n +0000384071 00000 n +0000384222 00000 n +0000384372 00000 n +0000384523 00000 n +0000384674 00000 n +0000384824 00000 n +0000384975 00000 n +0000385125 00000 n +0000385276 00000 n +0000385424 00000 n +0000385571 00000 n +0000385720 00000 n +0000385870 00000 n +0000386020 00000 n +0000386170 00000 n +0000386319 00000 n +0000386469 00000 n +0000386619 00000 n +0000386769 00000 n +0000386919 00000 n +0000387069 00000 n +0000387217 00000 n +0000387366 00000 n +0000387514 00000 n +0000387663 00000 n +0000387813 00000 n +0000387963 00000 n +0000388111 00000 n +0000388259 00000 n +0000388406 00000 n +0000388556 00000 n +0000391302 00000 n +0000391451 00000 n +0000391602 00000 n +0000388762 00000 n +0000371296 00000 n +0000369966 00000 n +0000388704 00000 n +0000391752 00000 n +0000391901 00000 n +0000392050 00000 n +0000392200 00000 n +0000392350 00000 n +0000392501 00000 n +0000392651 00000 n +0000392802 00000 n +0000392950 00000 n +0000393100 00000 n +0000393247 00000 n +0000393395 00000 n +0000393544 00000 n +0000393695 00000 n +0000393844 00000 n +0000393993 00000 n +0000394143 00000 n +0000394293 00000 n +0000394444 00000 n +0000394595 00000 n +0000394742 00000 n +0000394890 00000 n +0000395039 00000 n +0000395188 00000 n +0000395338 00000 n +0000395487 00000 n +0000395638 00000 n +0000395790 00000 n +0000395938 00000 n +0000396089 00000 n +0000396240 00000 n +0000396389 00000 n +0000396536 00000 n +0000396686 00000 n +0000396836 00000 n +0000396982 00000 n +0000397128 00000 n +0000397276 00000 n +0000397425 00000 n +0000397574 00000 n +0000397721 00000 n +0000397868 00000 n +0000398015 00000 n +0000398164 00000 n +0000398314 00000 n +0000398463 00000 n +0000398611 00000 n +0000398760 00000 n +0000398909 00000 n +0000399059 00000 n +0000399210 00000 n +0000399361 00000 n +0000399512 00000 n +0000399662 00000 n +0000399813 00000 n +0000399964 00000 n +0000400115 00000 n +0000400265 00000 n +0000400416 00000 n +0000400566 00000 n +0000400715 00000 n +0000400866 00000 n +0000401017 00000 n +0000401168 00000 n +0000401318 00000 n +0000401469 00000 n +0000401619 00000 n +0000401771 00000 n +0000401923 00000 n +0000402075 00000 n +0000402225 00000 n +0000402376 00000 n +0000402527 00000 n +0000402679 00000 n +0000402828 00000 n +0000402978 00000 n +0000403128 00000 n +0000403278 00000 n +0000403428 00000 n +0000403579 00000 n +0000403730 00000 n +0000403881 00000 n +0000404032 00000 n +0000404183 00000 n +0000404333 00000 n +0000404484 00000 n +0000404634 00000 n +0000404785 00000 n +0000404936 00000 n +0000405088 00000 n +0000405238 00000 n +0000405388 00000 n +0000405538 00000 n +0000405688 00000 n +0000405839 00000 n +0000405990 00000 n +0000406141 00000 n +0000406292 00000 n +0000406441 00000 n +0000406591 00000 n +0000406740 00000 n +0000406890 00000 n +0000407038 00000 n +0000409709 00000 n +0000409857 00000 n +0000410006 00000 n +0000410155 00000 n +0000410306 00000 n +0000410454 00000 n +0000410602 00000 n +0000410749 00000 n +0000410900 00000 n +0000407245 00000 n +0000390220 00000 n +0000388861 00000 n +0000407187 00000 n +0000411052 00000 n +0000411200 00000 n +0000411350 00000 n +0000411500 00000 n +0000411649 00000 n +0000411797 00000 n +0000411946 00000 n +0000412096 00000 n +0000412243 00000 n +0000412392 00000 n +0000412540 00000 n +0000412691 00000 n +0000412842 00000 n +0000412991 00000 n +0000413140 00000 n +0000413291 00000 n +0000413441 00000 n +0000413592 00000 n +0000413743 00000 n +0000413892 00000 n +0000414042 00000 n +0000414193 00000 n +0000414342 00000 n +0000414493 00000 n +0000414645 00000 n +0000414791 00000 n +0000414942 00000 n +0000415089 00000 n +0000415237 00000 n +0000415386 00000 n +0000415535 00000 n +0000415685 00000 n +0000415832 00000 n +0000415979 00000 n +0000416126 00000 n +0000416274 00000 n +0000416423 00000 n +0000416569 00000 n +0000416718 00000 n +0000416867 00000 n +0000417013 00000 n +0000417163 00000 n +0000417314 00000 n +0000417465 00000 n +0000417617 00000 n +0000417769 00000 n +0000417919 00000 n +0000418070 00000 n +0000418222 00000 n +0000418372 00000 n +0000418523 00000 n +0000418674 00000 n +0000418825 00000 n +0000418976 00000 n +0000419126 00000 n +0000419277 00000 n +0000419424 00000 n +0000419574 00000 n +0000419725 00000 n +0000419877 00000 n +0000420025 00000 n +0000420175 00000 n +0000420325 00000 n +0000420475 00000 n +0000420626 00000 n +0000420777 00000 n +0000420928 00000 n +0000421079 00000 n +0000421231 00000 n +0000421383 00000 n +0000421534 00000 n +0000421684 00000 n +0000421835 00000 n +0000421985 00000 n +0000422136 00000 n +0000422288 00000 n +0000422440 00000 n +0000422591 00000 n +0000422742 00000 n +0000422891 00000 n +0000423041 00000 n +0000423189 00000 n +0000423337 00000 n +0000423485 00000 n +0000423633 00000 n +0000423782 00000 n +0000423932 00000 n +0000424080 00000 n +0000424228 00000 n +0000425985 00000 n +0000426134 00000 n +0000426282 00000 n +0000426432 00000 n +0000426582 00000 n +0000426732 00000 n +0000426883 00000 n +0000424434 00000 n +0000408699 00000 n +0000407370 00000 n +0000424376 00000 n +0000427034 00000 n +0000427182 00000 n +0000427333 00000 n +0000427482 00000 n +0000427632 00000 n +0000427784 00000 n +0000427933 00000 n +0000428083 00000 n +0000428227 00000 n +0000428372 00000 n +0000428520 00000 n +0000428668 00000 n +0000428818 00000 n +0000428968 00000 n +0000429118 00000 n +0000429269 00000 n +0000429418 00000 n +0000429569 00000 n +0000429721 00000 n +0000429873 00000 n +0000430025 00000 n +0000430177 00000 n +0000430329 00000 n +0000430481 00000 n +0000430632 00000 n +0000430783 00000 n +0000430933 00000 n +0000431083 00000 n +0000431234 00000 n +0000431384 00000 n +0000431536 00000 n +0000431688 00000 n +0000431837 00000 n +0000431987 00000 n +0000432138 00000 n +0000432289 00000 n +0000432441 00000 n +0000432589 00000 n +0000432741 00000 n +0000432950 00000 n +0000425443 00000 n +0000424533 00000 n +0000432892 00000 n +0000602514 00000 n +0000433462 00000 n +0000433288 00000 n +0000433062 00000 n +0000433404 00000 n +0000435414 00000 n +0000435125 00000 n +0000433535 00000 n +0000435241 00000 n +0000435299 00000 n +0000437338 00000 n +0000437164 00000 n +0000435500 00000 n +0000437280 00000 n +0000439150 00000 n +0000438976 00000 n +0000437424 00000 n +0000439092 00000 n +0000441140 00000 n +0000440966 00000 n +0000439236 00000 n +0000441082 00000 n +0000443281 00000 n +0000443107 00000 n +0000441226 00000 n +0000443223 00000 n +0000602639 00000 n +0000445294 00000 n +0000445120 00000 n +0000443367 00000 n +0000445236 00000 n +0000447155 00000 n +0000446981 00000 n +0000445380 00000 n +0000447097 00000 n +0000448648 00000 n +0000448474 00000 n +0000447241 00000 n +0000448590 00000 n +0000448734 00000 n +0000448760 00000 n +0000449431 00000 n +0000450082 00000 n +0000450324 00000 n +0000450992 00000 n +0000451610 00000 n +0000452135 00000 n +0000452203 00000 n +0000452902 00000 n +0000453068 00000 n +0000453094 00000 n +0000453512 00000 n +0000453981 00000 n +0000454297 00000 n +0000454998 00000 n +0000455631 00000 n +0000456144 00000 n +0000456704 00000 n +0000461077 00000 n +0000461327 00000 n +0000469222 00000 n +0000469605 00000 n +0000471502 00000 n +0000471737 00000 n +0000481091 00000 n +0000481436 00000 n +0000485549 00000 n +0000491641 00000 n +0000491922 00000 n +0000503665 00000 n +0000520428 00000 n +0000520979 00000 n +0000537504 00000 n +0000539870 00000 n +0000540113 00000 n +0000547913 00000 n +0000549688 00000 n +0000549959 00000 n +0000551195 00000 n +0000551422 00000 n +0000553002 00000 n +0000563238 00000 n +0000563570 00000 n +0000577517 00000 n +0000582362 00000 n +0000582634 00000 n +0000596522 00000 n +0000602746 00000 n +0000602866 00000 n +0000602986 00000 n +0000603106 00000 n +0000603231 00000 n +0000603321 00000 n +0000603422 00000 n +0000607743 00000 n +0000607920 00000 n +0000608097 00000 n +0000608271 00000 n +0000608714 00000 n +0000609102 00000 n +0000609538 00000 n +0000610190 00000 n +0000611056 00000 n +0000611678 00000 n +0000612839 00000 n +0000613658 00000 n +0000614039 00000 n +0000614230 00000 n +0000614408 00000 n +0000614593 00000 n +0000614775 00000 n +0000614957 00000 n +0000615142 00000 n +0000615325 00000 n +0000615503 00000 n +0000615673 00000 n +0000615844 00000 n +0000616014 00000 n +0000616185 00000 n +0000616355 00000 n +0000616526 00000 n +0000616695 00000 n +0000616864 00000 n +0000617035 00000 n +0000617205 00000 n +0000617376 00000 n +0000617546 00000 n +0000617717 00000 n +0000617887 00000 n +0000618058 00000 n +0000618232 00000 n +0000618408 00000 n +0000618579 00000 n +0000618764 00000 n +0000618975 00000 n +0000619186 00000 n +0000619397 00000 n +0000619607 00000 n +0000619822 00000 n +0000620037 00000 n +0000620252 00000 n +0000620467 00000 n +0000620681 00000 n +0000620895 00000 n +0000621109 00000 n +0000621323 00000 n +0000621539 00000 n +0000621746 00000 n +0000621949 00000 n +0000622151 00000 n +0000622354 00000 n +0000622556 00000 n +0000622759 00000 n +0000622960 00000 n +0000623161 00000 n +0000623364 00000 n +0000623566 00000 n +0000623769 00000 n +0000623971 00000 n +0000624174 00000 n +0000624375 00000 n +0000624556 00000 n +0000624726 00000 n +0000624897 00000 n +0000625014 00000 n +0000625131 00000 n +0000625247 00000 n +0000625364 00000 n +0000625485 00000 n +0000625611 00000 n +0000625736 00000 n +0000625859 00000 n +0000625983 00000 n +0000626062 00000 n +0000626179 00000 n +0000626299 00000 n +0000626383 00000 n +0000626423 00000 n +0000626701 00000 n +trailer +<< /Size 1882 +/Root 1880 0 R +/Info 1881 0 R +/ID [<4B8860802C43093AAD5A72697D455020> <4B8860802C43093AAD5A72697D455020>] >> +startxref +627157 +%%EOF diff --git a/old/36114-pdf 2011-05-11.zip b/old/36114-pdf 2011-05-11.zip Binary files differnew file mode 100644 index 0000000..bb29cfe --- /dev/null +++ b/old/36114-pdf 2011-05-11.zip diff --git a/old/36114-t 2011-05-11.tex b/old/36114-t 2011-05-11.tex new file mode 100644 index 0000000..6debb02 --- /dev/null +++ b/old/36114-t 2011-05-11.tex @@ -0,0 +1,7028 @@ +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % +% % +% The Project Gutenberg EBook of Relativity: The Special and the General % +% Theory, by Albert Einstein % +% % +% This eBook is for the use of anyone anywhere at no cost and with % +% almost no restrictions whatsoever. You may copy it, give it away or % +% re-use it under the terms of the Project Gutenberg License included % +% with this eBook or online at www.gutenberg.org % +% % +% % +% Title: Relativity: The Special and the General Theory % +% A Popular Exposition, 3rd ed. % +% % +% Author: Albert Einstein % +% % +% Translator: Robert W. Lawson % +% % +% Release Date: May 15, 2011 [EBook #36114] % +% % +% Language: English % +% % +% Character set encoding: ISO-8859-1 % +% % +% *** START OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** % +% % +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % + +\def\ebook{36114} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% +%% Packages and substitutions: %% +%% %% +%% book: Required. %% +%% inputenc: Latin-1 text encoding. Required. %% +%% %% +%% ifthen: Logical conditionals. Required. %% +%% %% +%% amsmath: AMS mathematics enhancements. Required. %% +%% amssymb: Additional mathematical symbols. Required. %% +%% %% +%% alltt: Fixed-width font environment. Required. %% +%% array: Enhanced tabular features. Required. %% +%% %% +%% perpage: Start footnote numbering on each page. Required. %% +%% %% +%% multicol: Twocolumn environment for index. Required. %% +%% makeidx: Indexing. Required. %% +%% %% +%% caption: Caption customization. Required. %% +%% graphicx: Standard interface for graphics inclusion. Required. %% +%% wrapfig: Illustrations surrounded by text. Required. %% +%% %% +%% calc: Length calculations. Required. %% +%% %% +%% fancyhdr: Enhanced running headers and footers. Required. %% +%% %% +%% geometry: Enhanced page layout package. Required. %% +%% hyperref: Hypertext embellishments for pdf output. Required. %% +%% %% +%% %% +%% Producer's Comments: %% +%% %% +%% OCR text for this ebook was obtained on May 7, 2011, from %% +%% http://www.archive.org/details/relativitythespe00einsuoft. %% +%% %% +%% The Methuen book catalogue from the original has been omitted. %% +%% %% +%% Minor changes to the original are noted in this file in three %% +%% ways: %% +%% 1. \Change{}{} for typographical corrections, showing %% +%% original and replacement text side-by-side. %% +%% 2. \Add{} for inconsistent/missing punctuation. %% +%% 3. [** TN: Note]s for lengthier or stylistic comments. %% +%% \Add is implemented in terms of \Change, so redefining \Change %% +%% will "restore" typographical errors in the original. %% +%% %% +%% %% +%% Compilation Flags: %% +%% %% +%% The following behavior may be controlled by boolean flags. %% +%% %% +%% ForPrinting (false by default): %% +%% If true, compile a print-optimized PDF file: Taller text block,%% +%% two-sided layout, US Letter paper, black hyperlinks. Default: %% +%% screen optimized file (one-sided layout, blue hyperlinks). %% +%% %% +%% %% +%% Things to Check: %% +%% %% +%% %% +%% Spellcheck: .................................. OK %% +%% %% +%% lacheck: ..................................... OK %% +%% Numerous false positives from commented code %% +%% %% +%% PDF pages: 154 (if ForPrinting set to false) %% +%% PDF page size: 4.75 x 7" %% +%% PDF bookmarks: created, point to ToC entries %% +%% PDF document info: filled in %% +%% Images: 5 pdf diagrams %% +%% %% +%% Summary of log file: %% +%% * No over- or under-full boxes. %% +%% %% +%% Compile History: %% +%% %% +%% May, 2011: adhere (Andrew D. Hwang) %% +%% texlive2007, GNU/Linux %% +%% %% +%% Command block: %% +%% %% +%% pdflatex x3 %% +%% makeindex %% +%% pdflatex x3 %% +%% %% +%% %% +%% May 2011: pglatex. %% +%% Compile this project with: %% +%% pdflatex 36114-t.tex ..... THREE times %% +%% makeindex 36114-t.idx %% +%% pdflatex 36114-t.tex ..... THREE times %% +%% %% +%% pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %% +%% %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\listfiles +\documentclass[12pt]{book}[2005/09/16] + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[latin1]{inputenc}[2006/05/05] + +\usepackage{ifthen}[2001/05/26] %% Logical conditionals + +\usepackage{amsmath}[2000/07/18] %% Displayed equations +\usepackage{amssymb}[2002/01/22] %% and additional symbols + +\usepackage{alltt}[1997/06/16] %% boilerplate, credits, license +\usepackage{array}[2005/08/23] %% extended array/tabular features + +\usepackage{perpage}[2006/07/15] + +\usepackage{multicol}[2006/05/18] +\usepackage{makeidx}[2000/03/29] + +\usepackage[font=footnotesize,labelformat=empty]{caption}[2007/01/07] +\usepackage{graphicx}[1999/02/16]%% For diagrams +\usepackage{wrapfig}[2003/01/31] %% and wrapping text around them + +\usepackage{calc}[2005/08/06] + +% for running heads +\usepackage{fancyhdr} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%% Interlude: Set up PRINTING (default) or SCREEN VIEWING %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% ForPrinting=true false (default) +% Asymmetric margins Symmetric margins +% 1 : 1.62 text block aspect ratio 3 : 4 text block aspect ratio +% Black hyperlinks Blue hyperlinks +% Start major marker pages recto No blank verso pages +% +% Chapter-like ``Sections'' start both recto and verso in the scanned +% book. This behavior has been retained. +\newboolean{ForPrinting} + +%% UNCOMMENT the next line for a PRINT-OPTIMIZED VERSION of the text %% +%\setboolean{ForPrinting}{true} + +%% Initialize values to ForPrinting=false +\newcommand{\Margins}{hmarginratio=1:1} % Symmetric margins +\newcommand{\HLinkColor}{blue} % Hyperlink color +\newcommand{\PDFPageLayout}{SinglePage} +\newcommand{\TransNote}{Transcriber's Note} +\newcommand{\TransNoteCommon}{% + The camera-quality files for this public-domain ebook may be + downloaded \textit{gratis} at + \begin{center} + \texttt{www.gutenberg.org/ebooks/\ebook}. + \end{center} + + This ebook was produced using OCR text provided by the University of + Toronto Robarts Library through the Internet Archive. + \bigskip + + Minor typographical corrections and presentational changes have been + made without comment. + \bigskip +} + +\newcommand{\TransNoteText}{% + \TransNoteCommon + + This PDF file is optimized for screen viewing, but may easily be + recompiled for printing. Please consult the preamble of the \LaTeX\ + source file for instructions and other particulars. +} +%% Re-set if ForPrinting=true +\ifthenelse{\boolean{ForPrinting}}{% + \renewcommand{\Margins}{hmarginratio=2:3} % Asymmetric margins + \renewcommand{\HLinkColor}{black} % Hyperlink color + \renewcommand{\PDFPageLayout}{TwoPageRight} + \renewcommand{\TransNote}{Transcriber's Note} + \renewcommand{\TransNoteText}{% + \TransNoteCommon + + This PDF file is optimized for printing, but may easily be + recompiled for screen viewing. Please consult the preamble + of the \LaTeX\ source file for instructions and other particulars. + } +}{% If ForPrinting=false, don't skip to recto + \renewcommand{\cleardoublepage}{\clearpage} +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%% End of PRINTING/SCREEN VIEWING code; back to packages %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\ifthenelse{\boolean{ForPrinting}}{% + \setlength{\paperwidth}{8.5in}% + \setlength{\paperheight}{11in}% +% ~1:1.62 + \usepackage[body={4.5in,7.3in},\Margins]{geometry}[2002/07/08] +}{% + \setlength{\paperwidth}{4.75in}% + \setlength{\paperheight}{7in}% + \raggedbottom +% ~3:4 + \usepackage[body={4.5in,6in},\Margins,includeheadfoot]{geometry}[2002/07/08] +} + +\providecommand{\ebook}{00000} % Overridden during white-washing +\usepackage[pdftex, + hyperref, + hyperfootnotes=false, + pdftitle={The Project Gutenberg eBook \#\ebook: Relativity}, + pdfauthor={Albert Einstein}, + pdfkeywords={University of Toronto, The Internet Archive, Andrew D. Hwang}, + pdfstartview=Fit, % default value + pdfstartpage=1, % default value + pdfpagemode=UseNone, % default value + bookmarks=true, % default value + linktocpage=false, % default value + pdfpagelayout=\PDFPageLayout, + pdfdisplaydoctitle, + pdfpagelabels=true, + bookmarksopen=true, + bookmarksopenlevel=-1, + colorlinks=true, + linkcolor=\HLinkColor]{hyperref}[2007/02/07] + + +%%%% Fixed-width environment to format PG boilerplate %%%% +\newenvironment{PGtext}{% +\begin{alltt} +\fontsize{8.1}{9}\ttfamily\selectfont}% +{\end{alltt}} + +%% No hrule in page header +\renewcommand{\headrulewidth}{0pt} + +% Top-level footnote numbers restart on each page +\MakePerPage{footnote} + +% Running heads +\newcommand{\FlushRunningHeads}{\clearpage\fancyhf{}\cleardoublepage} +\newcommand{\InitRunningHeads}{% + \setlength{\headheight}{15pt} + \pagestyle{fancy} + \thispagestyle{plain} + \ifthenelse{\boolean{ForPrinting}} + {\fancyhead[RO,LE]{\thepage}} + {\fancyhead[R]{\thepage}} +} + +\newcommand{\SetOddHead}[1]{% + \fancyhead[CO]{\textbf{\MakeUppercase{#1}}} +} + +\newcommand{\SetEvenHead}[1]{% + \fancyhead[CE]{\textbf{\MakeUppercase{#1}}} +} + +\newcommand{\BookMark}[2]{\phantomsection\pdfbookmark[#1]{#2}{#2}} + +% ToC formatting +\AtBeginDocument{\renewcommand{\contentsname}% + {\protect\thispagestyle{plain}% + \protect\centering\normalfont\large\textbf{CONTENTS}}} + +\newcommand{\ToCFont}{\centering\normalfont\normalsize\scshape} +\newcommand{\TableofContents}{% + \FlushRunningHeads + \InitRunningHeads + \SetOddHead{Contents} + \BookMark{0}{Contents} + \tableofcontents +} + +% For internal bookkeeping +\newcommand{\ToCAnchor}{} + +%\ToCLine[type]{<label>}{Title}{xref} +\newcommand{\ToCLine}[4][chapter]{% + \label{toc:#4}% + \ifthenelse{\not\equal{\pageref{toc:#4}}{\ToCAnchor}}{% + \renewcommand{\ToCAnchor}{\pageref{toc:#4}}% + \noindent\makebox[\textwidth][r]{\hfill\scriptsize PAGE}\\% + }{}% + \settowidth{\TmpLen}{\;\pageref{#4}}% + \noindent\strut\parbox[b]{\textwidth-\TmpLen}{\small% + \ifthenelse{\not\equal{#2}{}}{% Write unit number at start of line + \ifthenelse{\equal{#1}{appendix}}{% + \settowidth{\TmpLen}{III.}% Widest appendix number + }{% + \settowidth{\TmpLen}{XXVIII.}% Widest chapter number + } + \makebox[\TmpLen][r]{#2}\hspace{0.5em}% + }{}% Empty second argument => no unit number + \raggedright\hangindent6em #3\dotfill}% + \makebox[\TmpLen][r]{\pageref{#4}}% +} + +% Index formatting +\makeindex +\makeatletter +\renewcommand{\@idxitem}{\par\hangindent 30\p@\global\let\idxbrk\nobreak} +\renewcommand\subitem{\idxbrk\@idxitem --- \let\idxbrk\relax} +\renewcommand\subsubitem{\idxbrk\@idxitem --- --- \let\idxbrk\relax} +\renewcommand{\indexspace}{\par\penalty-3000 \vskip 10pt plus5pt minus3pt\relax} + +\renewenvironment{theindex}{% + \setlength\columnseprule{0.5pt}\setlength\columnsep{18pt}% + \cleardoublepage + \phantomsection + \label{index} + \addtocontents{toc}{\ToCLine{}{\textsc{Index}}{index}} + \SetOddHead{Index} + \BookMark{0}{Index} + \begin{multicols}{2}[\SectTitle{Index}\small]% ** N.B. font size + \setlength\parindent{0pt}\setlength\parskip{0pt plus 0.3pt}% + \thispagestyle{plain}\let\item\@idxitem\raggedright% + }{% + \end{multicols}\FlushRunningHeads +} +\makeatother + +% Allows \Part to communicate with \Chapter +\newboolean{StartPart} +\setboolean{StartPart}{false} + +\newcommand{\SectTitle}[2][\large]{% + \section*{\centering#1\MakeUppercase{#2}} +} +\newcommand{\SectSubtitle}[2][\normalsize]{% + \subsection*{\centering#1\MakeUppercase{#2}} +} + +\newcommand{\Part}[3]{% + \setboolean{StartPart}{true} + \ifthenelse{\equal{#1}{I}}{% + \mainmatter + \begin{center} + \textbf{\LARGE RELATIVITY} + \end{center} + }{% + \FlushRunningHeads + }% + \InitRunningHeads + \BookMark{-1}{Part #1. #2} + \label{part:#1} + \SetEvenHead{Relativity} + \SetOddHead{#3} + \addtocontents{toc}{\protect\section*{\protect\ToCFont PART #1}} + \addtocontents{toc}{\protect\subsection*{\protect\ToCFont #2}} + \SectTitle[\Large]{Part #1} + \SectSubtitle{#2} + \bigskip +} + +%\Chapter[PDF name]{Number.}{Heading title} +\newcommand{\Chapter}[3][]{% + \ifthenelse{\boolean{StartPart}}{% + \setboolean{StartPart}{false}% + }{% + \newpage + } + \BookMark{0}{#2. #3} + \label{chapter:#2} + \thispagestyle{plain} + \addtocontents{toc}{\ToCLine{#2.}{#3}{chapter:#2}} + \SectTitle{#2} + \SectSubtitle{#3} +} + +\newcommand{\Section}[1]{% + \newpage + \thispagestyle{plain} + \SectTitle{#1} +} + +\newcommand{\Subsection}[2]{% + \subsection*{\centering\normalsize\normalfont(\Item{#1}) \textsc{#2}} + \ifthenelse{\not\equal{#1}{}}{% + \phantomsection + \label{subsection:#1} + \addtocontents{toc}{% + \ToCLine{(\protect\Item{#1})}{#2}{subsection:#1}% + }% + }{}% +} + +\newcommand{\Bibsection}[1]{% + \subsection*{\centering\normalsize\normalfont\textsc{#1}} +} + +\newcommand{\Preface}{% + \FlushRunningHeads + \InitRunningHeads + \SetOddHead{Relativity} + \SetEvenHead{Relativity} + \BookMark{0}{Preface} + \SectTitle{Preface}% +} + +\newcommand{\Appendix}[3]{% + \clearpage + \BookMark{0}{Appendix #1. #2} + \label{appendix:#1} + \thispagestyle{plain} + \SetOddHead{Appendix #1}% + \ifthenelse{\equal{#1}{I}}{% + \addtocontents{toc}{\protect\section*{\protect\ToCFont APPENDICES}} + }{} + \addtocontents{toc}{\ToCLine[appendix]{#1.}{#2 #3}{appendix:#1}} + \SectTitle{Appendix #1} + \subsection*{\centering\normalsize\normalfont% + \MakeUppercase{#2} \small\textsc{#3}} +} + +\newcommand{\Bibliography}[1]{% + \cleardoublepage + \phantomsection + \label{biblio} + \addtocontents{toc}{\ToCLine{}{\textsc{Bibliography}}{biblio}} + \thispagestyle{plain} + \SetOddHead{Bibliography} + \BookMark{0}{Bibliography} + \SectTitle{Bibliography}% + \SectSubtitle{#1}% +} + +\renewenvironment{itemize}{% + \begin{list}{}{\setlength{\topsep}{4pt plus 8pt}% + \setlength{\itemsep}{0pt plus 2pt}% + \setlength{\parsep}{4pt plus 2pt}% + \setlength{\leftmargin}{4em}}}{\end{list}} + +\newenvironment{CenterPage}{% + \thispagestyle{empty}% + \null\vfill% + \begin{center} + }{% + \end{center} + \vfill% +} + +\newenvironment{PubInfo}{% + \newpage + \begin{CenterPage} + \footnotesize + \settowidth{\TmpLen}{\textit{This Translation was first Published}\qquad} + \begin{tabular}{p{\TmpLen}@{\,}c}% + }{% + \end{tabular} + \end{CenterPage} +} + +\newcommand{\PubRow}[2]{% + \textit{#1}\dotfill & \textit{#2} \\ +} + +\newcommand{\Signature}[2][]{% + \setlength{\TmpLen}{\textwidth-2\parindent}% + \bigskip% + \parbox{\TmpLen}{\centering\small#1\hfill#2}% +} + +\newcommand{\Bibitem}[2]{% +\par\noindent\hangindent2\parindent\textit{#1}: #2\medskip% +} + +\newcommand{\ColHead}[3]{% +\multicolumn{#1}{c}{\settowidth{\TmpLen}{#2}% + \parbox[c]{\TmpLen}{\centering#3\medskip}}% +} + +\newcommand{\Input}[2][] + {\ifthenelse{\equal{#1}{}} + {\includegraphics{./images/#2.pdf}} + {\includegraphics[width=#1]{./images/#2.pdf}}% +} + +\newcounter{figno} +\newcommand{\Figure}[2][0.8\textwidth]{% +\begin{figure}[hbt!] + \refstepcounter{figno} + \centering + \Input[#1]{#2} + \caption{\textsc{Fig}.~\thefigno.} + \label{fig:\thefigno} +\end{figure} +} + +\newcommand{\WFigure}[2]{% +\begin{wrapfigure}{o}{#1} + \refstepcounter{figno} + \centering + \Input[#1]{#2} + \caption{\textsc{Fig}.~\thefigno.} + \label{fig:\thefigno} +\end{wrapfigure} +} + +\newcommand{\First}[1]{\textsc{\large #1}} + +% For corrections. +\newcommand{\Change}[2]{#2} +\newcommand{\Add}[1]{\Change{}{#1}} + +\newcommand{\PageSep}[1]{\ignorespaces} +\setlength{\emergencystretch}{1em} + +\newlength{\TmpLen} + +\DeclareInputText{176}{\ifmmode{{}^\circ}\else\textdegree\fi} +\DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi} + +\newcommand{\Tag}[1]{% + \phantomsection + \label{eqn:#1} + \tag*{\ensuremath{#1}} +} + +% and links +\newcommand{\Eqref}[1]{\hyperref[eqn:#1]{\ensuremath{#1}}} +\newcommand{\Figref}[1]{\hyperref[fig:#1]{Fig.~#1}} +\newcommand{\Partref}[1]{\hyperref[part:#1]{Part~#1}} +\newcommand{\Sectionref}[1]{\hyperref[chapter:#1]{Section~#1}} +\newcommand{\Srefno}[1]{\hyperref[chapter:#1]{#1}} +\newcommand{\Appendixref}[1]{\hyperref[appendix:#1]{Appendix~#1}} + +\newcommand{\ie}{\textit{i.e.}} +\newcommand{\eg}{\textit{e.g.}} +\newcommand{\NB}{\textit{N.B.}} +\newcommand{\Item}[1]{\textit{#1}} + +\newcommand{\itema}{(\Item{a})} +\newcommand{\itemb}{(\Item{b})} +\newcommand{\itemc}{(\Item{c})} + +\newcommand{\Z}{\phantom{0}} + +%%%%%%%%%%%%%%%%%%%%%%%% START OF DOCUMENT %%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} +\pagenumbering{Alph} +\pagestyle{empty} +\BookMark{-1}{Front Matter} +%%%% PG BOILERPLATE %%%% +\BookMark{0}{PG Boilerplate} +\begin{center} +\begin{minipage}{\textwidth} +\small +\begin{PGtext} +The Project Gutenberg EBook of Relativity: The Special and the General +Theory, by Albert Einstein + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Relativity: The Special and the General Theory + A Popular Exposition, 3rd ed. + +Author: Albert Einstein + +Translator: Robert W. Lawson + +Release Date: May 15, 2011 [EBook #36114] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** +\end{PGtext} +\end{minipage} +\end{center} +\newpage +%%%% Credits and transcriber's note %%%% +\begin{center} +\begin{minipage}{\textwidth} +\begin{PGtext} +Produced by Andrew D. Hwang. (This ebook was produced using +OCR text generously provided by the University of Toronto +Robarts Library through the Internet Archive.) +\end{PGtext} +\end{minipage} +\end{center} +\vfill + +\begin{minipage}{0.85\textwidth} +\small +\BookMark{0}{Transcriber's Note} +\subsection*{\centering\normalfont\scshape% +\normalsize\MakeLowercase{\TransNote}}% + +\raggedright +\TransNoteText +\end{minipage} +%%%%%%%%%%%%%%%%%%%%%%%%%%% FRONT MATTER %%%%%%%%%%%%%%%%%%%%%%%%%% +\frontmatter +\pagestyle{empty} +\begin{center} +\bfseries \Huge RELATIVITY \\ +\medskip +\normalsize THE SPECIAL \textit{\&} THE GENERAL THEORY \\ +\medskip +\small A POPULAR EXPOSITION +\vfill + +\footnotesize BY \\ +\Large ALBERT EINSTEIN, Ph.D. \\ +\smallskip\normalfont\scriptsize +PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN +\vfill + +\footnotesize AUTHORISED TRANSLATION BY \\ +\normalsize \textbf{ROBERT W. LAWSON, D.Sc.} \\ +\smallskip\scriptsize UNIVERSITY OF SHEFFIELD +\vfill + +\footnotesize WITH FIVE DIAGRAMS \\ +AND A PORTRAIT OF THE AUTHOR +\vfill\vfill + +THIRD EDITION +\vfill\vfill + + +\normalsize\bfseries METHUEN \& CO. LTD. \\ +36 ESSEX STREET W.C. \\ +LONDON +\end{center} +\PageSep{iv} +\begin{PubInfo} +\PubRow{This Translation was first Published}{August 19th 1920} +\PubRow{Second Edition}{September 1920} +\PubRow{Third Edition}{1920} +\end{PubInfo} +\PageSep{v} + + +\Preface + +\First{The} present book is intended, as far as possible, +to give an exact insight into the theory of Relativity +to those readers who, from a general +scientific and philosophical point of view, are interested +in the theory, but who are not conversant with the +mathematical apparatus\footnote + {The mathematical fundaments of the special theory of + relativity are to be found in the original papers of H.~A. Lorentz, + A.~Einstein, H.~Minkowski, published under the title \textit{Das + Relativitätsprinzip} (The Principle of Relativity) in B.~G. + Teubner's collection of monographs \textit{Fortschritte der mathematischen + Wissenschaften} (Advances in the Mathematical + Sciences), also in M.~Laue's exhaustive book \textit{Das Relativitätsprinzip}---published + by Friedr.\ Vieweg \&~Son, Braunschweig. + The general theory of relativity, together with the necessary + parts of the theory of invariants, is dealt with in the author's + book \textit{Die Grundlagen der allgemeinen Relativitätstheorie} (The + Foundations of the General Theory of Relativity) Joh.\ Ambr.\ + Barth,~1916; this book assumes some familiarity with the special + theory of relativity.} +of theoretical physics. The +work presumes a standard of education corresponding +to that of a university matriculation examination, +and, despite the shortness of the book, a fair amount +of patience and force of will on the part of the reader. +The author has spared himself no pains in his endeavour +\PageSep{vi} +to present the main ideas in the simplest and most intelligible +form, and on the whole, in the sequence and connection +in which they actually originated. In the interest +of clearness, it appeared to me inevitable that I should +repeat myself frequently, without paying the slightest +attention to the elegance of the presentation. I adhered +scrupulously to the precept of that brilliant theoretical +physicist L.~Boltzmann, according to whom matters of +elegance ought to be left to the tailor and to the cobbler. +I make no pretence of having withheld from the reader +difficulties which are inherent to the subject. On the +other hand, I have purposely treated the empirical +physical foundations of the theory in a ``step-motherly'' +fashion, so that readers unfamiliar with physics may +not feel like the wanderer who was unable to see the +forest for trees. May the book bring some one a few +happy hours of suggestive thought! + +\Signature[\textit{December}, 1916]{A. EINSTEIN} + + +\SectTitle{Note to the Third Edition} + +\First{In} the present year (1918) an excellent and detailed +manual on the general theory of relativity, written +by H.~Weyl, was published by the firm Julius +Springer (Berlin). This book, entitled \textit{Raum---Zeit---Materie} +(Space---Time---Matter), may be warmly recommended +to mathematicians and physicists. +\PageSep{vii} + + +\Section{Biographical Note} + +\First{Albert Einstein} is the son of German-Jewish +parents. He was born in~1879 in the +town of Ulm, Würtemberg, Germany. His +schooldays were spent in Munich, where he attended +the \textit{Gymnasium} until his sixteenth year. After leaving +school at Munich, he accompanied his parents to Milan, +whence he proceeded to Switzerland six months later +to continue his studies. + +From 1896 to 1900 Albert Einstein studied mathematics +and physics at the Technical High School in +Zurich, as he intended becoming a secondary school +(\textit{Gymnasium}) teacher. For some time afterwards he +was a private tutor, and having meanwhile become +naturalised, he obtained a post as engineer in the Swiss +Patent Office in~1902 which position he occupied till +1909. The main ideas involved in the most important +of Einstein's theories date back to this period. Amongst +these may be mentioned: \textit{The Special Theory of Relativity}, +\textit{Inertia of Energy}, \textit{Theory of the Brownian Movement}, +and the \textit{Quantum-Law of the Emission and Absorption of Light}~(1905). +These were followed some years +\PageSep{viii} +later by the \textit{Theory of the Specific Heat of Solid Bodies}, +and the fundamental idea of the \textit{General Theory of +Relativity}. + +During the interval 1909~to~1911 he occupied the post +of Professor \textit{Extraordinarius} at the University of Zurich, +afterwards being appointed to the University of Prague, +Bohemia, where he remained as Professor \textit{Ordinarius} +until~1912. In the latter year Professor Einstein +accepted a similar chair at the \textit{Polytechnikum}, Zurich, +and continued his activities there until~1914, when he +received a call to the Prussian Academy of Science, +Berlin, as successor to Van't~Hoff. Professor Einstein +is able to devote himself freely to his studies at the +Berlin Academy, and it was here that he succeeded in +completing his work on the \textit{General Theory of Relativity} +(1915--17). Professor Einstein also lectures on various +special branches of physics at the University of Berlin, +and, in addition, he is Director of the Institute for +Physical Research of the \textit{Kaiser Wilhelm Gesellschaft}. + +Professor Einstein has been twice married. His first +wife, whom he married at Berne in~1903, was a fellow-student +from Serbia. There were two sons of this +marriage, both of whom are living in Zurich, the elder +being sixteen years of age. Recently Professor Einstein +married a widowed cousin, with whom he is now living +in Berlin. + +\Signature{R. W. L.} +\PageSep{ix} + +\Section{Translator's Note} + +\First{In} presenting this translation to the English-reading +public, it is hardly necessary for me to +enlarge on the Author's prefatory remarks, except +to draw attention to those additions to the book which +do not appear in the original. + +At my request, Professor Einstein kindly supplied +me with a portrait of himself, by one of Germany's +most celebrated artists. \Appendixref{III}, on ``The +Experimental Confirmation of the General Theory of +Relativity,'' has been written specially for this translation. +Apart from these valuable additions to the book, +I have included a biographical note on the Author, +and, at the end of the book, an Index and a list of +English references to the subject. This list, which is more +suggestive than exhaustive, is intended as a guide to those +readers who wish to pursue the subject farther. + +I desire to tender my best thanks to my colleagues +Professor S.~R. Milner,~D.Sc., and Mr.~W.~E. Curtis, +A.R.C.Sc.,~F.R.A.S., also to my friend Dr.~Arthur +Holmes, A.R.C.Sc.,~F.G.S., of the Imperial College, +for their kindness in reading through the manuscript, +\PageSep{x} +for helpful criticism, and for numerous suggestions. I +owe an expression of thanks also to Messrs.\ Methuen +for their ready counsel and advice, and for the care +they have bestowed on the work during the course of +its publication. + +\Signature{ROBERT W. LAWSON} + +\noindent\textsc{The Physics Laboratory} \\ +\hspace*{\parindent}\textsc{The University of Sheffield} \\ +\hspace*{3\parindent}\textit{June} 12, 1920 +\PageSep{xi} +\TableofContents % [** TN: Auto-generate the table of contents] +\iffalse %%%% Start of table of contents text %%%% +CONTENTS + +PART I + +THE SPECIAL THEORY OF RELATIVITY + +PAGE + + I. Physical Meaning of Geometrical Propositions . 1 + II. The System of Co-ordinates . 5 +III. Space and Time in Classical Mechanics . . 9 + IV. The Galileian System of Co-ordinates . .11 + V. The Principle of Relativity (in the Restricted + Sense) . . . . . .12 + VI. The Theorem of the Addition of Velocities employed + in Classical Mechanics . . 16 +VII. The Apparent Incompatibility of the Law of + Propagation of Light with the Principle of + Relativity . . . . 17 + +VIII. On the Idea of Time in Physics . . .21 + IX. The Relativity of Simultaneity . . .25 + X. On the Relativity of the Conception of Distance 28 + XI. The Lorentz Transformation . . .30 + XII. The Behaviour of Measuring-Rods and Clocks + in Motion . . . . 35 +\PageSep{xii} +XIII. Theorem of the Addition of Velocities. The + Experiment of Fizeau . . 3 %[** TN: Edge of page cut off] + XIV. The Heuristic Value of the Theory of Relativity 4 + XV. General Results of the Theory . . .4, + XVI. Experience and the Special Theory of Relativity 4 +XVII. Minkowski's Four-dimensional Space . . 5; + +PART II +THE GENERAL THEORY OF RELATIVITY + +XVIII. Special and General Principle of Relativity . 5 + XIX. The Gravitational Field . . . .6 + XX. The Equality of Inertial and Gravitational Mass + as an Argument for the General Postulate + of Relativity ..... + XXI. In what Respects are the Foundations of Classical + Mechanics and of the Special Theory + of Relativity unsatisfactory? . + XXII. A Few Inferences from the General Principle of + Relativity ..... +XXIII. Behaviour of Clocks and Measuring-Rods on a + Rotating Body of Reference . + XXIV. Euclidean and Non-Euclidean Continuum + XXV. Gaussian Co-ordinates .... + XXVI. The Space-time Continuum of the Special + Theory of Relativity considered as a + Euclidean Continuum +\PageSep{xiii} +PAGE + + XXVII. The Space-time Continuum of the General + Theory of Relativity is not a Euclidean + Continuum . . . . 93 +XXVIII. Exact Formulation of the General Principle of + Relativity . . . . 97 + XXIX. The Solution of the Problem of Gravitation on + the Basis of the General Principle of + Relativity ..... 100 + +PART III + +CONSIDERATIONS ON THE UNIVERSE +AS A WHOLE + + XXX. Cosmological Difficulties of Newton's Theory 105 + XXXI. The Possibility of a ``Finite'' and yet ``Unbounded'' + Universe. . . . 108 + XXXII. The Structure of Space according to the + General Theory of Relativity . . 113 + +APPENDICES + + I. Simple Derivation of the Lorentz Transformation . 115 + II. Minkowski's Four-dimensional Space (``World'') + [Supplementary to Section XVII.] . . 121 +III. The Experimental Confirmation of the General + Theory of Relativity . . . .123 +(a) Motion of the Perihelion of Mercury . 124 +(b) Deflection of Light by a Gravitational Field 126 +(c) Displacement of Spectral Lines towards the + Red . . . . . 129 + +BIBLIOGRAPHY . . . . . . 133 + +INDEX . . . . . . .135 +\fi %%%% End of table of contents text %%%% +\PageSep{xiv} +\FlushRunningHeads +\begin{CenterPage} + \bfseries\LARGE RELATIVITY \\[8pt] + \normalsize THE SPECIAL AND THE GENERAL THEORY +\end{CenterPage} +\PageSep{1} +\index{Manifold|see{Continuum}}% + + +\Part{I}{The Special Theory of Relativity}{Special Theory of Relativity} +\index{Special theory of relativity|(}% + +\Chapter[Geometrical Propositions] +{I}{Physical Meaning of Geometrical +Propositions} + +\First{In} your schooldays most of you who read this +\index{Euclidean geometry}% +book made acquaintance with the noble building of +Euclid's geometry, and you remember---perhaps +with more respect than love---the magnificent structure, +on the lofty staircase of which you were chased about +for uncounted hours by conscientious teachers. By +reason of your past experience, you would certainly +regard everyone with disdain who should pronounce even +the most out-of-the-way proposition of this science to +be untrue. But perhaps this feeling of proud certainty +would leave you immediately if some one were to ask +you: ``What, then, do you mean by the assertion that +these propositions are true?'' Let us proceed to give +this question a little consideration. + +Geometry sets out from certain conceptions such as +\index{Geometrical ideas!truth of|(}% +``plane,'' ``point,'' and ``straight line,'' with which +\index{Plane}% +\index{Point}% +\index{Straight line|(}% +\PageSep{2} +we are able to associate more or less definite ideas, and +from certain simple propositions (axioms) which, +\index{Axioms}% +\index{Axioms!truth of}% +\index{Geometrical ideas!propositions}% +in virtue of these ideas, we are inclined to accept as +``true.'' Then, on the basis of a logical process, the +justification of which we feel ourselves compelled to +admit, all remaining propositions are shown to follow +from those axioms, \ie\ they are proven. A proposition +is then correct (``true'') when it has been derived in the +recognised manner from the axioms. The question +of the ``truth'' of the individual geometrical propositions +\index{Truth@{``Truth''}}% +is thus reduced to one of the ``truth'' of the +axioms. Now it has long been known that the last +question is not only unanswerable by the methods of +geometry, but that it is in itself entirely without meaning. +We cannot ask whether it is true that only one +straight line goes through two points. We can only +say that Euclidean geometry deals with things called +\index{Euclidean geometry}% +``straight lines,'' to each of which is ascribed the property +of being uniquely determined by two points +situated on it. The concept ``true'' does not tally with +the assertions of pure geometry, because by the word +``true'' we are eventually in the habit of designating +always the correspondence with a ``real'' object; +geometry, however, is not concerned with the relation +of the ideas involved in it to objects of experience, but +only with the logical connection of these ideas among +themselves. + +It is not difficult to understand why, in spite of this, +we feel constrained to call the propositions of geometry +``true.'' Geometrical ideas correspond to more or less +\index{Geometrical ideas}% +exact objects in nature, and these last are undoubtedly +the exclusive cause of the genesis of those ideas. Geometry +ought to refrain from such a course, in order to +\PageSep{3} +give to its structure the largest possible logical unity. +The practice, for example, of seeing in a ``distance'' +two marked positions on a practically rigid body is +something which is lodged deeply in our habit of thought. +We are accustomed further to regard three points as +being situated on a straight line, if their apparent +positions can be made to coincide for observation with +one eye, under suitable choice of our place of observation. + +If, in pursuance of our habit of thought, we now +supplement the propositions of Euclidean geometry by +\index{Euclidean geometry!propositions of}% +the single proposition that two points on a practically +rigid body always correspond to the same distance +\index{Distance (line-interval)}% +(line-interval), independently of any changes in position +to which we may subject the body, the propositions of +Euclidean geometry then resolve themselves into propositions +on the possible relative position of practically +\index{Relative!position}% +rigid bodies.\footnote + {It follows that a natural object is associated also with a + straight line. Three points $A$,~$B$ and~$C$ on a rigid body thus + lie in a straight line when, the points $A$~and~$C$ being given, $B$ + is chosen such that the sum of the distances $AB$~and~$BC$ is as + short as possible. This incomplete suggestion will suffice for + our present purpose.} +Geometry which has been supplemented +in this way is then to be treated as a branch of physics. +We can now legitimately ask as to the ``truth'' of +geometrical propositions interpreted in this way, since +we are justified in asking whether these propositions +are satisfied for those real things we have associated +with the geometrical ideas. In less exact terms we can +\index{Geometrical ideas}% +express this by saying that by the ``truth'' of a geometrical +proposition in this sense we understand its +validity for a construction with ruler and compasses. +\index{Straight line|)}% +\PageSep{4} + +Of course the conviction of the ``truth'' of geometrical +propositions in this sense is founded exclusively +on rather incomplete experience. For the present we +shall assume the ``truth'' of the geometrical propositions, +then at a later stage (in the general theory of +relativity) we shall see that this ``truth'' is limited, +and we shall consider the extent of its limitation. +\index{Geometrical ideas!truth of|)}% +\PageSep{5} + + +\Chapter{II}{The System of Co-ordinates} +\index{System of co-ordinates}% + +\First{On} the basis of the physical interpretation of distance +\index{Distance (line-interval)}% +\index{Distance (line-interval)!physical interpretation of}% +\index{Measuring-rod}% +\index{Reference-body}% +which has been indicated, we are also +in a position to establish the distance between +two points on a rigid body by means of measurements. +For this purpose we require a ``distance'' (rod~$S$) +which is to be used once and for all, and which we +employ as a standard measure. If, now, $A$~and~$B$ are +two points on a rigid body, we can construct the +line joining them according to the rules of geometry; +then, starting from~$A$, we can mark off the distance~$S$ +time after time until we reach~$B$. The number of +these operations required is the numerical measure +of the distance~$AB$. This is the basis of all measurement +of length.\footnote + {Here we have assumed that there is nothing left over, \ie\ + that the measurement gives a whole number. This difficulty + is got over by the use of divided measuring-rods, the introduction + of which does not demand any fundamentally new method.} + +Every description of the scene of an event or of the +position of an object in space is based on the specification +of the point on a rigid body (body of reference) +with which that event or object coincides. This applies +not only to scientific description, but also to everyday +life. If I analyse the place specification ``Trafalgar +\index{Place specification}% +\PageSep{6} +Square, London,''\footnote + {I have chosen this as being more familiar to the English + reader than the ``Potsdamer Platz, Berlin,'' which is referred to + in the original. (R.~W.~L.)} +I arrive at the following result. +The earth is the rigid body to which the specification +of place refers; ``Trafalgar Square, London,'' is a +well-defined point, to which a name has been assigned, +and with which the event coincides in space.\footnote + {It is not necessary here to investigate further the significance + of the expression ``coincidence in space.'' This conception is + sufficiently obvious to ensure that differences of opinion are + scarcely likely to arise as to its applicability in practice.} + +This primitive method of place specification deals +\index{Place specification}% +only with places on the surface of rigid bodies, and is +dependent on the existence of points on this surface +which are distinguishable from each other. But we +can free ourselves from both of these limitations without +altering the nature of our specification of position. +\index{Conception of mass!position}% +If, for instance, a cloud is hovering over Trafalgar +Square, then we can determine its position relative to +the surface of the earth by erecting a pole perpendicularly +on the Square, so that it reaches the cloud. The +length of the pole measured with the standard measuring-rod, +\index{Measuring-rod}% +combined with the specification of the position of +the foot of the pole, supplies us with a complete place +specification. On the basis of this illustration, we are +able to see the manner in which a refinement of the conception +of position has been developed. + +\itema~We imagine the rigid body, to which the place +specification is referred, supplemented in such a manner +that the object whose position we require is reached by +the completed rigid body. + +\itemb~In locating the position of the object, we make +use of a number (here the length of the pole measured +\PageSep{7} +with the measuring-rod) instead of designated points of +reference. + +\itemc~We speak of the height of the cloud even when the +pole which reaches the cloud has not been erected. +By means of optical observations of the cloud from +different positions on the ground, and taking into account +the properties of the propagation of light, we determine +the length of the pole we should have required in order +to reach the cloud. + +From this consideration we see that it will be advantageous +\index{Physics}% +if, in the description of position, it should be +possible by means of numerical measures to make ourselves +independent of the existence of marked positions +(possessing names) on the rigid body of reference. In +\index{Reference-body}% +the physics of measurement this is attained by the +\index{Physics!of measurement}% +application of the Cartesian system of co-ordinates. +\index{Cartesian system of co-ordinates}% + +This consists of three plane surfaces perpendicular +to each other and rigidly attached to a rigid body. +Referred to a system of co-ordinates, the scene of any +event will be determined (for the main part) by the +specification of the lengths of the three perpendiculars +or co-ordinates $(x, y, z)$ which can be dropped from the +scene of the event to those three plane surfaces. The +lengths of these three perpendiculars can be determined +by a series of manipulations with rigid measuring-rods +performed according to the rules and methods laid +down by Euclidean geometry. + +In practice, the rigid surfaces which constitute the +system of co-ordinates are generally not available; +furthermore, the magnitudes of the co-ordinates are not +actually determined by constructions with rigid rods, but +by indirect means. If the results of physics and astronomy +\index{Astronomy}% +are to maintain their clearness, the physical meaning +\PageSep{8} +of specifications of position must always be sought +in accordance with the above considerations.\footnote + {A refinement and modification of these views does not become + necessary until we come to deal with the general theory of + relativity, treated in the second part of this book.} + +We thus obtain the following result: Every description +of events in space involves the use of a rigid body +to which such events have to be referred. The resulting +relationship takes for granted that the laws of Euclidean +\index{Distance (line-interval)}% +\index{Euclidean geometry!propositions of}% +geometry hold for ``distances,'' the ``distance'' being +represented physically by means of the convention of +two marks on a rigid body. +\PageSep{9} + + +\Chapter{III}{Space and Time in Classical Mechanics} +\index{Classical mechanics}% +\index{Space}% + +\Change{}{``}\First{The} purpose of mechanics is to describe how +bodies change their position in space with +\index{Position}% +time.'' I should load my conscience with grave +sins against the sacred spirit of lucidity were I to +formulate the aims of mechanics in this way, without +serious reflection and detailed explanations. Let us +proceed to disclose these sins. + +It is not clear what is to be understood here by +\index{Reference-body|(}% +``position'' and ``space.'' I stand at the window of a +railway carriage which is travelling uniformly, and drop +a stone on the embankment, without throwing it. Then, +disregarding the influence of the air resistance, I see the +stone descend in a straight line. A pedestrian who +\index{Straight line}% +observes the misdeed from the footpath notices that the +stone falls to earth in a parabolic curve. I now ask: +Do the ``positions'' traversed by the stone lie ``in +reality'' on a straight line or on a parabola? Moreover, +\index{Parabola}% +what is meant here by motion ``in space''? From the +considerations of the previous section the answer is +self-evident. In the first place, we entirely shun the +vague word ``space,'' of which, we must honestly +acknowledge, we cannot form the slightest conception, +and we replace it by ``motion relative to a +practically rigid body of reference.'' The positions +relative to the body of reference (railway carriage or +embankment) have already been defined in detail in the +\PageSep{10} +preceding section. If instead of ``body of reference'' +we insert ``system of co-ordinates,'' which is a useful +\index{System of co-ordinates}% +idea for mathematical description, we are in a position +to say: The stone traverses a straight line relative to a +\index{Straight line}% +system of co-ordinates rigidly attached to the carriage, +but relative to a system of co-ordinates rigidly attached +to the ground (embankment) it describes a parabola. +\index{Parabola}% +With the aid of this example it is clearly seen that there +is no such thing as an independently existing trajectory +\index{Trajectory}% +(lit. ``path-curve''\footnotemark), but only a trajectory relative to a +\index{Path-curve}% +particular body of reference. +\footnotetext{That is, a curve along which the body moves.} + +In order to have a \emph{complete} description of the motion, +we must specify how the body alters its position \emph{with +time}; \ie\ for every point on the trajectory it must be +stated at what time the body is situated there. These +data must be supplemented by such a definition of +time that, in virtue of this definition, these time-values +can be regarded essentially as magnitudes (results of +measurements) capable of observation. If we take our +stand on the ground of classical mechanics, we can +satisfy this requirement for our illustration in the +following manner. We imagine two clocks of identical +\index{Clocks}% +construction; the man at the railway-carriage window +is holding one of them, and the man on the footpath +the other. Each of the observers determines +the position on his own reference-body occupied by the +stone at each tick of the clock he is holding in his +hand. In this connection we have not taken account +of the inaccuracy involved by the finiteness of the +velocity of propagation of light. With this and with a +\index{Velocity of light}% +second difficulty prevailing here we shall have to deal +in detail later. +\PageSep{11} + + +\Chapter{IV}{The Galileian System of Co-ordinates} +\index{Galileian system of co-ordinates}% +\index{System of co-ordinates}% + +\First{As} is well known, the fundamental law of the +mechanics of Galilei-Newton, which is known +\index{Galilei}% +\index{Newton}% +as the \emph{law of inertia}, can be stated thus: +\index{Law of inertia}% +A body removed sufficiently far from other bodies +continues in a state of rest or of uniform motion +in a straight line. This law not only says something +about the motion of the bodies, but it also +indicates the reference-bodies or systems of co-ordinates, +permissible in mechanics, which can be used +in mechanical description. The visible fixed stars are +\index{Fixed stars}% +bodies for which the law of inertia certainly holds to a +high degree of approximation. Now if we use a system +of co-ordinates which is rigidly attached to the earth, +then, relative to this system, every fixed star describes +a circle of immense radius in the course of an astronomical +day, a result which is opposed to the statement +\index{Astronomical day}% +of the law of inertia. So that if we adhere to this law +we must refer these motions only to systems of co-ordinates +relative to which the fixed stars do not move +in a circle. A system of co-ordinates of which the state +of motion is such that the law of inertia holds relative to +it is called a ``Galileian system of co-ordinates.'' The +laws of the mechanics of Galilei-Newton can be regarded +as valid only for a Galileian system of co-ordinates. +\index{Reference-body|)}% +\PageSep{12} + + +\Chapter{V}{The Principle of Relativity (In the +Restricted Sense)} + +\First{In} order to attain the greatest possible clearness, +let us return to our example of the railway carriage +supposed to be travelling uniformly. We call its +motion a uniform translation (``uniform'' because +\index{Uniform translation}% +it is of constant velocity and direction, ``translation'' +because although the carriage changes its position +relative to the embankment yet it does not rotate +in so doing). Let us imagine a raven flying through +the air in such a manner that its motion, as observed +from the embankment, is uniform and in a straight +line. If we were to observe the flying raven from +the moving railway carriage, we should find that the +motion of the raven would be one of different velocity +and direction, but that it would still be uniform +and in a straight line. Expressed in an abstract +manner we may say: If a mass~$m$ is moving uniformly +in a straight line with respect to a co-ordinate +system~$K$, then it will also be moving uniformly and in a +straight line relative to a second co-ordinate system~$K'$, +provided that the latter is executing a uniform +translatory motion with respect to~$K$. In accordance +with the discussion contained in the preceding section, +it follows that: +\PageSep{13} + +If $K$~is a Galileian co-ordinate system, then every other +\index{Galileian system of co-ordinates}% +co-ordinate system~$K'$ is a Galileian one, when, in relation +to~$K$, it is in a condition of uniform motion of translation. +\index{Motion!of heavenly bodies}% +Relative to~$K'$ the mechanical laws of Galilei-Newton +\index{Laws of Galilei-Newton}% +hold good exactly as they do with respect to~$K$. + +We advance a step farther in our generalisation when +we express the tenet thus: If, relative to~$K$, $K'$~is a +uniformly moving co-ordinate system devoid of rotation, +then natural phenomena run their course with respect to~$K'$ +according to exactly the same general laws as with +respect to~$K$. This statement is called the \emph{principle +of relativity} (in the restricted sense). + +As long as one was convinced that all natural phenomena +were capable of representation with the help of +classical mechanics, there was no need to doubt the +\index{Classical mechanics}% +\index{Classical mechanics!truth of}% +validity of this principle of relativity. But in view of +\index{Principle of relativity|(}% +the more recent development of electrodynamics and +\index{Electrodynamics}% +optics it became more and more evident that classical +\index{Optics}% +mechanics affords an insufficient foundation for the +physical description of all natural phenomena. At this +juncture the question of the validity of the principle of +relativity became ripe for discussion, and it did not +appear impossible that the answer to this question +might be in the negative. + +Nevertheless, there are two general facts which at the +outset speak very much in favour of the validity of the +principle of relativity. Even though classical mechanics +does not supply us with a sufficiently broad basis for the +theoretical presentation of all physical phenomena, +still we must grant it a considerable measure of ``truth,'' +since it supplies us with the actual motions of the +heavenly bodies with a delicacy of detail little short of +wonderful. The principle of relativity must therefore +\PageSep{14} +apply with great accuracy in the domain of \emph{mechanics}. +\index{Classical mechanics}% +But that a principle of such broad generality should +hold with such exactness in one domain of phenomena, +and yet should be invalid for another, is \textit{a~priori} not +very probable. + +We now proceed to the second argument, to which, +moreover, we shall return later. If the principle of relativity +(in the restricted sense) does not hold, then the +Galileian co-ordinate systems $K$,~$K'$, $K''$,~etc., which are +\index{Galileian system of co-ordinates}% +moving uniformly relative to each other, will not be +\emph{equivalent} for the description of natural phenomena. +\index{Equivalent}% +In this case we should be constrained to believe that +natural laws are capable of being formulated in a particularly +simple manner, and of course only on condition +that, from amongst all possible Galileian co-ordinate +systems, we should have chosen \emph{one}~($K_{0}$) of a particular +state of motion as our body of reference. We should +\index{Motion}% +then be justified (because of its merits for the description +of natural phenomena) in calling this system ``absolutely +at rest,'' and all other Galileian systems~$K$ ``in motion.'' +\index{Rest}% +If, for instance, our embankment were the system~$K_{0}$, +then our railway carriage would be a system~$K$, +relative to which less simple laws would hold than with +respect to~$K_{0}$. This diminished simplicity would be +due to the fact that the carriage~$K$ would be in motion +(\ie\ ``really'') with respect to~$K_{0}$. In the general laws +of nature which have been formulated with reference +to~$K$, the magnitude and direction of the velocity +of the carriage would necessarily play a part. We should +expect, for instance, that the note emitted by an organ-pipe +\index{Organ-pipe, note of}% +placed with its axis parallel to the direction of +travel would be different from that emitted if the axis +of the pipe were placed perpendicular to this direction. +\PageSep{15} +Now in virtue of its motion in an orbit round the sun, +\index{Motion!of heavenly bodies}% +our earth is comparable with a railway carriage travelling +with a velocity of about $30$~kilometres per~second. +If the principle of relativity were not valid we should +therefore expect that the direction of motion of the +earth at any moment would enter into the laws of nature, +and also that physical systems in their behaviour would +be dependent on the orientation in space with respect +to the earth. For owing to the alteration in direction +of the velocity of revolution of the earth in the course +of a year, the earth cannot be at rest relative to the +hypothetical system~$K_{0}$ throughout the whole year. +However, the most careful observations have never +revealed such anisotropic properties in terrestrial physical +\index{Terrestrial space}% +space, \ie\ a physical non-equivalence of different +directions. This is very powerful argument in favour +of the principle of relativity. +\index{Principle of relativity|)}% +\PageSep{16} + + +\Chapter{VI}{The Theorem of the Addition of Velocities +employed in Classical Mechanics} +\index{Addition of velocities}% +\index{Classical mechanics}% + +\First{Let} us suppose our old friend the railway carriage +to be travelling along the rails with a constant +velocity~$v$, and that a man traverses the length of +the carriage in the direction of travel with a velocity~$w$. +How quickly or, in other words, with what velocity~$W$ +does the man advance relative to the embankment +during the process? The only possible answer seems to +result from the following consideration: If the man were +to stand still for a second, he would advance relative to +the embankment through a distance~$v$ equal numerically +to the velocity of the carriage. As a consequence of +his walking, however, he traverses an additional distance~$w$ +relative to the carriage, and hence also relative to the +embankment, in this second, the distance~$w$ being +numerically equal to the velocity with which he is +walking. Thus in total he covers the distance $W = v + w$ +relative to the embankment in the second considered. +We shall see later that this result, which expresses +the theorem of the addition of velocities employed in +classical mechanics, cannot be maintained; in other +words, the law that we have just written down does not +hold in reality. For the time being, however, we shall +assume its correctness. +\PageSep{17} + + +\Chapter{VII}{The Apparent Incompatibility of the +Law of Propagation of Light with +the Principle of Relativity} +\index{Propagation of light}% + +\First{There} is hardly a simpler law in physics than +that according to which light is propagated in +empty space. Every child at school knows, or +believes he knows, that this propagation takes place +in straight lines with a velocity $c = 300,000$~km./sec. +At all events we know with great exactness that this +velocity is the same for all colours, because if this were +not the case, the minimum of emission would not be +observed simultaneously for different colours during +the eclipse of a fixed star by its dark neighbour. By +\index{DeSitter@{De Sitter}}% +\index{Eclipse of star}% +means of similar considerations based on observations +of double stars, the Dutch astronomer De~Sitter +\index{Double stars}% +was also able to show that the velocity of propagation +of light cannot depend on the velocity of motion +of the body emitting the light. The assumption that +this velocity of propagation is dependent on the direction +``in space'' is in itself improbable. + +In short, let us assume that the simple law of the +constancy of the velocity of light~$c$ (in vacuum) is +\index{Velocity of light}% +justifiably believed by the child at school. Who would +imagine that this simple law has plunged the conscientiously +thoughtful physicist into the greatest +\PageSep{18} +intellectual difficulties? Let us consider how these +difficulties arise. + +Of course we must refer the process of the propagation +of light (and indeed every other process) to a rigid +reference-body (co-ordinate system). As such a system +\index{Reference-body}% +let us again choose our embankment. We shall imagine +the air above it to have been removed. If a ray of +light be sent along the embankment, we see from the +above that the tip of the ray will be transmitted with +the velocity~$c$ relative to the embankment. Now let +us suppose that our railway carriage is again travelling +along the railway lines with the velocity~$v$, and that +its direction is the same as that of the ray of light, but +its velocity of course much less. Let us inquire about +the velocity of propagation of the ray of light relative +to the carriage. It is obvious that we can here apply the +consideration of the previous section, since the ray of +light plays the part of the man walking along relatively +to the carriage. The velocity~$W$ of the man relative +to the embankment is here replaced by the velocity +of light relative to the embankment. $w$~is the required +velocity of light with respect to the carriage, and we +\index{Velocity of light}% +have +\[ +w = c - v. +\] +The velocity of propagation of a ray of light relative to +the carriage thus comes out smaller than~$c$. + +But this result comes into conflict with the principle +of relativity set forth in \Sectionref{V}. For, like every +other general law of nature, the law of the transmission +of light \textit{in~vacuo} must, according to the principle of +relativity, be the same for the railway carriage as +reference-body as when the rails are the body of reference. +\PageSep{19} +But, from our above consideration, this would +appear to be impossible. If every ray of light is propagated +relative to the embankment with the velocity~$c$, +then for this reason it would appear that another law +of propagation of light must necessarily hold with respect +\index{Propagation of light}% +to the carriage---a result contradictory to the principle +of relativity. + +In view of this dilemma there appears to be nothing +else for it than to abandon either the principle of relativity +\index{Principle of relativity}% +or the simple law of the propagation of light \textit{in~vacuo}. +Those of you who have carefully followed the +preceding discussion are almost sure to expect that +we should retain the principle of relativity, which +appeals so convincingly to the intellect because it is so +natural and simple. The law of the propagation of +light \textit{in~vacuo} would then have to be replaced by a +more complicated law conformable to the principle of +relativity. The development of theoretical physics +shows, however, that we cannot pursue this course. +The epoch-making theoretical investigations of H.~A. +Lorentz on the electrodynamical and optical phenomena +\index{Electrodynamics}% +\index{Optics}% +\index{Lorentz, H. A.}% +connected with moving bodies show that experience +in this domain leads conclusively to a theory of electromagnetic +phenomena, of which the law of the constancy +of the velocity of light \textit{in~vacuo} is a necessary consequence. +Prominent theoretical physicists were therefore +more inclined to reject the principle of relativity, +in spite of the fact that no empirical data had been +found which were contradictory to this principle. + +At this juncture the theory of relativity entered the +arena. As a result of an analysis of the physical conceptions +of time and space, it became evident that \emph{in +\index{Space!conception of}% +\index{Time!conception of}% +reality there is not the least incompatibility between the +\PageSep{20} +principle of relativity and the law of propagation of light}, +\index{Principle of relativity}% +\index{Propagation of light}% +and that by systematically holding fast to both these +laws a logically rigid theory could be arrived at. This +theory has been called the \emph{special theory of relativity} +\index{Special theory of relativity}% +to distinguish it from the extended theory, with which +we shall deal later. In the following pages we shall +present the fundamental ideas of the special theory of +relativity. +\PageSep{21} + + +\Chapter{VIII}{On the Idea of Time in Physics} +\index{Time!in Physics}% + +\First{Lightning} has struck the rails on our railway +embankment at two places $A$~and~$B$ far distant +from each other. I make the additional assertion +that these two lightning flashes occurred simultaneously. +If I ask you whether there is sense in this statement, +you will answer my question with a decided +``Yes.'' But if I now approach you with the request +to explain to me the sense of the statement more +precisely, you find after some consideration that the +answer to this question is not so easy as it appears at +first sight. + +After some time perhaps the following answer would +occur to you: ``The significance of the statement is +clear in itself and needs no further explanation; of +course it would require some consideration if I were to +be commissioned to determine by observations whether +in the actual case the two events took place simultaneously +or not.'' I cannot be satisfied with this answer +for the following reason. Supposing that as a result +of ingenious considerations an able meteorologist were +to discover that the lightning must always strike the +places $A$~and~$B$ simultaneously, then we should be faced +with the task of testing whether or not this theoretical +result is in accordance with the reality. We encounter +\PageSep{22} +the same difficulty with all physical statements in which +the conception ``simultaneous'' plays a part. The +concept does not exist for the physicist until he has the +possibility of discovering whether or not it is fulfilled +in an actual case. We thus require a definition of +simultaneity such that this definition supplies us with +\index{Simultaneity}% +the method by means of which, in the present case, he +can decide by experiment whether or not both the +lightning strokes occurred simultaneously. As long +as this requirement is not satisfied, I allow myself to be +deceived as a physicist (and of course the same applies +if I am not a physicist), when I imagine that I am able +to attach a meaning to the statement of simultaneity. +(I would ask the reader not to proceed farther until he +is fully convinced on this point.) + +After thinking the matter over for some time you +then offer the following suggestion with which to test +simultaneity. By measuring along the rails, the +connecting line~$AB$ should be measured up and an +observer placed at the mid-point~$M$ of the distance~$AB$. +This observer should be supplied with an arrangement +(\eg\ two mirrors inclined at~$90°$) which allows him +visually to observe both places $A$~and~$B$ at the same +time. If the observer perceives the two flashes of +lightning at the same time, then they are simultaneous. + +I am very pleased with this suggestion, but for all +that I cannot regard the matter as quite settled, because +I feel constrained to raise the following objection: +``Your definition would certainly be right, if I only +knew that the light by means of which the observer +at~$M$ perceives the lightning flashes travels along the +length $A\longrightarrow M$ with the same velocity as along the +length $B\longrightarrow M$. But an examination of this supposition +\PageSep{23} +would only be possible if we already had at our +disposal the means of measuring time. It would thus +appear as though we were moving here in a logical circle.'' + +After further consideration you cast a somewhat +disdainful glance at me---and rightly so---and you +declare: ``I maintain my previous definition nevertheless, +because in reality it assumes absolutely nothing +about light. There is only \emph{one} demand to be made of +the definition of simultaneity, namely, that in every +real case it must supply us with an empirical decision +as to whether or not the conception that has to +be defined is fulfilled. That my definition satisfies +this demand is indisputable. That light requires the +same time to traverse the path $A\longrightarrow M$ as for the path +$B\longrightarrow M$ is in reality neither a \emph{supposition nor a hypothesis} +about the physical nature of light, but a \emph{stipulation} +which I can make of my own \Change{freewill}{free will} in order to arrive +at a definition of simultaneity.'' + +It is clear that this definition can be used to give an +exact meaning not only to \emph{two} events, but to as many +events as we care to choose, and independently of the +positions of the scenes of the events with respect to the +\index{Reference-body}% +body of reference\footnote + {We suppose further, that, when three events $A$,~$B$ and~$C$ + occur in different places in such a manner that $A$~is simultaneous + with~$,$ and $B$~is simultaneous with~$C$ (simultaneous + in the sense of the above definition), then the criterion for the + simultaneity of the pair of events $A$,~$C$ is also satisfied. This + assumption is a physical hypothesis about the law of propagation + of light; it must certainly be fulfilled if we are to maintain the + law of the constancy of the velocity of light \textit{in~vacuo}.} +(here the railway embankment). +We are thus led also to a definition of ``time'' in physics. +For this purpose we suppose that clocks of identical +\index{Clocks}% +construction are placed at the points $A$,~$B$ and~$C$ of +\PageSep{24} +\index{Simultaneity|(}% +the railway line (co-ordinate system), and that they +are set in such a manner that the positions of their +pointers are simultaneously (in the above sense) the +same. Under these conditions we understand by the +``time'' of an event the reading (position of the hands) +\index{Time!of an event}% +of that one of these clocks which is in the immediate +vicinity (in space) of the event. In this manner a +time-value is associated with every event which is +essentially capable of observation. + +This stipulation contains a further physical hypothesis, +the validity of which will hardly be doubted without +empirical evidence to the contrary. It has been assumed +that all these clocks go \emph{at the same rate} if they are of +identical construction. Stated more exactly: When +two clocks arranged at rest in different places of a +reference-body are set in such a manner that a \emph{particular} +position of the pointers of the one clock is \emph{simultaneous} +(in the above sense) with the \emph{same} position of the +pointers of the other clock, then identical ``settings'' +are always simultaneous (in the sense of the above +definition). +\PageSep{25} + + +\Chapter{IX}{The Relativity of Simultaneity} + +\First{Up} to now our considerations have been referred +\index{Reference-body}% +to a particular body of reference, which we +have styled a ``railway embankment.'' We +suppose a very long train travelling along the rails +with the constant velocity~$v$ and in the direction indicated +in \Figref{1}. People travelling in this train will +with advantage use the train as a rigid reference-body +(co-ordinate system); they regard all events in +%[Illustration: Fig. 1.] +\Figure{025} +reference to the train. Then every event which takes +place along the line also takes place at a particular +point of the train. Also the definition of simultaneity +can be given relative to the train in exactly the same +way as with respect to the embankment. As a natural +consequence, however, the following question arises: + +Are two events (\eg\ the two strokes of lightning $A$ +and~$B$) which are simultaneous \emph{with reference to the +railway embankment} also simultaneous \emph{relatively to the +train}? We shall show directly that the answer must +be in the negative. + +When we say that the lightning strokes $A$~and~$B$ are +\PageSep{26} +simultaneous with respect to the embankment, we +mean: the rays of light emitted at the places $A$~and~$B$, +where the lightning occurs, meet each other at the +mid-point~$M$ of the length $A\longrightarrow B$ of the embankment. +But the events $A$~and~$B$ also correspond to positions $A$~and~$B$ +\index{Time!of an event}% +on the train. Let $M'$~be the mid-point of the +distance $A\longrightarrow B$ on the travelling train. Just when +the flashes\footnote + {As judged from the embankment.} +of lightning occur, this point~$M'$ naturally +coincides with the point~$M$, but it moves towards the +right in the diagram with the velocity~$v$ of the train. If +an observer sitting in the position~$M'$ in the train did +not possess this velocity, then he would remain permanently +at~$M$, and the light rays emitted by the +flashes of lightning $A$~and~$B$ would reach him simultaneously, +\ie\ they would meet just where he is situated. +Now in reality (considered with reference to the railway +embankment) he is hastening towards the beam of light +coming from~$B$, whilst he is riding on ahead of the beam +of light coming from~$A$. Hence the observer will see +the beam of light emitted from~$B$ earlier than he will +see that emitted from~$A$. Observers who take the railway +train as their reference-body must therefore come +\index{Reference-body}% +to the conclusion that the lightning flash~$B$ took place +earlier than the lightning flash~$A$. We thus arrive at +the important result: + +Events which are simultaneous with reference to the +embankment are not simultaneous with respect to the +train, and \textit{vice versa} (relativity of simultaneity). Every +\index{Simultaneity|)}% +\index{Simultaneity!relativity of}% +reference-body (co-ordinate system) has its own particular +time; unless we are told the reference-body to which +the statement of time refers, there is no meaning in a +statement of the time of an event. +\PageSep{27} + +Now before the advent of the theory of relativity +it had always tacitly been assumed in physics that the +statement of time had an absolute significance, \ie\ +that it is independent of the state of motion of the body +of reference. But we have just seen that this assumption +is incompatible with the most natural definition +of simultaneity; if we discard this assumption, then +the conflict between the law of the propagation of +light \textit{in~vacuo} and the principle of relativity (developed +in \Sectionref{VII}) disappears. + +We were led to that conflict by the considerations +of \Sectionref{VI}, which are now no longer tenable. In +that section we concluded that the man in the carriage, +who traverses the distance~$w$ \emph{per~second} relative to the +carriage, traverses the same distance also with respect to +the embankment \emph{in each second} of time. But, according +to the foregoing considerations, the time required by a +particular occurrence with respect to the carriage must +not be considered equal to the duration of the same +occurrence as judged from the embankment (as reference-body). +Hence it cannot be contended that the +man in walking travels the distance~$w$ relative to the +railway line in a time which is equal to one second as +judged from the embankment. + +Moreover, the considerations of \Sectionref{VI} are based +on yet a second assumption, which, in the light of a +strict consideration, appears to be arbitrary, although +it was always tacitly made even before the introduction +of the theory of relativity. +\PageSep{28} + + +\Chapter{X}{On the Relativity of the Conception +of Distance} +\index{Distance (line-interval)}% +\index{Distance (line-interval)!relativity of}% + +\First{Let} us consider two particular points on the train\footnote + {\eg\ the middle of the first and of the hundredth carriage.} +travelling along the embankment with the +velocity~$v$, and inquire as to their distance apart. +We already know that it is necessary to have a body of +reference for the measurement of a distance, with respect +to which body the distance can be measured up. It is +the simplest plan to use the train itself as reference-body +(co-ordinate system). An observer in the train +measures the interval by marking off his measuring-rod +\index{Measuring-rod}% +in a straight line (\eg\ along the floor of the carriage) +as many times as is necessary to take him from the one +marked point to the other. Then the number which +tells us how often the rod has to be laid down is the +required distance. + +It is a different matter when the distance has to be +judged from the railway line. Here the following +method suggests itself. If we call $A'$~and~$B'$ the two +points on the train whose distance apart is required, +then both of these points are moving with the velocity~$v$ +along the embankment. In the first place we require to +determine the points $A$~and~$B$ of the embankment which +are just being passed by the two points $A'$~and~$B'$ at a +\PageSep{29} +particular time~$t$---judged from the embankment. +These points $A$~and~$B$ of the embankment can be determined +by applying the definition of time given in +\Sectionref{VIII}. The distance between these points $A$~and~$B$ +\index{Distance (line-interval)}% +is then measured by repeated application of the +measuring-rod along the embankment. + +\textit{A~priori} it is by no means certain that this last +measurement will supply us with the same result as +the first. Thus the length of the train as measured +from the embankment may be different from that +obtained by measuring in the train itself. This +circumstance leads us to a second objection which must +be raised against the apparently obvious consideration +of \Sectionref{VI}. Namely, if the man in the carriage +covers the distance~$w$ in a unit of time---\emph{measured from +the train},---then this distance---\emph{as measured from the +embankment}---is not necessarily also equal to~$w$. +\PageSep{30} + + +\Chapter{XI}{The Lorentz Transformation} + +\First{The} results of the last three sections show +that the apparent incompatibility of the law +of propagation of light with the principle of +relativity (\Sectionref{VII}) has been derived by means of +a consideration which borrowed two unjustifiable +hypotheses from classical mechanics; these are as +\index{Classical mechanics}% +follows: +\begin{itemize} +\item[(1)] The time-interval (time) between two events is +\index{Time-interval}% + independent of the condition of motion of the + body of reference. + +\item[(2)] The space-interval (distance) between two points +\index{Space!interval@{-interval}}% + of a rigid body is independent of the condition + of motion of the body of reference. +\end{itemize} + +If we drop these hypotheses, then the dilemma of +\Sectionref{VII} disappears, because the theorem of the addition +of velocities derived in \Sectionref{VI} becomes invalid. +The possibility presents itself that the law of the propagation +of light \textit{in~vacuo} may be compatible with the +principle of relativity, and the question arises: How +have we to modify the considerations of \Sectionref{VI} +in order to remove the apparent disagreement between +these two fundamental results of experience? This +question leads to a general one. In the discussion of +\PageSep{31} +\Sectionref{VI} we have to do with places and times relative +both to the train and to the embankment. How are +we to find the place and time of an event in relation to +the train, when we know the place and time of the +event with respect to the railway embankment? Is +there a thinkable answer to this question of such a +nature that the law of transmission of light \textit{in~vacuo} +does not contradict the principle of relativity? In +other words: Can we conceive of a relation between +place and time of the individual events relative to both +reference-bodies, such that every ray of light possesses +the velocity of transmission~$c$ relative to the embankment +and relative to the train? This question leads to +a quite definite positive answer, and to a perfectly definite +transformation law for the space-time magnitudes of +an event when changing over from one body of reference +to another. + +Before we deal with this, we shall introduce the +following incidental consideration. Up to the present +we have only considered events taking place along the +embankment, which had mathematically to assume the +function of a straight line. In the manner indicated +in \Sectionref{II} we can imagine this reference-body supplemented +laterally and in a vertical direction by means of +a framework of rods, so that an event which takes place +anywhere can be localised with reference to this framework. +Similarly, we can imagine the train travelling +with the velocity~$v$ to be continued across the whole of +space, so that every event, no matter how far off it +may be, could also be localised with respect to the second +framework. Without committing any fundamental error, +we can disregard the fact that in reality these frameworks +would continually interfere with each other, owing +\PageSep{32} +\index{Propagation of light}% +to the impenetrability of solid bodies. In every such +framework we imagine three surfaces perpendicular to +each other marked out, and designated as ``co-ordinate +\index{Coordinate@{Co-ordinate}!planes}% +planes'' (``co-ordinate system''). A co-ordinate +system~$K$ then corresponds to the embankment, and a +co-ordinate system~$K'$ to the train. An event, wherever +it may have taken place, would be fixed in space with +respect to~$K$ by the three perpendiculars $x$,~$y$,~$z$ on the +co-ordinate planes, and with regard to time by a time-value~$t$. +Relative to~$K'$, \emph{the +same event} would be fixed +in respect of space and time +by corresponding values $x'$,~$y'$, +$z'$,~$t'$, which of course are +not identical with $x$,~$y$, $z$,~$t$. +It has already been set +forth in detail how these +magnitudes are to be regarded +as results of physical measurements. +%[Illustration: Fig. 2.] +\Figure[2in]{032} + +Obviously our problem can be exactly formulated in +the following manner. What are the values $x'$,~$y'$, $z'$,~$t'$, +of an event with respect to~$K'$, when the magnitudes +$x$,~$y$, $z$,~$t$, of the same event with respect to~$K$ are given? +The relations must be so chosen that the law of the +transmission of light \textit{in~vacuo} is satisfied for one and the +same ray of light (and of course for every ray) with +respect to $K$ and~$K'$. For the relative orientation in +space of the co-ordinate systems indicated in the diagram +(\Figref{2}), this problem is solved by means of the +equations: +\begin{align*} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,}\displaybreak[1] \\ +\PageSep{33} +y' &= y\Add{,} \\ +z' &= z\Add{,} \\ +t' &= \frac{t - \dfrac{v}{c^{2}}·x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Change{}{.} +\end{align*} +This system of equations is known as the ``Lorentz +\index{Lorentz, H. A.!transformation}% +transformation.''\footnote + {A simple derivation of the Lorentz transformation is given + in \Appendixref{I}.} + +If in place of the law of transmission of light we had +taken as our basis the tacit assumptions of the older +mechanics as to the absolute character of times and +lengths, then instead of the above we should have +obtained the following equations: +\begin{align*} +x' &= x - vt\Add{,} \\ +y' &= y\Add{,} \\ +z' &= z\Add{,} \\ +t' &= t. +\end{align*} +This system of equations is often termed the ``Galilei +\index{Galilei!transformation}% +transformation.'' The Galilei transformation can be +obtained from the Lorentz transformation by substituting +an infinitely large value for the velocity of +light~$c$ in the latter transformation. + +Aided by the following illustration, we can readily +see that, in accordance with the Lorentz transformation, +the law of the transmission of light \textit{in~vacuo} +is satisfied both for the reference-body~$K$ and for the +reference-body~$K'$. A light-signal is sent along the +\index{Light-signal}% +positive $x$-axis, and this light-stimulus advances in +\index{Light-stimulus}% +accordance with the equation +\[ +x = ct, +\] +\PageSep{34} +\ie\ with the velocity~$c$. According to the equations of +the Lorentz transformation, this simple relation between +$x$~and~$t$ involves a relation between $x'$~and~$t'$. In point +of fact, if we substitute for~$x$ the value~$ct$ in the first +and fourth equations of the Lorentz transformation, +we obtain: +\begin{align*} +x' &= \frac{(c - v)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,} \\ +t' &= \frac{\left(1 - \dfrac{v}{c}\right)t}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +\end{align*} +from which, by division, the expression +\[ +x' = ct' +\] +immediately follows. If referred to the system~$K'$, the +propagation of light takes place according to this +equation. We thus see that the velocity of transmission +relative to the reference-body~$K'$ is also equal to~$c$. The +same result is obtained for rays of light advancing in +any other direction whatsoever. Of course this is not +surprising, since the equations of the Lorentz transformation +were derived conformably to this point of +view. +\PageSep{35} + + +\Chapter{XII}{The Behaviour of Measuring-Rods and +Clocks in Motion} + +\First{I place} a metre-rod in the $x'$-axis of~$K'$ in such a +manner that one end (the beginning) coincides with +the point $x' = 0$, whilst the other end (the end of the +rod) coincides with the point $x' = 1$. What is the length +of the metre-rod relatively to the system~$K$? In order +to learn this, we need only ask where the beginning of the +rod and the end of the rod lie with respect to~$K$ at a +particular time~$t$ of the system~$K$. By means of the first +equation of the Lorentz transformation the values of +these two points at the time $t = 0$ can be shown to be +\begin{align*} +x_{\text{(beginning of rod)}} + &= 0·\sqrt{1 - \frac{v^{2}}{c^{2}}}\Add{,} \\ +x_{\text{(end of rod)}} + &= 1·\sqrt{1 - \frac{v^{2}}{c^{2}}}, +\end{align*} +the distance between the points being~$\sqrt{1 - \dfrac{v^{2}}{c^{2}}}$. But +the metre-rod is moving with the velocity~$v$ relative to~$K$. +It therefore follows that the length of a rigid metre-rod +moving in the direction of its length with a velocity~$v$ +is $\sqrt{1 - v^{2}/c^{2}}$~of a metre. The rigid rod is thus +shorter when in motion than when at rest, and the +more quickly it is moving, the shorter is the rod. For +the velocity $v = c$ we should have $\sqrt{1 - v^{2}/c^{2}} = 0$, and +for still greater velocities the square-root becomes +\PageSep{36} +imaginary. From this we conclude that in the theory +of relativity the velocity~$c$ plays the part of a limiting +\index{Limiting velocity ($c$)}% +velocity, which can neither be reached nor exceeded +by any real body. + +Of course this feature of the velocity~$c$ as a limiting +velocity also clearly follows from the equations of the +Lorentz transformation, for these become meaningless +if we choose values of~$v$ greater than~$c$. + +If, on the contrary, we had considered a metre-rod +at rest in the $x$-axis with respect to~$K$, then we should +have found that the length of the rod as judged from~$K'$ +would have been~$\sqrt{1 - v^{2}/c^{2}}$; this is quite in accordance +with the principle of relativity which forms the +basis of our considerations. + +\textit{A~priori} it is quite clear that we must be able to +learn something about the physical behaviour of measuring-rods +and clocks from the equations of transformation, +for the magnitudes $x$,~$y$, $z$,~$t$, are nothing more nor +less than the results of measurements obtainable by +means of measuring-rods and clocks. If we had based +our considerations on the Galilei transformation we +\index{Galilei!transformation}% +should not have obtained a contraction of the rod as a +consequence of its motion. + +Let us now consider a seconds-clock which is permanently +\index{Seconds-clock}% +situated at the origin ($x' = 0$) of~$K'$. $t' = 0$ +and $t' = 1$ are two successive ticks of this clock. The +first and fourth equations of the Lorentz transformation +give for these two ticks: +\begin{align*} +t &= 0 \\ +\intertext{and} +t &= \frac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{align*} +\PageSep{37} + +As judged from~$K$, the clock is moving with the +velocity~$v$; as judged from this reference-body, the +\index{Reference-body}% +time which elapses between two strokes of the clock +is not one second, but $\dfrac{1}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}$~seconds, \ie\ a somewhat +larger time. As a consequence of its motion +the clock goes more slowly than when at rest. Here +also the velocity~$c$ plays the part of an unattainable +limiting velocity. +\index{Limiting velocity ($c$)}% +\PageSep{38} + + +\Chapter{XIII}{Theorem of the Addition of Velocities. +The Experiment of Fizeau} +\index{Addition of velocities}% + +\First{Now} in practice we can move clocks and +measuring-rods only with velocities that are +small compared with the velocity of light; hence +we shall hardly be able to compare the results of the +previous section directly with the reality. But, on the +other hand, these results must strike you as being very +singular, and for that reason I shall now draw another +conclusion from the theory, one which can easily be +derived from the foregoing considerations, and which +has been most elegantly confirmed by experiment. + +In \Sectionref{VI} we derived the theorem of the addition +of velocities in one direction in the form which also +results from the hypotheses of classical mechanics. This +theorem can also be deduced readily from the Galilei +\index{Galilei!transformation}% +transformation (\Sectionref{XI}). In place of the man +walking inside the carriage, we introduce a point moving +relatively to the co-ordinate system~$K'$ in accordance +with the equation +\[ +x' = wt'. +\] +By means of the first and fourth equations of the Galilei +transformation we can express $x'$~and~$t'$ in terms of $x$~and~$t$, +and we then obtain +\[ +x = (v + w)t. +\] +\PageSep{39} +This equation expresses nothing else than the law of +motion of the point with reference to the system~$K$ +(of the man with reference to the embankment). We +denote this velocity by the symbol~$W$, and we then +obtain, as in \Sectionref{VI}, +\[ +W = v + w. +\Tag{(A)} +\] + +But we can carry out this consideration just as well +on the basis of the theory of relativity. In the equation +\[ +x' = wt' +\] +we must then express $x'$~and~$t'$ in terms of $x$~and~$t$, making +use of the first and fourth equations of the \emph{Lorentz +\index{Lorentz, H. A.!transformation}% +transformation}. Instead of the equation~\Eqref{(A)} we then +obtain the equation +\[ +W = \frac{v + w}{1 + \dfrac{vw}{c^{2}}}, +\Tag{(B)} +\] +which corresponds to the theorem of addition for +velocities in one direction according to the theory of +relativity. The question now arises as to which of these +two theorems is the better in accord with experience. On +this point we are enlightened by a most important experiment +which the brilliant physicist Fizeau performed more +\index{Fizeau}% +\index{Fizeau!experiment of}% +than half a century ago, and which has been repeated +since then by some of the best experimental physicists, +so that there can be no doubt about its result. The +experiment is concerned with the following question. +Light travels in a motionless liquid with a particular +velocity~$w$. How quickly does it travel in the direction +of the arrow in the tube~$T$ (see the accompanying diagram, +\Figref{3}) when the liquid above mentioned is flowing +through the tube with a velocity~$v$? +\PageSep{40} + +In accordance with the principle of relativity we shall +\index{Propagation of light!in liquid}% +certainly have to take for granted that the propagation +of light always takes place with the same velocity~$w$ +\emph{with respect to the liquid}, whether the latter is in motion +with reference to other bodies or not. The velocity +of light relative to the liquid and the velocity of the +latter relative to the tube are thus known, and we +require the velocity of light relative to the tube. + +It is clear that we have the problem of \Sectionref{VI} +again before us. The tube plays the part of the railway +embankment or of the co-ordinate system~$K$, the liquid +plays the part of the carriage or of the co-ordinate +system~$K'$, and finally, the light plays the part of the +%[Illustration: Fig. 3.] +\Figure[2in]{040} +man walking along the carriage, or of the moving point +in the present section. If we denote the velocity of the +light relative to the tube by~$W$, then this is given +by the equation \Eqref{(A)}~or~\Eqref{(B)}, according as the Galilei +transformation or the Lorentz transformation corresponds +to the facts. Experiment\footnote + {Fizeau found $W = w + v\left(1 - \dfrac{1}{n^{2}}\right)$, where $n = \dfrac{c}{w}$ is the index of + refraction of the liquid. On the other hand, owing to the smallness + of~$\dfrac{vw}{c^{2}}$ as compared with~$1$, we can replace~\Eqref{(B)} in the first + place by $W = (w + v) \left(1 - \dfrac{vw}{c^{2}}\right)$, or to the same order of approximation + by $w + v \left(1 - \dfrac{1}{n^{2}}\right)$, which agrees with Fizeau's result.} +decides in favour +of equation~\Eqref{(B)} derived from the theory of relativity, and +the agreement is, indeed, very exact. According to +\PageSep{41} +recent and most excellent measurements by Zeeman, the +\index{Zeeman}% +influence of the velocity of flow~$v$ on the propagation of +light is represented by formula~\Eqref{(B)} to within one per +cent. %[** TN: [sic] two words] + +Nevertheless we must now draw attention to the fact +that a theory of this phenomenon was given by H.~A. +Lorentz long before the statement of the theory of +\index{Lorentz, H. A.}% +relativity. This theory was of a purely electrodynamical +nature, and was obtained by the use of particular +hypotheses as to the electromagnetic structure of matter. +This circumstance, however, does not in the least +diminish the conclusiveness of the experiment as a +crucial test in favour of the theory of relativity, for the +electrodynamics of Maxwell-Lorentz, on which the +\index{Electrodynamics}% +\index{Maxwell}% +original theory was based, in no way opposes the theory +of relativity. Rather has the latter been developed +from electrodynamics as an astoundingly simple combination +and generalisation of the hypotheses, formerly +independent of each other, on which electrodynamics +was built. +\PageSep{42} + + +\Chapter{XIV}{The Heuristic Value of the Theory of +Relativity} +\index{Heuristic value of relativity}% + +\First{Our} train of thought in the foregoing pages can be +epitomised in the following manner. Experience +has led to the conviction that, on the one hand, +the principle of relativity holds true, and that on the +other hand the velocity of transmission of light \textit{in~vacuo} +has to be considered equal to a constant~$c$. By uniting +these two postulates we obtained the law of transformation +for the rectangular co-ordinates $x$,~$y$,~$z$ and the time~$t$ +of the events which constitute the processes of nature. +\index{Processes of Nature}% +In this connection we did not obtain the Galilei transformation, +\index{Galilei!transformation}% +but, differing from classical mechanics, +the \emph{Lorentz transformation}. +\index{Lorentz, H. A.!transformation}% + +The law of transmission of light, the acceptance of +which is justified by our actual knowledge, played an +important part in this process of thought. Once in +possession of the Lorentz transformation, however, +we can combine this with the principle of relativity, +and sum up the theory thus: + +Every general law of nature must be so constituted +that it is transformed into a law of exactly the same +form when, instead of the space-time variables $x$,~$y$, $z$,~$t$ +of the original co-ordinate system~$K$, we introduce new +space-time variables $x'$,~$y'$, $z'$,~$t'$ of a co-ordinate system~$K'$. +\PageSep{43} +In this connection the relation between the +ordinary and the accented magnitudes is given by the +Lorentz transformation. Or, in brief: General laws +of nature are co-variant with respect to Lorentz transformations. +\index{Covariant@{Co-variant}}% + +This is a definite mathematical condition that the +theory of relativity demands of a natural law, and in +virtue of this, the theory becomes a valuable heuristic aid +in the search for general laws of nature. If a general +law of nature were to be found which did not satisfy +this condition, then at least one of the two fundamental +assumptions of the theory would have been disproved. +Let us now examine what general results the latter +theory has hitherto evinced. +\PageSep{44} + + +\Chapter{XV}{General Results of the Theory} + +\First{It} is clear from our previous considerations that the +(special) theory of relativity has grown out of electrodynamics +\index{Electrodynamics}% +and optics. In these fields it has not +\index{Optics}% +appreciably altered the predictions of theory, but it +has considerably simplified the theoretical structure, +\ie\ the derivation of laws, and---what is incomparably +\index{Derivation of laws}% +more important---it has considerably reduced the +number of independent hypotheses forming the basis of +\index{Basis of theory}% +theory. The special theory of relativity has rendered +the Maxwell-Lorentz theory so plausible, that the latter +\index{Lorentz, H. A.}% +\index{Maxwell}% +would have been generally accepted by physicists +even if experiment had decided less unequivocally in its +favour. + +Classical mechanics required to be modified before it +\index{Classical mechanics}% +could come into line with the demands of the special +theory of relativity. For the main part, however, +this modification affects only the laws for rapid motions, +in which the velocities of matter~$v$ are not very small as +compared with the velocity of light. We have experience +of such rapid motions only in the case of electrons +\index{Electron}% +and ions; for other motions the variations from the laws +\index{Ions}% +of classical mechanics are too small to make themselves +evident in practice. We shall not consider the motion +\index{Motion!of heavenly bodies}% +of stars until we come to speak of the general theory of +relativity. In accordance with the theory of relativity +\PageSep{45} +the kinetic energy of a material point of mass~$m$ is no +\index{Kinetic energy}% +longer given by the well-known expression +\[ +m\frac{v^{2}}{2}\Change{.}{,} +\] +but by the expression +\[ +\frac{mc^{2}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +This expression approaches infinity as the velocity~$v$ +approaches the velocity of light~$c$. The velocity must +therefore always remain less than~$c$, however great may +be the energies used to produce the acceleration. If +we develop the expression for the kinetic energy in the +form of a series, we obtain +\[ +mc^{2} + m\frac{v^{2}}{2} + \frac{3}{8}m\frac{v^4}{c^{2}} + \dots. +\] + +When $\dfrac{v^{2}}{c^{2}}$ is small compared with unity, the third +of these terms is always small in comparison with the +second, which last is alone considered in classical +mechanics. The first term~$mc^{2}$ does not contain +the velocity, and requires no consideration if we are only +dealing with the question as to how the energy of a +point-mass depends on the velocity. We shall speak +\index{Point-mass, energy of}% +of its essential significance later. + +The most important result of a general character to +\index{Conservation of energy}% +\index{Conservation of energy!mass}% +which the special theory of relativity has led is concerned +with the conception of mass. Before the advent of +\index{Conception of mass}% +relativity, physics recognised two conservation laws of +fundamental importance, namely, the law of the conservation +of energy and the law of the conservation of +mass; these two fundamental laws appeared to be quite +\PageSep{46} +independent of each other. By means of the theory of +relativity they have been united into one law. We shall +now briefly consider how this unification came about, +and what meaning is to be attached to it. + +The principle of relativity requires that the law of the +conservation of energy should hold not only with reference +to a co-ordinate system~$K$, but also with respect +to every co-ordinate system~$K'$ which is in a state of +uniform motion of translation relative to~$K$, or, briefly, +relative to every ``Galileian'' system of co-ordinates. +\index{Galileian system of co-ordinates}% +In contrast to classical mechanics, the Lorentz transformation +is the deciding factor in the transition from +one such system to another. + +By means of comparatively simple considerations +we are led to draw the following conclusion from +these premises, in conjunction with the fundamental +equations of the electrodynamics of Maxwell: A body +\index{Maxwell!fundamental equations}% +\index{Absorption of energy}% +moving with the velocity~$v$, which absorbs\footnote + {$E_{0}$~is the energy taken up, as judged from a co-ordinate + system moving with the body.} +an amount +of energy~$E_{0}$ in the form of radiation without suffering +\index{Radiation}% +an alteration in velocity in the process, has, as a consequence, +its energy increased by an amount +\[ +\frac{E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] + +In consideration of the expression given above for the +kinetic energy of the body, the required energy of the +body comes out to be +\[ +\frac{\left(m + \dfrac{E_{0}}{c^{2}}\right)c^{2}} + {\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +\PageSep{47} + +Thus the body has the same energy as a body of mass +$\left(m + \dfrac{E_{0}}{c^{2}}\right)$ moving with the velocity~$v$. Hence we can +say: If a body takes up an amount of energy~$E_{0}$, then +its inertial mass increases by an amount~$\dfrac{E_{0}}{c^{2}}$; the +\index{Inertial mass}% +inertial mass of a body is not a constant, but varies +according to the change in the energy of the body. +The inertial mass of a system of bodies can even be +regarded as a measure of its energy. The law of the +conservation of the mass of a system becomes identical +with the law of the conservation of energy, and is only +\index{Conservation of energy!mass}% +valid provided that the system neither takes up nor sends +out energy. Writing the expression for the energy in +the form +\[ +\frac{mc^{2} + E_{0}}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}, +\] +we see that the term~$mc^{2}$, which has hitherto attracted +our attention, is nothing else than the energy possessed +by the body\footnote + {As judged from a co-ordinate system moving with the body.} +before it absorbed the energy~$E_{0}$. + +A direct comparison of this relation with experiment +is not possible at the present time, owing to the fact that +the changes in energy~$E_{0}$ to which we can subject a +system are not large enough to make themselves +perceptible as a change in the inertial mass of the +system. $\dfrac{E_{0}}{c^{2}}$~is too small in comparison with the mass~$m$, +which was present before the alteration of the energy. +It is owing to this circumstance that classical mechanics +was able to establish successfully the conservation of +mass as a law of independent validity. +\PageSep{48} + +Let me add a final remark of a fundamental nature. +The success of the Faraday-Maxwell interpretation of +\index{Faraday}% +\index{Maxwell|(}% +electromagnetic action at a distance resulted in physicists +\index{Action at a distance}% +becoming convinced that there are no such things as +instantaneous actions at a distance (not involving an +intermediary medium) of the type of Newton's law of +\index{Newton's!law of gravitation}% +gravitation. According to the theory of relativity, +action at a distance with the velocity of light always +takes the place of instantaneous action at a distance or +of action at a distance with an infinite velocity of transmission. +This is connected with the fact that the +velocity~$c$ plays a fundamental rôle in this theory. In +\Partref{II} we shall see in what way this result becomes +modified in the general theory of relativity. +\PageSep{49} + + +\Chapter{XVI}{Experience and the Special Theory of +Relativity} +\index{Experience}% + +\First{To} what extent is the special theory of relativity +supported by experience? This question is not +easily answered for the reason already mentioned +in connection with the fundamental experiment of Fizeau. +\index{Fizeau}% +The special theory of relativity has crystallised out +from the Maxwell-Lorentz theory of electromagnetic +\index{Lorentz, H. A.}% +phenomena. Thus all facts of experience which support +the electromagnetic theory also support the theory of +\index{Electromagnetic theory}% +relativity. As being of particular importance, I mention +here the fact that the theory of relativity enables us to +predict the effects produced on the light reaching us +from the fixed stars. These results are obtained in an +exceedingly simple manner, and the effects indicated, +which are due to the relative motion of the earth with +reference to those fixed stars, are found to be in accord +with experience. We refer to the yearly movement of +the apparent position of the fixed stars resulting from the +motion of the earth round the sun (aberration), and to the +\index{Aberration}% +influence of the radial components of the relative +motions of the fixed stars with respect to the earth on +the colour of the light reaching us from them. The +\PageSep{50} +latter effect manifests itself in a slight displacement +of the spectral lines of the light transmitted to us from +a fixed star, as compared with the position of the same +spectral lines when they are produced by a terrestrial +source of light (Doppler principle). The experimental +\index{Doppler principle}% +arguments in favour of the Maxwell-Lorentz theory, +\index{Lorentz, H. A.|(}% +which are at the same time arguments in favour of the +theory of relativity, are too numerous to be set forth +here. In reality they limit the theoretical possibilities +to such an extent, that no other theory than that of +Maxwell and Lorentz has been able to hold its own when +tested by experience. + +But there are two classes of experimental facts +hitherto obtained which can be represented in the +Maxwell-Lorentz theory only by the introduction of an +\index{Maxwell|)}% +auxiliary hypothesis, which in itself---\ie\ without +making use of the theory of relativity---appears extraneous. + +It is known that cathode rays and the so-called +\index{beta-rays@{$\beta$-rays}}% +\index{Cathode rays}% +$\beta$-rays emitted by radioactive substances consist of +\index{Radioactive substances}% +negatively electrified particles (electrons) of very small +inertia and large velocity. By examining the deflection +of these rays under the influence of electric and magnetic +fields, we can study the law of motion of these particles +very exactly. + +In the theoretical treatment of these electrons, we are +faced with the difficulty that electrodynamic theory of +itself is unable to give an account of their nature. For +since electrical masses of one sign repel each other, the +negative electrical masses constituting the electron would +\index{Electron}% +necessarily be scattered under the influence of their +mutual repulsions, unless there are forces of another +kind operating between them, the nature of which has +\PageSep{51} +hitherto remained obscure to us.\footnote + {The general theory of relativity renders it likely that the + electrical masses of an electron are held together by gravitational +\index{Electron!electrical masses of}% + forces.} +If we now assume +that the relative distances between the electrical masses +constituting the electron remain unchanged during the +motion of the electron (rigid connection in the sense of +classical mechanics), we arrive at a law of motion of the +electron which does not agree with experience. Guided +by purely formal points of view, H.~A.~Lorentz was the +first to introduce the hypothesis that the particles +constituting the electron experience a contraction +in the direction of motion in consequence of that motion, +the amount of this contraction being proportional to +the expression~$\sqrt{1 - \dfrac{v^{2}}{c^{2}}}$. This hypothesis, which is +not justifiable by any electrodynamical facts, supplies us +then with that particular law of motion which has +been confirmed with great precision in recent years. + +The theory of relativity leads to the same law of +motion, without requiring any special hypothesis whatsoever +as to the structure and the behaviour of the +electron. We arrived at a similar conclusion in \Sectionref{XIII} +in connection with the experiment of Fizeau, the +\index{Fizeau}% +result of which is foretold by the theory of relativity +without the necessity of drawing on hypotheses as to +the physical nature of the liquid. + +The second class of facts to which we have alluded +has reference to the question whether or not the motion +of the earth in space can be made perceptible in terrestrial +experiments. We have already remarked in \Sectionref{V} +that all attempts of this nature led to a negative result. +Before the theory of relativity was put forward, it was +\PageSep{52} +difficult to become reconciled to this negative result, +for reasons now to be discussed. The inherited +prejudices about time and space did not allow any +\index{Time!conception of}% +\index{Space}% +doubt to arise as to the prime importance of the +Galilei transformation for changing over from one +\index{Galilei!transformation}% +body of reference to another. Now assuming that the +Maxwell-Lorentz equations hold for a reference-body~$K$, +\index{Maxwell}% +we then find that they do not hold for a reference-body~$K'$ +moving uniformly with respect to~$K$, if we +assume that the relations of the Galileian transformation +exist between the co-ordinates of $K$~and~$K'$. It +thus appears that of all Galileian co-ordinate systems +one~($K$) corresponding to a particular state of motion +is physically unique. This result was interpreted +physically by regarding $K$ as at rest with respect to a +hypothetical æther of space. On the other hand, +all co-ordinate systems~$K'$ moving relatively to~$K$ were +to be regarded as in motion with respect to the æther. +\index{Aether}% +\index{Aether!-drift}% +To this motion of~$K'$ against the æther (``æther-drift'' +relative to~$K'$) were assigned the more complicated +laws which were supposed to hold relative to~$K'$. +Strictly speaking, such an æther-drift ought also to be +assumed relative to the earth, and for a long time the +efforts of physicists were devoted to attempts to detect +the existence of an æther-drift at the earth's surface. + +In one of the most notable of these attempts Michelson +\index{Michelson|(}% +devised a method which appears as though it must be +decisive. Imagine two mirrors so arranged on a rigid +body that the reflecting surfaces face each other. A +ray of light requires a perfectly definite time~$T$ to pass +from one mirror to the other and back again, if the whole +system be at rest with respect to the æther. It is found +by calculation, however, that a slightly different time~$T'$ +\PageSep{53} +is required for this process, if the body, together with +the mirrors, be moving relatively to the æther. And +\index{Aether!-drift}% +yet another point: it is shown by calculation that for +a given velocity~$v$ with reference to the æther, this +time~$T'$ is different when the body is moving perpendicularly +to the planes of the mirrors from that resulting +when the motion is parallel to these planes. Although +the estimated difference between these two times is +exceedingly small, Michelson and Morley performed an +\index{Morley}% +experiment involving interference in which this difference +should have been clearly detectable. But the experiment +gave a negative result---a fact very perplexing +to physicists. Lorentz and FitzGerald rescued the +\index{FitzGerald}% +\index{Lorentz, H. A.|)}% +theory from this difficulty by assuming that the motion +of the body relative to the æther produces a contraction +of the body in the direction of motion, the amount of contraction +being just sufficient to compensate for the difference +in time mentioned above. Comparison with the +discussion in \Sectionref{XII} shows that also from the standpoint +of the theory of relativity this solution of the +difficulty was the right one. But on the basis of the +theory of relativity the method of interpretation is +incomparably more satisfactory. According to this +theory there is no such thing as a ``specially favoured'' +(unique) co-ordinate system to occasion the introduction +of the æther-idea, and hence there can be no æther-drift, +nor any experiment with which to demonstrate it. +Here the contraction of moving bodies follows from +the two fundamental principles of the theory without +the introduction of particular hypotheses; and as the +prime factor involved in this contraction we find, not +the motion in itself, to which we cannot attach any +meaning, but the motion with respect to the body of +\PageSep{54} +reference chosen in the particular case in point. Thus +for a co-ordinate system moving with the earth the +mirror system of Michelson and Morley is not shortened, +\index{Michelson|)}% +\index{Morley}% +but it \emph{is} shortened for a co-ordinate system which is at +rest relatively to the sun. +\PageSep{55} + + +\Chapter{XVII}{Minkowski's Four-dimensional Space} +\index{Minkowski|(}% +\index{Space}% + +\First{The} non-mathematician is seized by a mysterious +shuddering when he hears of ``four-dimensional'' +things, by a feeling not unlike that awakened by +thoughts of the occult. And yet there is no more +common-place statement than that the world in which +\index{World}% +we live is a four-dimensional space-time continuum. +\index{Continuum}% + +Space is a three-dimensional continuum. By this +\index{Space co-ordinates}% +\index{Three-dimensional}% +\index{Time!coordinate@{co-ordinate}}% +we mean that it is possible to describe the position of a +point (at rest) by means of three numbers (co-ordinates) +$x$,~$y$,~$z$, and that there is an indefinite number of points +in the neighbourhood of this one, the position of which +can be described by co-ordinates such as $x_{1}$,~$y_{1}$,~$z_{1}$, which +may be as near as we choose to the respective values of +the co-ordinates $x$,~$y$,~$z$ of the first point. In virtue of the +latter property we speak of a ``continuum,'' and owing +to the fact that there are three co-ordinates we speak of +it as being ``three-dimensional.'' + +Similarly, the world of physical phenomena which was +briefly called ``world'' by Minkowski is naturally +four-dimensional in the space-time sense. For it is +composed of individual events, each of which is described +by four numbers, namely, three space +co-ordinates $x$,~$y$,~$z$ and a time co-ordinate, the time-value~$t$. +The ``world'' is in this sense also a continuum; +for to every event there are as many ``neighbouring'' +\PageSep{56} +events (realised or at least thinkable) as we care to +choose, the co-ordinates $x_{1}$,~$y_{1}$, $z_{1}$,~$t_{1}$ of which differ +by an indefinitely small amount from those of the +event $x$,~$y$, $z$,~$t$ originally considered. That we have not +been accustomed to regard the world in this sense as a +\index{World}% +four-dimensional continuum is due to the fact that in +physics, before the advent of the theory of relativity, +time played a different and more independent rôle, as +compared with the space co-ordinates. It is for this +reason that we have been in the habit of treating time +as an independent continuum. As a matter of fact, +according to classical mechanics, time is absolute, +\ie\ it is independent of the position and the condition +of motion of the system of co-ordinates. We see this +expressed in the last equation of the Galileian transformation +($t' = t$). + +The four-dimensional mode of consideration of the +``world'' is natural on the theory of relativity, since +according to this theory time is robbed of its independence. +This is shown by the fourth equation of the +Lorentz transformation: +\[ +t' = \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\] +Moreover, according to this equation the time difference~$\Delta t'$ +\index{Space!interval@{-interval}}% +\index{Time-interval}% +of two events with respect to~$K'$ does not in general +vanish, even when the time difference~$\Delta t$ of the same +events with reference to~$K$ vanishes. Pure ``space-distance'' +of two events with respect to~$K$ results in +``time-distance'' of the same events with respect to~$K'$. +But the discovery of Minkowski, which was of importance +\PageSep{57} +for the formal development of the theory of relativity, +does not lie here. It is to be found rather in +the fact of his recognition that the four-dimensional +space-time continuum of the theory of relativity, in its +\index{Continuum!three-dimensional}% +most essential formal properties, shows a pronounced +relationship to the three-dimensional continuum of +Euclidean geometrical space.\footnote + {Cf.\ the somewhat more detailed discussion in \Appendixref{II}.} +In order to give due +prominence to this relationship, however, we must +replace the usual time co-ordinate~$t$ by an imaginary +magnitude~$\sqrt{-1}·ct$ proportional to it. Under these +conditions, the natural laws satisfying the demands of +the (special) theory of relativity assume mathematical +forms, in which the time co-ordinate plays exactly the +same rôle as the three space co-ordinates. Formally, +these four co-ordinates correspond exactly to the three +space co-ordinates in Euclidean geometry. It must be +\index{Euclidean geometry}% +\index{Euclidean space}% +clear even to the non-mathematician that, as a consequence +of this purely formal addition to our knowledge, +the theory perforce gained clearness in no mean +measure. + +These inadequate remarks can give the reader only a +vague notion of the important idea contributed by Minkowski. +Without it the general theory of relativity, of +which the fundamental ideas are developed in the following +pages, would perhaps have got no farther than its +long clothes. Minkowski's work is doubtless difficult of +\index{Minkowski|)}% +access to anyone inexperienced in mathematics, but +since it is not necessary to have a very exact grasp of +this work in order to understand the fundamental ideas +of either the special or the general theory of relativity, +I shall at present leave it here, and shall revert to it +only towards the end of \Partref{II}. +\index{Special theory of relativity|)}% +\PageSep{58} +% [Blank page] +\PageSep{59} + + +\Part{II}{The General Theory of Relativity}{General Theory of Relativity} +\index{General theory of relativity|(}% + +\Chapter{XVIII}{Special and General Principle of +Relativity} +\index{Laws of Galilei-Newton!of Nature}% + +\First{The} basal principle, which was the pivot of all +our previous considerations, was the \emph{special} +principle of relativity, \ie\ the principle of the +physical relativity of all \emph{uniform} motion. Let us once +\index{Uniform translation}% +more analyse its meaning carefully. + +It was at all times clear that, from the point of view +of the idea it conveys to us, every motion must only +be considered as a relative motion. Returning to the +illustration we have frequently used of the embankment +and the railway carriage, we can express the fact of the +motion here taking place in the following two forms, +both of which are equally justifiable: +\begin{itemize} +\item[\itema] The carriage is in motion relative to the embankment. + +\item[\itemb] The embankment is in motion relative to the + carriage. +\end{itemize} + +In \itema~the embankment, in \itemb~the carriage, serves as +the body of reference in our statement of the motion +taking place. If it is simply a question of detecting +\PageSep{60} +or of describing the motion involved, it is in principle +\index{Motion}% +immaterial to what reference-body we refer the motion. +\index{Reference-body}% +As already mentioned, this is self-evident, but it must +not be confused with the much more comprehensive +statement called ``the principle of relativity,'' which +\index{Principle of relativity}% +we have taken as the basis of our investigations. + +The principle we have made use of not only maintains +that we may equally well choose the carriage or the +embankment as our reference-body for the description +of any event (for this, too, is self-evident). Our principle +rather asserts what follows: If we formulate the general +laws of nature as they are obtained from experience, +\index{Experience}% +by making use of +\begin{itemize} +\item[\itema] the embankment as reference-body, +\item[\itemb] the railway carriage as reference-body, +\end{itemize} +then these general laws of nature (\eg\ the laws of +mechanics or the law of the propagation of light \textit{in~vacuo}) +have exactly the same form in both cases. This can +also be expressed as follows: For the \emph{physical} description +of natural processes, neither of the reference-bodies +$K$,~$K'$ is unique (lit.\ ``specially marked out'') as +compared with the other. Unlike the first, this latter +statement need not of necessity hold \textit{a~priori}; it is +not contained in the conceptions of ``motion'' and +``reference-body'' and derivable from them; only +\emph{experience} can decide as to its correctness or incorrectness. + +Up to the present, however, we have by no means +maintained the equivalence of \emph{all} bodies of reference~$K$ +in connection with the formulation of natural laws. +Our course was more on the following lines. In the +first place, we started out from the assumption that +there exists a reference-body~$K$, whose condition of +\PageSep{61} +\index{Law of inertia}% +motion is such that the Galileian law holds with respect +to it: A particle left to itself and sufficiently far removed +from all other particles moves uniformly in a straight +line. With reference to~$K$ (Galileian reference-body) the +laws of nature were to be as simple as possible. But +in addition to~$K$, all bodies of reference~$K'$ should be +given preference in this sense, and they should be exactly +equivalent to~$K$ for the formulation of natural laws, +provided that they are in a state of \emph{uniform rectilinear +and non-rotary motion} with respect to~$K$; all these +bodies of reference are to be regarded as Galileian +reference-bodies. The validity of the principle of +relativity was assumed only for these reference-bodies, +but not for others (\eg\ those possessing motion of a +different kind). In this sense we speak of the \emph{special} +principle of relativity, or special theory of relativity. + +In contrast to this we wish to understand by the +``general principle of relativity'' the following statement: +All bodies of reference $K$,~$K'$,~etc., are equivalent +for the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion. But before proceeding farther, it +ought to be pointed out that this formulation must be +replaced later by a more abstract one, for reasons which +will become evident at a later stage. + +Since the introduction of the special principle of +relativity has been justified, every intellect which +strives after generalisation must feel the temptation +to venture the step towards the general principle of +relativity. But a simple and apparently quite reliable +consideration seems to suggest that, for the present +at any rate, there is little hope of success in such an +attempt. Let us imagine ourselves transferred to our +\PageSep{62} +\index{Law of inertia}% +old friend the railway carriage, which is travelling at a +uniform rate. As long as it is moving uniformly, the +occupant of the carriage is not sensible of its motion, +and it is for this reason that he can without reluctance +interpret the facts of the case as indicating that the +carriage is at rest but the embankment in motion. +Moreover, according to the special principle of relativity, +this interpretation is quite justified also from a physical +point of view. + +If the motion of the carriage is now changed into a +non-uniform motion, as for instance by a powerful +\index{Non-uniform motion}% +application of the brakes, then the occupant of the +carriage experiences a correspondingly powerful jerk +forwards. The retarded motion is manifested in the +mechanical behaviour of bodies relative to the person +in the railway carriage. The mechanical behaviour is +different from that of the case previously considered, +and for this reason it would appear to be impossible +that the same mechanical laws hold relatively to the non-uniformly +moving carriage, as hold with reference to the +carriage when at rest or in uniform motion. At all +events it is clear that the Galileian law does not hold +with respect to the non-uniformly moving carriage. +Because of this, we feel compelled at the present juncture +to grant a kind of absolute physical reality to non-uniform +motion, in opposition to the general principle +of relativity. But in what follows we shall soon see +that this conclusion cannot be maintained. +\PageSep{63} + + +\Chapter{XIX}{The Gravitational Field} + +``\First{If} we pick up a stone and then let it go, why does it +fall to the ground?'' The usual answer to this +question is: ``Because it is attracted by the earth.'' +Modern physics formulates the answer rather differently +for the following reason. As a result of the more careful +study of electromagnetic phenomena, we have come +to regard action at a distance as a process impossible +without the intervention of some intermediary medium. +If, for instance, a magnet attracts a piece of iron, we +cannot be content to regard this as meaning that the +magnet acts directly on the iron through the intermediate +empty space, but we are constrained to imagine---after +the manner of Faraday---that the magnet +\index{Faraday}% +always calls into being something physically real in +the space around it, that something being what we call a +``magnetic field.'' In its turn this magnetic field +\index{Magnetic field}% +operates on the piece of iron, so that the latter strives +to move towards the magnet. We shall not discuss +here the justification for this incidental conception, +which is indeed a somewhat arbitrary one. We shall +only mention that with its aid electromagnetic phenomena +can be theoretically represented much more +satisfactorily than without it, and this applies particularly +\index{Electromagnetic theory!waves}% +to the transmission of electromagnetic waves. +\PageSep{64} +The effects of gravitation also are regarded in an analogous +\index{Gravitation}% +manner. + +The action of the earth on the stone takes place indirectly. +The earth produces in its surroundings a +gravitational field, which acts on the stone and produces +\index{Gravitational field}% +its motion of fall. As we know from experience, the +intensity of the action on a body diminishes according +to a quite definite law, as we proceed farther and farther +away from the earth. From our point of view this +means: The law governing the properties of the gravitational +field in space must be a perfectly definite one, in +order correctly to represent the diminution of gravitational +action with the distance from operative bodies. +It is something like this: The body (\eg\ the earth) produces +a field in its immediate neighbourhood directly; +the intensity and direction of the field at points farther +removed from the body are thence determined by +the law which governs the properties in space of the +gravitational fields themselves. + +In contrast to electric and magnetic fields, the gravitational +field exhibits a most remarkable property, which +is of fundamental importance for what follows. Bodies +which are moving under the sole influence of a gravitational +field receive an acceleration, \emph{which does not in the +\index{Acceleration}% +least depend either on the material or on the physical +state of the body}. For instance, a piece of lead and +a piece of wood fall in exactly the same manner in a +gravitational field (\textit{in~vacuo}), when they start off from +rest or with the same initial velocity. This law, which +holds most accurately, can be expressed in a different +form in the light of the following consideration. + +According to Newton's law of motion, we have +\index{Newton's!law of motion}% +\[ +(\text{Force}) = (\text{inertial mass}) × (\text{acceleration}), +\] +\PageSep{65} +where the ``inertial mass'' is a characteristic constant +\index{Inertial mass}% +of the accelerated body. If now gravitation is the +cause of the acceleration, we then have +%[** TN: Re-breaking next two displayed equations] +\begin{multline*} +(\text{Force}) + = (\text{gravitational mass}) \\ + × (\text{intensity of the gravitational field}), +\index{Gravitational mass}% +\end{multline*} +where the ``gravitational mass'' is likewise a characteristic +constant for the body. From these two relations +follows: +\begin{multline*} +(\text{acceleration}) + = \frac{(\text{gravitational mass})}{(\text{inertial mass})} \\ + × (\text{intensity of the gravitational field}). +\end{multline*} + +If now, as we find from experience, the acceleration is +to be independent of the nature and the condition of the +body and always the same for a given gravitational +field, then the ratio of the gravitational to the inertial +mass must likewise be the same for all bodies. By a +suitable choice of units we can thus make this ratio +equal to unity. We then have the following law: +The \emph{gravitational} mass of a body is equal to its \emph{inertial} +mass. + +It is true that this important law had hitherto been +recorded in mechanics, but it had not been \emph{interpreted}. +A satisfactory interpretation can be obtained only if we +recognise the following fact: \emph{The same} quality of a +body manifests itself according to circumstances as +``inertia'' or as ``weight'' (lit.\ ``heaviness''). In the +\index{Inertia}% +\index{Weight (heaviness)}% +following section we shall show to what extent this is +actually the case, and how this question is connected +with the general postulate of relativity. +\PageSep{66} + + +\Chapter{XX}{The Equality of Inertial and Gravitational +Mass as an Argument for the +General Postulate of Relativity} + +\First{We} imagine a large portion of empty space, so far +removed from stars and other appreciable +masses, that we have before us approximately +the conditions required by the fundamental law of Galilei. +It is then possible to choose a Galileian reference-body for +this part of space (world), relative to which points at +rest remain at rest and points in motion continue permanently +in uniform rectilinear motion. As reference-body +let us imagine a spacious chest resembling a room +\index{Chest}% +with an observer inside who is equipped with apparatus. +Gravitation naturally does not exist for this observer. +He must fasten himself with strings to the floor, +otherwise the slightest impact against the floor will +cause him to rise slowly towards the ceiling of the +room. + +To the middle of the lid of the chest is fixed externally +a hook with rope attached, and now a ``being'' (what +\index{Being@{``Being''}}% +kind of a being is immaterial to us) begins pulling at +this with a constant force. The chest together with the +observer then begin to move ``upwards'' with a +uniformly accelerated motion. In course of time their +velocity will reach unheard-of values---provided that +\PageSep{67} +we are viewing all this from another reference-body +which is not being pulled with a rope. + +But how does the man in the chest regard the process? +The acceleration of the chest will be transmitted to him +\index{Acceleration}% +by the reaction of the floor of the chest. He must +therefore take up this pressure by means of his legs if +he does not wish to be laid out full length on the floor. +He is then standing in the chest in exactly the same way +as anyone stands in a room of a house on our earth. +If he release a body which he previously had in his +hand, the acceleration of the chest will no longer be +transmitted to this body, and for this reason the body +will approach the floor of the chest with an accelerated +relative motion. The observer will further convince +himself \emph{that the acceleration of the body towards the floor +of the chest is always of the same magnitude, whatever +kind of body he may happen to use for the experiment}. + +Relying on his knowledge of the gravitational field +\index{Gravitational field}% +(as it was discussed in the preceding section), the man +in the chest will thus come to the conclusion that he +and the chest are in a gravitational field which is constant +with regard to time. Of course he will be puzzled for +a moment as to why the chest does not fall, in this +gravitational field. Just then, however, he discovers +the hook in the middle of the lid of the chest and the +rope which is attached to it, and he consequently comes +to the conclusion that the chest is suspended at rest in +the gravitational field. + +Ought we to smile at the man and say that he errs +in his conclusion? I do not believe we ought to if we +wish to remain consistent; we must rather admit that +his mode of grasping the situation violates neither reason +nor known mechanical laws. Even though it is being +\PageSep{68} +accelerated with respect to the ``Galileian space'' +first considered, we can nevertheless regard the chest +as being at rest. We have thus good grounds for +extending the principle of relativity to include bodies +of reference which are accelerated with respect to each +other, and as a result we have gained a powerful argument +for a generalised postulate of relativity. + +We must note carefully that the possibility of this +mode of interpretation rests on the fundamental +property of the gravitational field of giving all bodies +\index{Gravitational mass}% +the same acceleration, or, what comes to the same thing, +on the law of the equality of inertial and gravitational +mass. If this natural law did not exist, the man in +the accelerated chest would not be able to interpret +the behaviour of the bodies around him on the supposition +of a gravitational field, and he would not be justified +on the grounds of experience in supposing his reference-body +to be ``at rest.'' + +Suppose that the man in the chest fixes a rope to the +inner side of the lid, and that he attaches a body to the +free end of the rope. The result of this will be to stretch +the rope so that it will hang ``vertically'' downwards. +If we ask for an opinion of the cause of tension in the +rope, the man in the chest will say: ``The suspended +body experiences a downward force in the gravitational +field, and this is neutralised by the tension of the rope; +what determines the magnitude of the tension of the +rope is the \emph{gravitational mass} of the suspended body.'' +On the other hand, an observer who is poised freely in +space will interpret the condition of things thus: ``The +rope must perforce take part in the accelerated motion +of the chest, and it transmits this motion to the body +attached to it. The tension of the rope is just large +\PageSep{69} +enough to effect the acceleration of the body. That +which determines the magnitude of the tension of the +rope is the \emph{inertial mass} of the body.'' Guided by +\index{Inertial mass}% +this example, we see that our extension of the principle +of relativity implies the \emph{necessity} of the law of the +equality of inertial and gravitational mass. Thus we +have obtained a physical interpretation of this law. + +From our consideration of the accelerated chest we +see that a general theory of relativity must yield important +results on the laws of gravitation. In point of +\index{Gravitation}% +fact, the systematic pursuit of the general idea of relativity +has supplied the laws satisfied by the gravitational +field. Before proceeding farther, however, I +must warn the reader against a misconception suggested +by these considerations. A gravitational field exists +for the man in the chest, despite the fact that there was +no such field for the co-ordinate system first chosen. +Now we might easily suppose that the existence of a +gravitational field is always only an \emph{apparent} one. We +might also think that, regardless of the kind of gravitational +field which may be present, we could always +choose another reference-body such that \emph{no} gravitational +field exists with reference to it. This is by no means +true for all gravitational fields, but only for those of +quite special form. It is, for instance, impossible to +choose a body of reference such that, as judged from it, +the gravitational field of the earth (in its entirety) +vanishes. + +We can now appreciate why that argument is not +convincing, which we brought forward against the +general principle of relativity at the end of \Sectionref{XVIII}. +It is certainly true that the observer in the railway +carriage experiences a jerk forwards as a result of the +\PageSep{70} +application of the brake, and that he recognises in this the +non-uniformity of motion (retardation) of the carriage. +But he is compelled by nobody to refer this jerk to a +``real'' acceleration (retardation) of the carriage. He +\index{Acceleration}% +might also interpret his experience thus: ``My body of +reference (the carriage) remains permanently at rest. +With reference to it, however, there exists (during the +period of application of the brakes) a gravitational +field which is directed forwards and which is variable +with respect to time. Under the influence of this field, +the embankment together with the earth moves non-uniformly +in such a manner that their original velocity +in the backwards direction is continuously reduced.'' +\PageSep{71} + + +\Chapter{XXI}{In what Respects are the Foundations +of Classical Mechanics and of the +Special Theory of Relativity unsatisfactory?} +\index{Classical mechanics}% +\index{Laws of Galilei-Newton!of Nature}% + +\First{We} have already stated several times that +classical mechanics starts out from the following +law: Material particles sufficiently far +removed from other material particles continue to +move uniformly in a straight line or continue in a +state of rest. We have also repeatedly emphasised +that this fundamental law can only be valid for +bodies of reference~$K$ which possess certain unique +states of motion, and which are in uniform translational +motion relative to each other. Relative to other reference-bodies~$K$ +the law is not valid. Both in classical +mechanics and in the special theory of relativity we +therefore differentiate between reference-bodies~$K$ +relative to which the recognised ``laws of nature'' can +be said to hold, and reference-bodies~$K$ relative to which +these laws do not hold. + +But no person whose mode of thought is logical can +rest satisfied with this condition of things. He asks: +``How does it come that certain reference-bodies (or +their states of motion) are given priority over other +reference-bodies (or their states of motion)? \emph{What is +\PageSep{72} +the reason for this preference?}\Change{}{''} In order to show clearly +what I mean by this question, I shall make use of a +comparison. + +I am standing in front of a gas range. Standing +alongside of each other on the range are two pans so +much alike that one may be mistaken for the other. +Both are half full of water. I notice that steam is being +emitted continuously from the one pan, but not from the +other. I am surprised at this, even if I have never seen +either a gas range or a pan before. But if I now notice +a luminous something of bluish colour under the first +pan but not under the other, I cease to be astonished, +even if I have never before seen a gas flame. For I +can only say that this bluish something will cause the +emission of the steam, or at least \emph{possibly} it may do so. +If, however, I notice the bluish something in neither +case, and if I observe that the one continuously emits +steam whilst the other does not, then I shall remain +astonished and dissatisfied until I have discovered +some circumstance to which I can attribute the different +behaviour of the two pans. + +Analogously, I seek in vain for a real something in +classical mechanics (or in the special theory of relativity) +to which I can attribute the different behaviour +of bodies considered with respect to the reference-systems +$K$~and~$K'$.\footnote + {The objection is of importance more especially when the state + of motion of the reference-body is of such a nature that it does + not require any external agency for its maintenance, \eg\ in + the case when the reference-body is rotating uniformly.} +Newton saw this objection and +\index{Newton}% +attempted to invalidate it, but without success. But +E.~Mach recognised it most clearly of all, and because +\index{Mach, E.}% +of this objection he claimed that mechanics must be +\PageSep{73} +placed on a new basis. It can only be got rid of by +means of a physics which is conformable to the general +principle of relativity, since the equations of such a +theory hold for every body of reference, whatever +may be its state of motion. +\PageSep{74} + + +\Chapter{XXII}{A Few Inferences from the General +Principle of Relativity} + +\First{The} considerations of \Sectionref{XX} show that the +general principle of relativity puts us in a position +to derive properties of the gravitational field in a +\index{Gravitational field}% +purely theoretical manner. Let us suppose, for instance, +that we know the space-time ``course'' for any natural +process whatsoever, as regards the manner in which it +takes place in the Galileian domain relative to a +Galileian body of reference~$K$. By means of purely +theoretical operations (\ie\ simply by calculation) we are +then able to find how this known natural process +appears, as seen from a reference-body~$K'$ which is +accelerated relatively to~$K$. But since a gravitational +field exists with respect to this new body of reference~$K'$, +our consideration also teaches us how the gravitational +field influences the process studied. + +For example, we learn that a body which is in a state +of uniform rectilinear motion with respect to~$K$ (in +accordance with the law of Galilei) is executing an +accelerated and in general curvilinear motion with +\index{Curvilinear motion}% +respect to the accelerated reference-body~$K'$ (chest). +This acceleration or curvature corresponds to the influence +on the moving body of the gravitational field +prevailing relatively to~$K'$. It is known that a gravitational +field influences the movement of bodies in this +\PageSep{75} +way, so that our consideration supplies us with nothing +essentially new. + +However, we obtain a new result of fundamental +\index{Propagation of light!in gravitational fields}% +importance when we carry out the analogous consideration +for a ray of light. With respect to the Galileian +reference-body~$K$, such a ray of light is transmitted +rectilinearly with the velocity~$c$. It can easily be shown +that the path of the same ray of light is no longer a +straight line when we consider it with reference to the +accelerated chest (reference-body~$K'$). From this we +conclude, \emph{that, in general, rays of light are propagated +curvilinearly in gravitational fields}. In two respects +this result is of great importance. + +In the first place, it can be compared with the reality. +Although a detailed examination of the question shows +that the curvature of light rays required by the general +theory of relativity is only exceedingly small for the +gravitational fields at our disposal in practice, its estimated +magnitude for light rays passing the sun at +grazing incidence is nevertheless $1.7$~seconds of arc. +This ought to manifest itself in the following way. +As seen from the earth, certain fixed stars appear to be +in the neighbourhood of the sun, and are thus capable +of observation during a total eclipse of the sun. At such +times, these stars ought to appear to be displaced +outwards from the sun by an amount indicated above, +as compared with their apparent position in the sky +when the sun is situated at another part of the heavens. +The examination of the correctness or otherwise of this +deduction is a problem of the greatest importance, the +early solution of which is to be expected of astronomers.\footnote + {By means of the star photographs of two expeditions equipped + by a Joint Committee of the Royal and Royal Astronomical + Societies, the existence of the deflection of light demanded by + theory was confirmed during the solar eclipse of 29th~May, 1919. +\index{Solar eclipse}% + (Cf.\ \Appendixref{III}.)} +\PageSep{76} + +In the second place our result shows that, according +to the general theory of relativity, the law of the constancy +of the velocity of light \textit{in~vacuo}, which constitutes +\index{Velocity of light}% +one of the two fundamental assumptions in the +special theory of relativity and to which we have +already frequently referred, cannot claim any unlimited +validity. A curvature of rays of light can only take +place when the velocity of propagation of light varies +with position. Now we might think that as a consequence +of this, the special theory of relativity and with +it the whole theory of relativity would be laid in the +dust. But in reality this is not the case. We can only +conclude that the special theory of relativity cannot +claim an unlimited domain of validity; its results +hold only so long as we are able to disregard the influences +of gravitational fields on the phenomena +(\eg\ of light). + +Since it has often been contended by opponents of +the theory of relativity that the special theory of +relativity is overthrown by the general theory of relativity, +it is perhaps advisable to make the facts of the +case clearer by means of an appropriate comparison. +Before the development of electrodynamics the laws +\index{Electrodynamics}% +of electrostatics were looked upon as the laws of +\index{Electrostatics}% +electricity. At the present time we know that +\index{Electricity}% +electric fields can be derived correctly from electrostatic +considerations only for the case, which is never +strictly realised, in which the electrical masses are quite +at rest relatively to each other, and to the co-ordinate +system. Should we be justified in saying that for this +\PageSep{77} +reason electrostatics is overthrown by the field-equations +of Maxwell in electrodynamics? Not in the least. +\index{Maxwell!fundamental equations}% +Electrostatics is contained in electrodynamics as a +limiting case; the laws of the latter lead directly to +those of the former for the case in which the fields are +invariable with regard to time. No fairer destiny +could be allotted to any physical theory, than that it +should of itself point out the way to the introduction +of a more comprehensive theory, in which it lives on +as a limiting case. + +In the example of the transmission of light just dealt +with, we have seen that the general theory of relativity +enables us to derive theoretically the influence of a +gravitational field on the course of natural processes, +\index{Gravitational field}% +the laws of which are already known when a gravitational +field is absent. But the most attractive problem, +to the solution of which the general theory of relativity +supplies the key, concerns the investigation of the laws +satisfied by the gravitational field itself. Let us consider +this for a moment. + +We are acquainted with space-time domains which +behave (approximately) in a ``Galileian'' fashion under +suitable choice of reference-body, \ie\ domains in which +gravitational fields are absent. If we now refer such +a domain to a reference-body~$K'$ possessing any kind +of motion, then relative to~$K'$ there exists a gravitational +field which is variable with respect to space and +time.\footnote + {This follows from a generalisation of the discussion in \Sectionref{XX}.} +The character of this field will of course depend +on the motion chosen for~$K'$. According to the general +theory of relativity, the general law oi the gravitational +field must be satisfied for all gravitational fields obtainable +\PageSep{78} +in this way. Even though by no means all gravitational +fields can be produced in this way, yet we may +entertain the hope that the general law of gravitation +\index{Gravitation}% +will be derivable from such gravitational fields of a +special kind. This hope has been realised in the most +beautiful manner. But between the clear vision of +this goal and its actual realisation it was necessary to +surmount a serious difficulty, and as this lies deep at +the root of things, I dare not withhold it from the reader. +We require to extend our ideas of the space-time continuum +\index{Continuum!space-time}% +still farther. +\PageSep{79} + + +\Chapter{XXIII}{Behaviour of Clocks and Measuring-Rods +on a Rotating Body of Reference} + +\First{Hitherto} I have purposely refrained from +speaking about the physical interpretation of +space- and time-data in the case of the general +theory of relativity. As a consequence, I am guilty of a +certain slovenliness of treatment, which, as we know +from the special theory of relativity, is far from being +unimportant and pardonable. It is now high time that +we remedy this defect; but I would mention at the +outset, that this matter lays no small claims on the +patience and on the power of abstraction of the reader. + +We start off again from quite special cases, which we +\index{Galileian system of co-ordinates}% +have frequently used before. Let us consider a space-time +domain in which no gravitational field exists +relative to a reference-body~$K$ whose state of motion +\index{Reference-body!rotating}% +has been suitably chosen. $K$~is then a Galileian reference-body +as regards the domain considered, and the +results of the special theory of relativity hold relative +to~$K$. Let us suppose the same domain referred to a +second body of reference~$K'$, which is rotating uniformly +with respect to~$K$. In order to fix our ideas, we shall +imagine~$K'$ to be in the form of a plane circular disc, +which rotates uniformly in its own plane about its +centre. An observer who is sitting eccentrically on the +\PageSep{80} +disc~$K'$ is sensible of a force which acts outwards in a +radial direction, and which would be interpreted as an +effect of inertia (centrifugal force) by an observer who +\index{Centrifugal force}% +was at rest with respect to the original reference-body~$K$. +But the observer on the disc may regard his disc as a +reference-body which is ``at rest''; on the basis of the +general principle of relativity he is justified in doing this. +The force acting on himself, and in fact on all other +bodies which are at rest relative to the disc, he regards +as the effect of a gravitational field. Nevertheless, +the space-distribution of this gravitational field is of a +kind that would not be possible on Newton's theory of +\index{Newton's!law of gravitation}% +gravitation.\footnote + {The field disappears at the centre of the disc and increases + proportionally to the distance from the centre as we proceed + outwards.} +But since the observer believes in the +general theory of relativity, this does not disturb him; +he is quite in the right when he believes that a general +law of gravitation can be formulated---a law which not +only explains the motion of the stars correctly, but +also the field of force experienced by himself. + +The observer performs experiments on his circular +disc with clocks and measuring-rods. In doing so, it +\index{Clocks}% +\index{Measuring-rod}% +is his intention to arrive at exact definitions for the +signification of time- and space-data with reference +to the circular disc~$K'$, these definitions being based on +his observations. What will be his experience in this +enterprise? + +To start with, he places one of two identically constructed +clocks at the centre of the circular disc, and the +other on the edge of the disc, so that they are at rest +relative to it. We now ask ourselves whether both +clocks go at the same rate from the standpoint of the +\PageSep{81} +non-rotating Galileian reference-body~$K$. As judged +from this body, the clock at the centre of the disc has +no velocity, whereas the clock at the edge of the disc +is in motion relative to~$K$ in consequence of the rotation. +\index{Rotation}% +According to a result obtained in \Sectionref{XII}, it follows +that the latter clock goes at a rate permanently slower +than that of the clock at the centre of the circular disc, +\ie\ as observed from~$K$. It is obvious that the same effect +would be noted by an observer whom we will imagine +sitting alongside his clock at the centre of the circular +disc. Thus on our circular disc, or, to make the case +more general, in every gravitational field, a clock will +go more quickly or less quickly, according to the position +in which the clock is situated (at rest). For this reason +it is not possible to obtain a reasonable definition of time +with the aid of clocks which are arranged at rest with +\index{Clocks}% +respect to the body of reference. A similar difficulty +presents itself when we attempt to apply our earlier +definition of simultaneity in such a case, but I do not +\index{Simultaneity}% +wish to go any farther into this question. + +Moreover, at this stage the definition of the space +\index{Space co-ordinates}% +co-ordinates also presents insurmountable difficulties. +If the observer applies his standard measuring-rod +\index{Measuring-rod}% +(a rod which is short as compared with the radius of +the disc) tangentially to the edge of the disc, then, as +judged from the Galileian system, the length of this rod +will be less than~$1$, since, according to \Sectionref{XII}, moving +bodies suffer a shortening in the direction of the motion. +On the other hand, the measuring-rod will not experience +a shortening in length, as judged from~$K$, if it is applied +to the disc in the direction of the radius. If, then, the +observer first measures the circumference of the disc +with his measuring-rod and then the diameter of the +\PageSep{82} +disc, on dividing the one by the other, he will not obtain +as quotient the familiar number $\pi = 3.14\dots$, but +a larger number,\footnote + {Throughout this consideration we have to use the Galileian + (non-rotating) system~$K$ as reference-body, since we may only + assume the validity of the results of the special theory of relativity + relative to~$K$ (relative to~$K'$ a gravitational field prevails).} +whereas of course, for a disc which is +at rest with respect to~$K$, this operation would yield~$\pi$ +\index{Value of $\pi$}% +exactly. This proves that the propositions of Euclidean +\index{Euclidean geometry}% +geometry cannot hold exactly on the rotating disc, nor +in general in a gravitational field, at least if we attribute +the length~$1$ to the rod in all positions and in every +orientation. Hence the idea of a straight line also loses +\index{Straight line}% +its meaning. We are therefore not in a position to +define exactly the co-ordinates $x$,~$y$,~$z$ relative to the +disc by means of the method used in discussing the +special theory, and as long as the co-ordinates and times +of events have not been defined, we cannot assign an +exact meaning to the natural laws in which these occur. + +Thus all our previous conclusions based on general +relativity would appear to be called in question. In +reality we must make a subtle detour in order to be +able to apply the postulate of general relativity exactly. +I shall prepare the reader for this in the +following paragraphs. +\PageSep{83} + + +\Chapter{XXIV}{Euclidean and Non-Euclidean Continuum} +\index{Continuum}% + +\First{The} surface of a marble table is spread out in front +of me. I can get from any one point on this +table to any other point by passing continuously +from one point to a ``neighbouring'' one, and repeating +this process a (large) number of times, or, in other words, +by going from point to point without executing ``jumps.'' +I am sure the reader will appreciate with sufficient +clearness what I mean here by ``neighbouring'' and by +``jumps'' (if he is not too pedantic). We express this +property of the surface by describing the latter as a +continuum. + +Let us now imagine that a large number of little rods +of equal length have been made, their lengths being +small compared with the dimensions of the marble +slab. When I say they are of equal length, I mean that +one can be laid on any other without the ends overlapping. +We next lay four of these little rods on the +marble slab so that they constitute a quadrilateral +figure (a square), the diagonals of which are equally +long. To ensure the equality of the diagonals, we make +use of a little testing-rod. To this square we add +similar ones, each of which has one rod in common +with the first. We proceed in like manner with each of +these squares until finally the whole marble slab is +\PageSep{84} +laid out with squares. The arrangement is such, that +each side of a square belongs to two squares and each +corner to four squares. + +It is a veritable wonder that we can carry out this +business without getting into the greatest difficulties. +We only need to think of the following. If at any +moment three squares meet at a corner, then two sides +of the fourth square are already laid, and, as a consequence, +the arrangement of the remaining two sides of +the square is already completely determined. But I +am now no longer able to adjust the quadrilateral so +that its diagonals may be equal. If they are equal +of their own accord, then this is an especial favour +of the marble slab and of the little rods, about which I +can only be thankfully surprised. We must needs +experience many such surprises if the construction is to +be successful. + +If everything has really gone smoothly, then I say +that the points of the marble slab constitute a Euclidean +\index{Distance (line-interval)}% +\index{Continuum!Euclidean}% +continuum with respect to the little rod, which has been +used as a ``distance'' (line-interval). By choosing +one corner of a square as ``origin,'' I can characterise +every other corner of a square with reference to this +origin by means of two numbers. I only need state +how many rods I must pass over when, starting from the +origin, I proceed towards the ``right'' and then ``upwards,'' +in order to arrive at the corner of the square +under consideration. These two numbers are then the +``Cartesian co-ordinates'' of this corner with reference +\index{Cartesian system of co-ordinates}% +to the ``Cartesian co-ordinate system'' which is determined +by the arrangement of little rods. + +By making use of the following modification of this +abstract experiment, we recognise that there must also +\PageSep{85} +\index{Measurement of length}% +be cases in which the experiment would be unsuccessful. +We shall suppose that the rods ``expand'' by an amount +proportional to the increase of temperature. We heat +the central part of the marble slab, but not the periphery, +in which case two of our little rods can still be +brought into coincidence at every position on the table. +But our construction of squares must necessarily come +into disorder during the heating, because the little rods +on the central region of the table expand, whereas +those on the outer part do not. + +With reference to our little rods---defined as unit +lengths---the marble slab is no longer a Euclidean continuum, +and we are also no longer in the position of defining +Cartesian co-ordinates directly with their aid, +since the above construction can no longer be carried +out. But since there are other things which are not +influenced in a similar manner to the little rods (or +perhaps not at all) by the temperature of the table, it is +possible quite naturally to maintain the point of view +that the marble slab is a ``Euclidean continuum.'' +This can be done in a satisfactory manner by making a +more subtle stipulation about the measurement or the +comparison of lengths. + +But if rods of every kind (\ie\ of every material) were +to behave \emph{in the same way} as regards the influence of +temperature when they are on the variably heated +marble slab, and if we had no other means of detecting +the effect of temperature than the geometrical behaviour +of our rods in experiments analogous to the one +described above, then our best plan would be to assign +the distance \emph{one} to two points on the slab, provided that +the ends of one of our rods could be made to coincide +with these two points; for how else should we define +\PageSep{86} +the distance without our proceeding being in the highest +measure grossly arbitrary? The method of Cartesian +co-ordinates must then be discarded, and replaced by +another which does not assume the validity of Euclidean +\index{Continuum!Euclidean}% +\index{Continuum!non-Euclidean}% +\index{Euclidean geometry}% +\index{Euclidean space}% +geometry for rigid bodies.\footnote + {Mathematicians have been confronted with our problem in the + following form. If we are given a surface (\eg\ an ellipsoid) in + Euclidean three-dimensional space, then there exists for this + surface a two-dimensional geometry, just as much as for a plane + surface. Gauss undertook the task of treating this two-dimensional +\index{Gauss}% + geometry from first principles, without making use of the + fact that the surface belongs to a Euclidean continuum of + three dimensions. If we imagine constructions to be made with + rigid rods \emph{in the surface} (similar to that above with the marble + slab), we should find that different laws hold for these from those + resulting on the basis of Euclidean plane geometry. The surface + is not a Euclidean continuum with respect to the rods, and we + cannot define Cartesian co-ordinates \emph{in the surface}. Gauss + indicated the principles according to which we can treat the + geometrical relationships in the surface, and thus pointed out + the way to the method of Riemann of treating multi-dimensional, +\index{Riemann}% + non-Euclidean \textit{continua}. Thus it is that mathematicians + long ago solved the formal problems to which we are led by the + general postulate of relativity.} +The reader will notice that +the situation depicted here corresponds to the one +brought about by the general postulate of relativity +(\Sectionref{XXIII}). +\PageSep{87} + + +\Chapter{XXV}{Gaussian Co-ordinates} + +\First{According} to Gauss, this combined analytical +\index{Gauss}% +and geometrical mode of handling the problem +can be arrived at in the following way. We +imagine a system of arbitrary curves (see \Figref{4}) +drawn on the surface of the table. These we designate +as $u$-curves, and we indicate each of them by +means of a number. The curves $u = 1$, $u = 2$ and +$u = 3$ are drawn in the diagram. Between the curves +$u = 1$ and $u = 2$ we must imagine an infinitely large +number to be drawn, all of which correspond +%[Illustration: Fig. 4.] +\WFigure{2in}{087} +to real +numbers lying between $1$~and~$2$. We have then +a system of $u$-curves, and +this ``infinitely dense'' system +covers the whole surface +of the table. These +$u$-curves must not intersect +each other, and through each +point of the surface one and +only one curve must pass. +Thus a perfectly definite +value of~$u$ belongs to every point on the surface of the +marble slab. In like manner we imagine a system of +$v$-curves drawn on the surface. These satisfy the same +conditions as the $u$-curves, they are provided with numbers +\PageSep{88} +in a corresponding manner, and they may likewise +be of arbitrary shape. It follows that a value of~$u$ and +a value of~$v$ belong to every point on the surface of the +table. We call these two numbers the co-ordinates +of the surface of the table (Gaussian co-ordinates). +\index{Gaussian co-ordinates|(}% +For example, the point~$P$ in the diagram has the Gaussian +co-ordinates $u = 3$, $v = 1$. Two neighbouring points $P$ +and~$P'$ on the surface then correspond to the co-ordinates +\begin{align*} +&P: &&u, v \\ +&P': &&u + du, v + dv, +\end{align*} +where $du$~and~$dv$ signify very small numbers. In a +similar manner we may indicate the distance (line-interval) +\index{Distance (line-interval)}% +between $P$~and~$P'$, as measured with a little +rod, by means of the very small number~$ds$. Then +according to Gauss we have +\[ +ds^{2} = g_{11}\, du^{2} + 2g_{12}\, du\, dv + g_{22}\, dv^{2}, +\] +where $g_{11}$,~$g_{12}$,~$g_{22}$, are magnitudes which depend in a +perfectly definite way on $u$~and~$v$. The magnitudes $g_{11}$,~$g_{12}$ +and~$g_{22}$ determine the behaviour of the rods relative +to the $u$-curves and $v$-curves, and thus also relative +to the surface of the table. For the case in which the +points of the surface considered form a Euclidean continuum +\index{Continuum!Euclidean}% +with reference to the measuring-rods, but +only in this case, it is possible to draw the $u$-curves +and $v$-curves and to attach numbers to them, in such a +manner, that we simply have: +\[ +ds^{2} = du^{2} + dv^{2}. +\] +Under these conditions, the $u$-curves and $v$-curves are +straight lines in the sense of Euclidean geometry, and +\index{Euclidean geometry}% +\index{Straight line}% +they are perpendicular to each other. Here the Gaussian +co-ordinates are simply Cartesian ones. It is clear +\PageSep{89} +that Gauss co-ordinates are nothing more than an +association of two sets of numbers with the points of +the surface considered, of such a nature that numerical +values differing very slightly from each other are +associated with neighbouring points ``in space.'' + +So far, these considerations hold for a continuum +\index{Continuum!four-dimensional}% +of two dimensions. But the Gaussian method can be +applied also to a continuum of three, four or more +dimensions. If, for instance, a continuum of four +dimensions be supposed available, we may represent +it in the following way. With every point of the +continuum we associate arbitrarily four numbers, $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$, which are known as ``co-ordinates.'' Adjacent +points correspond to adjacent values of the co-ordinates. +If a distance~$ds$ is associated with the adjacent points +\index{Adjacent points}% +$P$~and~$P'$, this distance being measurable and well-defined +from a physical point of view, then the following +formula holds: +\[ +ds^{2} = g_{11}\, {dx_{1}}^{2} + + 2g_{12}\, dx_{1}\, dx_{2} \Add{+} \dots + + g_{44}\, {dx_{4}}^{2}, +\] +where the magnitudes $g_{11}$,~etc., have values which vary +with the position in the continuum. Only when the +continuum is a Euclidean one is it possible to associate +the co-ordinates $x_{1}$\Add{,}\ldots\Add{,}~$x_{4}$ with the points of the +continuum so that we have simply +\[ +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2}. +\] +In this case relations hold in the four-dimensional +continuum which are analogous to those holding in our +three-dimensional measurements. + +However, the Gauss treatment for~$ds^{2}$ which we have +given above is not always possible. It is only possible +when sufficiently small regions of the continuum under +consideration may be regarded as Euclidean continua. +\PageSep{90} +For example, this obviously holds in the case of the +marble slab of the table and local variation of temperature. +The temperature is practically constant for a small +part of the slab, and thus the geometrical behaviour of +the rods is \emph{almost} as it ought to be according to the +rules of Euclidean geometry. Hence the imperfections +\index{Continuum!non-Euclidean}% +of the construction of squares in the previous section +do not show themselves clearly until this construction +is extended over a considerable portion of the surface +of the table. + +We can sum this up as follows: Gauss invented a +\index{Gauss}% +method for the mathematical treatment of continua in +general, in which ``size-relations'' (``distances'' between +\index{Size-relations}% +neighbouring points) are defined. To every point of a +continuum are assigned as many numbers (Gaussian co-ordinates) +as the continuum has dimensions. This is +done in such a way, that only one meaning can be attached +to the assignment, and that numbers (Gaussian co-ordinates) +\index{Gaussian co-ordinates|)}% +which differ by an indefinitely small amount +are assigned to adjacent points. The Gaussian co-ordinate +system is a logical generalisation of the Cartesian +co-ordinate system. It is also applicable to non-Euclidean +continua, but only when, with respect to the defined +``size'' or ``distance,'' small parts of the continuum +under consideration behave more nearly like a Euclidean +system, the smaller the part of the continuum under +our notice. +\PageSep{91} + + +\Chapter{XXVI}{The Space-Time Continuum of the Special +Theory of Relativity considered as +a Euclidean Continuum} +\index{Continuum!four-dimensional}% +\index{Continuum!space-time|(}% + +\First{We} are now in a position to formulate more +exactly the idea of Minkowski, which was +\index{Minkowski}% +only vaguely indicated in \Sectionref{XVII}. +In accordance with the special theory of relativity, +certain co-ordinate systems are given preference +for the description of the four-dimensional, space-time +continuum. We called these ``Galileian co-ordinate +\index{Galileian system of co-ordinates}% +systems.'' For these systems, the four co-ordinates +$x$,~$y$, $z$,~$t$, which determine an event or---in other +words---a point of the four-dimensional continuum, are +defined physically in a simple manner, as set forth in +detail in the first part of this book. For the transition +from one Galileian system to another, which is moving +uniformly with reference to the first, the equations of +the Lorentz transformation are valid. These last +\index{Lorentz, H. A.!transformation}% +form the basis for the derivation of deductions from the +special theory of relativity, and in themselves they are +nothing more than the expression of the universal +validity of the law of transmission of light for all Galileian +\index{Propagation of light}% +systems of reference. + +Minkowski found that the Lorentz transformations +satisfy the following simple conditions. Let us consider +\PageSep{92} +two neighbouring events, the relative position of which +in the four-dimensional continuum is given with respect +\index{Continuum!four-dimensional}% +to a Galileian reference-body~$K$ by the space co-ordinate +\index{Coordinate@{Co-ordinate}!differences}% +\index{Coordinate@{Co-ordinate}!differentials}% +differences $dx$,~$dy$,~$dz$ and the time-difference~$dt$. With +reference to a second Galileian system we shall suppose +that the corresponding differences for these two events +are $dx'$,~$dy'$, $dz'$,~$dt'$. Then these magnitudes always +fulfil the condition\footnote + {Cf.\ Appendices I~and~II\@. The relations which are derived + there for the co-ordinates themselves are valid also for co-ordinate + \emph{differences}, and thus also for co-ordinate differentials + (indefinitely small differences).} +\[ +dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2} + = dx'^{2} + dy'^{2} + dz'^{2} - c^{2}\, dt'^{2}. +\] + +The validity of the Lorentz transformation follows +from this condition. We can express this as follows: +The magnitude +\[ +ds^{2} = dx^{2} + dy^{2} + dz^{2} - c^{2}\, dt^{2}, +\] +which belongs to two adjacent points of the four-dimensional +space-time continuum, has the same value +for all selected (Galileian) reference-bodies. If we replace +$x$,~$y$, $z$,~$\sqrt{-1}\,ct$, by $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, we also obtain the +result that +\[ +ds^{2} = {dx_{1}}^{2} + {dx_{2}}^{2} + {dx_{3}}^{2} + {dx_{4}}^{2} +\] +is independent of the choice of the body of reference. +We call the magnitude~$ds$ the ``distance'' apart of the +two events or four-dimensional points. + +Thus, if we choose as time-variable the imaginary +variable~$\sqrt{-1}\,ct$ instead of the real quantity~$t$, we can +regard the space-time continuum---in accordance with +the special theory of relativity---as a ``Euclidean'' +\index{Continuum!Euclidean}% +four-dimensional continuum, a result which follows +from the considerations of the preceding section. +\PageSep{93} + + +\Chapter{XXVII}{The Space-Time Continuum of the +General Theory of Relativity is +not a Euclidean Continuum} + +\First{In} the first part of this book we were able to make use +of space-time co-ordinates which allowed of a simple +and direct physical interpretation, and which, according +to \Sectionref{XXVI}, can be regarded as four-dimensional +Cartesian co-ordinates. This was possible on the basis +of the law of the constancy of the velocity of light. But +according to \Sectionref{XXI}, the general theory of relativity +cannot retain this law. On the contrary, we arrived at +the result that according to this latter theory the +velocity of light must always depend on the co-ordinates +when a gravitational field is present. In connection +\index{Gravitational field}% +with a specific illustration in \Sectionref{XXIII}, we found +that the presence of a gravitational field invalidates the +definition of the co-ordinates and the time, which led us +to our objective in the special theory of relativity. + +In view of the results of these considerations we are +led to the conviction that, according to the general +principle of relativity, the space-time continuum cannot +be regarded as a Euclidean one, but that here we have +the general case, corresponding to the marble slab with +local variations of temperature, and with which we +made acquaintance as an example of a two-dimensional +\PageSep{94} +continuum. Just as it was there impossible to construct +\index{Continuum!two-dimensional}% +\index{Continuum!four-dimensional}% +a Cartesian co-ordinate system from equal rods, so +here it is impossible to build up a system (reference-body) +from rigid bodies and clocks, which shall be of +\index{Clocks}% +such a nature that measuring-rods and clocks, arranged +\index{Measuring-rod}% +rigidly with respect to one another, shall indicate position +and time directly. Such was the essence of the +difficulty with which we were confronted in \Sectionref{XXIII}. + +But the considerations of Sections \Srefno{XXV}~and~\Srefno{XXVI} +show us the way to surmount this difficulty. We refer the +four-dimensional space-time continuum in an arbitrary +manner to Gauss co-ordinates. We assign to every +\index{Gaussian co-ordinates}% +point of the continuum (event) four numbers, $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$ (co-ordinates), which have not the least direct +physical significance, but only serve the purpose of +numbering the points of the continuum in a definite +but arbitrary manner. This arrangement does not even +need to be of such a kind that we must regard $x_{1}$,~$x_{2}$,~$x_{3}$ as +``space'' co-ordinates and $x_{4}$~as a ``time'' co-ordinate. + +The reader may think that such a description of the +world would be quite inadequate. What does it mean +to assign to an event the particular co-ordinates $x_{1}$,~$x_{2}$, +$x_{3}$,~$x_{4}$, if in themselves these co-ordinates have no +significance? More careful consideration shows, however, +that this anxiety is unfounded. Let us consider, +for instance, a material point with any kind of motion. +If this point had only a momentary existence without +duration, then it would be described in space-time by a +single system of values $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$. Thus its permanent +existence must be characterised by an infinitely large +number of such systems of values, the co-ordinate values +of which are so close together as to give continuity; +\PageSep{95} +corresponding to the material point, we thus have a +(uni-dimensional) line in the four-dimensional continuum. +\index{Continuity}% +In the same way, any such lines in our continuum +correspond to many points in motion. The only statements +having regard to these points which can claim +a physical existence are in reality the statements about +their encounters. In our mathematical treatment, +such an encounter is expressed in the fact that the two +lines which represent the motions of the points in +question have a particular system of co-ordinate values, +$x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, in common. After mature consideration +the reader will doubtless admit that in reality such +encounters constitute the only actual evidence of a +time-space nature with which we meet in physical +statements. + +When we were describing the motion of a material +\index{Encounter (space-time coincidence)}% +point relative to a body of reference, we stated +nothing more than the encounters of this point with +particular points of the reference-body. We can also +determine the corresponding values of the time by the +observation of encounters of the body with clocks, in +\index{Clocks}% +conjunction with the observation of the encounter of the +hands of clocks with particular points on the dials. +It is just the same in the case of space-measurements by +means of measuring-rods, as a little consideration will +show. + +The following statements hold generally: Every +physical description resolves itself into a number of +statements, each of which refers to the space-time +coincidence of two events $A$~and~$B$. In terms of +Gaussian co-ordinates, every such statement is expressed +by the agreement of their four co-ordinates $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$. +Thus in reality, the description of the time-space +\PageSep{96} +continuum by means of Gauss co-ordinates completely +\index{Gaussian co-ordinates|(}% +replaces the description with the aid of a body of reference, +without suffering from the defects of the latter +mode of description; it is not tied down to the Euclidean +character of the continuum which has to be represented. +\index{Continuum!space-time|)}% +\PageSep{97} + + +\Chapter{XXVIII}{Exact Formulation of the General +Principle of Relativity} +\index{General theory of relativity}% + +\First{We} are now in a position to replace the provisional +formulation of the general principle +of relativity given in \Sectionref{XVIII} by +an exact formulation. The form there used, ``All +bodies of reference $K$,~$K'$,~etc., are equivalent for +the description of natural phenomena (formulation of +the general laws of nature), whatever may be their +state of motion,'' cannot be maintained, because the +use of rigid reference-bodies, in the sense of the method +followed in the special theory of relativity, is in general +not possible in space-time description. The Gauss +co-ordinate system has to take the place of the body of +reference. The following statement corresponds to the +fundamental idea of the general principle of relativity: +``\emph{All Gaussian co-ordinate systems are essentially equivalent +for the formulation of the general laws of nature.}'' + +We can state this general principle of relativity in still +another form, which renders it yet more clearly intelligible +than it is when in the form of the natural +extension of the special principle of relativity. According +to the special theory of relativity, the equations +which express the general laws of nature pass over into +equations of the same form when, by making use of the +Lorentz transformation, we replace the space-time +\index{Lorentz, H. A.!transformation}% +\PageSep{98} +variables $x$,~$y$, $z$,~$t$, of a (Galileian) reference-body~$K$ +by the space-time variables $x'$,~$y'$, $z'$,~$t'$, of a new reference-body~$K'$. +According to the general theory +of relativity, on the other hand, by application of +\emph{arbitrary substitutions} of the Gauss variables $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, +\index{Arbitrary substitutions}% +the equations must pass over into equations of the same +form; for every transformation (not only the Lorentz +\index{Lorentz, H. A.!transformation}% +transformation) corresponds to the transition of one +Gauss co-ordinate system into another. + +If we desire to adhere to our ``old-time'' three-dimensional +\index{Law of inertia}% +view of things, then we can characterise +the development which is being undergone by the +fundamental idea of the general theory of relativity +as follows: The special theory of relativity has reference +to Galileian domains, \ie\ to those in which no gravitational +field exists. In this connection a Galileian reference-body +\index{Galileian system of co-ordinates}% +serves as body of reference, \ie\ a rigid +body the state of motion of which is so chosen that the +Galileian law of the uniform rectilinear motion of +``isolated'' material points holds relatively to it. + +Certain considerations suggest that we should refer +the same Galileian domains to \emph{non-Galileian} reference-bodies +\index{Non-Galileian reference-bodies}% +also. A gravitational field of a special kind is +\index{Gravitational field}% +then present with respect to these bodies (cf.\ Sections \Srefno{XX} +and~\Srefno{XXIII}). + +In gravitational fields there are no such things as rigid +\index{Time!in Physics}% +bodies with Euclidean properties; thus the fictitious rigid +body of reference is of no avail in the general theory of +relativity. The motion of clocks is also influenced by +\index{Clocks|(}% +gravitational fields, and in such a way that a physical +definition of time which is made directly with the aid of +clocks has by no means the same degree of plausibility +as in the special theory of relativity. +\PageSep{99} +\index{Laws of Galilei-Newton!of Nature}% +\index{Time!coordinate@{co-ordinate}}% + +For this reason non-rigid reference-bodies are used, +which are as a whole not only moving in any way +whatsoever, but which also suffer alterations in form +\textit{ad~lib.}\ during their motion. Clocks, for which the law of +motion is of any kind, however irregular, serve for the +definition of time. We have to imagine each of these +clocks fixed at a point on the non-rigid reference-body. +\index{Reference-mollusk|(}% +These clocks satisfy only the one condition, that the +``readings'' which are observed simultaneously on +adjacent clocks (in space) differ from each other by an +\index{Space!point@{-point}}% +indefinitely small amount. This non-rigid reference-body, +which might appropriately be termed a ``reference-mollusk,'' +is in the main equivalent to a Gaussian four-dimensional +co-ordinate system chosen arbitrarily. +That which gives the ``mollusk'' a certain comprehensibleness +as compared with the Gauss co-ordinate +system is the (really unjustified) formal retention of +the separate existence of the space co-ordinates as +\index{Space co-ordinates}% +opposed to the time co-ordinate. Every point on the +mollusk is treated as a space-point, and every material +point which is at rest relatively to it as at rest, so long as +the mollusk is considered as reference-body. The +general principle of relativity requires that all these +mollusks can be used as reference-bodies with equal +right and equal success in the formulation of the general +laws of nature; the laws themselves must be quite +independent of the choice of mollusk. + +The great power possessed by the general principle +of relativity lies in the comprehensive limitation which +is imposed on the laws of nature in consequence of what +we have seen above. +\PageSep{100} + + +\Chapter{XXIX}{The Solution of the Problem of Gravitation +on the Basis of the General +Principle of Relativity} + +\First{If} the reader has followed all our previous considerations, +he will have no further difficulty in +understanding the methods leading to the solution +of the problem of gravitation. + +We start off from a consideration of a Galileian +domain, \ie\ a domain in which there is no gravitational +field relative to the Galileian reference-body~$K$. The +\index{Galileian system of co-ordinates}% +behaviour of measuring-rods and clocks with reference +\index{Measuring-rod}% +to~$K$ is known from the special theory of relativity, +likewise the behaviour of ``isolated'' material points; +the latter move uniformly and in straight lines. + +Now let us refer this domain to a random Gauss co-ordinate +system or to a ``mollusk'' as reference-body~$K'$. +Then with respect to~$K'$ there is a gravitational +field~$G$ (of a particular kind). We learn the behaviour +of measuring-rods and clocks and also of freely-moving +material points with reference to~$K'$ simply by mathematical +transformation. We interpret this behaviour +as the behaviour of measuring-rods, clocks and material +\index{Clocks|)}% +points under the influence of the gravitational field~$G$. +\index{Gravitational field}% +Hereupon we introduce a hypothesis: that the influence +of the gravitational field on measuring-rods, +\index{Gaussian co-ordinates|)}% +\PageSep{101} +clocks and freely-moving material points continues to +take place according to the same laws, even in the case +when the prevailing gravitational field is \emph{not} derivable +\index{Gravitational field}% +from the Galileian special case, simply by means of a +transformation of co-ordinates. + +The next step is to investigate the space-time +behaviour of the gravitational field~$G$, which was derived +from the Galileian special case simply by transformation +of the co-ordinates. This behaviour is formulated +in a law, which is always valid, no matter how the +\index{Matter}% +reference-body (mollusk) used in the description may +\index{Reference-mollusk|)}% +be chosen. + +This law is not yet the \emph{general} law of the gravitational +field, since the gravitational field under consideration is +of a special kind. In order to find out the general +law-of-field of gravitation we still require to obtain a +generalisation of the law as found above. This can be +obtained without caprice, however, by taking into +consideration the following demands: +\begin{itemize} +\item[\itema] The required generalisation must likewise satisfy + the general postulate of relativity. + +\item[\itemb] If there is any matter in the domain under consideration, + only its inertial mass, and thus +\index{Inertial mass}% + according to \Sectionref{XV} only its energy is of + importance for its effect in exciting a field. + +\item[\itemc] Gravitational field and matter together must + satisfy the law of the conservation of energy +\index{Conservation of energy}% +\index{Conservation of energy!impulse}% +\index{Kinetic energy}% + (and of impulse). +\end{itemize} + +Finally, the general principle of relativity permits +us to determine the influence of the gravitational field +on the course of all those processes which take place +according to known laws when a gravitational field is +\PageSep{102} +absent, \ie\ which have already been fitted into the +frame of the special theory of relativity. In this connection +we proceed in principle according to the method +which has already been explained for measuring-rods, +\index{Measuring-rod}% +clocks and freely-moving material points. +\index{Clocks}% + +The theory of gravitation derived in this way from +\index{Gravitation}% +the general postulate of relativity excels not only in +its beauty; nor in removing the defect attaching to +classical mechanics which was brought to light in \Sectionref{XXI}; +\index{Classical mechanics}% +nor in interpreting the empirical law of the equality +of inertial and gravitational mass; but it has also +\index{Gravitational mass}% +\index{Inertial mass}% +already explained a result of observation in astronomy, +\index{Astronomy}% +against which classical mechanics is powerless. + +If we confine the application of the theory to the +case where the gravitational fields can be regarded as +being weak, and in which all masses move with respect +to the co-ordinate system with velocities which are +small compared with the velocity of light, we then obtain +as a first approximation the Newtonian theory. Thus +the latter theory is obtained here without any particular +assumption, whereas Newton had to introduce the +\index{Newton}% +hypothesis that the force of attraction between mutually +attracting material points is inversely proportional to +the square of the distance between them. If we increase +the accuracy of the calculation, deviations from +the theory of Newton make their appearance, practically +all of which must nevertheless escape the test of +observation owing to their smallness. + +We must draw attention here to one of these deviations. +According to Newton's theory, a planet moves +round the sun in an ellipse, which would permanently +maintain its position with respect to the fixed stars, +if we could disregard the motion of the fixed stars +\index{Motion!of heavenly bodies}% +\PageSep{103} +themselves and the action of the other planets under +consideration. Thus, if we correct the observed motion +of the planets for these two influences, and if Newton's +theory be strictly correct, we ought to obtain for the +orbit of the planet an ellipse, which is fixed with reference +to the fixed stars. This deduction, which can +be tested with great accuracy, has been confirmed +for all the planets save one, with the precision that is +capable of being obtained by the delicacy of observation +attainable at the present time. The sole exception +is Mercury, the planet which lies nearest the sun. Since +\index{Mercury}% +\index{Mercury!orbit of}% +the time of Leverrier, it has been known that the ellipse +\index{Leverrier}% +corresponding to the orbit of Mercury, after it has been +corrected for the influences mentioned above, is not +stationary with respect to the fixed stars, but that it +rotates exceedingly slowly in the plane of the orbit +and in the sense of the orbital motion. The value +obtained for this rotary movement of the orbital ellipse +was $43$~seconds of arc per~century, an amount ensured +to be correct to within a few seconds of arc. This +effect can be explained by means of classical mechanics +\index{Classical mechanics}% +only on the assumption of hypotheses which have +little probability, and which were devised solely for +this purpose. + +On the basis of the general theory of relativity, it +is found that the ellipse of every planet round the sun +must necessarily rotate in the manner indicated above; +that for all the planets, with the exception of Mercury, +this rotation is too small to be detected with the delicacy +of observation possible at the present time; but that in +the case of Mercury it must amount to $43$~seconds of +arc per century, a result which is strictly in agreement +with observation. +\PageSep{104} + +Apart from this one, it has hitherto been possible to +make only two deductions from the theory which admit +of being tested by observation, to wit, the curvature +\index{Curvature of light-rays}% +of light rays by the gravitational field of the sun,\footnote + {Observed by Eddington and others in~1919. (Cf.\ \Appendixref{III}.)} +\index{Eddington}% +and a displacement of the spectral lines of light reaching +\index{Displacement of spectral lines}% +us from large stars, as compared with the corresponding +lines for light produced in an analogous manner terrestrially +(\ie\ by the same kind of molecule). I do not +doubt that these deductions from the theory will be +confirmed also. +\index{General theory of relativity|)}% +\PageSep{105} + + +\Part{III}{Considerations on the Universe as +a Whole}{Considerations on the Universe} + +\Chapter{XXX}{Cosmological Difficulties of Newton's +Theory} +\index{Newton}% + +\First{Apart} from the difficulty discussed in \Sectionref{XXI}, +there is a second fundamental difficulty +attending classical celestial mechanics, which, +\index{Celestial mechanics}% +to the best of my knowledge, was first discussed in +detail by the astronomer Seeliger. If we ponder over +\index{Seeliger}% +the question as to how the universe, considered as a +whole, is to be regarded, the first answer that suggests +itself to us is surely this: As regards space (and time) +\index{Space}% +\index{Time!conception of}% +the universe is infinite. There are stars everywhere, +so that the density of matter, although very variable +in detail, is nevertheless on the average everywhere the +same. In other words: However far we might travel +through space, we should find everywhere an attenuated +swarm of fixed stars of approximately the same kind +and density. + +This view is not in harmony with the theory of +Newton. The latter theory rather requires that the +universe should have a kind of centre in which the +\PageSep{106} +density of the stars is a maximum, and that as we +proceed outwards from this centre the group-density +\index{Group-density of stars}% +of the stars should diminish, until finally, at great +distances, it is succeeded by an infinite region of emptiness. +The stellar universe ought to be a finite island in +\index{Stellar universe}% +the infinite ocean of space.\footnote + {\textit{Proof}---According to the theory of Newton, the number of + ``lines of force'' which come from infinity and terminate in a +\index{Lines of force}% + mass~$m$ is proportional to the mass~$m$. If, on the average, the + mass-density~$\rho_{0}$ is constant throughout the universe, then a + sphere of volume~$V$ will enclose the average mass~$\rho_{0}V$. Thus + the number of lines of force passing through the surface~$F$ of the + sphere into its interior is proportional to~$\rho_{0}V$. For unit area + of the surface of the sphere the number of lines of force which + enters the sphere is thus proportional to~$\rho_{0}\dfrac{V}{F}$ or to~$\rho_{0}R$. Hence + the intensity of the field at the surface would ultimately become + infinite with increasing radius~$R$ of the sphere, which is impossible.} + +This conception is in itself not very satisfactory. +It is still less satisfactory because it leads to the result +that the light emitted by the stars and also individual +stars of the stellar system are perpetually passing out +into infinite space, never to return, and without ever +again coming into interaction with other objects of +nature. Such a finite material universe would be +destined to become gradually but systematically impoverished. + +In order to escape this dilemma, Seeliger suggested a +\index{Intensity of gravitational field}% +\index{Seeliger}% +modification of Newton's law, in which he assumes that +\index{Newton's!law of gravitation}% +for great distances the force of attraction between two +masses diminishes more rapidly than would result from +the inverse square law. In this way it is possible for the +mean density of matter to be constant everywhere, +even to infinity, without infinitely large gravitational +fields being produced. We thus free ourselves from the +\PageSep{107} +distasteful conception that the material universe ought +to possess something of the nature of a centre. Of +course we purchase our emancipation from the fundamental +difficulties mentioned, at the cost of a modification +and complication of Newton's law which has +neither empirical nor theoretical foundation. We can +imagine innumerable laws which would serve the same +purpose, without our being able to state a reason why +one of them is to be preferred to the others; for any +one of these laws would be founded just as little on +more general theoretical principles as is the law of +Newton. +\PageSep{108} + + +\Chapter{XXXI}{The Possibility of a ``Finite'' and yet +``Unbounded'' Universe} +\index{Universe (World) structure of}% + +\First{But} speculations on the structure of the universe +also move in quite another direction. The +development of non-Euclidean geometry led to +\index{Euclidean geometry}% +\index{Non-Euclidean geometry}% +the recognition of the fact, that we can cast doubt on the +\emph{infiniteness} of our space without coming into conflict +with the laws of thought or with experience (Riemann, +\index{Riemann}% +Helmholtz). These questions have already been treated +\index{Helmholtz}% +in detail and with unsurpassable lucidity by Helmholtz +and Poincaré, whereas I can only touch on them +\index{Poincare@{Poincaré}}% +briefly here. + +In the first place, we imagine an existence in two-dimensional +\index{Being@{``Being''}}% +\index{Space!two-dimensional}% +space. Flat beings with flat implements, +and in particular flat rigid measuring-rods, are free to +move in a \emph{plane}. For them nothing exists outside of +\index{Plane}% +this plane: that which they observe to happen to +themselves and to their flat ``things'' is the all-inclusive +reality of their plane. In particular, the constructions +of plane Euclidean geometry can be carried out by +means of the rods, \eg\ the lattice construction, considered +\index{Lattice}% +in \Sectionref{XXIV}. In contrast to ours, the universe of +these beings is two-dimensional; but, like ours, it extends +to infinity. In their universe there is room for an +infinite number of identical squares made up of rods, +\PageSep{109} +\ie\ its volume (surface) is infinite. If these beings say +their universe is ``plane,'' there is sense in the statement, +\index{Plane}% +\index{Universe!Euclidean}% +because they mean that they can perform the constructions +of plane Euclidean geometry with their rods. +\index{Euclidean geometry}% +In this connection the individual rods always represent +\index{Distance (line-interval)}% +the same distance, independently of their position. + +Let us consider now a second two-dimensional existence, +but this time on a spherical surface instead of on +\index{Spherical!surface}% +a plane. The flat beings with their measuring-rods +and other objects fit exactly on this surface and they +are unable to leave it. Their whole universe of observation +extends exclusively over the surface of the sphere. +Are these beings able to regard the geometry of their +universe as being plane geometry and their rods withal +as the realisation of ``distance''? They cannot do +this. For if they attempt to realise a straight line, they +\index{Straight line}% +will obtain a curve, which we ``three-dimensional +beings'' designate as a great circle, \ie\ a self-contained +line of definite finite length, which can be measured +up by means of a measuring-rod. Similarly, this +universe has a finite area that can be compared with the +area of a square constructed with rods. The great +charm resulting from this consideration lies in the +recognition of the fact that \emph{the universe of these beings is +finite and yet has no limits}. + +But the spherical-surface beings do not need to go +on a world-tour in order to perceive that they are not +\index{World}% +living in a Euclidean universe. They can convince +themselves of this on every part of their ``world,'' +provided they do not use too small a piece of it. Starting +from a point, they draw ``straight lines'' (arcs of circles +as judged in three-dimensional space) of equal length +in all directions. They will call the line joining the +\PageSep{110} +free ends of these lines a ``circle.'' For a plane surface, +the ratio of the circumference of a circle to its diameter, +both lengths being measured with the same rod, is, +according to Euclidean geometry of the plane, equal to +a constant value~$\pi$, which is independent of the diameter +\index{Value of $\pi$}% +of the circle. On their spherical surface our flat beings +would find for this ratio the value +\[ +\pi = \frac{\sin\left(\dfrac{r}{R}\right)}{\left(\dfrac{r}{R}\right)}, +\] +\ie\ a smaller value than~$\pi$, the difference being the +more considerable, the greater is the radius of the +circle in comparison with the radius~$R$ of the ``world-sphere.'' +\index{World!sphere@{-sphere}}% +By means of this relation the spherical beings +can determine the radius of their universe (``world''), +even when only a relatively small part of their world-sphere +is available for their measurements. But if this +part is very small indeed, they will no longer be able to +demonstrate that they are on a spherical ``world'' and +not on a Euclidean plane, for a small part of a spherical +surface differs only slightly from a piece of a plane of +the same size. + +Thus if the spherical-surface beings are living on a +planet of which the solar system occupies only a negligibly +small part of the spherical universe, they have no means +of determining whether they are living in a finite or in +an infinite universe, because the ``piece of universe'' +to which they have access is in both cases practically +plane, or Euclidean. It follows directly from this +discussion, that for our sphere-beings the circumference +of a circle first increases with the radius until the ``circumference +\PageSep{111} +\index{Universe (World) structure of!circumference of}% +of the universe'' is reached, and that it +\index{Universe!Euclidean}% +\index{Universe!spherical}% +thenceforward gradually decreases to zero for still +further increasing values of the radius. During this +process the area of the circle continues to increase +more and more, until finally it becomes equal to the +total area of the whole ``world-sphere.'' +\index{World!sphere@{-sphere}}% + +Perhaps the reader will wonder why we have placed +our ``beings'' on a sphere rather than on another closed +surface. But this choice has its justification in the fact +that, of all closed surfaces, the sphere is unique in possessing +the property that all points on it are equivalent. I +admit that the ratio of the circumference~$c$ of a circle +to its radius~$r$ depends on~$r$, but for a given value of~$r$ +it is the same for all points of the ``world-sphere''; +in other words, the ``world-sphere'' is a ``surface of +constant curvature.'' + +To this two-dimensional sphere-universe there is a +three-dimensional analogy, namely, the three-dimensional +spherical space which was discovered by Riemann. Its +\index{Riemann}% +points are likewise all equivalent. It possesses a finite +volume, which is determined by its ``radius'' ($2\pi^{2}R^{3}$). +Is it possible to imagine a spherical space? To imagine +a space means nothing else than that we imagine an +epitome of our ``space'' experience, \ie\ of experience +that we can have in the movement of ``rigid'' bodies. +In this sense we \emph{can} imagine a spherical space. + +Suppose we draw lines or stretch strings in all directions +from a point, and mark off from each of these +the distance~$r$ with a measuring-rod. All the free end-points +\index{Measuring-rod}% +of these lengths lie on a spherical surface. We +\index{Spherical!space}% +can specially measure up the area~($F$) of this surface +by means of a square made up of measuring-rods. If +the universe is Euclidean, then $F = 4\pi r^{2}$; if it is spherical, +\PageSep{112} +then $F$~is always less than~$4\pi r^{2}$. With increasing +values of~$r$, $F$~increases from zero up to a maximum +value which is determined by the ``world-radius,'' but +\index{World!radius@{-radius}}% +for still further increasing values of~$r$, the area gradually +diminishes to zero. At first, the straight lines which +radiate from the starting point diverge farther and +farther from one another, but later they approach +each other, and finally they run together again at a +``counter-point'' to the starting point. Under such +\index{Counter-Point}% +conditions they have traversed the whole spherical +space. It is easily seen that the three-dimensional +spherical space is quite analogous to the two-dimensional +spherical surface. It is finite (\ie\ of finite volume), and +\index{Spherical!space}% +has no bounds. + +It may be mentioned that there is yet another kind +of curved space: ``elliptical space.'' It can be regarded +\index{Elliptical space}% +as a curved space in which the two ``counter-points'' +are identical (indistinguishable from each other). An +elliptical universe can thus be considered to some +\index{Universe!elliptical}% +extent as a curved universe possessing central symmetry. + +It follows from what has been said, that closed spaces +without limits are conceivable. From amongst these, +the spherical space (and the elliptical) excels in its +simplicity, since all points on it are equivalent. As a +result of this discussion, a most interesting question +arises for astronomers and physicists, and that is +whether the universe in which we live is infinite, or +whether it is finite in the manner of the spherical universe. +Our experience is far from being sufficient to +enable us to answer this question. But the general +theory of relativity permits of our answering it with a +moderate degree of certainty, and in this connection the +difficulty mentioned in \Sectionref{XXX} finds its solution. +\PageSep{113} + + +\Chapter{XXXII}{The Structure of Space according to +the General Theory of Relativity} +\index{Motion!of heavenly bodies}% +\index{Universe (World) structure of}% + +\First{According} to the general theory of relativity, +the geometrical properties of space are not independent, +but they are determined by matter. +Thus we can draw conclusions about the geometrical +structure of the universe only if we base our considerations +on the state of the matter as being something +that is known. We know from experience that, for a +suitably chosen co-ordinate system, the velocities of +the stars are small as compared with the velocity of +transmission of light. We can thus as a rough approximation +arrive at a conclusion as to the nature of +the universe as a whole, if we treat the matter as being +at rest. + +We already know from our previous discussion that the +behaviour of measuring-rods and clocks is influenced by +\index{Clocks}% +\index{Measuring-rod}% +gravitational fields, \ie\ by the distribution of matter. +\index{Gravitational field}% +This in itself is sufficient to exclude the possibility of +the exact validity of Euclidean geometry in our universe. +\index{Euclidean geometry}% +But it is conceivable that our universe differs +only slightly from a Euclidean one, and this notion +seems all the more probable, since calculations show +that the metrics of surrounding space is influenced only +to an exceedingly small extent by masses even of the +\PageSep{114} +magnitude of our sun. We might imagine that, as +regards geometry, our universe behaves analogously +\index{Universe!elliptical}% +\index{Universe!space expanse (radius) of}% +\index{Universe!spherical}% +to a surface which is irregularly curved in its individual +parts, but which nowhere departs appreciably from a +plane: something like the rippled surface of a lake. +Such a universe might fittingly be called a quasi-Euclidean +universe. As regards its space it would be +infinite. But calculation shows that in a quasi-Euclidean +universe the average density of matter +would necessarily be \emph{nil}. Thus such a universe could +not be inhabited by matter everywhere; it would +present to us that unsatisfactory picture which we +portrayed in \Sectionref{XXX}. + +If we are to have in the universe an average density +of matter which differs from zero, however small may +be that difference, then the universe cannot be quasi-Euclidean. +\index{Quasi-Euclidean universe}% +On the contrary, the results of calculation +indicate that if matter be distributed uniformly, the +universe would necessarily be spherical (or elliptical). +Since in reality the detailed distribution of matter is +not uniform, the real universe will deviate in individual +parts from the spherical, \ie\ the universe will be quasi-spherical. +\index{Quasi-spherical universe}% +But it will be necessarily finite. In fact, the +theory supplies us with a simple connection\footnote + {For the ``radius''~$R$ of the universe we obtain the equation + \[ + R^{2} = \frac{2}{\kappa \rho}. + \] + The use of the C.G.S. system in this equation gives $\dfrac{2}{\kappa} = 1.08 × 10^{27}$; +is the average density of the matter.} +between +the space-expanse of the universe and the average +density of matter in it. +\PageSep{115} + + +\Appendix{I}{Simple Derivation of the Lorentz +Transformation}{[Supplementary to \Sectionref{XI}]} +\index{Lorentz, H. A.!transformation}% + +\First{For} the relative orientation of the co-ordinate +systems indicated in \Figref{2}, the $x$-axes of both +systems permanently coincide. In the present +case we can divide the problem into parts by considering +first only events which are localised on the $x$-axis. Any +such event is represented with respect to the co-ordinate +system~$K$ by the abscissa~$x$ and the time~$t$, and with +respect to the system~$K'$ by the abscissa~$x'$ and the +time~$t'$. We require to find $x'$~and~$t'$ when $x$~and~$t$ are +given. + +A light-signal, which is proceeding along the positive +\index{Light-signal}% +axis of~$x$, is transmitted according to the equation +\[ +x = ct +\] +or +\[ +x - ct = 0. +\Tag{(1)} +\] +Since the same light-signal has to be transmitted relative +to~$K'$ with the velocity~$c$, the propagation relative to +the system~$K'$ will be represented by the analogous +formula +\[ +x' - ct' = 0. +\Tag{(2)} +\] +Those space-time points (events) which satisfy~\Eqref{(1)} must +\PageSep{116} +also satisfy~\Eqref{(2)}. Obviously this will be the case when +the relation +\[ +(x' - ct') = \lambda(x - ct)\Change{.}{} +\Tag{(3)} +\] +is fulfilled in general, where $\lambda$~indicates a constant; for, +according to~\Eqref{(3)}, the disappearance of~$(x - ct)$ involves +the disappearance of~$(x' - ct')$. + +If we apply quite similar considerations to light rays +which are being transmitted along the negative $x$-axis, +we obtain the condition +\[ +(x' + ct') = \mu(x + ct). +\Tag{(4)} +\] + +By adding (or subtracting) equations \Eqref{(3)}~and~\Eqref{(4)}, and +introducing for convenience the constants $a$~and~$b$ in +place of the constants $\lambda$~and~$\mu$, where +\begin{align*} +a &= \frac{\lambda + \mu}{2} +\intertext{and} +b &= \frac{\lambda - \mu}{2}, +\end{align*} +we obtain the equations +\[ +\left. +\begin{aligned} +x' &= ax - bct\Add{,} \\ +ct' &= act - bx. +\end{aligned} +\right\} +\Tag{(5)} +\] + +We should thus have the solution of our problem, +if the constants $a$~and~$b$ were known. These result +from the following discussion. + +For the origin of~$K'$ we have permanently $x' = 0$, and +hence according to the first of the equations~\Eqref{(5)} +\[ +x = \frac{bc}{a} t. +\] + +If we call~$v$ the velocity with which the origin of~$K'$ is +moving relative to~$K$, we then have +\[ +v = \frac{bc}{a}. +\Tag{(6)} +\] +\PageSep{117} + +The same value~$v$ can be obtained from equation~\Eqref{(5)}, +if we calculate the velocity of another point of~$K'$ +relative to~$K$, or the velocity (directed towards the +\index{Relative!velocity}% +negative $x$-axis) of a point of~$K$ with respect to~$K'$. In +short, we can designate~$v$ as the relative velocity of the +two systems. + +Furthermore, the principle of relativity teaches us +that, as judged from~$K$, the length of a unit measuring-rod +\index{Measuring-rod}% +which is at rest with reference to~$K'$ must be exactly +the same as the length, as judged from~$K'$, of a unit +measuring-rod which is at rest relative to~$K$. In order +to see how the points of the $x'$-axis appear as viewed +from~$K$, we only require to take a ``snapshot'' of~$K'$ +\index{Instantaneous photograph (snapshot)}% +from~$K$; this means that we have to insert a particular +value of~$t$ (time of~$K$), \eg\ $t = 0$. For this value of~$t$ +we then obtain from the first of the equations~\Eqref{(5)} +\[ +x' = ax. +\] + +Two points of the $x'$-axis which are separated by the +distance $\Delta x' = 1$ when measured in the $K'$~system are +thus separated in our instantaneous photograph by the +distance +\[ +\Delta x = \frac{1}{a}. +\Tag{(7)} +\] + +But if the snapshot be taken from~$K'$\Change{}{ }($t' = 0$), and if +we eliminate~$t$ from the equations~\Eqref{(5)}, taking into +account the expression~\Eqref{(6)}, we obtain +\[ +x' = a\left(1 - \frac{v^{2}}{c^{2}}\right)x. +\] + +From this we conclude that two points on the $x$-axis +and separated by the distance~$1$ (relative to~$K$) will +be represented on our snapshot by the distance +\[ +\Delta x' = a\left(1 - \frac{v^{2}}{c^{2}}\right). +\Tag{(7a)} +\] +\PageSep{118} + +But from what has been said, the two snapshots +must be identical; hence $\Delta x$~in~\Eqref{(7)} must be equal to +$\Delta x'$~in~\Eqref{(7a)}, so that we obtain +\[ +a^{2} = \frac{1}{1 - \dfrac{v^{2}}{c^{2}}}. +\Tag{(7b)} +\] + +The equations \Eqref{(6)}~and~\Eqref{(7b)} determine the constants $a$~and~$b$. +By inserting the values of these constants in~\Eqref{(5)}, +we obtain the first and the fourth of the equations +given in \Sectionref{XI}. +\[ +\left. +\begin{aligned} +x' &= \frac{x - vt}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}\Add{,} \\ +t' &= \frac{t - \dfrac{v}{c^{2}}x}{\sqrt{1 - \dfrac{v^{2}}{c^{2}}}}. +\end{aligned} +\right\} +\Tag{(8)} +\] + +Thus we have obtained the Lorentz transformation +\index{Lorentz, H. A.!transformation}% +for events on the $x$-axis. It satisfies the condition +\[ +x'^{2} - c^{2} t'^{2} = x^{2} - c^{2} t^{2}. +\Tag{(8a)} +\] + +The extension of this result, to include events which +take place outside the $x$-axis, is obtained by retaining +equations~\Eqref{(8)} and supplementing them by the relations +\[ +\left. +\begin{aligned} +y' &= y\Add{,} \\ +z' &= z. +\end{aligned} +\right\} +\Tag{(9)} +\] +In this way we satisfy the postulate of the constancy of +the velocity of light \textit{in~vacuo} for rays of light of arbitrary +\index{Velocity of light}% +direction, both for the system~$K$ and for the system~$K'$. +This may be shown in the following manner. + +We suppose a light-signal sent out from the origin +\index{Light-signal}% +of~$K$ at the time $t = 0$. It will be propagated according +to the equation +\[ +r = \sqrt{x^{2} + y^{2} + z^{2}} = ct, +\] +\PageSep{119} +or, if we square this equation, according to the equation +\[ +x^{2} + y^{2} + z^{2} - c^{2} t^{2} = 0. +\Tag{(10)} +\] + +It is required by the law of propagation of light, in +\index{Propagation of light}% +conjunction with the postulate of relativity, that the +transmission of the signal in question should take place---as +judged from~$K'$---in accordance with the corresponding +formula +\[ +r' = ct', +\] +or, +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} = 0. +\Tag{(10a)} +\] +In order that equation~\Eqref{(10a)} may be a consequence of +equation~\Eqref{(10)}, we must have +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = \sigma(x^{2} + y^{2} + z^{2} - c^{2} t^{2}). +\Tag{(11)} +\] + +Since equation~\Eqref{(8a)} must hold for points on the +$x$-axis, we thus have $\sigma = 1$. It is easily seen that the +Lorentz transformation really satisfies equation~\Eqref{(11)} +\index{Lorentz, H. A.!transformation}% +for $\sigma = 1$; for \Eqref{(11)}~is a consequence of \Eqref{(8a)}~and~\Eqref{(9)}, +and hence also of \Eqref{(8)}~and~\Eqref{(9)}. We have thus derived +the Lorentz transformation. + +The Lorentz transformation represented by \Eqref{(8)}~and~\Eqref{(9)} +still requires to be generalised. Obviously it is +immaterial whether the axes of~$K'$ be chosen so that +they are spatially parallel to those of~$K$. It is also not +essential that the velocity of translation of~$K'$ with +respect to~$K$ should be in the direction of the $x$-axis. +A simple consideration shows that we are able to +construct the Lorentz transformation in this general +sense from two kinds of transformations, viz.\ from +Lorentz transformations in the special sense and from +purely spatial transformations, which corresponds to +the replacement of the rectangular co-ordinate system +\PageSep{120} +by a new system with its axes pointing in other +directions. + +Mathematically, we can characterise the generalised +Lorentz transformation thus: +\index{Lorentz, H. A.!transformation!(generalised)}% + +It expresses $x'$,~$y'$, $z'$,~$t'$, in terms of linear homogeneous +functions of $x$,~$y$, $z$,~$t$, of such a kind that the relation +\[ +x'^{2} + y'^{2} + z'^{2} - c^{2} t'^{2} + = x^{2} + y^{2} + z^{2} - c^{2} t^{2} +\Tag{(11a)} +\] +is satisfied identically. That is to say: If we substitute +their expressions in $x$,~$y$, $z$,~$t$, in place of $x'$,~$y'$, +$z'$,~$t'$, on the left-hand side, then the left-hand side of~\Eqref{(11a)} +agrees with the right-hand side. +\PageSep{121} + + +\Appendix{II}{Minkowski's Four-dimensional Space +(``World'')}{[Supplementary to \Sectionref{XVII}]} + +\First{We} can characterise the Lorentz transformation +\index{Lorentz, H. A.!transformation}% +still more simply if we introduce the imaginary~$\sqrt{-1}·ct$ +in place of~$t$, as time-variable. If, in +accordance with this, we insert +\begin{align*} +x_{1} &= x\Add{,} \\ +x_{2} &= y\Add{,} \\ +x_{3} &= z\Add{,} \\ +x_{4} &= \sqrt{-1}·ct, +\end{align*} +and similarly for the accented system~$K'$, then the +condition which is identically satisfied by the transformation +can be expressed thus: +\[ +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + x_{4}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2} + {x_{4}}^{2}. +\Tag{(12)} +\] + +That is, by the afore-mentioned choice of ``co-ordinates,'' +\Eqref{(11a)}~is transformed into this equation. + +We see from~\Eqref{(12)} that the imaginary time co-ordinate~$x_{4}$ +\index{Cartesian system of co-ordinates}% +\index{Euclidean geometry}% +\index{Euclidean space}% +\index{Space!three-dimensional}% +\index{Time!in Physics}% +enters into the condition of transformation in exactly +the same way as the space co-ordinates $x_{1}$,~$x_{2}$,~$x_{3}$. It +is due to this fact that, according to the theory of +\PageSep{122} +relativity, the ``time''~$x_{4}$ enters into natural laws in the +same form as the space co-ordinates $x_{1}$,~$x_{2}$,~$x_{3}$. + +A four-dimensional continuum described by the +\index{Continuum!four-dimensional}% +``co-or\-di\-nates'' $x_{1}$,~$x_{2}$, $x_{3}$,~$x_{4}$, was called ``world'' by +\index{World}% +\index{World!point@{-point}}% +Minkowski, who also termed a point-event a ``world-point.'' +\index{Minkowski}% +From a ``happening'' in three-dimensional +space, physics becomes, as it were, an ``existence'' in +the four-dimensional ``world.'' + +This four-dimensional ``world'' bears a close similarity +to the three-dimensional ``space'' of (Euclidean) +analytical geometry. If we introduce into the latter a +new Cartesian co-ordinate system $(x_{1}', x_{2}', x_{3}')$ with +the same origin, then $x_{1}'$,~$x_{2}'$,~$x_{3}'$, are linear homogeneous +functions of $x_{1}$,~$x_{2}$,~$x_{3}$, which identically satisfy the +equation +\[ +x_{1}'^{2} + x_{2}'^{2} + x_{3}'^{2} + = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2}. +\] +The analogy with~\Eqref{(12)} is a complete one. We can +regard Minkowski's ``world'' in a formal manner as a +four-dimensional Euclidean space (with imaginary +time co-ordinate); the Lorentz transformation corresponds +to a ``rotation'' of the co-ordinate system in the +\index{Rotation}% +four-dimensional ``world.'' +\PageSep{123} + + +\Appendix{III}{The Experimental Confirmation of the +General Theory of Relativity}{} +\index{Theory}% + +\First{From} a systematic theoretical point of view, we +may imagine the process of evolution of an empirical +science to be a continuous process of induction. +\index{Induction}% +Theories are evolved and are expressed in +short compass as statements of a large number of individual +observations in the form of empirical laws, +\index{Empirical laws}% +from which the general laws can be ascertained by comparison. +Regarded in this way, the development of a +science bears some resemblance to the compilation of a +classified catalogue. It is, as it were, a purely empirical +enterprise. + +But this point of view by no means embraces the whole +of the actual process; for it slurs over the important +part played by intuition and deductive thought in the +\index{Deductive thought}% +\index{Intuition}% +development of an exact science. As soon as a science +has emerged from its initial stages, theoretical advances +are no longer achieved merely by a process of arrangement. +Guided by empirical data, the investigator +rather develops a system of thought which, in general, +is built up logically from a small number of fundamental +assumptions, the so-called axioms. We call such a +\index{Axioms}% +system of thought a \emph{theory}. The theory finds the +\PageSep{124} +\index{Classical mechanics}% +\index{Darwinian theory}% +justification for its existence in the fact that it correlates +a large number of single observations, and it is just here +that the ``truth'' of the theory lies. +\index{Theory!truth of}% + +Corresponding to the same complex of empirical data, +there may be several theories, which differ from one +another to a considerable extent. But as regards the +deductions from the theories which are capable of +being tested, the agreement between the theories may +be so complete, that it becomes difficult to find such +deductions in which the two theories differ from each +other. As an example, a case of general interest is +available in the province of biology, in the Darwinian +\index{Biology}% +theory of the development of species by selection in +the struggle for existence, and in the theory of development +which is based on the hypothesis of the hereditary +transmission of acquired characters. + +We have another instance of far-reaching agreement +between the deductions from two theories in Newtonian +mechanics on the one hand, and the general theory of +relativity on the other. This agreement goes so far, +that up to the present we have been able to find only +a few deductions from the general theory of relativity +which are capable of investigation, and to which the +physics of pre-relativity days does not also lead, and +this despite the profound difference in the fundamental +assumptions of the two theories. In what follows, we +shall again consider these important deductions, and we +shall also discuss the empirical evidence appertaining to +them which has hitherto been obtained. + + +\Subsection{a}{Motion of the Perihelion of Mercury} +\index{Perihelion of Mercury|(}% + +According to Newtonian mechanics and Newton's +\index{Newton's!law of gravitation}% +law of gravitation, a planet which is revolving round the +\PageSep{125} +sun would describe an ellipse round the latter, or, more +correctly, round the common centre of gravity of the +sun and the planet. In such a system, the sun, or the +common centre of gravity, lies in one of the foci of the +orbital ellipse in such a manner that, in the course of a +planet-year, the distance sun-planet grows from a +minimum to a maximum, and then decreases again to +a minimum. If instead of Newton's law we insert a +\index{Newton}% +somewhat different law of attraction into the calculation, +we find that, according to this new law, the motion +would still take place in such a manner that the distance +sun-planet exhibits periodic variations; but in this +case the angle described by the line joining sun and +planet during such a period (from perihelion---closest +proximity to the sun---to perihelion) would differ from~$360°$. +The line of the orbit would not then be a closed +one, but in the course of time it would fill up an annular +part of the orbital plane, viz.\ between the circle of +least and the circle of greatest distance of the planet from +the sun. + +According also to the general theory of relativity, +which differs of course from the theory of Newton, a +small variation from the Newton-Kepler motion of a +\index{Kepler}% +planet in its orbit should take place, and in such a way, +that the angle described by the radius sun-planet +between one perihelion and the next should exceed that +corresponding to one complete revolution by an amount +given by +\[ ++\frac{24\pi^{3} a^{2}}{T^{2} c^{2} (1-e^{2})}. +\] + +(\NB---One complete revolution corresponds to the +angle~$2\pi$ in the absolute angular measure customary in +physics, and the above expression gives the amount by +\PageSep{126} +which the radius sun-planet exceeds this angle during +the interval between one perihelion and the next.) +In this expression $a$~represents the major semi-axis of +the ellipse, $e$~its eccentricity, $c$~the velocity of light, and +$T$~the period of revolution of the planet. Our result +may also be stated as follows: According to the general +theory of relativity, the major axis of the ellipse rotates +round the sun in the same sense as the orbital motion +of the planet. Theory requires that this rotation should +amount to $43$~seconds of arc per~century for the planet +Mercury, but for the other planets of our solar system its +\index{Mercury}% +\index{Mercury!orbit of}% +magnitude should be so small that it would necessarily +escape detection.\footnote + {Especially since the next planet Venus has an orbit that is +\index{Venus}% + almost an exact circle, which makes it more difficult to locate + the perihelion with precision.} + +In point of fact, astronomers have found that the +theory of Newton does not suffice to calculate the +observed motion of Mercury with an exactness corresponding +to that of the delicacy of observation attainable +at the present time. After taking account of all +the disturbing influences exerted on Mercury by the +remaining planets, it was found (Leverrier---1859---and +\index{Leverrier}% +Newcomb---1895) that an unexplained perihelial +\index{Newcomb}% +movement of the orbit of Mercury remained over, the +amount of which does not differ sensibly from the above-mentioned +$+43$~seconds of arc per~century. The uncertainty +of the empirical result amounts to a few +seconds only. +\index{Perihelion of Mercury|)}% + + +\Subsection{b}{Deflection of Light by a Gravitational +Field} + +In \Sectionref{XXII} it has been already mentioned that, +\PageSep{127} +according to the general theory of relativity, a ray of +light will experience a curvature of its path when passing +\index{Curvature of light-rays}% +\index{Curvature of light-rays!space}% +through a gravitational field, this curvature being similar +to that experienced by the path of a body which is +projected through a gravitational field. As a result of +this theory, we should expect that a ray of light which +is passing close to a heavenly body would be deviated +towards the latter. For a ray of light which passes the +sun at a distance of $\Delta$~sun-radii from its centre, the +angle of deflection~($\alpha$) should amount to +\[ +\alpha = \frac{\text{$1.7$~seconds of arc}}{\Delta}. +\] +It may be added that, according to the theory, half of +this deflection is produced by the +Newtonian field of attraction of the +sun, and the other half by the geometrical +modification (``curvature'') +of space caused by the sun. + +%[Illustration: Fig. 5.] +\WFigure{1in}{127} +This result admits of an experimental +\index{Solar eclipse}% +test by means of the photographic +registration of stars during +a total eclipse of the sun. The only +reason why we must wait for a total +eclipse is because at every other +time the atmosphere is so strongly +illuminated by the light from the +sun that the stars situated near the +sun's disc are invisible. The predicted effect can be +seen clearly from the accompanying diagram. If the +sun~($S$) were not present, a star which is practically +infinitely distant would be seen in the direction~$D_{1}$, as +observed from the earth. But as a consequence of the +\PageSep{128} +deflection of light from the star by the sun, the star +will be seen in the direction~$D_{2}$, \ie\ at a somewhat +greater distance from the centre of the sun than corresponds +to its real position. + +In practice, the question is tested in the following +way. The stars in the neighbourhood of the sun are +photographed during a solar eclipse. In addition, a +\index{Solar eclipse}% +\index{Stellar universe!photographs}% +second photograph of the same stars is taken when the +sun is situated at another position in the sky, \ie\ a few +months earlier or later. As compared with the standard +photograph, the positions of the stars on the eclipse-photograph +ought to appear displaced radially outwards +(away from the centre of the sun) by an amount +corresponding to the angle~$\alpha$. + +We are indebted to the Royal Society and to the +Royal Astronomical Society for the investigation of +this important deduction. Undaunted by the war and +by difficulties of both a material and a psychological +nature aroused by the war, these societies equipped +two expeditions---to Sobral (Brazil), and to the island of +Principe (West Africa)---and sent several of Britain's +most celebrated astronomers (Eddington, Cottingham, +\index{Cottingham}% +\index{Eddington}% +Crommelin, Davidson), in order to obtain photographs +\index{Crommelin}% +\index{Davidson}% +of the solar eclipse of 29th~May, 1919. The relative +discrepancies to be expected between the stellar photographs +obtained during the eclipse and the comparison +photographs amounted to a few hundredths of a millimetre +only. Thus great accuracy was necessary in +making the adjustments required for the taking of the +photographs, and in their subsequent measurement. + +The results of the measurements confirmed the theory +in a thoroughly satisfactory manner. The rectangular +components of the observed and of the calculated +\PageSep{129} +deviations of the stars (in seconds of arc) are set forth +in the following table of results: +\[ +\begin{array}{@{}c*{2}{>{\quad}cc}@{}} +%[** TN: Re-break first column heading to improve overall width] +\ColHead{1}{Number of}{Number of\\ the Star.} & +\ColHead{2}{Observed. Calculated.}{First Co-ordinate. \\[2pt] +$\overbrace{\text{Observed. Calculated.}}$} & +\ColHead{2}{Observed. Calculated.}{Second Co-ordinate. \\[2pt] +$\overbrace{\text{Observed. Calculated.}}$} \\ +11 & -0.19 & -0.22 & +0.16 & +0.02 \\ +\Z5 & +0.29 & +0.31 & -0.46 & -0.43 \\ +\Z4 & +0.11 & +0.10 & +0.83 & +0.74 \\ +\Z3 & +0.20 & +0.12 & +1.00 & +0.87 \\ +\Z6 & +0.10 & +0.04 & +0.57 & +0.40 \\ +10 & -0.08 & +0.09 & +0.35 & +0.32 \\ +\Z2 & +0.95 & +0.85 & -0.27 & -0.09 +\end{array} +\] + +\Subsection{c}{Displacement of Spectral Lines towards +the Red} +\index{Displacement of spectral lines}% + +In \Sectionref{XXIII} it has been shown that in a system~$K'$ +which is in rotation with regard to a Galileian system~$K$, +clocks of identical construction, and which are considered +\index{Clocks}% +\index{Clocks!rate of}% +at rest with respect to the rotating reference-body, +go at rates which are dependent on the positions +of the clocks. We shall now examine this dependence +quantitatively. A clock, which is situated at a distance~$r$ +from the centre of the disc, has a velocity relative to~$K$ +which is given by +\[ +v = \omega r, +\] +where $\omega$~represents the angular velocity of rotation of the +disc~$K'$ with respect to~$K$. If $\nu_{0}$~represents the number +of ticks of the clock per unit time (``rate'' of the clock) +relative to~$K$ when the clock is at rest, then the ``rate'' +of the clock~($\nu$) when it is moving relative to~$K$ with +a velocity~$v$, but at rest with respect to the disc, will, +in accordance with \Sectionref{XII}, be given by +\[ +\nu = \nu_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}, +\] +\PageSep{130} +or with sufficient accuracy by +\[ +\nu = \nu_{0} \left(1 - \tfrac{1}{2}\, \frac{v^{2}}{c^{2}}\right). +\] +This expression may also be stated in the following +form: +\[ +\nu = \nu_{0} \left(1 - \frac{1}{c^{2}}\, \frac{\omega^{2} r^{2}}{2}\right). +\] +If we represent the difference of potential of the centrifugal +force between the position of the clock and the +centre of the disc by~$\phi$, \ie\ the work, considered negatively, +which must be performed on the unit of mass +against the centrifugal force in order to transport it +\index{Centrifugal force}% +from the position of the clock on the rotating disc to +the centre of the disc, then we have +\[ +\phi = -\frac{\omega^{2} r^{2}}{2}. +\] +From this it follows that +\[ +\nu = \nu_{0} \left(1 + \frac{\phi}{c^{2}}\right). +\] +In the first place, we see from this expression that two +clocks of identical construction will go at different rates +when situated at different distances from the centre of +the disc. This result is also valid from the standpoint +of an observer who is rotating with the disc. + +Now, as judged from the disc, the latter is in a gravitational +\index{Gravitational field!potential of}% +field of potential~$\phi$, hence the result we have +obtained will hold quite generally for gravitational +fields. Furthermore, we can regard an atom which is +emitting spectral lines as a clock, so that the following +statement will hold: + +\emph{An atom absorbs or emits light of a frequency which is +\PageSep{131} +dependent on the potential of the gravitational field in +\index{Gravitational field!potential of}% +which it is situated.} + +The frequency of an atom situated on the surface of a +\index{Frequency of atom}% +heavenly body will be somewhat less than the frequency +of an atom of the same element which is situated in free +space (or on the surface of a smaller celestial body). +Now $\phi = -K\dfrac{M}{r}$, where $K$~is Newton's constant of +\index{Newton's!constant of gravitation}% +gravitation, and $M$~is the mass of the heavenly body. +Thus a displacement towards the red ought to take place +for spectral lines produced at the surface of stars as +compared with the spectral lines of the same element +produced at the surface of the earth, the amount of this +displacement being +\[ +\frac{\nu_{0} - \nu}{\nu_{0}} = \frac{K}{c^{2}}\, \frac{M}{r}. +\] + +For the sun, the displacement towards the red predicted +by theory amounts to about two millionths of +the wave-length. A trustworthy calculation is not +possible in the case of the stars, because in general +neither the mass~$M$ nor the radius~$r$ is known. + +It is an open question whether or not this effect +exists, and at the present time astronomers are working +with great zeal towards the solution. Owing to the +smallness of the effect in the case of the sun, it is difficult +to form an opinion as to its existence. Whereas +Grebe and Bachem (Bonn), as a result of their own +\index{Bachem}% +\index{Grebe}% +measurements and those of Evershed and Schwarzschild +\index{Evershed}% +\index{Schwarzschild}% +on the cyanogen bands, have placed the existence of +\index{Cyanogen bands}% +the effect almost beyond doubt, other investigators, +particularly St.~John, have been led to the opposite +\index{St. John@{St.\ John}}% +opinion in consequence of their measurements. +\PageSep{132} + +Mean displacements of lines towards the less refrangible +end of the spectrum are certainly revealed by +statistical investigations of the fixed stars; but up +to the present the examination of the available data +does not allow of any definite decision being arrived at, +as to whether or not these displacements are to be +referred in reality to the effect of gravitation. The +results of observation have been collected together, +and discussed in detail from the standpoint of the +question which has been engaging our attention here, +in a paper by E.~Freundlich entitled ``Zur Prüfung der +allgemeinen Relativitäts-Theorie'' (\textit{Die Naturwissenschaften}, +1919, No.~35, p.~520: Julius Springer, Berlin). + +At all events, a definite decision will be reached during +the next few years. If the displacement of spectral +lines towards the red by the gravitational potential +does not exist, then the general theory of relativity +will be untenable. On the other hand, if the cause of +the displacement of spectral lines be definitely traced +to the gravitational potential, then the study of this +displacement will furnish us with important information +\index{Mass of heavenly bodies}% +as to the mass of the heavenly bodies. +\PageSep{133} + + +\backmatter +\BookMark{-1}{Back Matter} +\Bibliography{WORKS IN ENGLISH ON EINSTEIN'S THEORY} + +\Bibsection{Introductory} + +\Bibitem{The Foundations of Einstein's Theory of Gravitation} +{Erwin Freundlich (translation by H.~L.~Brose). +Camb.\ Univ.\ Press, 1920.} + +\Bibitem{Space and Time in Contemporary Physics}{Moritz Schlick +(translation by H.~L.~Brose). Clarendon Press, +Oxford, 1920.} + + +\Bibsection{The Special Theory} + +\Bibitem{The Principle of Relativity}{E.~Cunningham. Camb.\ +Univ.\ Press.} + +\Bibitem{Relativity and the Electron Theory}{E.~Cunningham, Monographs +on Physics. Longmans, Green \&~Co.} + +\Bibitem{The Theory of Relativity}{L.~Silberstein. Macmillan \&~Co.} + +\Bibitem{The Space-Time Manifold of Relativity}{E.~B.~Wilson +and G.~N.~Lewis, \textit{Proc.\ Amer.\ Soc.\ Arts \&~Science}, +vol.~xlviii., No.~11, 1912.} + + +\Bibsection{The General Theory} + +\Bibitem{Report on the Relativity Theory of Gravitation}{A.~S. +Eddington. Fleetway Press Ltd., Fleet Street, +London.} +\PageSep{134} + +\Bibitem{On Einstein's Theory of Gravitation and its Astronomical +Consequences}{W.~de~Sitter, \textit{M.~N.~Roy.\ Astron.\ +Soc.},~lxxvi.\ p.~699, 1916; lxxvii.\ p.~155, 1916; lxxviii.\ +p.~3, 1917.} + +\Bibitem{On Einstein's Theory of Gravitation}{H.~A.~Lorentz, \textit{Proc.\ +Amsterdam Acad.}, vol.~xix. p.~1341, 1917.} + +\Bibitem{Space, Time and Gravitation}{W.~de~Sitter: \textit{The +Observatory}, No.~505, p.~412. Taylor \&~Francis, Fleet +Street, London.} + +\Bibitem{The Total Eclipse of 29th~May, 1919, and the Influence of +Gravitation on Light}{A.~S.~Eddington, \textit{ibid.}, +March~1919.} + +\Bibitem{Discussion on the Theory of Relativity}{\textit{M.~N.~Roy.\ Astron.\ +Soc.}, vol.~lxxx.\ No.~2, p.~96, December~1919.} + +\Bibitem{The Displacement of Spectrum Lines and the Equivalence +Hypothesis}{W.~G.~Duffield, \textit{M.~N.~Roy.\ Astron.\ Soc.}, +vol.~lxxx.\Change{;}{} No.~3, p.~262, 1920.} + +\Bibitem{Space, Time and Gravitation}{A.~S.~Eddington, Camb.\ Univ.\ +Press, 1920.} + + +\Bibsection{Also, Chapters in} + +\Bibitem{The Mathematical Theory of Electricity and Magnetism} +{J.~H. Jeans (4th~edition). Camb.\ Univ.\ Press, 1920.} + +\Bibitem{The Electron Theory of Matter}{O.~W.~Richardson. Camb.\ +Univ.\ Press.} +\PageSep{135} +\printindex % [** TN: Auto-generate the index] +\iffalse %%%% Start of index text %%%% +INDEX + +Aberration 49 + +Absorption of energy 46 + +Acceleration 64, 67, 70 + +Action at a distance 48 + +Addition of velocities 16, 38 + +Adjacent points 89 + +Aether 52 + drift@{-drift}#drift 52, 53 + +Arbitrary substitutions 98 + +Astronomy 7, 102 + +Astronomical day 11 + +Axioms 2, 123 + truth of 2 + +Bachem 131 + +Basis of theory 44 + +Being@{``Being''}#Being 66, 108 + +beta-rays@{$\beta$-rays}#rays 50 + +Biology 124 + +Cartesian system of co-ordinates 7, 84, 122 + +Cathode rays 50 + +Celestial mechanics 105 + +Centrifugal force 80, 130 + +Chest 66 + +Classical mechanics 9, 13, 14, 16, 30, 44, 71, 102, 103, 124 + truth of 13 + +Clocks 10, 23, 80, 81, 94, 95, 98-100, 102, 113, 129 + rate of 129 + +Conception of mass 45 + position 6 + +Conservation of energy 45, 101 + impulse 101 + mass 45, 47 + +Continuity 95 + +Continuum 55, 83 + two-dimensional 94 + three-dimensional 57 + four-dimensional 89, 91, 92, 94, 122 + space-time 78, 91-96 + Euclidean 84, 86, 88, 92 + non-Euclidean 86, 90 + +Coordinate@{Co-ordinate}#Co-ordinate + differences 92 + differentials 92 + planes 32 + +Cottingham 128 + +Counter-Point 112 + +Covariant@{Co-variant}#Co-variant 43 + +Crommelin 128 + +Curvature of light-rays 104, 127 + space 127 + +Curvilinear motion 74 + +Cyanogen bands 131 + +Darwinian theory 124 + +Davidson 128 + +Deductive thought 123 + +Derivation of laws 44 + +Desitter@{De Sitter}#De Sitter 17 + +Displacement of spectral lines 104, 129 + +Distance (line-interval) 3, 5, 8, 28, 29, 84, 88, 109 + physical interpretation of 5 + relativity of 28 + +Doppler principle 50 %. + +Double stars 17 + +Eclipse of star 17 + +Eddington 104, 128 +%\PageSep{136} + +Electricity 76 + +Electrodynamics 13, 19, 41, 44, 76 + +Electromagnetic theory 49 + waves 63 + +Electron 44, 50 %. + electrical masses of 51 + +Electrostatics 76 + +Elliptical space 112 + +Empirical laws 123 + +Encounter (space-time coincidence) 95 + +Equivalent 14 + +Euclidean geometry 1, 2, 57, 82, 86, 88, 108, 109, 113, 122 + propositions of 3, 8 + +%[** TN: Add explicit "Euclidean" heading] +Euclidean space 57, 86, 122 + +Evershed 131 + +Experience 49, 60 + +Faraday 48, 63 + +FitzGerald 53 + +Fixed stars 11 + +Fizeau 39, 49, 51 + experiment of 39 + +Frequency of atom 131 + +Galilei 11 + transformation 33, 36, 38, 42, 52 + +Galileian system of co-ordinates + 11, 13, 14, 46, 79, 91, 98, 100 + +Gauss 86, 87, 90 + +Gaussian co-ordinates 88-90, 94, 96-100 + +General theory of relativity 59-104, 97 + +Geometrical ideas 2, 3 + propositions 1 + truth of 2-4 + +Gravitation 64, 69, 78, 102 + +Gravitational field 64, 67, 74, 77, 93, 98, 100, 101, 113 + potential of 130, 131 + +%[** TN: Add explicit "Gravitational" heading] +Gravitational mass 65, 68, 102 + +Grebe 131 + +Group-density of stars 106 + +Helmholtz 108 + +Heuristic value of relativity#Heuristic 42 + +Induction 123 + +Inertia 65 + +Inertial mass 47, 65, 69, 101, 102 + +Instantaneous photograph (snapshot) 117 + +Intensity of gravitational field 106 + +Intuition 123 + +Ions 44 + +Kepler 125 + +Kinetic energy 45, 101 + +Lattice 108 + +Law of inertia 11, 61, 62, 98 + +Laws of Galilei-Newton 13 + of Nature 60, 71, 99 + +Leverrier 103, 126 + +Light-signal 33, 115, 118 + +Light-stimulus 33 + +Limiting velocity ($c$)#Limiting 36, 37 + +Lines of force 106 + +Lorentz, H. A.#Lorentz 19, 41, 44, 49, 50-53 + transformation 33, 39, 42, 91, 97, 98, 115, 118, 119, 121 + (generalised) 120 + +Mach, E.#Mach 72 + +Magnetic field 63 + +Manifold|see{Continuum} 0 + +Mass of heavenly bodies 132 + +Matter 101 + +Maxwell 41, 44, 48-50, 52 + fundamental equations 46, 77 + +Measurement of length 85 + +Measuring-rod 5, 6, 28, 80, 81, 94, 100, 102, 111, 113, 117 + +Mercury 103, 126 + orbit of 103, 126 + +Michelson 52-54 + +Minkowski 55-57, 91, 122 +%\PageSep{137} + +Morley 53, 54 + +Motion 14, 60 + of heavenly bodies 13, 15, 44, 102, 113 + +Newcomb 126 + +Newton 11, 72, 102, 105, 125 + +Newton's + constant of gravitation 131 + law of gravitation 48, 80, 106, 124 + law of motion 64 + +Non-Euclidean geometry 108 + +Non-Galileian reference-bodies 98 + +Non-uniform motion 62 + +Optics 13, 19, 44 + +Organ-pipe, note of 14 + +Parabola 9, 10 + +Path-curve 10 + +Perihelion of Mercury 124-126 + +Physics 7 + of measurement 7 + +Place specification 5, 6 + +Plane 1, 108, 109 + +Poincare@{Poincaré}#Poincaré 108 + +Point 1 + +Point-mass, energy of#Point-mass 45 + +Position 9 + +Principle of relativity 13-15, 19, 20, 60 + +Processes of Nature 42 + +Propagation of light 17, 19, 20, 32, 91, 119 + in liquid 40 + in gravitational fields 75 + +Quasi-Euclidean universe 114 + +Quasi-spherical universe 114 + +Radiation 46 + +Radioactive substances 50 + +Reference-body 5, 7, 9-11, 18, 23, 25, 26, 37, 60 + rotating 79 + +%[** TN: Add explicit "Reference-" heading] +Reference-mollusk 99-101 + +Relative + position 3 + velocity 117 + +Rest 14 + +Riemann 86, 108, 111 + +Rotation 81, 122 + +Schwarzschild 131 + +Seconds-clock 36 + +Seeliger 105, 106 + +Simultaneity 22, 24-26, 81 + relativity of 26 + +Size-relations 90 + +Solar eclipse 75, 127, 128 + +Space 9, 52, 55, 105 + conception of 19 + +Space co-ordinates 55, 81, 99 + +Space + interval@{-interval}#interval 30, 56 + point@{-point}#point 99 + two-dimensional 108 + three-dimensional 122 + +Special theory of relativity 1-57, 20 + +Spherical + surface 109 + space 111, 112 + +St. John@{St.\ John}#St.~John 131 + +Stellar universe 106 + photographs 128 + +Straight line 1-3, 9, 10, 82, 88, 109 + +System of co-ordinates 5, 10, 11 + +Terrestrial space 15 + +Theory 123 + truth of 124 + +Three-dimensional 55 + +Time + conception of 19, 52, 105 + coordinate@{co-ordinate}#co-ordinate 55, 99 + in Physics 21, 98, 122 + of an event 24, 26 + +Time-interval 30, 56 + +Trajectory 10 + +Truth@{``Truth''}#Truth 2 + +Uniform translation 12, 59 + +Universe (World) structure of 108, 113 + circumference of 111 +%\PageSep{138} + +Universe + elliptical 112, 114 + Euclidean 109, 111 + space expanse (radius) of 114 + spherical 111, 114 + +Value of $\pi$#$\pi$ 82, 110 + +Velocity of light 10, 17, 18, 76, 118 + +Venus 126 + +Weight (heaviness) 65 + +World 55, 56, 109, 122 + +World + point@{-point}#point 122 + radius@{-radius}#radius 112 + sphere@{-sphere}#sphere 110, 111 + +Zeeman 41 +\fi %%%% End of index text %%%% +\PageSep{139} +% [Blank page] +\PageSep{140} +\ifthenelse{\boolean{ForPrinting}}{\cleardoublepage\null}{} +\newpage +\begin{CenterPage} + \scriptsize + PRINTED BY \\[2pt] + MORRISON AND GIBB LIMITED \\[2pt] + EDINBURGH +\end{CenterPage} +%%%%%%%%%%%%%%%%%%%%%%%%% GUTENBERG LICENSE %%%%%%%%%%%%%%%%%%%%%%%%%% + +\cleardoublepage +\BookMark{0}{PG License} +\SetEvenHead{Licensing} +\SetOddHead{Licensing} +\pagenumbering{Roman} +\begin{PGtext} +End of the Project Gutenberg EBook of Relativity: The Special and the +General Theory, by Albert Einstein + +*** END OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** + +***** This file should be named 36114-pdf.pdf or 36114-pdf.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/6/1/1/36114/ + +Produced by Andrew D. Hwang. (This ebook was produced using +OCR text generously provided by the University of Toronto +Robarts Library through the Internet Archive.) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +http://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need, are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at http://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +http://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at http://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit http://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including checks, online payments and credit card donations. +To donate, please visit: http://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart is the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + http://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. +\end{PGtext} + +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % +% % +% End of the Project Gutenberg EBook of Relativity: The Special and the % +% General Theory, by Albert Einstein % +% % +% *** END OF THIS PROJECT GUTENBERG EBOOK RELATIVITY *** % +% % +% ***** This file should be named 36114-t.tex or 36114-t.zip ***** % +% This and all associated files of various formats will be found in: % +% http://www.gutenberg.org/3/6/1/1/36114/ % +% % +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % + +\end{document} +### +@ControlwordReplace = ( + ['\\Preface', 'Preface'], + ['\\ie', 'i.e.'], + ['\\eg', 'e.g.'], + ['\\NB', 'N.B.'], + ['\\itema', '(a)'], + ['\\itemb', '(b)'], + ['\\itemc', '(c)'] + ); + +@ControlwordArguments = ( + ['\\BookMark', 1, 0, '', '', 1, 0, '', ''], + ['\\item', 0, 1, '', ' '], + ['\\Part', 1, 1, '', ' ', 1, 1, '', '', 1, 0, '', ''], + ['\\Chapter', 0, 0, '', '', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Section', 1, 1, '', ''], + ['\\Subsection', 1, 1, '(', ') ', 1, 1, '', ''], + ['\\SectTitle', 1, 1, '', ''], + ['\\Appendix', 1, 1, '', ' ', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Bibliography', 1, 1, 'Bibliography: ', ''], + ['\\Bibsection', 1, 1, '', ''], + ['\\Bibitem', 1, 1, '', ' ', 1, 1, '', ''], + ['\\PubRow', 1, 1, '', ' ', 1, 1, '', ''], + ['\\Signature', 0, 1, '', ' ', 1, 1, '', ''], + ['\\Change', 1, 0, '', '', 1, 1, '', ''], + ['\\Add', 1, 1, '', ''], + ['\\PageSep', 1, 0, '', ''], + ['\\Figure', 0, 0, '', '', 1, 1, '', ''], + ['\\WFigure', 1, 0, '', '', 1, 1, '', ''], + ['\\Figref', 1, 1, 'Fig. ', ''], + ['\\Partref', 1, 1, 'Part ', ''], + ['\\Sectionref', 1, 1, 'Section ', ''], + ['\\Srefno', 1, 1, '', ''], + ['\\Appendixref', 1, 1, 'Appendix ', ''], + ['\\Eqref', 1, 1, '', ''], + ['\\First', 1, 1, '', ''] + ); +### +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2010.5.6) 15 MAY 2011 15:31 +entering extended mode + %&-line parsing enabled. +**36114-t.tex +(./36114-t.tex +LaTeX2e <2005/12/01> +Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov +ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon +ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i +nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp +eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia +n, swedish, ukenglish, pinyin, loaded. +(/usr/share/texmf-texlive/tex/latex/base/book.cls +Document Class: book 2005/09/16 v1.4f Standard LaTeX document class +(/usr/share/texmf-texlive/tex/latex/base/bk12.clo +File: bk12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +) +\c@part=\count79 +\c@chapter=\count80 +\c@section=\count81 +\c@subsection=\count82 +\c@subsubsection=\count83 +\c@paragraph=\count84 +\c@subparagraph=\count85 +\c@figure=\count86 +\c@table=\count87 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) (/usr/share/texmf-texlive/tex/latex/base/inputenc.sty +Package: inputenc 2006/05/05 v1.1b Input encoding file +\inpenc@prehook=\toks14 +\inpenc@posthook=\toks15 +(/usr/share/texmf-texlive/tex/latex/base/latin1.def +File: latin1.def 2006/05/05 v1.1b Input encoding file +)) (/usr/share/texmf-texlive/tex/latex/base/ifthen.sty +Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) +) (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty +Package: amsmath 2000/07/18 v2.13 AMS math features +\@mathmargin=\skip43 +For additional information on amsmath, use the `?' option. +(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 +(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 +\@emptytoks=\toks16 +\ex@=\dimen103 +)) (/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d +\pmbraise@=\dimen104 +) (/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count88 +LaTeX Info: Redefining \frac on input line 211. +\uproot@=\count89 +\leftroot@=\count90 +LaTeX Info: Redefining \overline on input line 307. +\classnum@=\count91 +\DOTSCASE@=\count92 +LaTeX Info: Redefining \ldots on input line 379. +LaTeX Info: Redefining \dots on input line 382. +LaTeX Info: Redefining \cdots on input line 467. +\Mathstrutbox@=\box26 +\strutbox@=\box27 +\big@size=\dimen105 +LaTeX Font Info: Redeclaring font encoding OML on input line 567. +LaTeX Font Info: Redeclaring font encoding OMS on input line 568. +\macc@depth=\count93 +\c@MaxMatrixCols=\count94 +\dotsspace@=\muskip10 +\c@parentequation=\count95 +\dspbrk@lvl=\count96 +\tag@help=\toks17 +\row@=\count97 +\column@=\count98 +\maxfields@=\count99 +\andhelp@=\toks18 +\eqnshift@=\dimen106 +\alignsep@=\dimen107 +\tagshift@=\dimen108 +\tagwidth@=\dimen109 +\totwidth@=\dimen110 +\lineht@=\dimen111 +\@envbody=\toks19 +\multlinegap=\skip44 +\multlinetaggap=\skip45 +\mathdisplay@stack=\toks20 +LaTeX Info: Redefining \[ on input line 2666. +LaTeX Info: Redefining \] on input line 2667. +) (/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2002/01/22 v2.2d +(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2001/10/25 v2.2f +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 132. +)) (/usr/share/texmf-texlive/tex/latex/base/alltt.sty +Package: alltt 1997/06/16 v2.0g defines alltt environment +) (/usr/share/texmf-texlive/tex/latex/tools/array.sty +Package: array 2005/08/23 v2.4b Tabular extension package (FMi) +\col@sep=\dimen112 +\extrarowheight=\dimen113 +\NC@list=\toks21 +\extratabsurround=\skip46 +\backup@length=\skip47 +) (/usr/share/texmf-texlive/tex/latex/bigfoot/perpage.sty +Package: perpage 2006/07/15 1.12 Reset/sort counters per page +\c@abspage=\count100 +) (/usr/share/texmf-texlive/tex/latex/tools/multicol.sty +Package: multicol 2006/05/18 v1.6g multicolumn formatting (FMi) +\c@tracingmulticols=\count101 +\mult@box=\box28 +\multicol@leftmargin=\dimen114 +\c@unbalance=\count102 +\c@collectmore=\count103 +\doublecol@number=\count104 +\multicoltolerance=\count105 +\multicolpretolerance=\count106 +\full@width=\dimen115 +\page@free=\dimen116 +\premulticols=\dimen117 +\postmulticols=\dimen118 +\multicolsep=\skip48 +\multicolbaselineskip=\skip49 +\partial@page=\box29 +\last@line=\box30 +\mult@rightbox=\box31 +\mult@grightbox=\box32 +\mult@gfirstbox=\box33 +\mult@firstbox=\box34 +\@tempa=\box35 +\@tempa=\box36 +\@tempa=\box37 +\@tempa=\box38 +\@tempa=\box39 +\@tempa=\box40 +\@tempa=\box41 +\@tempa=\box42 +\@tempa=\box43 +\@tempa=\box44 +\@tempa=\box45 +\@tempa=\box46 +\@tempa=\box47 +\@tempa=\box48 +\@tempa=\box49 +\@tempa=\box50 +\@tempa=\box51 +\c@columnbadness=\count107 +\c@finalcolumnbadness=\count108 +\last@try=\dimen119 +\multicolovershoot=\dimen120 +\multicolundershoot=\dimen121 +\mult@nat@firstbox=\box52 +\colbreak@box=\box53 +) (/usr/share/texmf-texlive/tex/latex/base/makeidx.sty +Package: makeidx 2000/03/29 v1.0m Standard LaTeX package +) (/usr/share/texmf-texlive/tex/latex/caption/caption.sty +Package: caption 2007/01/07 v3.0k Customising captions (AR) +(/usr/share/texmf-texlive/tex/latex/caption/caption3.sty +Package: caption3 2007/01/07 v3.0k caption3 kernel (AR) +(/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty +Package: keyval 1999/03/16 v1.13 key=value parser (DPC) +\KV@toks@=\toks22 +) +\captionmargin=\dimen122 +\captionmarginx=\dimen123 +\captionwidth=\dimen124 +\captionindent=\dimen125 +\captionparindent=\dimen126 +\captionhangindent=\dimen127 +)) (/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty +Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) +(/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty +Package: graphics 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) +(/usr/share/texmf-texlive/tex/latex/graphics/trig.sty +Package: trig 1999/03/16 v1.09 sin cos tan (DPC) +) (/etc/texmf/tex/latex/config/graphics.cfg +File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive +) +Package graphics Info: Driver file: pdftex.def on input line 90. +(/usr/share/texmf-texlive/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX +\Gread@gobject=\count109 +)) +\Gin@req@height=\dimen128 +\Gin@req@width=\dimen129 +) (/usr/share/texmf-texlive/tex/latex/wrapfig/wrapfig.sty +\wrapoverhang=\dimen130 +\WF@size=\dimen131 +\c@WF@wrappedlines=\count110 +\WF@box=\box54 +\WF@everypar=\toks23 +Package: wrapfig 2003/01/31 v 3.6 +) (/usr/share/texmf-texlive/tex/latex/tools/calc.sty +Package: calc 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) +\calc@Acount=\count111 +\calc@Bcount=\count112 +\calc@Adimen=\dimen132 +\calc@Bdimen=\dimen133 +\calc@Askip=\skip50 +\calc@Bskip=\skip51 +LaTeX Info: Redefining \setlength on input line 75. +LaTeX Info: Redefining \addtolength on input line 76. +\calc@Ccount=\count113 +\calc@Cskip=\skip52 +) (/usr/share/texmf-texlive/tex/latex/fancyhdr/fancyhdr.sty +\fancy@headwidth=\skip53 +\f@ncyO@elh=\skip54 +\f@ncyO@erh=\skip55 +\f@ncyO@olh=\skip56 +\f@ncyO@orh=\skip57 +\f@ncyO@elf=\skip58 +\f@ncyO@erf=\skip59 +\f@ncyO@olf=\skip60 +\f@ncyO@orf=\skip61 +) (/usr/share/texmf-texlive/tex/latex/geometry/geometry.sty +Package: geometry 2002/07/08 v3.2 Page Geometry +\Gm@cnth=\count114 +\Gm@cntv=\count115 +\c@Gm@tempcnt=\count116 +\Gm@bindingoffset=\dimen134 +\Gm@wd@mp=\dimen135 +\Gm@odd@mp=\dimen136 +\Gm@even@mp=\dimen137 +\Gm@dimlist=\toks24 +(/usr/share/texmf-texlive/tex/xelatex/xetexconfig/geometry.cfg)) (/usr/share/te +xmf-texlive/tex/latex/hyperref/hyperref.sty +Package: hyperref 2007/02/07 v6.75r Hypertext links for LaTeX +\@linkdim=\dimen138 +\Hy@linkcounter=\count117 +\Hy@pagecounter=\count118 +(/usr/share/texmf-texlive/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +) (/etc/texmf/tex/latex/config/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) (/usr/share/texmf-texlive/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options ( +HO) +) +Package hyperref Info: Option `hyperfootnotes' set `false' on input line 2238. +Package hyperref Info: Option `bookmarks' set `true' on input line 2238. +Package hyperref Info: Option `linktocpage' set `false' on input line 2238. +Package hyperref Info: Option `pdfdisplaydoctitle' set `true' on input line 223 +8. +Package hyperref Info: Option `pdfpagelabels' set `true' on input line 2238. +Package hyperref Info: Option `bookmarksopen' set `true' on input line 2238. +Package hyperref Info: Option `colorlinks' set `true' on input line 2238. +Package hyperref Info: Hyper figures OFF on input line 2288. +Package hyperref Info: Link nesting OFF on input line 2293. +Package hyperref Info: Hyper index ON on input line 2296. +Package hyperref Info: Plain pages OFF on input line 2303. +Package hyperref Info: Backreferencing OFF on input line 2308. +Implicit mode ON; LaTeX internals redefined +Package hyperref Info: Bookmarks ON on input line 2444. +(/usr/share/texmf-texlive/tex/latex/ltxmisc/url.sty +\Urlmuskip=\muskip11 +Package: url 2005/06/27 ver 3.2 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 2599. +\Fld@menulength=\count119 +\Field@Width=\dimen139 +\Fld@charsize=\dimen140 +\Choice@toks=\toks25 +\Field@toks=\toks26 +Package hyperref Info: Hyper figures OFF on input line 3102. +Package hyperref Info: Link nesting OFF on input line 3107. +Package hyperref Info: Hyper index ON on input line 3110. +Package hyperref Info: backreferencing OFF on input line 3117. +Package hyperref Info: Link coloring ON on input line 3120. +\Hy@abspage=\count120 +\c@Item=\count121 +) +*hyperref using driver hpdftex* +(/usr/share/texmf-texlive/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX +\Fld@listcount=\count122 +) +\c@pp@a@footnote=\count123 +\@indexfile=\write3 +\openout3 = `36114-t.idx'. + +Writing index file 36114-t.idx +\c@figno=\count124 +\TmpLen=\skip62 +(./36114-t.aux) +\openout1 = `36114-t.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 566. +LaTeX Font Info: ... okay on input line 566. +(/usr/share/texmf-texlive/tex/latex/ragged2e/ragged2e.sty +Package: ragged2e 2003/03/25 v2.04 ragged2e Package (MS) +(/usr/share/texmf-texlive/tex/latex/everysel/everysel.sty +Package: everysel 1999/06/08 v1.03 EverySelectfont Package (MS) +LaTeX Info: Redefining \selectfont on input line 125. +) +\CenteringLeftskip=\skip63 +\RaggedLeftLeftskip=\skip64 +\RaggedRightLeftskip=\skip65 +\CenteringRightskip=\skip66 +\RaggedLeftRightskip=\skip67 +\RaggedRightRightskip=\skip68 +\CenteringParfillskip=\skip69 +\RaggedLeftParfillskip=\skip70 +\RaggedRightParfillskip=\skip71 +\JustifyingParfillskip=\skip72 +\CenteringParindent=\skip73 +\RaggedLeftParindent=\skip74 +\RaggedRightParindent=\skip75 +\JustifyingParindent=\skip76 +) +Package caption Info: hyperref package v6.74m (or newer) detected on input line + 566. +(/usr/share/texmf/tex/context/base/supp-pdf.tex +[Loading MPS to PDF converter (version 2006.09.02).] +\scratchcounter=\count125 +\scratchdimen=\dimen141 +\scratchbox=\box55 +\nofMPsegments=\count126 +\nofMParguments=\count127 +\everyMPshowfont=\toks27 +\MPscratchCnt=\count128 +\MPscratchDim=\dimen142 +\MPnumerator=\count129 +\everyMPtoPDFconversion=\toks28 +) +-------------------- Geometry parameters +paper: class default +landscape: -- +twocolumn: -- +twoside: true +asymmetric: -- +h-parts: 9.03374pt, 325.215pt, 9.03375pt +v-parts: 4.15848pt, 495.49379pt, 6.23773pt +hmarginratio: 1:1 +vmarginratio: 2:3 +lines: -- +heightrounded: -- +bindingoffset: 0.0pt +truedimen: -- +includehead: true +includefoot: true +includemp: -- +driver: pdftex +-------------------- Page layout dimensions and switches +\paperwidth 343.28249pt +\paperheight 505.89pt +\textwidth 325.215pt +\textheight 433.62pt +\oddsidemargin -63.23625pt +\evensidemargin -63.23624pt +\topmargin -68.11151pt +\headheight 12.0pt +\headsep 19.8738pt +\footskip 30.0pt +\marginparwidth 98.0pt +\marginparsep 7.0pt +\columnsep 10.0pt +\skip\footins 10.8pt plus 4.0pt minus 2.0pt +\hoffset 0.0pt +\voffset 0.0pt +\mag 1000 +\@twosidetrue \@mparswitchtrue +(1in=72.27pt, 1cm=28.45pt) +----------------------- +(/usr/share/texmf-texlive/tex/latex/graphics/color.sty +Package: color 2005/11/14 v1.0j Standard LaTeX Color (DPC) +(/etc/texmf/tex/latex/config/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package color Info: Driver file: pdftex.def on input line 130. +) +Package hyperref Info: Link coloring ON on input line 566. +(/usr/share/texmf-texlive/tex/latex/hyperref/nameref.sty +Package: nameref 2006/12/27 v2.28 Cross-referencing by name of section +(/usr/share/texmf-texlive/tex/latex/oberdiek/refcount.sty +Package: refcount 2006/02/20 v3.0 Data extraction from references (HO) +) +\c@section@level=\count130 +) +LaTeX Info: Redefining \ref on input line 566. +LaTeX Info: Redefining \pageref on input line 566. +(./36114-t.out) (./36114-t.out) +\@outlinefile=\write4 +\openout4 = `36114-t.out'. + +LaTeX Font Info: Try loading font information for U+msa on input line 600. +(/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd +File: umsa.fd 2002/01/19 v2.2g AMS font definitions +) +LaTeX Font Info: Try loading font information for U+msb on input line 600. +(/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd +File: umsb.fd 2002/01/19 v2.2g AMS font definitions +) [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] [1 + +] [2] [3 + + +] [4] [5] [6] [7] (./36114-t.toc [8 + + + +] [9]) +\tf@toc=\write5 +\openout5 = `36114-t.toc'. + +[10] [11 + + +] [1 + +] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] +[19] [20] [21] [22] <./images/025.pdf, id=519, 338.26375pt x 50.1875pt> +File: ./images/025.pdf Graphic file (type pdf) +<use ./images/025.pdf> [23 <./images/025.pdf>] [24] [25] [26] [27] [28] <./imag +es/032.pdf, id=581, 194.7275pt x 150.5625pt> +File: ./images/032.pdf Graphic file (type pdf) +<use ./images/032.pdf> [29] [30 <./images/032.pdf>] [31] [32] [33] [34] [35] [3 +6] [37] <./images/040.pdf, id=649, 222.8325pt x 39.14626pt> +File: ./images/040.pdf Graphic file (type pdf) +<use ./images/040.pdf> [38 <./images/040.pdf>] [39] [40] [41] [42] [43] [44] [4 +5] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55 + + +] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [7 +1] [72] [73] [74] [75] [76] [77] [78] [79] [80] <./images/087.pdf, id=880, 209. +78375pt x 129.48375pt> +File: ./images/087.pdf Graphic file (type pdf) +<use ./images/087.pdf> [81 <./images/087.pdf>] [82] [83] [84] [85] [86] [87] [8 +8] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98 + + +] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108 + +] [109] [110] [111] [112] [113] [114 + +] [115] [116 + +] [117] [118] [119] <./images/127.pdf, id=1169, 99.37125pt x 212.795pt> +File: ./images/127.pdf Graphic file (type pdf) +<use ./images/127.pdf> [120 <./images/127.pdf>] [121] [122] [123] [124] [125] [ +126 + + +] (./36114-t.ind [127] [128 + +] [129] [130] [131] [132]) [133 + + +] [1 + +] [2] [3] [4] [5] [6] [7] [8] (./36114-t.aux) + + *File List* + book.cls 2005/09/16 v1.4f Standard LaTeX document class + bk12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +inputenc.sty 2006/05/05 v1.1b Input encoding file + latin1.def 2006/05/05 v1.1b Input encoding file + ifthen.sty 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) + amsmath.sty 2000/07/18 v2.13 AMS math features + amstext.sty 2000/06/29 v2.01 + amsgen.sty 1999/11/30 v2.0 + amsbsy.sty 1999/11/29 v1.2d + amsopn.sty 1999/12/14 v2.01 operator names + amssymb.sty 2002/01/22 v2.2d +amsfonts.sty 2001/10/25 v2.2f + alltt.sty 1997/06/16 v2.0g defines alltt environment + array.sty 2005/08/23 v2.4b Tabular extension package (FMi) + perpage.sty 2006/07/15 1.12 Reset/sort counters per page +multicol.sty 2006/05/18 v1.6g multicolumn formatting (FMi) + makeidx.sty 2000/03/29 v1.0m Standard LaTeX package + caption.sty 2007/01/07 v3.0k Customising captions (AR) +caption3.sty 2007/01/07 v3.0k caption3 kernel (AR) + keyval.sty 1999/03/16 v1.13 key=value parser (DPC) +graphicx.sty 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) +graphics.sty 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) + trig.sty 1999/03/16 v1.09 sin cos tan (DPC) +graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive + pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX + wrapfig.sty 2003/01/31 v 3.6 + calc.sty 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) +fancyhdr.sty +geometry.sty 2002/07/08 v3.2 Page Geometry +geometry.cfg +hyperref.sty 2007/02/07 v6.75r Hypertext links for LaTeX + pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +kvoptions.sty 2006/08/22 v2.4 Connects package keyval with LaTeX options (HO +) + url.sty 2005/06/27 ver 3.2 Verb mode for urls, etc. + hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX +ragged2e.sty 2003/03/25 v2.04 ragged2e Package (MS) +everysel.sty 1999/06/08 v1.03 EverySelectfont Package (MS) +supp-pdf.tex + color.sty 2005/11/14 v1.0j Standard LaTeX Color (DPC) + color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive + nameref.sty 2006/12/27 v2.28 Cross-referencing by name of section +refcount.sty 2006/02/20 v3.0 Data extraction from references (HO) + 36114-t.out + 36114-t.out + umsa.fd 2002/01/19 v2.2g AMS font definitions + umsb.fd 2002/01/19 v2.2g AMS font definitions +./images/025.pdf +./images/032.pdf +./images/040.pdf +./images/087.pdf +./images/127.pdf + 36114-t.ind + *********** + + ) +Here is how much of TeX's memory you used: + 5734 strings out of 94074 + 81940 string characters out of 1165154 + 147634 words of memory out of 1500000 + 8516 multiletter control sequences out of 10000+50000 + 17695 words of font info for 67 fonts, out of 1200000 for 2000 + 645 hyphenation exceptions out of 8191 + 34i,18n,44p,464b,649s stack positions out of 5000i,500n,6000p,200000b,5000s +</usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmbx10.pfb></usr/share/texmf +-texlive/fonts/type1/bluesky/cm/cmbx12.pfb></usr/share/texmf-texlive/fonts/type +1/bluesky/cm/cmbxti10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmcs +c10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmex10.pfb></usr/share +/texmf-texlive/fonts/type1/bluesky/cm/cmmi10.pfb></usr/share/texmf-texlive/font +s/type1/bluesky/cm/cmmi12.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/ +cmr10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmr12.pfb></usr/shar +e/texmf-texlive/fonts/type1/bluesky/cm/cmr7.pfb></usr/share/texmf-texlive/fonts +/type1/bluesky/cm/cmr8.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cms +y10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmsy7.pfb></usr/share/ +texmf-texlive/fonts/type1/bluesky/cm/cmsy8.pfb></usr/share/texmf-texlive/fonts/ +type1/bluesky/cm/cmti10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cm +ti12.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmtt10.pfb></usr/shar +e/texmf-texlive/fonts/type1/bluesky/cm/cmtt8.pfb> +Output written on 36114-t.pdf (154 pages, 664963 bytes). +PDF statistics: + 1881 PDF objects out of 2073 (max. 8388607) + 401 named destinations out of 1000 (max. 131072) + 418 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/old/36114-t 2011-05-11.zip b/old/36114-t 2011-05-11.zip Binary files differnew file mode 100644 index 0000000..93820c0 --- /dev/null +++ b/old/36114-t 2011-05-11.zip |
