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important; } + .pgbrk {page-break-after: always; } + .newpg {page-break-before: always; } + .ctr {text-indent: 0; text-align: center; } + .above2 {padding-top: 2em; } + .above4 {padding-top: 4em; } + .nw {white-space: nowrap; } + .nopad {padding: 0 ! important; } + cite, em {font-style: italic; } + +</style> +</head> +<body> + + +<pre> + +The Project Gutenberg EBook of The Romance of Mathematics, by P. Hampson + +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: The Romance of Mathematics + Being the Original Researches of a Lady Professor of Girtham + College in Polemical Science, with some Account of the Social + Properties of a Conic; Equations to Brain Waves; Social Forces; + and the Laws of Political Motion. + +Author: P. Hampson + +Release Date: August 29, 2008 [EBook #26481] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK THE ROMANCE OF MATHEMATICS *** + + + + +Produced by David Wilson and the Online Distributed +Proofreading Team at https://www.pgdp.net (This file was +produced from images generously made available by The +Internet Archive/Canadian Libraries) + + + + + + +</pre> + + + + +<hr class="pg" /> + + + +<div class="frontmatter"> +<h3 class="pgbrk noscr"><a name="png.001" id="png.001"></a><span class="ns">[</span><span + class="pgmark">i</span><span class="ns">]<br + /></span><small>THE</small><br + />ROMANCE OF MATHEMATICS.</h3> + +<h1><a name="png.003" id="png.003"></a><span class="ns">[</span><span + class="pgmark">iii</span><span class="ns">]<br + /></span><small>THE</small><br + />Romance of Mathematics:</h1> + +<h2><small>BEING</small><br + />THE ORIGINAL RESEARCHES<br + /><small>OF</small><br + /><img src="images/ladyprof.png" width="500" height="43" + alt="A Lady Professor of Girtham College" title="" /><br + /><small>IN</small></h2> + +<h4><i>Polemical Science, with some Account of the Social<br + />Properties of a Conic; Equations to Brain<br + />Waves; Social Forces; and the Laws<br + />of Political Motion.</i></h4> + +<h3><small>BY</small><br + /><big>P. HAMPSON, M.A.,</big><br + /><small>ORIEL COLLEGE, OXFORD.</small></h3> + +<h4>LONDON:<br + />ELLIOT STOCK, 62, PATERNOSTER ROW.<br + />1886.</h4> + +</div> + + + + +<div class="main"> +<h2><a name="png.005" id="png.005"></a><span class="ns">[</span><span + class="pgmark">v</span><span class="ns">]<br + /></span>INTRODUCTION.</h2> + + +<p class="noindent"><span class="smc">The</span> lectures, essays, and other matter +contained in these pages have been discovered +recently in a well-worn desk which +was formerly the property of a Lady Professor +of Girtham College; and as they +contain some original thoughts and investigations, +they have been considered +worthy of publication.</p> + +<p>How they came into the possession of +the present writer it is not his intention to +disclose; but inasmuch as they seemed to +his unscientific mind to contain some important +discoveries which might be useful to +the world, he determined to investigate +thoroughly the contents of the mysterious +desk, and make the public acquainted with +its profound treasures. He found some +documents which did not refer exactly to +the subject of ‘Polemical Mathematics;’ +but knowing the truth of the Hindoo +<a name="png.006" id="png.006"></a><span class="ns">[</span><span + class="pgmark">vi</span><span class="ns">] + </span>proverb, ‘The words of the wise are +precious, and never to be disregarded,’ +and feeling sure that this Lady Professor +of Girtham College was entitled to that +appellation, he ventured to include them +in this volume, and felt confident that in +so doing he would be carrying out the +intention of the Authoress, had she expressed +any wishes on the subject. In +fact, as he valued the interests of the State +and his own peace of mind, he dared not +withhold any particle of that which he +conceived would confer a lasting benefit +on mankind.</p> + +<p>Internal evidence seems to show that +the earlier portion of the MS. was written +during the period when the authoress was +still <i>in statu pupillari</i>; but her learning +was soon recognised by the Collegiate +Authorities, and she was speedily elected +to a Professorship. Her lectures were +principally devoted to the abstruse subject +of Scientific Politics, and are worthy of the +attention of all those whose high duty it is +to regulate the affairs of the State.</p> + +<p class="pgbrk">The Editor has been able to gather from +<a name="png.007" id="png.007"></a><span class="ns">[</span><span + class="pgmark">vii</span><span class="ns">] + </span>the varied contents of the desk some +details of the Author’s life, which increase +the interest which her words excite; and +he ventures to hope that the public will +appreciate the wisdom which created such +a profound impression upon those whose +high privilege it was to hear the lectures +for the first time in the Hall of Girtham +College.</p> + + + + + + +<h2><a name="png.009" id="png.009"></a><span class="ns">[</span><span + class="pgmark">ix</span><span class="ns">]<br + /></span>CONTENTS.</h2> + +<hr class="tb" /> + +<table class="toc" summary="Table of Contents"> +<tr><td><small>PAPER</small></td><td></td><td class="pg"><small>PAGE</small></td></tr> + +<tr><td class="cn">I.</td><td class="chap">Some Remarks on Female Education:</td></tr> + +<tr><td></td><td class="details"> +Cambridge Man’s Powers of Application.—Torturing +Ingenuity of +Examiners.—Slaying an Enemy.—‘Concentration.’—‘Tangential +Action.’—‘Gravity’</td> +<td class="pg"><a href="#png.013">1</a></td></tr> + +<tr><td class="cn">II.</td><td class="chap">Lecture on the Theory of +Brain Waves and the Transmigration +and Potentiality +of Mental Forces</td><td class="pg"><a href="#png.027">15</a></td></tr> + +<tr><td class="cn">III.</td><td class="chap">The Social Properties of a Conic +Section, and the Theory of +Polemical Mathematics:</td></tr> + +<tr><td></td><td class="details"> +‘Circle.’—‘Parabola.’—‘Ellipse.’ +‘Eccentricity of Curves’</td><td class="pg"><a href="#png.037">25</a></td></tr> + +<tr><td class="cn"><a name="png.010" id="png.010"></a><span class="ns">[</span><span + class="pgmark">x</span><span class="ns">]<br + /></span>IV.</td><td class="chap">The Social Properties of a Conic +Section (<i>continued</i>):</td></tr> + +<tr><td></td><td class="details"> +‘Ellipse.’—Most favoured State.—Alarming +Result of Suppression of +House of Lords.—Analogies of +Nature.—Directrix.—Contact of +Curves and States.—‘Hyperbola.’—Problems.—Radical +Axis and Patriotism.—Extension +of Franchise to +Women.—<span class="smc">Correspondence </span></td><td class="pg"><a href="#png.051">39</a></td></tr> + +<tr><td class="cn">V.</td><td class="chap">Social Forces, with some Account +of Polemical Kinematics:</td></tr> + +<tr><td></td><td class="details"> +The Use of Imagination in Scientific +Discovery.—Kinetic and Potential +Energy.—Social Statics and +Dynamics.—Attractive Forces.—Cohesion.—Formation +of States.—Inertia.—Dr. +Tyndall on Social +Forces</td><td class="pg"><a href="#png.083">71</a></td></tr> + +<tr><td class="cn">VI.</td><td class="chap">Social Forces (<i>continued</i>): Polemical +Statics and Dynamics:</td></tr> + +<tr><td></td><td class="details"> +‘Personal Equation.’—Public +Opinion, how calculated.—Impulsive +Forces.—Friction.—Progress</td><td class="pg"><a href="#png.101">89</a></td></tr> + +<tr><td class="cn"><a name="png.011" id="png.011"></a><span class="ns">[</span><span + class="pgmark">xi</span><span class="ns">]<br + /></span>VII.</td><td class="chap">Laws of Political Motion:</td></tr> + +<tr><td></td><td class="details"> +M. Auguste Comte on Political +Science.—First Law of Motion.—The +Biology of Politics.—Stages of +Growth and Decay of States.—Doctrine +of Nationality.—Doctrine of +Independence.—Law of Morality.—Ignorance +of Electors and Selfishness +of Statesmen opposed to Action of +Law.—Final ‘Reign of Law’</td><td class="pg"><a href="#png.113">101</a></td></tr> + +<tr><td class="cn">VIII.</td><td class="chap">The Principle of Polemical Cohesion:</td></tr> + +<tr><td></td><td class="details"> +Centralization.—Co-operation of +States.—Marriage.—Trade Unions.—International +Law</td><td class="pg"><a href="#png.127">115</a></td></tr> + +<tr><td></td><td class="chap">Extracts from the Diary of the +Lady Professor</td><td class="pg"><a href="#png.137">125</a></td></tr> + +<tr><td></td><td class="chap">Conclusion</td><td class="pg"><a href="#png.141">129</a></td></tr> + +</table> + + + + + +<h2><a name="png.013" id="png.013"></a><span class="ns">[</span><span + class="pgmark">1</span><span class="ns">]<br + /></span>PAPER I.</h2> + +<h3>SOME REMARKS OF A GIRTHAM GIRL ON +FEMALE EDUCATION.</h3> + + +<p><small>[<i>This essay upon Female Education was evidently +written when the future Professor of Girtham +College was still in the lowlier condition of studentship, +before she attained that eminence for which +her talents so justly entitled her. Its unfinished +condition tends to show that it was probably +evolved during moments of relaxation from severer +studies, without any idea of subsequent publication.</i>]</small></p> + +<p class="noindent above2"><span class="smc">Oh</span>, why should I be doomed to the +degradation of bearing such a foolish +appellation! A Girtham Girl! I suppose +we have to thank that fiend of invention +who is responsible for most of the titular +foibles and follies of mankind—artful Alliteration. +The two <em>G</em>’s, people imagine, +run so well together; and it is wonderful +that they do not append some other delectable +title, such as ‘The Gushing Girl of +Girtham,’ or ‘The Glaring Girl of Glittering +<a name="png.014" id="png.014"></a><span class="ns">[</span><span + class="pgmark">2</span><span class="ns">] + </span>Girtham.’ O Alliteration! Alliteration! +what crimes have been wrought in thy +name! Little dost thou think of the mischief +thou hast done, flooding the world +with meaningless titles and absurd phrases. +How canst thou talk of ‘Lyrics of +Loneliness,’ ‘Soliloquies of Song,’ ‘Pearls +of the Peerage’? Why dost thou stay +thine hand? We long for thee to enrich +the world with ‘Dreams of a Dotard,’ +the ‘Dog Doctor’s Daughters,’ and other +kindred works. Exercise thine art on these +works of transcendent merit, but cease to +style thy humble, but rebellious, servant a +Girtham Girl!</p> + +<p>But what’s in a name? Let the world’s +tongue wag. I am a student, a hard-working, +book-devouring, never-wearied student, +who burns her midnight oil, and drinks the +strong bohea, to keep her awake during +the long hours of toil, like any Oxford or +Cambridge undergraduate. I often wonder +whether these mighty warriors in the lists—the +class lists, I mean—really work half +so hard as we poor unfortunate ‘Girls of +Girtham.’ Now that I am writing in strict +<a name="png.015" id="png.015"></a><span class="ns">[</span><span + class="pgmark">3</span><span class="ns">] + </span>confidence, so that not even the walls can +hear the scratchings of my pen, or understand +the meaning of all this scribbling, I +beg to state that I have my serious doubts +upon the subject; and when last I attended +a soirée of the Anthropological +Society, sounds issued forth from the +windows of the snug college rooms, which +could not be taken as evidences of profound +and undisturbed study.</p> + +<p>Sometimes I glance at the examination +papers set for these hard-working students, +in order that they may attain the glorious +degree of B.A., and astonish their sisters, +cousins, and aunts by the display of these +magic letters and all-resplendent hood. +And again I say in strict confidence that +if this same glorious hood does not adorn +the back of each individual son of Alma +Mater, he ought to be ashamed of himself, +and not to fail to assume a certain +less dignified, but expressive, three-lettered +qualification. But before those Tripos +Papers I bow my head in humble adoration. +They sometimes take my breath +away even to read the terrible excruciating +<a name="png.016" id="png.016"></a><span class="ns">[</span><span + class="pgmark">4</span><span class="ns">] + </span>things, which seem to turn one’s brain +round and round, and contort the muscles +of one’s face, and stop the pulsation of +one’s heart, when one tries to grasp the +horrid things.</p> + +<p>Here is a fair example of the ingenuity +of the hard-hearted examiners, who resemble +the inquisitors presiding over the +tortures of the rack, and giving the hateful +machine just one turn more by way of +bestowing a parting benediction on their +miserable victims:</p> + +<p>‘A uniform rod’ (it is a marvellous act +of mercy that the examiner invented it +<em>uniform</em>; it is strange that its thickness +did not vary in some complicated manner, +and become a veritable birch-rod!) ‘of +length 2<i>c</i>, rests in stable equilibrium’ +(stable! another act of leniency!), ‘with +its lower end at the vertex of a cycloid +whose plane is vertical’ (why not incline +it at an angle of 30°?) ‘and vertex downwards, +and passes through a small, smooth, +fixed ring situated in the axis at a distance +<i>b</i> from the vertex. Show that if the equilibrium +be slightly disturbed, the rod will +<a name="png.017" id="png.017"></a><span class="ns">[</span><span + class="pgmark">5</span><span class="ns">] + </span>perform small oscillations with its lower +end on the arc of the cycloid in the time</p> + +<table class="math" summary="4[pi]sqrt(a{c^2+3(b-c)^2}/3g(b^2-4ac))"> +<tr><td rowspan="2">4π</td><td rowspan="2"><big class="enorm">√</big></td> +<td class="dfrac"><i>a</i>{<i>c</i>² + 3(<i>b - c</i>)²}</td><td rowspan="2">,</td></tr> +<tr><td class="dfrac">3<i>g</i>(<i>b</i>² - 4<i>ac</i>)</td></tr> +</table> + +<p class="noindent">where 2<i>a</i> is the length +of the axis of the cycloid.’</p> + +<p>A sweet pretty problem, truly! And +there are hundreds of the same kind—birch-rods +for every back! How the +examiner must have rejoiced when he +invented this diabolical rod, with its equilibrium, +its oscillations, its cycloid, and +other tormenting accessories. And yet, I +suppose, before my days of studentship +are over, I shall be called upon to attack +some such impregnable fortresses of mathematics, +when I hope to be declared equal +to some twentieth wrangler, if I escape +the misfortune of sharing a portion of the +‘wooden spoon.’</p> + +<p>Ah, you male sycophants! You would +prevent us from competing with you; you +would separate yourselves on your island +of knowledge, and sink the punt which +would bear us over to your privileged +shore. Of all the twaddle—forgive me, +male sycophants!—that the world has ever +<a name="png.018" id="png.018"></a><span class="ns">[</span><span + class="pgmark">6</span><span class="ns">] + </span>heard, I think the greatest is that which +you have talked about female education. +And the best of it is, you are so anxious +about our welfare; you are so afraid that +we should injure our health by overmuch +mental exertion; you profess to think that +our brains are not calculated to stand the +strain of continued mental exercise; you +think that competition is not good for the +female mind; that we are too competitive +by nature—too ambitious! Yes, we are +so ambitious that we would enter the +lists with those who are asked in Public +Examinations to find the simple interest +on £1,000 for 5 years at 6¼ per cent.; +so ambitious that we would compete with +those who are requested to disclose the +first aorist middle of <i title="Greek: tuptô">τυπτω</i>. Oh, think of +the mental strain involved in such questions! +How it must ruin your health to +find out how many times a wheel of radius +6 feet will turn round between York and +London, a distance of 200 miles! It is +quite wonderful how your brains, my dear +male sycophants, can stand such fearful demands +upon your intelligence and industry!</p> + +<p><a name="png.019" id="png.019"></a><span class="ns">[</span><span + class="pgmark">7</span><span class="ns">]<br + /></span>But you are so kind to us, so afraid of +our health! Really, we are much obliged +to you. If you married one of us, or +became our guardian, or left us a legacy, +we should then recognise your interest in +us, and be very grateful to you for your +good advice. But as matters stand, we +are quite capable of taking care of ourselves. +We will promise not to work too +hard, if you will promise not to weary us +with your paternal jurisdiction.</p> + +<p>But, male sycophants, I want a word +with you. Why do you object to our +taking degrees, or going in for examinations +in order to qualify ourselves for our +duties in life? You need not speak out +loud if you would rather not. Are you +not just a little afraid that we might eclipse +you? And it is not pleasant to be beaten +by a woman, is it? And then you profess +to think that we ought to be all housewives +and cooks, and knitters of stockings, +and sewers-on of our husbands’ buttons; +but what if we have no husbands, no +buttons to sew? And is it not a little +selfish, my dear male sycophant, to wish +<a name="png.020" id="png.020"></a><span class="ns">[</span><span + class="pgmark">8</span><span class="ns">] + </span>to keep us all to yourself? to attend upon +the wants of the lords of creation, who +often distinguish themselves so much in +the domain of science?</p> + +<p>Now, look me straight in the face (no +shirking, sir!). Is it not jealousy—green-eyed, +false-tongued jealousy—which saps +your generous instincts, and makes you +talk rubbish and nonsense about strains, +and brains, and ambition, and the like? +And if that is not hypocritical, I do not +know what is.</p> + +<p>Well, good-day to you, male sycophant! +I really have not time to indulge myself in +scolding you any more. You are a good +creature, no doubt; and when you have +shown us what you can do, and can estimate +the capacity of the female brain, and +take a common-sense view of things, we +will recognise your privilege to speak; +and when I am the presiding genius of +Girtham College, I will grant you the use +of our hall for the purpose of lecturing to us +on ‘Women’s Rights,’ or, as you may prefer +to entitle your discourse, ‘Men’s Wrongs.’</p> + +<p class="tbstars">* * * * *</p> + +<p><a name="png.021" id="png.021"></a><span class="ns">[</span><span + class="pgmark">9</span><span class="ns">]<br + /></span>Oh, this is shameful! I really am very +sorry. Here have I been wasting a good +half-hour in dreaming, and slaying an +imaginary enemy with envenomed words +and frequent dabs of ink. If I cannot +concentrate my mind more on these +mathematical researches, I fear a dreadful +‘plough’ will harrow my feelings at the end +of my sojourn in these halls of learning.</p> + +<p>Concentration! How many of our +words and ideas and thoughts are derived +from that primal fount of all arts and +sciences—mathematics! Here is one +which owes its origin to the mathematically +trained mind of some early philological +professor, who had learnt to apply +his scientific knowledge to the enrichment +of his native tongue. He quoted to +himself the words of the Roman poet:</p> + +<div class="stanza"> +<div class="indent6">‘Ego cur, acquirere pauca</div> +<div>Si possum, invideor, cum lingua Catonis et Ennî</div> +<div>Sermonem patrium ditaverit, et nova rerum</div> +<div>Nomina protulerit? Licuit, semperque licebit.’</div> +</div> + +<p>His mind conceived endless figures of +circles and ellipses scattered promiscuously +over the page, defying the attempts of the +<a name="png.022" id="png.022"></a><span class="ns">[</span><span + class="pgmark">10</span><span class="ns">] + </span>student to reduce them to order. What +must he do before he can apply his +formulæ and equations, determine their +areas, or describe their eccentric motion? +He must reduce them to a common +centre, and then he can proceed to +calculate the abstruse problems in connection +with the figures described. They +may be the complex motions of double-star +orbits, or the results of the impact of +various projectiles on the tranquil surface +of a pool. It matters not—the principle +is the same; he must concentrate, and +reduce to a common centre.</p> + +<p>This is the great defect of those who +have no accurate mathematical knowledge; +they cannot concentrate their minds with +the same degree of intensity upon the +work which lies before them. Their +thoughts fly off at a tangent, as mine do +very often; but then I have not been +classed yet in the Tripos; and, O male +poetical sycophant, you may be right after +all when you say:</p> + +<div class="stanza"> +<div>‘O woman! in our hours of ease</div> +<div>Uncertain, coy and hard to please,</div> +<div>As variable as the noon-day shade.’</div> +</div> + +<p class="noindent"><a name="png.023" id="png.023"></a><span class="ns">[</span><span + class="pgmark">11</span><span class="ns">]<br + /></span>Yes, as variable as the most variable +quantities <i>x</i>, <i>y</i>, <i>z</i>. I, a student of Girtham +College, blush to own that my thoughts +very often fly off at a tangent.</p> + +<p>‘Fly off at a tangent!’ All hail to +thee, most noble mathematical phrase! +Here is another fine mathematical expression, +plainly exemplifying the action +of centrifugal force. The faster the +wheel turns, the greater is the velocity of +the discarded particles which fly off along +the line, perpendicular to the radius of +the circle. The world travels very fast +now; the increased velocity of the transit +of earthly bodies, the rate at which they +live, the multiplicity of engagements, +etc., have made the social world revolve +so fast that the speed would have startled +the torpid life of the last century. And +what is the result? Men’s thoughts fly off +at a tangent; they are unable to concentrate +their minds on any given subject; +they are content with hasty generalisms, +with short magazine articles on important +subjects, which really require large volumes +and patient study to elucidate them fully.</p> + +<p><a name="png.024" id="png.024"></a><span class="ns">[</span><span + class="pgmark">12</span><span class="ns">]<br + /></span>What we want to do is to increase the +attractive force, in order to prevent this +tangential motion—to increase the <em>force of +gravity</em>.</p> + +<p>‘Well,’ says the young lady who loves +to revel in the ‘Ghastly Secret of the +Moated Dungeon,’ or the ‘Mysteries of +Footlight Fancy,’ ‘you are <em>grave</em> enough. +Pray don’t increase your gravity!’</p> + +<p>Thank you, gentle critic. I will, in +turn, ask you one favour. Leave for once +the ‘Mysteries of Footlight Fancy;’ seek +to know no more ‘ghastly secrets,’ and +increase <em>your gravity</em>—your mental +weight; and hence your attraction in the +eyes of all who are worth attracting will be +marvellously increased, by understanding +a little about Newton’s law of universal +gravitation, and don’t fly off at a tangent.</p> + +<hr class="tb" /> + +<p>At the end of this portion of the MS. +the editor of these papers discovered a +photograph which, from subsequent inquiry, +proved to be that of the accomplished +authoress of the above reflections. +<a name="png.025" id="png.025"></a><span class="ns">[</span><span + class="pgmark">13</span><span class="ns">] + </span>The face is one of considerable beauty, +with eyes as clear, steadfast, and open as +the day. There is a degree of firmness +about the mouth, but it is a sweet and +pretty one notwithstanding; and a smile, +half scornful, half playful, can be detected +lurking about the corners of the lips, +which do not seem altogether fitted for +pronouncing hard mathematical terms and +abstruse scientific problems. This photograph +might have been the identical one +which nearly brought an enamoured youth +into grave difficulties by its secretion in +the folds of his blotting-paper during +examination. The said enamoured youth +had evidently placed it there for the sake +of its inspiring qualities; and it was said +that all his hopes of gaining the hand of +the fair original depended upon his passing +that same examination. But the +wakeful eye of a stern examiner had +watched him as he turned again and +again to consult the sweet face which +beamed from beneath his blotting-paper; +and he narrowly escaped expulsion from +the Senate-house on the charge of +<a name="png.026" id="png.026"></a><span class="ns">[</span><span + class="pgmark">14</span><span class="ns">] + </span>‘cribbing.’ Certainly he took a mean advantage +of his fellow-sufferers, if this were the +identical photograph, for it portrays a +most inspiring face. Forgive us, lenient +reader; one moment! There—thank you—we +have done. And now we will proceed +to disclose the researches and original +problems which the MS. contains.</p> + +<p class="pgbrk">Evidently the collegiate authorities were +not slow in recognising the talents of the +assiduous student, and elected her without +much delay to a Professorship of +Girtham. In this capacity the learned +lady delivered several lectures, of which +the second MS. contains the first of the +<ins class="TN" title="Transcriber's note: + original reads 'eries'">series</ins>.</p> + + + + +<h2><a name="png.027" id="png.027"></a><span class="ns">[</span><span + class="pgmark">15</span><span class="ns">]<br + /></span>PAPER II.</h2> + +<h3>LECTURE ON THE THEORY OF BRAIN WAVES +AND THE TRANSMIGRATION AND POTENTIALITY +OF MENTAL FORCES.</h3> + + +<p class="noindent"><span class="smc">Professors and Students of the +University of Girtham, my Lords, +Ladies, and Gentlemen</span>,—I have the +honour to bring before you this evening +some original conceptions and discoveries +which have been formulated by me during +my researches in the boundless field of +mathematical knowledge; and though you +may be inclined at first to pronounce +them as somewhat hastily conceived hypotheses, +I hope to be able to demonstrate +the actual truth of the propositions which +I shall now endeavour to enunciate. It +is with some feelings of diffidence that I +stand before so august an assembly as the +present; and if I were not actually +<a name="png.028" id="png.028"></a><span class="ns">[</span><span + class="pgmark">16</span><span class="ns">] + </span>convinced of the accuracy of my calculations, +I should never have presumed to appear +before you in the character of a lecturer. +But ‘<i>Magna est veritas, et prævalebit</i>.’ +I cast aside maiden timidity; I +clothe myself in the professorial robe which +you have bestowed upon me, and sacrifice +my own feelings on the altar of Truth.</p> + +<p>I have been engaged, as you are doubtless +aware, for some years in the pursuit +of mathematical research, exploring the +mines of science, which have of late been +worked very persistently, but often, like +the black diamond mines, at a loss. Concurrently +with these researches, I have +speculated on the great social problems +which perplex the minds of men, both +individually and collectively. And I have +come to the conclusion that the same +laws hold good in both spheres of work; +that methods of mathematical procedure +are applicable to the grand social problems +of the day and to the regulation +of the mutual relations which exist +between man and man. Take, for +example, the Force of public opinion. Of +<a name="png.029" id="png.029"></a><span class="ns">[</span><span + class="pgmark">17</span><span class="ns">] + </span>what is it composed? It is the Resultant +of all the forces which act upon that +which is generally designated the ‘Social +System.’ Public opinion is a compromise +between the many elements which make +up human society; and compromise is a +purely mechanical affair, based on the +principle of the Parallelogram of Forces. +Sometimes disturbing forces exert their +influence upon the action of Public +Opinion, causing the system to swerve +from its original course, and precipitating +society into a course of conduct inconsistent +with its former behaviour; and it +is the duty of the Governing Body to +eliminate as far as possible such disturbing +forces, in order that society may +pursue the even tenor of its way.</p> + +<p>Professors, we have one great problem +to solve; and all questions social, political, +scientific, or otherwise, are only +fragments of that great problem. All +truths are but different aspects of different +applications of one and the same truth; +and although they may appear opposed, +they are not really so; and resemble +<a name="png.030" id="png.030"></a><span class="ns">[</span><span + class="pgmark">18</span><span class="ns">] + </span>lines which run in various directions, but +lovingly meet in one centre.</p> + +<p>Now, let us take for our consideration +the secret influence which men exert upon +each other, apart from that produced by +the power of speech (although that would +come under the same general law). As +mathematicians, you are aware that the +undulatory theory of light and heat and +sound are now accepted by scientific men +as the only sure basis of accurate calculation. +We know that the rays of light +travel in waves, and the equation representing +the waves is</p> + +<table class="math" summary="y = a/r sin(2[pi]/[lambda]) (vt-r)"> +<tr><td rowspan="2"><i>y</i> = </td><td><i>a</i></td><td rowspan="2"> sin </td> +<td>2π</td><td rowspan="2"> (<i>vt - r</i>),</td></tr> +<tr><td class="dfrac"><i>r</i></td><td class="dfrac">λ</td></tr> +</table> + +<p class="noindent">where <i>y</i> is the disturbance of the ether, +<i>a</i> the initial amplitude, <i>r</i> the distance +from the starting-point, λ the wave-length, +and <i>v</i> the velocity of light. Sound and +heat likewise have much the same form +of equation. Now, I maintain that the +waves of thought are governed by the +same laws, and can be determined by +an equation of the same form. You are +<a name="png.031" id="png.031"></a><span class="ns">[</span><span + class="pgmark">19</span><span class="ns">] + </span>aware that in all these equations a certain +quantity denoted by λ appears, and varies +for the different media through which the +sound, or light, or heat passes, and which +must be determined by experiment Now, +in my equation for brain waves, the same +quantity λ appears which must be determined +by the same method—by <em>experiment</em>. +But how is this to be done? After +mature deliberation and much careful +thought, I have discovered the method for +finding λ. This method is <em>mesmerism</em>. +We find the ratio of brain to brain—the +relative strength which one bears to +another; and then by an application of +our formula we can actually determine the +wave of thought, and read the minds of +our fellow-creatures. An unbounded field +for reflection and speculation is here suggested. +Like all great discoveries, the +elements of the problem have unconsciously +been utilized by many who are +unable to account for their method of +procedure. For example, thought-readers, +mesmerists, and the like, have unconsciously +been working on this principle, +<a name="png.032" id="png.032"></a><span class="ns">[</span><span + class="pgmark">20</span><span class="ns">] + </span>although lack of mathematical training +has prevented them from fully mastering +the details of the problem. Hence in +popular minds a kind of mystery has +hung about the actions of such people, +and excited the curiosity of mankind.</p> + +<p>The development of this theory of brain +waves may be of great practical utility to +the world. It shows that great care ought +to be exercised in the domain of thought, +as well as that of speech. For example: +A man has made a startling discovery, +from which he expects to receive considerable +worldly advantage. He would be +careful not to disclose his discovery in +speech to his acquaintances until his plans +are sufficiently matured, lest they should +impart it to the world, patent his device, +and reap the reward. But while he is +endeavouring to talk carelessly about it, +the wave of thought may be travelling +from brain to brain, suggesting the existence +of the discovery; and if the conditions +are favourable, and λ sufficiently +small, it is possible that the idea itself +may be conveyed. Of course the more +<a name="png.033" id="png.033"></a><span class="ns">[</span><span + class="pgmark">21</span><span class="ns">] + </span>complicated the discovery, the less likely +would the wave convey the conception. +Or suppose that one of the learned professorial +body of our sister university +should conceive an attachment for a lady-student +of Girtham College (of course a +very improbable supposition!), and the +infatuated <i>savant</i> became somewhat jealous +of another learned lecturer of the same +college (another improbability!), the fact +of his jealousy would be imparted to the +latter by a wave of thought, and might +cause considerable confusion in the serene +course of love or science. The fact of +the existence of the wave is indisputable. +What do all the stories of impressions and +double-sight teach us? How could the +intelligence of the death of Professor +Steele have been conveyed to his friend +and fellow-student, Professor Tait—the +one at Cambridge, the other at Edinburgh—were +it not for the existence of some +wave, which, like that of electricity, wings +its rapid flight unobserved by human eyes? +Are all the records of the Psychical Society +only myths and legends bred of +<a name="png.034" id="png.034"></a><span class="ns">[</span><span + class="pgmark">22</span><span class="ns">] + </span>superstitious fancy? It were hard to suppose +so.</p> + +<p>But if, gentlemen, and ladies especially, +you wish to keep your secret discoveries +to yourselves, watch over your thoughts as +well as your words; for my researches +prove, and the universal experience of +mankind corroborates the fact, that some +portion of your inmost thoughts and secret +desires are understood by your neighbours +(especially when λ is small!); that they +travel along the waves which I have attempted +to indicate; and if you would +desire to extend your influence in the +world, probe the secret instincts of mankind, +and prevent yourself from being +deceived and wronged—study the art and +science of Brain Waves.</p> + +<hr class="tb" /> + +<p>The following verses of rather doubtful +merit were found in connection with the +previous MS. They were evidently written +by a different hand; but inasmuch as they +were deemed worthy of preservation by +<a name="png.035" id="png.035"></a><span class="ns">[</span><span + class="pgmark">23</span><span class="ns">] + </span>the learned owner of the sealed desk, we +venture to publish them. They are closely +connected with the previous lecture, and +were evidently composed by an admirer +of the fair lecturer who did not share her +love for scientific research.</p> + +<div class="stanza"> +<div>Wavelet,<sup><a href="#fn.1" name="fna.1" id="fna.1">1</a></sup> wing thy airy flight;</div> +<div class="indent">Let thine amplitude be great;</div> +<div>Tell her all my thoughts to-night,</div> +<div class="indent">How I long to know my fate.</div> + +<div class="newverse"><br class="ns" +/>All the fields of Mathematics</div> +<div class="indent">I have roamed at her decree;</div> +<div>From Binomial and Quadratics,</div> +<div class="indent">To the strange hyperbole.<sup><a href="#fn.2" name="fna.2" id="fna.2">2</a></sup></div> + +<div class="newverse"><br class="ns" +/>I have soared through Differential,</div> +<div class="indent">Deeply drunk of Finite Boole;<sup><a href="#fn.3" name="fna.3" id="fna.3">3</a></sup></div> +<div>Though its breath is pestilential,</div> +<div class="indent">Reeking of the hateful School.</div> + +<div class="newverse"><br class="ns" +/>I have tried to shape a Conic,</div> +<div class="indent">Vainly read the Calculus;</div> +<div>But my feebleness is chronic,</div> +<div class="indent"><i>Morbus Mathematicus</i>.</div> + +<div class="newverse"><br class="ns" +/><a name="png.036" id="png.036"></a><span class="ns">[</span><span + class="pgmark">24</span><span class="ns">]<br + /></span>All my curves are cardioidal;</div> +<div class="indent">I confuse my <i>x</i> and <i>y</i>s,</div> +<div>Which they say is suicidal;</div> +<div class="indent">And my tutor vainly sighs.</div> + +<div class="newverse"><br class="ns" +/>Wavelet, tell her how I love her,</div> +<div class="indent">As she mounts her learned throne;</div> +<div>And that love I hope may cover</div> +<div class="indent">All the failings which I own.</div> + +<div class="newverse"><br class="ns" +/>Wavelet, cry to her for pity;</div> +<div class="indent">Bid her end this bitter woe;</div> +<div>I might do something ‘in the city,’</div> +<div class="indent">But never pass my Little-go.</div> +</div> + +<hr class="footnote" /> +<div class="footnote"> +<p><a href="#fna.1" name="fn.1" id="fn.1">1</a> We presume this is addressed to an imaginary +brain wave.</p> + +<p><a href="#fna.2" name="fn.2" id="fn.2">2</a> We observe here the dash of an indignant pen, +and a substituted for e. But now the rhyme is +spoiled. Gentle Muse, thou art sacrificed by the +stern hand of Mathematical Truth!</p> + +<p><a href="#fna.3" name="fn.3" id="fn.3">3</a> Query: Does the writer refer to the learned +treatise on Finite Differences by Professor Boole?</p> +</div> + + + +<h2><a name="png.037" id="png.037"></a><span class="ns">[</span><span + class="pgmark">25</span><span class="ns">]<br + /></span>PAPER III.</h2> + +<h3>LECTURE ON THE SOCIAL PROPERTIES OF +A CONIC SECTION, AND THE THEORY OF +POLEMICAL MATHEMATICS.</h3> + + +<p class="noindent"><span class="smc">Most Learned Professors and Students +of this University</span>,—From the +interest manifested in my first lecture, I +conclude that my method of investigation +has not proved altogether unsatisfactory +to you, and I hope ere long to produce +certain investigations which will probably +startle you, and revolutionize the current +thought of the age. The application of +mathematics to the study of Social +Science and Political Government has +curiously enough escaped the attention of +those who ought to be most conversant +with these matters. I shall endeavour to +prove in the present lecture that the +relations between individuals and the +Government are similar to those which +<a name="png.038" id="png.038"></a><span class="ns">[</span><span + class="pgmark">26</span><span class="ns">] + </span>mathematical knowledge would lead us +to postulate, and to explain on scientific +principles the various convulsions which +sometimes agitate the social and political +world.</p> + +<p>Indeed, by this method we shall be able +to prophesy the future of states and +nations, having given certain functions and +peculiarities appertaining to them, just as +easily as we can foretell the exact day and +hour of an eclipse of the moon or sun. In +order to do this, we must first determine +the <em>social properties of a conic section</em>.</p> + +<p>For the benefit of the unlearned and +ignorant, I will first state that a cone is +a solid figure described by the revolution +of a right-angled triangle about one of the +sides containing the right angle, which +remains fixed. The fixed side is called +the axis of the cone. Conic sections are +obtained by cutting the cone by planes. +It may easily be proved that if the angle +between the cutting plane and the axis be +equal to the angle between the axis and +the revolving side of the triangle which +generates the cone, the section described +<a name="png.039" id="png.039"></a><span class="ns">[</span><span + class="pgmark">27</span><span class="ns">] + </span>on the surface of the cone is a parabola; +if the former angle be greater than the +latter, the curve will be an ellipse; and if +less, the section will be a hyperbola.</p> + +<p>But the simplest conic section is, of +course, a circle, which is formed by a plane +at right angles to the axis of the cone; +and the simplest circle is that formed +by a plane passing through the apex of the +cone. All this is simple mathematics; +and let beginners consult more elementary +treatises than this one to satisfy themselves +on these points. But if they will +assume these things to be true, they will +know quite enough for our present +purpose. The simplest conic section +of all has been proved to be a <em>point</em>. +Now, this represents the simplest and +original form of society, a <em>single family</em>. +‘It is not good for man to be alone’ +was the first observation made by the +wise Creator upon the rational creature +whom He had introduced into +Paradise as its lord. Marriage is the +rudiment of all social life, from which +all others spring, out of which all others +<a name="png.040" id="png.040"></a><span class="ns">[</span><span + class="pgmark">28</span><span class="ns">] + </span>are developed. Around the parents’ knees +soon cluster a group of children, and in +their relation to each other we discern the +earliest forms of law and discipline—the +bonds by which society is held together. +When the children grow up, separate +households are formed; and then the +multiplication of families, the congregating +of men together for purposes of security +and mutual advantages in division of +labour; and thus is gradually formed a +state, which is only the development of +the family—the king representing the +parent, and ruling on the same principle.</p> + +<p>Mathematically speaking, our plane no +longer passes through the apex. The +point represented the single family; +but keeping the plane horizontal, we +move it along the axis, the sections +will become <em>circles</em>, which represent +mathematically the next simplest form of +society, where the centre is the seat of +government, which is connected with each +individual member of the social circle by +equal radii. The social property of a +circle is that of a monarchical government +<a name="png.041" id="png.041"></a><span class="ns">[</span><span + class="pgmark">29</span><span class="ns">] + </span>in its purest and simplest form. The +larger the circle becomes (<i>i.e.</i>, the further +you move the plane from the apex), the +greater the distance between the individual +and the monarch. Therefore, the more +independent the monarchy becomes, and +the less influence do individuals possess +over the ruling power. Hence, we may +infer that as years roll on, the government +will become more despotic; but the +stability of the country diminished, and +probably some individual particle, when +sufficiently withdrawn from the attraction +of the central head, will begin to revolve +on its own account, and spontaneously +generate a government of its own. We +may, therefore, conclude from mathematical +reasoning that an unlimited monarchy, +though advantageous for small states, is +not a safe form of government for a large +or populous country, inasmuch as the +people do not derive much benefit from +the sovereign; the mutual attraction, +which ought to exist in a flourishing state +between the ruler and the ruled, is +weakened; and the isolation of the +<a name="png.042" id="png.042"></a><span class="ns">[</span><span + class="pgmark">30</span><span class="ns">] + </span>monarch tends to make him still more +despotic. As a practical example of the +truth of the foregoing statement, I may +mention the present condition of Russia, +which shows that the result of an unlimited +monarchy, in a large and unwieldy +social circle, is such as we should have +reasonably expected from mathematical +investigations.</p> + +<p>Invariably, under the circumstances +which I have described, the country will +become disorganized; the sovereign will +cease to have any power over the people, +and the country will become a chaos, +without order, influence, or power.</p> + +<p>When the centre of a conic section +moves along the axis of the curve to +infinity, banished by the mutual consent +of the individual particles which compose +the curve, or the nation, a figure is formed, +called a <em>parabola</em>. This is the curve +which the most erratic bodies in the +universe describe in space, as they rush +along at a speed inconceivable to human +minds, and are supposed to produce all +kinds of mischief and injury to the +<a name="png.043" id="png.043"></a><span class="ns">[</span><span + class="pgmark">31</span><span class="ns">] + </span>worlds whose courses they wend their way +among.</p> + +<p>This curve, then, represents the position +which the nation assumes when the constituted +monarchy, the centre of the system, +has been <em>banished to infinity</em>. A revolution +has occurred; the monarch has been +dethroned; and it is not hard to see that +the same erratic course which the comet +pursues in its flight, is observable with +respect to the social system which is +represented by a parabola. We observe +with eager scrutiny the wanderings of +these erratic comets. They appear suddenly +with their vapoury tails; sometimes +they shine upon us with their soft, silvery +light, brilliant as another moon; sometimes +they stand afar off in the distant +skies, and deign not to approach our +steady-going earth, which pursues its +regular course day by day, and year by +year. Then, after a few days’ coy inspection +of our planet from different +points of view, they fly to other remote +parts of the universe, and do not condescend +to show themselves again for a +<a name="png.044" id="png.044"></a><span class="ns">[</span><span + class="pgmark">32</span><span class="ns">] + </span>hundred years or so. Such is the erratic +conduct of a heavenly body whose course +is regulated by a parabolic curve.</p> + +<p>We may look for similar eccentric behaviour +on the part of a community, +nation, or state, whose centre is at infinity, +whose constitution has been violently +disturbed, and whose monarchy is +situated in the far-off regions of unlimited +space. The erratic course of Republican +rule is proverbial. There is no stability, +no regularity. To-day we may observe its +brilliancy, which seems to laugh at and +eclipse the sombre shining of more +steady and enduring worlds; but ere to-morrow’s +moon has risen, it may have +vanished into the regions of eternal night, +and we look for its bright shining light in +the councils of the nations, but it has +ceased to shed its rays, and we are disappointed. +Sometimes it is asked, with +fear and trembling: ‘What would be the +effect if our earth were to come in contact +with the tail of a comet? Should we be +destroyed by the collision, and our ponderous +world cease to be?’ But we are +<a name="png.045" id="png.045"></a><span class="ns">[</span><span + class="pgmark">33</span><span class="ns">] + </span>assured that no such disastrous results +would follow. We have already passed +through the tails of many comets, but we +have not discovered any inconvenient +change in our ordinary mode of procedure. +It is probable that the comet’s +tail is composed of no solid substance.</p> + +<p>We may therefore infer by analogy that +a Republican State would not offer any +powerful resistance if it were to come into +collision with a nation possessing a more +settled form of government. A shower of +meteoric stones, like passing fireworks, +might take place; but beyond that +nothing would occur to excite the fear, +or arouse the energies of the more +favoured nation. As an example of the +weakness of a Republican State I may +mention France. There we see an industrious +race of people, endowed with +many natural gifts and graces, a country +rich and productive; and yet, owing to +the unsettled nature of its government, all +these natural advantages are neutralized; +its course amongst the nations is erratic +in the extreme, a spectacle of feeble +<a name="png.046" id="png.046"></a><span class="ns">[</span><span + class="pgmark">34</span><span class="ns">] + </span>administration; and it would offer no more +resistance to a colliding Power than the +empty vacuum of a comet’s tail. This +example will demonstrate to you the truth +of our theory with regard to the instability +of a social system which is geometrically +represented by a parabolic curve.</p> + +<p>We will now turn from this picture of +insecurity and unrest to another figure +which possesses most advantageous social +properties. I refer to the ellipse. An +ellipse is a curve formed by the section +of a cone by a plane surface inclined at +an angle to the vertical axis of the cone, +greater than the angle between the axis +and the generating line.</p> + +<p>Now, this is a curve which possesses +most attractive properties. It is the curve +which the earth and other planetary orbs +describe around the centre of the solar +system, as if nature intended that we +should take this figure as a guide in +choosing the most advantageous social +system. It possesses a centre, C, in view +of all the particles which compose the +curve, and connected with them by close +<a name="png.047" id="png.047"></a><span class="ns">[</span><span + class="pgmark">35</span><span class="ns">] + </span>ties. It has two foci, S and S', fixed +points, by the aid of which we may trace +the curve.</p> + +<p>In the interpretation of this figure, the +centre of the curve represents the throne +of monarchy. There is no tendency here +to revolutionize the State, to banish the +ruling power, and institute a Republican +form of government; but inasmuch as we +saw the weakness of an absolute monarchy +in large and populous States, as represented +by the circle, the wisdom of an +elliptical social system has ordained that +there shall be two foci, or houses of +representatives of the people, who shall +assist in regulating the progress of the +nation. Here we have a limited monarchy; +the throne is supported by the representatives +of the people; and the nearer these +foci of the nation are to the centre (<i>i.e.</i>, +in mathematical language, the less the +<em>eccentricity</em> of the curve), the more perfect +the system becomes—the greater the +happiness of the community.</p> + +<p>In cases where the <em>eccentricity</em> becomes +very great, the beauty of the curve is +<a name="png.048" id="png.048"></a><span class="ns">[</span><span + class="pgmark">36</span><span class="ns">] + </span>destroyed, and ultimately the ellipse is +merged into one straight line. Most +learned Professors, here we have a terrible +warning of the awful result of too much +eccentricity. Whether we regard the life +of the nation or of the individual, let all +bear in mind this alarming fact, that +eccentricity of thought, habit, or behaviour +may result, as in the case of this unfortunate +ellipse, which once presented such +fair and promising proportions to the +student’s admiring gaze, in the ‘sinister +effacement of a man,’ or the gradual absorption +of a State into an uninteresting +thing ‘which lies evenly between its extreme +points.’</p> + +<p>The great examples of Bacon, of Milton, +of Newton, of Locke, and of others, +happen to be directly opposed to the +popular inference that eccentricity and +thoughtlessness of conduct are the necessary +accompaniments of talent, and the +sure indications of genius. I am indebted +to Lacon for that reflection. You may +point to Byron, or Savage, or Rousseau, +and say, ‘Were not these eccentric people +<a name="png.049" id="png.049"></a><span class="ns">[</span><span + class="pgmark">37</span><span class="ns">] + </span>talented?’ ‘Certainly,’ I answer; ‘but +would they not have been better and +greater men if they had been less eccentric—if +they had restrained their caprice, +and controlled their <ins class="TN" title="Transcriber's note: + original lacks closing quote">passions?’</ins> Do not +imagine, my young students of this university, +that by being eccentric you will +therefore become great men and women +of genius. The world will not give you +credit for being brilliant because you affect +the extravagances which sometimes accompany +genius. Some of you ladies, I +perceive, have adopted a peculiar form of +dress, half male, half female; or, to be +more correct, three-fourths male, and one-fourth +female. Do not imagine that you +will thus attain to the highest honours in +this university by your eccentricity, unless +your talents are hid beneath your short-cut +hair, and brains are working hard under +your college head-gear. As well might we +expect to find that all females who wear +sage-green and extravagant æsthetic costumes +are really born artists and future +Royal Academicians. It is apparent that +many aspirers to fame and talent are eager +<a name="png.050" id="png.050"></a><span class="ns">[</span><span + class="pgmark">38</span><span class="ns">] + </span>to exhibit their eccentricities to the gaze +of the world, in order that they may persuade +the multitude that they possess the +genius of which eccentricity is falsely supposed +to be the outward sign.</p> + +<p>I may remark in passing that the eccentricity +of a parabolic curve is always <em>unity</em>. +What does this prove? You will remember +that a Republican State is represented by +a parabola. Therefore, however such a +nation may strive to alter its condition, +and secure a settled form of government, +its eccentricity will always remain the +same. It will always be erratic, peculiar, +unsettled; and this conclusion substantiates +our previous proposition with regard +to the condition of a social system represented +by a parabola.</p> + +<p class="pgbrk">With regard to other advantages afforded +by an elliptical social system, we will defer +the consideration of this important +subject until my next lecture.</p> + + + + + +<h2><a name="png.051" id="png.051"></a><span class="ns">[</span><span + class="pgmark">39</span><span class="ns">]<br + /></span>PAPER IV.</h2> + +<h3>THE SOCIAL PROPERTIES OF A CONIC +SECTION, AND THE THEORY OF POLEMICAL +MATHEMATICS—(<i>continued</i>).</h3> + + +<p class="noindent"><span class="smc">Most learned Professors and Students +of this University</span>,—You have already +gathered from my preceding lecture my +method of procedure in the investigation +of the corresponding properties of curves +and States. You have perceived that we +have here the elements of a new science, +which may be extended indefinitely, and +applied to the various departments of self-government +and State control. This new +science of polemical mathematics is in +itself an extension of the <em>principle of continuity</em>, +for the discovery of which Poncelet +is so justly renowned. We can prove by +geometry that the properties of one figure +may be derived from those of another +<a name="png.052" id="png.052"></a><span class="ns">[</span><span + class="pgmark">40</span><span class="ns">] + </span>which corresponds to it; and the new +science teaches us that if we can represent, +by projection or otherwise, a society of +particles or individuals on a plane surface, +the properties of the State so represented +are analogous to the properties of the +curve with which it corresponds. It is +only possible for me to touch upon the +elements of the science in these lectures, +but I hope to arouse an interest in these +somewhat unusual complications and +curious problems, that you may hereafter +make further discoveries in this unexplored +region of knowledge, and that the world +may reap the benefit of your labours and +abstruse studies. I have already, in my +previous lecture, touched upon the social +properties of the parabola, and examined +the constitution of erratic curves and +eccentric nations. It is my intention +to-day to speak of similar problems +which arise with reference to elliptical +States.</p> + +<p>But, first, let me answer an objection +which may have occurred to your minds. +<a name="png.053" id="png.053"></a><span class="ns">[</span><span + class="pgmark">41</span><span class="ns">] + </span>Am I wrong in my calculations in attributing +too much to the power and usefulness +of forms of government? Does the +well-being and happiness of a nation depend +on the government, or upon the +individuals who compose the nation? +Most assuredly, I assert, they rest upon +the former. Men love their country when +the good of every particular man is comprehended +in the public prosperity; they +undertake hazard and labour for the +government when it is justly administered. +When the welfare of every citizen is the +care of the ruling power, men do not +spare their persons or their purses for the +sake of their country and the support of +their sovereign. But where selfish aims +are manifest in Court or Parliament, the +people care not for State officials who are +indifferent to their country’s weal; they +become selfish too; Liberty hides her head, +and shakes off the dust of her feet ere she +leaves that doomed land, and the stability, +welfare, and prosperity of that country +cease.</p> + +<p><a name="png.054" id="png.054"></a><span class="ns">[</span><span + class="pgmark">42</span><span class="ns">]<br + /></span>I might refer you to many a stained +page of national history in order to prove +this. Compare the closing chapters of the +life of the Roman empire with the record +of the brave deeds of its ancient warriors +and valorous statesmen. Grecian preeminence +and virtue died when liberty +expired. I agree with Sidney when he +writes that it is absurd to impute this to +the change of times; for time changes +nothing, and nothing was changed in +those times but the government, and that +changed all things. These are his words: +‘As a man begets a man, and a beast a +beast, that society of men which constitutes +a government upon the foundation +of justice, virtue, and the common good, +will always have men to promote those +ends; and that which intends the advancement +of one man’s desires and +vanity will abound in those that will +foment them.’ I may not, therefore, be +altogether wrong in attributing the prosperity +and well-being of a nation to the +form of government which it possesses.</p> + +<p><a name="png.055" id="png.055"></a><span class="ns">[</span><span + class="pgmark">43</span><span class="ns">]<br + /></span>We will now proceed to the consideration +of the social advantages which an +elliptical State affords. This is the form +of government and social position which +we, as a nation, at present enjoy; and +from mathematical considerations I am +of opinion that it is the best, and hope +that no change will ever be made in our +constitution. You may remember that I +have previously stated that an ellipse has +a centre and two foci, in view of all the +particles which compose the curve, and +connected with them by close ties. The +centre, in the projected figure, represents +the monarchy, which is limited; and the +government is carried on by the aid of +the two houses of representatives of the +people, depicted in the projection by the +two foci.</p> + +<p>Now the social advantages of the ellipse +are given by the fact that the sum of the +distances of any point from the foci is +always constant. No particle is left out +in the cold; no one does not possess +the advantages of a social government. +<a name="png.056" id="png.056"></a><span class="ns">[</span><span + class="pgmark">44</span><span class="ns">] + </span>Though his distance may be far from the +Upper House, he has the advantage of +nearness to the Lower, and <i>vice versâ</i>. The +sum of the distances is constant. The +extinction of one focus, the House of +Lords, for example, would create a complete +disorganization of the whole system: +the other focus would set up a powerful +magnetic attraction, and a curious bulb-shaped +curve would be evolved, very +different from the beautiful symmetrical +form which the original figure presented +to the eye. The centre of the system +would be disturbed; and it is probable +that ere long it would disappear along the +axis and be vanished to infinity. Thus +the curve would become a parabola. This +is the alarming result of the extinction of +one focus. Abolish the House of Lords, +and you will soon find that the Throne +will be disturbed; the State will become +disorganized; the nation will become +confused by the magnetic force of the +Lower House, uncounteracted by any other +attraction; and very soon a complete +<a name="png.057" id="png.057"></a><span class="ns">[</span><span + class="pgmark">45</span><span class="ns">] + </span>revolution of the whole system will set +in: the monarch will be dethroned, and +a Republican form of government, with all +the eccentricities of a parabolic course, +will take the place of a more orderly and +settled constitution. This is a plain +deduction from our mathematical investigations; +and it behoves all our statesmen, +our philosophers and great men, our +fellow-citizens and the humblest artisans +in our manufacturing towns, to weigh well +this alarming result of the abolition of +that House which has been threatened +with destruction; and to ascertain for +themselves the truths upon which my proposition +and reasoning rest.</p> + +<p>I have already observed that the fact +that the earth’s orbit and that of other +planets are in the form of ellipses; that +the curvature of the earth is nearly the +same, ought to guide us in choosing this +particular curve as a model of the projection +of a complete and most advantageous +social system.</p> + +<p>The circle described on the major axis of +<a name="png.058" id="png.058"></a><span class="ns">[</span><span + class="pgmark">46</span><span class="ns">] + </span>an ellipse, is called the <em>auxiliary circle</em>, and +affords much assistance in the investigation +of the properties of an ellipse. As +we have already shown, the circle represents +the simplest form of monarchical +government. Hence, if we compare the +form of government represented by an +ellipse (<i>i.e.</i>, such as we now enjoy) with +that of a system where the king is the only +governing power, we may obtain great +assistance in solving complicated political +problems.</p> + +<p>In all conics there is a straight line +called the ‘directrix,’ which represents in +social or polemical science the laws of the +nation, and plays a prominent part in the +mutual relations of the individual particles. +For instance, in the case of the parabola, +the distance of any particle from the +directrix is equal to its distance from the +focus.</p> + +<p>From this we may conclude that if an +individual deviates at all from the path +which the laws (or, directrix) indicate, if +he does not show true respect to the +<a name="png.059" id="png.059"></a><span class="ns">[</span><span + class="pgmark">47</span><span class="ns">] + </span>decrees of the focal government, and +preserve the true position between them, +directly he is found deviating from his +course, he is quickly banished to a less +enlightened sphere. In an ellipse there +is less likelihood of his straying away from +the course which the directrix points out, +on account of the two-fold guidance which +he receives from the two foci.</p> + +<p>The following curious problem may be +noticed. If a parabola roll on another +parabola, their <ins class="TN" title="Transcriber's note: + original reads 'virtices'">vertices</ins> coinciding, the +focus of the first traces out the directrix +of the second.</p> + +<p>Here we come to the consideration of +the international relationship of States. +Two nations have the same form of +government (in this example this form is +Republican); their policies coincide: we +may conclude from this proposition that +the course which the government of one +nation will pursue, will be that which is +prescribed by the laws of the other.</p> + +<p>The subject of the contact of curves +presents many interesting problems with +<a name="png.060" id="png.060"></a><span class="ns">[</span><span + class="pgmark">48</span><span class="ns">] + </span>reference to Polemical Science, and may +be extended indefinitely. It is well known +that there are different orders of contact, +which are designated as the <em>first</em>, <em>second</em>, +or <em>third</em> order. This last order may be +termed the ‘marriage of curves,’ cemented +by the osculating circle, or ‘wedding-ring;’ +and when two nations have contact +of the third order, they have formed a +very close alliance, and by calculation we +can obtain the <em>radius of curvature</em>, or size +of the wedding-ring, by means of which +they may be united.</p> + +<p>The theory and nature of contact constitute +a branch of our newly discovered +science which we commend to the careful +consideration of those who have undertaken +the difficult and perplexing study of +international law. Alas! too many States +refuse this friendly contact, and, consequently, +<em>cut</em> each other, instead of +blending in sweet accord. Their peace is +at best an armed neutrality; and if they +have contact of only the <em>first</em> or <em>second</em> +order, we can prove mathematically that +<a name="png.061" id="png.061"></a><span class="ns">[</span><span + class="pgmark">49</span><span class="ns">] + </span>they are sure to intersect in some other +point or points; and divergence of policy +and disturbed relations are the results. +Contact of the <em>third, or highest, order</em> is +the only safe position for two allied, or +contiguous, States.</p> + +<p>With your permission I will add a few +words to those I have already uttered +with regard to the directrix. As necessary +as the directrix is to the curve, so are +the corresponding laws to the State. I +will prove this fact by a few examples. +English people have laws, and know how +to obey them; therefore their numbers +increase; they thrive and are prosperous. +A friendly critic of another nation has +said that the reason why Englishmen +rule the world, is because they know how +to obey. On the other hand, the gipsies +have no laws; hence they become fewer +and less powerful. What is the condition +of all tribes and nations which are not +governed by laws? They invariably +remain poor and miserable. They are in +want of a directrix; and if we could +<a name="png.062" id="png.062"></a><span class="ns">[</span><span + class="pgmark">50</span><span class="ns">] + </span>supplement the gift with foci and centre, they +would soon emerge from their savage condition, +and become more civilized.</p> + +<p>I have omitted to mention the hyperbolic +form of government. The curve +formed by the intersection of the surface +of a cone with a plane will be a hyperbola, +when the inclination of the cutting +plane to the axis of the cone is less than +the constant angle which the generating +line forms with the axis. It is manifest +that the plane will thus intersect the +higher cone, and produce the figure +which is known to mathematicians as +the hyperbola.</p> + +<p>We may hence deduce the following +property of the corresponding hyperbolic +State. We take cognizance of that higher +cone with which the mundane affairs of +the lower cone are closely connected. As +an example of this system we may mention +the vast temporal rule and power of the +Papal Throne, which formerly exercised +such marvellous sway over the nations of +Europe. By an appeal to a Higher +<a name="png.063" id="png.063"></a><span class="ns">[</span><span + class="pgmark">51</span><span class="ns">] + </span>Authority than that of earthly kings and +potentates was this rule exercised; but its +hyperbolic form is fast passing away, and +degenerating into that of a circle with +indefinitely small radius. We shall not, +therefore, discuss the complex polemical +problems which a hyperbolic State +suggests.</p> + +<p>I will now mention a few problems +which are easily capable of proof, and +deduce from them the necessary conclusions +which must follow when we apply +our newly discovered principles of polemical +science.</p> + +<p>1. ‘If from any point in a straight line +a pair of tangents be drawn to an ellipse, +the chords of contact will pass through a +fixed point.’</p> + +<p>I will not trouble you with the proof of +this proposition, as it is evident to all +mathematicians, and can easily be demonstrated. +But mark well the deductions, +when we interpret this mathematical language +in correct polemical terms. A State, +through various convulsions of its own, +<a name="png.064" id="png.064"></a><span class="ns">[</span><span + class="pgmark">52</span><span class="ns">] + </span>has merged into a condition represented +by a straight line, having lost its symmetry, +its beauty, its curvilinear proportion. +An individual unhappily situated +in this unfortunate community regards +with longing eyes the prosperous condition +of those who enjoy the social advantages +of a settled form of government, and other +blessings which accompany elliptical jurisdiction +and laws. [Two tangents are +drawn to an ellipse.] No matter where +the individual may be in the unhappy +envious straight line, the result of his reflection +will be the same. Sympathetic +chords are drawn, joining the points of +contact of the tangents with the curve; +they all pass through a fixed point. All +these conclusions of the various individuals +on the straight line will be the same. All +are of opinion that the elliptical form is +the best; and they mourn in secret over +the sad events which have occurred in +their own national life, their eccentricity, +their lawlessness, when they see the +advantages which their more staid and +sober-minded neighbours so freely enjoy.</p> + +<p><a name="png.065" id="png.065"></a><span class="ns">[</span><span + class="pgmark">53</span><span class="ns">]<br + /></span>2. The normal at any point of an ellipse +bisects the angle between the focal distances +of that point.</p> + +<p>The normal is the perpendicular from +the point on the major axis; it is the line +of thought directed by the observance of +just laws and rules. Hence this proposition +shows that the individual citizen, +when guided by sound judgment, regards +with equal favour and entire approval the +existence of both foci, or Houses of Legislature. +He considers that both are necessary +to his comfort, and the right regulation +of the State’s welfare. He cares not for +the <em>abnormal</em> condition of those who talk +as if the existence of either House were +unnecessary to his country’s weal, and +bestows a pitying glance on those wandering +lights, or disturbed erratic governments, +which do not possess the advantages +which from experience he has learned to +love and to respect. No matter what his +condition may be, the same opinions are +held by all classes, all ranks and degrees; +and if a <ins class="TN" title="Transcriber's note: + original reads 'self-opiniated'">self-opinionated</ins> particle think otherwise, +he ought to be transferred to a less +<a name="png.066" id="png.066"></a><span class="ns">[</span><span + class="pgmark">54</span><span class="ns">] + </span>enlightened sphere, and migrate to a parabolic +state, or uninteresting straight line. +And when he has changed his location, +he will look back on his old home and +old surroundings with longing eyes and an +aching heart, thinking of the blessings he +has lost by his own rash act. This can +be proved mathematically. He looks for +an ideal state of society, leaps after the +shadow his fancy has depicted; and when +he finds himself outside his former state, +he looks back with longing eyes at the +once-scorned focus. What is the focus of +a perpendicular on the tangent of an +ellipse from any external point? Can it +not be proved to be a <em>circle</em>? That is to +say, he will be more conservative than +ever. He would like to return to a primitive +form of government. Farewell to his +wild schemes and revolutionary measures! +Farewell to his disestablishments, abolitions, +and suppressions! The throne and +government have new attractions in his +eyes; loyalty, a new feeling, asserts its +benign influence; and if he could return +<a name="png.067" id="png.067"></a><span class="ns">[</span><span + class="pgmark">55</span><span class="ns">] + </span>to his former position, his normal conduct +would be straighter than ever, for +by sad experience he has learned the +value of those things which he once +despised.</p> + +<p>But we need not depend upon one +proof alone. Exactly the same result may +be obtained from the well-known proposition +which states that ‘the angle between +the tangent from any external point and +the focal distance is equal to the angle +between the other tangent and the focal +distance.’</p> + +<p>3. The same opinions are often held +by individuals in quite different walks and +classes of life. Let these individuals be +represented by points on an ellipse. Join +these, and we have a system of parallel +chords. Draw a straight line through the +middle points of these chords, and lo! it +will always pass through the centre. This +shows that the central thought of all people +is directed to the sovereign—that <em>loyalty</em> +is inherent in the hearts of those who +recognise elliptical laws.</p> + +<p><a name="png.068" id="png.068"></a><span class="ns">[</span><span + class="pgmark">56</span><span class="ns">]<br + /></span>I will conclude this lecture with a few +remarks on the nature and properties of +the <em>radical axis</em>. This name was first +given, I believe, by M. Gaultier, of Tours, +and for a full account of its nature I refer +you to the <cite>Journal de l’École Polytechnique</cite>, +xvi., 1813. The radical axis of two circles +is the line perpendicular to the line joining +the centres, from any point of which +the tangents to the circles are equal. Let +us suppose that one circle becomes a point, +and that this point is situated on the circumference +of the first circle. What is +the result? The radical axis becomes +the tangent to the circle. Hence we +may conclude that in a social system of +monarchical government the radical axis +is perpendicular to the line attaching the +individual with the monarch. Therefore +we may conclude that the radical axis +indicates a tendency of particles, or individuals, +to fly off at a tangent, at right +angles to the connecting-link between the +individual and the king. When any motion +takes place, this is evident, and this +<a name="png.069" id="png.069"></a><span class="ns">[</span><span + class="pgmark">57</span><span class="ns">] + </span>tendency is called centrifugal force. Sad is +it for the State when this force is called +into play, and the radical axis is a standing +menace to the stability of States and +nations. The only way to counteract its +baneful, disturbing influence is to increase +the attraction of the monarch on the individual, +which nullifies the former force, +and prevents further mischief. This is the +method which nature itself adopts in the +motions of the planetary worlds; the attraction +of the sun prevents any disturbance +which might be caused in the course +of the planets by the action of centrifugal +force, and nature suggests this plan for +our adoption. Increase the attraction of +the Throne; rigidly connect each individual +by the strong chords of affection, advantage +and utility with the ruling power; +and then, though the radical axis may be +there, it will cease to indicate any motion +along it, it will not prevail over the counteracting +influence of loyalty, and the stability +of the social system and the happiness of +the individuals will be the results.</p> + +<div class="stanza"> +<div class="indent6"><a name="png.070" id="png.070"></a><span class="ns">[</span><span + class="pgmark">58</span><span class="ns">]<br + /></span>‘I would serve my King,</div> +<div>Serve him with all my fortune here at home,</div> +<div>And serve him with my person in the wars;</div> +<div>Watch for him, fight for him, bleed for him, die for him,</div> +<div>As every true-born subject ought.’</div> +</div> + +<p class="noindent">This, most noble professors, is the language +of true patriotic loyalty. Let the +monarch be loved and loving, let the +laws be just and equal, happy will be the +people, prosperous the realm. There are +those who counsel different things, and +preach sedition and the breaking-up of +laws; but those who advocate such doctrines +lack that judicial mathematical +training which we, students and professors +of Girtham College, have acquired. If +polemical mathematics, the science of the +future, should become more widely studied; +if its results were disseminated far and +wide; above all, if the proper position +which women ought to occupy in the +counsels of the nation were assigned to +them, we should hear less of these wild +schemes and foolish theories, and the influence +of women would tend greatly to +<a name="png.071" id="png.071"></a><span class="ns">[</span><span + class="pgmark">59</span><span class="ns">] + </span>promote the stability and security of the +State.</p> + +<p>Why, let me ask, should woman be +excluded from that position which is so +justly hers? from those duties which she +can discharge so faithfully? It has been +said that if we wish to know the political +and moral condition of a State, we must +ask what rank women hold in it. We are +told that women have more strength in +their looks than men have in their laws. +Why, then, do men debar her from those +fields of occupation wherein she may +labour for the nation’s good, and use her +influence, which they acknowledge to be +great, in those callings wherein she may +most easily benefit the State, and the +country she so ardently loves?</p> + +<p>At some future time I hope to speak +more fully on this subject; and in concluding +this lecture, I will remark that +English politics need a leavening influence +which will counteract the evil tendencies +and corrupt theories which, in spite of our +advantageous social system, at present +<a name="png.072" id="png.072"></a><span class="ns">[</span><span + class="pgmark">60</span><span class="ns">] + </span>exist; and this leavening influence will be +best produced by the admission of those +into the counsels of the nation who are +acknowledged to have a benign and healthy +influence—the women of England. Let +women have their proper share in the +government of the country, and I have +no fear lest we shall preserve our elliptical +constitution, and all the advantages which +we at present enjoy.</p> + +<hr class="tb" /> + +<p>[<span class="smc">Editorial Note.</span>]—In the bundle of +papers which contained the foregoing +lectures, some letters of great interest +were found, which show that the fame +of the learned Lady Professor of Girtham +College had already gone abroad, and +attracted the attention of the leading +statesmen of the day. It is to be regretted +that the answers to these letters +are not forthcoming, as it might be proved +from them that the science of polemical +mathematics has already influenced the +minds of our legislators in their conduct +<a name="png.073" id="png.073"></a><span class="ns">[</span><span + class="pgmark">61</span><span class="ns">] + </span>of affairs at home and abroad. The +following letter is of unique interest, and +may be taken as evidence of the favourable +impression which this new science +has made on the mind of one of our +greatest thinkers and statesmen:</p> + +<p class="address"><small>Downing Street,</small></p> +<p class="date"><small>May, 18—</small></p> + +<p><span class="smc">My dear Lady Professor</span>,—The +report of the amazing results of your +scientific researches has reached me, and +I congratulate you most heartily on the +originality and acumen which you have +displayed in your investigations. A new +light has dawned upon our country. +Instead of groping in the darkness of +political warfare, ensnared by party ties +and jealousies, the statesmen of the future +will be able to calculate and determine the +correct course with mathematical precision +and perfect accuracy. No one can +dispute the truth of a proposition in +Euclid, or the genuineness of Newton’s +laws; and if your method enables men to +<a name="png.074" id="png.074"></a><span class="ns">[</span><span + class="pgmark">62</span><span class="ns">] + </span>calculate and determine the correct political +course of action, to solve political +problems as easily as exponential equations, +why—then adieu to the bickerings +of party, the querulous complaints of the +Opposition! Nay, joy to the Ministry! +There will be no Opposition! Our statesmen +will be able to guide the great ship of +the State by means of charts which know +no error; and they will resemble an +association of savants met together to +determine the exact moment of the +transit of Venus, or to examine the degree +of density of a comet’s tail.</p> + +<p>This condition of Parliamentary procedure +is much to be desired; you have +shown how such an ideal state of things +may be obtained. In the name of the +Government I thank you for your endeavours +on behalf of your country’s +welfare, and look forward to a further +development of your admirably conceived +system. As in the domain of ordinary +science there are complex questions +which defy the acumen of the philosopher; +<a name="png.075" id="png.075"></a><span class="ns">[</span><span + class="pgmark">63</span><span class="ns">] + </span>so in polemical science there may be +questions which present the same difficulties +and complications. But as the first +are daily yielding before the persevering +attacks of the mathematician, so I doubt +not polemical science will soon overcome +the various problems which may +arise.</p> + +<p>But it is mainly on my own account +that I venture to address you. I desire +to consult you with regard to certain +matters—political complications—which +have recently occupied the attention of +Her Majesty’s Ministers. By the help of +your new science, can you aid us in our +deliberations? Of course, I am writing +to you in <em>strict confidence</em>, and beg that you +will keep this communication profoundly +secret. I fear that would be a hard task +for many of your sex, who do not possess +your knowledge and powers of mind; +but I have great confidence in your discretion.</p> + +<p>These are the problems which are +presented to us for solution:</p> + +<p><a name="png.076" id="png.076"></a><span class="ns">[</span><span + class="pgmark">64</span><span class="ns">]<br + /></span>1. Some members of the Cabinet are +secretly in favour of Protection, and the +country is rather stirred by the question. +Can you, from your knowledge of the +contact of curves and nations, help us to +determine what course we ought to take +with regard to Spain, for example? Are +the principles of Adam Smith mathematically +correct?</p> + +<p>2. I observe that England is represented +mathematically by an ellipse. Are we +right in assuming that Ireland is a portion +of that ellipse? Or, on the other hand, +in our chart of nations, must we describe +that troublesome country as a rotating +parabola, or complex figure, altogether outside +our more favoured State?</p> + +<p>3. Do you consider, from your minute +observation of our social system, that the +form of our elliptical government is +gradually undergoing a change, and that +a revolutionary parabolic tendency is +observable in the action of individual +particles?</p> + +<p>4. Is it not possible that the differences +<a name="png.077" id="png.077"></a><span class="ns">[</span><span + class="pgmark">65</span><span class="ns">] + </span>in the policy of the various nations of +Europe; the difficulties which beset the +carrying out of international law; the +jealousies, quarrels, and rivalries of +States might disappear, if the same form +of government (<i>i.e.</i>, elliptical) were adopted +in each?</p> + +<p>If you will kindly favour Her Majesty’s +Ministers with your opinion on these +questions, they will owe you a debt of +gratitude, which they, as representatives of +the nation, will do their utmost to repay.</p> + +<p>With every good wish for your further +success in the regions of polemical science,</p> + +<p class="sig1">I beg to remain,</p> +<p class="sig2">My dear Lady Professor,</p> +<p class="sig3">Your faithful servant,</p> +<div class="cutout"> +<p class="cutbordertop"><img src="images/tuc.png" width="201" height="11" + alt="" title="" /></p> +<sup><a href="#fn.4" name="fna.4" id="fna.4">4</a></sup> +<p class="cutborderbot"><img src="images/cut.png" width="201" height="11" + alt="" title="" /></p> +</div> + +<p><ins class="TN" title="Transcriber's note: + original lacks closing bracket">[<span class="smc">Editorial Note.</span>]</ins>—The next letter +is not of quite the same pleasing nature +as the foregoing, and shows that it is +<a name="png.078" id="png.078"></a><span class="ns">[</span><span + class="pgmark">66</span><span class="ns">] + </span>impossible to please everyone, even if that +happy consummation were desirable. This +letter was evidently called forth by some +remarks which the learned Lady Professor +had made in her third lecture with reference +to eccentricity in dress. Our +readers will recollect that the professor +pointed out that an extravagant ‘bloomer’ +costume—half male, half female—was no +more a sign of genius than æsthetic +dresses, always betokened the artist.<sup><a href="#fn.5" name="fna.5" id="fna.5">5</a></sup> +This latter statement evidently gave great +offence to the members of a society +which called itself the ‘Æsthetic and +Dress Improvement Association,’ and +the following letter is the result of one of +their solemn conclaves:</p> + +<p class="address"><small>Oscar Villa, South Kensington,</small></p> +<p class="date"><small>June, 18—.</small></p> + +<p>The Secretary of the Æsthetic and +Dress Improvement Association presents +his compliments to the Lady Professor of +Girtham College, and begs to contradict +emphatically her statements with regard +<a name="png.079" id="png.079"></a><span class="ns">[</span><span + class="pgmark">67</span><span class="ns">] + </span>to a subject upon which she is evidently +in entire and lamentable ignorance, and +to protest against her aspersions upon +the artistic studies of this and kindred +societies. He begs to state that true +æsthetes are <em>not</em> eccentric (they leave that +to lady professors and her Philistine followers); +that to dress becomingly is one +of the principal objects of life, and that +true greatness is achieved as much by the +study of the art of dress as by any other +noble pursuit or graceful accomplishment. +Are not Horatio Postlethwaite, Leonara +Saffronia Gillan, Vandyke Smithson entitled +to greatness? And yet their laurels +have been won solely by the art of dress. +Perhaps the lady professor has never read +‘Sartor Resartus’! In conclusion, he +would ask the Lady Professor to refrain +from casting obloquy upon the work of +the Association which he has the honour +to represent; to prevail upon her pupils +to abandon the unfeminine attire which +some of them have assumed, contrary to +the first principles of art; to array themselves +in flowing robes of sage-green and +<a name="png.080" id="png.080"></a><span class="ns">[</span><span + class="pgmark">68</span><span class="ns">] + </span>other choice colours (patterns enclosed), +and to study art, instead of absurd mathematics, +which no one can understand, and +do no one any good.</p> + +<p class="hangsig"> +(Approved by the Committee of the +Æsthetic and Dress Improvement +Association.)</p> +<p class="hangsig"><small>June, 18—.</small></p> + + +<p class="above2"><ins class="TN" title="Transcriber's note: + original showed period outside bracket">[<span class="smc">Editorial Note.</span>]</ins>—The next letter, +written by a pupil of the Lady Professor, +requires no explanation, and speaks for +itself.</p> + + +<p class="address"><small>Jesus College, Cambridge,</small></p> +<p class="date"><small>March, 18—.</small></p> + +<p class="smc">My dear Tutor,</p> + +<p>You will be glad to hear that after +superhuman exertions I have at last succeeded +in passing my Little-go, and I am +eternally grateful to you for all you have +done for me. I should never have got +through if it had not been for you. All +the coaches in Cambridge would never +have managed it, but you drove me +through in a canter. And why? I never +could make up my mind to work for them; +<a name="png.081" id="png.081"></a><span class="ns">[</span><span + class="pgmark">69</span><span class="ns">] + </span>but when I coached with you, you made +me like it. I almost revelled in the +Binomial when you wrote it out for me; +and then I could not help listening to +you; and you looked so grieved when I +would not learn, and made me feel such +a brute; so somehow or other you drove +some mathematics into my head, and I +pulled through. By-the-bye, I think you +must have tried the ‘brain wave’ dodge +with the examiners, as five out of the six +propositions in Euclid, which you told me +to get up specially, were set! I wish I +could read people’s thoughts; can you read +mine? If I were a Don, or a Fellow, or +something, I would advise the University +to have some lady professors like you to +teach the men, instead of some of these +sleepy old tutors. It would be a great +improvement, and I am sure we should +get through a great deal more work.</p> + +<p>They have given me a place in the Jesus +Eight, which I shall take now that I am +released from your professorial ban, and +have time for rowing. But I don’t half +like giving up mathematics. You see, I +<a name="png.082" id="png.082"></a><span class="ns">[</span><span + class="pgmark">70</span><span class="ns">] + </span>have grown fond of the study. Do you +think you could make a wrangler of me? +At any rate, I should like to come to your +lectures again. May I?</p> + +<p class="sig2 smc">Your Grateful Pupil.</p> +<p class="sig3 anon">* * *</p> + + +<hr class="footnote" /> +<div class="footnote"> +<p><a href="#fna.4" name="fn.4" id="fn.4">4</a> It is to be regretted that this letter has evidently +fallen into the hands of some autograph +collector, who has ruthlessly cut off the signature; +but the reader will easily determine, after careful perusal +of the document, from whose pen it emanated.</p> + +<p><a href="#fna.5" name="fn.5" id="fn.5">5</a> Cf. page <a class="nopad" href="#png.048">36</a>.</p> +</div> + + + +<h2><a name="png.083" id="png.083"></a><span class="ns">[</span><span + class="pgmark">71</span><span class="ns">]<br + /></span>PAPER V.</h2> + +<h3>A LECTURE UPON SOCIAL FORCES, WITH +SOME ACCOUNT OF POLEMICAL KINEMATICS.</h3> + + +<p><span class="smc">Most noble Professors and Students +of Girtham College</span>,—Since last ‘I +wandered ’twixt the pole and heavenly +hinges, ’mongst encentricals, centres, concentricks, +circles, and epicycles,’ like the +great Albumazar, and found them full of +life and wisdom for the guidance of our +States and laws, I have turned my attention +to the Applied Mathematics, in order +to determine what other truths this shaft +may yield.</p> + +<p>The strength of all sciences, according +to Bacon, consists in their harmony; and +it is truly marvellous how perfect this +harmony is, if our ears are tuned aright to +hear it. We have observed how the +<a name="png.084" id="png.084"></a><span class="ns">[</span><span + class="pgmark">72</span><span class="ns">] + </span>beautiful and regular laws of curves and +cones correspond to the social laws of +States and nations, guiding them as if by +word of counsel, admonishing them on +what principle they ought to regulate +their governments and inter-relations. We +have seen that the laws which govern +thought and light and sound are almost +identical, and that harmony pervades not +merely the ordinary sciences, but extends +her benign influence over these newly +discovered fields of scientific research, +which I claim to have discovered.</p> + +<p>All this may appear at first sight surprising; +but the real philosopher, who +knows that all kinds of truth are intimately +connected, will receive such revelations +of science with satisfaction rather +than astonishment; for this new science, +which has opened itself out before me, is +only an extension of other well-known +laws and discoveries which have come +down to us from the remote past.</p> + +<p>If my investigations should appear to +you, most noble professors, somewhat novel +and imaginary, remember the maxim of +<a name="png.085" id="png.085"></a><span class="ns">[</span><span + class="pgmark">73</span><span class="ns">] + </span>the sage, that in the infancy of science +there is no speculation which does not +merit careful examination; and the most +remote and fanciful explanations of facts +have often been found the true ones. +Perhaps some ‘self-opinionated particle’ +(I speak mathematically) may have been +inclined to laugh at our theories and discoveries, +as the wise fools of the day +laughed at Kepler and his laws; but time +has changed the world’s laughter into +praise, and a century hence our discoveries +may rank among the achievements of +modern science. As Cicero says, ‘Time +obliterates the fictions of opinions, but +confirms the decisions of nature.’</p> + +<p>I have not shunned, most noble professors, +to enlist Imagination under the +banner of Geometry; for I am fully persuaded +that it is a powerful organ of +knowledge, and is as much needed by the +mathematician as by the poet or novelist. +It is, I fear, often banished with too much +haste from the fields of intellectual research +by those who take upon themselves +to give laws to philosophy. We need +<a name="png.086" id="png.086"></a><span class="ns">[</span><span + class="pgmark">74</span><span class="ns">] + </span>imagination to form an hypothesis; and +without hypotheses science would soon +become a lifeless and barren study, a +horse-in-the-mill affair ever strolling round +and round, unconscious of the grinding +corn. In my previous investigations my +imagination pictured the symmetry of +curves and States; the hypothesis followed +that the laws which regulated them were +identical, and you have observed how the +supposition was confirmed by our subsequent +calculations.</p> + +<p>In this lecture I propose to examine +some of the forces which exist in our +social system, and shall endeavour to +estimate them by methods of mathematical +procedure and analogical reasoning. +We will begin with the old definition +of Force as <em>that which puts matter into +motion, or which stops, or changes, a +motion once commenced</em>. When a mass +is in motion, it has a capacity for doing +work, which is called <em>Energy</em>; and when +this energy is caused by the motion of a +body it is called Kinetic Energy (in +mathematical language <span class="nw">KE = ½ MV²</span>). +<a name="png.087" id="png.087"></a><span class="ns">[</span><span + class="pgmark">75</span><span class="ns">] + </span>Another form of kinetic energy is called +Potential Energy, which is in reality the +capacity of a body for doing work <em>owing +to its position</em>. For example we may take +an ordinary eight-day clock. When the +weights are wound up, they have a certain +amount of potential energy stored up, +which will counteract the friction of the +wheels and the resistance of the air on +the pendulum. Or, again, we have the +example of a water-wheel: first the water +in the reservoir, being higher than the +wheel, has an amount of potential energy. +This is converted into kinetic energy in +striking against the paddles, and after this +we have potential energy again produced +by the action of the fly-wheel.</p> + +<p>By the principle of conservation of +energy, if we consider the whole universe, +not our planet alone (for its heat and +energy are continually diminished to some +slight degree), we find that <em>no energy is lost</em>.</p> + +<p>Force is recognised as acting in two +ways: in <em>Statics</em>, so as to compel rest, or +to prevent change of motion; and in +<em>Kinetics</em>, so as to produce or to change +<a name="png.088" id="png.088"></a><span class="ns">[</span><span + class="pgmark">76</span><span class="ns">] + </span>motion; and the whole science which investigates +the action of force is called +<em>Dynamics</em>.</p> + +<p>All this is of course pure mathematics, +and I have made these elementary observations +for the benefit of my younger +hearers, the students of this University. +My grave and reverend seniors will pardon, +I am sure, the repetition of facts well +known to them for the sake of those who +are less informed than themselves.</p> + +<p>Now before I proceed further, I will +endeavour to point out that these elementary +truths of physical science hold good +in our social system. Each individual is +a mass, acted on by numerous forces, +capable of ‘doing work,’ which work can +be measured and his velocity calculated. +Some individuals have a vast <em>potential +energy</em>; that is to say, from their position +and station in the social system, they have +a power which is capable of producing +work which a less exalted individual has +not. Like the weights in an eight-day +clock, or the water in a reservoir, they +have a capacity for doing work, owing to +<a name="png.089" id="png.089"></a><span class="ns">[</span><span + class="pgmark">77</span><span class="ns">] + </span>the position to which they have been +raised. How vast the influence of a +Primate or a Premier, a General or a +King! And yet their power is chiefly +potential energy, arising from the position +they occupy, not from the individuals +themselves. Schiller has described this in +poetical language, which, strange to say, is +mathematically correct:</p> + +<div class="stanza"> +<div>‘Yes, there’s a patent of nobility</div> +<div class="indent">Above the meanness of our common state;</div> +<div>With what they <em>do</em> the vulgar natures buy</div> +<div class="indent">Their titles; and with what they <em>are</em>, the <em>great</em>.’</div> +</div> + +<p>Other forces may have raised these men +to their exalted positions; but their influence +is due to their height, their potential +energy. Placed on a lower level, they +would cease to have that power. How +calm the dignity of this potential rank! +The water in the reservoir is scarcely +ruffled or disturbed, as if unconscious of +its power; when it has lost its force it +rushes along with a sullen murmur and a +roar, howling and hissing and boiling in +endless torture, until—</p> + +<div class="stanza"> +<div>‘It gains a safer bed, and steals at last</div> +<div>Along the mazes of the quiet vale.’</div> +</div> + +<p><a name="png.090" id="png.090"></a><span class="ns">[</span><span + class="pgmark">78</span><span class="ns">]<br + /></span>So the vulgar crowd rushes on, with +plenty of kinetic force, making noise +enough and looking very busy; while +those who seem to sleep in calm forgetfulness, +exercise their potential energy, and +do the real work of turning the great +engine of the State.</p> + +<p>There are attractive and repulsive forces +(more commonly the latter, the cynic will +say) in our social system, but each individual +is the centre of various forces acting +upon him. In nature all matter possesses +the force of gravity, and whatever the +size of two particles may be, they mutually +attract each other. The earth attracts the +moon; the moon attracts the earth. A +stone thrown up into the air exercises an +infinitesimal force upon the earth; so in +the social system every individual, however +small and insignificant he may be, +exercises some attractive force upon his +neighbour. There is no one in the world +who does not exercise some influence for +good or for evil upon his fellows.</p> + +<p>The force of <em>cohesion</em> is manifest in +society as in nature, that force, I mean, +<a name="png.091" id="png.091"></a><span class="ns">[</span><span + class="pgmark">79</span><span class="ns">] + </span>which resists the separation of a body’s +particles. Different bodies possess different +powers of cohesion, <i>e.g.</i>, the cohesion +of chalk is far less than that of flint embedded +in it; even the same body possesses +different powers of cohesion in different +directions, <i>e.g.</i>, it is easier to split wood in +the direction of the fibres than perpendicular +to them. If by our old principle +of continuity we change the words ‘bodies’ +into ‘States’ or ‘individuals,’ we shall see +that the same laws hold good in social +science as in natural philosophy.</p> + +<p>These are a few analogous laws which I +have taken almost at random; but it must +strike the most casual listener to my +remarks that it is wondrous strange that +men, regarded as social beings, should +possess the same qualities, and be governed +by the same laws, as the rest of <em>matter</em>. As +Bishop Butler says, ‘the force of analogy +consists in the frequency of the supposed +analogous facts, and the real resemblance +of the things compared.’ It appeals to +the reasoning faculty, and may form a solid +argument. Hence, if we can prove the +<a name="png.092" id="png.092"></a><span class="ns">[</span><span + class="pgmark">80</span><span class="ns">] + </span>similarity of various laws and conditions, we +may not be wrong in assuming by analogy +the identity of those laws and conditions.</p> + +<p>I have stated my case in this manner in +order to convince the gainsayers, if any +such there be, and to banish any doubts +or questionings which may have arisen +in your minds. I will now proceed with +some further investigations, full of the +most profound interest and importance.</p> + +<p>Doubtless many of the lady-students +present are in the habit of welcoming +peaceful evening in with a potent draught +of ‘the cup which cheers but not +inebriates;’ and as men are great +flatterers (for imitation is the greatest +flattery), I believe the male portion of my +audience have been known to follow that +excellent example. Some perhaps are in +the habit of burning the midnight oil, and +keep their eyes open by means of this +fruit of the hermit’s pious zeal, endowed +by high omnipotence with the power of +hindering sleep;<sup><a href="#fn.6" name="fna.6" id="fna.6">6</a></sup> but that practice I do +<a name="png.093" id="png.093"></a><span class="ns">[</span><span + class="pgmark">81</span><span class="ns">] + </span>not advise, as that delicate portion of our +system, the nerves, especially of women, +often becomes injured by such stimulating +doses. However, you will have observed +(if you do not follow the modern pernicious +fashion of taking tea without sugar) +that numerous bubbles are formed upon +the surface of the liquid. After a few +moments these unite into one central +mass of bubbles by the force of mutual +attraction.</p> + +<p>It appears from considerations which +are detailed in works on physical astronomy, +that two particles of matter placed at +any sensible distance apart attract each other +with a force directly proportional to the product +of their masses, and inversely proportional +to the square of their distance.</p> + +<p>Now, suppose that we have a number +of circular masses situated upon a plane +<a name="png.094" id="png.094"></a><span class="ns">[</span><span + class="pgmark">82</span><span class="ns">] + </span>surface, they will attract each other with a +force which may be determined with +exactitude; and the greater the masses +the greater the force. We will now apply +this to polemical science. The agricultural +settlement is the first stage in the +civilization and formation of a State. +How did this arise? First, a single family +immigrated to some uncultivated parts +of the country, perhaps accompanied by +others, who formed a little colony. Other +settlements were made in other parts of +the land; and thus the country became +overspread with these detached and separate +communities. An eminent writer +declares that these settlements can be +traced in the beginnings of every race +which has made progress; that they were +characteristic of those races in Greece and +Italy, in Asia and Africa, which grew into +the opulent and famous cities in which so +much in the early history of civilization +was developed. The colonies of England +have been formed in the same way, just +as in olden time England itself was occupied +when the Roman power ceased.</p> + +<p><a name="png.095" id="png.095"></a><span class="ns">[</span><span + class="pgmark">83</span><span class="ns">]<br + /></span>These settlements correspond to the +circular masses situated on the plane +surface; they were quite separate from +each other, each having its own laws, its +own headman or ruler, its own assembly +or parish council. But as time elapsed, +the force of mutual attraction set in; +by degrees these separate settlements +were drawn together by force which increased +in proportion as the settlements +increased; until at last one united kingdom +was formed under one king, governed +by uniform laws and regulations. The +bubbles have blended, the circles have +come together, and one large circle or +other curve is the result. This may be +called the <em>Law of Social Attraction</em>. In +accordance with the results of one of my +previous lectures, I have taken the circle +as representing the simplest form of +government, which figure, in the case of +the elementary settlements, must have +been small.</p> + +<p>Many of you, most noble professors, +are doubtless accustomed to make experiments +with the microscope. I will +<a name="png.096" id="png.096"></a><span class="ns">[</span><span + class="pgmark">84</span><span class="ns">] + </span>suggest a simple one, which illustrates +very forcibly what I am endeavouring to +show you. Take some particles of copper, +and scatter them at intervals over the +surface of an object-glass, and pour some +sulphuric acid upon the glass. Now, what +is the result? A beautiful network of +apparently golden texture spreads itself +gradually over the whole area of the +glass. Steadily it pursues its way, and +the result is beautiful to behold. The +minute particles of copper were the original +settlements scattered over the land; +the sulphuric acid the civilizing agent; +and the final picture of a united civilized +homogeneous nation is well represented +by the progressive and finally glorious +network of gold. This example is of +course outside our present subject, but it +serves as a beautiful illustration.</p> + +<p>As an instance of the attractive force +exercised by small communities upon each +other, I may mention the united kingdom +of Germany, which is composed of numerous +small States and nations, which have +been drawn together by the power of +<a name="png.097" id="png.097"></a><span class="ns">[</span><span + class="pgmark">85</span><span class="ns">] + </span>mutual attraction. Until recently they +were each self-contained, separate constitutions, +with their own kings and forms of +government; but the attracting force, +assisted by forces from without, has +proved too much for them, and the great +and powerful united kingdom of Germany +is the result.</p> + +<p>But why, you may ask, have not the +people in Hindustan united in the same +way? There the agricultural settlements +remain as they did ages ago; separate +petty chieftains rule under the all-governing +power of England. Why have they +not united?</p> + +<p>To this objection I reply that there is +in social science, as in Nature, a <i>vis inertia</i>; +that is to say, there is a tendency in +matter to remain at rest if unmoved by +any external agency, and also of persisting +to move, after it has once been set in +motion. The <i>vis <ins class="TN" title="Transcriber's note: + original reads 'inetiar'">inertia</ins></i> of some bodies +is greater than that of others, and depends +upon their weight and density. Now it +so happens that the moral <i>vis inertia</i> of +the Hindustani is very great, hence their +<a name="png.098" id="png.098"></a><span class="ns">[</span><span + class="pgmark">86</span><span class="ns">] + </span>tendency to amalgamation is small. They +remain in the state in which they happen +to be.</p> + +<p>On the other hand the inertia of Englishmen +is small, of Englishwomen smaller, +and therefore their power of combining +is greater. Here let me observe that the +quality of inertia is one which ought to be +removed as far as possible from each +social system. Inertia was regarded as a +capital crime by the Egyptians. Solon +ordained that inert persons should be put +to death, and not contaminate the community. +As savages bury living men, so +does inertia practise the same barbarous +custom upon States and individuals. +Observe the putrid state of inert water, +the clear and sparkling beauty of the +moving stream, bearing away by the force +of its own motion aught that might contaminate +it. Men more often resemble +the stagnant water than the rivulet. A +healthy social state enforces labour by +natural laws, and banishes inertia as much +as possible from the system. If the +principles of some noisy English +<a name="png.099" id="png.099"></a><span class="ns">[</span><span + class="pgmark">87</span><span class="ns">] + </span>politicians were fully carried out, and all +things made ‘<em>free</em>,’ inertia would be increased, +and listless indolence pervade the +masses of our countrymen. I may say +that inertia is not entirely unknown in our +sister University of Cambridge.</p> + +<p>The existence of social forces is supported +by the testimony of Dr. Tyndall, +who plainly recognises their power, though +he does not attempt to expound their +origin. ‘Thoughtful minds are driven to +seek, in the interaction of social forces, +the genesis and development of man’s +moral nature. If they succeed in their +search—and I think they are sure to +succeed—social duty would be raised to +a higher level of significance, and the +deepening sense of social duty would, it +is to be hoped, lessen, if not obliterate, +the strife and heart-burnings which now +beset and disguise our social life.’ I +accept with gratification Dr. Tyndall’s +conclusions: to determine, examine, trace, +calculate these social forces which exercise +such a powerful influence on our characters, +our lives, our customs, which produce the +<a name="png.100" id="png.100"></a><span class="ns">[</span><span + class="pgmark">88</span><span class="ns">] + </span>greatness of the State, or drag it down +with irresistible strength from its pinnacle +of glory to an abyss of degradation; to +estimate such forces is the great and noble +object of our lectures and researches in +this University. Prosecute, most noble +professors, your studies in this direction +with all the energy of your enlightened +intellects, and there is yet hope that this +new science, which I have endeavoured to +sketch out, however feebly, may be the +means of saving our beloved nation from +degradation and ruin, and raising her to +a higher level of glory and honour. I +hope to continue the subject of social +forces in my next lecture.</p> + + +<hr class="footnote" /> +<div class="footnote"> +<p><a href="#fna.6" name="fn.6" id="fn.6">6</a> A Chinese legend relates that a pious hermit, +who in his watchings and prayers had often been +overtaken by sleep, so that his eyelids closed, in +holy wrath against the weakness of the flesh, cut +them off, and threw them on the ground. But a +god caused a tea-shrub to spring out of them, the +leaves of which exhibit the form of an eyelid bordered +with lashes, and possess the gift of hindering +sleep.—Dr. <span class="smc">Ure</span>.</p> +</div> + + + + +<h2><a name="png.101" id="png.101"></a><span class="ns">[</span><span + class="pgmark">89</span><span class="ns">]<br + /></span>PAPER VI.</h2> + +<h3>ON SOCIAL FORCES (<i>continued</i>)—POLEMICAL +STATICS AND DYNAMICS.</h3> + + +<p class="noindent"><span class="smc">Most Noble Professors and Students +of Girtham</span>,—We have embarked upon a +stormy sea of speculation, on a voyage of +grand discovery, and the dangerous waves +of adverse criticism, and the deceptive +under-current of prejudice, often make the +steersman’s lot by no means an enviable +one. But our vessel is sound and perfectly +equipped, and therefore I do not fear to +guide her across the great unknown.</p> + +<p>It may have occurred to you that the +problems which present themselves for +solution in social science are far more +difficult and complicated than those which +arise in ordinary mathematics. That is +undoubtedly the case; but this extra +degree of difficulty is due to the fact that +<a name="png.102" id="png.102"></a><span class="ns">[</span><span + class="pgmark">90</span><span class="ns">] + </span>we make no assumptions; we take the +things as they really are, not as they are +assumed to be. In physical science, if +we take into consideration the resistance +of the air, the curvature of the earth, the +rigid connection which exists between +particles in the same body, and a host of +other things which are often conveniently +neglected in elementary works, how complicated +the various problems become! +So we must not be surprised at some of +the difficulties which occur in social +science, as nothing is neglected; the whole +problem is before us, and having solved it +we need not make allowances for any +falsely assumed <i>data</i>.</p> + +<p>It is possible that other professors of +this science may come to slightly different +conclusions to those which I have arrived +at. That is only to be expected, because +their original observations may have +slightly varied. But in physical science +allowances are made for different observers. +In astronomy, for example, we find the +value of the ‘Personal Equation.’ One +observer on looking through the telescope +<a name="png.103" id="png.103"></a><span class="ns">[</span><span + class="pgmark">91</span><span class="ns">] + </span>may take the meridian of a star rather +differently from another watcher of the +heavenly bodies, and the <em>personal equation</em> +is used to make allowances for this +quickness, or slowness, of observation. +So in social science there must be a +personal equation too, and our object +ought to be, in the ordinary affairs of life +as well as in the higher duties of scientific +action, to make our personal equation as +small as possible. But until the old +proverb, ‘<i>Quot homines, tot sententiæ</i>,’ has +ceased to have any meaning, there will be +abundant need of this most useful aid to +accuracy.</p> + +<p>The close connection which exists between +social forces and material forces is +plainly shown by the doctrine of the conservation +of energy. ‘This doctrine,’ says +Dr. Tyndall, ‘recognises in the material +universe a constant sum of power made +up of items among which the most Protean +fluctuations are incessantly going on. It +is as if the body of nature were alive, the +thrill and interchange of its energies resembling +those of an organism. The +<a name="png.104" id="png.104"></a><span class="ns">[</span><span + class="pgmark">92</span><span class="ns">] + </span>parts of the stupendous whole shift and +change, augment and diminish, appear and +disappear; while the total of which they +are the parts remains quantitatively immutable, +<em>plus</em> accompanies <em>minus</em>, gain +accompanies loss, no item varying in the +slightest degree without an absolutely +equal change of some other item in the +opposite direction.’ So do the forces in +the social world ebb and flow, rise and +fall, carrying on the same universal law +which regulates the energy of material +force.</p> + +<p>I will now proceed to enumerate some +of those forces which exercise such a +powerful influence on society.</p> + +<p>First, let us take the force of <em>Public +Opinion</em>, which seems to exercise a relentless +sway over the minds and manners of +men. This is a very subtle and secret +force, which is most difficult to trace, and +resembles electricity in the science of +physics. We cannot see it, but are only +able to judge of its power by its results. +Its point of application is not in the individual, +but in the collection of individuals +<a name="png.105" id="png.105"></a><span class="ns">[</span><span + class="pgmark">93</span><span class="ns">] + </span>who make up the social system; and it is, +in reality, the resultant of, or the compromise +between, the various elementary +forces which make up human society. +Yes, compromise is a purely mechanical +affair, based on the principle of the parallelogram +of forces; and as public opinion +is the result of a compromise, we may +calculate its force. For example: ‘It is +required to know the state of public +opinion in the matter of politics, when +the results of a General Election show +that the Conservatives are to the Liberals +as <span class="nw">10 : 9</span>.’</p> + +<p>Let OC be the direction of the Conservative +force.</p> + +<p>Let OL be that of the Liberal.</p> + +<p>Then by <i>data</i> <span class="nw">OC : OL :: 10 : 9</span>.</p> + +<p class="ctr"><img src="images/illus-105.png" width="270" height="110" + alt="Diagram: parallelogram with leading diagonal" title="" /></p> + +<p>Complete the parallelogram, and join +OP.</p> + +<p><a name="png.106" id="png.106"></a><span class="ns">[</span><span + class="pgmark">94</span><span class="ns">]<br + /></span>Then OP represents the force of public +opinion in magnitude and direction.</p> + +<p>N.B.—The direction of OL is determined +by the amount of deviation of the +policy of the Liberals from that of the +Conservatives.</p> + +<p>As in physical, so in social science, +impulsive forces sometimes act, and effectually +disturb our system and our calculations. +Public opinion is very liable to +the action of disturbing forces. Panic is +an impulsive force, which defies the power +of the most learned professors of social +science to determine its magnitude and +direction. Some strange unforeseen catastrophe—the +fascination caused by a brilliant +and unscrupulous orator, a cruel wrong, a +blind revenge for real or imaginary injustice—will +sometimes rouse one element of +passion latent in the vast body of public +opinion; so that it breaks with all that +hitherto restrained and balanced it, and +precipitates society into a course of conduct +inconsistent with its former behaviour, +and bloodshed, revolution, the breaking-up +of laws, are the terrible results of panic +or revengeful passion.</p> + +<p><a name="png.107" id="png.107"></a><span class="ns">[</span><span + class="pgmark">95</span><span class="ns">]<br + /></span>Society is, as it were, split up by the +terrible action of such impulsive forces, +just as wood is split up by the repeated +blows of the hatchet. It is, therefore, the +duty of statesmen to increase the power +or force of cohesion, to strengthen the +fibres of the State, so that the force of +such impulsive blows may not be felt, nor +disturb the continuity of the framework +of the State. If such measures had been +adopted in the neighbouring country of +France, much misery might have been +avoided, and the terrible revolutions which +have so frequently convulsed her social +system entirely prevented.</p> + +<p><em>Friction</em> is another disturbing element +in our calculations, and although it may +be made a useful servant, it is a bad +master in mathematics, as in polemics. +Without the aid of friction, progress would +be impossible. For example: Take the +case of a man with perfectly smooth skates +on perfectly hard, smooth ice; he would +be unable to reach the land unless he had +provided himself with some stones, by +throwing which he would just be able to +<a name="png.108" id="png.108"></a><span class="ns">[</span><span + class="pgmark">96</span><span class="ns">] + </span>get to his destination by a backward +motion. The engine would be unable to +proceed on its iron road if it were not for +friction. The same is true in polemical +science: the government of the country +would not be able to be carried on under +our present conditions if it were not for <em>party +friction</em>. But suppose it increased indefinitely, +party friction becomes party <em>obstruction</em>; +and the engine of the State would no +longer proceed smoothly and evenly along +its appointed course at the rate of sixty +miles an hour, but would resemble an old-fashioned +coach, up to its axle-trees in +mud, its motion altogether stopped by the +action of party friction.</p> + +<p>We have seen that forces have two ways +of acting: that of compelling rest and +that of producing motion. In statics +forces act so as to prevent any change +of motion, or disturb the body’s original +position. In kinetics, on the contrary, +the power is recognised as acting so as +to produce or change a body’s motion. +Now, in polemical science we have these +two ways of considering the action of +<a name="png.109" id="png.109"></a><span class="ns">[</span><span + class="pgmark">97</span><span class="ns">] + </span>forces. There is the <em>statical</em> or <em>conservative</em> +force, which compels rest, which seeks +security, stability, and peace, and is not +ardently devoted to change. It reduces +the system to equilibrium. There are, of +course, two kinds of equilibrium—<em>stable</em> +and <em>unstable</em>—according as the social +and political system is in a healthy or +unhealthy state. If a body is in stable +equilibrium, and any slight motion takes +place, the body will return immediately to +its former position; but if in unstable, it +will decline further and further away from +its original position, and be entirely upset. +So a healthy and sound conservative equilibrium +is not disturbed by outside forces, +and the State will resume its former +position of stability and rest when the +opposing force is withdrawn. But an unhealthy +and insecure conservatism is as +easily disturbed as an egg balanced on its +narrow end.</p> + +<p>The kinetics of society, that is to say +the Radical way of estimating force, is +the party of motion, generally supposed +to be the ‘party of progress.’ It has +<a name="png.110" id="png.110"></a><span class="ns">[</span><span + class="pgmark">98</span><span class="ns">] + </span>therefore many attractions in the eyes +of those who delight in motion, speed, +and rushing about. To run at full speed, +to feel the keen air upon one’s face, to +experience the delightful sensation of +freedom of will, and limb, are joys which +cannot be denied. Such exercise is beneficial +to the system, bodily or political. +Motion is the life of all things; it is +characteristic of nature; it adores nature; +because it is an emblem and characteristic +of life. The ceaseless rolling of the ocean +waves, the swaying of the trees, the bending +of the flowers, the waving of the corn, +all these fill us with pleasure; whereas a +flat uninteresting plain, unrelieved by the +motion of terrestrial objects, is depressing +to the spirit. So there is much to be said +in favour of motion, and Carlyle has +defined progress as ‘living movement.’ +And men love this ‘living movement,’ and +take up the Laureate’s cry:</p> + +<div class="stanza"> +<div class="indent6">‘Forward, forward, let us range,</div> +<div>Let the great world spin for ever down the ringing</div> +<div class="indent6">Grooves of change.’</div> +</div> + +<p class="noindent">But, after all, there is a danger in this +<a name="png.111" id="png.111"></a><span class="ns">[</span><span + class="pgmark">99</span><span class="ns">] + </span>everlasting motion. We cannot tell +whither this progress may lead. It may +be along a safe sure road; but perchance +a precipice may open out before us; and +rejoicing in the acceleration of our +velocity, with eyes intent upon some +distant heights of glory and ambition, we +may not discover our danger until it is too +late to stop, and a terrible plunge into an +unknown abyss of turmoil and tumultuous +waves is the alarming result of an unguarded +policy of unrestrained ‘progress.’ I recall +to my mind the quaint words of Holmes +which aptly illustrate my contention.</p> + +<div class="stanza"> +<div>‘If the wild filly, “Progress”, thou would’st ride,</div> +<div>Have young companions ever at thy side;</div> +<div>But wouldst thou stride the staunch old mare, “Success,”</div> +<div>Go with thine elders, though they please thee less.’</div> +</div> + +<p>Progress and success do not always go +together hand in hand; and while motion +is essential to life, it is not always safe to +urge a country forward at too great a +speed; and security and stability are quite +as important to the nation’s life as actual +progress.</p> + +<p>There are other impulsive forces which +<a name="png.112" id="png.112"></a><span class="ns">[</span><span + class="pgmark">100</span><span class="ns">] + </span>act occasionally in the sphere of politics, +and which baffle all our calculations, and +exclude scientific considerations of the +polemical problems which arise. <em>Ambition</em> +is such an impulsive force, and when the +rulers of the people are actuated by it, +and struggle for money, place, and power, +politics is degraded from its position as a +science, and it becomes impossible to +estimate the result of forces so generated.</p> + +<p class="pgbrk">In my next lecture I propose to treat +the important subject of the Laws which +govern States and Governments, and +which regulate, generate, and control the +social forces which we have seen at work +in the body politic.</p> + + + + + +<h2><a name="png.113" id="png.113"></a><span class="ns">[</span><span + class="pgmark">101</span><span class="ns">]<br + /></span>PAPER VII.</h2> + +<h3>LAWS OF POLITICAL MOTION.</h3> + + +<p class="noindent"><span class="smc">Since</span> the last time I had the honour of +addressing you on polemical matters, I +have met with a passage in the writings of +M. Auguste Comte which afforded me +much pleasure. It seemed to be the one +word for which I had been waiting, and +confirmed many of my own impressions +and speculations. He lays down two +propositions: first, that the constructive +politics of the future must be based on the +history of the past; and second, that +political science is a composite study, and +presupposes the complete apprehension of +every branch of science, beginning with +the physical, such as astronomy, and +ending with the moral, such as ethics and +sociology. M. Comte evidently does not +regard as a vain dream and imaginative +<a name="png.114" id="png.114"></a><span class="ns">[</span><span + class="pgmark">102</span><span class="ns">] + </span>speculation the theory that it will be +possible for statesmen to calculate a +policy, and to determine a course of +action by purely scientific considerations. +May I entertain the hope that in this +university, where all branches of physical +science have found a home, and are +studied by most able and learned professors, +the science of politics may be +pursued under most favourable circumstances? +I trust that each professor will +bring before me the results of their +deliberations, and contribute to the growth +of this particular science for which our +university has already become deservedly +famous.</p> + +<p>My present lecture is devoted to the +important consideration of <em>Law</em>. At first +sight it may appear to you that the wills +and passions of mankind are so diverse +and unknowable, that it would be absurd +to suppose that they can be calculated, or +rendered amenable to any law. But Professor +Amos has pointed out that in proportion +as we examine history, and compare +the actions present and past of different +<a name="png.115" id="png.115"></a><span class="ns">[</span><span + class="pgmark">103</span><span class="ns">] + </span>nations and states, the more uniform does +human nature appear; the more calculable +the actions, sentiments, and emotions of +large masses of people. As we have +already stated, the difficulties of the study +are not likely to deter the professors of +Girtham College from the pursuit of any +particular branch of science.</p> + +<p><i>A priori</i> we might suppose from analogy +that these polemical laws existed, as there +is no department of nature which is not +governed by law. It is an essential feature +in nature, and also in government. +What is political economy but the study +of certain laws of nature? These were +first discovered by Adam Smith, and have +since been traced and estimated by such +men as Ricardo, the two Mills, Professor +Cairnes, Jevons, and many others. Moreover, +our physical constitutions are +governed by laws, which physicians have +determined, and which it is perilous to +resist. Our moral constitution is also +governed by laws, which evidently exist, +although it is difficult to find them out. +But the nation is only an assemblage of +<a name="png.116" id="png.116"></a><span class="ns">[</span><span + class="pgmark">104</span><span class="ns">] + </span>individuals; and since individuals are +so governed, it is only natural to suppose +that the nation, composed of individuals, +is so constituted and controlled. And +not only is that true, but we shall see +that polemical laws are as permanent and +universal, as invariable and irreversible, +as the laws of nature which regulate the +courses of the heavenly bodies, and raise +the tides, or depress the sandstone hills.</p> + +<p>We may notice first the preponderant +impulse observable in a nation’s life in +favour of supporting existing facts and +institutions; and every reformer has +discovered the difficulty and danger of +changing or opposing the customs and +habits of the people. As a wheel will +travel most smoothly along a well-worn +groove, whereby friction is diminished, so +there is a natural national tendency always +to run along those paths with which the +habits and customs of the people have +made them familiar. This law is nothing +else than Newton’s first law of motion, +which is quite as applicable to human +masses as to lifeless matter. The +<a name="png.117" id="png.117"></a><span class="ns">[</span><span + class="pgmark">105</span><span class="ns">] + </span>tendency of matter to remain at rest, if unmoved +by any external agency, and of +persisting to move after it has once been +set in motion, is a conservative tendency; +and is as true in political science as in +any other.</p> + +<p>The special branch of our science, +which we may call the <em>Biology of Politics</em>, +shows how absolute is the domain of law +in polemical matters. The law of human +life is that men are born, grow, become +strong and vigorous, and then decay and +die. This is the law of life, to which +we must all yield an enforced obedience. +This same law is observed to be at work +in the heavenly bodies; and astronomy +shows us that planets are born, flourish, +and at length die, just as our human +bodies do. The moon is, as you may +have observed, a dead planet, such as our +earth may be some day. The same +growth and decay are also manifest in +national life. First, there is the birth of +the nation, which sometimes lies a long +time in a dormant state, and then wakes +up to life and energy. China and Russia +<a name="png.118" id="png.118"></a><span class="ns">[</span><span + class="pgmark">106</span><span class="ns">] + </span>are examples of dormant States, just +waking from a long sleep of childishness +and ignorance. The next stage is the +strong an healthy period of its existence, +which England is at present enjoying; +and then, after various stages of gradual +decline, we come to the senile period of +national life, when every energy and +faculty, every national feeling and power +of invention, are completely exhausted. +As an example of this depressing condition, +we may mention Turkey and several +of the effete States of South America. +Sometimes, when life is nearly extinct in +the human body, physicians have made +use of the power of galvanism, in order to +revive the dying energies. This process +of galvanizing a State into life was tried +by Lord Palmerston and others on the +worn-out frame of Turkey. But such +attempts can only meet with partial and +transitory success; and where the loss of +national power and faculty betokens the +senile period of the nation’s existence, it +is vain to attempt to restore its former +life and energy. The study of the biology +<a name="png.119" id="png.119"></a><span class="ns">[</span><span + class="pgmark">107</span><span class="ns">] + </span>of politics presents many interesting and +important details in this special branch +of knowledge; and I commend this part +of our subject to the special attention of +the professor of physiology. The law of +development is observable in nations as +in nature. Recent scientific discoveries +have tended to take away all ideas of +<em>chance</em> in the workings of nature, and have +substituted <em>law</em> instead of it. It would +be unscientific and incorrect to speak of +the world being formed by the ‘fortuitous +concourse of atoms.’ So we cannot speak +of a State being generated in this manner. +Laws—economical, geographical, natural—preside +over the formation of States and +nations, and produce their further development.</p> + +<p>The laws of political motion occupy +the same prominent place in our new +science as Newton’s laws do in ordinary +dynamics. These are very important in +calculating the positions which various +States will occupy in the future. First, +we have the <em>doctrine of nationality</em>, which +prevented the progress of Austria into +<a name="png.120" id="png.120"></a><span class="ns">[</span><span + class="pgmark">108</span><span class="ns">] + </span>Italy, and of the Bourbons in Naples, and +produced the amalgamation of the small +German States in the great empire of +Germany. The second law of political +motion is the doctrine of the <em>independence</em> +of all true States, and the equality +of all States to each other. This had its +growth in feudalism; and all the chief +wars of modern times have been the result +of the efforts of nature to establish this +law of independence. The doctrine of +intervention is a modification of the preceding +law, and is applicable when the +law of necessity demands its use, such as +the restoration of order after protracted +anarchy, the abolition of slave trade, etc. +The third law is the <em>law of morality</em>. +Just as for each man there exists a <em>right</em> +and a <em>wrong</em>; just as <em>duty</em> and <em>conscience</em> +are certain elements in his daily motion, +which dictate his course of action, +although he may chose to neglect them; +so a nation is bound by the same moral +laws which govern the individual; and +a nation errs if it transgresses them. +Christianity is the agent which has +<a name="png.121" id="png.121"></a><span class="ns">[</span><span + class="pgmark">109</span><span class="ns">] + </span>produced so powerful an influence in making +men obey the dictates of conscience and +walk in the path of duty; and I read +with thankfulness the conclusion of Mr. +Amos, that Christianity has triumphed +quite as much in moralizing secular +politics as it has in the sphere of individual +life.</p> + +<hr class="tb" /> + +<p>These are some of the principal laws of +motion which I have observed at work in +various States and nations. Inasmuch as +political science embraces, in addition to +the physical sciences, all those branches +which are contained in ethics, economics, +jurisprudence, sociology and others, the +laws of each are generally applicable to the +whole grand subject of which my lectures +treat. Other general laws may be deduced, +and have been enumerated in my previous +lectures, from the social properties of curves +and conics; and when our researches are +complete we may hope to produce a code +of laws for the guidance of our statesmen +which maybe of immense use in determining +<a name="png.122" id="png.122"></a><span class="ns">[</span><span + class="pgmark">110</span><span class="ns">] + </span>the policies of the future. Already +there is strong evidence that the affairs of +this country are being conducted on sound +scientific principles, rather than by any +species of guess-work or haphazard contrivances. +The use of history is recognised +as extremely important in determining +a future line of conduct; and statesmen +are in the habit of endeavouring to find +from their study of the past what is the +logical sequence of events. Just as mathematicians +endeavour to determine the law +of a series of figures, and having found the +law, can write down the next, and the next, +<i>ad infinitum</i>; so scientific politicians may +be able soon to establish the various laws +of a series of events, and calculate their +course of actions. That there is considerable +progress in this direction is manifest +by the value which they place upon statistics, +and their continued use of this important +information.</p> + +<p>There are a few great evils in our present +system which are strongly opposed to any +scientific methods in politics; and in the +interests of the country as well as those of +<a name="png.123" id="png.123"></a><span class="ns">[</span><span + class="pgmark">111</span><span class="ns">] + </span>science they ought to be removed. One +great evil is the want of political and +scientific knowledge on the part of the +electors, who are in the habit of choosing +their representatives on personal grounds, +or party considerations, rather than on +sound principles of political science. All +this is opposed to any idea of law. Owing +to the ignorance of the electors they fall an +easy prey to adventurers and unprincipled +politicians, who make all kinds of specious +promises, tempt them with all manner of +baits, and make self-interest instead of the +welfare of the State the principle of voting. +Selfishness is the ruin of social life and intercourse, +the destroyer of all happiness, +peace, and mutual trust in family life or in +society. It is the root of most of the faults, +vices, and crimes in the individual; and +who can tell the endless disasters which +will befall the State, where selfishness is the +chief motive-power of the electors and the +elected? A selfish statesman, one who goes +into Parliament to gain his own ends and +forward his own personal interests, is a disgrace +to society—</p> + +<div class="stanza"> +<div><a name="png.124" id="png.124"></a><span class="ns">[</span><span + class="pgmark">112</span><span class="ns">]<br + /></span>‘Feeling himself, his own low self, the whole,</div> +<div>When he by sacred sympathy might make</div> +<div>The whole one self. Self, that no alien knows!</div> +<div>Self, far diffused as fancy’s wing can travel!</div> +<div>Self, spreading still, oblivious of its own,</div> +<div>Yet all of all possessing!’</div> +</div> + +<p>I have said that the ignorance of the +electorate makes them an easy prey to such +men; and until they have learnt to detect +the false from the true, until they become +acquainted with the elements of political +science, and have been taught that their +own selfish interests are not the highest +aims of social government, it is vain to +hope for a reasonable method of regulating +the affairs of the nation, based upon +logical laws and scientific principles.</p> + +<p>And how is this work of educating the +electors to be accomplished? Not, I +maintain, by furious speeches and rhetorical +displays; not by bribery, baits and +banter; but by patient, never-ceasing +labour, by lectures on history and science, +by individual instruction, is the great work +to be accomplished upon which the security +and stability of the country depend.</p> + +<p class="pgbrk">Then we may hope that the ‘Reign of +<a name="png.125" id="png.125"></a><span class="ns">[</span><span + class="pgmark">113</span><span class="ns">] + </span>Law’ in polemical science may be ushered +in with the joyful acclamations of an enlightened +and united people, and its benign +influence extend from the throne of the +monarch and the council-chamber of his +ministers to the hearth of the cottager. +Politicians will rule by law; policies be calculated +by laws; people vote by law; and +then methinks I see in my mind (to use +the words of the blind old poet) a noble +and puissant nation rousing herself like a +strong man after sleep, and shaking her invincible +locks; methinks I see her as an +eagle, renewing her mighty youth, and kindling +her undazzled eyes at the full mid-day +beam; purging and unsealing her long-abused +sight at the fountain itself of +heavenly radiance; while the whole noise +of timorous and flocking birds flutter about +amazed at what she means. Such is the +glorious vision of the ‘Reign of Law.’ Let +it be the business of every Englishman and +Englishwoman to arrange the framework of +our social and political system, that law +may have an uninterrupted sway; then +shall we be a united, prosperous, and +<a name="png.126" id="png.126"></a><span class="ns">[</span><span + class="pgmark">114</span><span class="ns">] + </span>contented people, and the reign of lawless +agitators, bribery-mongers, and counterfeit +statesmen will have passed away into the +oblivion and obscurity of a more suitable +but less favoured region.</p> + + + + +<h2><a name="png.127" id="png.127"></a><span class="ns">[</span><span + class="pgmark">115</span><span class="ns">]<br + /></span>PAPER VIII.</h2> + +<h3>ON THE PRINCIPLE OF POLEMICAL COHESION.</h3> + + +<p class="noindent"><span class="smc">In</span> my previous lectures I have had occasion +to mention the principle of cohesion; +but it plays so vital a part in the constitution +of States and their relations to each +other that I consider it advisable to devote +this lecture entirely to it.</p> + +<p>This is a large and comprehensive +subject, and embraces such principles as +the Centralization of States; the Co-operation +of States; Monogamic Marriage; +Unions; Free Trade, and many +others equally important. We have +already noticed that cohesion is a well-known +property of matter; that its +influence is not confined to the regions of +physical sciences; and that it is the +<a name="png.128" id="png.128"></a><span class="ns">[</span><span + class="pgmark">116</span><span class="ns">] + </span>manifest duty of all governments to increase +the force of cohesion.</p> + +<p>Various methods have been tried to +accomplish this purpose. The principle +of Feudalism was one of the earliest +attempts to produce the cohesion of the +nation; and, in an elementary condition of +society, it was partly successful. The +theories of ‘Divine Right’ and ‘Social +Contract’ were other methods which have +been adopted; and the unity of the +Christian Church has been the great +means of producing the cohesion of the +State in olden times; and its aid may be +again required for the same beneficent +object in future complications and social +disruptions.</p> + +<p>But it is always advantageous in scientific +pursuits to go back to first principles; and +we will adopt that method in our present +investigations. The social unit is the +family; the multiplication of families +makes the tribe; the multiplication of +tribes makes the State; and, therefore, we +shall not be far wrong if we consider the +family tie as the first principle of political +<a name="png.129" id="png.129"></a><span class="ns">[</span><span + class="pgmark">117</span><span class="ns">] + </span>cohesion. I am in agreement with several +learned thinkers upon this subject when +I say that marriage is a most important +political factor; and as marriage cannot +take place without women, it is evident +that women play a very important part in +promoting the cohesion of the State.</p> + +<p>This prominent position was duly +assigned to women by one of our greatest +political philosophers, M. Auguste Comte, +who strongly opposed the fatal fallacy of +ancient political systems, which greatly +overestimated the powers of men, and +depreciated those of women. If the +superiority of bodily strength be the sole +cause of greatness in political and intellectual +pursuits, then, most noble lords of +creation, we yield to you the palm—you +are our masters in this respect. But if, on +the other hand, it can be shown that +physical strength is not a requisite for +great achievements in these occupations; +if the powers of endurance, elasticity, +adaptability, nervous energy, and patience +are quite as needful as mere animal +strength; then we women are quite as +<a name="png.130" id="png.130"></a><span class="ns">[</span><span + class="pgmark">118</span><span class="ns">] + </span>capable, and indeed more capable than +men, for achieving political greatness. In +the ‘good old days,’ when the law of +might was right, and the strongest arm was +the most powerful machinery in the +government of the country, women were +compelled naturally to occupy a less prominent +position in the conduct of the +affairs of the nation; and for centuries +they have been degraded by a dominating +tradition, and supposed incapable of +performing duties for which they were +mentally well suited. But those militant +days are past. Animal strength and +brute force are no longer needed in the +councils of the nation; and the time has +arrived when women should cease to be +oppressed by the disparaging, illogical +deductions of former generations, and +when their assistance ought to be invoked +in the great work of promoting the +nation’s welfare.</p> + +<p>I have stated that marriage is an important +political factor; and, therefore, +women have always occupied a primary, +though obscure, part in political affairs. +<a name="png.131" id="png.131"></a><span class="ns">[</span><span + class="pgmark">119</span><span class="ns">] + </span>The cohesion of the State has been +produced by the secret influence of +family life. But it may be asked, What +kind of marriage is most conducive to +national cohesion? This question has +been carefully and conclusively answered +by a learned scientific writer, who shows +that polygamic marriage never exists in an +advanced state, as instanced by the +history of Judaism and Mohammedanism; +that a strict form of monogamic marriage +is essential to political greatness and true +progress in civilization. The cohesion of +the State is destroyed by polygamy, and +by any system which relaxes the binding +nature of the marriage tie. ‘Domestic +disorganization is a sure augury of political +disruption.’</p> + +<p>Cohesion, the essential property of all +rightly constituted nations, is often in +danger of being lost when the State is +geographically very large, or when local +interests have greater power than the +attractive force of the central government. +To obviate this evil, the method of centralization +has been adopted with satisfactory +<a name="png.132" id="png.132"></a><span class="ns">[</span><span + class="pgmark">120</span><span class="ns">] + </span>results, as in the case of the United States +of America, and Germany.</p> + +<p>By this means the local authorities are +brought into close relationship with the +central head, and the centrifugal influences +of independent interests and customs +are counteracted by the force of +central attraction. Centralization increases +the importance of the whole body, and, +like the pendulum of a clock, regulates the +movements of the whole State. In some +cases it tends to make the government +despotic, when the local governments are +entirely under the control of the central; +and every enactment, and scheme, and +plan checked and supervised by the chief +officers of the State. Such was the system +adopted in France by Napoleon III. +But cohesion without the enforcement of +a hard and rigid connection, a general +supervision without severe tyrannical jurisdiction, +are the best methods of securing +the unity of composite States.</p> + +<p>But the force of cohesion is evidently +at work in the nation apart from centralization. +Men who have a community of +<a name="png.133" id="png.133"></a><span class="ns">[</span><span + class="pgmark">121</span><span class="ns">] + </span>interests unite together for the purposes of +strength and mutual assistance. They +combine for the sake of securing means +of support in sickness, and form benefit +societies, such as the Order of Oddfellows +or Foresters. This force of cohesion has +produced trade unions, and similar institutions +which exist for the purpose of +protecting a common interest, and giving +expression to the concurrent opinions of +the members. These have their legitimate +use in every civilized State, in spite of +some of the disadvantages which follow in +their train. There are, of course, opposed +interests in every community: <em>attractive</em> +forces, which produce trade unions, +guilds, corporations, companies, and the +like; and <em>repulsive</em> forces, which result +from the opposed interests of employers +and employed, landlords and tenants, and +similar pairs of different classes in the +community. As time goes on, and the +State advances with it, these forces will +gain in strength; the cohesion of classes +will become greater; association will grow +as naturally as the bubbles form on the +<a name="png.134" id="png.134"></a><span class="ns">[</span><span + class="pgmark">122</span><span class="ns">] + </span>surface of our evening beverage. It is a +law of nature, and therefore cannot be +resisted. But the repulsive forces will be +no less strong, and to calculate the +resultant of these contending interests will +be the problem for practical statesmen to +solve.</p> + +<p>The force of cohesion is also evidently +at work, not only in individual States, but +also amongst the nations of Europe, and +of the world. That is to say, there is an +evident desire for co-operation on the part +of those nations who have attained to the +highest degree of civilization and internal +cohesion. International law is based on +the principle of cohesion, and every day it +is gaining power and favour in the eyes of +our leading statesmen. The doctrine of +Free Trade, which, if universally adopted, +would be of the greatest service to mankind, +results from a desire for co-operation; +and whatever evils may result from one-sided +Free Trade in this country at the +present time, there can be no doubt that +ultimately the complete system will be +adopted.</p> + +<p><a name="png.135" id="png.135"></a><span class="ns">[</span><span + class="pgmark">123</span><span class="ns">]<br + /></span>Sad is the fate of a nation when the +force of cohesion is weakened. The first +revolution in France is a proof of this +assertion; there was no cohesion, no common +faith, or loyalty to the throne and +Government; and indeed the Government, +which was rotten to the core, was +hardly likely to awake any feelings of +loyalty and respect; and therefore the +social disruption which followed was only +a natural sequence of events, and was +prophesied with the accuracy with which +an astronomer can foretell an eclipse. +But that is not all; when the cohesion of +the State is destroyed, it takes a long time +to restore the action of the force; and, as +in the case of France, further disruption is +sure to take place.</p> + +<p>In this lecture I have already enumerated +some of the ways in which this force +acts; there are doubtless others which +will suggest themselves to you. But I +contend that the prosperity of the State, +and the peace of the world, depend upon +cohesion. Let this be your work, most +noble professors, to promote the action of +<a name="png.136" id="png.136"></a><span class="ns">[</span><span + class="pgmark">124</span><span class="ns">] + </span>this helpful and life-giving force. Promote, +as far as in you lies, the sacred +union of family life. Encourage the +generous feelings of true loyalty and +patriotism amongst the people of this +realm of England; counsel our statesmen +with regard to the primary necessity of +national cohesion, and the advantages of +international co-operation; and your work +will be blessed; your names will rank with +those heroes of the sword and of the pen +who have raised our beloved country to +her present pinnacle of greatness and +prosperity; and your memory will live in +the hearts of your grateful countrymen.</p> + +<p class="above2">[<span class="smc">Editorial Note.</span>]—We regret to state +that the various MSS. in the sealed desk +are nearly exhausted, and are therefore +compelled to present the series of lectures +on polemical studies in an incomplete +form. But we had the good fortune to +light upon a brief diary which discloses +some interesting information with regard +to the Author’s life and occupations. We +append a few extracts:</p> + +<h3 class="smc"><a name="png.137" id="png.137"></a><span class="ns">[</span><span + class="pgmark">125</span><span class="ns">]<br + /></span>Extracts from the Author’s Diary.</h3> + + +<p><i>June 3rd</i>.—Arnold called again to-day—the +fifth time during the last fortnight! +His attention is rather overpowering, and +wastes much of my valuable time. He +says he hates science—the heathen!—and +wants me to lecture in classics. He affirms +that mathematics are dry and hard—too +hard for women, and tend to make them +unsympathetic and critically severe. I am +afraid I was rather severe with him. But +really he is very trying, and always seems +to talk like a Greek chorus in the most +profound platitudes. Arnold is a classical +tutor at Clare College. My old pupil +is getting on famously. Poor fellow! he +seems quite oppressed with his work. But +he is making great progress, and sticks +to his books like—a student of Girtham +College!</p> + +<p><i>June 4th</i>.—Lectured on the Scientific +Basis of Blackstone’s Commentaries; afterwards +received pupils until 1 p.m. Really +Blanch <span class="nw">S——</span> is more tiresome than ever. +<a name="png.138" id="png.138"></a><span class="ns">[</span><span + class="pgmark">126</span><span class="ns">] + </span>It appears that she has taken up with a +young undergraduate of King’s, and there +is no prospect of any improvement in her +work unless this nonsense is terminated. +How foolish some of my sex are, in spite of +their improved opportunities! I blush for +them! Arnold has sent me a copy of Robert +Browning’s ‘Belaustion,’ in order to make +me like classics, and give up science. +Misguided young man! He has written +some tolerable verses on the fly-leaf; but +I have no intention of playing Belaustion +to his ‘entranced youth.’ These are his +verses:</p> + +<div class="stanza"> +<div>‘My lady dear, if I may call you so,</div> +<div>For you are dearer than all else beside,</div> +<div>I know the love you bear to golden verse,</div> +<div>To golden thoughts enshrined in classic lore,</div> +<div>To all that’s beautiful; so here I send</div> +<div>Some echoes of the songs of ancient days,</div> +<div>Attuned and chanted by an English bard,</div> +<div>Who fires one’s old love for the rolling lines</div> +<div>Of youthful Hellas; may your cultured ear</div> +<div>Receive, and gladly welcome his sweet song.</div> +<div>And while we revel in the poet’s dream,</div> +<div>And hear his actors speak, we’ll play our parts.</div> +<div>You, sweet Belaustion on the temple-steps,</div> +<div>Taking your captors captive by your voice;</div> +<div>And I, the youth who, more entranced than all,</div> +<div>Was bound by fetters that he would not loose;</div> +<div>And so we’ll play our part. What say you, dear?’</div> +</div> + +<p><a name="png.139" id="png.139"></a><span class="ns">[</span><span + class="pgmark">127</span><span class="ns">]<br + /></span><i>June 6th</i>.—Have just seen our new +Professor of Physics, Amelia Cordial, who +is an excellent woman, and well suited for +the high office which she holds. She has +told me of the foolish conduct of Lady +Mary, who is evidently of opinion that +the professorial mantle ought to have +fallen on her shoulders. Really, this +jealousy in the ranks of the learned is +most disgraceful; and the bickerings which +arise from disappointed ambition, the envyings +and silly quarrels, are the weak places +in our female collegiate system.</p> + +<p>Such good news! The wrangler list is +just out, and my hard-working pupil is +<em>bracketed twelfth!</em> This is really delightful, +and abundantly repays us for all our +hard toil. But really I have not found +working with him distasteful; he is such +an excellent pupil, so painstaking and +eager, that I have quite looked forward to +his coming, and found him much more +interesting than some of these foolish +maidens. But I almost dread seeing him. +He will be so elated and overpoweringly +grateful, whereas I ought to be grateful to +<a name="png.140" id="png.140"></a><span class="ns">[</span><span + class="pgmark">128</span><span class="ns">] + </span>him for all his work for me; for I am sure +he would never have gone in for the Tripos +if I had not persuaded him. Well, I +wonder why he does not come to tell me +of his triumph.</p> + +<p><i>June 7th</i>.—<em>It</em> has come! and I half +expected it. My eager pupil writes with +all the energy and love of his noble nature +to ask me to be his wife! He says <em>that</em> +is all he cares for, and only values his +Honours as a step to a higher honour and +dignity, that of gaining my love and being +my husband. All this is very nice to read; +but a terribly difficult problem is placed +before me for solution. I do indeed love +this dear, good fellow—no one could help +doing so, I am sure; but do I not love +science more? There is a stringent regulation +in this University that no one shall +occupy the position of professor who is +bound by any domestic ties or cares. All +married women are excluded. If I say +‘Yes,’ I must resign my high position, +leave this beloved college, give no more +lectures to entranced audiences. In the +interests of science, ought I to refuse, and +<a name="png.141" id="png.141"></a><span class="ns">[</span><span + class="pgmark">129</span><span class="ns">] + </span>sacrifice my heart’s affections for the cause +of mathematics? But if I say ‘No,’ I +must give up—<em>him</em>; sacrifice his happiness +too, and blight his life. Was ever +anyone so perplexed? Science, aid thine +obedient servant! May I not determine +this vital question by thine all-pervading +light?…</p> + +<p class="tbstars">* * * * *</p> + +<p>[<span class="smc">Editorial Note.</span>]—We had just arrived +at this exciting moment in the life +of the learned and accomplished lady +whose writings form the subject of these +pages—a moment when love and science +were trembling in the balance—when a +footstep was heard upon the stairs leading +to our study, and ere we could secrete our +MS. the door was opened, and a well-known +voice exclaimed:</p> + +<p>‘I do not know why you should have +become so studious lately, Ernest, and +why you should refuse to take me into +your confidence. You spend hours and +hours in this room all by yourself, writing +away, and never say a word to me about +the subject of your literary work. There +<a name="png.142" id="png.142"></a><span class="ns">[</span><span + class="pgmark">130</span><span class="ns">] + </span>was a time when things were different, and +you were not so slow in availing yourself +of my help, and asking my advice.’</p> + +<p>We murmured something about taking +up the pen which had been laid aside by +a far abler hand, and our deep gratitude +for past assistance in our work, which could +never be forgotten.</p> + +<p>‘And do you think that I cannot help +you now?’ our visitor replied, in a very +injured tone of voice. ‘Is the old power +dead, because it has not recently been +used? Ernest, I think you very ungrateful +not to confide in me. Come, tell me +what you are writing.’</p> + +<p>A suggestion about the proverbial +curiosity of women rose to our lips, but +died away without utterance. In the +meantime, her eyes wandered over our +study-table strewed with papers, and lighted +upon the well-worn desk.</p> + +<p>‘Why, Ernest, where did you find this? +My dear old desk, which has been lost +ever so long! I do believe you have been +ransacking its contents! Why did you +<a name="png.143" id="png.143"></a><span class="ns">[</span><span + class="pgmark">131</span><span class="ns">] + </span>not tell me that you had found it? What +are you doing with my papers, sir?’</p> + +<p>The mischief was out! We tried to +explain that the world ought not to be +deprived of that which would benefit mankind; +that the peace and prosperity of +the country might be sacrificed if it were +deprived of these discoveries of science, +which were calculated to secure such beneficial +results.</p> + +<p>At length we gained our point, and obtained +the full sanction of the late Lady +Professor of Girtham College to publish +her papers. Thus her obedient pupil is +enabled to repay his late instructress for +all her kindness to him, and in some +measure to compensate the scientific and +political world for the loss of one of its +most original investigators in the regions +of polemical studies, which, not without a +struggle, she resigned when she deigned +to become his wife.</p> + +<p class="ctr above4"><small>THE END.</small></p> + +</div> + +<p class="ctr above4 pgbrk"><small><i>Elliot Stock, Paternoster Row, London.</i></small></p> + +<hr class="pg" /> + + + + + + + + + +<pre> + + + + + +End of Project Gutenberg's The Romance of Mathematics, by P. 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