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+*** START OF THE PROJECT GUTENBERG EBOOK 78241 ***
+
+
+
+
+Transcriber’s Notes:
+
+  Underscores “_” before and after a word or phrase indicate _italics_
+    in the original text.
+  Equal signs “=” before and after a word or phrase indicate =bold=
+    in the original text.
+  Small capitals have been converted to SOLID capitals.
+  Illustrations have been moved so they do not break up paragraphs.
+  Deprecated spellings have been preserved.
+  Typographical and punctuation errors have been silently corrected.
+
+
+
+
+HARPER’S LIBRARY _of_ LIVING THOUGHT
+
+[Illustration]
+
+[Illustration]
+
+[Illustration: _Fig. 1._—Haloes in cleavage flake of Biotite. ×70.]
+
+[Illustration: _Fig. 2._—Radium Halo (lower part of field) and Thorium
+Halo (upper part of field) in Biotite cut across cleavage. ×100.]
+
+[Illustration: _Fig. 3._—Haloes in cleavage flake of Biotite. ×85]
+
+[Illustration: _Fig. 4._—Haloes due to Ra. emanation (inner disc), Ra.
+A and Ra. B. ×450.
+
+PLEOCHROIC HALOES]
+
+
+
+
+                          THE AGE OF THE EARTH
+
+                                   BY
+                             ARTHUR HOLMES
+                            B.Sc., A.R.C.S.
+
+                     MEMBER OF THE IMPERIAL COLLEGE
+               FELLOW OF THE GEOLOGICAL SOCIETY OF LONDON
+                FELLOW OF THE ROYAL GEOGRAPHICAL SOCIETY
+
+              ILLUSTRATED WITH TWENTY FIGURES AND DIAGRAMS
+
+                          LONDON AND NEW YORK
+                           HARPER & BROTHERS
+
+                        45 ALBEMARLE STREET, W.
+                                  1913
+
+                      _Published March, 1913_
+
+                                   TO
+                    PROFESSOR THE HON. R. J. STRUTT
+                                  AND
+                         PROFESSOR W. W. WATTS
+                              IN GRATITUDE
+                           FOR EARLY TRAINING
+                               AND ADVICE
+
+
+
+
+PREFACE
+
+
+It is perhaps a little indelicate to ask of our Mother Earth her age,
+but Science acknowledges no shame and from time to time has boldly
+attempted to wrest from her a secret which is proverbially well
+guarded. On January 30th, 1911, I placed before the Natural History
+Society of the Royal College of Science a brief account of some of
+these attempts, and out of that paper this little book has gradually
+developed. In the present survey of the subject—the measurement of
+geological time—I have endeavoured to give as full and complete
+an account of the chief methods of attack as space would allow. My
+particular object has been to draw attention to their respective
+limitations and to test the validity of the various assumptions on
+which they are based. So far, the most remarkable feature of the
+problem lies in the extraordinary discrepancy between the conclusions
+drawn from the two most prominent methods of dealing with it. I have
+sought to mitigate the severity of this disagreement by discussing the
+possibility and consequences of reconciliation and by suggesting a
+path along which reconciliation may be found. If my treatment should
+stimulate a greater interest in the time problem, or provide material
+for further discussion, it cannot fail to bring nearer the ultimate
+solution of a question which for more than a century has had an
+unrivalled notoriety for provoking controversy.
+
+I desire to acknowledge my gratitude to Prof. J. Joly and the Council
+of the Royal Dublin Society for permission to use the admirable series
+of micro-photographs which constitute the Frontispiece; to Prof. P.
+Lowell for his photographs of the Polar Caps of Mars; and to Sir Wm.
+Crookes and the Council of the Royal Society for the photograph and
+radiograph of a piece of pitchblende.
+
+To a number of friends who have helped me in revising the proof-sheets,
+and to others who have turned my rough sketches into finished diagrams,
+I wish to tender my thanks.
+
+Finally, I have a special pleasure in expressing my gratitude for
+the valuable assistance which has been afforded me by my friend Mr.
+R. W. Lawson, of Armstrong College, Newcastle-upon-Tyne. While the
+manuscript was in preparation I had the benefit of his suggestions and
+friendly criticism, and at a later stage he kindly verified many of my
+calculations. I am indebted to him in particular for the mathematical
+treatment of the final section of Appendix A (dealing with the uranium
+time-average) and for the two diagrams with which it is illustrated.
+
+                                            ARTHUR HOLMES.
+
+    GEOLOGICAL DEPARTMENT,
+      IMPERIAL COLLEGE, S.W.
+        _December 1st, 1912._
+
+
+
+
+CONTENTS
+
+
+                                                 PAGE
+    PREFACE                                       ix
+    LIST OF ILLUSTRATIONS                        xii
+
+    CHAP.
+       I. THE TIME PROBLEM AND ITS HISTORY         1
+      II. TIME AND TIDE IN THE SOLAR SYSTEM       22
+     III. ASTRONOMICAL CONSIDERATIONS             32
+      IV. THE WORK OF DENUDATION                  48
+       V. THE SALINITY AND AGE OF THE OCEANS      61
+      VI. SEDIMENTATION AND GEOLOGICAL TIME       76
+     VII. RADIOACTIVITY                           91
+    VIII. THE THERMAL ENERGY OF THE SUN          110
+      IX. THE THERMAL ENERGY OF THE EARTH        122
+       X. RADIOACTIVE MINERALS AND THEIR AGES    137
+      XI. REVIEW OF THE EVIDENCE                 166
+
+    APPENDIX A                                   177
+    APPENDIX B                                   184
+    INDEX                                        191
+
+
+
+
+LIST OF ILLUSTRATIONS
+
+
+                 _Figures printed as plates_
+    FIG. 1}
+    FIG. 2} Pleochroic Haloes                    _Frontispiece_
+    FIG. 3}
+    FIG. 4}
+
+                                                    FACING PAGE
+    FIG. 5} Spiral Nebulæ                                 28
+    FIG. 6}
+
+    FIG. 7} Polar Caps of Mars                            39
+    FIG. 8}
+
+    FIG. 12} Photographs of Pitchblende                   92
+    FIG. 13}
+
+                    _Figures printed in text_
+                                                         PAGE
+    FIG. 9. Glacial Movement in S. Scandinavia            40
+    FIG. 10. Upper Cretaceous Strata of Colorado          45
+    FIG. 11. Section illustrating the Formation
+               of Sediments on Continental Shelf          83
+    FIG. 14. Apparatus for Estimating Radium             106
+    FIG. 15. Pleochroic Haloes of the Uranium Family     108
+    FIG. 16. Temperature Gradients                       127
+    FIG. 17. Geological Time Scales                      172
+
+    APPENDIX A—
+             Graph I                                     180
+             Graph II                                    181
+
+    Table of Radioactive Elements                        190
+
+
+
+
+THE AGE OF THE EARTH
+
+
+
+
+CHAPTER I
+
+THE TIME PROBLEM AND ITS HISTORY
+
+
+    Primitive races and their creation myths—The chronologies
+    of Eastern sages—The demands of geology opposed by
+    theological prejudice—Bishop Ussher’s date of the
+    creation of the world—The Deluge and the Doctrine of
+    Catastrophism—Ludicrous conceptions of fossils—The rise
+    and eventual success of Uniformitarianism—Leonardo da
+    Vinci—Steno—Generelli—Desmarest—Hutton—Scrope—Lyell—Ussher’s
+    chronology rejected—Geological time no longer limited—The
+    hour-glass of denudation and deposition—Darwin’s excessive
+    drafts on time—The conservation of energy—Geology
+    limited once again—Thomson on the age of the earth and
+    sun, 1862—The great controversy—Huxley, 1869—Perry and
+    the correspondence in Nature, 1895—Sir G. Darwin and the
+    birth of the moon—Clarence King’s estimate of the age
+    of the earth—Time implied by the stratified rocks—Joly
+    on the salinity and age of the oceans—The significance
+    of radioactivity—Emission of energy by radium and its
+    widespread distribution—Radioactivity provides a new
+    measure of time—Controversy again—Methods of dealing with
+    the problem—The inadequate testimony of biology.
+
+The most primitive races of mankind, strenuously engaged in the daily
+struggle for existence, appear to have given little thought to the
+antiquity of the world on which they lived. Even at the present day
+there exist barbaric tribes to whom it has never occurred that the
+earth may have had a beginning. The conception of creation, of the
+production of order from chaos, indicates a marked intellectual
+advance, but into the myths and legends of which this idea was so often
+the inspiration, the element of time did not usually enter.
+
+The East African natives have traditions of the upheaval of mountains
+and of the freeing of the earth from bondage, legends which may have
+had a foundation in the phenomena exhibited by volcanoes and glaciers.
+If the question “When?” is asked, the natural reply is merely a look of
+astonishment, and persistent enquiry elicits nothing more definite than
+a vague “Long ago.” Anything else, of course, could not be expected
+from a people whose conceptions of the development of the universe
+are limited to a recognition of the alternation of seasons and the
+insistent mysteries of life and death.
+
+The priests and philosophers who flourished during the ancient
+civilizations of the East, speculated in greater detail and devoted
+some attention to the elaboration of a chronology of earth history.
+The Chaldeans had a well-deserved reputation for astronomy, and their
+known observations go back for more than 6000 years. Cicero relates
+that their venerable priesthood had records of stellar observations
+stretching back for 470,000 years; a fanciful period which tallies with
+the date assigned by the Chaldeans to the origin of Man. According
+to the same remarkable system, the earth had already existed for 215
+myriads[1] of years. The Persian sages, led by Zoroaster believed that
+the total duration of the world’s existence was limited to 12,000
+years. The Hebrew chronological tables are familiar to everyone, and
+the restricted interpretation which was placed upon them during the
+Middle Ages, when they affected European beliefs so powerfully, will be
+presently referred to. Opposed to these ideas of a definite beginning
+were the more abstract conceptions of Indian philosophers, who regarded
+Time and the Earth as eternal.
+
+[Footnote 1: A myriad = 10,000.]
+
+To determine the age of the earth, or to express the actual problem
+with more accuracy, to measure the duration of geological time, became
+a definite scientific aspiration only during the last century. The
+ultimate purpose of Geology is essentially to elucidate the history of
+the earth, a record of which is imperfectly written in the stratified
+and igneous rocks to which access is possible. As the characters and
+sequence of the various formations gradually became better understood,
+it was found that the story they disclosed was one of successive
+changes of life and scene of the most impressive kind. The immensity
+of time which seemed to be indicated was at first a fruitful source
+of confusion and prejudice, for it brought geology into disrepute at
+an early period, owing to the widely prevalent idea that the writings
+of Moses fixed the antiquity of the universe beyond dispute. It is
+indicated by a marginal reference in most English Bibles that the
+creation of the world took place in the year 4004 B.C. This
+famous estimate, which probably represents the most limited period ever
+assigned to the past duration of our planet, was put forward in 1650 by
+Bishop Ussher. Some such date as this had been generally believed
+in during the Middle Ages as marking the epoch of transition from
+chaos to an ordered world. The corresponding Byzantine date was 5509
+B.C. The whole of geological history had therefore to be
+squeezed into about six or seven thousand years, and this limitation
+naturally demanded some extraordinary hypotheses to uphold it. As
+Prof. Sollas says, “In the days when Geology was young, it found a
+careful foster-mother in Theology, who watched over its early growth
+with anxious solicitude, and stored its receptive mind with the most
+beautiful stories which the young science never tired of transforming
+into curious fancies of its own, which it usually styled ‘Theories of
+the Earth.’”
+
+At the time of the revival of learning at the close of the 15th
+century, men’s ideas of the earth’s past history were largely dominated
+by the exaggerated effects ascribed to the Noachian Deluge. This
+devastating catastrophe was the type of a succession of destructive
+cataclysms which was believed to have preceded it. Supported by Jewish
+cosmogony, and in harmony with the scriptures, this view prevailed as
+the Doctrine of Catastrophism until well into the 19th century. It
+was believed by some writers that all sediments were deposited during
+the Flood; others, impressed by the succession of different types of
+deposits found far from the present sea-level, and often containing
+fossils, considered that one flood was insufficient. As far back as the
+9th century Rhabanus Maurus, in explaining this phenomenon, called to
+his aid three great universal floods, the two later ones being
+contemporaneous with Jacob and Moses respectively, but these floods
+apparently were not as convincing as that of the time of Noah, for
+they appear no more in geological literature. Marine sedimentation of
+antediluvial times was believed by some to have been extraordinarily
+active, and this was added to the effects of the Deluge to relieve the
+latter of the enormous amount of work for which it was held responsible.
+
+Fossils were regarded with suspicion and jealousy, and most of the
+early naturalists resolutely set themselves against the obvious
+deduction to be drawn from them. About 300 B.C., Theophrastus had
+failed to see in them the evidence of past life, and according to
+this philosopher a “plastic virtue latent in the earth” was supposed
+in some mysterious way to have given them birth. The process was
+occasionally explained as being akin to crystallisation, but other
+authors, gifted with more fascinating powers of imagination though
+with less philosophic insight, called to their aid the occult powers
+of “lapidifying juice” and the obscure consequences of “tumultuous
+movements of terrestrial exhalations.” There were even those who
+thought that fossils were the work of the devil, subtly designed to
+draw believers away from the faith.
+
+Nevertheless, there were, from time to time, more rational thinkers
+to whom such ideas were both repugnant and untenable. Endowed with
+a keener perception than their fellows, and with a more critical
+temperament, they felt compelled to regard fossils as organic remains.
+Leonardo da Vinci (1452-1519) and Steno (1631-1686) were amongst the
+most illustrious of these early observers. The work of Steno, published
+in 1669, shows how seriously he was handicapped by the orthodox belief
+that only a few thousand years had elapsed since the beginning of
+the world. Any ideas which demanded longer periods were contrary to
+revealed truth and were therefore bitterly opposed. Steno demonstrated
+not only the true nature of fossils, but also the orderly succession
+of stratified deposits. He traced the structure of the rocks to their
+subsequent movements, and their surface features to the destructive
+agencies of denudation. These remarkable investigations distinguished
+Steno as an observer far in advance of his age. The revelation of a
+tiny chapter of the earth’s past history which was thus afforded him
+must surely have suggested the necessity of calling more liberally upon
+time. However, whether or not he recognised how hopelessly inadequate
+was the period at his disposal, he remained the victim of theological
+prejudice, and cautiously avoided speculations as to the antiquity of
+the earth.
+
+Gradually, as the result of careful and patient work like that of
+Steno, the foundation stones of modern geology were laid in the face
+of a bitter antagonism. Generelli in Italy in 1749, and Desmarest in
+France in 1777 established the importance of the slow but ever active
+processes at work in the evolution of the earth’s surface features. It
+was found no longer legitimate to evoke forces more intense, upheavals
+more violent, or catastrophes more devastating than those of present
+experience.
+
+Closely following these courageous authors, and independently of their
+influence, came in 1785 the _Theory of the Earth_ of Hutton. In
+this epoch-making work the principle was defined which made dynamical
+geology possible and which has proved to be of the greatest assistance
+in wresting from the rocks their history. It was asserted that the
+activity of the agencies which had moulded the earth’s surface in
+the past and brought it to its present condition still remained
+undiminished in intensity. In existing causes lay the key with which to
+unlock the secrets of the past.
+
+The doctrine of Uniformitarianism, as it came to be called, naturally
+implied that the earth’s age should be restricted no longer by dogmatic
+obstinacy. To Hutton time scarcely presented a difficulty. He found it
+at his unlimited disposal both in past and future, and he concluded
+his enquiries with the assurance that he found “no vestige of a
+beginning—no prospect of an end.” He did not, however, infer that
+the world had neither beginning nor end, a view for which some of his
+critics held him responsible. On the contrary, he carefully pointed out
+that in tracing back the course of events we are at last limited in
+our retrospect, and that beyond the dim horizon of those early times
+stretches an unknown past. Concerning this past, Hutton preserves an
+open mind. It is not time which fails but data; and as he says “to
+reason without data is nothing but delusion.”
+
+Hutton’s convictions were regarded with righteous horror by the
+official leaders of the day, most of whom combined the study of theology
+with that of their favourite science, and demanded in the latter a
+harmonious agreement with the scriptures. From their point of view
+Catastrophism had the advantage, and they were firmly persuaded of its
+truth. Fifty years had yet to elapse before the superiority of many of
+Hutton’s opinions came to be generally recognised, and even then the
+fallacies underlying the earlier doctrines were but grudgingly admitted.
+
+The opening years of the 19th century were signalised by the work
+of Lamarck and Cuvier in palæontology. Lamarck recognised that
+fossil shells were most commonly of marine types and that in the
+gently accumulating sediments of the sea-bottom they were buried and
+preserved. In the succession of faunas which he studied, and in his
+belief that by some law of development they were all related, he found
+a cogent argument in favour of the great antiquity of the earth.
+Cuvier, however, was led by his researches to extend the conception
+of great world convulsions. Time after time the earth’s inhabitants
+had been destroyed and entombed, only to be replaced by the creation
+of fresh types after the force of the cataclysm had subsided. The
+Deluge was the last of these upheavals, and a scientific proof of its
+widespread effects was drawn from the superficial deposits found in so
+many parts of the globe.
+
+Until the barren ideas of Catastrophism had been abandoned, the past
+provided little more than an exercise for the imagination. But the
+immature days of geology were passing away. The solid work of William
+Smith prepared the way for an accurate historical development of the
+science. Scrope drew attention to the importance of studying geological
+processes actually in operation, and arrived at conclusions essentially
+the same as those of Hutton. Finally, during the years 1830-1833, the
+first edition of Lyell’s _Principles_ was issued, a work which set
+flowing the full tide of Uniformitarianism. Ten years previously Lyell
+had felt compelled to renounce the unsound doctrines of his teachers,
+and with the publication of these carefully reasoned volumes he became
+the champion of the rival position. He denied the former existence
+of catastrophes of an order of magnitude different from those of the
+present. In their place he demanded only time. A short but convulsive
+past was to be exchanged for a longer one, uniform and comparatively
+tranquil throughout.
+
+Lyell’s views did not find many ready adherents among the older
+geologists. Buckland at Oxford and Sedgwick at Cambridge had long
+taught a system of geology which they believed to be in accordance with
+the first few chapters of Genesis. Eventually, however, they found
+that under more careful examination the evidence of a universal flood
+faded away, and with them and their generation the tendency to demand a
+literal agreement between geological theory and the writings of Moses
+gradually disappeared. A new fraternity of geologists arose whose ideas
+were limited by fewer prejudices, and who found the time barriers
+raised against them no longer.
+
+Geology was now able to stand firm on its own evidence, and to insist
+without fear of contradiction that long periods must have elapsed during
+the slow accumulation of strata. The burden of reconciliation now fell
+upon the theologians. Happily, the days of malice and persecution had
+gone by, and in the light of a more broad-minded criticism it was
+found that the Church had nothing to lose by the rejection of Bishop
+Ussher’s chronology. The first three words of the Bible, “In the
+beginning,” were interpreted afresh, and from the indefinite lapse of
+time which they seemed to imply the geologist was allowed to draw at
+will.
+
+From this period until 1862, when Thomson (Lord Kelvin) attacked the
+problem in an entirely new way, there was no necessity to apologise
+for the most extensive drafts on the bank of time, and no further
+restraint was felt in estimating the antiquity of the earth. But the
+data were still inadequate, and many mistakes were made. Most of the
+estimates put forward were afterwards regarded as wildly extravagant,
+and naturally, they have no intrinsic value to-day. The stratified
+rocks, representing the aggregate accumulation of material denuded from
+the lands, afforded a valuable time-index. It was recognised that the
+processes of denudation and deposition, like a gigantic hour-glass,
+had been recording time since land and sea were first defined. But the
+record was perplexingly difficult to read, and the time units, based on
+estimates of present rates of erosion and sedimentation, were little
+more than guesses, uncertain and even misleading.
+
+The only interpretation worthy of serious consideration was that of
+John Phillips, who concluded in 1860 that the time required for the
+deposition of the complete succession of strata lay between 38 and 96
+million years. As an example of one of the more extravagant demands,
+mention may be made of Darwin’s estimate in 1859 of the time elapsed
+since the latter part of the Cretaceous period. From the rate of chalk
+erosion in Kent, he deduced that the excavation of the Wealden valleys
+had required a period of 300 million years. Referring to this estimate,
+Jukes gave his opinion that while it might be a hundred times too
+great, it was equally probable that it was a hundred times too small.
+Evidently 30,000 million years, in the absence of more reliable data,
+was not considered an absurdly excessive period for the erosion of the
+Weald. It should be noticed, however, that after the publication of
+Thomson’s views, Darwin withdrew this estimate from the _Origin of
+Species_.
+
+We must now return to consider the problem as it appeared to the
+leading physicists of half a century ago. In 1842 Mayer, and during the
+following year Joule, had placed the conception of the conservation
+of energy on a firm experimental basis, and started the principles of
+thermo-dynamics on their brilliant career through the sciences. Twenty
+years later, Thomson invaded the domain of Geology, hoping to reform
+its speculations and bring them into accordance with the doctrines
+of the conservation and degradation of energy, doctrines which were
+apparently set in defiance by the orthodox tenets of the science.
+
+As early as 1852 he had shown that under the laws to which matter and
+energy are subject, the earth within a finite period of past time must
+have been unfit as a habitation for life. This general conclusion he
+afterwards worked out in detail, determined to protest against what he
+considered the immoderate application of the principle of Uniformity.
+So profoundly did he influence geological opinion, that for nearly
+fifty years the question of the earth’s antiquity centred around his
+name. A short account of his contributions to the physical aspect of
+the subject, and of the famous controversy which they aroused, cannot
+therefore be dispensed with.
+
+In 1855 Thomson indicated the way in which observations of underground
+temperatures might be applied to the determination of absolute dates
+in geological history. Already the origin and maintenance of the sun’s
+heat had been discussed by Mayer and Helmholtz, and during the years
+1860 and 1861 Thomson dealt with their respective suggestions. During
+the following year, 1862, came the epoch-making papers _On the Age of
+the Sun’s Heat_, and _On the Secular Cooling of the Earth_.
+
+The age of the sun’s heat evidently restricts geological time in a
+very decided way, and Thomson drew attention to the necessity of the
+fact that unless the sun were a perpetual miracle, it could not have
+continued to radiate heat-energy for an unlimited period. His guarded
+conclusion was that the sun most probably has not illuminated the earth
+for 100 million years, and almost certainly not for 500 million years.
+
+Regarding the earth as a globe which had gradually cooled down, he
+tried to show that the principles of thermo-dynamics had been
+disregarded by geologists. From the earth’s present store of heat, as
+revealed by underground temperature gradients, he calculated that the
+consolidation of the crust took place about 100 million years ago.
+Owing to the uncertainty of much of the data on which this estimate was
+based, he allowed wide limits. Had a solid crust formed permanently
+less than 20 million years ago, underground heat should be greater
+than is actually observed. Had it formed at a date more remote than
+400 million years ago, then the temperature gradient near the surface
+should have been notably less than it is.
+
+In 1865 appeared a remarkable little paper in which attention was
+drawn to the earth’s thermal history, and particularly to its more
+energetic youth, the object again being to refute the doctrine of
+Uniformity. During the next year Thomson delivered the Rede Lecture
+on _The Dissipation of Energy_, and showed the importance of the
+tides in terrestrial dynamics. All over the ocean the effect of the
+friction set up by moving water is either to accelerate or to retard
+the earth’s rotation. The final result was, he asserted, to retard the
+earth as though a gigantic friction brake were being slowly applied.
+The ultimate tendency was towards a state when relative motion between
+earth and moon should be no more.
+
+In 1868, in an address on _Geological Time_, Thomson gathered
+together his three limiting criteria, and further developed the
+application of tidal friction to the question. In his discussion
+the earth’s figure was supposed to be a survival from the period of
+consolidation; a permanent record of terrestrial conditions at that
+time. This being so, the rate of rotation could be computed under which
+that form would be in fluid equilibrium.
+
+The three maximum time limits which Thomson drew from his arguments
+were respectively 500, 400, and 1000 million years, with a lower limit
+of 20 million years. The final conclusion was “that the existing state
+of things on the earth ... must be limited within some such period of
+past time as one hundred million years.”
+
+The reply to this series of attacks on what was supposed to be
+orthodox geological opinion, came from Huxley in 1869. He did not deny
+the consequences of the dissipation of energy in the cases to which
+attention had been directed, but decided in favour of the geological
+evidence, which indicates, as time has more and more substantiated,
+that “they have made no practical difference to the earth during the
+period of which a record is preserved in the stratified rocks.”
+
+Thomson returned to the attack a month or two later, protesting once
+more against this attitude. At the close of his address, he said: “A
+large proportion of British popular geologists of the present day have
+been longer contented than other scientific men to look upon the sun
+as Fontenelle’s roses looked upon their gardener. ‘Our gardener,’ say
+they, ‘must be a very old man; within the memory of roses he is the
+same as he has always been; it is impossible he can ever die, or be
+other than he is.’”
+
+There were no further contributions to the problem until 1876, when
+Thomson revised the former conclusion which he had based on the
+distribution of underground heat, and narrowed his limits to 50 and
+90 million years. In later years he reduced both these limits still
+further, though he was always more prudent than Tait, who with little
+justification cut down the time allowance in a most alarming way. Tait
+wrote in 1875, “Ten million years is about the utmost that can be
+allowed from the physical point of view for all the changes that have
+taken place on the earth’s surface since vegetable life of the lowest
+known form was capable of existing there.” Assertions such as this
+were among the most embarrassing circumstances that geologists had to
+face. The late Sir George Darwin was more kindly disposed, although his
+contributions to the question were considered to support the physical
+arguments. Believing that the moon had been derived from the earth by
+the separation of an enormous tidal wave, he calculated that since this
+stupendous event at least 56 million years must have passed.
+
+The physical evidence appeared at first to be irrefutable, and the
+estimates based upon it equally certain. Yet earth history could
+not comfortably be squeezed into less than 100 million years. The
+stratified rocks were there in undoubted succession; mile after mile
+of thickness with no indication of more rapid accumulation than that
+of modern deposits. In spite of this, however, a prejudice in favour
+of short estimates was gradually aroused, and some attempt was made
+to hurry up geological activities in the past in renunciation of the
+principles of Uniformitarianism. But many geologists refused to give
+way and vigorously attacked the physical stronghold, searching out and
+exposing all the assumptions, and noting with satisfaction the
+uncertainty of much of the data and its doubtful applicability. A few
+physicists themselves denied that the limited estimates were securely
+founded.
+
+In 1895 the controversy was re-opened by the publication in
+_Nature_ of a correspondence initiated by Prof. Perry. While Perry
+had previously accepted Kelvin’s conclusions, he now challenged the
+validity of all three. The strongest criticism was directed against
+Kelvin’s assumption of a homogeneous earth. It was shown that if the
+rocks of the interior, under high temperatures and pressures, were to
+conduct heat ten times as well as those near the surface, then Kelvin’s
+figures would need to be increased fifty-six times. To settle this
+point adequate data were not then forthcoming, but Perry stated his
+belief that, if geologists had sound reasons for demanding long periods
+of time, he saw nothing which denied them four times the greatest (1000
+million years) of Kelvin’s estimates.
+
+Kelvin wrote that he would rather know the date of the _consistentior
+status_ than that of the Norman Conquest, so interesting did he
+find the subject. After remarking that 100 million years were ample to
+satisfy Geikie, he said, “I should be exceedingly frightened to meet
+him now with only 20 million in my mouth.” However, Kelvin carefully
+examined the data referring to the conductivities of rocks and decided
+that they were not favourable to Perry’s suggestion. Thus fortified, he
+lent his support to the independent estimate of 24 million years which
+had been arrived at in 1893 by Clarence King.
+
+Kelvin’s last pronouncement of his views was in 1897, when he delivered
+an address on _The Age of the Earth as an Abode Fitted for Life_.
+He then narrowed down his earlier estimates to 20 and 40 million years.
+To most geologists these limits were seriously in conflict with the
+requirements of their science. A feeble attempt was made to force an
+agreement, but it was generally held that the sedimentary succession
+implied a period three times as long. An independent mode of reckoning
+geological time was developed by Prof. Joly in 1899. He made a careful
+study of the amount of sodium annually removed from the land by solvent
+denudation, and calculated the time during which the total quantity
+of sodium now held by the oceans could have accumulated. The period
+closely approached 100 million years, and thus further support was
+added to the testimony of the rocks, for with the birth of the ocean
+their deposition must have commenced.
+
+Among many of the more optimistic geologists there was a prevalent
+expectation that some flaw would ultimately be found in the physical
+arguments. Their anticipation was realised ten years ago in the most
+surprising and unexpected way. In 1903 came the discovery by Curie
+and Laborde that radium maintains a temperature above that of its
+environment owing to the spontaneous evolution of heat involved in
+its disintegration. Other investigators found that radium and its
+radioactive associates were widely distributed in the earth’s surface
+materials. In all waters and gases of natural origin, and all rocks and
+soils, traces of these elements have been detected. We owe a great deal
+to the careful researches of Prof. Strutt, which have shown
+conclusively that the earth can no longer be regarded merely as a
+cooling body. A newly recognised source of heat must now be taken into
+account, and indeed, so relatively abundant is the supply, that our
+present difficulty is to understand why the earth is not hotter than we
+actually find it.
+
+With these discoveries the long controversy was finally buried, and
+Kelvin’s treatment of the problem was proved to have been fallacious.
+Kelvin lived just long enough to know something of the first attempts
+to utilise the principles of radioactivity in solving the vexed problem
+of time. The discovery of radium did not only destroy the validity
+of the older thermal arguments; but also, it led directly to the
+elaboration of a new and more refined method. As we shall see in the
+sequel, every radioactive mineral can be regarded as a chronometer
+registering its own age with exquisite accuracy. The record is not
+always completely preserved, but a few attempts have been made to read
+it, and in the more favourable cases, periods of enormous duration have
+been revealed. Indeed, if our interpretation is correct, some of the
+oldest Archean rocks must date back 1600 million years.
+
+Not many years ago geologists were dissatisfied with the shortness of
+their time allowance; to-day they are confronted with an embarrassing
+superabundance. Certainly, it has been dogmatically denied that
+radioactive minerals can have the great ages which have been attributed
+to them, or that they can account for more than a small proportion of
+the earth’s loss of heat. But such denials do not help to remove the
+difficulty; they rather tend to aggravate it. In the face of two rival
+and mutually inconsistent systems of earth chronology, neither of
+which can be rejected with impunity, it becomes essential to examine
+most carefully the fundamental assumptions underlying each method, in
+the hope of detecting the subtle errors which are responsible for so
+glaring a disagreement. In this way alone can a means of reform be
+indicated and the road made clear for the construction of a time-scale
+which will be acceptable to all.
+
+It is obvious that as yet we cannot measure the earth’s absolute age if
+by that expression is meant the time which has elapsed since our planet
+first existed. Kelvin’s work most nearly approached this desideratum,
+but, as we have seen, it was doomed to ultimate failure, though not
+indeed, to discredit. Sir George Darwin’s calculation of the lapse of
+time since the birth of the moon stands apart; his results are limited
+only by a definite minimum, and otherwise are sufficiently elastic to
+meet any reasonable demand. But this convenience, added to the doubtful
+validity of the hypothesis on which his estimates were based, detracts
+from their value. It would be unfair to expect too much of them, for
+they were only put forward in support of a hypothesis which would have
+been immediately disproved if ridiculously long or short time periods
+had been involved.
+
+As we shall see in the following chapter we are still far from
+understanding the sequence of events which led up to the origin of the
+earth. All we can hope to do is to fix the dates of critical periods
+of its history and assign its origin to a point still more remote. The
+different methods which have been elaborated to deal with the problem
+are all based on a common principle. The rates of certain changes
+at the present day are determined as accurately as possible, and in
+imagination, the respective processes are traced backward in time,
+until limiting conditions are arrived at. Thus, Kelvin takes us back
+to a time when the earth was not yet a solid globe; Darwin traces back
+the moon’s history until he finds it revolving close to the earth; Joly
+bids us imagine the oceans in their original freshness, free, or nearly
+so, from salt; Geikie finds an end at last to the long succession of
+stratified rocks and seeks to estimate the time they represent. Last
+of all, and most brimful of promise, there lies in the mechanism of
+radioactivity an elegant method for assigning a date to the period of
+crystallisation of every igneous rock in which suitable minerals can be
+found.
+
+The testimony of biology scarcely calls for consideration here, for
+as Huxley pointed out, biology must take its time-scale from geology.
+The procession of life forms shows broadly that the time involved must
+have been very great; and, moreover, where we first meet it in the
+Cambrian rocks, it is already far on its journey. This is usually taken
+to signify that pre-Cambrian time must be at least as long as that
+which has elapsed since. Such a statement can only be regarded as very
+conservative.
+
+Prof. Poulton considers that the process of evolution must have
+required much longer periods of time than those estimated by the
+geologists. Sollas, on the contrary, is satisfied that 26 millions of
+years would be ample to meet all the demands of biology. It is obvious
+that a numerical estimate cannot be derived from the succession of
+organic forms, for the rate of change of species is as yet known only
+relatively. The influence of changing environment is complex beyond the
+possibility of exact analysis, and any method of chronology based on
+the development and ultimate extinction of past types would necessarily
+give results of very unequal value. The little shell _Lingula_ has
+retained its individuality with but little deviation from its original
+form throughout the time represented by the fossiliferous strata, but
+the same record is eloquent of the gradual unfolding of fauna after
+fauna, culminating at last in the highly specialised organisms of
+to-day.
+
+
+
+
+CHAPTER II
+
+TIME AND TIDE IN THE SOLAR SYSTEM
+
+
+    Early ideas of cosmogony—The Laplacian hypothesis—Tidal
+    friction in the earth-moon system—Its application by Kelvin
+    to the question of the earth’s antiquity—Its application
+    by Sir G. Darwin to the history of the moon and the date
+    of its birth—Difficulties in the way of the Laplacian
+    hypothesis—The Planetesimal hypothesis—The origin of the
+    ancestral solar nebula and its transformation into the solar
+    system—Early stages of the earth’s history.
+
+Speculative fancies concerning the origin of the world form the subject
+matter of many of the earliest writings on record, and throughout the
+intellectual history of mankind the problem has proved to be one of
+supreme fascination. It was not, however, until quite recent times
+that the efforts of imagination gave place to reasoned hypotheses,
+tempered by a more sober regard for physical probabilities. At first,
+on having attained the status of a science, geology steadfastly
+refused to consider seriously the cosmogonic fantasies then current.
+It was Hutton, who by advocating the direct observation of nature in
+place of the old scholastic arguments, first delivered geology from
+the inevitable wranglings that would necessarily have arisen from so
+premature a discussion of the beginning of things. Cosmogony, in spite
+of this, continued to receive attention from workers in other sciences,
+and while to-day we are still unable from geological facts alone to
+trace back with confidence the details of the earth’s beginning, yet
+the uncertainty which justified Hutton in entirely disregarding the
+earth’s genesis no longer exists. Astronomy, physics, and chemistry
+have all contributed to the elucidation of what may be called the
+prehistoric period, and have done much to remove our modern ideas from
+the dangerous quicksands of speculation.
+
+It is becoming more and more evident that many of the fundamental
+problems of geology can be solved only with reference to the processes
+involved in the making of the earth and in its subsequent evolution.
+The dynamic agencies at work to-day are genetically the outcome of the
+ancestral forces which first moulded our planet, and theoretically, the
+tectonics and constitution of the earth’s crust should lead back to
+a more complete understanding of its initial condition. But the mind
+of man is impatient of delay; shrewd guesses are made and gradually
+adjusted to known facts, with the result that many geological doctrines
+are founded not on observation alone, but also in part on fundamental
+hypotheses.
+
+During the 19th century scientific thought was powerfully influenced
+by the achievement of Laplace, for it was he who first presented the
+famous Nebular hypothesis in a consistent and acceptable form. Previous
+thinkers, notably Buffon in 1745, and Kant in 1755, had put forward
+similar generalisations, but they fell into certain errors which
+Laplace escaped, and their expositions lacked the completeness and
+authority which his mathematical genius guaranteed. In the _Système
+du Monde_, published in 1796, Laplace attempted to trace the gradual
+evolution of the solar system from a spheroidal nebula, under the
+normal operation of natural laws. He started with a hot gaseous nebula
+of lens-like shape extending beyond the present orbit of the outermost
+planet and rotating slowly in the same direction as that of the sun.
+The average density of such a nebula would be about ¹/₂₅₀,₀₀₀,₀₀₀
+that of ordinary air. As Laplace explicitly states that the sun was
+already foreshadowed in the nebula as a strongly condensed central
+nucleus, the outer atmosphere must have been of inconceivable tenuity,
+a condition maintained only by intense heat. Through the loss of this
+heat by radiation, and under the influence of its own gravitation, the
+nebula would slowly contract. In accordance with the laws of dynamics,
+contraction would necessarily be accompanied by a compensating increase
+in the rate of rotation. At a certain stage, the centrifugal force at
+the Equator would balance the attraction of gravity, and a ring of
+gas would be left behind. The same process of ring separation would
+afterwards be repeated from time to time as contraction progressed,
+and each ring being inherently unstable, would rupture, ultimately
+forming a spheroidal mass with the requisite directions of rotation and
+revolution. The Asteroids, a group of tiny planets revolving in the
+zone between Mars and Jupiter, probably represent a ring which failed
+to coalesce into a single planet. In their newly-born condition the
+planets were still hot and gaseous, and by the operation of the same
+mechanical agencies on a smaller scale most of them detached a second
+generation of rings, and these having aggregated in turn became the
+satellites. The great central nucleus, continuing to contract after the
+last planetary ring had been abandoned, became the sun.
+
+On this hypothesis the earth was originally a hot fluid globe with
+a heavy atmosphere consisting of the vapours of its more volatile
+constituents. As it contracted it rotated faster and faster, until a
+limiting velocity was attained which allowed the separation of the
+ring which ultimately condensed to form the moon. At a later stage the
+earth began to solidify and the crust first made its appearance. The
+lighter igneous rocks, the granites and corresponding lavas, presumably
+formed the outer layers, while beneath this zone the more basic magmas
+arranged themselves in the order of their density. When cooling had
+sufficiently progressed, the waters condensed to form the oceans, and
+with the emergence of the lands, denudation began for the first time
+and the earth’s historical period was inaugurated.
+
+At the time of the birth of the moon the rotatory velocity of the
+earth must have been very rapid compared with that of the present day,
+and an obvious deduction is that the earth has gradually slowed down
+in the course of its history—in spite of the accelerative effect of
+contraction—and is probably still being retarded. From a comparative
+study of ancient and modern eclipses, Dunthorne demonstrated in 1749
+that the earth appeared to be losing time. More than a century later,
+Adams showed from a revision of all the data, that the loss amounted to
+22 seconds in a century, although he was careful to point out that the
+assumptions on which his calculation was based were themselves not
+securely founded. It was Kant who started the idea that the ceaseless
+operation of tidal friction would tend to bring about this result. Long
+afterwards Kelvin indicated the way in which tidal retardation might be
+applied to estimate the date of the earth’s solidification. He supposed
+that the form then assumed by the earth had survived in its essential
+features throughout geological history. Subsequent diminution of the
+rate of rotation was not considered to be attended by a corresponding
+change of oblateness. Granting this assumption, the present figure
+of the earth ought to inform us of the rate of rotation under which
+it would be in fluid equilibrium at the time of consolidation. After
+making these concessions to speculation, Kelvin safeguarded himself by
+assigning wide limits to the earth’s age. His maximum estimate was a
+liberal 1000 million years, but he further stated his opinion that if a
+much higher antiquity than 100 million years were demanded, the polar
+flattening and equatorial bulging should be more marked than we find
+them.
+
+These conclusions were necessarily somewhat vague, and based as they
+were on a very questionable assumption, they were readily susceptible
+to damaging criticism. It is known from the concordant evidence
+afforded by seismic, geo-physical, and astronomical phenomena that
+the earth is essentially solid throughout with a rigidity more than
+twice that of steel. So far our conception of the earth is similar to
+Kelvin’s, but the postulate that such a body could resist rotational
+changes without modification in shape, cannot now be granted. As a
+whole the earth tends to conform to the laws of fluids, though its
+response may be tardy and the alteration of form may lag considerably
+behind the ultimate cause. This being so, it would be more correct to
+refer Kelvin’s time limits to the period of “lag” rather than to the
+period of the earth’s history as a solid globe.
+
+Sir G. Darwin’s departure from the ring conception of Laplace in the
+case of the moon, and his alternative theory of the moon’s origin and
+history are well known. Tracing back to their logical conclusions the
+effects of tidal friction in the earth-moon system, he has developed
+one of the most fascinating romances in the domain of cosmogony.
+Unfortunately it is impossible to apply any definite dates to the
+critical stages of this history, if for no other reason than the
+imperfection of our present lunar and tidal theories. His lower
+estimate of the time which has elapsed since the disruptive catastrophe
+lies between 50 and 60 million years, but the actual time would
+certainly be much greater. Indeed, Darwin himself, referring to the
+problem of cosmical time after the advent of radium and the overthrow
+of the older standards, wrote, “I feel with some degree of confidence
+that if the tidal theory shall ultimately be condemned it will not meet
+its execution on the score of lack of time.” A recent discussion of
+the problem by Prof. Chamberlin and his colleagues is unfavourable to
+Darwin’s view. After a careful study of the rate of tidal retardation
+they show that the lengthening of the day is of the order of one second
+in 500,000 years, and that if the physical condition of the earth has
+remained essentially as at present, at least 220,000 million years must
+have elapsed since the day occupied 20 of our present hours and the
+month 29 such days. Yet just after the birth of the moon, as outlined
+by Darwin, day and month were alike in duration, each being equal to
+about three of our present hours. It must be confessed that, after all,
+we know but little of the moon’s history with certainty.
+
+At the time of its announcement to the world the Laplacian theory was
+remarkably in accordance with the knowledge of the time. But as further
+discoveries were made, numerous inconsistencies and contradictions
+arose. Not only were certain of the movements of the planets and
+satellites found to be in a retrograde direction, but, besides these
+awkward facts, at every stage of the postulated development of the
+solar system insuperable mechanical difficulties appear which render
+the truth of the hypothesis highly improbable. Finally, in the dynamics
+of the system there are so many discrepancies between the requirements
+of theory and the actual circumstances that Prof. Moulton and Dr. See
+both insist that it could not have originated in the way that Laplace
+imagined. The heavens have been diligently searched for nebulæ of
+the Laplacian type, but no certain case has been observed. The vast
+majority conform to the spiral type and to a nebula of this kind appeal
+has been made in the recently developed Planetesimal hypothesis of
+Chamberlin and Moulton.
+
+[Illustration: FIG. 5.
+
+Symmetrical Nebula in Piscium, M 74.]
+
+[Illustration: FIG. 6.
+
+Whirlpool Nebula in Canes Venatici, M 51.
+
+SPIRAL NEBULÆ.]
+
+The general structure of a spiral nebula is immediately suggestive
+of tidal action. From a central nucleus two spiral arms emerge at
+diametrically opposite points. Often they are beautifully defined
+(Figs. 5, 6), but seen from the side they appear as discs of misty
+light. In the arms nebulous knots and irregularities are generally
+apparent, the precursors, perhaps, of a system of bodies analogous in
+their distribution to the planets. To account for the existence of a
+spiral form, conditions of extreme tidal distortion are suggested. In
+the case of our ancestral sun such conditions would be brought about
+by the close approach of another celestial body. As the stranger
+drew near, the tidal stresses set up would gradually increase until
+explosive outbursts of matter from the sun were projected in the
+plane of attraction, one on the near side, another on the far side.
+The result of the combined attractions of the two suns on the ejected
+material would be to develop a spiral structure. An enormous number of
+tiny planets or planetesimals would thus begin to circulate about the
+sun, associated with scattered knots of larger dimensions which would
+form the nuclei of the future planets and satellites. These knots would
+at once begin to grow by coalescence at the expense of the vast numbers
+of planetesimals associated with them in adjacent zones. Dynamically
+the scheme is sound, and the many suggestive consequences which unfold
+themselves explain away most of the difficulties which proved so
+embarrassing to the Laplacian hypothesis. Into a discussion of these
+advantages space does not allow us to enter, but it may be said that of
+all the attempts to grapple with the fundamental problem of the genesis
+of the solar system, the Planetesimal hypothesis appears to be the
+most successful. It is to be welcomed, apart from its many convincing
+features, if only because of its stimulation to the further study of
+the early stages of earth history.
+
+The earth began on this hypothesis as a nebular knot, and it has since
+grown up to its present mass by the capture of outside planetesimals.
+It is very unlikely that it was ever in a molten condition. Internal
+heat arose in part from the condensation of the mass during the
+period of its growth. The temperature would slowly rise until the
+fusion point of certain of the constituents was reached and the
+liquid tongues and pockets thus formed would then tend to move away
+from the centre—the lighter and less viscous stony material being
+squeezed upwards relatively to a network of the heavier and more rigid
+metallic material. Once vulcanism had been initiated in this way the
+process would continue until a highly metallic nucleus had collected.
+Surrounding it there would gradually form a thick zone of silicate
+rocks, the differentiation from the original heterogeneous mixture of
+stony and metallic constituents being due to the selective fusion of
+the former. In dealing with the question of the earth’s heat in a later
+chapter, the value, and indeed the necessity of this conception will be
+realised.
+
+The atmosphere and oceans must have been derived from the planetesimals
+themselves, and on analogy with rocks and meteorites, the planetesimals
+would not be lacking in the raw material from which to evolve them.
+Even now, the outer 70 miles of the earth’s crust would be competent to
+supply all the nitrogen of the atmosphere, the water of the oceans
+and the vast quantity of carbon-dioxide represented by limestones and
+carbonaceous deposits. With the existence of an ocean and atmosphere,
+a new factor in surface differentiation arose. Mechanical and chemical
+denudation became possible, and the first sediments were deposited.
+Although the earth’s growth had not yet ceased, all the agents occupied
+in its subsequent development were now at work and its geological
+history may be said to have definitely commenced.
+
+
+
+
+CHAPTER III
+
+ASTRONOMICAL CONSIDERATIONS
+
+
+    The Great Ice Age—Extension of glaciation—Croll’s
+    ingenious hypothesis—Inadequacy of the explanation—The
+    ice caps of Mars—De Geer’s discovery of the annual layers
+    of glacial clay in Sweden—Application to the measurement
+    of time—Sederholm’s observations in Finland—Cyclic
+    sedimentation in the Cretaceous strata of Colorado—Its
+    correlation by Gilbert with an astronomical time unit.
+
+In the last chapter mention was made of Kelvin’s work on tidal
+friction and of Sir G. Darwin’s speculations as to the early history
+of the earth-moon system. Their conclusions depended very largely on
+a cosmogony which has failed to meet with general acceptance. A very
+different appeal to astronomical causes was made by Croll in his famous
+attempt to account for the anomalous conditions of the glacial period.
+Here we may also consider the correlation by Baron De Geer and Mr. G.
+K. Gilbert of certain unusual phases of sedimentation with the seasonal
+and climatic changes brought about respectively by the earth’s motion
+and its periodic fluctuations. All of these investigations find a
+common basis in their direct reference to astronomical considerations.
+
+In the course of its history the earth has undoubtedly passed through
+several periods of extreme cold, periods when Arctic conditions swept
+down from their polar strongholds and invaded the temperate zones and
+even the tropics. Ice and snow have left their traces in many a grooved
+and striated surface, and in gently rounded outlines the landscape
+often betrays their former presence. Erratics and perched blocks,
+terminal and lateral moraines, lakes and alluvial terraces, U-shaped
+and hanging valleys all bear witness to the wide extension of the
+vanished glaciers of the past. Relics of glaciation have been preserved
+in the Cambrian or pre-Cambrian rocks of Norway, China, Australia
+and South Africa. Still more remarkable are the records of a Permian
+ice age found in the rocks of South America, South Africa, India and
+Australia. No unequivocal evidence of glaciation in later periods is
+forthcoming until the advent of the Pleistocene. The Great Ice Age
+through which the earth has so recently passed was not, however, a
+single epoch of glacial extension. Four episodes in the climatic cycle
+can be recognised—a genial episode, a period of falling temperature
+and glacial advance, a glacial episode, and finally, a period of rising
+temperature and glacial retreat. That this cycle has been four times
+repeated is the testimony of the Eastern Alps as interpreted by Prof.
+Penck. In the British area the ebb and flow of temperature has not left
+so clear a record, and a more continuous and persistent glaciation
+appears to be indicated.
+
+At the time of the maximum advance of the ice, all northern Europe lay
+buried beneath an immense ice sheet, which was fed by enormous glaciers
+slowly creeping down from the uplands. Curiously enough, Siberia, which
+in parts experiences the coldest winter in the world, is not now and
+was not then covered by the ice-field. Farther south the ice collected
+in the Pyrenees, Alps, Caucasus and in the great Asiatic ranges
+and descended in all directions far below the level of the present
+snow-line. In Canada and the United States the ice mantle proceeded
+from three great centres—from Labrador along the Atlantic coast,
+from the Keewatin district by Hudson’s Bay and from the Cordilleras
+along the Pacific coast. In the tropics and in the southern hemisphere
+the story is the same. Down the slopes of Kenia, Kilima N’jaro and
+Ruwenzori, the towering peaks of Central East Africa, the glaciers
+descended 5000 feet below their present termination. Kosciusko in
+New South Wales bears conspicuous traces of a former ice-cap which
+completely shrouded all but the highest peaks of the plateau. From the
+highlands of Tasmania and New Zealand, and from the Cordilleras and
+Andes of Patagonia and Chili the evidences of a prolonged glaciation
+are equally clear.
+
+No satisfactory theory of climate has yet been propounded which affords
+an adequate explanation of this universal lowering of the snow-line.
+Whether or not the temperature fluctuations were synchronous all
+over the earth is difficult to decide, but that a colder climate
+characterised the southern no less than the northern hemisphere cannot
+be doubted. The causes to which appeal has been made in accounting for
+climatic changes are of three classes,—astronomical, geographical and
+atmospheric. In general the various tendencies will be opposed to one
+another and by their interference prevent the attainment of universal
+extremities of climate. Occasionally, however, circumstances may
+arise when their joint action will lead in a single direction. A wide
+extension of tropical or polar conditions would then be expected to
+follow.
+
+Of the three contributory causes, only one, the astronomical, bears
+any determinable relation with time. The theory that secular variation
+of terrestrial climates results from the changing eccentricity of the
+earth’s orbit, was first proposed by Adhémar. In 1868 James Croll
+greatly elaborated and extended this theory, presenting it with such
+a formidable array of quantitative data and yet in such an attractive
+form that it exerted a considerable influence on the geological thought
+of the day. Not only did it seem to offer an acceptable means of escape
+from the maze of difficulties by which the problem was shrouded, but in
+addition it promised a faithful chronology fixing the date and duration
+of the Ice Age with almost ideal precision.
+
+Laplace established the fact that the ellipticity of the earth’s
+orbit is subject to periodic oscillations between certain limits.
+Sometimes the path is nearly circular but at other times it becomes a
+more flattened ellipse. If the earth were the only planet, its orbit
+would suffer no change; that it does is due to the attractions of the
+sister planets. Nevertheless, the orbit is essentially stable, and the
+yearly journey always occupies the same time. Formulæ were devised by
+Leverrier from which it was possible to calculate with some accuracy,
+the actual value of the eccentricity at any given period in past or
+future within a few million years of the present. Croll utilised these
+formulæ to compute the dates of maximum and minimum eccentricity for
+the past three million years. He found three important periods when
+that factor was specially high, betraying a type of orbit more than
+usually flattened. These were:
+
+    (_a_) from 2,500,000 to 2,600,000 years ago.
+    (_b_)  ”     720,000 to   980,000   ”    ”
+    (_c_)  ”      80,000 to   240,000   ”    ”
+
+It was to the last of these that the Glacial Period was assigned.
+
+When the earth is at perihelion, i.e. in that part of its orbit which
+lies nearest to the sun, it enjoys a more generous radiation than
+falls upon it at aphelion, when it is farthest from the sun. But this
+alone does not determine the time of summer and winter. At present
+the northern winter and southern summer occur when the earth is in
+perihelion. As is well known, this is owing to the inclination of
+the earth’s axis and the blanketing effect of the atmosphere. In the
+northern hemisphere, the greater thickness of air presented to the
+sun’s rays during the winter keeps out more heat than is gained by
+the relative closeness to the sun. However, this condition is not
+permanent. As discovered by Hipparchus in the year 134 B.C.,
+the positions of summer and winter and of the equinoxes on the ecliptic
+are subject to a slow forward movement. In 26,000 years they make the
+complete circuit, and so in the course of time the relation of the
+seasons to perihelion is slowly altered.
+
+The _precession of the equinoxes_ was shown by Newton to be a
+dynamical consequence of the spinning of the earth about a tilted axis.
+While this change is progressing, the position of perihelion is also
+shifting, and the resultant period is thereby reduced on the average
+to 21,000 years. Thus, in about 10,000 years from now the northern
+hemisphere will enjoy summer at perihelion. At the same time, the
+northern winter will occur at aphelion. The cold season will then be
+longer and more severe than now, and the annual accumulation of snow
+correspondingly increased. If, in addition, we suppose the orbital
+eccentricity to approach its maximum value, the northern hemisphere
+would then be in the grip of winter for nearly four months of the year,
+and the cold would become still more bitter than before. As a slight
+compensation for the rigours of the winter, the summer, though short,
+would be very much hotter. It was extremes such as these, accompanied
+perhaps by favourable geographical conditions, that Croll postulated
+for his glacial period. He believed that the snow and ice which would
+collect during a long frosty winter would successfully resist the
+evaporative powers of the summer, and that permanent snow-fields would
+therefore arise. Once started, the snowy mantle would tend to continue.
+A great deal of heat could be absorbed without raising the temperature
+above freezing-point, and the result of evaporation would be the
+creation of a thick blanket of fog, an effective agent in guarding the
+ice against the ravages of the summer radiance.
+
+A peculiarity of Croll’s hypothesis is that glacial epochs could not
+exist in both hemispheres at the same time. South of the Equator the
+summer would be longer than it is at present, and the winter would not
+only be short, but also comparatively mild. The climate would be that
+of a genial interglacial period. The alternation of glacial epochs
+between north and south is a necessary consequence of Croll’s view, but
+when the facts are examined they are found to be unfavourable to this
+assumption. In Sweden the last period of extension of the ice appears
+to have been synchronous with that in New South Wales, the close of
+each being dated, if our present time-scale is reliable, at 15,000
+to 20,000 years ago. Both date and coincidence are decisive against
+the theory. Although Croll’s hypothesis achieved a great popularity,
+geologists were not wanting who considered the suggested causes to
+be utterly inadequate to produce so radical a change of climate. It
+happened that during the penultimate period of extreme eccentricity,
+which began nearly a million years ago, the astronomical conditions
+were more favourable to glaciation than they have been since. The
+question therefore arose why no traces had been preserved in the
+deposits of that time. Indeed, since the Cambrian, many hundreds of
+glacial periods should have come and gone. Had this been the case, and
+corroborative evidence sufficiently convincing, the earth’s chronology
+would have been written boldly in its rocks. But Croll’s brave attempt
+to number the ages was unsuccessful, and his attractive theory no
+longer holds the field.
+
+[Illustration: FIG. 7.
+
+At maximum: full extent of white.
+
+At minimum: inner circle.
+
+NORTH POLAR CAP.]
+
+[Illustration: FIG. 8.
+
+At maximum: full extent of white.
+
+At minimum: disappears entirely.
+
+SOUTH POLAR CAP.
+
+MARS.]
+
+A gigantic experiment illustrating the very conditions which Croll
+postulated has been recently shown to us by Prof. Lowell. For his
+working model we must look to the sky and carefully watch the changing
+seasons of Mars. The eccentricity of the orbit of Mars is much higher
+than that of the earth could ever have been, and moreover, the southern
+winter falls near aphelion. The conditions for a permanent ice-cap
+over the south polar regions are therefore ideal. The actual facts are
+surprising, and on the accompanying plate Prof. Lowell has depicted
+them admirably. During the winter a large snow-cap collects around the
+south pole, but in summer it is entirely dispersed. Around the north
+pole the winter snow-cap is less extensive, but all through the summer
+it never quite disappears. While the long southern winter undoubtedly
+makes possible a greater accumulation of snow, the hot short summer
+more than compensates by its superior powers of evaporation. A
+permanent and widely extended ice-field evidently could not originate.
+This demonstration of Croll’s hypothesis in actual practice does not
+present an altogether complete analogy to terrestrial conditions.
+The surface temperature of Mars and the thermal properties of its
+atmosphere may be widely different from ours, and the excessive rate
+at which the polar caps diminish in the spring clearly indicates the
+comparative thinness of the deposit. But in spite of these differences,
+the remarkable conclusion stands unassailed—that the evaporative power
+of the short hot summer of the south exceeds that of the long but
+cooler summer of the north.
+
+[Illustration: FIG. 9.
+
+Directions of Glacial Movement in Southern Scandinavia.]
+
+It was stated above that since the culmination of the last glacial
+epoch more than 15,000 years have elapsed. Of the several methods which
+have been employed to determine this period only one can be dealt with
+here. The present genial climate has not greatly varied during the last
+7000 years. As we trace back the record of temperature still farther a
+gradual fall can be discerned, accompanied by a wide extension of the
+ice. Fig. 9 depicts the directions of movement of the last continental
+glacier of Scandinavia and its southern boundary across Jutland and
+the Baltic provinces. As it retreated, it left the terminal moraine
+known as the Baltic ridge, and its southern limit was gradually pushed
+back till it extended to what is now the coast of Scania. From this
+point its recession has been followed in great detail by De Geer, who
+has made a careful study of the deposits which, extending from the
+Baltic up to the Scandinavian ice-shed, mark the progress of its annual
+retreat. Upon his observations he has founded a system of geological
+chronology which is of the greatest importance in that it marks the
+first effort towards absolute accuracy.
+
+Each spring and summer, as the glacier thawed, a great deal of sand
+and clay was set free and carried away in suspension by the numerous
+streams which flowed from under the melting ice. The coarser material,
+on reaching the sea, settled down almost at once, but the finest
+particles of clay, able to remain in suspension much longer, were not
+completely deposited. Then came the autumn and winter, and the freezing
+of the streams. The sea received no further supply of sediment, and the
+load of fine mud slowly settled on the sea-bottom to form a thin layer
+of pure clay, sharply differentiated from the coarser bed below. The
+following year the glacier retreated a few hundred feet to the north,
+and the material then liberated was sorted out as before and again
+deposited in two well-marked seasonal layers. As this process continued
+year after year the area of deposit moved northwards with the ice, and
+the annual layers of sediment thus became superimposed one upon the
+other like wedge-shaped tiles on a roof. The width of each bed is
+generally less than thirty miles, for even the finest mud cannot be
+traced beyond that distance. This being the case, no vertical section
+contains all the layers, and it is rarely that more than a hundred can
+be counted in one place. The total thickness of the recessional deposit
+seldom exceeds thirty feet.
+
+De Geer successfully attempted the difficult task of counting the
+annual bands of glacial clay deposited throughout the period of retreat
+from the Scanian coast. Fortunately, any given set of layers can be
+traced from one locality to another, and as each ribbon of sediment
+dies out the higher beds are followed up in the same way until the
+whole series has been examined from bottom to top. The late-glacial
+beds number about 5000, and the time which has elapsed since the
+ice border reached the eastern coast of Scania is therefore 12,000
+years.[2] The time of recession from the Baltic ridge to the Scanian
+coast remains to be estimated. Much of the record is hidden beneath the
+waters of the Baltic, and in North Germany De Geer’s method has not yet
+been applied. It appears, however, that the withdrawal of the ice was
+not uniform. It began slowly and reluctantly, but towards the north
+became more rapid. In the region of Stockholm the retreat was five
+times as fast as in Scania. We may therefore assume that in the still
+earlier stages the time taken was considerably more than that required
+for a retreat over an equal distance in Scania. The latter would
+have occupied rather more than 2500 years, and on this basis Sollas
+provisionally accepts 5000 years as the period during which the ice
+front was driven back to the south coast of Sweden. In this way the
+whole interval which has passed since the culmination of the last
+glacial episode is determined to be greater than 15,000 years, with
+17,000 years as a probable value.
+
+[Footnote 2: The post-glacial layers number about 7000.]
+
+Amongst the Archean rocks of N.W. Finland, Prof. Sederholm has found
+in the Bottnian schists and phyllites primary characters which are
+strikingly similar to those of the banded glacial clays. Under the
+microscope their textures are distinctly clastic, and each composite
+stratum is sharply divided into two thin bands, the coarser one
+originally of sand and marking the beginning of a new year of
+deposition, the finer one originally of clay. Sederholm interprets
+the phenomenon on a uniformitarian basis as indicating that, even in
+those remote times, there was a marked difference in the seasons. By
+measuring the thickness of many thousands of annual layers, he finds
+their mean thickness to be about five inches. The total thickness of
+the banded phyllites amounts to 10,000 feet and the time they appear to
+represent is therefore only 24,000 years. This conclusion is probably
+far from the truth, for, as Sederholm particularly emphasises, it is
+difficult to know what is meant by the _thickness_ of a deposit,
+so many arbitrary and misleading elements enter into its determination.
+
+From De Geer’s work, it might have been said at first that a thickness
+of thirty feet was deposited in a hundred years, but as the deposit
+was traced over the country, it became equally evident, that with no
+apparent thickening of the formation, deposition had gone on for 5000
+years, and considering the growth northwards from the Baltic ridge,
+perhaps for 10,000 years. The whole difficulty lies in determining
+which parts of a formation are strictly contemporaneous. A measurement
+of thickness is significant only in relation to the immediate area of
+deposit and to the rate at which it moves landwards or seawards. The
+_thickness_ of a formation and the _maximum thickness_ of the
+layers formed in successive years may differ enormously, as De Geer’s
+researches have made so evident. For the same reason the term _rate
+of deposit_ is loose and misleading unless it is clear to what it
+refers.
+
+Another astronomical method of estimating time, though embracing much
+longer periods, has been applied by Gilbert to certain formations
+in Colorado. The basin of the Arkansas River is largely occupied by
+Cretaceous sediments, a succession of which is given in the adjoining
+diagram. At the four stages marked A, B, C and D the argillaceous
+shales give place to a calcareous type, and in these there is a regular
+alternation of thin layers of limestone and of calcareous shale. At A
+the average thickness of a pair of beds is 1·5 feet, and the number
+of repetitions is 15. At B the limestones are more massive, but the
+parting shales are very thin. Here again the average thickness of two
+adjacent beds is 1·5 feet. The limestones at C are less pure, and each,
+with its associated layer of shale, amounts on the average to about 2·7
+feet. At D the succession is similar.
+
+[Illustration: FIG. 10.
+
+Vertical Section of the Upper Cretaceous strata of Colorado. Below are
+the Comanchian or Lower Cretaceous beds; above are the Transition beds
+to the Eocene.]
+
+To explain the remarkably regular alternation of conditions which
+determined this uniform rhythm of sedimentation, purely terrestrial
+causes appear to be insufficient. Upheaval and subsidence of the
+earth’s crust, and the changing distribution of land and sea, are
+characterised rather by their irregularity than by any rhythmic
+sequence. While there is undoubtedly a rough periodicity in earth
+movements, yet it is discernible only on the broadest scale and is out
+of all proportion to the requirements of this case. Gilbert therefore
+suggests an astronomical cause. Of the several cyclic changes to which
+it is reasonable to appeal, the annual revolution of the earth, and
+the variation of the eccentricity of its orbit, demand periods which
+are in the first case too short (one year), and in the second too long
+(91,000 years). As we have already seen, the relation of the seasons
+to the position of perihelion repeats itself about every 21,000 years,
+and this astronomical cycle seems better adapted to meet the case.
+The climatic changes which accompany the precession of the equinoxes
+might influence the character of sedimentation in many ways. With a
+changing circulation of winds and currents, argillaceous material might
+be transported and deposited at one time and calcareous at another. On
+land, vegetation might predominate during part of the cycle, and the
+surface waters would then dissolve more calcium carbonate than during
+a period when vegetation became sparse. At the same time mechanical
+erosion would be impeded in the first
+instance, but would be more active in the second.
+
+It is evident that the shale was deposited more rapidly than the
+limestone, for when the principal deposit was calcareous the thickness
+is 1·5 feet, whereas, in the case of the less calcareous beds, it
+rises to 2·7 feet. In the normal shales a conservative estimate of the
+equivalent thickness would be 4 feet. Adopting the astronomical time
+unit of 21,000 years, the rate of deposit would then be of the order:
+
+    Limestone, 1 foot in 14,000 years.
+    Shale,     1 foot in  5,000 years.
+
+On this basis the 3900 feet of shale in the Benton, Niobrara and Pierre
+formations represent about 20 million years, for in this example
+the term _thickness_ seems to have a definite meaning. If the
+assumptions are correct, the duration of the whole Cretaceous period
+must therefore be considerably greater than this.
+
+
+
+
+CHAPTER IV
+
+THE WORK OF DENUDATION
+
+
+    Transference of material from land to sea—The denudation
+    ratio—Weathering of rocks—The work of chemical
+    denudation—Summary of the data—Composition of the saline
+    matter in the oceans and of that annually carried to the
+    oceans—The work of mechanical denudation—Suspended
+    and bottom loads of rivers—Mississippi not a good
+    average case—Dole and Stabler’s work in the United
+    States—Application to the whole land area—Total
+    material removed and rate of degradation of land—Marine
+    erosion—Types and quantities of sediments annually produced.
+
+The purely geological methods which have been devised to investigate
+our problem are of two kinds. The first attempts to apply a time-scale
+to the sedimentary rocks and was, historically, the earliest to be
+proposed; the second, due to Joly, deals with the accumulation of salt
+in the oceans. The one is concerned with material carried away from the
+land mechanically; the other with the material removed in solution. The
+various agents of weathering, of which rain and frost are the chief,
+disintegrate the surface rocks and supply the rivers with their load of
+detritus. The turbid condition of rivers when in flood, heavily charged
+with alluvial matter, is a familiar and convincing proof that the
+effect of erosion in conjunction with the transporting power of running
+water must always be to wear down the land areas. In the dynamical
+study of denudation and sedimentation the first essential is to know
+the rate at which the rivers are working. Measurements of their load of
+silt and dissolved salts and of their annual discharge to the sea make
+it possible to arrive at reliable estimates of their activity.
+
+Incidentally, it is useful to determine the ratio which solvent
+denudation bears to the whole. The _denudation ratio_, as it may
+conveniently be called, is the ratio of the load of dissolved material
+to the total load carried both in solution and in suspension.
+
+The amount of material removed in solution from the surface rocks is
+not quite the same as that which is carried to the oceans. A small
+proportion is abstracted from the over-ground circulation by the waters
+which sink below the surface, and while some of this is undoubtedly
+brought up again through the agency of springs, it seems possible, as
+Prof. Schwarz has boldly suggested, that certain constituents, such as
+iron and magnesium, may be permanently removed from the earth’s crust
+by downward migration. In the denudation ratio this possibility is left
+out of account as having no bearing on the study of sedimentation.
+
+A rough estimate of the denudation ratio may be made by considering the
+weathering and decay of rocks _in situ_. Soluble constituents are
+withdrawn by leaching and a residue of the more stable minerals and
+alteration products is left behind. Weathering involves not only the
+abstraction of material but also the introduction of fresh material
+from external sources. Oxidation, hydration, and carbonatisation are
+the most typical reactions, and they must be allowed for in determining
+the proportion of the original rock lost by solution. This can be done
+approximately by assuming that some element—aluminium being usually
+chosen—has remained invariable during the course of decomposition.
+From the analysis of a large number of fresh rocks and of their altered
+equivalents, it is found that on an average 30% is dissolved, leaving a
+residue of 70%. The denudation ratio ought therefore to be about 0·3.
+
+The direct determination of the work of chemical denudation requires
+three distinct sets of measurements: (_a_) the annual discharge
+of rivers into the oceans; (_b_) the analysis of their waters;
+(_c_) the measurement of their drainage areas. Mellard Reade was
+the first to point out the importance of these factors in the study of
+dynamical geology. In 1879 he collected such information as was then
+available and deduced from it the quantity of rock material annually
+removed from the whole land area, his estimate being 5280 million tons.
+Sir John Murray’s corresponding estimate of 1887, which was based on
+analyses of the waters of nineteen of the world’s principal rivers, was
+4975 million tons.
+
+Until 1909 this figure could not be improved upon, but in that year
+there was published by the United States Geological Survey the results
+of the detailed and systematic work carried out by R. B. Dole and H.
+Stabler. For the first time an attempt had been made to measure the
+discharge, drainage areas, salinity, and suspended load of all the
+important rivers of a large continental area. The estimates represent
+the averages of observations made daily for a year or longer, and in
+the case of the discharge, the measurements extended over at least
+seven years.
+
+Seasonal variations and the effects of floods are apt to be misleading,
+and a long continued series of observations is necessary if their
+relative importance is not to be over—or under—estimated. The amount
+of material in solution varies but slightly from year to year, and the
+average of one year’s results is within 10% of the true mean value. The
+annual discharge varies much more than this, and still more inconstant
+is the load of suspended material, which, in certain years, may differ
+from the average value by 50%. These figures indicate how difficult
+it is to introduce exact measurements into geology with any hope of
+finality.
+
+A summary of all the best data now available has recently been given
+by Dr. F. W. Clarke, and covers about 28 million square miles of the
+drainage areas of the earth. The details are given in the following
+table:
+
+    -----------+---------------+------------------------
+               |               |  SOLVENT DENUDATION.
+               | DRAINAGE AREA | TONS ANNUALLY REMOVED.
+    CONTINENT. | IN SQ. MILES. +---------+--------------
+               |               | PER SQ. |  FROM WHOLE
+               |               |  MILE.  |    AREA.
+    -----------+---------------+---------+--------------
+    N. America |   6,000,000   |  70·5   |   423,000,000
+    S. America |   4,000,000   |  45·5   |   182,000,000
+    Europe     |   3,000,000   |  90·0   |   270,000,000
+    Asia       |   7,000,000   |  75·0   |   525,000,000
+    Africa     |   8,000,000   |  40·0   |   320,000,000
+               |  ----------   |  ----   | -------------
+               |  28,000,000   |  61·0   | 1,708,000,000
+    -----------+---------------+---------+--------------
+
+The total land area of the globe is estimated by Murray at 55·7
+million square miles, but of this 11·5 million square miles are areas
+of internal drainage, such as the Great Basin of the United States
+and the Asiatic depressions, which contribute nothing to the ocean.
+The circumpolar regions, representing 4·5 million square miles, must
+also be left out of account, and the remaining 39·7, or say, 40
+million square miles, is that from which the oceans are fed. If the
+figures given above be accepted as typical, then the annual addition
+of material to the oceans by solution amounts to 2440 million tons.
+Some of this, however, is derived from the atmosphere—chiefly as
+carbon-dioxide. Applying the necessary correction of nearly 10%, there
+remains 2220 million tons as the amount actually derived from the
+rocks. Murray’s estimate, it will be noticed, is almost exactly twice
+that of Clarke.
+
+The composition of the saline matter carried to the oceans may be found
+by suitably weighing each analysis of river water according to the
+discharge of the latter. The general mean of all such results is given
+in the table opposite, together with the total amount of each substance
+in the ocean. The small traces of elements other than those listed are
+quite insignificant.
+
+    ---------------------+----------------------+--------------------
+                         |   ANNUAL ADDITION    | TOTAL SALINE MATTER
+          CONSTITUENT.   |   OF SALINE MATTER   |  OF THE OCEANS IN
+                         | IN MILLIONS OF TONS .|  MILLIONS OF TONS.
+    ---------------------+----------------------+--------------------
+        SiO₂             |          284         |
+        Fe₂O₃Al₂O₃       |           67         |
+        Mg               |           83         |   1,535,000,000
+        Ca               |          497         |     490,000,000
+        Na               |          156         |  12,616,000,000
+        K                |           37         |     454,000,000
+        Cl               |          138         |  22,800,000,000
+        Br               |                      |      78,000,000
+        CO₃              |          857         |      80,300,000
+        NO₃              |           22         |
+        SO               |          299         |   3,172,000,000
+    ---------------------+----------------------+--------------------
+          Total          |         2440         |  41,230,000,000
+    ---------------------+----------------------+--------------------
+      Annual discharge of river water
+        into ocean                      = 24·3 × 10¹² tons
+      Volume of ocean water             = 307,496,000 cubic miles
+      Density of ocean water            = 1·026 (mean)
+      Mass of ocean water               = 1,178,270 × 10¹² tons
+    -----------------------------------------------------------------
+
+It is obvious from a comparison of these two columns that the annual
+increment of dissolved matter is not permanently retained by the
+oceans. The greater proportion is precipitated by chemical and organic
+agencies, and either becomes incorporated with detrital material or
+goes to form individual sediments. The chief substances produced are
+calcium and magnesium carbonate, gypsum, limonite, and silica. Rather
+more than one-third of the carbonates appear to associate themselves
+intimately with sands and muds. The greater part of the remaining
+two-thirds is deposited as limestone on the continental shelves (after
+being used by various organisms in shell-making) in waters which are
+comparatively free from terrigenous sediment. The abstraction of gypsum
+from the ocean takes place at irregular intervals under suitable
+conditions of concentration. Of the limonite and silica, the chief
+precipitation takes place on the continental shelves where they
+associate themselves with the detrital sediments. The history of
+potassium is rather obscure, but on the contrary, that of sodium
+appears to be the simplest of all. That it is stored up in the oceans
+is an assumption which is granted as justifiable by most geologists.
+
+The only new factor required in order to estimate the mechanical work
+of denudation is the load of material carried by the rivers. Besides
+the silt transported in suspension, larger fragments are carried by
+rolling along the stream bottom. Measurements of the bottom load are
+lacking except in a solitary case—that of the Mississippi—in which
+it amounted to about 10% of the whole. It is difficult to define any
+precise difference between bottom load and suspended load, the former
+being only a limiting case of the latter. When the water is fully
+charged with rock debris the highest proportions are found near the
+bottom and sides, and at a point in mid-stream at about one-third the
+depth from the surface—the position of the stream lines of maximum
+velocity. In clear water the rolling power reaches its maximum value,
+for apart from fluid friction, energy is expended in no other way. Most
+rivers fall between these extremes. In making actual measurements,
+samples are taken from representative points in the river and used to
+give the average over the whole section. In the final estimate it seems
+probable that a large proportion of the bottom load is accounted for.
+Even if a correction ought to be applied it would be pedantic to do
+so except for rivers which have been under observation for several
+consecutive years, since the variation from the mean annual load is
+very great from year to year. The Nile varies by 40% and the Potomac
+by as much as 100%. In the United States the mean variation is about
+50%. With uncertain data of this kind a correction of less that 10% may
+safely be disregarded.
+
+Of all the rivers of the world, the Mississippi has been most favoured
+by measurements of the kinds required, and many estimates of the rate
+of continental degradation, of the rate of deposition of sediments and
+of the age of the earth have been based upon them. There is no doubt,
+however, that the Mississippi is working more rapidly than any other
+river of importance in North America, except, perhaps, the Colorado
+River. The high declivity in the west, the Tertiary elevation of the
+plains to which the streams are not yet adjusted, and the abundance
+of easily eroded glacial drift are all factors which promote this
+activity. In the case of rivers other than those of North America for
+which data are available, the same high rate of denudation obtains; the
+Rhone and the Po, for example, being amongst the most energetic workers
+in the world. Generalising for the whole earth from these rivers alone,
+would obviously give misleading results. The work of Dole and Stabler
+again comes to our aid, and in the following table their aggregate
+measurements for the whole area of the United States are tabulated.
+Similar evidence for four widely separated rivers is also given:
+
+    ----------------+-----------+----------------------+----------
+                    |           | MILLIONS OF TONS OF  |
+                    |           |   MATERIAL REMOVED   |
+    DRAINAGE BASINS.| AREA IN   |      PER YEAR.       | DENUDATION
+                    | SQ. MILES.+-----------+----------+  RATIO.
+                    |           |IN SOLUTION|    IN    |
+                    |           |           |SUSPENSION|
+    ----------------+-----------+-----------+----------+----------
+    United States   | 3,088,500 |   241·5   |   468    |   0·34
+    Mississippi     | 1,265,000 |   122     |   304    |   0·29
+    Nile            | 1,100,000 |    21     |    52    |   0·29
+    Uruguay         |   150,000 |     7·5   |    15    |   0·33
+    Rhone           |    34,800 |     8·5   |    36    |   0·19
+    ----------------+-----------+-----------+----------+----------
+
+Leaving out the Mississippi because of its inclusion in the United
+States and weighing each result according to the area over which it
+holds, the mean denudation ratio is 0·31, a figure which agrees very
+well with our previous estimate. If now we use the denudation ratio to
+calculate the material removed by mechanical denudation over the whole
+land surface, we should not be far from the truth. It is clear that
+if from the 40 million square miles which drain into the oceans the
+quantity of material carried in solution represents 0·3 of the total
+material removed, then, as the former amounts to 2440 millions of tons
+annually, the quantity carried away mechanically must be 5700 million
+tons. That this figure is of the right order is favoured by another
+consideration. The mean elevation of North America is very nearly that
+of all the land areas of the earth. Moreover, according to Clarke’s
+figures the rate of denudation over North America is slightly higher
+than the average for all the lands, but more closely approaches it than
+does that of any other continental area. We may therefore take the rate
+of denudation of North America as a fair average and apply it with some
+confidence to all the drainage areas of the globe. Doing this, the
+total amount of suspended material annually discharged into the oceans
+is computed to be 6000 million tons.
+
+We may sum up the work of denudation in round figures as follows:
+
+    Material annually removed in  solution      2500 million tons
+    Material annually removed in  suspension    6000    ”     ”
+                                                -----------------
+                                 Total          8500 million tons
+
+These figures may also be expressed in terms of the rate at which the
+land areas are being worn down. By solvent denudation a degradation
+of one foot in 30,000 years is implied, and by mechanical denudation,
+one foot in 12,000 years. Taking both together the average rate of
+denudation is found to be _one foot in 8600 years_. It should
+be clearly understood that individual areas may be lowered at rates
+very different from this. The maximum rate is attained in the Irawadi
+basin, one foot of which is removed in 400 years. The Po is also an
+exceptional river, and lowers its basin by one foot in 850 years.
+On the other hand, in the Hudson Bay district of North America the
+drainage only carries away one foot in 47,000 years.
+
+No minimum figure can be given, for wherever deposition of sediment
+takes place on the land areas the temporary rate of denudation locally
+becomes negative. In making these calculations, the density of rock
+material is taken as 2·6; the weight of a cubic foot as 165 lbs;
+and the weight of a cubic mile as 10,800 million tons. Although the
+surface covering of loam or earth weighs only about 100 lbs per cubic
+foot, the denser and more closely packed underlying rock need alone be
+considered, for it is by its decay and expansion that the superficial
+blanket above is produced.
+
+Our final problem is to determine the nature and quantity of the
+sediments which are ultimately formed on the continental shelves. This
+can only be done roughly, but the results will suffice to serve our
+purpose. First of all, two serious difficulties must be met before the
+way is open to take this step. So far, marine denudation has been left
+out of account. It is not yet possible to make a wholly satisfactory
+estimate of the relative magnitude of the supply of detritus captured
+directly by the sea. The unknown factor is the average encroachment
+of the sea upon the coasts. For the British Isles, Croll suggested
+an average of three feet per century, and the figure assumed by Sir
+A. Geikie about the same time was ten feet per century. A much later
+estimate by Prof. Watts places the average retreat of the English
+coast at a hundred feet per century. Along parts of our East coast
+marine erosion is still more rapid than this, the conditions being
+exceptionally favourable. On the other hand, Geikie considers that all
+the force of the Atlantic beating upon the N.W. coast of Scotland may
+not wear it away at more than one foot per century. What the average
+between these extremes may be can only be guessed at. If for
+convenience we accept Geikie’s figure as affording a likely average for
+all the coast lines of the earth (125,000 miles), and if the average
+height of the cliffs be taken as 150 feet, then the mass of material
+annually removed will be about 700 million tons.
+
+The other difficulty is concerned with the annual amount of material
+which remains in the oceans in solution, and also of that which is
+deposited on the ocean floor outside the limits of the continental
+shelves. For the former, a knowledge of the age of the oceans is
+necessary. Considering all the evidence, the amount retained at the
+present day seems to be about 200 million tons, but this is certainly
+too high as a figure representing the average increase throughout the
+history of the oceans.
+
+For the deep-sea deposits little more than a guess is possible,
+although we can now approximate to the right order of magnitude by
+considering the circulation of radium. The radium in the material
+removed from the lands is redistributed between the sediments on the
+continental shelves, the deep-sea deposits and the water of the oceans.
+Applying our present knowledge of the distribution of radium (see p.
+131) the annual mass of the deep-sea deposits is found to be about ¹/₃₀
+of the whole, i.e. about 300 million tons.
+
+The difficulties can scarcely be avoided by balancing them against
+each other. There still remain 200 million tons (700 - 300 - 200)
+to be added to the 8500 million tons already found as the total for
+sub-aerial denudation. This gives us 8700, or as an extra safeguard,
+say 9000 million, tons as the mass of sediment annually deposited on
+the continental shelves. It is unfortunate that to arrive at this
+figure an element of doubt should be introduced by associating the
+results of careful experimental work with the vague conclusions just
+arrived at. The bugbear of the whole investigation is marine erosion;
+but if it is remembered that the figures given in that connection are
+meant to be suggestive rather than final, no erroneous impression need
+be carried away.
+
+If the sediments ultimately formed are shales (20% quartz), sandstones
+(75% quartz) and limestones (75% calcium carbonate), their proportions
+will be as follows:
+
+    Shales       70% or 6300 million tons.
+    Sandstones   16% “  1440    ”     ”
+    Limestones   14% ”  1260    ”     ”
+                --------------------------
+        Total   100% =  9000 million tons.
+
+In the two following chapters the application of denudational
+statistics to the measurement of geological time will be considered.
+
+
+
+
+CHAPTER V
+
+THE SALINITY AND AGE OF THE OCEANS
+
+
+    Halley’s proposal in 1715—Joly’s application of modern
+    data in 1899—Further studies by Sollas, Clarke, and
+    Becker—Data of the problem—Corrections for disseminated
+    sodium, wind-borne sodium, human agencies, and marine
+    erosion—Uniformity not capable of proof—Importance of
+    cyclic circulation of sodium—Origin of chlorine now fixed
+    in salt—Hour-glass method applied—Land areas of the past
+    and their elevation compared with those of to-day.
+
+In 1715 the famous astronomer Edmund Halley published a paper which he
+entitled, _A short Account of the Cause of the Saltness of the Ocean,
+and of the several Lakes that emit no rivers; with a Proposal by help
+thereof to discover the Age of the World_. He showed that since the
+water removed from lakes by evaporation is perfectly fresh, “the saline
+particles brought in by the rivers remain behind, while the fresh
+evaporate; and hence it is evident that the salt in the lakes will be
+continually augmented and the water grow salter and salter.” Applying
+the same principle to the oceans, he wrote, “It is not improbable but
+that the ocean itself is become salt from the same cause, and we are
+thereby furnished with an argument for estimating the duration of
+all things.” Two hundred years ago it seemed hopeless to attempt to
+determine the annual increment of salt added to the oceans, but Halley
+used his argument “to refute the ancient notion some have of late
+entertained of the eternity of the world.” The paper was completely
+forgotten, until Dr. G. F. Becker again drew attention to it a year or
+two ago.
+
+As we saw in the last chapter, the analysis of river waters has now
+made possible a determination of the annual amount of material carried
+in solution by the rivers into the oceans. T. Mellard Reade was the
+first to contemplate the application of solvent denudation to the
+measurement of geological time, and the data he gathered together
+in support of his arguments came as a great surprise to those who
+had concentrated attention merely on the mechanical work of erosion.
+No independent advance, however, was possible until 1899, when Joly
+pointed out that of the many elements which enter into the composition
+of sea water, sodium alone tends to accumulate. All the others are
+sooner or later rejected, associating themselves with the detrital
+sediments, or forming chemical or organic sediments by their ultimate
+precipitation. Joly then proceeded to use sodium as the age-index of
+the oceans. He assumed that the annual increment Naᵣ of sodium added
+to the oceans by all the rivers of the world has remained practically
+constant throughout geological time. If Naₒ represents the total amount
+of sodium now accumulated, the ratio Naₒ/Naᵣ gives the time which has
+elapsed since the oceans first existed and denudation began to wear
+down the lands. Joly’s first estimate was from 80 to 90 million years,
+and shortly afterwards he increased this to 100 million years. Sollas
+attacked the problemafresh in 1909, and from a most careful survey of
+all the data and a detailed enquiry into every phase of the subject,
+he concluded that the most probable estimate of the age of the oceans
+would appear to lie between 80 and 150 million years.
+
+In 1910 a further study was made by Clarke and Becker. The latter
+departed from the uniformitarian basis on which all the other
+calculations had been founded. He inferred that sodium accumulation
+progressed more rapidly in the past than at present. All the original
+sodium must have been derived from igneous rocks, and Becker considers
+that at the time when the oceans were first possible the surface of the
+earth must have consisted exclusively of such rocks. At the present
+day three-quarters of the land areas are covered by sedimentary rocks
+which can supply no further important additions to the sodium content
+of the ocean. Assuming that the production of sodium has been always
+proportional to the area of igneous exposures, and that the total land
+area of the globe has averaged 80% of the present area, he finds that
+the age indicated is about 70 million years.
+
+We may now proceed to examine the problem in detail. The fundamental
+data on which the method is based may be summarised as follows:
+
+    Mean density of the ocean (Murray)              1·026
+    Volume of the ocean (Murray)    323,800,000 cu. miles
+        ”       ”       (Joly)      339,248,000    ”
+        ”       ”       (Clarke)    302,000,000    ”
+        ”       ”       (Karsten)   307,496,000    ”
+
+Clarke now accepts the latter as being the best estimate, and we
+therefore calculate that the
+
+    Mass of the ocean =                     1,178,270 × 10¹² tons.
+    Total salinity of the ocean (Dittmar)         3·5%
+    Sodium of the ocean (Dittmar)                1·08%
+    Accumulated sodium, Naₒ =                  12,600 × 10¹² tons.
+    Annual increment, Naᵣ =                    156,000,000 tons.
+
+From these values the quotient Naₒ/Naᵣ gives the age of the oceans to a
+first approximation as 80·8 million years. This figure, however, cannot
+be regarded as final. Two of the assumptions on which it is based are
+that all the sodium liberated from igneous rocks is contained in the
+ocean, and that all the sodium carried annually to the ocean has been
+liberated from such rocks for the first time. The obvious corrections
+to be applied will increase the numerator of the ratio and decrease
+the denominator, thereby increasing the age estimate. The degree to
+which the numerator must be augmented is, as far as we know, relatively
+insignificant. Saline deposits, such as those of the Stassfurt
+district, are only of trivial importance. The salt of the ocean, if
+spread regularly over the whole land areas, would form a layer about
+120 feet thick, and all the beds of rock salt which have accumulated by
+evaporation become negligible beside this vast quantity. The amount of
+sodium in ground waters and disseminated through the sedimentary rocks
+is to be taken into consideration more carefully. Marine sediments at
+the time of their formation are saturated with sea water, and, when
+raised up to form land, they must, therefore, be strongly charged with
+salt. The actual proportion of sodium abstracted from the ocean in this
+way cannot at one time be very great, probably not more than 1% of the
+whole. Throughout geological time, however, a certain amount of sodium
+has been in cyclic circulation between land and sea. A rough idea of
+the influence of this circulation on the age estimate may be gained
+from a knowledge of the total volume of the sedimentary rocks, and of
+their average pore space.
+
+Neither of these factors is yet known with the desirable accuracy, but
+as far as present needs are concerned, the total bulk of the sediments,
+excluding deep-sea deposits, may be placed at 70 million cubic miles,
+and their pore space at 10%. The latter figure is probably too low,
+for fresh sediments have a pore space of 40% to 50% of their volume,
+and in consolidated sandstones 20% is common. Many of the sediments
+have been denuded and re-deposited time after time; on the average,
+probably three times. On the other hand, if the ocean has progressively
+increased in salinity, its average sodium content must have been
+about half that of the present. Basing our calculations on these
+considerations, the total volume of sediments which have ever existed
+is about 210 million cubic miles; the pore space to be filled by sea
+water would then be 21 million cubic miles. The total amount of sodium
+precipitated within the rocks by evaporation could not therefore exceed
+420 million million tons, and at the present rate of denudation its
+removal would require nearly three million years. To what extent this
+result would be increased by absorption effects, whereby interstitial
+salt solutions are concentrated in order that they may be in
+equilibrium with normal sea water, cannot be estimated. This corrective
+factor would probably not be large.
+
+A still more important cyclic circulation is brought about by
+wind-borne sea salt. Fine particles of spray are swept from the foaming
+crests of waves by the wind and carried often many miles inland. Near
+the coast the salt blown over the land is naturally most abundant. It
+falls in sea fret and rain, and is ultimately returned to the sea in
+the drainage from the land. Fortunately, the amount of sodium supplied
+in this way can be estimated by analyses of rainwater and a measurement
+of the rainfall. As before, the cyclic sodium must be excluded from
+that entering into the denominator as primary sodium. Joly allows an
+additive time correction of 10%, Clarke of 7%, and Becker of 6%. The
+time estimate is therefore increased by a further five or six million
+years.
+
+Clarke has suggested that the present rate of sodium accumulation has
+been accelerated by human agencies. Nearly six million tons of sodium
+are annually produced as common salt, and, as sewage and chemical
+refuse, much of this is again returned to the oceans. Subtracting this
+from the denominator, the age is increased by other three million years.
+
+A number of corrections may be made to decrease the first rough
+estimate of the ocean’s age. Solvent denudation due to marine erosion
+must not be forgotten. Experiments by Joly have shown that sea water
+is several times (2½-14) more active as a solvent than fresh water. He
+attributes to its action over the tide-swept strand—covering a total
+area of about 60,000 square miles—a supply of sodium amounting to 3%
+of that derived from the normal drainage areas. This is a very liberal
+estimate, and in applying a negative correction of three million years
+we are granting all that can reasonably be claimed.
+
+Finally, there are other possibilities of uncertain magnitude which
+deserve mention. The ocean may conceivably have contained sodium
+before the fluviatile contributions commenced. By volcanic eruptions,
+sodium-bearing materials may be cast widespread over the sea.
+_Juvenile_ waters expelled from igneous magmas may presumably
+afford a supply of sodium. The importance of saline waters derived from
+the heated interior of the earth has been particularly insisted upon
+by the great geologist Suess. As a source of sodium, such waters are
+probably of little moment, for the whole amount of sodium in the ocean
+is already more than explained by the erosion of igneous rocks. Solvent
+denudation involves a loss from average igneous rock of 1·57% due to
+sodium abstraction alone. According to Clarke, the average sodium
+content of igneous rocks is 2·52%, and the amount retained by the
+detrital material which goes to make up the sediments is 0·95% of the
+original rock. Now, if the total mass of sodium which has accumulated
+in geological time is 12·6 × 10¹⁵ tons and this represents 1·57% of the
+igneous rock in which it originally occurred, it is evident that the
+mass of the igneous rocks which have been denuded away amounts to 800
+× 10¹⁵ tons. The mass of one cubic mile of rock may be taken as 10,800
+million tons, and hence the volume of igneous rock which has been
+removed is 74 million cubic miles. The sediments derived from the
+latter ought therefore to occupy a volume of the same order. A number
+of independent estimates of the volume of sediments existing on the
+land areas have been attempted, and while no great accuracy can be
+hoped for, it is significant that all agree in assigning a volume
+somewhat greater than 74 million cubic miles. The sediments hidden
+under the oceans would add still further to the total. If any reliance
+at all is to be placed on these estimates, it is clear that the sodium
+in the ocean ought to be more than it is; at any rate, there would
+appear to be little room for sodium derived from other sources, such as
+the interior of the earth.
+
+We may sum up the results of this discussion as follows:
+
+    Approximate age, Naₒ/Naᵣ         =  81 million years.
+    Correction for
+      (_a_) Disseminated Sodium      =   3 million years.
+      (_b_) Wind-borne Sodium        =   6    ”      ”
+      (_c_) Human agencies           =   3    ”      ”
+      (_d_) Marine erosion           =  -3    ”      ”
+                                     --------------------
+    Age of the oceans                   90 million years.
+
+Another assumption on which this computation is founded must now be
+examined; that is, the practical uniformity of the annual addition of
+sodium throughout the period involved. Little weight can be attached to
+the argument that the source of supply has been gradually impoverished
+in alkalies, for the soils from limestones, which are among the poorest
+of the alkali-bearing rocks, may contain more sodium than do the soils
+derived from granites. The sedimentary rocks being less able to resist
+erosion are more rapidly disintegrated and removed than are the igneous
+rocks. The composition of streams considered in relation to the rocks
+which they drain is of interest here. Hanamann has shown that in the
+Elbe and its tributaries three times more sodium is carried away from a
+square mile of Cretaceous sediments than from an equal area of granite.
+In the same connection, it is well known that the waters flowing
+through stratified rocks carry more salt than those from igneous rocks.
+The greater exposure of the latter in former land areas, if such were
+the case, would certainly not contribute a greater sodium income to
+the ocean than if sedimentary rocks prevailed. Joly considers that an
+approximate uniformity has been preserved whatever the distribution of
+rock types may have been. It would not, however, be difficult to prove
+by actual analyses that a greater area of igneous rocks would result in
+a reduction of the sodium increment, and that the present rate may be
+too high because of the predominance of sedimentaries.
+
+This unexpected conclusion raises the question of the validity of the
+method at its most critical point. Can we be sure that the cyclic
+circulation of sodium has been taken sufficiently into consideration?
+The only source to which the anomalous proportion of sodium from
+sedimentary rocks can be traced, apart from the factors already dealt
+with, is constituted by the ground waters. These waters often contain
+minute quantities of salt of which the origin is very obscure. Whence
+came the chlorine? Igneous rocks themselves only contain about 2% of
+the chlorine necessary to convert the liberated sodium into salt. The
+emission of chlorine from volcanoes and solfataras probably affords
+the necessary supply, but most of this never reaches the ground waters
+directly. Becker, dealing with the same difficulty in the case of river
+water, calculates that 40% of the annual sodium increment is combined
+with chlorine of which the origin cannot be traced. He accordingly
+rejects this amount as not being of normal or primary origin. If it
+has all been derived from the oceans, which he regards as an extreme
+possibility, it must be subtracted from the apparent income, since it
+is simply a circulation of capital.
+
+A _maximum_ figure for the age of the oceans (still on the
+assumption of uniformity) ought theoretically to be attainable by
+accepting the whole of the sodium-chloride of the rivers as cyclic. We
+have the following figures:
+
+    Chlorine                        = 138 million tons.
+    Sodium combined with chlorine   =  87    ”      ”
+    Sodium uncombined with chlorine =  69    ”      ”
+                                      -----------------
+        Total Sodium, Naᵣ           = 156 million tons.
+
+The unchloridised sodium implies an age of 180 million years, an
+estimate which would in general be condemned as excessive.
+
+The difficulties presented by sediments and ground waters are almost
+insuperable, and it may be safer to adopt a means by which they can
+be entirely disregarded. The sodium lost from igneous rocks amounts
+by mass to 1·57% of the latter. Igneous and metamorphic rocks are at
+present exposed over one-fifth of the drainage areas, or 8,000,000
+square miles. Many of the metamorphic rocks are partially or wholly
+of sedimentary origin, and ought not to enter into the computation.
+We have already seen that the average rate of denudation is one foot
+in 8600 years, and at this rate, one cubic mile of primary rock, or
+10,800 million tons, would be denuded away in 4·54 years. In one year
+the supply of sodium would therefore be 37 million tons, and the time
+required for the accumulation of the existing store of sodium in the
+oceans would be 340 million years.
+
+We meet with a curious discrepancy at this point. The actual amount
+of unchloridised sodium is 69 million tons, while that which is drawn
+from the igneous rocks cannot exceed 36 million tons. In each case
+sub-aerial denudation alone is being considered, so that the failure
+to take marine denudation into account does not affect the matter.
+The figures imply that a great deal of unchloridised sodium is drawn
+from the sedimentaries. Even if the extreme assumption is made for the
+moment, that the igneous rocks lose all their sodium, 2·52%, the annual
+supply could only reach 60 million tons. The discrepancy is evidently
+due to the facts that sediments freshly formed from primary rocks
+retain a considerable percentage of sodium, and that it is only after
+the material has been re-assorted, perhaps several times, that the
+element is withdrawn to the extent indicated by Clarke’s average
+figures. At the present day, even when the igneous rocks have been
+deprived of 37 million tons of sodium, the sedimentary rocks, to bring
+up the total to 69 million tons, must lose more than half of their
+primary sodium. It is interesting to observe that if all the sodium
+now carried each year to the oceans—156 million tons—were derived
+directly from the rocks, igneous and sedimentary, the latter would be
+obliged to lose nearly twice as much sodium as they actually contain!
+This remarkable conclusion indicates either that our statistics of
+the annual production of sediments are hopelessly wrong, or else that
+the chloridised sodium is almost wholly cyclic. The latter inference,
+supported as it is by the impossibility of otherwise accounting for the
+chlorine, thus receives further support.
+
+In the application of the above data to the age question, it has been
+tacitly assumed that the present exposures of primary rocks are neither
+greater nor less in area than the average of such exposures since the
+oceans began.
+
+It is impossible to know what the average may have been, for while
+the original lands must have been entirely formed of igneous or
+pseudo-igneous planetesimal material, it is equally certain that
+their area was but a fraction of that of the present land areas. The
+evolution of the earth’s surface features has tended to intensify the
+difference between the ocean depths and the mountain heights. The ocean
+basins have gradually deepened and become more stable, and their
+relative permanence is generally admitted. The lands are now more
+extensive than ever they have been; initially it is probable that only
+low and scattered islands emerged from the shallow primitive seas. We
+are faced here with many vague problems. The volume of the seas may
+have been less than it is to-day; the original rocks were probably not
+granitic in type, and were certainly poor in sodium; carbon-dioxide
+seems to have been the chief atmospheric companion of nitrogen, and
+solvent denudation would be correspondingly more vigorous. How far
+all these considerations affect the point at issue cannot be decided.
+To discuss them would lead us into a complex maze of speculation. The
+original basis of our calculation may afford as near an approach to
+the truth as could be arrived at by any other reasonable hypothesis of
+changing land areas, and of their composition.
+
+On this view it is possible to calculate a _minimum_ figure for
+the age of the oceans, but it must be remembered that the results
+based on an assumption, which is merely a uniformitarian guess, are
+themselves equally uncertain. If the igneous rocks had lost all their
+sodium, we have already found that the annual supply would be 60
+million tons, and the sediments would be destitute of that element.
+The age would then be at least 210 million years. The contradiction
+between this minimum figure and the maximum deduced from the total
+unchloridised sodium, viz. 180 million years, is explicable on one or
+both of two further possibilities, that the average exposure of igneous
+rocks in the past has been greater than that of the present day,
+or that the amount of primary sodium now being derived from the
+sedimentary rocks is considerably above the average for the past. Our
+interpretation of the data is made particularly difficult because
+of the widespread covering of glacial detritus, rich in felspathic
+constituents and easily eroded.
+
+The contradictory results become still worse when it is remembered that
+the rate of denudation—one foot in 8600 years—is probably too high to
+be safely applied to areas of igneous rocks. Analysis of river waters
+draining such areas indicate a rate which is only about a half of the
+above. But even this correction is surpassed in importance by one
+arising out of the possibility that the present standard of measurement
+may be misleading in not being typical of geological time. The mean
+height of the drainage areas is subject to much fluctuation. By
+denudation it is steadily reduced; by earth movements, and particularly
+during the periods of intense diastrophism, it may become unusually
+great. It seems not unlikely that we are now near a period of extreme
+continental elevation, and that the geological processes which are
+thereby quickened up, cannot be accepted as affording a true standard.
+This suggestion will be dealt with further in the next chapter.
+
+The high figures—210-340 million years—given above, must not be
+supposed to possess any serious value. The whole discussion merely
+serves to betray the uncertainty of the method and the doubtful
+applicability of even the most accurate data. For the present we can
+only conclude that our knowledge of the part played by sodium and
+chlorine in the constant redistribution of the materials of the earth’s
+crust is still lamentably imperfect, and that quantitative deductions
+drawn from it must be regarded as being purely provisional.
+
+
+
+
+CHAPTER VI
+
+SEDIMENTATION AND GEOLOGICAL TIME
+
+
+    The maximum thickness of the sedimentary rocks—Rate
+    of deposit—Uniformitarian basis of the method as
+    usually applied—Arguments against the validity of this
+    assumption—Present a period of land extension and
+    continental elevation—Present geological rates not
+    true standards—Ideal sedimentation curve and rates
+    of deposit—Difficulties in the application of the
+    data—Summary of time estimates based on this method—The
+    hour-glass method applied to the accumulation of sediments
+    and of calcium carbonate.
+
+The most familiar method of estimating geological time is based upon
+the total observed thickness of stratified rocks and the rate at which
+they may have been deposited. Our knowledge of the so-called maximum
+thickness of each of the stratigraphical systems has been carefully
+summarised by Sollas, to whom we owe the following table.
+
+_Maximum Thickness of the Geological Systems._
+
+                              FEET
+    Recent and Pleistocene    4,000
+    Pliocene                 13,000
+    Miocene                  14,000
+    Oligocene                12,000
+    Eocene                   20,000
+                             ------
+                                     63,000 feet.
+    Cretaceous               44,000
+    Jurassic                  8,000
+    Triassic                 17,000
+                             ------
+                                     69,000   ”
+    Permian                  12,000
+    Carboniferous            29,000
+    Devonian                 22,000
+                             ------
+                                     63,000   ”
+    Silurian                 15,000
+    Ordivician               17,000
+    Cambrian                 26,000
+                             ------
+                                     58,000   ”
+    Algonkian                82,000  82,000   ”
+    Archean                    ?       ?
+                                    -------------
+    Total                           335,000 feet.
+                                    -------------
+
+The rate of deposit of sediment on the ocean floor is a factor over
+which there has been much dispute. The rate varies between very wide
+limits, according to distance from the shore and from the mouths
+of great and active rivers. What is generally sought is to give an
+estimate which will correspond to the maximum thickness of accumulated
+material, i.e. an estimate of the average maximum rate of deposit. The
+same rate is then applied in turn to the whole of the geological column
+in the hope that no serious error will be introduced by the assumption
+of uniformity. This attitude was taken up in defence against the
+attacks of Kelvin and his followers. The tendency to invoke more active
+geological agencies in the past, greater floods and tidal waves, a more
+stupendous upheaval of mountains and more violent volcanic eruptions,
+did not commend itself to most geologists. Geikie stated the case very
+clearly in his eloquent address of 1892, when he affirmed that “the
+geological record furnishes a mass of evidence which no arguments drawn
+from other departments of Nature can explain away, and which, it seems
+to me, cannot be satisfactorily interpreted save with an allowance of
+time much beyond the narrow limits which recent physical speculation
+would concede.” But while the conception of greater activity in the
+past met with little favour, the assertion of uniformity was as far as
+geologists dared to go. No one suggested that we might be living in an
+age of more than average activity. Yet there are many reasons which
+favour this hypothesis in preference to the alternative views.
+
+That the average land area of the past was less than that of to-day has
+already been stated. According to the palæo-geographical researches of
+Mr. C. Schuchert, the mean area of North America since Cambrian times
+has been four-fifths of its present area. In the case of the other
+continents a smaller fraction would probably be more representative. Of
+very much greater importance is the fact that the average height of the
+land areas above sea-level has often been less than it is, so that the
+present average is excessive when viewed from the broader standpoint of
+geological time. The chief defect in the time estimates based on the
+rate of sedimentation lies, according to Chamberlin, in the too full
+dependence on standards derived from the geological processes now in
+action. It is tacitly assumed that current rates are representative,
+or that the departure from the mean rate is not such as to involve any
+grave error. Joly, for example, in discussing the divergent evidence of
+geological processes and radioactive minerals, points out that to bring
+the different methods into agreement we must assume “that the rivers
+are now bearing to the sea about 14 times the average percentage of
+the past—_not less_ than 9 times.” Then he says, “It seems quite
+impossible to find any explanation of such an increase.”
+
+In the present high relief of the earth’s surface at least a partial
+explanation may be found. Prof. Chamberlin writes in a private
+communication to the author: “Because of the relatively high gradients,
+the wash of clastic material from the slopes and its deposition in
+the basins, as well as the transfer of salts to the sea, are to-day
+more rapid than in average times. We seem to be at, or near, one of
+the great extremes of intensification of the processes of solution and
+degradation. And so, whether conclusions are based upon degradation
+and clastic deposition, or upon solvent action and the accumulation of
+solutes in the sea, the present rates are high rates, and if these are
+made the basis of time estimates, the estimates are minimum ones. There
+are abundant evidences that periods of base-levelling have occupied
+a notable part of geological time. There is cogent evidence that the
+Archean and Proterozoic (Algonkian) terranes were reduced well towards
+base-level in pre-Cambrian times, and that subsequently extensive
+base-levelling clearly seems to have intervened at repeated intervals.
+To me the evidence seems to support the existence of a dozen or a score
+of stages of peneplanation, some of which appear to have made a notable
+advance toward complete base-levelling.”
+
+During those intervals, when the average continental height was low,
+denudation and deposition would proceed very slowly. How slowly,
+we have no adequate means for determining. A very careful study of
+drainage basins with reference to their mean elevation would be a step
+towards a sounder method than it has yet been possible to apply. That
+the departure from present rates, in past time, may have been very
+considerable, is indicated crudely by a very simple calculation. It
+has been found experimentally that the carrying power of water varies
+as the sixth power of its velocity. Roughly, we may say it varies as
+the sixth power of the mean square of the heights of the drainage
+basin from which it finds its way to the sea. If this were strictly
+true, then, if the present day contours of the land were reduced to
+half their value, the power of removing material would be reduced to
+less than one four-thousandth. Of course, other factors would begin to
+operate which would prevent the attainment of any variation as extreme
+as this. Nevertheless, our faith in the value of present standards as
+applied to geological time cannot but be seriously shaken. Chamberlin
+feels warranted in thinking “that the substitution of mean velocities
+of denudation, deposition, and saline accumulation, if it could be made
+to approach the realities of the case, would have the effect of
+multiplying by a considerable figure the best estimates that have been
+made on the basis of current velocities.” Other factors tending to
+increase the age estimate are numerous, but comparatively insignificant
+beside those already briefly discussed.
+
+In the last chapter we concluded with an estimate of the quantity of
+different types of sediment which are now annually deposited.
+
+    Shales        6300 million tons.
+    Sandstones    1440    ”      ”
+    Limestones    1260    ”      ”
+                  ------------------
+                  9000 million tons.
+
+If it be assumed that all the arenaceous sediments form littoral,
+deltaic and estuarine types, i.e. that they are concentrated over an
+area of say 100,000 square miles, the rate of accumulation would be one
+foot in 150 years, or dealing only with fresh unconsolidated sediment,
+of one foot in about 100 years. But these figures are obviously too
+high, for a great deal of sandstone comes under shallow water marine
+types. Fortunately, in the deltaic deposits of two important rivers
+human remains of recognised age are found buried; and from measurements
+of the thickness in each case it is known that the Nile has deposited
+loose sediment at one foot in 320 years, and the Po at one foot in 174
+years.
+
+We have here, as in all deltaic deposits, a mode of growth analogous to
+that of the glacial clays studied by De Geer. It by no means follows
+that these rivers will continue to raise their beds at the same rates,
+for the main growth of deposit is not upwards, but seawards.
+
+To get a rough idea of the rate of sedimentation, the ideal section
+opposite has been constructed. The continental shelves are assumed
+on the average to be representable as a band of 100 miles in width
+fringing a coastline of 100,000 miles. The average thickness of a
+deposit laid down according to this plan would be about 0·4 of the
+greatest thickness, the latter, on the scale of the diagram, having
+reached 400 feet. In the particular case illustrated the land is slowly
+sinking, and as the sea encroaches upon it the deposits gradually
+overlap.
+
+If deposited over one square mile, as consolidated sediments of density
+2·5, our 9000 million tons of material would form a rectangular mass
+4570 feet in thickness. Being deposited over the ten million square
+miles of the continental shelf, the average thickness of the layer is
+0·000457 feet, corresponding to a rate of deposit of one foot in 2200
+years. The maximum rate is therefore one foot in 880 years. If this
+figure be applied to the total thickness of the geological column,
+then, disregarding its imperfection, the time implied would be about
+300 million years.
+
+The distribution of conglomerate, sandstone and shale is sufficiently
+indicated in the diagram. It is difficult to know how to distribute the
+argillaceous and calcareous types. They are mutually exclusive, for
+limestone cannot form by organic agencies in places where mechanical
+detritus is being deposited. They are therefore taken together, on the
+basis that where one is not being formed the other is.
+
+[Illustration: FIG. 11.
+
+Section illustrating the formation of Sediments on the Continental
+Shelf while the latter is being slowly depressed.]
+
+The following table gives the rates of deposit at various distances
+from the shore, for the case illustrated in Fig. 11:
+
+    -------------------------+--------------------------------
+                             | YEARS FOR DEPOSIT OF ONE FOOT.
+          DISTANCE FROM      +----------------+---------------
+         SHORE IN MILES.     |     FRESH      | CONSOLIDATED
+                             | DENSITY = 1·8. | DENSITY = 2·5.
+    -------------------------+----------------+---------------
+               {  0          |                |
+               { 10          |      2,780     |    2,000
+    Sandstones { 20 }        |      1,670     |    1,200
+               { 30 }        |      1,120     |      880
+               { 40 }        |      1,430     |    1,030
+                 50 }        |      2,280     |    1,660
+                 60 } Shales |      5,210     |    3,750[3]
+                 70 }        |     10,420     |    7,500[4]
+                 80 }        |     13,900     |   10,000[5]
+                 90 }        |     20,850     |   15,000[6]
+                100 }        |     41,700     |   30,000
+    -------------------------+----------------+---------------
+
+[Footnote 3: Cf. Rates of deposit of the Cretaceous sediments of
+Colorado, p. 47.]
+
+[Footnote 4: Cf. Rates of deposit of the Cretaceous sediments of
+Colorado, p. 47.]
+
+[Footnote 5: Cf. Rates of deposit of the Cretaceous sediments of
+Colorado, p. 47.]
+
+[Footnote 6: Cf. Rates of deposit of the Cretaceous sediments of
+Colorado, p. 47.]
+
+These figures, however, have but little value, for there is no
+single law of deposition. The effects of ocean currents, of earth
+movement, and of the presence or absence of great rivers should all
+be considered, and they provide a problem so complex that as yet it
+is hopelessly beyond a general solution. Difficulties are encountered
+at every stage; not only are the estimated rates of doubtful value,
+but their application is discredited by our ignorance as to what
+constitutes the real maximum thickness of sediments.
+
+As already indicated, the latter difficulty is due to the tendency for
+successive beds to overlap while the cycle of deposition is running
+its course. As was admirably stated by Prof. Watts in his Presidential
+address to the Geological Society in 1911, deltaic deposits gradually
+extending seawards are more characteristic during periods when the
+land is being elevated relative to sea-level. On the contrary, during
+periods of depression estuarine conditions prevail and the beds grow
+landwards.
+
+The same problem has been attacked by Sederholm from a rather different
+point of view. He says, “As the layers successively formed cover each
+other like scales or roof-tiles, no vertical section contains them all.
+If we mean by maximum thickness the sum of the maxima of the layers
+formed in successive years, it certainly measures millions of feet.”
+In this case the rates of deposit as ordinarily found would not, of
+course, be applicable.
+
+Before proceeding farther, it may be well to review the various
+estimates of time which have been founded upon the geological method.
+The earlier geologists believed that the sediments were deposited
+widespread over the ocean floor and the rate of deposition was
+therefore taken as even less than that of denudation. Then came the
+_Challenger_ expedition in 1872-5, and it became certain that
+the formation of all except the less important deep-sea deposits
+takes place almost entirely on the submarine continental shelves. A
+considerable modification of the estimated rates of deposition was then
+made necessary and the time periods were correspondingly shortened.
+
+    ------+--------------+------------+-----------+----------
+          |              |            |  RATE OF  |
+          |              |  MAXIMUM   |  DEPOSIT  |  TIME IN
+    DATE. |    AUTHOR.   | THICKNESS  | YEARS FOR | MILLIONS
+          |              |  IN FEET.  | ONE FOOT. | OF YEARS.
+    ------+--------------+------------+-----------+----------
+    1860  | Phillips     |  72,000    |   1332    |     96
+    1869  | Huxley       | 100,000    |   1000    |    100
+    1871  | Haughton     | 177,200    |   8616    |   1526
+    1878  | Haughton     | 177,200    |     ?     |    200
+    1883  | Winchell     |     —      |     —     |      3
+    1889  | Croll        |  12,000[7] |   6000[8] |     72
+    1890  | de Lapparent | 150,000    |    600    |     90
+    1892  | Wallace      | 177,200    |    158    |     28
+    1892  | Geikie       | 100,000    | 730-6800  | 73-680
+    1893  | McGee        | 264,000    |   6000    |   1584
+    1893  | Upham        | 264,000    |    316    |    100
+    1893  | Walcott      |     —      |      —    |  45-70
+    1893  | Reade        |  31,680[9] |   3000[10]|     95
+    1895  | Sollas       | 164,000    |    100    |     17
+    1897  | Sederholm    |     —      |      —    |  35-40
+    1899  | Geikie       |     —      |      —    |    100
+    1900  | Sollas       | 265,000    |    100    |     26·5
+    1908  | Joly         | 265,000    |    300    |     80
+    1909  | Sollas       | 335,800    |    100    |     80
+    ------+--------------+------------+-----------+----------
+
+[Footnote 7: Spread evenly over the land areas.]
+
+[Footnote 8: Rate of denudation.]
+
+[Footnote 9: Spread evenly over the land areas.]
+
+[Footnote 10: Rate of denudation.]
+
+Most of these estimates are little more than rough guesses. We do not
+know how much of the story is lost to us, or how much is hidden away.
+The time which has usually been regarded as expressing the geological
+requirements most adequately is 100 million years. The fanciful figures
+arrived at by Winchell, and McGee (who suggested a probable age of 6000
+million years) are merely illustrations of how the data could be
+twisted to produce impossibly extreme results. The latest estimate, due
+to Sollas, includes an allowance of 25·4 million years for the duration
+of pre-Cambrian time—the same period as that which has apparently
+elapsed since. A further allowance is made for unconformities, those
+gaps in the sequence which are unrepresented by sediment. Taking the
+great unconformities as probably numbering six, each being equivalent
+to 40,000 feet of sediment, 24 million years are added. For minor
+unconformities and interruptions in the record other 5 millions are
+granted and the total is thus brought up to 80 million years.
+
+In an attempt to free ourselves from the difficulties with which
+this method is beset, we may adopt a mode of procedure similar to
+that followed in the last chapter. It was there assumed that the
+total volume of the sediments which have ever existed amounts to some
+210 million cubic miles. The present annual supply of sediment when
+ultimately compressed and consolidated would occupy 0·83 of a cubic
+mile. If the present rate of accumulation were reliable, geological
+time would then be of the order 250 million years. A still nearer
+approach to the truth may be made by calculating on a uniformitarian
+basis how long the existing sediments, which we placed at 70 cubic
+miles, have taken to form. From the 8,000,000 square miles of igneous
+and metamorphic rocks, one cubic mile would be denuded away in 4·54
+years, which implies that one cubic mile of consolidated sedimentaries
+would be formed in about five years. The age then works out at 350
+million years. Making a further correction for the slower rate of
+denudation of igneous rocks, this figure may perhaps be doubled.
+Finally, there is the correction for average rate in place of present
+rate, and to what extent this would increase the estimate it is
+impossible to say.
+
+We may revert to the maximum thickness of the sedimentary rocks to
+support the estimate of the total volume of sediments which has ever
+existed. On the basis of the sedimentation curve, the sediments have
+been deposited on an area of 10 million square miles, and if laid down
+everywhere at their average maximum thickness, 60 miles, they would
+cover about 0·4 of that area. The total volume which can ever have
+existed, leaving unconformities out of the question, is therefore, 60 ×
+10,000,000 × 0·4 cubic miles, or 240 million cubic miles.
+
+Finally, a crude estimate may be based on the amount of calcium
+carbonate which has accumulated in geological time. Several estimates
+of the volume of limestones in existence have been made, e.g.:
+
+    Dana        18·40 million cubic miles.
+    Reade       10·00    ”      ”     ”
+    Van Hise     6·25    ”      ”     ”
+
+The limestones now forming make up 14% of the total sediments which
+collect on the continental shelves. On the land the proportion must be
+lower than this, because limestone is denuded at a rate well above the
+average. If we take limestone formations at 10%, the volume would be
+about 7 million cubic miles, a figure not far from that of Van Hise.
+The calcium carbonate may now be estimated. Limestones contain on an
+average 75% and shales and sandstones together about 7%. The total
+volume, calculated at density 2·6, would therefore be in round figures
+10 million cubic miles.[11] Igneous rock contains 3·43% of calcium, and
+if in the process of denudation all of this is dissolved and removed,
+the present rate of production of calcium would be equivalent to 1
+cubic mile of calcium carbonate in 32 years, on the same basis as in
+previous calculations. The time estimate at this rate would be 320
+million years.
+
+[Footnote 11: Leith finds 12·5-22 million cubic miles.]
+
+We may now sum up our various results as follows:
+
+    1. _Accumulation of Sodium._                 MILLION YEARS.
+        (_a_) Uncorrected quotient Naₒ/Naᵣ            80·8
+        (_b_) Partially corrected Naₒ/Naᵣ               90
+        (_c_) Unchloridised sodium alone               180
+        (_d_) Primary sodium alone                     210-340
+
+    2. _Accumulation of Sediments._
+        (_a_) Maximum thickness                        300
+        (_b_) Total volume which has ever existed      250
+        (_c_) Total volume now existing                350
+
+    3. _Accumulation of CaCo₃._
+        (_a_) Total volume now existing                320
+
+Not one of these estimates is to be regarded as final; the
+uncertainties are too many and too great. The whole trend of this
+chapter has been to show that whatever may be the true reading of the
+hour-glass of denudation and deposition, it ought probably to be very
+much higher than has been generally assumed.
+
+
+
+
+CHAPTER VII
+
+RADIOACTIVITY
+
+
+    Geological application—Röntgen rays—Becquerel
+    rays—Mme. Curie and the discovery of Radium—The
+    gold-leaf electroscope—The nature of α-, β- and
+    γ-rays—Helium and its production from radium—The
+    heat output of radium—Transformation of the radium
+    atom—Disintegration theory—The half-life period of
+    radium and its generation from uranium—The uranium,
+    thorium and actinium families—Direct measurement of
+    the heat output—Radioactivity independent of external
+    influences—Pleochroic haloes—Measurement of radium in
+    rocks and minerals.
+
+In the limited space at our disposal, only a brief outline of the
+salient facts of the new science of radioactivity can be given. It is
+necessary to give some account of these recent discoveries because
+of their immediate application to the study of the earth itself.
+In a science like geology, the function of which is to study the
+consequences of energy transformations in the earth’s crust during the
+long ages of her gyrations through space, the recognition of sources of
+energy previously undreamed of is a stimulant to research which must
+profoundly affect the interpretations of the phenomena we observe. For
+our present purpose it will be necessary to review only those facts
+which have a bearing on the question of the earth’s age, and of its
+thermal history.
+
+In 1895 Röntgen gave his first account of _A New Kind of
+Radiation_. This extraordinary radiation, now familiar to us as
+the X, or Röntgen rays, revealed itself by its remarkable property of
+passing through objects which are entirely opaque to ordinary light.
+It was found, for example, that a photographic plate was not protected
+from its influence by being wrapped in black paper, but was affected
+just as though it had been exposed.
+
+This discovery awakened the deepest interest amongst all scientific
+workers, and the idea arose that phosphorescence and the Röntgen
+rays might in some way be vitally connected. Certain substances,
+after being exposed to sunlight, are able to shine in the dark with
+a phosphorescent light, and it was this radiation which was examined
+from the new point of view. Working on these lines, with uranium salts,
+Becquerel found, almost by accident, that they gave out rays which
+were capable of penetrating black paper and making themselves evident
+by their effect upon a photographic plate wrapped within it. This
+observation in 1896 marks the commencement of the harvest of wonderful
+discoveries which have revolutionised our conception of the structure
+of matter.
+
+[Illustration: FIG. 12.
+
+Taken in the dark by its own rays.]
+
+[Illustration: FIG. 13.
+
+Taken in ordinary daylight.
+
+PHOTOGRAPHS OF PITCHBLENDE.]
+
+The emission of rays was found to be an inherent property of uranium
+and entirely independent of the phosphorescence exhibited by certain
+of its compounds. Physical and chemical changes made no difference;
+the radioactive properties evidently belonged to the atom itself, for
+they could be detected under whatever conditions uranium happened to
+be present. Mme. Curie at once began an exhaustive examination of all
+the other known elements, and came to the conclusion that thorium alone
+possessed radioactive properties similar to those of uranium. In the
+course of her researches, she found that uranium-bearing minerals such
+as pitchblende (uraninite) were far more active in their emission of
+rays than could be accounted for by the uranium present. Systematically
+following up so significant a fact, she traced the activity to the
+bismuth and barium separated from these minerals. In 1898 two new
+elements were announced. One, associated with bismuth, was called
+Polonium; the other, found in minute quantities with the barium, was
+appropriately named Radium.
+
+The spontaneous radiations of these elements, collectively known as the
+Becquerel rays, were soon distinguished from the Röntgen rays by their
+greater complexity. Their analysis is largely due to the scientific
+genius of Rutherford, who has classed them into three well-marked
+types, the Alpha or α-, Beta or β-, and Gamma or γ-rays. The instrument
+chiefly employed in their detection is the gold-leaf electroscope,
+which not only is simple in construction, but is capable of extreme
+sensitiveness. Under ordinary conditions the air is a good insulator,
+and a charged electroscope loses its charge only very slowly. However,
+if radium is brought near the instrument, the discharge proceeds much
+more rapidly, the effect of the Becquerel rays being to ionise the
+air and so render it conductive to electricity. In the electroscope
+this effect can be readily observed and accurately measured, for the
+leaf falls at a regular rate, which depends on the intensity of the
+radiation. The sensitiveness of this method so far surpasses that of
+the most delicately adjusted balance that by its means a quantity of
+radium can be detected which would need to be multiplied thousands of
+millions of times before the balance would turn to its weight.
+
+It is easy—by interposing between the electroscope and the radium a
+gradually increasing thickness of suitable material such as thin sheet
+aluminium—to establish the existence of three kinds of rays which
+differ greatly in their power of penetrating matter. The γ-rays are, on
+the average, about a hundred times more penetrating than the β-rays,
+and these in turn are equally the superior of the α-rays. In each case
+the penetration in different materials depends approximately on their
+density. The three types can also be distinguished by their behaviour
+in a strong magnetic field. Giesel showed that the β-rays were
+deflected in such a way as to indicate that they consisted of particles
+carrying a negative charge of electricity. The α-rays were much more
+difficult to deflect, but Rutherford successfully turned them from
+their path by applying a very intense field, and from the direction
+of their deflection he concluded that they consisted of positively
+charged particles. The γ-rays have, however, resisted all attempts made
+to alter their course. Their real nature is not yet beyond dispute,
+and from the great similarity between their properties and those of
+the Röntgen rays they are generally considered to be, like the latter,
+either electro-magnetic pulses in the ether, or uncharged corpuscles of
+a kind not yet understood.
+
+When an electric discharge is passed through a high-vacuum tube, rays
+are emitted from the cathode which, on reaching the walls of the
+tube, produce a yellowish-green phosphorescence. The cathode rays
+are identical with β-rays in every essential respect, and both are
+proved to be tiny, negatively charged particles, called electrons. The
+velocities of both cathode and β-particles are inconceivably high;
+in the latter case even approaching that of light. Now Röntgen rays,
+whatever may be their true nature, are set up by the sudden stoppage of
+electrons when they impinge upon the anti-cathode of a vacuum tube. In
+the same way it is supposed that the β-rays, by their sudden expulsion,
+give rise at the same moment to γ-rays. It is a significant fact in
+this connection that the β- and γ-rays are always associated together,
+whereas the α-ray may be quite independent.
+
+The story of the brilliant researches which culminated in the
+measurement of the mass of an electron, and of the charge it carries,
+is one of the most fascinating in the annals of science. But here we
+must be content with the bare statement that the electron has only
+¹/₁₇₀₀ of the mass of a hydrogen atom. The application of similar
+methods to the α-particle has demonstrated that it is of atomic
+dimensions, and consists either of a hydrogen atom with a single ionic
+charge, or of a helium atom with twice that charge. Other evidence
+decides conclusively in favour of the second alternative.
+
+Of all the elements, helium has probably the most interesting history.
+It was first discovered in the sun during the eclipse of 1868, but it
+was not until 1895 that it was detected in terrestrial materials. In
+that year Sir W. Ramsay identified it in uranium- and thorium-bearing
+minerals by means of its highly characteristic spectrum. Even then,
+before radioactivity had been recognised, the association of helium
+with these elements had forced itself upon his notice. In 1902 the
+genetic relationship between helium and certain of the radioactive
+elements was predicted by Rutherford and Soddy. During the following
+year Ramsay and Soddy working in conjunction sought for, and actually
+observed, its generation from radium. Using a radium preparation from
+which helium was at first entirely absent they were able to prove,
+with the aid of the spectroscope, that in the course of a few months
+sufficient of the gas had been generated to be identified. This
+important discovery has received abundant confirmation during the last
+decade, and to-day we even know the number of helium atoms which a gram
+of radium emits in a given time. Moreover, the production of helium has
+been demonstrated from uranium, thorium and actinium, and from most of
+the other radioactive elements which are characterised by the emission
+of α-rays. The rate of generation of helium will be considered in more
+detail in Chapter X, where it finds an important application.
+
+An observation of fundamental importance was made by Curie and Laborde
+in 1903 when they discovered that radium is able to maintain a
+temperature above that of its environment. The source of this emission
+of heat lies in the kinetic energy of the Becquerel rays. Projected
+from radium, they are sooner or later completely absorbed by the
+matter through which they penetrate. Simultaneously, their energy is
+given up to the molecules with which they collide, and it therefore
+reappears as heat. By far the greater proportion—over 85%—of the
+energy is carried by the relatively heavy α-particles which move with
+velocities nearly one-tenth that of light. Knowing their masses and
+velocities, and the number liberated per hour from a gram of radium, it
+is a simple dynamical problem to calculate their total kinetic energy.
+Expressing this quantity in heat units, it is found to be equivalent
+to an hourly production of 113 calories. (Ap. A, p. 177.) As we shall
+see later, this figure is in close agreement with the results of direct
+measurements.
+
+The most remarkable feature about these phenomena is that they appear
+to continue unceasingly. Year after year the spontaneous production of
+helium goes on, accompanied by a steady evolution of heat. But what
+of the atoms that remain? They evidently cannot continue to be the
+same element after having given up part of their energy and expelled
+from themselves the material particles of the α- and β-rays. A close
+examination reveals the genesis of a new element—a gaseous substance
+known as radium emanation. Its atom represents the residual fraction
+of the radium atom after the separation of a single α-particle. The
+emanation is highly unstable; so rapidly does it give up energy and
+liberate helium that its original intense activity decreases by half
+every four days. In its place arises another product, radium A, of
+still more transitory existence. A long succession of similar
+transmutations has been traced, each accompanied by a setting free of
+energy.
+
+In 1902 Rutherford and Soddy advanced the theory of the disintegration
+of the radioactive atoms. The radium atom is essentially unstable and
+ultimately breaks up, explosively emitting α- and β-particles. Each
+atom has a certain expectation of life which distinguishes it from the
+atoms of other radioactive substances; but such is the distribution
+of instability that a constant proportion of the total number of
+atoms present is always breaking up. Out of a million atoms of radium
+a definite number disintegrates each second, and the proportion has
+been proved to be invariable in every case it has been possible to
+test. From element to element it is this proportion, and therefore the
+average promise of life, which varies. An equilibrium between formation
+and transformation is gradually attained, and once it is established
+a given quantity of radium produces as many atoms of emanation as the
+emanation produces of radium A, and so on. When in equilibrium the
+longer-lived radio-elements are present in greater quantity than those
+of shorter lives in order to compensate for their comparatively slow
+rate of decay, and so to enable them to keep pace with their more
+rapidly changing associates.
+
+We may now calculate the average life period of radium. The volume of
+emanation in equilibrium with one gram of radium has been measured and
+found to be O·58 cubic millimetres—less than the volume of a pin’s
+head. The rate of change into radium A also lends itself to direct
+measurement, and from these two quantities it can be shown (see Ap. A,
+p. 179) that in one year ¹/₂₆₀₀ of the radium originally in existence
+must undergo transformation. The same result can be arrived at more
+directly. We know the number of atoms in a gram of radium and also the
+number of helium atoms expelled in the course of a year. The proportion
+which has suffered disruption follows at once, and is found to be
+¹/₂₅₀₀.
+
+From evidence of this kind it is concluded that after about 1850 years
+only half of any given quantity of radium then maintains its identity
+as that element. Now it is clear that radium must have a progenitor by
+which it is formed as fast as it decays, or otherwise there could now,
+after the lapse of millions of years, be none in existence.
+
+That progenitor is undoubtedly uranium—an element which disintegrates
+so slowly that its half-life period is three million times as long
+as that of radium. This association is revealed by the study of
+radioactive minerals. For every gram of uranium there exists in
+equilibrium with it, 3·4 × 10⁻⁷ grams of radium. The constancy of
+this proportion points to a genetic connection and admits of no other
+interpretation. The generation of radium has been experimentally
+verified by Soddy, who observed it after a number of years in a uranium
+preparation originally quite free from it. In practice this work is
+complicated, and the desired effects are retarded, by the intermediate
+production of another radio-element, ionium, which has an average life
+many times longer than that of radium. The time taken to establish
+equilibrium is therefore very long. The primary minerals from which the
+equilibrium ratio of radium to uranium is deduced, have existed
+for hundreds of millions of years and so far as they have remained
+unaltered by percolating waters they afford a safe guide. But in
+secondary minerals, like autunite, the age of which is often to
+be reckoned only in thousands of years, the equilibrium stage has
+not always been reached, and the ratio between the two elements is
+consequently somewhat lower than that found in the older minerals.
+
+In the accompanying diagram the complete family of uranium is
+summarised together with the half-life period of each member and the
+rays it emits. Another series of elements related in the same way
+is derived from thorium which is a parent of even longer life than
+uranium. As to the final products of transformation, which, being
+stable, ought to survive and in the course of time to accumulate,
+helium is the only one which has been directly observed. That lead is
+the end product of the uranium series is most probable, as we shall see
+in a later chapter. Of the stable element to which the thorium series
+ultimately leads we are still in ignorance. Neither lead nor bismuth,
+which suggest themselves by their appropriate atomic weights, satisfy
+the conditions, for their presence in a mineral bears no relation to
+the quantity of thorium (see p. 190).
+
+The actinium group of radio-elements calls for little notice here.
+Boltwood finds a fixed ratio between actinium and uranium in minerals,
+and the former would therefore appear to be a descendant of uranium
+just as radium is. Actinium, however, does not fall in the main line of
+descent. There is some probability that it marks the beginning of a
+collateral series, also springing from uranium. The proportion of
+uranium which disintegrates in this direction rather than towards
+radium can only be very small.[12] It is possible that uranium atoms, or
+those of one of its products, may be of two different types, according
+to their internal structure, and that on disruption each may give rise
+to an independent chain of elements.
+
+[Footnote 12: About 8%.]
+
+The heat output of radium and its relation to the energy of the
+α-particle has already been mentioned. The first direct measurement
+of the heat generated was made by Curie and Laborde. Using suitably
+constructed calorimeters, they were able to demonstrate a regular
+evolution of about 100 calories in an hour from a gram of radium—heat
+enough to raise the temperature of an equal mass of water from freezing
+to boiling-point. The radium in these experiments was in radioactive
+equilibrium with the emanation and radium A, B and C, so that
+altogether four α-particles were disengaged for each atom of radium
+which transformed. The approximate correctness of this first estimate
+will be seen from the following table, in which the best results up to
+date are quoted:
+
+    1903. Curie and Laborde        100 }
+    1904. Rutherford and Barnes    110 }  gram calories
+    1904. Runge and Precht         105 }  emitted per
+    1908. v. Schweidler and Hess   118 }   hour per
+    1909. Duane                    120 }     gram
+    1911. Duane                    117 }  of radium
+    1912. St. Meyer and Hess       132 }
+
+The correspondence of these results with the theoretical figure, 113
+calories, which represents about 85% of the energy,[13] is eminently
+satisfactory (see Ap. A, p. 177).
+
+[Footnote 13: Atomic recoil 6%, β-rays 4%, γ-rays 5%, approximately.]
+
+The disintegration theory affords a simple explanation of the origin
+of this energy. From the new point of view the atom is no longer
+indivisible, no longer the ultimate foundation of all matter; rather is
+it regarded as a tiny universe of electrons, a whirling assemblage of
+charged particles. These minute entities move with very high velocities
+within the atom itself. In general the energy is locked up, but in the
+radioactive elements the atomic structure is unstable and from time
+to time some of the energy can escape. The intrinsic energy of the
+atom itself is the real source of the heat liberated by radium, and
+the apparent permanence of its output is simply an expression of the
+immense supplies of energy which an atom can store within itself.
+
+The essential features of radioactivity are two: the spontaneous
+emission of Becquerel rays, and the atomic character of the change. The
+radiation from a radioactive substance is proportional to the quantity
+of the substance and to nothing else. Temperature, being a function of
+molecular movement, is without influence upon atomic transformation.
+Experiments made at temperatures ranging between that of liquid air and
+1600° C. show that the same law of disintegration holds throughout.
+Similarly, the effect of very high pressures indicates that these
+inter-atomic processes are quite independent of any external influence.
+Whether in solution or in chemical combination, whether taking part
+in energetic chemical reactions or suffering bombardment by its own
+radiations, the atom continues to obey the law which determines its
+life period, unmoved by any experiences through which we can oblige
+it to pass. The radioactive properties are simply superimposed upon
+the chemical and other properties of the substance, and as far as
+laboratory conditions are concerned, they are entirely spontaneous and
+can in no way be affected.
+
+Whether or not radioactivity is a general property of atomic
+matter cannot yet be announced. Potassium and rubidium are feebly
+radioactive—a thousand times less than uranium—and emit β-rays. It
+has been thought that some other metals may share in a minor degree the
+same attributes, but up to the present no reliable results have been
+forthcoming.
+
+In its geological applications radioactivity possesses a great
+interest. The most important bearing of all lies in the part it
+plays as a source of terrestrial heat. Radium is widespread amongst
+the surface materials of the earth’s crust. Rocks and soils, and
+natural waters all contain radium as a constituent, widely diffused
+but always present. In the following two chapters the influence of
+radio-thermal action in the earth and sun, and on speculations as to
+their ages, will be dealt with. Before passing on to these cosmic
+aspects of the subject, a brief account may be given of the way in
+which minute quantities of radium can be detected and accurately
+measured—quantities which in rocks average little more than a
+billionth of a gram in each gram of the rock.
+
+Radium itself is not directly dealt with; it is the emanation in
+equilibrium with it which is actually measured. The emanation is
+separated from a suitable amount of rock, mixed with air, and
+introduced into an electroscope. After about three hours, the emanation
+has generated radium A, B and C in their equilibrium amounts, and the
+emission of three sets of α-particles then steadily proceeds. In the
+electroscope, the rate of fall of the changed leaf depends directly on
+the conductivity of the air or on the number of ions which are utilised
+as carriers of electricity. Now each α-particle, in virtue of its
+enormous energy, is capable of producing in air about 100,000 ions, and
+the total number present is therefore determined almost wholly by the
+number of α-particles. The β- and γ-rays certainly have an ionising
+effect, but so small that in this connection it may be ignored. To be
+quite sure that all the ions are taking an active part in the discharge
+and collapse of the leaf, it is only necessary to observe the latter
+before its divergence from the central support falls to less than, say,
+10°. The rate of collapse can easily be gauged by observing the leaf
+through a microscope with a divided scale attached to the eyepiece,
+the time during which the leaf passes over a given number of divisions
+being taken with a stop watch. The rate of fall is proportional to
+the conductivity, which depends in turn on the number of α-particles
+expelled, and therefore on the quantity of emanation present in
+the electroscope; this quantity, provided that it was initially in
+equilibrium with the radium in the original rock, determines the amount
+of that element which was present. A constant can be determined once
+for all by experiment with known materials, which directly connects the
+rate of fall in scale divisions per hour with the equivalent amount of
+radium or uranium in grams. Some idea of the delicacy of the method may
+be gained from a particular example. In the apparatus devised by Prof.
+Strutt and used both in his own investigations and those of the present
+writer, a leakage of one scale division per hour corresponds to 9 ×
+10⁻¹³ grams of radium.
+
+To use this apparatus it is necessary to bring the rock into solution
+before the emanation can be extracted. The solution is stored up for a
+few weeks until the equilibrium amount has been generated and the flask
+A containing it is then attached to the water condenser B (Fig. 14).
+The emanation can be expelled by vigorous boiling, and greatly diluted
+with air, it passes out into the gas-holder C. The stream condenses in
+B and drops back. At the end of an hour the cooling water is run out of
+B and the steam then drives all the air charged with emanation into C.
+In order that none should be allowed to escape back, the connection at
+D is closed. Meanwhile the electroscope F has been exhausted and the
+emanation is made to pass into it through the tap at E, the gas-holder
+being slowly filled with water. After three hours the measurements may
+then be made.
+
+[Illustration: FIG. 14.
+
+Apparatus for estimating Radium by its Emanation.]
+
+Joly has recently varied this method in order to save the labour
+attending the process of getting a rock into clear solution. The
+mixture of finely-powdered rock and fusion mixture is heated in an
+electric tube-furnace, and the expelled gases containing the emanation
+are drawn straight from the furnace. Carbon-dioxide is absorbed by
+soda-lime, and the remaining gas is collected and finally passed
+into the electroscope as before. The absence or presence of thorium
+makes no appreciable difference in these measurements, for the
+life of its emanation is many thousands of times less than that of
+radium emanation. Joly has utilised this fact in his solution-method
+for determining minute quantities of thorium in rocks and minerals—a
+method similar in principle to that described above for radium.
+
+The presence of radioactive elements in rocks sometimes reveals itself
+in a most beautiful way. In mica, cordierite, hornblende, chlorite,
+tourmaline, and a few other minerals, small circular spots known as
+pleochroic haloes are sometimes seen. A tiny crystal can generally be
+detected in the centre, usually of zircon, but sometimes of apatite,
+epidote, rutile, or sphene. Until quite lately the nature and origin of
+these intensely pleochroic spots was entirely unknown. Joly showed in
+1907 that they are due to the radioactivity of tiny inclusions around
+which they spread spherically outwards. The α-rays discharged from
+the minute central crystals are able to ionise the biotite (or other
+mineral) and this effect, to which the colouring action is due, spreads
+just as far as the α-particle can penetrate. The range of the different
+α-particles from the uranium family is given overleaf, both for air and
+for biotite.
+
+    -----------------------+-----------------------
+                           | RANGE IN MILLIMETRES.
+                           +---------+-------------
+     SOURCE OF Α-PARTICLE. |         |
+                           | IN AIR. | IN BIOTITE.
+    -----------------------+---------+-------------
+    Radium C               |   70·6  |    0·033
+    Radium A               |   48·3  |    0·023
+    Ra. Emanation          |   42·3  |    0·020
+    Radium F               |   38·6  |    0·018
+    Radium                 |   35·4  |    0·017
+    Ionium                 |   28·0  |    0·013
+    Uranium 1 and 2        |   27·0  |    0·013
+    -----------------------+---------+-------------
+
+Now Bragg has shown that the ionising effect of an α-particle is
+greatest just before it comes to rest. We should therefore expect to
+find a number of intensely coloured spherical shells existing around
+the central crystal and corresponding in each case to one or other of
+the range limits here given. In section, and magnified 700 diameters,
+the appearance of the shells would be as in the following diagram.
+
+[Illustration: FIG. 15.
+
+Pleochroic Haloes in Biotite due to Uranium and its transformation
+products. Magnified 700 diameters.]
+
+The dimensions of the actual haloes are exactly in agreement with
+the distances to which the different α-particles can travel, and
+occasionally the successive spheres of ionisation and colouring are
+beautifully developed. In the biotite of Co. Carlow granite, Joly has
+found several very perfect examples, and by his courtesy four of his
+photographs are reproduced in the Frontispiece. Not only is the proof
+that the haloes are due to α-rays conclusive beyond question, but
+the correctness of Bragg’s laws from which the range in biotite is
+calculated are established in an unexpected way. Thorium haloes are
+also found (as in Fig. 2, upper left-hand part of the field), and these
+again have diameters in perfect accord with the demands of theory.
+
+A point of interest in the history of igneous rocks is that the haloes
+disappear when the rock is heated. The presence of well-formed haloes,
+therefore, implies the maintenance for very long periods of fairly
+uniform conditions. So slowly do these haloes form that it may become
+possible, when they have been further investigated, to give a rough
+minimum estimate of the age of the minerals in which they occur. The
+radioactivity of a zircon is much more intense than that of the rock
+enclosing it, but the smallness of the quantities involved is such
+that two or three weeks may elapse between the expulsion of successive
+α-particles or helium atoms. By the accumulative effects of millions
+of these atoms a spherical halo, faint in youth, but assuming a deeper
+tint with age, is gradually produced.
+
+
+
+
+CHAPTER VIII
+
+THE THERMAL ENERGY OF THE SUN
+
+
+    The sun’s heat and the conservation of energy—Mayer’s
+    meteoric hypothesis—Helmholtz and contraction under
+    gravity—The earth’s dependency upon solar radiation—The
+    work of Kelvin and Ritter—The insufficient contributions of
+    atomic disintegration—Arrhenius’ view of the importance of
+    molecular energy—Cyclic development of the universe.
+
+Before the doctrine of the conservation of energy was established, the
+steady radiation of solar light and heat was not, in its quantitative
+aspect, a phenomenon to be wondered at. Regarding the sun merely as a
+gigantic fire, philosophers such as Leibnitz and Kant were satisfied
+that the intense emission of energy was sustained simply by combustion.
+As soon as the chemistry of combustibles came to be studied, it was
+at once evident that the energy derived from burning alone would be
+hopelessly insufficient. If the sun had been originally a colossal
+mass of the most powerful explosives known to us, then, under the
+most favourable conditions for maintaining the present output of
+heat, all would have been at an end within a few thousand years. The
+total amount of available energy would not have sufficed even for the
+historical period—a period which is merely a ripple in the vast ocean
+of geological time.
+
+What, then, can be the source of the energy which for millions of years
+has enabled the sun to bathe the earth in a welcome glow of light and
+heat? How is the loss to be accounted for? For how long can the sun
+continue to radiate its energy without becoming perceptibly colder?
+These critical questions must have appealed to Mayer with some force
+when he recognised the truth that energy could neither be created nor
+destroyed. For the first time a sound explanation became an imperative
+demand. Mayer realised that in the collision and friction of bodies,
+heat energy is acquired in strict equivalence to the energy of motion
+which has apparently disappeared. He saw that the mechanical generation
+of heat would be of vastly greater importance in cosmic evolution than
+the limited possibilities of combustion. A piece of coal falling into
+the sun from infinite space would yield, by the stoppage of its motion,
+six thousand times as much heat as it could provide by burning.
+
+Applying these principles, Mayer thought that the sun’s heat might be
+traced to the kinetic energy of swarms of meteorites. These bodies
+falling into the sun with enormous velocities, would be competent, if
+only the supply were ample, to generate the heat annually required.
+Kelvin at first also advocated this view, but he was soon compelled to
+relinquish it in favour of another explanation less at variance with
+known facts. The observations of astronomers were all against there
+being a circulation and influx of meteorites to the extent required by
+the sun if income and expenditure of heat were to balance. Comets would
+suffer resistance in their passage round the sun. The rotational
+velocity of the sun would be constantly impeded, and probably, far back
+in the past, it would have been brought to a standstill. The sun’s mass
+would be appreciably increased every year, and an immediate effect
+of this would be to hurry up the earth in its orbit, so that each
+year would be notably shorter than the preceding one. Happily for the
+stability of the solar system, there is no evidence for an infalling of
+meteorites on the scale first contemplated.
+
+In 1856, Helmholtz, another early worker in the domain of energy, found
+a more satisfactory escape from the dilemma. Instead of looking outside
+the sun for the origin of the heat supply, he sought for an internal
+source, and found one—certainly a more efficient substitute—in the
+contraction of the sun’s diameter under its own strong gravitation.
+Knowing the amount of heat annually radiated, it is easy to calculate
+that a shrinkage of 1000 feet would make up the loss for five years.
+The decrease in the apparent diameter would, at this rate, never become
+detectable in human experience. Helmholtz imagined a time when the
+sun existed as a nebula spreading far out into space. As it slowly
+cooled and contracted, the mechanical work of shrinkage would reappear
+as heat. Assuming the present sun to be a globe of uniform density,
+Helmholtz calculated that its past history must have been restricted to
+about 20 million years.
+
+The annual output of heat had been determined by Pouillet, and his
+result, which was too low, was used by Helmholtz in this estimate. The
+solar constant of radiation is measured by the heat in calories, which
+would be absorbed in one minute by a surface of one square centimetre
+placed outside the earth’s atmosphere at right angles to the sun’s
+rays. Allowance is made in this way for the absorptive effects of gases
+and of the load of dust held by the lower strata of the atmosphere.
+Pouillet’s value in these units was 1·76 and the results of subsequent
+experiments, made up to 1905, varied between his figure and 4·1.
+This was unsatisfactory, and, under the auspices of the Smithsonian
+Institution, work has recently been done to clear up the discrepancy.
+The constant is now known with some certainty to be 1·95. Using this
+figure the duration of the sun’s heat would, according to Helmholtz, be
+limited to 18 million years.
+
+The surface temperature of the earth can owe but little to its internal
+energy. Taking the temperature gradient at 1° C. in 32 metres, and the
+average conductivity of rock as 0·004, the temperature maintained by
+this flow of heat alone would reach only 34° Absolute (239° C. below
+zero). It is evident then that the genial warmth of the greater part
+of the earth’s surface is maintained almost wholly by the absorption
+of solar radiation. For this reason the active life of our planet is
+intimately bound up with that of the sun, and any age limit assigned
+to the latter becomes a still more embarrassing restriction in its
+application to the earth.
+
+We may now return to our discussion of the sun’s vast expenditure of
+energy, armed with data worthy of confident acceptance, and with the
+knowledge that, for at least as long as the earth has been a habitable
+globe, so long has the sun emitted its life-giving rays at a rate
+not very different from that of the present. The evidence of geology
+is clear on this point. The geographical distribution of plants and
+coral reefs in past ages betrays no sign of a steadily cooling sun. In
+some of the oldest sedimentary rocks which are known, the imprints of
+raindrops have been found, and the size and force of the latter were
+evidently not very different from those which fall to-day by the shores
+of seas and lakes. The intensity of climatic forces has remained, on
+the average, unchanged.
+
+Kelvin somewhat mitigated the consequences of Helmholtz’s extreme view
+in his later treatment of the problem. Helmholtz had assumed a sun of
+uniform density; but Kelvin pointed out that, as the density probably
+increases enormously towards the centre, the amount of heat which
+has been already available may have been very much greater than that
+previously calculated. Kelvin’s cautious spirit was not shared by his
+contemporaries, who readily accepted the smaller estimates. The more
+daring investigations of Ritter, and of other physicists who followed
+his lead, did not support any period which exceeded 12 million years.
+Ritter showed that as the sun contracted from the nebulous state its
+temperature would at first begin to rise. Not only would contraction
+supply the energy necessary to sustain radiation, but an even greater
+quantity of energy would be available for heating purposes. An
+interesting summary of Ritter’s work will be found in the second of
+the fascinating little volumes by Arrhenius on _The Life of the
+Universe_.
+
+Geologists found no consolation in these speculative studies, and
+even from Kelvin’s more liberal allowance of time, an element of
+embarrassment was not absent. While an annual shrinkage of the sun’s
+diameter by 200 feet would suffice for the present, yet, unless at
+some time the sun’s temperature begins to fall, it is not clear why
+shrinkage should continue. Cooling is none the less certain because it
+is temporarily delayed, nor because its rate is for a time diminished.
+Increasing density would gradually put an end to effective contraction,
+and the sun would then cool as a white-hot ball would do—its capacity
+for replenishing its losses having been exhausted for ever. If this
+were all, then, in the course of a few more million years, an icy
+death would overtake the earth. In the last gleams of the fading solar
+twilight our planet would disappear—a barren and frozen world.
+
+More recent views lead to a less pessimistic outlook, and the
+twilight of the sun, though ultimately inevitable, is removed to
+an indeterminately remote future. Gravitation is manifestly an
+insufficient cause to maintain the sun’s heat for the periods required.
+We need a supply not for less than a dozen million years, nor even for
+the 100 million years which would have satisfied geologists a decade
+ago. Some source a hundred times as fruitful as contraction under
+gravity is required. Happily there is no longer any need to regard the
+sun as a serious difficulty, for there are locked within its atoms and
+molecules stores of potential energy capable of fulfilling every
+terrestrial requirement.
+
+The importance of radio-thermal action in the sun was pointed out by
+Rutherford and Soddy in 1903. A month or two later, W. E. Wilson made
+a calculation of the amount of radium which, if distributed throughout
+the sun, would entirely explain the evolution of its radiant energy.
+He found that 2·5 parts of radium in every million of the sun’s mass
+would be necessary. In uranium the equilibrium amount of radium is only
+0·34 part in a million, so that, even if the sun consisted entirely
+of uranium and its disintegration products, the heat generated would
+account for only one-seventh of the total expenditure. Wilson used in
+his calculation a solar constant of three calories per minute, which
+is certainly too high. His result must also be modified to allow for
+the heating effects of the other radioactive bodies. According to the
+most recent determinations, a million grams of uranium would give out
+77 calories per hour, and in the same time a million grams of thorium
+would give out one-third as much, each element being in radioactive
+equilibrium. The energy from the sun when divided throughout its mass
+averages 300 calories per hour per cubic metre. To sustain this steady
+evolution of heat four million grams of uranium would be required. The
+average weight of a cubic metre of solar matter is only 1·44 million
+grams, so that by no possibility could more than one-third of the sun’s
+heat be accounted for by radioactivity.
+
+That radioactive bodies do exist in the sun can admit of little doubt.
+Helium was first known as a solar element and its abundance suggested
+the presence of those radioactive elements from which it could have
+been generated. Direct spectroscopic evidence has not yet revealed any
+traces of radium, and, indeed, so minute are the quantities involved
+that until recently there was little hope of detecting it in this way.
+Uranium lines have now been found in the sun’s spectrum, and unless the
+laws of radioactivity are totally different at the temperature of the
+sun, we may safely assume that uranium exists in equilibrium with its
+associated elements. The sun’s radiation is destitute of the Becquerel
+rays, but this in no way denies their emission from solar matter.
+Before reaching the earth, the rays would be obliged to pass through
+both solar and terrestrial atmospheres, and the latter alone would be
+more than sufficient to absorb them completely.
+
+In the materials of the earth’s crust, uranium only averages about one
+part in 150,000, and thorium one part in 50,000. If the proportions of
+these elements which enter into the constitution of the sun are of the
+same order, their contributions to the sun’s energy can only be very
+small. The importance of radio-thermal phenomena is not felt until
+cooling has progressed to a more advanced stage, as exemplified by the
+earth, when the heat lost is balanced against that set free by atomic
+disintegration. We must therefore find some other means of escape from
+the embarrassment of a rapidly cooling sun.
+
+Arrhenius has made a bold attempt in this direction. He calls to his
+aid a universal law, first enunciated by Le Chatelier, which may be
+stated as follows: _If a system in equilibrium is subjected to
+external influences which disturb its equilibrium, then the internal
+reaction within the system will be such as to oppose the external
+influences_, i.e. the normal effects of the latter will be partially
+overcome. This general statement may be illustrated by the particular
+example to which the chief appeal is made. In the chemical changes
+which constitute combustion, heat is evolved, and the reaction is said
+to be exothermic. But the heat so liberated tends all the while to
+prevent the reaction from proceeding, and were an external source of
+heat of sufficient intensity applied so as to raise the temperature,
+the compounds previously formed would be again separated into their
+constituent elements. The liberated elements possess a greater quantity
+of intrinsic energy than when they are united to form a compound. That
+is to say, not all the heat supplied is able to exercise its normal
+effect of raising temperature; the internal reaction is responsible
+for the withdrawal and absorption of _part_ of the energy. If
+now still more heat is applied the same opposing tendency continues,
+and the elements will again combine, this time forming endothermic
+compounds characterised by further absorption of heat, and consequently
+by higher intrinsic energy than that which the free elements possessed.
+The system shows a conservative disinclination to be made hotter, and
+as more and more heat is supplied, enormous quantities of energy are
+accumulated in the recesses of the molecule itself. In the case of
+water, the general tendency is well illustrated. Ice at the freezing
+point absorbs 80 calories and becomes water at the same temperature.
+Water at boiling-point absorbs 540 calories and becomes steam. This
+in turn, when raised to about 3000° C., dissociates into hydrogen
+and oxygen, the absorption of energy being 3800 calories. Although
+laboratory conditions do not allow us to experiment further, there are
+no grounds on which to suggest that this is the end of the process.
+
+While matter thus opposes an increasing temperature by its internal
+reactions, it nevertheless resists the reverse change quite as
+actively, and for the same reason. If an intensely energetic exothermic
+compound be allowed to cool, it will strenuously refuse to do so at
+numerous stages. The energy previously gained is emitted steadily or
+explosively according to the thermal environment.
+
+In discussing the constitution of the sun and the source of its
+powerful radiation, this _Law of Reaction_, as it is called,
+finds a pertinent application. With its help Arrhenius has pointed
+out the path which appears to lead us safely out of the difficulty in
+which we were left by Helmholtz. The chromosphere which, disregarding
+the mysterious corona, constitutes the outermost strata of the solar
+atmosphere, is largely composed of free elements at a temperature of
+6000°-7000° C. Lower down in the photosphere, 9000° C. is probably
+attained. Temperature and pressure both increase enormously with
+depth, and indeed, the average solar temperature has been estimated at
+a thousand times that of the chromosphere. Under these conditions it
+seems reasonable to suppose that the sun’s interior is characterised
+by compounds charged with a high concentration of energy. Brought by
+convection currents towards the surface such highly explosive compounds
+would dissociate with expansion and an immense evolution of heat. It
+may be to explosions of this sort that the prominences are due. These
+violently projected gaseous tongues are shot out with velocities which
+sometimes reach a thousand times that of the swiftest rifle bullet.
+Since energy is proportional to the square of the velocity, it would
+appear from this that solar energies are at least a million times
+greater than those of our most powerful explosives. It has already been
+stated that if the life of the sun depended solely on the latter it
+would endure for only a few thousand years. As it is, the energy seems
+amply sufficient to last a million times as long. Here then, furnishing
+a regular and sufficient income from within, we have found an almost
+inexhaustible source of heat, which is competent to maintain the sun’s
+present expenditure for inconceivably long ages, as most probably it
+already has done in the past.
+
+True, we are in the face of a new difficulty. Whence arose this
+absorption and concentration of energy in the first place? It is
+evident that once extinct, our sun could not be re-awakened to the
+warmth of its former activity merely by collision. Gravitational energy
+alone affords no escape from the ultimate _Wärmetod_, the thermal
+extinction towards which the universe would appear to be tending. If
+the development of the universe be everywhere toward the equalisation of
+temperature implied by the laws of thermo-dynamics, the question
+arises—Why, in the abundance of past time, has this melancholy
+state not already overtaken us? Either we must believe in a definite
+beginning, in the creation of a universe furiously ablaze with energy,
+or else we must assume that the phenomena which we have studied simply
+reflect our limited experience. Toward the latter alternative we
+readily incline, the more so because of the hint it affords of cyclic
+processes in the scheme of Nature. Not only is energy being diffused;
+somewhere, our hazy conception tells us, energy is being elevated and
+stored up. With profound insight, Spencer pointed out in 1864 that it
+is to the attenuated nebulæ that we should look for the absorption and
+concentration of energy. In the universe nothing is lost, and perhaps
+its perfect mechanism is the solitary and only possible example of
+perpetual motion. In its cyclic development we may find the secret of
+its eternity and discover that the dismal theory of thermal extinction
+is, after all, but a limited truth.
+
+
+
+
+CHAPTER IX
+
+THE THERMAL ENERGY OF THE EARTH
+
+
+    Temperature gradients, conductivity, and the rate at which
+    the earth loses energy—Kelvin’s attempt to estimate the age
+    of the earth—King’s treatment of the problem—Estimates by
+    Becker and Suzuki—The distribution of radium in rocks—The
+    thermal equilibrium of the earth—Concentration of radium
+    towards the surface—Constitution of the earth.
+
+As the earth’s crust is penetrated by bore-holes, tunnels and mines, a
+steady increase of temperature with depth is encountered. The rate of
+increase varies greatly from place to place as the following records
+show:
+
+         LOCALITY.           DEPTH.         TEMP. GRADIENT.
+
+    Anzin, France             —            1° C. in 15·3 metres
+    Wigan                    750 metres    1° C. “  30·0   ”
+    Sperenberg              1700   ”       1° C. ”  36·5   ”
+    Mt. Cenis Tunnel        1600   ”       1° C. “  43·0   ”
+    Minas Geraes, Brazil      —            1° C. ”  86·0   ”
+    Calumet, Michigan       1430   ”       1° C. “  12·20  ”
+
+Such a variation would naturally be expected when the chemical
+reactions of weathering, cementation and metamorphism are remembered,
+and the unequal distribution of radioactive elements in the earth’s
+crust. The solution of silicates by ground waters takes place with
+liberation of heat, and it has been estimated that 120 calories are
+released when one gram of rock is decomposed by weathering. The
+processes of metamorphism take place at the expense of the earth’s
+heat, and the net result of the complete cycle in which (a) an igneous
+rock is eroded, (b) the resulting sediments buried and transformed
+into schists and (c) the latter brought again to the surface by earth
+movement and denudation, is a running down of energy involving a
+permanent loss. Moreover, the earth loses heat from the interior, not
+only by conduction, but also by convection. The circulation of ground
+waters and the activities of vulcanism—which include the upward
+movement of molten magmas, heated waters and gases—all result in the
+transference of heat from the interior to the outer zones of the crust.
+It is generally accepted, that when cooling by convection is left out
+of account, the temperature gradient due to conduction alone is of the
+order of 1° C. in 32 metres. If this estimate should be in error, it is
+more likely to be too high than too low.
+
+To calculate the rate at which heat escapes from the earth by
+conduction from the interior, it is necessary to know the average
+conductivity of rocks. This factor, in turn, varies greatly in
+different materials, but in the case of the most predominant rocks the
+conductivity is accurately known, and the value _k_ = 0·004 may
+be accepted as very close to the true average value. The variation of
+conductivity with increasing temperature and pressure scarcely affects
+the problem. The former tends to diminish the conductivity, the latter
+to augment it. As far as our present knowledge goes, these two effects
+almost exactly balance each other, and the assumption that
+conductivity remains fairly constant with depth is therefore justified.
+If _r_ represent the earth’s radius, and _d_θ/_dr_ the
+temperature gradient, θ being the temperature, then the quantity of
+heat which passes from the surface per second is given by
+
+                   _d_θ
+    4π_r_² × _k_ ×  ——— and can be readily calculated.
+                   _dr_
+
+According to the Laplacian hypothesis, the earth’s original store of
+heat was derived from the nebula from which it separated. Kelvin made
+the assumption that as the molten globe cooled down it was preserved
+by convection currents at a temperature nearly uniform from centre to
+surface. On attaining the point of solidification, it would gradually
+become solid throughout, most probably starting from the centre, and
+only when solidification was complete could the surface continue to
+cool further. The problem which Kelvin set himself to solve was this:
+Given a solid globe originally at a uniform temperature of 7000° F.
+(3871° C.), and subsequently cooling down, to calculate the time which
+would be required for the establishment of the present surface gradient.
+
+Taking the most probable values for conductivity _k_, density
+of rock ρ, specific heat of rock σ, and temperature gradient
+_d_θ/_dr_, he applied his data to Fourier’s differential
+equation for the linear conduction of heat—
+
+    _d_θ      _k_   _d_²θ
+     ———  =   ——— · ———
+    _dt_       ρσ   _dr_²
+
+Solving this equation for the unknown factor _t_, the required
+time period was found. The high initial temperature was chosen from
+very meagre data, as representing a maximum figure for the
+melting-point of rock. Kelvin was particularly anxious that his
+treatment should provide an over- rather than an under-estimate of
+time. The experiments of Dr. C. Barus have shown that diabase, a good
+typical rock, becomes thoroughly liquid at 1200° C. If Kelvin had
+used this temperature instead of his arbitrary 3871° C., his periods
+of cooling would have been reduced to less than one-tenth of those
+actually arrived at.
+
+For enormous periods of time, the development of a temperature gradient
+would be restricted to the earth’s outer zones. The interior, in
+complete thermal isolation, would remain unaffected, its loss of heat
+being quite insensible. The limited thickness of the outer shell, in
+which cooling would make itself felt, is made clear by the following
+figures:
+
+    160 miles in  100 million years.
+    240   ”   ”   240    ”      ”
+    320   ”   ”   600    ”      ”
+    570   ”   ”  1000    ”      ”
+
+The different periods which Kelvin favoured in his famous contributions
+to this problem have already been mentioned, and are tabulated below.
+
+    1862.     96   million years (limits 20-400).
+    1876.  50-90      ”      ”
+    1897.  20-40      ”      ”
+
+Clarence King, in 1893, applied a new criterion to the subject, taking
+into consideration the effect of pressure in raising the melting-point
+of rocks, and the necessity for an earth which should be stable under
+the influence of tidal stresses. Barus had measured the melting-point
+of diabase at various pressures, and a law of variation of
+melting-point with depth was formulated on his experimental results.
+If this law were to hold as far as the centre, diabase would there be
+able to exist in the solid state at any temperature below 76,000° C.
+Thus the hypothesis arose that solidification would begin at the centre
+owing to the high pressure obtaining there. Under these conditions,
+however, a temperature gradient was already developed. If the gradient
+were to exceed the rate by which the fusion point of rocks is raised
+by pressure, the former would catch up, and at a certain depth the
+temperature would reach the fusion point and a zone of fluid rock would
+be inevitable.
+
+King accepted diabase as a representative rock, and rejected any
+distribution of heat which would demand a liquid zone in that part of
+the earth’s crust where diabase or similar rocks would be expected to
+prevail. This procedure is justified by the consideration that were
+such a zone to exist, the earth would be incapable of maintaining tidal
+stability, and the crust would break down. King found that in the
+admissible cases, the initial temperature of crustal solidification
+would not exceed 2000° C., and that the period of cooling, which
+would reduce the gradient to that of the present was limited by 24
+million years. Higher initial temperature would involve fluidity, and
+superior age necessitate a lower surface gradient. The following curves
+represent the gradients of Kelvin’s earth of 100 million years, and
+King’s earth of 20 million years, in relation to the diabase
+fusion point curve. It will be seen that according to King’s argument,
+Kelvin’s earth implies the impossible condition of a liquid zone from A
+to B.
+
+[Illustration: FIG. 16.
+
+Temperature Gradients in relation to the Fusion point of Diabase.]
+
+In 1910, Becker attempted to deal with the same problem without relying
+on the temperature gradient, it being considered that owing to the
+presence of radium in rocks the gradient could not be trusted. In its
+place he assumes that the crustal strains associated with upheaval
+and subsidence are completely relieved at the surface of easiest
+fusion—and that according to the calculations of Hayford on isostatic
+compensation, the present depth of that surface is 71 miles. At that
+depth, therefore, the temperature curve and the diabase curve approach
+most closely, so that the additional temperature required to produce
+fusion and relief of strain there becomes a minimum. In the above
+diagram, C would represent the point of easiest fusion. Becker
+justifies his choice of diabase by showing that on the Laplacian law
+of density, rocks of this type become predominant at depths greater
+than 40 miles, the more acid rocks, lying above, being more refractory.
+Tidal stability is provided for by rejecting any temperature curve
+which crosses the diabase line in the zone of basic rocks. The most
+probable earth, according to Becker, is one with an initial temperature
+of 1300° C., which would attain a surface gradient of 1° C. in 42
+metres in 60 million years. He concludes that only “a tenth of the heat
+emitted by the earth can be ascribed to radioactivity plus all other
+exothermic chemical transformations.”
+
+A Japanese estimate of the time elapsed since the molten surface of the
+earth began to solidify appeared in 1912. Suzuki makes the assumption
+that a thin solid crust has gradually increased in thickness, so that
+the latent heat of fusion liberated at the junction of solid and liquid
+rock is equal to the heat lost at the surface. The present thickness
+of the crust is assumed, on the authority of Milne and Arrhenius to
+lie between 30 and 40 miles. Granting these postulates, the thermal
+constants for basalt and granite lead to an age of 20 to 60 million
+years according to the thickness of the crust and the material of which
+it is composed.
+
+It is surprising that Becker and Suzuki should have treated the
+problem in this restricted way. The heat evolution attending atomic
+disintegration was established in 1903, and in dealing with the earth
+this phenomenon must be regarded as one of fundamental importance.
+To ignore the significance of radio-thermal energy is to reduce the
+problem to a mathematical exercise, interesting, no doubt, but with
+little value in its geological application. Let us make a simple
+calculation of the quantity of radium, which, if uniformly distributed
+throughout the earth, would make good the loss of heat. If Q is the
+heat generated per second by the radium in each cubic centimetre, then
+we have
+
+               _d_θ
+4π_r_² × _k_ × ———— = ⁴/₃ × π_r_³Q,
+               _dr_
+
+      whence, Q = 6 × 10⁻¹⁵ calories per second.
+                = 2·16 × 10⁻¹¹ calories per hour.
+
+Now 1 gram of radium in complete radioactive equilibrium emits 216
+calories per hour and consequently all the heat would be supplied by
+10⁻¹³ grams per cubic centimetre, or 1·8 × 10⁻¹⁴ grams per gram of
+earth material.
+
+    RADIUM PER GRAM OF IGNEOUS ROCK IN BILLIONTHS (10⁻¹²) OF A GRAM.
+
+   +-----------------+------------+-------------+----------+-----------+
+   |    OBSERVER.    |     ACID.  |INTERMEDIATE.|  BASIC.  |ULTRABASIC.|
+   +-----------------+------+-----+-----+-------+----+-----+----+------+
+   |Strutt           |11[14]| 2·59|   4 |  2·25 |  9 | 0·52|  4 | 0.46 |
+   |Farr and Florence| 3    | 1·83|   4 |  1·68 |  6 | 0·54|    |      |
+   |Buchner          | 8    | 2·61|  15 |  1·64 |  4 | 0·73|    |      |
+   |Fletcher         | 4    | 0·85|  20 |  0·85 |  5 | 0·71|    |      |
+   |Holmes           | 8    | 2·80|     |       |  4 | 0·85| 10 | 0·51 |
+   +-----------------+------+----+------+-------+----+-----+----+------+
+   |Mean             |34    | 2·63|  43 |  1·28 | 28 | 0·66| 14 | 0·50 |
+   |Joly             |86    | 3·01|  48 |  2·57 | 31 | 1·28|    |      |
+   +------------------+-----+-----+-----+-------+----+-----+----+------+
+
+[Footnote 14: The number of rocks examined in each case is given in the
+first of each pair of columns.]
+
+Turning to the rocks themselves, the actual amount of radium is found
+to be a hundred times more than we want. Strutt was the first to
+discover this embarrassing richness, and his results, with those of
+later investigators, are summarised in the adjoining table. Joly’s
+results are given apart from those of other observers, for they were
+arrived at by the fusion method, and, moreover, separate rocks were
+not examined. A composite mixture of typical rock specimens was made
+up and a single analysis then sufficed to determine the average radium
+content. It will be noticed that Joly’s results are consistently
+higher than those found by the solution-method. Joly claims that his
+own procedure is more reliable than that followed in the solution
+method. Up to 1909, Joly had himself employed the latter method in
+the examination of 126 igneous rocks. In striking disagreement with
+the results of other workers, he found an average radium content of 7
+× 10⁻¹² grams per gram of rock. An explanation of the discrepancy is
+not yet forthcoming, but in the light of his most recent work, which
+gives an average of 2·5 × 10⁻¹², he has now suggested that his earlier
+results be set aside. Measurements of thorium in rocks are not yet
+so plentiful as those of radium, and most of our present knowledge
+of the distribution of this element is due to Joly and Fletcher. The
+most probable averages of the data now available may be summarised as
+follows:
+
+    ------------------+-----------------------------------------
+                      |        AVERAGE PER GRAM OF ROCK.
+      TYPE OF ROCK.   +---------------------+-------------------
+                      |        RADIUM.      |     THORIUM.
+    ------------------+---------------------+-------------------
+    Igneous           |   2·5 × 10⁻¹² grs.  | 2·0 × 10⁻⁵ grs.
+    Sedimentary       |   1·5 × 10⁻¹²  ”    | 1·0 × 10⁻⁵  ”
+    Metamorphic       |   2·0 × 10⁻¹²  ”    | 1·5 × 10⁻⁵  ”
+    Deep-sea deposits |   5·0 × 10⁻¹²  ”    |
+    ------------------+---------------------+-------------------
+
+Accepting these figures for igneous rocks provisionally and combining
+them with the respective heat emission of radium and thorium in
+complete radioactive equilibrium, viz.,
+
+    Radium[15] per gram 6   × 10⁻² calories per second.
+    Thorium     ”   ”   7·5 × 10⁻⁹    ”      ”     ”
+
+[Footnote 15: Equivalent to 3,000,000 grs. of uranium.]
+
+it is clear that each gram of the earth’s crust is a source of heat
+supplying on an average 15 × 10⁻¹⁴ calories per second on account of
+its radium content, and 15 × 10⁻¹⁴ calories on account of its thorium
+content. The total heat emission is therefore of the same order in each
+case, and amounts altogether to 30 × 10⁻¹⁴ calories per second. The
+whole mass of the earth is 6 × 10²⁷ grams, and if this were the source
+of as much radio-thermal energy throughout, the supply of heat in 1000
+million years would have been sufficient to raise its temperature to
+about 40,000° C., and the present gradient should be many times greater
+than it is. This conclusion cannot be reconciled with the evidence
+afforded by the crustal rocks, both their structure and temperature
+gradients being decisively against any such possibility.
+
+There are three cases which may be considered. The earth may be in
+thermal equilibrium, gaining as much heat as it loses and cooling only
+as the slow decay of the radio-elements permits; or it may be growing
+hotter, or, which is very unlikely, it may be cooling more rapidly than
+it would do if in radio-thermal equilibrium. The first case is the one
+now regarded with most favour. If the earth has cooled at all, and
+there seems to be no sound reason why we should altogether abandon that
+venerable conception, it must at some time have attained a condition
+of equilibrium. With the slow march of atomic disintegration its own
+rate of cooling would then keep time. The temperature gradient would be
+maintained solely by radioactivity for an immeasurably long period.
+
+The superabundance of radium which seemed to be implied by Strutt’s
+original work is certainly, as he then suggested, restricted to the
+surface rocks. The interior of the earth must be relatively free from
+radium and thorium. It is easy to calculate the thickness of the outer
+zone of the earth’s crust, which would suffice to supply the stream
+of heat passing to the surface. The temperature θᵣ at any distance
+_r_ from the surface is given by the following equation, where
+_k_ is conductivity, _h_ the heat production of radium and
+thorium per second, in each gram of rock, ρ the density of the rock,
+and D the total depth of the radioactive layer:
+
+         _hr_ρ    _r_
+    θᵣ = ————(D - ———)
+          _κ_      2
+
+At the base _r_ becomes equal to D and the temperature θᴰ is therefore
+given by
+
+         _h_ρD²
+    θᴰ = —————
+          2_κ_
+
+Using the figures given above, the thickness of the radioactive layer
+would be restricted to about ten miles and the basal temperature would
+reach only 250° C. This result cannot be held to express the facts, for
+there can be no doubt that the radium and thorium content decreases
+with depth for the same reason that the type of rock varies with
+depth. A glance at the table on p. 130 will show that there is a rough
+proportionality between the acidity or percentage of silica of a rock
+and its radium content. The more basic rocks are much poorer in radium,
+and, as would be expected, in thorium also. Now we have good reason to
+suppose that the more deep-seated rocks of the earth’s crust are of
+basic and ultra-basic composition, and that below the 30-mile crustal
+zone they are exclusively ultra-basic, perhaps similar in composition
+to the material of stony meteorites, with which they agree almost
+exactly in density (3·4). This information, which it might be thought
+would be for ever withheld from us, is derived from the study of
+earthquake waves. The latter in passing through the earth’s interior
+carry with them a record of the type of material they have penetrated.
+Within the stony zone, which extends downwards for several hundred
+miles, and separated from it somewhat sharply, lies the heavy core of
+the earth (density about 7·8), probably of metallic composition, like
+the iron meteorites. If we may judge from the latter, this nucleus is
+entirely free from radium, and that there is safety in this analogy is
+indicated by the very low radium content of such native iron as has
+found its way in basaltic magmas up to the surface.
+
+We have already seen (p. 30) that a first differentiation of the
+original heterogeneous material from which the earth was built would
+result in the formation of a metallic core surrounded by a stony zone.
+The further differentiation of the latter, whereby the crust with its
+abundant variety of acid and basic rocks was developed, is of too
+complex a nature to be considered here. It is very probable that as the
+more siliceous constituents separated and became concentrated towards
+the surface, they carried with them their store of radio-elements.
+In this way, basing our ideas on evidence quite independent of the
+temperature gradient, we are led to the remarkable conclusion that the
+radium and thorium of the earth are to be found almost exclusively in
+the earth’s crust. The most probable depth of the radioactive layer
+may therefore be placed at 30 miles and the basal temperature in this
+case would be about 750° C., which would be more in accordance with the
+requirements of volcanic phenomena. Moreover, it must not be forgotten
+that the heat lost by the upward movement and convection currents
+of rock magmas, heated waters and gases, has also to be accounted
+for. The radio-thermal equivalent must be substantially increased to
+include this phase of the subject. The basal temperature of 750° C.
+is only a minimum, and the higher temperatures demanded by geology
+are not therefore inconsistent with the facts. However, until more
+data are accumulated, it would be rash to attempt to deduce the exact
+distribution of the radio-elements in the crust, but already we may
+assert with confidence that the crustal average is somewhat lower than
+that of the surface rocks in which granitic types form so large a
+proportion. What the average actually may be cannot yet be decided.
+
+Kelvin’s problem must now be reversed. It is impossible to deduce the
+earth’s age from its thermal condition. We can only say that the age
+must be very much greater than Kelvin calculated. The new problem which
+presents itself is to determine the thermal history of the earth,
+accepting its antiquity as a known or partially known factor. The
+science of radioactivity is a welcome addition to the tools which the
+geologist employs in his difficult task of elucidating the earth’s
+history, and it is peculiarly valuable in helping him just where he has
+hitherto had most cause for despair.
+
+
+
+
+CHAPTER X
+
+RADIOACTIVE MINERALS AND THEIR AGES
+
+
+    The rate of helium production from uranium and thorium—Lead
+    the final product of the uranium family—Its accumulation
+    in geological time—Lead and helium ratios as a measure
+    of geological time—Assumptions to be granted—Value of
+    analyses in deciding quality of material for estimating
+    ratios—Necessity for fresh, stable, primary rock
+    minerals—Strutt’s work on the helium ratio—The lead
+    ratio—Boltwood’s collection of analyses—Examples, with
+    geological data—The author’s work on the Devonian minerals
+    of Norway.
+
+As we saw in Chapter VII the α-particles which are emitted at certain
+points in the line of descent of the radioactive elements have been
+identified with helium. Fortunately the evidence is conclusive, for
+upon this identification depends the latest and most elegant method yet
+devised of measuring geological time.
+
+When all the members of a genetically related series of radio-elements
+are in equilibrium, the transformation proceeds in such a way that an
+equal number of atoms of each element disintegrates in the same time.
+When an atom of uranium disintegrates it does so with the production
+of two atoms of helium. At the same time, as indicated in the diagram,
+page 190, each of six other members of the family also emit a single
+atom of helium. Consequently, the total number of helium atoms which
+are liberated in the course of the complete transformation of a
+single atom of uranium is eight. From this result and the remarkable
+measurement made by Rutherford and Geiger—that 3·4 × 10¹⁰ α-particles
+or atoms of helium are expelled per second from a gram of radium—it
+is possible to calculate that the annual production of helium from
+a gram of uranium in equilibrium with all the other products of the
+series is 10·7 × 10⁻⁸ cubic centimetres. Measurements of the ionising
+power of thorium and its chain of dependent elements may be utilised to
+calculate the same rate in the case of the thorium family. It is found
+that one gram of thorium is equivalent in helium generation to 0·26
+gram of uranium. The details of these calculations will be found in
+Appendix A.
+
+While there is little uncertainty in these indirect results, it is
+gratifying to know that Prof. Strutt, during 1909-10, verified them
+both by a direct appeal to experiment. In certain minerals which
+contain radioactive constituents, the evolution and accumulation of
+helium must have been steadily proceeding for very long periods. Before
+a direct determination of the rate of helium production can be made, it
+is evidently necessary to use material entirely free from that element.
+Strutt worked with richly radioactive minerals, from large quantities
+of which he expelled completely the accumulated store of helium. This
+was done by preparing solutions with every precaution to avoid the
+presence of undissolved particles of mineral, and afterwards boiling
+them till the helium was removed. The solutions were then put aside
+until a fresh supply of helium had been generated in sufficient
+quantity to be detected and measured. To isolate the gas from the
+solutions and accurately to determine its volume was obviously a matter
+of great experimental difficulty, so minute were the volumes dealt
+with. However, as the result of the exquisite delicacy of his methods,
+Strutt brought his experiments to a successful issue.
+
+The minerals used were pitchblende and thorianite, the former
+containing uranium alone, and the latter both uranium and thorium.
+The annual production of helium per gram of the parent element (in
+radioactive equilibrium with its respective family) was found to be:
+
+    (_a_) in the case of uranium:
+               10·6 × 10⁻⁸ ccs. or 1·88 × 10⁻¹¹ grams.
+               10·7 × 10⁻⁸ ccs. was the calculated estimate.
+
+    1 cc. would therefore be formed in 9,600,000 years.
+
+    (_b_) in the case of thorium: 2·4 × 10⁻⁸ ccs.
+
+    1 gram of thorium is therefore equivalent in its
+    rate of helium generation to 0·23 grams of uranium,
+    the calculated estimate being 0·26 grams.
+
+The remarkable concordance of these results with the theoretical
+requirements is an eloquent tribute to the refined methods and
+experimental skill with which the measurements were carried out.
+
+Experiments carried out by Boltwood and Rutherford in 1911 afford
+an equally striking confirmation of the conclusions on which the
+theoretical results were based. They measured the rate of production
+of helium from radium, the latter being in equilibrium with its
+early disintegration products, three of which also emit α-particles.
+Radio-lead and polonium were completely removed. The annual evolution
+of helium to be expected was 158 cubic millimetres. The first direct
+determinations were made by Sir James Dewar in 1908, and his best
+results corresponded to 169 cubic millimetres. Boltwood and Rutherford
+arrived at a much closer agreement, their figure being 156 cubic
+millimetres.
+
+These results cannot fail to inspire the conviction that our atomic
+theory of matter is essentially correct. We are in possession of two
+experimental facts. The number of helium atoms expelled per second from
+a gram of radium has been directly counted, and the volume of helium
+accumulated in a year has been directly measured. The number of atoms
+in a given volume of helium (at N.P.T.) can be deduced at once, and the
+calculation is independent of any underlying theory. Calculation gives
+2·69 × 10¹⁹ atoms per cubic centimetre; the atomic theory demands 2·72
+× 10¹⁹.
+
+Although there can now be no doubt that helium is one of the stable
+disintegration products, yet there is no direct evidence as to the
+identity of the ultimate products in the direct line of descent. In the
+uranium series indirect evidence points to lead with a considerable
+degree of certainty, but the end product of the thorium family is still
+unrecognised. In every uranium-bearing mineral the parent element
+slowly breaks down, while the final product of the transformation
+accumulates at its expense. Hence, if lead is the favoured element it
+ought to be found in association with uranium in all minerals which
+contain the latter. Moreover, in minerals which can be proved to be
+of the same antiquity, the amount of lead per gram of uranium should
+be constant; further, in minerals of various geological ages the
+proportion of lead should vary according to the latter. A mineral which
+began its accumulation of lead in pre-Cambrian times should certainly
+contain more at the present time than one in which lead has been
+collecting only since, say, the Tertiary outburst of igneous activity.
+The same statements apply equally well to the case of helium.
+
+In so far as these principles may be used conversely to test the
+identity of lead with the ultimate product, they lend every support to
+that important conclusion. Dr. Hillebrand, the leading authority on the
+analysis of uranium-bearing minerals, has never in the course of a long
+experience found uranium unaccompanied by lead. It was this constant
+association which led Boltwood, in 1905, to suggest the probability of
+a genetic relationship existing between these two elements. In 1907,
+Boltwood went farther and showed that for minerals of the same age the
+amount of lead for each gram of uranium, or the ratio Pb/U, was, in
+general, nearly constant. He collected all the best analyses of primary
+uranium minerals, but unfortunately he omitted to give the geological
+details of their occurrence. As will be seen in the present chapter,
+when the relative ages of the minerals are compared with their lead
+ratios, a striking proportionality discloses itself.
+
+The evidence of atomic weights is also favourable to lead. The complete
+disintegration of an original atom of uranium may be expressed as
+follows:
+
+      U   ➜    3He + Ra    ➜    8He + Pb
+    238·5    3·994 226·36     3·994 207·08
+             ————————————     —————————————
+    238·5       238·34           239·03
+
+Atomic weights are appended to each symbol, and the totals, which
+should be equal, are placed underneath. The agreement is close, but
+not as convincing as one could desire. Two alternative explanations of
+the discrepancies are suggested. Either lead is not the final product,
+or the atomic weights of both radium and uranium are too low by about
+0·5. Neither alternative can readily be granted, but it may be pointed
+out that since uranium is the heaviest known element and radium follows
+not far behind, any impurities whatever, with the exception of thorium,
+would have the effect of lowering the observed atomic weights.
+
+Accepting the above equation as substantially correct, the mass of
+lead generated in one year from a gram of uranium can now easily be
+calculated. For eight atoms of helium, one of lead is produced, or,
+mass for mass, six and a half times as much.
+
+Consequently, as a gram of uranium involves the annual production of
+1·88 × 10⁻¹¹ grams of helium, the associated lead which remains must
+amount to 1·22 = 10⁻¹⁰ grams. If this rate were constant we could find
+how long it would take for any mass of uranium to become completely
+converted into helium and lead. However, the rate is not constant, but
+is proportional at every moment to the quantity of uranium remaining
+unchanged. As the parent element becomes exhausted, it disintegrates
+more and more slowly.
+
+Now in very considerable periods amounting to hundreds of millions of
+years only a very small fraction of the uranium originally in existence
+is decayed. For this reason, if only a small proportion of lead or
+helium has collected in a mineral since it began its life-history, then
+no serious error will be made in assuming their rates of evolution to
+have been constant. In minerals which have been in existence for 400
+million years the slowing down is only about 5%. If an appreciable
+error should arise in ignoring this decline, then in place of the
+present day percentage of uranium the time-average must be substituted
+(see Ap. A, p. 179); that is to say, the amount of uranium which, if it
+did break up at a regular rate, would evolve the same quantities of the
+ultimate products.
+
+Having calculated this uranium average, Uₘ, with the necessary
+approximation, the total quantity of lead or helium accumulated in a
+mineral would then provide a direct measure of its age.
+
+Using lead as the age-index, and knowing its percentage, Pbₜ, in the
+mineral, then the time it has taken to collect, i.e. the age of the
+mineral, Pbₜ, is given by Pbₜ/Uₘ × 8200 million years.
+
+Using helium as the age-index, both thorium and uranium must be
+estimated. The amount of thorium may be conveniently expressed in terms
+of uranium, since the latter is four times as active in its helium
+production as thorium. The total equivalent quantity of uranium, Uₑ,
+is thus known, and thorium then need play no further part in the
+calculations. It is found most convenient to measure the amount of
+helium, Heₜ, as the volume in cubic centimetres per gram of mineral. In
+this notation the age is given by Heₜ/Uₑ × 9·6 million years.
+
+The validity of this procedure evidently demands the granting of
+certain obvious assumptions. Our choice of suitable minerals will
+not only be limited by these considerations, but the reason for a
+particular choice will be justified. The assumptions fall under the
+following headings:
+
+  (_a_) That no appreciable amount of lead or helium was present
+           at the genesis of the mineral.
+
+  (_b_) That no lead, helium, or uranium has subsequently been
+           added or removed by external agencies.
+
+  (_c_) That no lead or helium has originated by any other
+           radioactive process than those already suggested.
+
+The first and second suppositions bring up the whole problem of the
+origin of minerals. It is possible, by means of a physical examination,
+to decide whether a mineral is of the same age as the rock in which it
+occurs, or whether it is older or younger. In igneous rocks, such as a
+granite, the majority of the minerals are of the same antiquity as the
+rock, that is, they date from the period of consolidation of the rock
+magma. The component mineral particles of most sedimentary and detrital
+rocks existed long before the strata were laid down, whereas the
+cementing materials by which they are consolidated are partly furnished
+by percolating solutions and therefore may be subsequent to the period
+of deposition. In the same category come those ore deposits which
+occupy the fissures and crevices of pre-existing formations.
+
+In whatever way a mineral may occur, its history can always be
+traced back either directly or by conjecture to an igneous rock, and
+it is rarely that it is possible to go beyond the magma from which
+such a rock must have consolidated. And even if this can be done in
+exceptional cases, there lies behind still another magma to which the
+material can be referred. Consequently, the minerals of igneous rocks
+are regarded as primary or original, and here we may briefly consider a
+few facts relative to their crystallisation from a molten condition.
+
+A molten rock is regarded as a solution in which the numerous
+constituents are dissolved one in another. Now certain of the
+constituents can only remain in solution provided the latter is, with
+regard to them, very dilute. That is to say, they are only slightly
+soluble in a solvent composed of the rest of the rock material.
+Consequently, substances of which these constituents form an essential
+part will, as a general rule, be the first to crystallise; as examples,
+zircon, sphene, and apatite may be cited. For the same reason it
+happens that the magma does not remain homogeneous, but rejects certain
+of the rarer elements which collect together in a subsidiary magma of
+peculiar composition. To this concentrate of exceptional constituents,
+the gases and water vapour expelled during solidification are also
+added, and serve to maintain it in a state of æquo-igneous fusion,
+even when the bulk of the rock has already crystallised. The residual
+liquors yield the minerals of pegmatites and of drusy cavities. Certain
+minerals which are conspicuously rare in the body of the normal rock,
+are often developed on a large scale in pegmatite dykes, and it is from
+these that the most perfect and beautiful crystal forms are generally
+obtained.
+
+Amongst the elements of limited solubility in a rock magma, uranium
+and thorium must be placed. The accessory minerals of ordinary
+igneous rocks, such as those already mentioned—zircon, sphene, and
+apatite—are rich in the radioactive elements when compared with
+commoner minerals like felspar and hornblende. In general, the richness
+of a mineral in uranium seems to depend on its position in the order of
+consolidation. The minerals first to be formed claim the greater part
+of the available store. The original surplus, unable to dissolve in the
+magma, is held over, and, should it be rich in radioactive ingredients,
+uranium- and thorium-bearing minerals may be formed during the later
+stage of pegmatitic intrusions. It is a striking fact that, as primary
+constituents, these minerals invariably occur in pegmatites associated
+with granite or syenite. As examples, pitchblende or uraninite,
+thorite, thorianite, and monazite may be mentioned.
+
+We must now consider the part played by lead and helium during the
+genesis of minerals. Before the consolidation of the magma, both
+these elements must, of course, have been generated within it for
+an unknown period. As to the effect of physical conditions upon
+radioactive transformations it has already been shown (p. 102) that
+all the evidence points to the conclusion that these atomic changes
+are independent of the temperatures and pressures under which a molten
+magma exists. The helium already present at the time of crystallisation
+appears to behave physically in no way different from the other gases.
+There is no evidence that it tends to congregate in any particular
+mineral. A small proportion may be distributed through the resulting
+rock, but probably the larger share is expelled.
+
+The lead which may be originally present follows a similar course.
+The metal is rejected, not only by the primary magma but, with rare
+exceptions, by the residual magma also. It finds no definite place
+in igneous rocks. Doubtless a certain amount of lead is retained in
+the molecular network of crystals, but that amount is not high. In
+the rocks of Leadville, Colorado, Hillebrand found an average of less
+than 0·002 per cent of lead. In the nepheline syenite of Southern
+Norway, using specimens free from minerals which one would expect to
+be comparatively rich in accumulated lead, the present writer was able
+to determine a percentage of only 0·0004. If, then, there should be
+initially a greater quantity of original lead, where are we to look for
+it? Probably the most of it goes to form lead-ores, such as galena.
+Separated from the pegmatites it appears in the later phases of
+ore deposition which follow on the heels of igneous activity. In
+company with hot gases, sulphide solutions, and a number of metallic
+companions, our lead is carried away and deposited in the fissures
+encountered by the mineralised waters. If the agency of magmatic gases
+appears to have been an important factor in the production of ore
+bodies, the origin of the latter is said to be pneumatolytic. Brögger
+has shown that in Southern Norway galena was one of the minerals to be
+formed in this way.
+
+In the last phase of this complex series of operations, magmatic waters
+contribute their share to the filling of mineral veins, and it is
+amongst these hydatogenetic ores that galena is most usually found.
+The important point is that lead, for the most part, is drawn from the
+primary magma at, or perhaps before, the time of crystallisation, and
+it is not until the igneous activities have declined that it again
+appears in an active rôle.
+
+Let us now consider the effect of the original distribution of lead and
+helium in a newly-formed rock. It will be clear that an analysis of
+the rock as a whole would give values of Pb/U and of He/U much higher
+than those corresponding to the period since consolidation. Of the
+total amounts of lead and helium, part would be originally segregated
+in the rock and part would be due to subsequent genesis. In most rocks,
+the former part is of sufficient magnitude altogether to invalidate
+the use of the ratios as age indices. This difficulty can be avoided
+by confining attention to particular minerals—indeed, to just those
+minerals which concentrate within themselves the radioactive parent
+elements. Within them lead and helium may accumulate to such a degree
+that the amount initially present becomes negligible. Zircon from the
+Devonian syenites of Southern Norway contains more than twenty times
+as much lead as the rock in which it occurs. Roughly, we may say that
+since the zircon came into being its content of lead has multiplied
+twenty times. Thorite may accumulate a hundred or a thousand times as
+much lead as it possessed at first. For the same reason, minerals like
+zircon and sphene often contain hundreds of times as much helium as
+the rock from which they are taken, and there is little possibility
+of error in assuming that they have themselves generated the whole of
+their supply.
+
+Another difficulty, and a more serious one, must now be faced. Can we
+be sure that for periods of hundreds of thousands years a mineral has
+remained comparatively unaltered by external agencies? With regard
+to helium there is undoubtedly a tendency to escape. Strutt has
+demonstrated that when a radioactive mineral has been powdered, helium
+begins to leak, rapidly at first, then at a diminishing rate. Even
+crystals washed out of their original matrix showed a considerable
+leakage of helium. The observed rate of escape always exceeds the rate
+of generation, and it therefore follows that during the life-history of
+a mineral the conditions must be specially favourable to the retention
+of helium, for otherwise the latter could not have accumulated.
+Nevertheless, these experiments prove conclusively that the majority of
+minerals do not contain their full store of helium, and it is a matter
+for surprise that they contain so much. Consequently, ages deduced from
+the helium content of minerals can be regarded only as a fraction of
+the true age.
+
+Dealing with lead and uranium, we must consider the tendency to
+alteration of the minerals in which they occur. From the surface down
+to the permanent level of the ground waters, rock material is subject
+to weathering. The more soluble constituents are leached out and
+complex silicate minerals are decomposed by the combined action of
+water, oxygen, and carbon-dioxide. It is in this belt of weathering
+that igneous rocks suffer most change. Many of the primary minerals
+are broken down and alteration products take their place. All the
+reactions involve considerable increase in volume, and not only are
+minerals altered in place, but material is carried away and deposited
+elsewhere as secondary minerals. Can we be sure that lead and uranium
+have remained untouched during this redistribution? In some cases we
+cannot, but fortunately for our purpose many of the most valuable
+minerals, like zircon, are dense and exceptionally stable. A mineral is
+only stable over a limited range of conditions. It adapts itself more
+or less readily to its physical environment. Certain minerals, however,
+are much more capable than others of withstanding great changes without
+undergoing metamorphism or alteration, and amongst these are many of
+the uranium-bearing minerals.
+
+When there has been a migration of lead or uranium, an appeal to
+analysis will rarely fail to dispel the difficulty by disclosing the
+fact. It is inconsistent with the chemical properties of these elements
+that both should have been affected in the same proportion, and hence
+the ratio of lead to uranium obtained from different minerals of the
+same geological age affords an immediate test of the extent to which
+they have suffered from alteration in the course of their history.
+If the analyses give consistent results, it can be safely assumed
+that the effects of alteration have been inconsiderable; if there are
+marked discrepancies the results must be rejected as valueless from
+a chronological point of view. A microscopical examination of the
+minerals before analysis is a useful safeguard, for in this way altered
+material can often be detected. It is clear that reliable conclusions
+can only be drawn from minerals which are undoubtedly _fresh_.
+
+Becker has criticised the method by directing attention to a suite of
+minerals from Llano Co., Texas. Their geological age is well defined.
+The Burnet granites with which they are associated are intrusive into
+a series of schists and quartzites, metamorphosed sediments of late
+Algonkian time. The Cambrian rocks lie upon this complex and the period
+of intrusion is therefore between two limits which are not very far
+apart. The lead ratios of these minerals are far from being constant,
+as the following examples show:
+
+    Yttrialite      1·15
+    Yttrialite      0·51
+    Mackintoshite   0·39
+    Uraninite       0·17
+    Fergusonite     1·04
+    Fergusonite     0·30
+
+Boltwood found a satisfactory agreement in four cases, the ratio being
+0·17, but, as he pointed out himself, most of the minerals from this
+locality are unsuitable, because of incipient or advanced alteration.
+The quartzose pegmatites in which the minerals occur are riddled with
+alteration products and secondary minerals, and the whole series is
+altogether unfavourable to accurate age determination. It is doubtful
+whether the apparent agreement of the ratios quoted by Boltwood ought
+to be accepted without further verification; for the present they
+cannot be regarded without suspicion.
+
+This example shows how the actual results indicate the vicissitudes,
+varying from mineral to mineral, which the lead and uranium contents
+may have undergone. The method confirms or denies the validity of its
+application in every case. Judging from the relative solubilities of
+the constituents in question, uranium is likely to be abstracted from
+a mineral during the process of weathering more readily than lead,
+and consequently the age deduced from a weathered or altered specimen
+should in general be too high. A differential effect of this kind would
+account for the high ratios given by the Llano Co. minerals.
+
+Strict attention must be paid to the question of origin, and secondary
+minerals avoided as carefully as altered primary minerals. Pitchblende
+is often secondary, e.g. when it occurs in veins with metalliferous
+sulphides. Other examples, of a rather different type, are autunite
+and carnotite. Secondary minerals are necessarily more recent than the
+rocks in which they occur, and many of them date back to no very remote
+period. Autunite is sometimes formed quite near the surface, within
+a few inches in fact. Its antiquity cannot therefore be more than a
+few thousand years, and in this time a detectable quantity of lead
+could not be generated. The traces actually found were probably in the
+original possession of the mineral. In an analysis made by the writer,
+only 0·06% of lead was found in specimens of autunite from Mozambique,
+where it occurs in bright green flakes attached to the large biotite
+crystals of pegmatitic dykes. In keeping with the age of the pegmatites
+and the high proportion of uranium—45%—it should have contained a
+hundred times as much had it been a primary mineral. The paucity of
+lead in autunite has even been put forward as an argument against the
+contention that lead is the ultimate product of disintegration of the
+uranium family. We now see how baseless is this argument when the
+origin of the mineral is remembered. It is not surprising that autunite
+should contain so little lead; on the contrary, it contains much more
+than the uranium can account for in the time at its disposal.
+
+From these considerations it will be obvious that the only minerals
+to be chosen as material from which to determine the lead-ratio are
+fresh, stable primary rock-minerals. Having decided this, there remains
+a third possibility which might cast doubt upon the method. It can be
+objected that lead may originate as a product of some element other
+than uranium. Analytical results show clearly that thorium cannot give
+rise to lead, or a more proportionate relationship between these two
+elements would have announced the fact. There is also a possibility
+that certain of the longer-lived members of the uranium family may
+themselves be segregated in a mineral, independently of uranium. If
+so, they would gradually disintegrate, leaving no trace of themselves
+other than the residual helium and lead. In a magma containing 10%
+uranium, the radium would amount only to 0·0000034%. In actual magmas,
+even of pegmatites, the quantity present is always much less than
+this, and even if it be allowed that such tiny quantities may saturate
+the magmatic solution, the precipitation and concentration in any
+particular mineral would not be sufficient to leave an appreciable
+residue of lead.
+
+The application of the accumulation of helium in minerals to the
+measurement of geological time, was first suggested by Rutherford in
+1905, when he wrote: “I think that, when the constants required for
+these calculations are more definitely fixed, this method will probably
+give fairly trustworthy information as to the probable age of some of
+the radioactive minerals of the earth’s crust, and indirectly as to the
+age of the rocks in which they are found.”
+
+During the years 1908-10, Strutt examined a great number of minerals,
+and determined the helium ratio whenever practicable. His first set
+of experiments dealt with phosphatic nodules and phosphatised bones.
+These may sometimes contain fifty times as much uranium as average rock
+material, and they have a further advantage in that they can be found
+in strata of nearly every age. As they frequently consist of fossils
+characteristic of the formations in which they occur, their age is
+well defined. However, the power of retaining helium is both poor
+and variable in the case of these phosphates, and the time relation
+is therefore obscured. Such materials never retain more than a small
+fraction of the helium which has been generated within them.
+
+More suitable in their power of retention are certain iron ores,
+from which significant results were obtained. The helium ratio, and
+therefore the numerical age derived from it, showed a marked dependency
+upon the geological age of the mineral, as the following examples
+illustrate:
+
+    ---------+---------------------+--------------
+    MINERAL. |   GEOLOGICAL AGE.   | MILLIONS OF
+             |                     |   YEARS.
+    ---------+---------------------+--------------
+    Siderite | Upper Oligocene     |      8·4
+    Hæmatite | Eocene              |     30·8
+    Hæmatite | Upper Carboniferous |    141·9
+    Hæmatite | Devonian            |    145·2
+    ---------+---------------------+--------------
+
+Strutt next investigated the more compact minerals of igneous rocks,
+notably zircon and sphene. Zircon can be obtained from rocks belonging
+to several periods of igneous activity, and being a durable and stable
+mineral it is peculiarly fitted to retain the helium generated within
+it. Even allowing that the helium found does not represent the whole
+amount generated, it is unlikely that the fraction lost will vary as
+conspicuously as in the case of phosphates. In so far as that fraction
+depends on the structure of the mineral it is probably more uniform for
+zircon than for most other minerals. The helium ratio ought therefore
+to stand in a close relation to the geological age of the specimen.
+That it does so is clearly demonstrated by Strutt’s results, which are
+given below. The geological ages have been taken from the most recent
+literature, and are given in greater detail than those published in the
+original paper. Where two periods are bracketed together they are to
+be understood as referring to the limits between which the age of the
+igneous rock may fall.
+
+    -------------------------+---------------------+--------------
+           LOCALITY.         |   GEOLOGICAL AGE.   |   MILLIONS
+                             |                     |   OF YEARS.
+    -------------------------+---------------------+--------------
+    Mt. Somma, Vesuvius      | { Recent            |
+                             | { Pleistocene       |     0·1
+                             |                     |
+    Mayen, Eifel             |   Pleistocene       |     1·0
+                             |                     |
+    Campbell I., N.Z.        |   Pliocene          |     2·5
+                             |                     |
+    Expailly, Auvergne       |   Miocene           |     6·3
+                             |                     |
+    Brevig, Norway           |   Devonian          |    54
+                             |                     |
+    Cheyenne Canon,          | { Upper Cambrian    |
+      Colorado               | { Archean           |   141
+                             |                     |
+    Green River,             | { Carboniferous     |
+      N. Carolina            | { Archean           |   147
+                             |                     |
+    Ural Mts.                |   Pre-Devonian      |   209
+                             |                     |
+    Ceylon                   |   Archean           |   286
+                             |                     |
+    _Blue Ground_, Kimberley |   Archean           |   321
+                             |                     |
+    Sebastopol, Ontario      |   Archean           |   622
+    -------------------------+---------------------+--------------
+
+The results for sphene add but little to the above table, for most of
+the rocks from which workable quantities of sphene can be obtained are
+of pre-Cambrian age. The most notable helium ratio was from a specimen
+occurring in the Archean rocks of Ontario, and corresponded to an age
+of 715 million years. Summarising all the data afforded by Strutt’s
+work, we may graduate the geological column with a time-scale. It must
+be clearly understood, however, that the ages as expressed in years
+are, in the case of the helium ratio, minimum values only. How much
+greater the time represented by the geological periods actually is will
+appear from the ages as deduced from the lead-ratio. A few of these are
+placed in the table below for comparison.
+
+    -------------------------+-----------------------------------
+                             | TIME-SCALE IN MILLIONS OF YEARS.
+     THE GEOLOGICAL SYSTEMS. +------------------+----------------
+                             |   HELIUM RATIO.  |  LEAD RATIO.
+    -------------------------+------------------+----------------
+         Pleistocene         |        1         |       --
+         Pliocene            |        2·5       |       --
+         Miocene             |        6·3       |       --
+         Oligocene           |        8·4       |       --
+         Eocene              |       30·8       |       --
+         Cretaceous          |       --         |       --
+         Jurassic            |       --         |       --
+         Triassic            |       --         |       --
+         Permian             |       --         |       --
+         Carboniferous       |      146         |      340
+         Devonian            |      145         |      370
+         Silurian            | }                | }
+         Ordivician          | }                | }    430
+         Cambrian            | }    209         |       --
+         Algonkian           | }                |   1000-1200
+         Archean             |      710         |   1400-1600
+    -------------------------+------------------+----------------
+
+The application of the lead-ratio to the measurement of the antiquity
+of minerals was first due to Boltwood. He tested its reliability by an
+appeal to the best analyses published up to 1907. Some of these, with
+geological details, will now be given.
+
+In Glastonbury, and also in Portland, Connecticut, primary uraninite
+is found in the felspar quarries. The pegmatite in which the mineral
+occurs is associated with a granite which intrudes Lower Carboniferous
+strata. It is probably to be referred to the close of the Carboniferous
+period, and is certainly pre-Triassic. Five different specimens gave
+lead ratios in striking agreement, corresponding to an age of 340
+million years.
+
+It should be observed in all the following tables that in calculating
+the lead ratios the time-average of uranium has been used, and not the
+amount actually present. The statement of analyses is, of course, in
+percentage.
+
+    ----------+-------+--------
+     URANIUM. | LEAD. | RATIO.
+    ----------+-------+--------
+        70    |  2·9  | 0·041
+        70    |  3·0  | 0·042
+        70    |  2·8  | 0·039
+        72    |  3·0  | 0·041
+        72    |  2·9  | 0·040
+    ----------+-------+--------
+
+Similar crystals of uraninite have been furnished by the pegmatites of
+Branchville, Connecticut. The intruded strata are of either Silurian or
+Ordivician age, and the evidence suggests that the period of intrusion
+is possibly coincident with that of the earth movements which commenced
+at the close of the Ordivician. Here again the lead ratios closely
+agree, the age being 430 million years:
+
+    ----------+-------+--------
+     URANIUM. | LEAD.  | RATIO.
+    ----------+-------+--------
+        74    |  4·0  | 0·052
+        75    |  4·0  | 0·051
+        74    |  4·0  | 0·052
+        66    |  3·5  | 0·051
+    ----------+-------+--------
+
+In North Carolina uraninite occurs in coarse pegmatites which are mined
+for their large flakes of mica. In this instance a good agreement is
+scarcely to be expected, as secondary products abound, and the three
+specimens from Spruce Pine which were examined by Hillebrand showed
+signs of incipient alteration. The fourth specimen was from South
+Carolina and this again lacked the freshness which is so essential.
+Zircon is also found in the North Carolina pegmatites, and the writer
+has examined two sets of specimens with the results given below. The
+material in this case appeared to be quite fresh.
+
+The geological period is difficult to establish with certainty. The
+relations of the Appalachian rocks of Carolina are so obscure that
+the required age may be anywhere from pre-Cambrian to Carboniferous.
+Judging from the lead ratios, one is tempted to suggest that the age
+is not far from the Silurian, but until our time-scale is better
+determined one must be chary in this converse application of the
+method. It may confidently be hoped that in this way the geologist will
+be greatly helped in his attempt to unravel the history of igneous
+activity in the earth’s crust. But the time is not yet, for the
+accumulation of facts and data has only just commenced.
+
+    -----------+----------+--------+--------------
+      MINERAL. | URANIUM. |  LEAD. | RATIO Pb/U.
+    -----------+----------+--------+--------------
+     Uraninite |  77      | 3·9    |    0·049
+     Uraninite |  77      | 4·2    |    0·052
+     Uraninite |  67      | 3·3    |    0·047
+     Uraninite |  71      | 3·3    |    0·045
+     Zircon    |   0·076  | 0·0036 |    0·046
+     Zircon    |   0·130  | 0·0055 |    0·041
+    -----------+----------+--------+--------------
+
+Other series of minerals could be given from the pre-Cambrian rocks
+of North America, Ceylon, and Mozambique, but it is unnecessary to
+multiply details further. In all cases the Archean seems to date from
+1200-1600 million years.
+
+We now turn to the pre-Cambrian rocks of Scandinavia and Finland, and
+for comparison with those of N. America the following classifications
+and correlations may be given. The chief unconformities are indicated
+by wavy lines. It should be pointed out that the correlation of the
+pre-Cambrian rocks over wide areas is, perhaps, the most difficult task
+the geologist has to attempt, and the scheme given opposite is based
+more on analogy than direct evidence.
+
+    _Fennoscandia._      _North America._
+
+    Jotnian            Keweenawan        }
+                                         }
+    Jatulian           Upper Huronian    }
+                                         }
+    Upper Kalevian     Mid. Huronian     } Algonkian
+                                         }
+    Lower Kalevian                       }
+                       Lower Huronian    }
+    Bottnian                             }
+
+    Ladogian           Laurentian        }
+    Katarchean         Keewatin          } Archean
+
+It is not yet possible to support this correlation by a concordant
+system of chronology. Igneous rocks occur at most of the horizons, but
+it is extremely difficult to get samples of suitable mineral species
+for analysis. However, there is no doubt that in the future a definite
+time estimate will be attached to each of the above periods. When
+we are in full possession of this knowledge, and only then, will a
+reliable correlation of these rocks be possible.
+
+The analyses collected by Boltwood include two groups which are of
+minerals taken from the pegmatites of Southern Norway, rocks famous
+for the occurrence of rare minerals. The first group, from the igneous
+complex of the Moss district, of which the average age is 1000 million
+years, is as follows:
+
+    ------------+----------+-------+--------
+      MINERAL.  | URANIUM. | LEAD. | RATIO.
+    ------------+----------+-------+--------
+    Uraninite   |   66     |  8·4  | 0·12
+    Uraninite   |   68     |  7·8  | 0·11
+    Annerdödite |   15     |  2·2  | 0·135
+    Uraninite   |   66     |  9·3  | 0·13
+    Uraninite   |   57     |  8·0  | 0·13
+    Uraninite   |   65     |  8·8  | 0·135
+    Uraninite   |   68     |  8·8  | 0·12
+    Uraninite   |   76     |  9·0  | 0·11
+    Thorite     |    8·2   |  1·2  | 0·13
+    ------------+----------+-------+--------
+
+The second group, from the complex of Arendal, demands an age of 1200
+million years. The Scandinavian geologists believe that both groups of
+rocks are younger than the quartzites and other metamorphic sediments
+with which they are always associated, and that the latter rocks are of
+late Archean age. Sederholm, however, thinks they may be equivalent to
+his Kalevian division. The geological evidence, as far as it goes, does
+not point to any difference in the ages of these two sets of Norwegian
+minerals, but, on the other hand, there is no positive evidence that
+the ages are the same. An analogy made in ignorance cannot be held
+to constitute a proof. Field work in this case does not disqualify
+the testimony of the radioactive minerals; it rather invites their
+co-operation in the perplexing task of disentangling the intricate
+structural relations of the rocks.
+
+    ----------+----------+-------+-------------
+     MINERAL. | URANIUM. | LEAD. | RATIO Pb/U.
+    ----------+----------+-------+-------------
+    Uraninite |   56     |  9·8  |    0·14
+    Uraninite |   61     | 10·2  |    0·15
+    Uraninite |   56     |  9·4  |    0·15
+    Thorite   |    9     |  1·5  |    0·16
+    Orangite  |    7·5   |  1·2  |    0·15
+    Xenotime  |    2·9   |  0·62 |    0·19
+    ----------+----------+-------+-------------
+
+Amongst these rocks correlation is exceedingly difficult, and even
+their relative ages are hidden in obscurity. Högbom holds that the
+massifs of Moss and Arendal are contemporaneous with the Ser-archean
+granites of Sweden. Similar hyperites and quartzites are found in
+nearly every locality and the granites always appear to be younger than
+these. After their intrusion, an enormous thickness of rock was denuded
+away before the Jatulian sediments were laid down. The physical break
+here indicated is one of the greatest in the history of the earth,
+and undoubtedly represents an immense lapse of time. The granites and
+pegmatites must therefore be considerably older than the Jatulian rocks.
+
+With a view to testing the constancy of the lead-ratio in a series of
+minerals from a single igneous complex, the author, in 1911, made a
+number of experiments on carefully chosen material. There occurs in the
+Christiania district of Norway, a geologically depressed area of nearly
+4000 square miles, which is separated by faults from the surrounding
+pre-Cambrian rocks on every side. Within this area there is a nearly
+complete sequence of early Palæozoic rocks, surmounted by a few beds of
+red sandstone of Lower Devonian age. Over these beds and intercalated
+with them are lava flows; and finally, penetrating the whole mass, and
+representing a later phase of the same period of igneous activity,
+are great intrusions of plutonic rocks. Amongst the earliest of the
+intrusions is a series of thorite-bearing nepheline-syenites. Brögger
+believes them to be of Middle or Lower Devonian age, most probably the
+latter. The minerals occurring in them are, in many instances, notably
+radioactive, and thus they afford an admirable series in which to
+investigate the consanguinity of lead and uranium. A suite of minerals
+was obtained from Brevig, and estimations of these elements made, with
+the following results:
+
+    --------------+--------------+--------------+-------
+                  |   URANIUM.   |     LEAD.    |
+       MINERAL.   | GRS. PER 100 | GRS. PER 100 | Pb/U
+                  | GRS. MINERAL | GRS. MINERAL |
+    --------------+--------------+--------------+-------
+    Thorite       |   10·1040    |     0·4279   | 0·042
+    Orangite      |    1·2437    |     0·0570   | 0·046
+    Orangite      |    1·1825    |     0·0542   | 0·046
+    Thorite       |    0·4072    |     0·0196   | 0·048
+    Homelite      |    0·2442    |     0·0121   | 0·049
+    Zircon        |    0·1941    |     0·0085   | 0·044
+    Pyrochlore    |    0·1923    |     0·0120   | 0·062
+    Pyrochlore    |    0·1855    |     0·0093   | 0·050
+    Biotite       |    0·1602    |     0·0069   | 0·043
+    Tritomite     |    0·0631    |     0·0026   | 0·041
+    Freyalite     |    0·0526    |     0·0028   | 0·053
+    Mosandrite    |    0·0432    |     0·0024   | 0·056
+    Aegerine      |    0·0253    |     0·0015   | 0·060
+    Astrophyllite |    0·0140    |     0·0007   | 0·050
+    Catapleite    |    0·0132    |     0·0009   | 0·068
+    Nepheline     |    0·0010    |     0·0004   | 0·400
+    Felspar       |    0·0006    |     0·0003   | 0·500
+    --------------+--------------+--------------+-------
+
+It will be noticed, that with a few exceptions, the value of the ratio
+increases as the percentage of uranium diminishes. This is probably
+due to the relative importance of lead originally entangled in the
+minerals at the period of their crystallisation. Thus it would seem in
+the case of nepheline and felspar that almost the whole of the lead
+found was originally present, while that which has since been generated
+is very small in comparison. Minerals with so little uranium contain
+too much occluded lead to be reliable, and are, of course, valueless in
+age-estimations. When sufficient uranium is held by a mineral, the lead
+generated becomes increasingly important, until the original amount
+is of negligible consequence. There is always the possibility that in
+some of the richer minerals larger quantities of lead were occluded
+than in felspar, but the agreement among the ratios renders this
+improbable. Rejecting all the results after that of biotite because of
+the low percentage of uranium, and omitting that of the first specimen
+of pyrochlore because the estimation could not be verified owing to
+lack of material, the mean ratio is 0·046. Replacing the uranium
+percentage by its time-average value, the ratio becomes 0·045 and
+the corresponding age 370 million years. It may be thought somewhat
+arbitrary to select certain results preferentially, but in view of the
+interpretation placed upon them the choice is not unfair, nor without
+justification.
+
+Most of the available evidence drawn from radioactive minerals has now
+been passed in review. As yet it is a meagre record, but, nevertheless,
+a record brimful of promise. Radioactive minerals, for the geologist,
+are clocks wound up at the time of their origin. After a few years’
+preliminary work, we are now confident that the means of reading these
+time-keepers is in our possession. Not only can we read them, but if
+they have been tampered with and are recording time incorrectly, we
+can, in most cases, detect the error and so safeguard ourselves against
+false conclusions.
+
+
+
+
+CHAPTER XI
+
+REVIEW OF THE EVIDENCE
+
+
+    The discrepancy between the geological and radioactive
+    methods of estimating time—Uniformity of the rate of
+    decay of uranium—Joly’s criticism—Comparison of the two
+    time-scales—Doubtful assumptions made in the geological
+    arguments—Possibility of reconciliation no longer hopeless.
+
+Of the various methods which have been devised to solve the problem of
+the earth’s age, only two, the geological and the radioactive, have
+successfully withstood the force of destructive criticism. The other
+arguments may be dismissed without further discussion, as in every
+case their cogency has been vitiated by the detection of a fundamental
+error. From the mists of controversy which for half a century have
+hung over the subject, the two _hour-glass_ methods alone emerge,
+and the final issue must be fought out between them. In the one the
+world itself is the hour-glass, and the accumulating materials are
+salt, the sedimentary rocks and calcium carbonate. Three concordant
+sets of results may be drawn from this triple scheme of measurement,
+but it must not be supposed that they are altogether independent. Each
+set of data is intimately related to the others and all stand or fall
+together. In the other case the accumulating materials are helium and
+lead, and the hour-glass is constituted by the minerals in which they
+collect. Provided that the field-evidence is clear and convincing
+and that the relative geological age of a mineral specimen can be
+determined, the construction of an exact and precise time-scale is
+a task which can be dealt with successfully in the laboratory. The
+problem has advanced from the qualitative to the quantitative stage,
+and for the first time in historical geology accurate measurement
+founded on delicate experimental work has become possible.
+
+It is a matter for regret that confidence in this pioneer work has
+been shaken by the advocates of the geological methods of attack. The
+surprises which radioactivity had in store for us have not always been
+received as hospitably as they deserved. With the advent of radium
+geologists were put under a great obligation, for the old controversy
+was settled overwhelmingly in their favour. But the pendulum has swung
+too far, and many geologists feel it impossible to accept what they
+consider the excessive periods of time which seem to be inferred.
+That there exists a serious discrepancy obviously points to a flaw
+in the underlying assumptions of one or the other or both of the
+methods. Evidently we are at the parting of the ways. The fundamental
+assumptions on which the arguments are based cannot both be right.
+One of them must be rejected. Which is it to be? Let us consider each
+in turn, and discuss the consequences of the two possible forms of
+reconciliation.
+
+The only assumption which can reasonably be called into question is
+that of uniformity, and it is involved equally in both calculations. It
+is here, at the root of the problem, that the discrepancy really lies.
+If we favour the uniformity of geological processes—a well-worn
+doctrine which has done good service—then we must reject uniformity
+of radioactive disintegration. Joly has drawn attention to the latter
+possibility. He asks: Is it assured that the parent substance, uranium,
+has always in the past disintegrated at the rate determined by its
+present average life period? As far as we know, the rate of decay
+for substances of rapid transformation is constant, and independent
+of temperature and pressure changes. On the grounds that a large
+number of radioactive bodies decay at a constant rate, it is believed
+that this constancy is a definite attribute of all the radioactive
+elements. In the case of uranium this assumption cannot be proved for
+periods commensurate with its half-life period. On analogy with the
+behaviour of the shorter lived elements, it is probable that had we
+lived in Cambrian times and experimented with Archean uranium-bearing
+minerals just as has been done during the last decade, the half-life
+period would then have been exactly the same as we now find it—about
+5400 million years. In the case of radium emanation there can be no
+doubt that experiments in Cambrian times would have given results
+concordant with ours. It would be as unphilosophic to doubt this as
+to believe that the laws of physics and chemistry vary with time. The
+difference between uranium and its daughter elements, the difference
+which suggests to Joly a possible distinction, is simply one of origin.
+We are in complete ignorance of the genesis of uranium. It is not
+impossible that, owing its origin to some process other than atomic
+transformation, the particular distribution of intrinsic energy among
+its atoms may not be such as to maintain a constant rate of decay.
+At the moment of its birth every radioactive atom has a definite
+expectancy of life, and when a sufficiently large number of atoms is
+under observation a definite fraction disintegrates every second. There
+is this difference in the case of parent elements. As they become aged
+with reference to the time of their origin, they are not reinforced
+by the addition of fresh, newly-born atoms, as are the other members
+of each series. Joly’s supposition seems to be that in the absence
+of this reinforcement the uranium in its early stages may possibly
+disintegrate more rapidly than it does now. However, it is not found
+that the younger atoms of the short-lived elements are, on an average,
+more prone to rapid decay than are their older companions. Whether an
+element is in equilibrium with the higher members of its family, or
+whether it is separated from them, its transformation proceeds with
+unaffected regularity.
+
+It is very improbable that reconciliation will be found in the
+supposition of a progressive retardation of the rate of decay of
+uranium. There are three possibilities. Uranium may have disintegrated
+in the past exactly as it now does; or it may have decayed more slowly
+or more rapidly. The latter two alternatives do not favourably commend
+themselves. There is no evidence which can be cited in their support.
+On the other hand, the hypothesis of _constant_ change is deduced
+from a well-established series of experimental facts, and is remarkably
+in accordance with the general phenomena of radioactivity. Uranium,
+in other respects, does not present any anomaly, and with regard
+to the mechanism of its decay physicists are not likely to regard
+it as an exceptional case without very definite reasons for doing
+so. The discordance between the time estimates drawn from the rates
+of geological and radioactive changes cannot be held to constitute
+a sufficient reason for rejecting current opinions unless it is
+conclusively demonstrated that the geological estimates are beyond
+question. In the future the case for uranium may be established
+more securely, when the dynamics of atomic disintegration, and the
+conditions upon which the distribution of unstable atoms depends,
+becomes more intimately understood. At present there is only one
+means of testing the constancy of uranium decay, but unfortunately
+it affords only negative evidence. The range of α-particles from a
+radioactive element is connected in some way with its rate of decay.
+If then, uranium in the past disintegrated more rapidly, the radius of
+its particular pleochroic halo ought to record the difference. It is
+improbable that any variation—assuming for the moment that there were
+a variation—could be detected even in the most favourable cases.
+
+We now turn with a double interest to the geological estimates. If it
+can be shown that they ought to be largely increased, as Chamberlin
+and a few other geologists believe, then not only is a reconciliation
+at once made possible, but, in turn, the constancy of uranium decay is
+placed beyond doubt. Little need be added to the discussion in Chapter
+VI. It was there indicated that one factor previously over-looked—the
+average height of the continents in geological time—very largely
+controls the rate of denudation and therefore of sedimentation. Let us
+make an attempt to discover how past rates must be related to those
+of the present to make possible a complete reconciliation. In Fig. 17
+the discrepancy is illustrated graphically by comparing the respective
+time scales from the close of the Archean (gneiss and granite phase) to
+the present day. All the sediments of which relics have remained to us
+are in this way taken into consideration. Lying buried in the Archean,
+the base of the record is obscured beyond recognition by the prevalence
+of metamorphic and plutonic igneous rocks. The extent to which the
+earliest sediments have been lost in the evolution of the earth’s
+crust, and the part they have played in the genesis of granites and
+gneisses are questions which betray our ignorance and offer food merely
+for wild speculations. These possibilities, however, do not touch the
+immediate point at issue, for in their time relations they lie outside
+the limits to which this discussion is restricted.
+
+The curve A is plotted strictly against the maximum observed thickness
+of sediments, and corresponding to it is the sedimentation line A′
+to which is granted 300 million years. According to these two graphs
+the greatest error lies beyond the Cambrian. The average rate of
+denudation and of sediment accumulation must now be nine times that
+of the pre-Cambrian periods, but if post-Cambrian is compared with
+present the ratio is reduced to two-and-a-half. In the B series, the
+lead ratios are plotted in a straight line and the stratigraphical
+column is extended in accordance with the palæontological evidence that
+pre-Cambrian time is at least as long as that which has elapsed since
+the beginning of the Cambrian. On this basis present rates are four
+times the average for post-Archean time.
+
+[Illustration: FIG. 17.
+
+Geological Time Scales.]
+
+Assuming that the true time-scale lies somewhere between the extremes
+of A and B, we are led to two conclusions which, if accepted, greatly
+lessen the severity of the discordance between A and A′ and B and
+B′. From A and A′ it appears that pre-Cambrian denudation took place
+much more slowly than has since been typical. This proposition is in
+complete accordance with the view that the pre-Cambrian continents,
+when viewed in the light of the reconstructed geographies of the later
+periods, were of limited area and restricted elevation. From B and
+B′ the broad time conception of palæontology gains further support,
+and the existence of great gaps in the pre-Cambrian succession is
+suggested. It is well known that the most important unconformities of
+the whole geological record are to be found in the imperfect succession
+of the earliest formations. It is impossible to do more than guess
+at the duration of time periods which are without their sedimentary
+equivalents. On the most extreme assumption, the Algonkian sediments
+should be represented not by 82,000 feet, but by more than 300,000
+feet. Unwilling though we may be to consider the record imperfect to
+this incredible degree, it is of importance to point out that had such
+an immense thickness existed in successive periods of time, the sodium
+content of the ocean would not necessarily be in any way different
+from what it is. The same amount of primary rock material may have
+been broken up, but instead of a reassorting of the materials to form
+three successive sets of sediments (on a rough average) we would be
+obliged to postulate six or more repetitions of the sorting process.
+The question need not be pursued farther. The suggestion here put
+forward is, that in the limitations of pre-Cambrian geography and in
+the imperfection of the sedimentary relics of those remote times, the
+discrepancy which is peculiar to the pre-Cambrian finds an adequate
+explanation.
+
+If this be allowed, all that remains is to decide whether it is
+inconsistent with geological principles to assert that the modern
+hour-glass is running at two-and-a-half to four times its average
+rate. The decision depends largely on the broad point of view from
+which geological interpretation proceeds. From the standpoint of
+Catastrophism little progress was made. Uniformity proved a great
+advance, but in detail it is apt to lead us astray if applied too
+dogmatically. Modern interpretation is based on the more philosophic
+conception of Evolution, and in place of the earlier idea which was
+insisted upon by the older physicists—that changes have been such as
+would accompany a gradual running down of the earth’s internal kinetic
+energy—the _form_ of development now favoured is that of cycles
+of phenomena, recurring in their broad features again and again and not
+necessarily hampered in their activity by any progressive diminution in
+the store of available energy. Igneous action, deposition of sediments,
+marine transgression and recession, are all rhymic phenomena and
+the factor common to each one, whether as cause or effect, is
+earth-movement.
+
+The conditions of the present day cannot then be accepted as
+representing average conditions, unless it were by a happy accident.
+Amidst all the details of earthquakes and volcanic eruptions some great
+cycle is now running its course, and only in relation to the particular
+phase of the cycle under which we happen to pursue our investigations
+will our conclusions be strictly tenable. Although we cannot hope to
+judge the exact place which the present takes in the larger scheme of
+terrestrial activity, yet in comparison with the past, the present
+epoch would seem to approach just those extremes most favourable to
+a high rate of denudation, and to a rapid accumulation of sediments.
+Marine recession, brought about by deepening of the ocean basins, and
+raising of the land areas have together brought about continental
+expansion and elevation. The vulcanism of the present day, whether
+regarded as a closing phase of a period of igneous action, or as the
+initiation of a new cycle, probably affords an example of more than
+average intensity and violence. The weathering capacity of rain must be
+enhanced in proportion to its content of dissolved acid gases, and this
+in turn is conditioned by the prevalence of vulcanism. Still another
+factor leading to higher rates, though of a different category, is
+due to recent glaciation. Over wide areas easily eroded deposits are
+exposed, the areas being generally those which would resist denudation
+most successfully. In Fennoscandia, for example, four-fifths of the
+pre-Cambrian shield is buried beneath a thin covering of moraine.
+
+It is not suggested that present rates have never before been reached,
+but only that they are characteristic of the more intense phases of
+denudation rather than of average conditions. If this be granted,
+reconciliation of the rival time estimates is no longer hopeless. There
+can be no doubt that agreement will never be brought about by the more
+convincing testimony of experimental demonstration. It must be almost
+entirely a question of interpretation. An attempt has been made to show
+that in the geological evidence there is nothing impossibly at variance
+with the dictates of the radioactive minerals. With the acceptance of
+a reliable time-scale, geology will have gained an invaluable key to
+further discovery. In every branch of the science its mission will be
+to unify and correlate, and with its help a fresh light will be thrown
+on the more fascinating problems of the Earth and its Past.
+
+
+
+
+APPENDIX A
+
+
+(_a_) _Kinetic Energy of α-particles_
+
+1 gram of radium in equilibrium with emanation,
+Ra. A B and C generates heat at the rate of =132
+calories per hour= (85% due to α-particles).
+
+    e = charge on α-particle = 9·3 × 10⁻¹⁰ E.S. units.
+                             = 3·1 x 10⁻²⁰ E.M.   ”
+
+    m = mass of α-particle     }
+    v = velocity of α-particle } see Table below.
+
+    N = number of α-particles liberated from 1 gram of
+          radium = 3·4 × 10¹⁰ per second.
+
+    Energy E transformed per second is given by—
+
+           Nmv²
+    E = ½∑ ——— × e
+            e
+
+        Ne   mv²
+      = —— ∑ ——
+         2    e
+
+    +---------------+---------------+----------------+
+    |               |       v       |      mv²/e     |
+    |    Element.   | Cms. per sec. |   E.M. Units.  |
+    +---------------+---------------+----------------+
+    | Radium        |   1·56 × 10⁹  |  4·78 × 10¹⁴   |
+    | Ra. emanation |   1·70 × 10⁹  |  5·65 × 10¹⁴   |
+    | Ra. A         |   1·77 × 10⁹  |  6·12 × 10¹⁴   |
+    | Ra. C         |   2·06 × 10⁹  |  8·37 × 10¹⁴   |
+    +---------------+---------------+----------------+
+
+    Substituting these values, we have—
+
+    Ne = 3·4 × 10¹⁰ × 3·1 × 10⁻²⁰ = 10·5 × 10⁻¹⁰ E.M. units.
+
+                  mv²
+                ∑ —— = 10¹⁴(4·78 + 5·65 + 6·12 + 8·37)
+                   e
+                      = 24·9 × 10¹⁴ E.M. units;
+
+             whence E = 13·1 × 10⁵ ergs per second
+
+                      = 4·73 × 10⁹ ergs per hour.
+
+    Now 4·19 × 10⁷ ergs = 1 gram-calorie.
+        ∴ E = 113 calories per hour.
+
+
+        (_b_) _Production of helium from Uranium and Thorium in
+               equilibrium with all their disintegration products._
+
+        _Uranium_—
+
+        N = number of helium atoms liberated from 1 gram
+        of radium alone = 3·4 × 10¹⁰ per second.
+           (_Rutherford and Geiger_, 1908).
+
+        The equilibrium ratio of radium to uranium is
+        3·4 × 10⁻⁷. Hence for each gram of uranium in
+        equilibrium the number of atoms produced amounts to—
+
+        3·4 × 10¹⁰ × 3·4 × 10⁻⁷ × 8 per second = 29·1 × 10¹¹ per year.
+
+       Now the number of helium molecules, and therefore of atoms,
+       in 1 cc. of the gas at N.P.T. is 2·72 × 10¹⁹.
+
+       The annual production of helium must consequently be
+
+           29·1 × 10¹¹
+          ————————————  ccs.,
+           2·72 × 10¹⁹
+
+       i.e. 10·7 × 10⁻⁸ ccs., or 1·88 × 10⁻¹¹ grs. per gram of uranium.
+
+      An experimental determination gave 10·6 × 10⁻⁸ ccs.
+      (_Strutt_, 1910).
+
+
+_Thorium_—
+
+The ionising power, or the energy of the α-particles from 1 gram of
+thorium, is 0·325 of that from 1 gram of uranium, each element being in
+complete equilibrium.
+
+Average range of α-particles from thorium and its products = 5·4 cms.
+
+Average range of α-particles from uranium and its products = 4·3 cms.
+
+The average thorium α-particle is therefore 1·25 times as energetic as
+the average uranium α-particle.
+
+Hence the actual production of α-particles or helium atoms from
+thorium is only 0·325/1·25 = 0·26 of that of uranium.
+
+Experimental determinations 0·23 (_Strutt_, 1910),
+                            0·27 (_Rutherford and Geiger_, 1910).
+
+
+(_c_) _Half-life Period of Radium._
+
+(1) The number of α-particles emitted from 1 gram of radium per second
+(n = 3·4 × 10¹⁰) is equal to the number of atoms disintegrating per
+second.
+
+If N is the number of atoms in 1 gr. radium, then λ, the fraction which
+transforms per second, is given by—
+
+         n
+    λ = ——.
+         N
+
+    The number of atoms in 1 gr. hydrogen is 6·24 × 10²³,
+    and as the atomic weight of radium is 226 times that
+    of hydrogen,
+
+      N = 2·76 × 10²¹.
+    ∴ λ = 1·25 × 10⁻¹¹ gr. per sec.
+        = 3·94 × 10⁻⁴  gr. per year.
+
+    =Half-Life period= = 0·69315/λ = =1760 years=.
+
+(2) 1 gr. of radium is in radioactive equilibrium with 0·58 cubic
+millimetre, or 5·7 × 10⁻⁶ grs. of emanation (atomic wt. = 222).
+
+If λ₁ = 2·085 × 10⁻⁶ is the fraction of emanation transforming per
+second, we have—
+
+    λ = 5·7  × 10⁻⁶ × λ₁
+      = 1·19 × 10¹¹ gr. per sec.;
+
+    whence—=Half-Life period = 1850 years.=
+
+The earlier values given for the half-life period were 1760 and 2000
+years, but the lower figure seems most accurate, with 1850 years as a
+probable value.
+
+The half-life of uranium would then be—
+
+       1850
+    —————————— = =5400 million years=.
+    3·4 × 10⁻⁷
+
+
+(_d_) _Time-Average of Uranium_
+
+     Uₜ = Quantity of uranium remaining after a time t.
+     Uₒ = Quantity of uranium originally present (t = o).
+     Uₘ = Time-average of uranium during time t.
+      λ = Disintegration constant of uranium.
+    Pbₜ = Lead accumulated during time t.
+    Heₜ = Helium    ”         ”   time t.
+
+[Illustration: Graph I]
+
+Graph I represents the rate of decay of uranium—according to the
+exponential law—
+
+            (  -λₜ)
+    Uₜ = Uₒ ( e   ).
+
+There is one rate of decay which, if it remained constant throughout
+the time t, would have a total effect equivalent to that produced by
+the actual slowly decreasing rate of decay. This average rate is
+represented by some point on the curve, and the corresponding quantity
+of uranium, Uₘ, is the time-average. Equating the amount of uranium
+transformed in each case, we have—
+
+             Uₒ - Uₗ = λUₘt
+
+                        Uₒ - Uₜ
+    whence        Uₘ = ————————     (_a_).
+                          λt
+
+[Illustration: Graph II]
+
+For periods less than 2000 million years, the time-average is nearly
+equal to the arithmetic mean of Uₒ and Uₗ.
+
+          Uₒ + Uₗ
+    Uₘ = ————————      (_b_).
+            2
+
+The value of Uₘ for 2000 million years is,
+
+        according to equation (_a_), equal to 0·874 Uₒ
+    and    ”       ”     ”    (_b_)    ”    “ 0·879 Uₒ.
+
+The ages of minerals rarely exceed 1500 million years, and therefore
+the error involved by using equation (_a_) in preference to
+(_b_) is quite negligible.
+
+In Graph II the ratio Uₘ/Uₜ, i.e. the factor by which the present
+uranium content of a mineral must be multiplied in order to obtain the
+true time-average, is plotted against time.
+
+An approximation to the age, t, of a mineral is afforded by the ratio
+Pbₜ/Uₜ. From the graph the factor corresponding to this time can be
+obtained, and thence the time-average. This in turn can be utilised to
+give the more correct age represented by Pbₜ/Uₘ.
+
+A more straightforward method of correction is as follows:
+
+Uₒ can be determined from known quantities according to the following
+equation:
+
+               Uₔ = Uₜ + Pbₜ + Heₜ
+                  = Uₜ + 1·15 Pbₜ;
+    whence, =Uₘ = Uₗ + 0·575 Pbₜ=.
+
+The age of the mineral is then given by the ratio =Pbₜ/Uₘ=, or
+directly from Graph II.
+
+
+(_e_) _Analyses made by the Author of Radium in Igneous Rocks_
+
+(_cited on p. 130_)
+
+    _Acid Rocks_—              _Ra. per gram of rock_
+
+    Granite, Mozambique       5·84 × 10⁻¹² grs.
+       ”         ”            2·61       ”
+       ”         ”            1·77       ”
+       ”     N. Nigeria       3·09       ”
+       ”     Rhodesia         2·43       ”
+       ”     Transvaal        2·12       ”
+       ”     South Africa     1·81       ”
+       ”       ”     ”        2·73       ”
+
+    _Basic Rocks_—
+
+      Basalt, Mozambique     0·94 × 10⁻¹² grs.
+      Dolerite    ”          0·85       ”
+      Gabbro      ”          1·07       ”
+      Norite      ”          0·54       ”
+
+    _Ultrabasic Rocks_—
+
+    Composite analysis of 10 specimens from
+    Scotland, New Zealand, Africa,
+    and Canada          0·51 × 10⁻¹² grs.
+
+
+
+
+APPENDIX B
+
+BIBLIOGRAPHY
+
+
+CHAPTER I
+
+    Thomson (Kelvin). _Rep. Brit. Ass._, p. 1819. 1855.
+    —— _Proc. Glasgow Phil. Soc._, Vol. IV, p. 272. 1860.
+    —— _Phil. Mag._, February, 1862, p. 158. 1861.
+    —— _Popular Lectures and Addresses_
+              [_P.L.A._], Vol. I, p. 349. 1862.
+    —— _Natural Philosophy_, Appendix D.
+    —— _P.L.A._, Vol. II, p. 6. 1865.
+    —— _P.L.A._, Vol. II, p. 10. 1868.
+    Huxley. _Presidential Address, Quart. Journ. Geol. Soc. 1869._
+    Thomson. _P.L.A._, Vol. II, p. 73. 1869.
+    —— _P.L.A._, Vol. II, p. 238. 1876.
+    —— _P.L.A._, Vol. I, p. 369. 1887.
+    King. _Am. Journ. Science_, p. 1. 1893.
+    Correspondence in _Nature_. Perry, Kelvin, Tait.
+          January 3rd, March 7th, April 18th. 1895.
+    Poulton. _Rep. Brit. Ass._, p. 808. 1896.
+    Kelvin. _Phil. Mag._, January, 1899, p. 66. 1897.
+    Correspondence in _Nature_. 1903.
+          Wilson. July 9th.
+          Darwin. September 24th.
+          Joly. October 1st.
+    Correspondence in _Nature_.
+          Kelvin, Strutt, Lodge, etc. September 20th. 1906.
+
+    For other references see below.
+
+CHAPTER II
+
+    Chamberlin and Salisbury. _Geology_, Vol. II, Chaps. I and II. 1909.
+    T. C. Chamberlin and other Writers. _The Tidal Problem._
+          Carnegie Inst. of Washington. Pub. No. 107. 1909.
+    Darwin. _The Tides._ 1911.
+    Poincaré. _Hypothèses cosmogoniques._ Paris. 1911.
+
+CHAPTER III
+
+    Croll. _Phil. Mag._ May, 1868.
+    —— _Climate and Time._ 1875.
+    De Geer. _Geol. Fören i Stockholm Föhr Band 32._ 1910.
+    Gilbert. _Journ. of Geol._, Vol. III, p. 121. 1895.
+    Lowell. _Evolution of Worlds_, p. 197. 1910.
+    Sederholm. _Bull. Comm. Géol. de Finlande_, No. 30, pp. 7-15. 1911.
+    Sollas. _Ancient Hunters._ 1911.
+
+CHAPTER IV
+
+    Babb. _Science_, Vol. XXI, p. 343. 1893.
+    Clarke. _Data of Geo. Chemistry. Geol. Sur., U.S.A. Bull. 491._
+    —— _Smith. Misc. Collect._, Vol. LVI, No. 5. 1910.
+    Dittmar. _Challenger_ Report, Vol. I, p. 203. 1884.
+    Dole and Stabler. _Water Supply Papers. Geol. Sur., U.S.A._,
+         Nos. 234 and 236. 1910.
+    Geikie. _Trans. Geol. Soc., Glasgow_, p. 153. 1868.
+
+    Humphreys and Abbott. _Physics and Hydraulics of Mississippi River_,
+         p. 148. 1876.
+    Merrill. _Rocks, Rock weathering and Soils._ 1897.
+    Murray. _Scot. Geog. Mag._, Vol. III, p. 65. 1887.
+    —— _Scot. Geog. Mag._, Vol. IV, p. 38. 1888.
+    Reade. _Chemical Denudation in Relation to Geological Time._ 1901.
+    Russell. _River Development._ 1898.
+    Schwarz. _Causal Geology._ 1910.
+    Tylor. _Phil. Mag._, April, p. 258. 1853.
+
+CHAPTER V
+
+    Ackroyd. _Chem. News_, p. 265. 1901.
+    —— _Geol. Mag._, p. 445 and p. 558. 1901.
+    Becker. _Science_, Vol. XXXI, p. 459. 1910.
+    —— _Smith. Misc. Collect._, Vol. LVI, No. 6. 1910.
+    Clarke. _Smith. Misc. Collect._, Vol. LVI, No. 5. 1910.
+    —— _Proc. Am. Phil. Soc._, p. 214. 1912.
+    Fisher. _Geol. Mag._, p. 124 and p. 132. 1900.
+    Halley. _Phil. Trans._, Vol XXIX, p. 296. 1715.
+    Hanamann. _Landesdurchforschung Böhmens. Archiv.
+          Natur._, Vol. IX. Vol. X. 1894. 1898.
+    —— _Cited in Clarke’s Data_, 2nd ed., p. 92.
+    Joly. _Trans. Roy. Soc., Dublin_, Vol. VII, p. 23. 1899.
+    —— _Rep. Brit. Ass._, p. 369. 1900.
+    —— _Geol. Mag._, p. 344 and p. 504. 1901.
+    —— _Radioactivity and Geology_, p. 236. 1909.
+    —— _Phil. Mag._, p. 357. September, 1911.
+    Karsten. _Inaug. Diss., Kiel._ 1894.
+    Rudzki. _Bull. Acad. Sci., Cracovie._ February, 1901.
+    Sollas. _Presidential Address, Quar. Journ. Geol. Soc._,
+          Vol. LXV. 1909.
+
+CHAPTER VI
+
+    Blake. _Geol. Mag._, p. 72. 1903.
+    Croll. _Stellar Evolution_, p. 48. 1889.
+    Geikie. _Rep. Brit. Ass._ 1892.
+    —— _Nature._ August 4th, 1892.
+    —— _Rep. Brit. Ass._, p. 727. 1899.
+    Haughton. _Manual of Geology_, p. 101. 1871.
+    —— _Nature_, p. 266. 1878.
+    Holmes. _Nature._ July 6th, 1911.
+    Joly. _Radioactivity and Geology._ 1909.
+    de Lapparent. _Bull. Soc. Géol. de France_,
+          Vol. XVIII, p. 351. 1890.
+    —— _Géologie_, p. 225, p. 261, and p. 1958. 1906.
+    Lyell. _Principles._ Tenth Edn., Vol. I, p. 301. 1867.
+    McGee. _Science_, Vol. XXI, p. 309. 1893.
+    Phillips. _Life on the Earth_, p. 119. 1860.
+    Reade. _Geol. Mag._, p. 99. 1893.
+    Sederholm. _Naturen, Helsingfors_, Nos. 33 and 34. 1897.
+    Sollas. _Nature._ April 4th, 1895.
+    —— _Rep. Brit. Ass._, p. 711. 1900.
+    —— _The Age of the Earth and other Geological Studies._ 1905.
+    —— _Presidential Address, Quar. Journ. Geol. Soc._,
+            Vol. LXV. 1909.
+    Upham. _Am. Journ. Science_, Vol. XLV, p. 217. 1893.
+    Walcott. _Journ. Geol._, Vol. I, p. 675. 1893.
+    Watts. _Presidential Address, Quar. Journ. Geol. Soc._,
+           Vol. LXVII. 1911.
+    Wallace. _Island Life_, p. 222. 1892.
+    Winchell. _World Life_, Chicago, p. 378. 1883.
+
+CHAPTER VII
+
+    Mme. Curie. _Traité de Radioactivité._ 1910.
+    Ramsay and Soddy. _Proc. Roy. Soc. A._, Vol. LXXII, p. 204. 1903.
+    Russell. _Proc. Roy. Soc. A._, Vol. LXXXVI, p. 240. 1912.
+    Rutherford. _Radioactive Substances._ 1912.
+    Rutherford and Soddy. _Phil. Mag._, Vol. IV, p. 582. 1902.
+    Rutherford and Geiger. _Proc. Roy. Soc. A._,
+          Vol. LXXXI, p. 151. 1908.
+    Rutherford and Royds. _Phil. Mag._, Vol. XVII, p. 281. 1909.
+    Whytlaw-Gray and Ramsay. _Proc. Roy. Soc. A._,
+          Vol. LXXXVI, p. 270. 1912.
+
+CHAPTER VIII
+
+    Abbott. _The Sun._ 1910.
+    Arrhenius. _The Life of the Universe_, Vol. II, p. 193.
+    Helmholtz. _Phil. Mag._, p. 516. 1856.
+    Rutherford and Soddy. _Phil. Mag._ May, 1903.
+
+CHAPTER IX
+
+    Becker. _Bull. Geol. Soc. Am._, p. 113. 1908.
+    —— _Smith. Inst. Misc. Collect._, Vol. LVI, No. 6.
+
+    Buchner. _Proc. Konink. Akad. van Wetensch. te Amsterdam._
+                 October, 1910, February, 1911, and April, 1912.
+    Chamberlin. _Journ. Geol._, p. 674. 1911.
+    Eve and McIntosh. _Phil. Mag._ August, 1907.
+    —— _Trans. Roy. Soc. Canada_, p. 69. 1910.
+    Farr and Florance. _Phil. Mag._ November, 1909.
+    Fletcher. _Phil. Mag._ July, 1910.
+    —— _Phil. Mag._ January, 1911.
+    —— _Phil. Mag._ June, 1911.
+    —— _Phil. Mag._ February. 1912.
+    Joly. _Rep. Brit. Ass._, p. 677. 1908.
+    —— _Radioactivity and Geology_, 1909.
+    —— _Phil. Mag._ October, 1909.
+    —— _Phil. Mag._ July and August, 1910.
+    —— _Phil. Mag._ July, 1911.
+    —— _Cong. Internat. de Rad. and d’Elec._, p. 370. 1911.
+    —— _Phil. Mag._ February, 1912.
+    —— _Phil. Mag._ October, 1912.
+    King. _Am. Journ. Science_, p. 1. 1893.
+    Strutt. _Proc. Roy. Soc. A._, Vol. LXXIX, p. 472. 1906.
+    —— _Proc. Roy. Soc. A._, Vol. LXXXIV, p. 377. 1910.
+    Suzuki. _Proc. Math.-Phys. Soc., Tokyo_, p. 204. 1912.
+
+CHAPTER X
+
+    Becker. _Bull. Geol. Soc., Am._, Vol. XIX, p. 113. 1908.
+    Boltwood. _Am. Journ. Science_, p. 260. 1905.
+    —— _Am. Journ. Science_, Vol. XXIII, p. 77. 1907.
+    Boltwood and Rutherford. _Phil. Mag._, Vol. XXII, p. 586. 1911.
+    Dewar. _Proc. Roy. Soc. A._, Vol. LXXXI, p. 280. 1908.
+    —— _Proc. Roy. Soc. A._, Vol. LXXXIII, p. 404, 1910.
+    Holmes. _Proc. Roy. Soc. A._, Vol. LXXXV, p. 248, 1911.
+    Joly. _Radioactivity and Geology_, p. 211. 1909.
+    —— _Phil. Mag._ September, 1911.
+    Kœnigsberger. _Geol. Rundschau_, Vol. I, p. 245. 1910.
+    Rutherford. _Radioactivity_, p. 486. 1905.
+    Strutt. _The Accumulation of Helium._
+    —— _Proc. Roy. Soc. A._, Vol. LXXXI, p. 272. 1908.
+    ——   ——   Vol. LXXXII, p. 166. 1909.
+    ——   ——   Vol. LXXXIII, p. 96. 1910.
+    ——   ——   Vol. LXXXIII, p. 298. 1910.
+    ——   ——   Vol. LXXXIV, p. 195. 1910.
+    ——   ——   Vol. LXXXIV, p. 380. 1910.
+
+[Illustration: THE RADIOACTIVE ELEMENTS
+
+URANIUM FAMILY
+
+ACTINIUM FAMILY
+
+THORIUM FAMILY]
+
+
+
+
+INDEX
+
+
+    α-particles, deflection of, 94
+    — nature of, 95
+    — penetration of, 94, 107, 108
+    — heating effect of, 96, 97
+    — kinetic energy of, 177
+    — atoms of helium, 96
+    Actinium and uranium, 100
+    Adams, 25
+    Age of earth, 86, 89, 125, 157
+    — minerals, 154-64
+    — moon, 15, 27
+    — oceans, 68, 89
+    — sediments, 86, 89
+    — sun, 112, 113, 120
+    Arrhenius, energy of sun, 117
+    Atmosphere, origin of, 25, 30
+    — as thermal blanket, 36
+    Atomic theory, 40
+    Atoms in 1 cc. helium, 140
+    — in 1 gr. hydrogen, 179
+    — in 1 gr. radium, 179
+    — disintegration of, 98, 102
+    — constitution of, 102
+    Autunite, age of, 100, 153
+    — radium-ratio in, 100
+    — lead-ratio in, 153
+
+    β-particles, deflection of, 94
+    — nature of, 95
+    — from potassium, 103
+    Barus, diabase fusion point, 125, 126
+    Barnes and Rutherford, heat output of radium, 101
+    Basic rocks, radium in, 130
+    — distribution of, 128, 134
+    Becker, age of oceans, 62, 63, 70
+    — age of earth, 127
+    Becquerel, discovery of radioactivity, 92
+    Becquerel rays, 93
+    Biology and the earth’s age, 20, 21
+    Boltwood,constancy of radium-ratio, 99
+    — origin of actinium, 100
+    — test of lead-ratio, 158
+    Boltwood and Rutherford, production of helium, 139
+    Bragg, ionisation, 107
+    Bückner, radium in rocks, 130
+    Buffon, 23
+
+    Calcium carbonate, accumulation of, 88, 89
+    Catastrophism, 4, 8
+    Chaldean chronology, 2
+    Chamberlin, planetismal hypothesis, 28-30
+    — tidal theory, 27
+    — rate of denudation, 79, 80, 81
+    _Challenger_ expedition, 85
+    Chlorine in rain, 66
+    — in rivers, 53, 70
+    — in sea, 53
+    — in rocks, 70
+    Chronology, Chaldean, 2
+    — Persian, 3
+    — Hebrew, 3
+    — Indian, 3
+    — Byzantine, 4
+    Clarke, sodium in rocks, 67, 70, 71
+    — chemical denudation, 51-3
+    — volume of oceans, 63
+    — age of oceans, 63, 66
+    Cosmical energy, 120
+    Croll, glacial theory, 35-9
+    — marine erosion, 58
+    — age of earth, 86
+    Crust of earth, thickness of, 128, 134
+    — evolution of, 30, 134
+    Crystallisation of rock magmas, 145-8
+    Curie, Mme., radioactivity of thorium, 92
+    — discovery of radium, 93
+    Curie and Laborde, heating effect of radium, 96, 101
+    Cuvier, 8
+    Cycles of denudation and deposition, 85, 174, 175
+    Cyclic sedimentation, 44
+    — circulation of salt, 66-70
+
+    Dana, volume of limestone, 88
+    Darwin, geological time, 11
+    Darwin, Sir G., moon’s history, 15, 19
+    — age of moon, 27
+    Decay, radioactive, 98
+    — physical independence of, 102
+    — possible variation with time, 168
+    Deep-sea deposits, 59
+    Deluge, 4, 8
+    Denudation, initiation of, 25, 31
+    Denudation, chemical, 50, 54
+    — mechanical, 54
+    — marine, 58, 66
+    — present rates of, 78, 80
+    Deposition, 47, 81-5
+    Dewar, production of helium, 140
+    Diabase, fusion point, 125, 126, 128
+    Dittmar, salinity of oceans, 64
+    Dole and Stabler, denudation of N. America, 50, 55
+    Duane, heating effect of radium, 101
+
+    Earth, origin of, 22 _et seq._
+    — early history of, 25, 29, 73
+    — heat of, 12-16, 30, 122
+    — interior of, 134
+    — distribution of radium, 131-5
+    Earthquakes, 134
+    Electroscope, 93, 104
+    Emanation of radium, 97, 104
+    End products, 100, 140
+    Energy, conservation of, 11, 111
+    Eve and McIntosh, radium in rocks, 130
+
+    Farr and Florance, radium in rocks, 130
+    Fletcher, radium in rocks, 130
+    Fossils, early ideas, 5
+
+    γ-rays, nature of, 94
+    Geer, De, glacial clays, 41-4
+    Geiger and Rutherford, counting of α-particles, 138
+    Geikie, age of earth, 86
+    — marine erosion, 58
+    — on geological time, 78
+    Glacial periods, 33
+    Glacial periods, chronology of, 36 _et seq._
+    Glacial clays in Sweden, 41
+    Glaciation, indications of, 33, 34
+    — cause of, 35
+    Gilbert, Cretaceous sediments of Colorado, 44
+
+    Haloes, pleochroic, 107-9
+    Halley, salinity of oceans, 61
+    Heat, emission of, by radium, 96, 97, 101
+    —   —   by uranium, 116, 131, 132
+    —   —   by thorium, 116, 132
+    — escaping from earth, 122-4, 132
+    — of the sun, 110 _et seq._
+    Helium, discovery of, 95, 96
+    — from radio-elements, 96
+    — rate of evolution of, 138
+    — leakage of, 149
+    — as end product, 149
+    — accumulation of, 154
+    —   —   in phosphates, 154
+    —   —   in iron ores, 155
+    —   —   in zircons, 156
+    —   —   in sphenes, 156
+    Helium-ratio, as age-index, 143
+    Helmholtz, 12, 112
+    Hutton, 7, 22
+    Huxley, reply to Kelvin, 14, 20
+
+    Igneous rocks, exposures of, 71, 72, 73
+    — sodium in, 67
+    — radium in, 131
+    — thorium in, 131
+    Ionisation, 93, 104
+    Ionium, 99
+    Iron meteorites, 134
+    Iron ores, helium in, 155
+
+    Joly, estimation of radium, 105
+    —   —   thorium, 107
+    — radium in rocks, 131
+    — thorium in rocks, 131
+    — age of the earth, 86
+    — age of the oceans, 17, 20, 62
+    — on radioactive decay, 168
+
+    Kant, 23, 26, 110
+    Kelvin, duration of earth’s heat, 12-17, 124, 125
+    —   —   sun’s heat, 12-14, 111
+    — tidal retardation, 13, 26, 27
+
+    Lamarck, 8
+    Land, area of, 52
+    — degradation of, 57
+    Laplace, 23, 28, 35
+    Laplacian hypothesis, 23-25
+    — difficulties of, 28
+    Lapparent, de, 86
+    Lead in igneous rocks, 147
+    — genetic connection with uranium, 100, 140, 141
+    — in uranium minerals, 158-164
+    — rate of production of, 142
+    Lead-ratio as age-index, 143
+    Lowell, Polar caps of Mars, 39
+    Lyell, _Principles_, 9
+
+    Mars, Polar caps of, 39
+    Mass of electron, 95
+    — of hydrogen atom, 179
+    Mayer, sun’s heat, 12, 111
+    Meteorites and sun’s heat, 111
+    — radium in, 134
+    Mica, pleochroic haloes in, 109
+    Minerals, radium-ratio in, 99, 100
+    — actinium-ratio in, 100
+    — lead-ratio in, 141, 143
+    — helium-ratio in, 143
+    — choice of, 153
+    Mississippi as denuding agent, 55
+    — bottom load of, 54
+    Moon, 15, 19, 20, 27, 28
+    Moses and geology, 3, 9
+    Moulton, 28
+    Murray, area of land, 52
+    — salinity of rivers, 50
+    — volume of ocean, 63
+
+    Nebulæ, Laplacian, 24, 28
+    — spiral, 28, 29
+    Nebular hypothesis, 23-25, 28
+    Nile, annual deposit of, 81
+    North America, denudation of, 50, 56
+
+    Oceans, origin of, 25, 50
+    — mass of, 53, 64
+    — volume of, 53, 63
+    — saline content of, 53
+    — age of, 68, 89
+    Origin of earth, 22, _et seq._
+
+    Perry, 16
+    Phillips, 10
+    Phosphates, helium in, 154
+    Phosphorescence of uranium salts, 92
+    Pitchblende. _See_ Uraninite
+    Pleochroic haloes, 107-109, 170
+    Polonium, discovery of, 93
+    Poulton, biology and geological time, 21
+    Products, final radioactive, 100, 140
+
+    Radioactive disintegration, 98
+    —   —   physical independence of, 102
+    Radioactive layer, 133
+    Radiation from uranium, 92
+    Radium, discovery of, 93
+    — detection of, 93, 103-107
+    — emanation from, 98, 104
+    — helium from, 96, 138-140
+    — α-rays from, 96, 138
+    — half-life of, 98, 99, 179
+    — atomic weight of, 142
+    — genesis from uranium, 99
+    — heating effect of, 96, 101, 129, 131
+    — end products of, 100
+    — in earth’s crust, 103, 131
+    — in igneous rocks, 131
+    — in sediments, 131
+    — in sun, 117
+    Ramsay, helium in minerals, 96
+    Reade, chemical denudation, 50, 62
+    — age of earth, 86
+    — volume of limestone, 88
+    River water, volume of, 53
+    — sediment in, 56, 57
+    — salinity of, 53
+    Rocks, radium in, 130, 131
+    — thorium in, 131
+    — chlorine in, 70
+    — sodium in, 67
+    Röntgen rays, discovery of, 92
+    — nature of, 94
+    Runge and Precht, heat output of radium, 101
+    Rutherford, age of minerals, 154
+    — Becquerel rays, 93
+    Rutherford and Barnes, heat output of radium, 101
+    Rutherford and Geiger, counting of α-particles, 138
+    Rutherford and Soddy, disintegration hypothesis, 96, 98
+    — radium and sun’s heat, 116
+
+    Schwarz, 49
+    Schuchert, 78
+    Schweidler v. and Hess, heat output of radium, 101
+    Sederholm, annual deposits, 43
+    — thickness of sediments, 43, 85
+    Sediment carried by rivers, 57
+    Sediments, volume of, 65, 68, 88
+    — pore space of, 65
+    — thickness of, 43, 44, 76, 77
+    — rate of deposit of, 81, 84
+    — rate of accumulation of, 47
+    — radium in, 131
+    — thorium in, 131
+    — sodium in, 67
+    — on Continental shelf, 83
+    — oceanic, 59
+    — time represented by, 86
+    Sedimentation, cyclic, 41, 43, 44
+    Soddy, generation of helium, 96
+    —   —   radium, 99
+    Sodium in rivers, 53, 64
+    — in ocean, 53, 64
+    — in igneous rocks, 67, 71
+    — in sediments, 67
+    — age of ocean, 64
+    — wind-borne, 66
+    — in sewage, 66
+    Solar system, origin of, 23 _et seq._
+    Solar constant, 113
+    Sollas, thickness of sediments, 76
+    — age of earth, 86, 87
+    — age of oceans, 62, 63
+    — biology and time, 21
+    — glacial retreat, 43
+    Steno, 5, 6
+    St. Meyer and Hess, heat output of radium, 101
+    Strutt, determination of radium, 105
+    — radium in rocks, 129, 130
+    — rate of generation of helium, 139
+    — leakage of helium, 149
+    — accumulation of helium, 154-157
+    Sun, origin of, 25
+    — helium in, 95, 117
+    — radium in, 117
+    — temperature of, 119
+    — duration of heat of, 12, 14, 112, 114, 120
+    Suzuki, age of earth, 128
+
+    Temperature—gradient of earth’s crust, 122
+    — due to radium, 128, 132
+    Thermal conductivity of rocks, 123
+    Thomson. _See_ Kelvin
+    Thorianite, generation of helium by, 139
+    Thorium, discovery as a radio-element, 92
+    — family of elements, 100, 190
+    — end product of, 100
+    — heat output of, 131
+    — distribution of, in rocks, 131
+    Tidal retardation, 13, 26, 27
+    Transformation, radioactive, 97, 98
+    — end products of, 100
+
+    Unconformities, 160
+    Underground temperature, 12, 13, 122-8
+    Uniformitarianism, rise of, 7, 9
+    — criticised, 12, 78, 174
+    Uraninite, generation of helium by, 139
+    — lead-ratio of, 151, 158-62
+    Uranium, atomic weight of, 142
+    — discovery as a radio-element, 92
+    — phosphorescence of salts 91, 92
+    — range of α-rays from, 178
+    — family of, 100, 190
+    — end products of, 100, 140-142
+    — generation of radium from, 99
+    —   —   helium from, 142
+    —   —   lead from, 142
+    — heat output of, 116, 131
+    — half-life period of, 179
+    — time-average of, 143, 179-182
+    Uranium-bearing minerals—
+      Llano Co., 151, 152
+      Connecticut, 158, 159,
+      Carolina, 159, 160
+      S. Norway, 161, 162
+      Brevig, 163, 164
+      Mozambique, 153, 160
+    — alteration of, 150-153
+    Ussher, chronology of, 3, 10
+
+    Van Hise, 88
+    Velocity of α-particles, 177
+
+    Watts, marine erosion, 58
+    — cycle of deposition, 85
+    Weathering of rocks, 48, 49
+    — of minerals, 150
+    Wilson, W. E., sun’s heat, 116
+
+    Zircon, helium-ratio in, 156
+    — lead-ratio in, 160, 164
+    Zoroaster, chronology of, 3
+
+            WILLIAM BRENDON AND SON, LTD.
+                PRINTERS, PLYMOUTH
+
+*** END OF THE PROJECT GUTENBERG EBOOK 78241 ***