The cover image was created by the transcriber and is placed in the public domain.

THE EARTH’S BEGINNING

WORKS BY

SIR ROBERT S. BALL,

M.A., LL.D., F.R.S.

THE STORY OF THE HEAVENS.

With 24 Coloured Plates and Numerous Illustrations. New Edition. 10s. 6d.

THE EARTH’S BEGINNING.

With 4 Coloured Plates and Numerous Illustrations. New Edition. 7s. 6d.

THE STORY OF THE SUN.

With 11 Full Page Coloured and other Plates and Numerous Illustrations. 7s. 6d.

STAR-LAND.

Being Talks with Young People about the Wonders of the Heavens With Rembrandt Frontispiece and 94 Illustrations in Text. 7s. 6d.

CASSELL & COMPANY, Limited, London,

New York, Toronto & Melbourne.

AN ENGLISH SUNSET TINGED BY KRAKATOA.
(From a Drawing made at Chelsea at 4.40 p.m. on Nov. 26th, 1883, by Mr. W. Ascroft.)

THE

Earth’s Beginning

BY

SIR ROBERT S. BALL, M.A., LL.D., F.R.S.

Lowndean Professor of Astronomy and Geometry in the University of Cambridge,

Author of “Star-Land,” “The Story of the Heavens,”

etc. etc.

WITH FOUR COLOURED PLATES AND

NUMEROUS ILLUSTRATIONS

NEW EDITION

CASSELL AND COMPANY, LIMITED

LONDON, NEW YORK, TORONTO AND MELBOURNE

MCMIX

First Edition October 1901.

Reprinted December 1901, 1903.

Enlarged Edition 1909.

ALL RIGHTS RESERVED

FOREWORD

Since these lectures were delivered in the Royal Institution of Great Britain there has been much advance in our knowledge of astronomy. The simultaneous advance in other sciences allied with astronomy has been, perhaps, even more remarkable. I am glad to avail myself of the opportunity afforded by a new issue of “The Earth’s Beginning” to draw attention to certain recent developments of science which relate in a very striking way to the subject of this volume, namely, the famous Nebular Theory of the origin of the solar system. It appears to me that these recent developments tend to reduce greatly, even if they do not altogether remove, the chief outstanding difficulty which has hitherto retarded the acceptance of the Nebular Theory.

I have explained in Chapter VI. those views of Helmholtz which have for so long provided the received explanation of the maintenance of solar heat. Calculation shows that if the sun’s heat has been maintained by the contraction of the primæval nebula—and this was the supposition of Helmholtz—the orb of day cannot have radiated with its present intensity for a period much longer than twenty million years.

But from the evidence of geology it must now be admitted that the existence of our earth, indeed even that part of its existence during which it has been the abode of life, has endured for a period far in excess of that which this calculation would allow. It therefore seems to follow that the theory of Helmholtz does not provide an adequate explanation of such an amazing phenomenon as the continuance of a sufficient supply of sunbeams throughout the vast periods demanded by geological phenomena.

There is another entirely different line of reasoning by which Professor John Joly has recently taught us the immense antiquity of our earth. His argument is based upon an estimate of the time that must have elapsed since the waters of the ocean, which had previously been sustained in the great vapours of the atmosphere, were deposited in the ocean beds. When the earth had become sufficiently cool to permit of the vapours now forming the ocean passing from the gaseous to the liquid form, the oceans descended from the heavens above to the earth beneath in the form of fresh water. In the lapse of subsequent ages the sea has become salt because ordinary river water, which always contains some small quantity of salt in solution, is continually bearing salt down to the sea. No doubt water is constantly being abstracted from the sea by evaporation, but only fresh water is thus removed, so in this cycle of change the salt in the sea must be gradually accumulating. Thus, day by day, though no doubt extremely slowly, the sea has been growing more and more salt.

Professor Joly has made an estimate of the quantity of salt daily added to the sea by all the rivers of the globe. He has also made an estimate of the total quantity of salt which is at present contained in the sea. He has thus the means of forming an estimate of the number of years necessary for the sea to have become converted from its primæval freshness to its present saltness. His result is not a little astonishing. The saltness of the sea could not be accounted for unless the rivers had been running into the sea for at least a hundred million years. This period is five times as long as the total period during which the sun could have been shining if the Helmholtzian view were correct.

Of course, there are many elements of uncertainty in such a calculation. We have assumed that the total flow of the rivers is practically constant, and that our estimate fairly represents the average salinity of river water. We have also made a large assumption in supposing that we have accurately estimated the total volume of salt in the oceans. But taken in conjunction with the geological evidence already referred to, taken in conjunction with the immense periods of time that have been required for the evolution of life on the globe by the process of natural selection, the conclusion arrived at is inevitable. It seems impossible to doubt that the sun must have been shining and that our solar system must have existed in practically the same form as it is at present for periods enormously greater than would have been possible if the heat of the sun had been sustained by the solar contraction only.

The difficulty here indicated has been not unjustly considered the most serious difficulty with which the development of modern physical and astronomical science has been confronted. The time during which the sun must have lasted, according to the received explanation of the source of its heat and the time during which the sun has actually lasted, as shown by the facts of geology, present a wide discrepancy. Science demands that some reconciliation must be effected, yet how is that to be accomplished? There is only one possible solution of the problem. It is obvious that there must have been some vast reserve of heat in the sun in comparison with which the quantity of heat yielded by the contraction may be deemed insignificant. Until this new source of solar energy had been discovered, our knowledge of the physics of the solar system lay under a reproach, which it was the bounden duty of men of science to endeavour to remove.

During the last few years lines of research carried on in various directions have, in a most unexpected manner, thrown much light on the origin of the sun’s heat, and, indeed, we may now say that the great difficulty which has for so long troubled us no longer exists in a serious form.

Recent discoveries show that matter possesses stores of energy which, if not actually boundless, are enormously in excess of what had been previously deemed possible. These stores of energy are available for supplying the heat of the sun, and it is easy to show that they are amply sufficient to furnish the necessary sunbeams for even the longest periods during which the claims of geology maintain that the sun must have been shining.

The researches of Professor Sir J. J. Thomson have shown how corpuscles of matter are sometimes moving with velocities enormously greater than those of any celestial body with which astronomy had made us acquainted. The case of high corpuscular velocity which is most generally known is that presented by radium, the particles from which are being continually shot forth in myriads. It is quite true that each of these corpuscles is excessively small, and it may be useful to give the following illustration bearing on the subject. Think of a number represented by unity followed by eighteen cyphers, or more concisely as 10¹⁸, and think of a line a kilometre long. If that line were divided into 10¹⁸ parts, each of those parts would represent the diameter of a corpuscle of radium. If that line were multiplied by 10¹⁸, the result would be a line so long that a ray of light would require a period of no less than 100,000 years to pass from one end to the other.

These corpuscles of radium are, no doubt, excessively small, but the velocity with which they are moving is comparable with the velocity of light. When a material object is moving with a velocity of that magnitude the energy it contains in virtue of that velocity is indeed startling. A very small grain of sand would, if moving with the velocity of light, contain, in virtue of that motion, the equivalent of more heat than could be produced by the combustion of a ton of the best coal. The late Dr. W. E. Wilson showed that if an excessively minute percentage of radium should be found to exist in the sun, it would completely account for the sustentation of the solar heat, and the Hon. R. Strutt has shown that the minute quantities of radium which he has proved to exist in terrestrial rocks would enormously protract the earth’s cooling. These discoveries have, in fact, completely changed the outlook on the problem of the sun’s heat, and, though no doubt much has yet to be done before the whole subject is cleared up, the great difficulty may be regarded as vanquished. Thus, the discovery of radium, and the wonderful phenomena associated therewith, has pointed out a possible escape from one of the gravest difficulties in science.

The most notable fact which emerges from the modern study of the structure of the heavens is the ever-increasing significance and importance of the spiral nebulæ. The following pages will have failed in their object if they have not succeeded in emphasising the fact that the spiral nebula is, next to a fixed star itself, the most characteristic type of object in the material universe. With every increase in the power of the telescope, and with every development of the application of photography to celestial portraiture, the importance of the spiral structure in nebulæ becomes of ever-increasing interest.

But I revert to this subject here for the purpose of taking notice of a suggestive paper by Mr. C. Easton in the “Astrophysical Journal,” Vol. XII., No. 2, September, 1900, entitled “A New Theory of the Milky Way.” This paper advances the striking view that the Milky Way is itself a spiral nebula, and certainly the considerations adduced by Mr. Easton seem to justify his remarkable conclusion.

It is first to be noticed that the Milky Way extends as an irregular band completely round the heavens, and that it follows very nearly the course of a great circle. The curious convolutions of the Milky Way, the varying star densities of its different parts, would, as shown by Mr. Easton, be completely accounted for if the Milky Way were a mighty spiral. We view the ordinary celestial spirals from the outside at an immense distance in space. We view the Milky Way from a position within the circuit of the nebula. It has, however, been shown by Mr. Easton that the centre of the Spiral Nebula is not exactly at the sun. The centre of the Milky Way is near that superb region of the galaxy which lies in Cygnus.

Thus, the significance of the spiral structure in the universe becomes greatly enhanced. The spirals abound in every part of the heavens; they are placed in every conceivable position and in every possible plane; they have every range in size from comparatively small objects, whose destiny is to evolve into a system like our solar system, up to stupendous objects which include a myriad of such systems. There is now the further interest that as the sun and the solar system are included within the Milky Way, and as the Milky Way is a spiral, this earth of ours is itself at this moment a constituent part of a great spiral.

Finally, I would say that, so far as I have been able to understand the subject, it appears to me that every advance in our knowledge of the heavens tends more and more to support the grand outlines of the Nebular Theory as imagined by Kant and Laplace.

R. S. B.

May 1, 1909.

CONTENTS

LIST OF ILLUSTRATIONS

THE EARTH’S BEGINNING.

CHAPTER I.
INTRODUCTION.

The Earth’s Beginning—The Nebular Theory—Many Applications of the Theory—The Founders of the Doctrine—Kant, Laplace, William Herschel: Their Different Methods of Work—The Vastness of the Problem—Voltaire’s Fable—The Oak-Tree—The Method of Studying the Subject—Inadequacy of our Time Conceptions.

I TRY in these lectures to give some account of an exceptionally great subject—a subject, I ought rather to say, of sublime magnificence. It may, I believe, be affirmed without exaggeration that the theme which is to occupy our attention represents the most daring height to which the human intellect has ever ventured to soar in its efforts to understand the great operations of Nature. The earth’s beginning relates to phenomena of such magnitude and importance that the temporary concerns which usually engage our thoughts must be forgotten in its presence. Our personal affairs, the affairs of the nation, and of the empire—indeed, of all nations and of all empires—nay, even all human affairs, past, present, and to come, shrink into utter insignificance when we are to consider the majestic subject of the evolution of that solar system of which our earth forms a part. We shall obtain a glimpse of what that evolution has been in the mighty chapter of the book of Nature on which we are now to enter.

The nebular theory discloses the beginning of this earth itself. It points out the marvellous process by which from original chaos the firm globe on which we stand was gradually evolved. It shows how the foundations of this solid earth have been laid, and how it is that we have land to tread on and air to breathe. But the subject has a scope far wider than merely in its relation to our earth. The nebular theory accounts for the beginning of that great and glorious orb the sun, which presides over the system of revolving planets, guides them in their paths, illuminates them with its light, and stimulates the activities of their inhabitants with its genial warmth. The nebular theory explains how it comes about that the sun still continues in these latter days to shine with the brilliance and warmth that it had throughout the past ages of human history and the vastly greater periods of geological time. Then, as another supreme achievement, it discloses the origin of the planets which accompany the sun, and shows how they have come to run their mighty courses; and it tells us how revolving satellites have been associated with the planets. The nebular theory has, indeed, a remarkable relation to all objects belonging to that wonderful scheme which we call the solar system.

It should also be noticed that the nebular theory often brings facts of the most diverse character into striking apposition. As it accounts for the continued maintenance of the solar radiation, so it also accounts for that beneficent rotation by which each continent, after the enjoyment of a day under the invigorating rays of the sun, passes in due alternation into the repose of night. The nebular theory is ready with an explanation of the marvellous structure revealed in the rings of Saturn, and it shows at the same time how the volcanoes of the moon acquired their past phenomenal activity, and why, after ages of activity, they have now at last become extinct. With equal versatility the nebular theory will explain why a collier experiences increasing heat as he descends the coalpit, and why the planet Jupiter is marked with those belts which have so much interest for the astronomer. The nebular theory offers an immediate explanation of the earthquake which wrought such awful destruction at Lisbon, while it also points out the cause of that healing warmth of the waters at Bath. Above all, the nebular theory explains that peerless discovery of cosmical chemistry which declares that those particular elements of which the sun is composed are no other than the elements which form the earth beneath our feet.

When a doctrine of such transcendent importance is proposed for our acceptance, it is fitting that we should look, in the first instance, to the source from which the doctrine has emanated. It would already have made good its claim to most careful hearing, though not perhaps to necessary acceptance, if it came to us bearing credentials which prove it to be the outcome of the thought and research of one endowed with the highest order of intellect. If the nebular theory had been propounded by only a single great leader of thought, the sublimity of the subject with which it deals would have compelled the attention of those who love to study the book of Nature. If it had appeared that a second investigator, also famous for the loftiest intellectual achievement, had given to the nebular theory the sanction of his name, a very much stronger claim for its consideration would at once have been established. If it should further appear that yet a third philosopher, a man who was also an intellectual giant, had been conducted to somewhat similar conclusions, we should admit, I need hardly say, that the argument had been presented with still further force. It may also be observed that there might even be certain conditions in the work of the three philosophers which would make for additional strength in the cause advocated; if it should be found that each of the great men of science had arrived at the same conclusion irrespective of the others, and, indeed, in total ignorance of the line of thought which his illustrious compeers were pursuing, this would, of course, be in itself a corroboration. If, finally, the methods of research adopted by these investigators had been wholly different, although converging to the establishment of the theory, then even the most sceptical might be disposed to concede the startling claim which the theory made upon his reason and his imagination.

All the conditions that I have assumed have been fulfilled in the presentation of the nebular theory to the scientific world. It would not be possible to point to three names more eminent in their respective branches of knowledge than those of Kant, Laplace, and William Herschel. Kant occupies a unique position by the profundity and breadth of his philosophical studies; Laplace applied the great discoveries of Newton to the investigation of the movements of the heavenly bodies, publishing the results in his immortal work, Mécanique Céleste; Herschel has been the greatest and the most original observer of the heavens since the telescope was invented. It is not a little remarkable that the great philosopher from his profound meditation, the great mathematician from a life devoted to calculations about the laws of Nature, the great observer from sounding the depths of the firmament, should each in the pursuit of his own line of work have been led to believe that the grand course of Nature is essentially expressed by the nebular theory. There have been differences of detail in the three theories; indeed, there have been differences in points which are by no means unimportant. This was unavoidable in the case of workers along lines so distinct, and of a subject where many of the elements were still unknown, as indeed many are still. Even at the present day no man can give a complete account of what has happened in the great evolution. But the monumental fact remains that these three most sagacious men of science, whose lives were devoted to the pursuit of knowledge, each approaching the subject from his own direction, each pursuing his course in ignorance of what the others were doing, were substantially led to the same result. The progress of knowledge since the time when these great men lived has confirmed, in ways which we shall endeavour to set forth, the sublime doctrine to which their genius had conducted them.

Immanuel Kant, whose grandfather was a Scotsman, was born in 1724 at Königsberg, where his life was spent as a professor in the University, and where he died in 1804. In the announcement of the application of the principle of evolution to the solar system, Laplace was preceded by this great German philosopher. The profound thinker who expounded the famous doctrine of time and space did not disdain to allow his attention to be also occupied with things more material than the subtleties of metaphysical investigation. As a natural philosopher Kant was much in advance of his time. His speculations on questions relating to the operations in progress in the material universe are in remarkable conformity with what is now accepted as the result of modern investigation. Kant outlined with a firmness inspired by genius that nebular theory to which Laplace subsequently and independently gave a more definite form, and which now bears his name.

Kant’s famous work with which we are now concerned appeared in 1755.[^[1]] In it he laid down the immortal principle of the nebular theory. The greatness of this book is acknowledged by all who have read it, and notwithstanding that the progress of knowledge has made it obvious that many of the statements it contains must now receive modification, Kant’s work contains the essential principle affirming that the earth, the sun, the planets, and all the bodies now forming the solar system did really originate from a vast contracting nebula. In later years Kant’s attention was diverted from these physical questions to that profound system of philosophy with which his name is chiefly associated. The nebular theory is therefore to be regarded as incidental to Kant’s great lifework rather than as forming a very large and important part of it.

[1]. We are now fortunately able to refer the English reader to the work of Professor W. Hastie, D.D., entitled “Kant’s Cosmogony,” Glasgow, 1900. Kant’s most interesting career is charmingly described in De Quincey’s “Last Days of Immanuel Kant.”

IMMANUEL KANT.
(From an old Print.)

At the close of the last century, while France was in the throes of the Revolution, a school of French mathematicians was engaged in the accomplishment of a task which marked an epoch in the history of human thought. Foremost among the mathematicians who devoted their energies to the discussion of the great problems of the universe was the illustrious Laplace. As a personal friend of Napoleon, Laplace received marked distinction from the Emperor, who was himself enough of a mathematician to be able to estimate at their true value the magnificent results to which Laplace was conducted.

It was at the commencement of Kant’s career, and before his great lifework in metaphysics was undertaken, that he was led to his nebular theory of the solar system. In the case of Laplace, on the other hand, the nebular theory was not advanced until the close of the great work of his life. The Mécanique Céleste had been written, and the fame of its author had been established for all time; and then in a few pages of a subsequent volume, called the Système du Monde, he laid down his famous nebular theory. In that small space he gave a wonderful outline of the history of the solar system. He had not read that history in any books or manuscripts; he had not learned it from any ancient inscriptions; he had taken it direct from the great book of Nature.

Influenced by the caution so characteristic of one whose life had been devoted entirely to the pursuit of the most accurate of all the sciences, Laplace accompanied his announcement of the nebular theory with becoming words of warning. The great philosopher pointed out that there are two methods of discovering the truths of astronomy. Some truths may be discovered by observing the heavenly bodies with telescopes, by measuring with every care their dimensions and their positions, and by following their movements with assiduous watchfulness. But there is another totally different method which has enabled many remarkable discoveries to be made in astronomy; for discoveries may be made by mathematical calculations which have as their basis the numerical facts obtained by actual observation. This mathematical method often yields results far more profound than any which can be obtained by the astronomer’s telescope. The pen of the mathematician is indeed an instrument which sometimes anticipates revelations that are subsequently confirmed by actual observation. It is an instrument which frequently performs the highly useful task of checking the deductions that might too hastily be drawn from telescopic observations. It is an instrument the scope of whose discoveries embraces regions immeasurably beyond the reach of the greatest telescope. The pen of the mathematician can give us information as to events which took place long before telescopes came into existence—nay, even unnumbered ages prior to the advent of man on this earth.

Laplace was careful to say that the nebular theory which he sketched must necessarily be judged by a standard different from that which we apply to astronomical truths revealed by telescopic observation or ascertained by actual calculation. The nebular theory, said the great French mathematician, has to be received with caution, inasmuch as from the nature of the case it cannot be verified by observation, nor does it admit of proof possessing mathematical certainty.

A large part of these lectures will be devoted to the evidence bearing upon this famous doctrine. Let it suffice here to remark that the quantity of evidence now available is vastly greater than it was a hundred years ago, and furthermore, that there are lines of evidence which can now be followed which were wholly undreamt of in the days of Kant and Laplace. The particular canons laid down by Laplace, to which we have just referred, are perhaps not regarded as so absolutely binding in modern days. If we were to reject belief in everything which cannot be proved either by the testimony of actual eye-witnesses or by strict mathematical deductions, it would, I fear, fare badly with not a few great departments of modern science. It will not be necessary to do more at present than just to mention, in illustration of this, the great doctrine of the evolution of life, which accounts for the existing races of plants and animals, including even man himself. I need hardly say that the Darwinian theory, which claims that man has come by lineal descent from animals of a lower type, admits of no proof by mathematics; it receives assuredly no direct testimony from eye witnesses; and yet the fact that man has so descended is, I suppose, now almost universally admitted.

In the case of the great German philosopher, as well as in the case of the great French mathematician, the enunciation and the promulgation of their nebular theories were merely incidental to the important scientific undertakings with which their respective lives were mainly occupied. The relation of the nebular theory to the main lifework of the third philosopher I have named, has been somewhat different. When William Herschel constructed the telescopes with which, in conjunction with his illustrious sister, he conducted his long night-watches, he discovered thousands of new nebulæ; he may, in fact, be said to have created nebular astronomy as we now know it. Ever meditating on the objects which his telescopes brought to light, ever striving to sound the mysteries of the universe, Herschel perceived that between a nebula which was merely a diffused stain of light on the sky, and an object which was hardly distinguishable from a star with a slight haze around it, every intermediate grade could be found. In this way he was led to the splendid discovery which announced the gradual transformation of nebulæ into stars. We have already noted how the profound mathematician was conducted to a view of the origin of the solar system which was substantially identical with that which had been arrived at by the consummate metaphysician. The interest is greatly increased when we find that similar conclusions were drawn independently from the telescopic work of the most diligent and most famous astronomical observer who has ever lived. Not from abstract speculation like Kant, not from mathematical suggestion like Laplace, but from accurate and laborious study of the heavens was the great William Herschel led to the conception of the nebular theory of evolution.

That three different men of science, approaching the study of perhaps the greatest problem which Nature offers us from points of view so fundamentally different, should have been led substantially to the same result, is a remarkable incident in the history of knowledge. Surely the theory introduced under such auspices and sustained by such a weight of testimony has the very strongest claim on our attention and respect.

In the discussion on which we are about to enter in these lectures we must often be prepared to make a special effort of the imagination to help us to realise how greatly the scale of the operations on which the attention is fixed transcends that of the phenomena with which our ordinary affairs are concerned. Our eyes can explore a region of space which, however vast, must still be only infinitesimal in comparison with the extent of space itself. Notwithstanding all that telescopes can do for us, our knowledge of the universe must be necessarily restricted to a mere speck in space, a speck which bears to the whole of space a ratio less—we might perhaps say infinitely less—than that which the area of a single daisy bears to the area of the continent where that daisy blooms. But we need not repine at this limitation; a whole life devoted to the study of a daisy would not be long enough to explore all the mysteries of its life. In like manner the duration of the human race would not be long enough to explore adequately even that small part of space which is submitted for our examination.

But it is not merely the necessary limits of our senses which restrict our opportunities for the study of the great phenomena of the universe. Man’s life is too short for the purpose. That our days are but a span is the commonplace of the preacher. But it is a commonplace specially brought home to us in the study of the nebular theory. A man of fourscore will allude to his life as a long one, and no doubt it may be considered long in relation to the ordinary affairs of our abode on earth; but what is a period of eighty years in the history of the formation of a solar system in the great laboratory of the universe? Such a period then seems to be but a trifle—it is nothing. Eighty years may be long enough to witness the growth of children and grandchildren; but it is too short for a single heartbeat in the great life of Nature. Even the longest lifetime is far too brief to witness a perceptible advance in the grand transformation. The periods of time demanded in the great evolution shadowed forth by the nebular theory utterly transcend our ordinary notions of chronology. The dates at which supreme events occurred in the celestial evolution are immeasurably more remote than any other dates which we are ever called upon to consider in other departments of science. The time of the story on which we are to be engaged is earlier, far earlier, than any date we have ever learned at school, or have ever forgotten since. The incidents of that period took place long before any date was written in figures—earlier than any of those very ancient dates which the geologists indicate not by figures indeed, but by creatures whose remains imbedded in the rocks suffice to give a character to the period referred to. The geologist will specify one epoch as that in which the fossilized bone of some huge extinct reptile was part of a living animal; he may specify another by the statement that the shell of some beautiful ammonite was then inhabited by a living form which swam in the warm primæval seas. The date of our story has at least this much certainty: that it is prior—immeasurably prior—to the time when that marvellous thing which we call life first came into being.

Voltaire has an instructive fable which I cannot resist repeating. It will serve, at all events, to bring before us the way in which the lapse of time ought to be regarded by one who desires to view the great operations of Nature in their proper proportions. He tells how an inhabitant of the star Sirius went forth on a voyage of exploration through the remote depths of space. In the course of his travels he visited many other worlds, and at length reached Saturn, that majestic orb, which revolved upon the frontier of the solar system, as then known. Alighting on the ringed globe for rest and investigation, the Sirian wanderer, in quest of knowledge, was successful in obtaining an interview with a stately inhabitant of Saturn who enjoyed the reputation of exceptional learning and wisdom. The Sirian hoped to have some improving conversation with this sage who dwelt on a globe so utterly unlike his own, and who had such opportunities of studying the majestic processes of Nature in remote parts of the universe. He thought perhaps they might be able to compare instructive notes about the constitution of the suns and systems in their respective neighbourhoods. The visitor accordingly prattled away gaily. He opened all his little store of knowledge about the Milky Way, about the Great Bear, and about the great Nebula in Orion; and then pausing, he asked what the Saturnian had to communicate in reply. But the philosopher remained silent. Eagerly pressed to make some response, the grave student who dwelt on the frontier globe at last said in effect: “Sirian, I can tell you but little of Nature. I can tell you indeed nothing that is really worthy of the great theme which Nature proposes; for the grand operations of Nature are very slow; they are so slow that the great transformations in progress around us would have to be watched for a very long time before they could be properly understood. To observe Nature so as to perceive what is really happening, it would be necessary to have a long life; but the lives of the inhabitants of Saturn are not long; none of us ever lives more than fifteen thousand years.”

Change is the order of Nature. Many changes no doubt take place rapidly, but the great changes by which the system has been wrought into its present form, those profound changes which have produced results of the greatest magnificence in celestial architecture are extremely slow. We should make a huge mistake if we imagined that changes—even immense changes—are not in progress, merely because our brief day is too short a period wherein to perceive them.

On the village green stands an oak-tree, a veteran which some say dates from the time of William the Conqueror, but which all agree must certainly have been a magnificent piece of timber in the days of Queen Elizabeth. The children play under that tree just as their parents and their grandparents did before them. A year, a few years, even a lifetime, may show no appreciable changes in a tree of such age and stature. Its girth does not perceptibly increase in such a period. But suppose that a butterfly whose life lasts but a day or two were to pass his little span in and about this venerable oak. He would not be able to perceive any changes in the tree during the insignificant period over which his little life extended. Not alone the mighty trunk and the branches, but even the very foliage itself would seem essentially the same in the minutes of the butterfly’s extreme old age as they did in the time of his life’s meridian or at the earliest moment of his youth. To the observations of a spectator who viewed it under such ephemeral conditions the oak-tree would appear steadfast, and might incautiously be deemed eternal. If the butterfly could reflect on the subject, he might perhaps argue that there could not be any change in progress in the oak-tree, because although he had observed it carefully all his life he could not detect any certain alteration. He might therefore not improbably draw the preposterous conclusion that the oak-tree must always have been just as large and just as green as he had invariably known it; and he might also infer that just as the oak-tree is now, so will it remain for all time.

Fig. 2.—A Faint Diffused Nebulosity (n.g.c. 1499; in Perseus).
(Photographed by Dr. Isaac Roberts, F.R.S.)

In our study of the heavens we must strive to avoid inferences so utterly fallacious as these which I have here tried to illustrate. Let it be granted that to our superficial view the sun and the moon, the stars and the constellations present features which appear to us as eternal as the bole of the oak seemed to the butterfly. But though the sun may seem to us always of the same size and always of the same lustre, it would be quite wrong to infer that the lustre and size of the sun are in truth unchanging. The sun is no more unchanging than the oak-tree is eternal. The sun and the earth, no less than the other bodies of the universe, are in process of a transformation no less astonishing than that wonderful transformation which in the course of centuries develops an acorn into the giant of the forest. We could not indeed with propriety apply to the great transformation of the sun the particular word growth; the character of the solar transformation cannot be so described. The oak-tree, of course, enlarges with its years, while the sun, on the other hand, is becoming smaller. The resemblance between the sun and the oak-tree extends no further than that a transformation is taking place in each. The rate at which each transformation is effected is but slow; the growth of the oak is too slow to be perceived in a day or two; the contraction of the sun is too slow to be appreciable within the centuries of human history.

Whatever the butterfly’s observation might have suggested with regard to the eternity of the oak, we know there was a time when that oak-tree was not, and we know that a time will come when that oak-tree will no longer be. In like manner we know there was a time when the solar system was utterly different from the solar system as we see it now; and we know that a time will come when the solar system will be utterly different from that which we see at present. The mightiest changes are most certainly in progress around us. We must not deem them non-existent, merely because they elude our scrutiny, for our senses may not be quick enough to perceive the small extent of some of these changes within our limited period of observation. The intellect in such a case confers on man a power of surveying Nature with a penetration immeasurably beyond that afforded by his organs of sense.

Fig. 3.—The Crab Nebula (n.g.c. 1952; in Taurus).
(Photographed by Dr. Isaac Roberts, F.R.S)

That the great oak-tree which has lived for centuries sprang from an acorn no one can doubt; but what is the evidence on which we believe this to have been the origin of a veteran of the forest when history and tradition are both silent? In the absence of authentic documents to trace the growth of that oak-tree from the beginning, how do we know that it sprouted from an acorn? The only reason we have for believing that the oak-tree has gone through this remarkable development is deduced from the observation of other oak-trees. We know the acorn that has just sprouted; we know the young sapling as thick as a walking stick; we know the vigorous young tree as stout as a man’s arm or as his body; we know the tree when it first approaches the dignity of being called timber; we can therefore observe different trees grade by grade in a continuous succession from the acorn to the monarch of five centuries. No one doubts for a moment that the growth as witnessed in the stages exhibited by several different trees, gives a substantially accurate picture of the development of any individual tree. Such is the nature of one of the arguments which we apply to the great problem before us. We are to study what the solar system has been in the course of its history by the stages which we witness at the present moment in the evolution of other systems throughout the universe. We cannot indeed read the history in time, but we can read it in space.

The mighty transformation through which the solar system has passed, and is even now at this moment passing, cannot be actually beheld by us poor creatures of a day. It might perhaps be surveyed by beings whose pulses counted centuries, as our pulses count seconds, by beings whose minutes lasted longer than the dynasties of human history, by beings to whom a year was comparable with the period since the earth was young, and since life began to move in the waters.

May I, with all reverence, try to attune our thoughts to the time conceptions required in this mighty theme by quoting those noble lines of the hymn—

“A thousand ages in Thy sight

Are like an evening gone,

Short as the watch that ends the night,

Before the rising sun.”

CHAPTER II.
THE PROBLEM STATED.

The Great Diurnal Motion—The Distinction between Stars and Planets—The Earth no more than a Planet—Relation of the Stars to the Solar System—Contrast between Aldebaran and Mars—Illustration of Star-distances—The Celestial Perspective—Illustration of an Attractive Force—Instructive Experiments—The Globe and the Tennis Ball—The Law of Gravitation—The Focal Ellipse—The Solar System as it is now Known—Statement of the Great Problem before us.

WHEN we raise our eyes to the heavens on a clear night, thousands of bright objects claim our attention. We observe that all these objects move as if they were fastened to the inside of an invisible sphere. They are seen gradually ascending from the east, passing across the south, and in due course sinking towards the west. The sun and the moon, as well as all the other bodies, alike participate in this great diurnal movement. The whole scheme of celestial objects seems to turn around the two points in the heavens that we call the Poles, and so far as the pole in the northern hemisphere is concerned, its position is most conveniently indicated by the proximity of the well-known Pole Star.

Except this great diurnal motion, the vast majority of the bodies on the celestial sphere have no other movement easily recognisable, and certainly none which it is necessary for us to consider at present. The groups in which the stars have been arranged by the poetical imagination of the ancients exist to-day, as they have existed during all the ages since they were first recognised, without any noticeable alteration in their lineaments. The stately belt of Orion is seen to-night as Job beheld it thousands of years ago; the stars in the Pleiades have not altered their positions, relatively to the adjacent stars nor their arrangement among themselves, since the time when astronomers in early Greece observed them. All the bodies which form these groups are therefore known as fixed stars.

But besides the fixed stars, which exist in many thousands, and, of course, the sun and the moon, there are other celestial objects, so few in number as to be counted on the fingers of one hand, which are in no sense fixed stars. It is quite true that these wandering bodies, or planets, as they are generally designated, bear a certain resemblance to the fixed stars. In each case the star or the planet appears as a bright point, like many other bright points in the heavens, and star and planet both participate in the general diurnal motion. But a little attention will show that while the stars, properly so called, retain their relative places for months and years and centuries, the planets change their places so rapidly that in the course of a few nights it is quite easy to see, even without the aid of any instrument, that they have independent motion.

We may compare the movements of these bodies to the movement of the moon, which nightly shifts her place over a long track in the sky; and although we are not able to see the stars in the vicinity of the sun, inasmuch as the brilliant light of the orb quenches the feeble radiance from such stars, there is no doubt that, did we see them, the sun itself would seem to move relatively to the stars, just as does the moon and just as do the planets.

The fundamental distinction between stars and planets was noticed by acute observers of Nature in the very earliest times. The names of the planets come to us as survivals from the time when the sun, the moon, and the stars were objects of worship, and they come to us bearing the names of the deities of which these moving globes were regarded as the symbols. But it was not the movements of the planets alone which called for the notice of the early observers of the skies. The brightness and certain other features peculiar to them also attracted the attention of the primitive astronomers. They could not fail to observe that when the beautiful planet Venus was placed so as to be seen to the greatest advantage, her orb was far brighter than any other object in the host of heaven, the sun and the moon both of course excepted. It was also obvious that Jupiter at its best exceeded the stars in lustre, and sometimes approached even to that of Venus itself. Though Mercury was generally so close to the sun as to be invisible among its beams, yet on the rare occasions when that planet was seen, just after sunset or just before sunrise, its lustre was such as to mark it out as one of the remarkable bodies in the heavens.

Thus the astronomers of the earliest ages pointed to the five planets and the sun and the moon as the seven wandering stars. The diligent attention of the learned of every subsequent period was given to the discovery of the character of their movements. The problems that these motions presented were, however, so difficult that not until after the lapse of thousands of years did their nature become understood. The supreme importance of the earth appeared so obvious to the early astronomers that it did not at first occur to them to assign to our earth a position which would reduce it to the same class as any of the celestial bodies. The obviously great size of our globe, the fact that to the uninstructed senses the earth seemed to be at rest, while the other bodies seemed to be in motion, and many other analogous circumstances, appeared to show that the earth must be a body totally different from the other objects distributed around us in space. It was only by slow degrees, and after much observation and reflection, and not a little controversy, that at last the true nature of our system was detected. Those who have been brought up from childhood in full knowledge of the rotation of the earth and of the other fundamental facts relating to the celestial sphere, will often find it difficult to realise the way such problems must have presented themselves to the observers of old, who believed, as for centuries men did believe, that the earth was a plane of indefinite extent fixed in space, and that the sun and the planets, the moon and the stars, were relatively small bodies whose movements must be accounted for as best they could be, consistently with the fixity and flatness of the earth.

Fig. 4.—Jupiter (May 30th, 1899, 10h. 9.5m.; g.m.t.).
(E. M. Antoniadi.)

But at last it began to be seen that the earth must be relegated to a position infinitely less important than that which the untutored imagination assigned to it. It was found that the earth was not an indefinite plane; it was rather a globe poised in space, without direct material support from any other body. It was found that the earth was turning round on its axis: while instead of the sun revolving around the earth, it was much more correct to say that the earth revolved around the sun. The astonishing truth was then disclosed that the five planets, Jupiter and Saturn, Mercury, Venus and Mars, stood in a remarkable relation to the earth. For as each of these planets was found to revolve round the sun, and as the earth also revolved round the sun, the assumed difference in character between the earth and the planets tended to vanish altogether. There was in fact no essential difference. If indeed the earth was smaller than Jupiter and Saturn, yet it was considerably greater and heavier than Mars or Mercury, and it was almost exactly the same size and weight as Venus. There was clearly nothing in the question of bulk to indicate any marked difference between our earth and the planets. It was also observed that there was no distinction to be drawn between the way in which the earth revolved round the sun and the movements of the planets. No doubt the earth is not so near the sun as Mercury; it is not so near the sun as even Venus; on the other hand the sun is nearer the earth than Mars, while Jupiter is a long way further off than Mars, and Saturn is even beyond Jupiter again. It is these considerations which justify us in regarding our earth as one of the planets. We have also to note the overwhelming magnitude of the sun in comparison with any one of the planets. It will suffice to give a single illustration. The sun is more than a thousand times as massive as Jupiter, and Jupiter is the greatest of the planets. This latter noble globe is in fact greater than all the rest of the planets put together.

But before we can fully realise the circumstances of the solar system, it will be necessary to see how the stars, properly so called, enter into the scheme of things celestial. The stars look so like the planets that it has not infrequently happened that even an experienced astronomer has mistaken one for the other. The planet Mars is often very like the star Aldebaran, and there are not a few first-magnitude stars which on a superficial view closely resemble Saturn. But how great is the intrinsic difference between a star and a planet! In the first place we have to note that every planet is a dark object like this earth of ours, possessing no light of its own, and dependent entirely on the sun for the supply of light by which it is illumined. But a star is totally different. The star is not a dark object, but is really an object which is in itself intensely luminous and brilliant; the star is in fact a sun-like body. How then, it may well be asked, does a star like Aldebaran, which is indeed a sun-like body, and in all probability is quite as large and quite as brilliant as the sun itself, bear even a superficial resemblance to an object like Mars, which would not be visible at all were it not for the illumination with which the beams from the sun endow it?

The explanation of this striking resemblance is to be sought in the relative distances of the two objects. A light which is near to the eye may produce an effect quite as great as a very much stronger light which is further away. The intensity of a light varies inversely as the square of the distance. If the distance of a light from the eye be doubled, then the intensity of that light is reduced to one-fourth. Now Aldebaran as a sun-like body emits light which is literally millions of times as great as the gleam of sunshine which starts back to us after reflection from Mars; but Aldebaran is, let us say, a million times as far away from us as Mars, and this being so, the light from Aldebaran would come to us with only a million-millionth part of the intensity that it would have if the star were at the same distance as the planet. There can be no doubt that if Aldebaran were merely at the same distance from the earth as Mars, then Aldebaran would dispense lustre like a splendid sun. By moving Aldebaran further off its light, or rather the light that arrives at the earth, will gradually decrease until by the time that the star is a million times as far as Mars, the light that it sends us is about equal to that of Mars. If it were removed further still, the light that it would send us would become less than that which we receive from Mars, and if still more remote, Aldebaran might cease to be visible altogether.

This illustration will suffice to explain the fundamental difference between planets and stars, notwithstanding the fact that the two classes of bodies bear to each other a resemblance which is extremely remarkable, even if it must be described as being in a sense accidental. But we now know that all of the thousands of stars are to be regarded as brilliant suns, some of which may not be so far off as Aldebaran, though doubtless some are very much further. The actual distances are immaterial, for the essential point to notice is that the five planets are distinguished from the stars, not merely by the fact that they are moving, while the stars are at rest, but by the circumstance that the planets are comparatively close to each other and close to the sun, while the stars are at distances millions of times as great as the distances which the planets are from each other and from the sun.

We are now enabled to place the scheme of things celestial in its proper perspective. I shall suppose that at a point in a field in the centre of England, somewhere near Leamington, let us say, we drive in a peg to represent the sun. Let us draw a circle with that peg as centre, a yard being the radius, and let that circle represent the track in which the earth goes round the sun. I do not indeed say that the orbit of the earth is exactly a circle, and the actual shape of that orbit we may have to refer to later. As, however, the apparent size of the sun does not greatly alter with the seasons, it is evident that the track which our earth pursues cannot be very different from a circular path. Inside this circle which we have drawn with a yard radius, we shall put two smaller circles which are to represent the path in which Venus moves, and the path in which Mercury moves. Outside the path of the earth we shall draw another circle with a radius of five yards; this will be the highway along which the majestic Jupiter wends his way. Inside the path of Jupiter we shall put a circle which will represent the track of Mars, and outside the path of Jupiter a circle with ten yards as radius will represent the track of Saturn. In each of these circles we shall suppose the corresponding planet to revolve, and the time of revolution will of course be greater the further the planet is from the sun. To complete one of its circuits the earth will require a year, Jupiter twelve years, while Saturn, which in the ancient astronomy moved on the frontier of the solar system, will need thirty years to accomplish its mighty journey.

We have thus obtained a plan of the solar system; but now we should like to indicate the positions which some of the stars are to occupy on the same scale. Let us, to begin with, see where the very nearest fixed star is to be placed. We may suppose that the field at the centre of England, in which our little diagram has been constructed, is a large one, so that we can represent the places of objects which are ten or twenty times as far from the sun as Saturn. It is, however, certain that no actual field would be large enough to contain within its bounds the points which would faithfully represent the positions of even the nearest fixed stars. The whole county of Warwick would not be nearly big enough for this purpose; indeed we may say that the whole of England, or indeed of the United Kingdom, would not be sufficiently extensive. If we represented the star at its true relative distance, it could not be put down anywhere within the bounds of the United Kingdom; the nearest object of this kind would have to be far away out on the continent of Europe, or far away out on the Atlantic Ocean, far away down near the equator, or far away up near the pole. This illustration will at all events give some notion of the isolated position of the sun, with the planets revolving around it, in relation to the rest of the host of heaven.

We thus learn that the real scheme of the universe is widely different from that which a superficial glance at the heavens would lead us to expect. We are now able to put our system into its proper perspective. We are to think of the universe as consisting of a myriad suns, each sun, however, being so far from the other suns that viewed from any one of its neighbours it appears only of star-like insignificance. Let us fix our attention on one of these suns in space, and imagine that around it, and comparatively close to it, there are a number of small particles in revolution, the particles being illumined by the light and warmed by the heat of the central body to which they are attached. Viewed from one of those particles, the sun to which they belong would doubtless appear as a great and glorious orb, while a glance from one of these particles to any of the other myriad suns in space will show these orbs reduced to mere points of stellar light by reason of their enormous distance. This sun and the particles around it, by which of course we shall understand the planets, constitute what we know as the solar system. This illustration may suffice to show the isolation of our system in space, and that isolation is due to the vast distances by which the sun and its attendant worlds are separated from the myriads of other bodies which form the sidereal heavens. We must next, so far as our present subject requires it, consider the laws according to which the planets belonging to that system revolve around the sun.

Let us think first of a single one of these bodies which, as is most natural, we shall take to be the earth itself, and now let us consider by what agency the movement of the earth around the sun is guided along the path which so closely resembles a circle. It must, of course, be borne in mind that there can be no direct material connection between the two bodies; there is no physical bond uniting the earth to the sun. It is, however, certain that some influence proceeding from the sun does really control the motion. We may perhaps illustrate what takes place in the following manner. Here is a globe, and here in my hand I hold a tennis ball, which is attached to a silken thread, the other end of the thread being attached to the ceiling. The tennis ball is to hang so that both globe and ball are about the same height from the floor. We put the globe directly underneath the point on the ceiling from which the silken thread hangs. If I draw the tennis ball aside and simply release it, then of course everybody knows what happens—it is hardly necessary to try the experiment—the tennis ball falls at once towards the globe and strikes it. We may, if we please, regard that tendency of the tennis ball towards the globe as a sort of attraction which the globe exercises upon the ball. I must, however, say that this is not a strictly accurate version of what actually takes place. The attraction of the earth for the tennis ball is of course largely neutralised by the support given by the silk thread. There is thus only a slight outstanding component of gravitation acting on the ball, and this component, which is virtually the effective force on the ball, tends to draw the ball directly towards the globe. For the purpose of our illustration we may neglect the direct attraction of the earth altogether; we may omit all thought of the tension of the silken thread. If there were indeed no attraction from the earth, the tennis ball might remain poised in space without falling; and if it were then attracted by the globe it would fly towards the globe just as we actually see it do. We are therefore justified in regarding the movement of the tennis ball as equivalent to that which would be produced if an attractive virtue resided in the globe by which it pulled the tennis ball. We may also imagine that the globe attracts the tennis ball in all its positions; for whatever be the point at which the ball is released it starts off straight towards the globe. This is our first experiment in which, having withdrawn the ball, it is merely released without receiving an initial impulse to one side.

Fig. 5.—Nebulous Region and Star-Cluster
(n.g.c. 2237-9 in Monoceros).
(Photographed by Dr. Isaac Roberts, F.R.S.)

Let us now try a different experiment. We withdraw the ball, and, instead of merely releasing it quietly and allowing it to drop directly to the globe, we give it a little throw sideways, perpendicular to the line joining it to the centre of the globe. If we start it with the proper speed, which a few trials will indicate, the ball can be made actually to move in a circle round the globe. If the initial speed be somewhat different, the path in which the tennis ball moves will not be a circle; it will rather be an ellipse of some form. Even if the speed be correct the orbit will always be an ellipse if the direction of the initial throw be not perpendicular to the line joining the ball to the centre of the globe. We can make the ball describe a very long ellipse or an ellipse which differs but little from a circle. But I would ask you to note particularly that, no matter how we may start the tennis ball into motion, it will, so long as it passes clear of the globe, move in an ellipse of some kind; but in making this statement we assume that a circle is a particular form of the ellipse.

And now for the lesson which we are to learn from this experiment, which, as it is so easily performed, I would wish everyone to try for himself. We have in this simple device an illustration of the movement of a planet around the sun. We see that this tennis ball can be made to move in a circle round the globe, and that as it performs this circular movement the globe is all the time attracting the ball towards it. Thus we illustrate the important law that when one body moves round another in a circular path this movement takes place in consequence of a force of attraction constantly exerted between the large body in the centre and the body revolving round it.

The principle here involved will provide the explanation of the movements of the planets round the sun. Each of the planets revolves round the sun in an orbit which is approximately circular, and each of the planets performs that movement because it is continually attracted by the sun. It is, however, necessary to add that there is a fundamental difference between the attraction of the sun for the planets and the attraction which the globe appeared to exert on the tennis ball in our experiment. The difference relates to the character of the forces in the two cases. If the tennis ball be drawn but a very small distance from the globe, the attraction between the two bodies is very slight. If the tennis ball be drawn to a greater distance from the globe, the attraction is increased correspondingly; and, indeed, in this experiment the attraction between the two bodies increases with the distance, and is said to be proportional to the distance.

But the case is very different in that particular kind of attraction by which the sun controls the movements of the planets. This attraction of gravitation, as it is called, also depends on the distance between the two bodies. But the attraction does not increase when the distance of the two bodies increases, for the change lies the other way. The attraction, in fact, diminishes more rapidly than the distance increases. If the distance between the sun and a planet be doubled, then the attraction between the two bodies is only a fourth of what the attraction was between the two bodies in the former case. This difference between the law of attraction as it exists in the solar system and the law of attraction which is exemplified in our little experiment produces a remarkable contrast in the resulting movements. The orbit in each case is, no doubt, an ellipse, but in the case of the tennis ball revolving round the globe the ellipse is so circumstanced that the fixed attracting body stood at its centre, while in the case of a planet revolving round the sun the conditions are not so simple. The sun does not stand in the centre of the ellipse. The sun is placed at that remarkable point of the ellipse so dear to the heart of the geometer, which he calls the focus.

The solar system consists, first, of the great regulating orb, the sun; then of the planets, each of which revolves in its own track round the sun; each of these tracks is an ellipse, and all these ellipses have this in common, that a focus in each is identical with the centre of the sun. In other respects the ellipses may be quite different. To begin with, they are not in the same plane, though it is most important to notice, as we shall have to discuss more fully hereafter, that these planes are not very much separated. The dimensions of the ellipses vary, of course, for the different planets, and the periods that the planets require for their several revolutions are also widely different in the cases of the different bodies; for the greater the diameter of a planet’s orbit, the longer is the time required for that planet to complete a single journey round the sun. The sun presiding at the common focus of the orbits while governing the planets by its attraction, at the same time that it illumines them with its light and warms them by its rays, gives the conception of the solar system.

But the planetary system I have here indicated is merely that system as known to the ancients. It is very imperfect from the standpoint of our present knowledge. The solar system as we now know it, when telescopes have been applied with such marvellous diligence and success to the discovery of new bodies, is a system of much greater complexity. To the five old planets have been added two new and majestic planets—Uranus and Neptune—which revolve outside the track of Saturn. Hundreds of smaller planets, invisible to the unaided eye, the asteroids as they are called, also describe their ellipses round the presiding luminary. And then just as the sun controls the planets revolving round it, so do many of the planets themselves preside over subordinate systems of revolving globes. Our earth has a single attendant, the moon, which, under the guidance of the earth’s attraction, performs its monthly journey; Jupiter has its five moons, while Mars has two, and Saturn eight or nine, besides his incomparable system of rings, and we must also add that Uranus has four satellites and Neptune one. To complete the tale of bodies in the solar system, we should add many thousands of comets, not to mention their more humble associates the meteors, which swarm in countless myriads. Finally, we are to remember that this elaborate system associated with the sun is an isolated object in the universe; it is but as a grain of sand in the extent of infinite space.

As we contemplate a system so wonderful, the question naturally arises, How came that system into being? We have to consider whether the laws of nature as we know them afford any rational explanation of the manner in which this system came into existence, any rational explanation of how the sun came to shine, how the earth had its beginning, how the planets came to revolve round the sun, and to rotate on their own axes. We have to seek for a rational explanation of the rings of Saturn, and of the satellites by which so many planets are attended. We have to show that a satisfactory explanation of these remarkable phenomena is forthcoming, and that it is provided by the famous doctrine of evolution, which it is the object of these lectures to discuss.

CHAPTER III.
THE FIRE-MIST.

Evolution of other Bodies in the Universe—The Nebulæ—Estimate of the Size of the Great Nebula in Orion—Photograph of that Nebula taken at Lick Observatory—The Dumb-bell Nebula—The Crossley Reflector—The late Professor Keeler—Astonishing Discovery of New Nebulæ—120,000 Nebulæ—The Continuous Chain from a Fluid Haze of Light to a Star—The Celestial Evolution.

WE commence this chapter with a scrutiny of the heavens, to see whether, among the bodies which it contains, we can discover any which appear at this moment to be in the condition through which our system has passed in some of its earlier stages.

So far as our unaided vision is concerned, we can see little or nothing in the skies which will render us assistance in our present endeavour. The objects that we do see in thousands are, of course, the stars, and, as we have already pointed out, the stars are sun-like objects, and as such have advanced many stages beyond the elementary condition. The stars are therefore not immediately available for the illustration we require. But when we come to look at the heavens through our telescopes we presently find that there are objects which were not visible to the eye, and which are neither stars nor planets. Closer examination of these objects with the powerful instruments of modern observatories, and especially with the help of those marvellous appliances which have enabled us to learn the actual chemistry of the heavenly bodies, supplies the suggestions that are required.

For not only does the telescope reveal myriads of stars which the naked eye cannot detect; not only does it reveal wonderful clusters in which thousands of stars are grouped closely together so as to form spectacles of indescribable magnificence, when we take into account the intrinsic splendour of each star-like point, but it also reveals totally different objects, known as nebulæ. These objects are not stars and are not composed of stars, but are vast extensions of matter existing in a far more elementary condition. It is to these curious bodies that we invite special attention at present. It is believed that they offer a remarkable illustration of the origin of the solar system. We shall first consider the best known object of this class. It is the Great Nebula in Orion.

Fig. 6.—The Great Nebula in Orion (Lick Observatory, California).
(From the Royal Astronomical Society Series.)

And here it may be well to give an estimate which will enable us to form some notion of the size of this object. We are accustomed to recognise the stars as presenting the appearance of mere points of light; but an object like the Great Nebula stretches over a wide area of the sky. As to the actual extent of the space which it occupies we cannot speak with confidence. The fact is that with every increase in the power of the telescope the nebula appears to encroach more and more on the darkness of space around. We give in Fig. [6] a representation of the Great Nebula as it appears on a photographic plate obtained at the Lick Observatory in California. But no picture can adequately represent the extraordinary delicacy of the object and the softness and tenderness with which the blue nebulous light fades into the black sky around. And it must not be imagined that the nebula, as seen on this picture, represents the utmost limits of the object itself. Every prolongation of the exposure, every increase in the sensitiveness of the plate, show more and more the extent of the nebula.

We shall, I doubt not, still be within the bounds of truth if we say that the nebula extends over an area ten times as great as that represented in this photograph. But we will take only the area of the object as shown in the photograph for the purpose of our calculation. Let us say that the nebula, as it is here represented, covers about two degrees square. I shall not attempt to express in miles the dimensions of an object so vast. I will try to give a conception of the size of the Great Nebula in a different manner. Let us employ the dimensions of our solar system for the purpose of comparison. Let us suppose that we draw, upon the scale of this celestial photograph, a map which shall represent the sun in the centre, the earth at her proper distance from the sun, and Jupiter in his orbit, which is five times the diameter of the earth’s orbit; and then let us mark the other planets at their respective distances, even to Neptune, revolving in his great ellipse, with a diameter thirty times that of the earth’s orbit. Let us then take the area of the orbit described by Neptune as a unit with which to measure the size of the Great Nebula in Orion. We shall certainly be well within the actual truth if we say that a million circles as big as that described by Neptune would not suffice to cover the area that is represented on this photograph. This will give some idea of the imposing dimensions of the Great Nebula in Orion.

But I would not have it to be supposed that the Great Nebula in Orion is unique, unless in respect to its convenient position. The circumstances of its situation in space happen to make it a comparatively easy object for observation by dwellers on the earth. There are, however, very many other nebulæ, although, with one exception—namely, the Great Nebula in Andromeda, to which we shall have to refer in a later chapter—they do not from our point of observation appear to be so brilliant as the nebula in Orion. The fact is that by large and powerful telescopes multitudes of these nebulæ are revealed, and the number ever tends to increase as greater depths in space are sounded. Many of the nebulæ are objects which possess sufficient detail to merit the particular attention which they receive from astronomers. It must, however, be confessed that by far the greater number of these objects are so dimly discerned that it is impossible to study their individual characteristics.

Among the nebulæ which possess sufficient individuality to merit study for our present purpose, I must mention the so-called Dumb-bell. This most interesting object can be seen in any good telescope. It requires, however, as indeed do all such objects, an instrument of the highest power to do it justice; in these modern days, however, the eye observation of nebulæ through great telescopes has been superseded by the employment of the photographic plate. I may take this opportunity of mentioning that a photograph really shows more details in the nebula than can be perceived even by the most experienced eye when applied to the most powerful telescope placed in the most favoured situation as to climate. Those lovers of nature who desire to observe celestial objects through a great telescope, and have not the opportunity of gratifying their wishes, may perhaps derive consolation from the fact that a good photograph actually represents the object much better than any eye can see it. More of the nebula is to be seen by looking at the photograph than has actually been directly observed by any astronomer.

We have chosen the Dumb-bell (Fig. [7]) and the Great Nebula in Orion as characteristic examples of this remarkable class of celestial objects; but there are many others to which I might refer, some of which we represent in these pages. The Crab Nebula (Fig. [3]) and others have been distinguished by special names; but I must forbear to dwell further on them, and rather hasten to give the results of recent observations which have enormously extended our knowledge of the nebulous bodies in the universe.

Let me first explain the source whence this extraordinary accession to our knowledge has arisen. We owe it to the astronomers at the Lick Observatory, that remarkable institution placed on the summit of Mount Hamilton in California. Many important discoveries had already been made with the noble instruments with which the famous Lick Observatory had originally been endowed by its founder; it is, however, by a recent addition to its magnificent apparatus that the discoveries have been made which are specially significant for our present purpose.

Many years ago Dr. A. A. Common, the distinguished English astronomer, constructed an exquisite reflecting telescope of three feet aperture (Fig. [8]). With this telescope Dr. Common himself obtained notable results in photographing the heavens, and his success earned the award of the Gold Medal of the Royal Astronomical Society. This telescope passed into the possession of Mr. E. Crossley, of Halifax, and some time later Mr. Crossley presented it to the Lick Observatory. The great mirror, after its voyage across the Atlantic, was duly erected on the top of Mount Hamilton, and fortunately for science Professor Keeler, whose early death astronomers of both continents greatly deplore, devoted himself to the study of the heavens with its aid. He encountered many difficulties, as might perhaps be expected in such a task as he proposed. His patience and skill, however, overcame them, and though death terminated his labours when his great programme had but little more than commenced, the work he had already accomplished has led to results of the most striking character. Of the skill that he obtained in photographing celestial nebulæ we have given illustrations in Figs. 6 and 7.

Fig. 7.—The Dumb-bell Nebula (Lick Observatory, California).
(From the Royal Astronomical Society Series.)

It is not to the individual portraits of notable nebulæ that we are now about to refer. The most striking characteristic of the sidereal heavens is not to be found in the fact that in one part of the sky we have a brilliant Sirius, in another a Capella, and in a third a Canopus, but in the fact that the heavens wherever we may test them are strewn with incalculable myriads of stars, many of which appear faint only on account of their distance and not because they are intrinsically small. In like manner the remarkable fact with regard to the nebulæ which has been disclosed by Keeler’s memorable researches with the Crossley Reflector is the existence not alone of the great nebulæ, but of unexpected scores of thousands of small nebulæ, or rather, I should say, of nebulæ which appear small, though doubtless in many cases these objects are intrinsically quite as splendid as the Dumb-bell Nebula or the Nebula in Orion. They only seem small in consequence of being many times further from us than are the more famous objects.

Professor Keeler’s experience was a remarkable one. He was photographing a well-known nebula with the Crossley Reflector, and he was a little surprised to find that on the same plate which gave him the nebula at which he was aiming there were no fewer than seven other small nebulous objects previously unknown to astronomers. It at first appeared to him that this must be an unusual number of nebulæ to find crowded together on one plate which covered no more than one square degree of the heavens, an area about five or six times as large as the area of the full moon. Subsequent experience, however, showed him that this fact, however astonishing, was not at all unusual. In fact, he found to his amazement that, expose the plate where he pleased, he generally obtained new nebulæ upon it, and sometimes even a much larger number than the seven which so greatly surprised him at first. I may mention just one or two instances. There is a well-known and interesting nebula in Pegasus which Professor Keeler photographed. When he developed the plate, which, of course, included a considerable region of the heavens in the vicinity of the particular nebula, he found to his astonishment that, besides the nebula he wanted, there were not less than twenty other nebulæ on the plate. But there is a more striking instance even than this. A plate directed to a part of the constellation of Andromeda, with the object of taking a portrait of a particular nebula of considerable interest, was found to contain not only the desired nebula, but no fewer than thirty-one other new nebulæ and nebulous stars. Nor have we in these statements exhausted the nebulous contents of these wonderful plates, if indeed we have rightly interpreted their nature. Professor Keeler tells us that he finds upon them a considerable number of objects which in all probability are also nebulæ, though they are so small that the telescope is unable to reveal them in their true character. Examination does little more than show these objects as points of light which, however, are apparently not stars.

In the remarkable paper from which I have taken these facts Professor Keeler makes an estimate which is founded on the examination of his plates. If the heavens were to be divided into panels, each one square degree in area, there would be about forty thousand panels. It follows that if we desired to photograph the whole heavens, and if each of the plates was to cover one square degree, forty thousand pictures would be needed for the representation of the whole celestial sphere. Keeler’s work convinced him that such plates taken by the Crossley Reflector would, on an average, each show at least three new nebulæ. He admitted it is quite possible that there may be regions of the sky in which no new nebulæ are to be found. But in the regions which he had so far tested he invariably found more than three nebulæ on each square degree; indeed, as we have seen, on some of his plates he found a much larger number of these remarkable objects. He therefore said that he makes but a very moderate estimate when he gives a hundred and twenty thousand as the probable number of the new nebulæ within the reach of the photographic plates of the Crossley Reflector.

The enormous extension which these investigations have given to our knowledge demands the serious attention of all interested in the heavens. The discoveries of the earlier astronomers had led to the knowledge of about six thousand nebulæ; the Crossley Reflector at the Lick Observatory has now rendered it practically certain that the number of nebulæ in the heavens must be at least twenty-fold as great as had been hitherto supposed.

Fig. 8.—The Crossley Reflector (Constructed by Dr. A. A.
Common F.R.S. and now at the Lick Observatory).

In subsequent chapters we are to present the evidence for the belief that this earth of ours, as well as the sun and all the other bodies which form the solar system, did once originate in a nebula. According to this view the materials which at present are found in the globes of the solar system were once distributed over a vast extent of space as a fire-mist, or nebula. It is surely very pertinent to be able to show that a nebula, such as we suppose to have been the origin of our system, is not a mere figment of the imagination. No doubt it is impossible for us now to show the original nebula from which the solar system has been evolved. It is nevertheless possible, as we have seen, to show that a hundred and twenty thousand nebulæ are now actually existing of every grade of magnitude. They range from such magnificent objects as the Great Nebula in Orion and the Dumb-bell Nebula, down to objects wholly invisible, not merely to the unaided eye, but even in the most powerful telescope, and only to be discerned as hazy spots of light on the photographic plates of an instrument such as the Crossley Reflector.

Though no eye has seen the actual stages in the grand evolution of our solar system, we may at least witness parallel stages in the evolution through which some of the myriads of other nebulæ are now passing. We find some of these nebulæ in that excessively diffused condition in which they are devoid of visible structure. Material in this form may be regarded as the primæval nebula. There is at least one of these extraordinary objects which is larger a great deal than even the Great Nebula in Orion, but altogether too faint to be seen except by the photographic plate. Here we find, as it were, the mother-substance in its most elementary stage of widest possible diffusion, from which worlds and systems, it may be, are yet to be evolved. From diffused objects such as shown in Fig. [5] we can pass to other nebulæ in which we see a certain advance being made in the process by which the nebula is transformed from the primitive condition. We can point to yet other nebulæ in which the advance to a further stage of development is more and more pronounced. Thus the various stages in the evolution of a system are to be witnessed, not indeed in the transformation of a single nebula, but by observing a properly arranged series of nebulæ in all gradations, from the diffused luminous haze to a star with a faint nebulous surrounding. Such was Herschel’s original argument, and its cogency has steadily increased from the time he first stated it down to the present hour.

CHAPTER IV.
NEBULÆ—APPARENT AND REAL.

The Globular Star-clusters—Structure of these Objects—Variability of Stars in the Cluster—Telescopic Resemblance of a Cluster to a Nebula—Resolution of a Nebula—Supposition that all Nebulæ may be Clusters—A Criterion for distinguishing a Nebula and a Cluster—Dark Lines on a bright Background characterise the Structure of a Star—Bright Lines on a dark Background characterise the Structure of a Nebula—Characteristics of the Spectrum of a true Nebula and of a Resolvable Nebula—Spectra of the Sun and Capella—Spectra of the Nebula in Orion and of a White Star compared—Number of Lines in a Nebular Spectrum—Criterion of a Nebular Spectrum—Spiral Nebula not Gaseous—Solar Spectra during an Eclipse—Bearing on the Nebular Theory—Herschel’s Work—The Objection to the Theory—The Objection Removed in 1864.

THERE is perhaps hardly any telescopic object more pleasing or more instructive than a globular cluster of stars when viewed through an instrument sufficiently powerful to do justice to the spectacle. There are several star-clusters of the class designated as “globular.” The most famous of these, or, at all events, the one best known to northern astronomers, is found in the constellation of Hercules, and is for most purposes sufficiently described by the expression, “The Cluster in Hercules.” The genuine lover of Nature finds it hard to withhold an exclamation of wonder and admiration when for the first time, or even for the hundredth time, the Cluster in Hercules is adequately displayed in the field of a first-class telescope.

Fig. 9.—The Cluster in Hercules.
(Photographed by Dr. W. E. Wilson, F.R.S.)

In Fig. [9] is a photograph of this celebrated object, which was taken by Dr. W. E. Wilson, F.R.S., at his observatory at Daramona, in Ireland. The picture has been obtained from an enlargement of the original photograph taken with the telescope in Mr. Wilson’s observatory. It is, however, precisely as Nature has given it, except for this enlargement. You will note that towards the margin of the cluster the several stars are seen separately, and in many cases with admirable distinctness. We do, however, occasionally find two or more stars so close together that their images overlap; and, indeed, in the centre of the cluster the stars are so close together that it is impossible to differentiate them, so as to see them as individual points of light. We need have no doubt, however, that the cluster is mainly composed of separate stars, although the difficulties interposed by our atmosphere, added to the necessary imperfections of our appliances, make it impossible for us to discriminate the individual stars.

In looking at a star group of this particular kind the observer may perhaps be reminded of a swarm of bees in flight from the hive, for the stars in the cluster are, on a vast scale, apparently associated in the same way as the bees, on a small scale, are associated in the swarm. We may also compare the stars in the cluster to the bees in the swarm in another respect. Each bee in the swarm is in incessant movement. There can be no doubt that each star in a globular cluster is unceasingly changing its position with reference to the others. The distance by which the cluster is separated from the earth renders it impossible for us to see those movements, at all events within those narrow limits of time over which our observations have as yet extended; but the laws of mechanics assure us that the mutual attraction of the stars in this cluster must give rise to incessant movements, and that this must be the case notwithstanding the fact that the relative places of the stars in the cluster show no alteration that can be recognised from one year’s end to another.

I may, however, mention that though there may be no movements in these stars great enough to be observed, yet the brightness of some of them shows most remarkable fluctuations. The investigations of Professor Bailey and other astronomers have, indeed, disclosed such curious variability in the brightness of some of these stars that if it were not for the exceedingly high authority by which this phenomenon has been guaranteed we should, perhaps, almost hesitate to believe so startling a fact. It has, however, been most certainly proved that many of the stars in certain globular clusters pass through a series of periodical changes of lustre. The period is a very short one as compared with the periods of better known variable stars, for in this case twenty-four hours are more than sufficient for a complete cycle of changes, and it not infrequently happens that in the course of a single quarter of an hour a star will lose or gain brightness to the extent of a whole magnitude. The phenomenon referred to is at the present moment engaging the careful attention of astronomers; but it offers a problem of which, indeed, it is not at present easy to see the solution.

Our immediate concern, however, with the globular star-clusters relates to a point hardly of such refinement as that to which I have just referred; it is one of a much more elementary nature. The photograph in the figure may be considered to represent the Cluster in Hercules as it would be seen with a telescope of very considerable visual power, for the object would assume a different appearance in a telescope which was not first class. The perfection of a really powerful instrument is tested by its capability of exhibiting as two separate points a pair of stars which are excessively close together, and which in an instrument of inferior power cannot be distinguished, but seem fused into a single object. The defining power of a telescope—that is to say, its capability for separating close double stars—is increased with the size of the instrument, always granting, of course, that there is equal optical perfection in both cases. It follows that the more powerful the telescope the more numerous are the stars which can be seen separately in a globular cluster.

If, however, a small telescope be used, or a telescope which, though of considerable size, has not the high optical perfection that is demanded in the best modern instruments, then adjacent stars are not always to be seen separately. It may be that the telescope, on account of its small size, cannot separate the objects sufficiently, or it may be that the imperfections of the telescope do not present the star as a point of light, but rather as a more or less diffused, luminous disc. In either case it may happen that a star overlaps other stars in its immediate neighbourhood, and consequently an object which is really a cluster of separate stars may fail altogether to present the appearance of a cluster.

I have been alluding to something which, as every astronomer knows, is of practical importance in the observatory. Like every one else who has ever used a telescope, I have myself seen the Cluster of Hercules with just the same misty appearance in a small telescope that an undoubted nebula possesses in the very finest instrument. It is, accordingly, sometimes impossible, merely by observation with a small instrument, to distinguish between what is certainly a cluster of stars and what is certainly a nebula. It has indeed not infrequently happened that an observer with a small telescope has discovered what appeared to him to be a nebula, and he has recorded it as such; and yet when the same object was subsequently examined with an instrument of greater defining power the nebulous character has been seen to have been wrongly attributed. The object in such a case is proved to be nothing more than a cluster of stars, of which the individual members are either intrinsically faint or exceedingly remote; it certainly is not a mass of that fire-mist or gaseous material which alone is entitled to be called a nebula.

It is therefore a question of importance in practical astronomy to decide whether objects which appear to be nebulæ are really entitled to the name, or whether the nebulous appearance may not be an optical illusion. The operation by which an object previously deemed to be a nebula is shown by the application of increased telescopic power to be a cluster of stars is commonly known as the resolution of a nebula. About fifty years ago the mighty six-foot reflecting telescope of Lord Rosse, and other great instruments, were largely employed on this work. It was, indeed, at that time held to be one of the special tasks which came most legitimately within the province of the big telescopes, to show that the so-called nebulæ of earlier observers were resolvable into star-clusters under the superior powers now brought to bear upon them.

The success with which this process was applied to many reputed nebulæ, which were thereby shown to be not entitled to the name, led not unnaturally to a certain conjecture. It was admitted that certain objects which had successfully resisted the resolving powers of inferior instruments were forced to confess themselves as mere star-clusters when greatly increased telescopic power was brought to bear on them; and it was conjectured that similar success would attend the attempts to resolve still other nebulæ. It was even supposed that every object described as a nebula could only be entitled to bear that designation provisionally, only indeed until some telescope of sufficient power should have been brought to bear on it. It seemed not unreasonable to surmise that every one of the so-called nebulæ is a cluster of stars, even though a telescope sufficiently powerful to effect its resolution might never be actually forthcoming.

I do not, indeed, believe that this opinion as to the ultimate resolvability of all nebulæ could have been shared by those who had much practical experience in the actual observation of these objects with the great telescopes, for the particular classes of nebulæ which in telescopes of superior powers resolved themselves into groups of stars had a characteristic appearance. After a little experience the observer soon learned to recognise those nebulæ which promised to be resolvable. The object might not indeed be resolvable with the powers at his disposal, but yet from its appearance he often felt that the nebula would be probably resolved if ever the time should come that greater powers were applied to the task.

It is easy to illustrate the question at issue by the help of the photograph of the Cluster in Hercules in Fig. [9]. Each of the stars is there distinct, except where they are much crowded in the centre. If, however, the photograph be examined through one of those large lenses which are often used for the purpose, and if the lens be held very much out of focus, the stars will not be distinguishable separately, and the whole object will be merely a haze of light. This illustration may help to explain how the different optical conditions under which an object is looked at may exhibit, at one time as a diffused nebula, an object which in better circumstances is seen to be a star-cluster.

The astronomer who was fortunate enough to have the use of a really great telescope would not fail to notice that, in addition to the so-called nebulæ already referred to, which were presumably resolvable, there were certain other objects, generally characterised by a bluish hue, which in no circumstances whatever presented the appearance of being composed of separate stars. We now know for certain that these bluish objects are not clusters of stars, but that they are in the strictest sense entitled to the name of nebulæ, and that they are gaseous masses or mists of fire-cloud. The full demonstration of this important point was not effected until 1864.

The fact that so very many of the nebulæ were resolved led not unreasonably to the presumption that all the nebulæ would in due time also yield. But there were many who could not accept this view, and there was a long discussion on the subject. At last, however, the improvements in astronomical methods have cleared up the question. Sir W. Huggins has shown that there are two totally distinct classes of nebulæ, or rather of so-called nebulæ. There are certain nebulæ which can be resolved, and there are certain nebulæ which cannot. A nebula which can be resolved would be a veritable cluster of stars, and is not really entitled to the name of nebula; a nebula which cannot be resolved would be entitled to the name, for it is a volume of gas or of gaseous material which is itself incandescent. We have been provided with a beautiful criterion by which we can decide to which of these classes any nebulous-looking object belongs.

The spectroscope is the instrument which discriminates the two different classes of objects. This remarkable apparatus, to which we owe so much in every department of astronomy, receives the beam of light from the celestial body. The instrument then analyses the light into its component rays, and conducts each one of those rays separately to a distinct place on the photographic plate. When the photograph is developed we find on the various parts of the plate the evidence as to the class of rays which have entered into the composition of the light that has been submitted to this very searching form of examination.

The light which comes from a star or any star-like body, including the sun itself, may first be described. That light, after passing through the spectroscope and having been conducted to the photographic plate, will produce a picture of dark lines on a bright background; this is, at least, the spectrum which a star generally presents. There are, indeed, many types of stellar spectra, for there are many different kinds of stars, and each kind of star is conveniently characterised by the particular spectrum that it yields. If the star be one of small magnitude, then the lines in its spectrum may be detected, but only with great difficulty. It not infrequently happens that the photograph of the spectrum of such a star will show no more than a continuous band of light without recognisable lines; and this is what occurs in the case of a resolvable nebula, where the stars are so closely associated that the spectrum of each separate star cannot be distinguished. The spectrum of a resolvable nebula is merely a streak of light, which is the joint effect of all the spectra. The spectrum is then too faint to show the rainbow hues which present such beautiful features in the spectrum of a bright star, as they do in the spectrum of the sun itself.

I give, in the adjoining figure (Fig. [10]), portions of the photographs of two spectra of celestial objects. They have been taken from the Atlas of representative stellar spectra in which Sir William and Lady Huggins have recorded the results of their great labours. Two spectra are represented in this picture, the uppermost being the spectrum of the sun, while the lower and broader one is the spectrum of the bright star Capella. It has not been possible within the limits of this picture to include the whole length of these two spectra, and it must therefore be understood that the photographs given in the Atlas are each about five times as long as the parts which are here reproduced.

Fig. 10.—Sun and Capella.
Sun above. Capella below.
(Sir William and Lady Huggins.)

But the characteristic portions of the spectra selected are sufficient for our present argument. It will be noted, first of all, that there is a singular resemblance between the details of the spectrum of the sun and those of the spectrum of the star. No doubt the breadth of the stellar picture in the lower line is greater than that of the solar picture in the upper line; but this point is not significant. The breadth of the spectrum of the sun could easily have been made as wide or wider if necessary. The breadth is immaterial, for the character of a spectrum is determined not by its breadth, but by those lines which cross it transversely. It will be seen that there are here a multitude of lines, some being very dark, and some so faint as to be hardly visible. Both spectra exhibit every variety of line, between the delicate marks which can barely be seen and the two bold columns on the right-hand side of the picture.

The characteristic of the spectrum is given by the number, the arrangement, the breadth, the darkness, and the definiteness of the lines by which it is crossed, and the first point that we note is the remarkable resemblance in these different respects between the two spectra. The lines are practically identical, at least so far as those parts of the spectrum represented in this picture are concerned. We have thus a striking illustration of the important fact, to which we have so often to make allusion, of the general resemblance of the sun to the stars. Not only do we know that if the sun were removed about a million times as far as it is at present its light would be reduced to that of a star, but that the star Capella transmits to us light consisting essentially of the same waves as those which enter into a beam of sunlight. No more striking illustration of the analogy between the sun and a star can be found than that which is given in this photograph from the famous Observatory at Tulse Hill.

But it must not be inferred that because the spectra of sun and star are like each other, they are therefore absolutely identical. There are many lines and details to be seen on the actual photographic plate which are too delicate to be reproduced in such copies as it is possible to make. When a close comparison is made on the actual plate itself of the lines in the solar spectrum and the lines in the spectrum of Capella, it is observed that, though they are the same so far as the more important lines are concerned, yet that there are many lines found in the spectrum of Capella which are not found in the spectrum of the sun.

Fig. 11.—Spectrum of Nebula in Orion and
Spectrum of a White Star.
(Sir William Huggins, K.C.B.)

The contrast between the spectrum of a nebula properly so called and the spectrum of a star is well illustrated by the accompanying picture (Fig. [11]), in which Sir W. Huggins exhibits the photograph of the spectrum of the Nebula in Orion in comparison with the spectrum of a star. The uppermost of the two is the spectrum of the star. It will be noted that this spectrum is very different from that which we have already seen in Capella. Instead of a vast multitude of lines resembling the lines of the solar spectrum, the spectrum of a star of the type here represented, of which we may take Sirius as the most striking example, exhibits but a few lines. We regard them as one system of lines, for we know they are physically connected. They are all alike due to the presence of a single element in the star, that element being in fact hydrogen. But though the spectra of Capella and Sirius are so totally different, the differences relate only to the distribution of the lines, and to their number, darkness, and width. In both cases we observe the characteristic of the light from an ordinary bright star, namely, that the spectrum is composed of a bright band with dark lines across it. It ought, perhaps, to be mentioned here that there are certain very special stars which do exhibit some bright lines in addition to a more ordinary spectrum; this is especially the case in the new stars which occasionally appear. Thus in the case of the new star which appeared in Perseus, in 1901, there were several remarkable bright lines. This most interesting object will be referred to again in a later chapter.

Widely different from the spectrum of any star whatever is the lower of the two spectra which are shown in the figure. This lower spectrum is that of the Great Nebula in Orion. At once we see the fundamental characteristic of a nebula; its spectrum exhibits five bright lines on a dark field. I do not say that the Great Nebula in Orion has not more than five lines; there are indeed many others, for Sir William Huggins has himself pointed out a considerable number, and the labours of other observers have added still more; but the five lines here set down are the principal lines. They are those most easily seen; the others are generally extremely delicate objects arranged in groups of five or six. But the lines which this picture shows are quite sufficient to exhibit that fundamental characteristic of the nebular spectrum, namely, a system of bright lines on a dark field. I may further mention that certain lines in the spectrum indicate the presence of the element hydrogen in the Great Nebula in Orion, and we owe to Dr. Copeland the interesting discovery that the remarkable element helium is also proved to exist in the nebula.

The pictures, at which we have been looking, will suffice to make clear the criterion, which astronomers now possess, for deciding whether an object which looks nebulous is really a gaseous nebula, or ought rather to be regarded as a star-cluster. If the object be a star-cluster, then the spectrum that it gives will be the resultant of the spectra of the stars, and this will be a continuous band of light. If the stars are bright enough, it may be that dark lines can be detected crossing the spectra, but in the case of the clusters it will be more usual to find the continuous band of light so faint that the dark lines, even if they are there, are not distinguishable.

If, on the other hand, the object at which we are looking, not being a cluster of stars, is indeed a mass of glowing gas, or true nebula, then the spectrum that it sends us is not the continuous spectrum such as we expect from the stars. The spectrum which the nebula proper transmits to the plate is said to be discontinuous. In some cases it is characterised by only a single bright line, and in others there may be two, or three, or four bright lines, or, as in the case shown in Fig. [11], the number of bright lines may be as many as five. It may indeed happen, in the case of some exquisite photographs, that the number of lines in the spectrum of the nebula will be increased to a score or possibly more. There may also be faint traces of a continuous spectrum present, this being due to the stars scattered through the object, from which perhaps even the most gaseous nebula is not entirely free. But the characteristic type of nebular spectrum is that in which the bright lines, be they one, or few, or many, are separated by intervals of perfect darkness. When it is found that the spectrum of a nebula can be thus described, it is correct to say that the nebula is truly a gaseous object.

In the lists given by Scheiner in his interesting book, “Astronomical Photography,” the number of gaseous nebulæ is set down as seventy-three. Of course no one pretends that this enumeration is exhaustive. It claims to be no more than a statement of the number of nebulæ which have been proved, by observations made up to the present, to be of a gaseous description. Seeing that there are, as we have already stated, many scores of thousands of nebulous-looking objects, it is probable that the number above given is not more than a small fraction of the number of gaseous nebulæ actually within reach of our instruments.

It may, however, be assumed that more than half the objects which are called nebulæ are not of the gaseous type. This is a point of some importance, which appears to follow from the facts stated by Professor Keeler in connection with his memorable researches with the Crossley Reflector. In a later chapter we discuss important questions connected with what are called spiral nebulæ. We may, however, here record that no spiral nebulæ have as yet been pronounced gaseous. Professor Keeler assures us that, of the one hundred and twenty thousand nebulæ which he estimates to be within reach of the Crossley Reflector, far more than half are of the spiral character. If, then, we assume that the spectra of spiral nebulæ are always continuous, it seems to follow that less than half the nebulous contents of the heavens possesses the discontinuous spectrum which is characteristic of a gaseous object.

We are not entitled to assume that a nebula, or reputed nebula, which shows a continuous spectrum, must necessarily be a cluster, not merely of star-like bodies, but of bodies with masses comparable with those of the ordinary stars. Our argument does most certainly suggest that the body which yields a continuous spectrum is not a gaseous body; but it may be going too far to assert that therefore it is a cluster of stars in the ordinary sense. We do often find true nebulæ and star-clusters in close association. The Nebula in the Pleiades (Fig. [13]) is an example.

It may be desirable to add a few words here as to the physical difference between a continuous spectrum and a discontinuous spectrum. The light from a body, known to be gaseous, shows through the prism the discontinuous spectrum of bright lines upon a dark background. If, on the other hand, a solid be raised to incandescence, such, for instance, as a platinum wire heated white-hot by an electric current, or a cylinder of lime submitted to an oxyhydrogen blowpipe, then the spectrum that it yields is continuous. All the colours of the rainbow, red, orange, yellow, green, blue, indigo, violet, are shown in such a spectrum as a continuous band of light, though the band is not crossed by dark lines. It would therefore appear that the continuous spectrum is characteristic of an incandescent solid, and the discontinuous spectrum of a glowing gas. But here it may be urged that the sun presents a difficulty. We so often refer to the spectrum of the sun as continuous, that it might at first appear as if the spectrum of the sun resembled that produced by radiation from a solid body. But, as is well known, the sun is not a solid body. Even if the sun be solid at the centre, it is certainly far from being solid in those superficial regions called the photosphere, from which alone its copious radiation is emitted. If the sun is not a solid body, how comes it to emit a radiation characterised in the same way as the radiation from a white-hot solid? Why does the solar spectrum not exhibit features characteristic of radiation from an incandescent gas? The point is well worthy of attention; it finds an explanation in the nature of the photosphere from which the sun’s radiation proceeds.

The photosphere, though not, of course, to be described as a solid body, does not most certainly, so far as its radiation is concerned, behave like a gaseous body. In the glowing clouds of the photosphere the carbon, of which they are composed, is not in the gaseous form; it has passed into solid particles, and it is these particles, in the highest condition of incandescence, which emit the solar radiation. Although these particles are sustained by the gases of the sun, and are associated in aggregations which form the dazzling clouds of the photosphere, yet each one of them, in so far as its individual radiation is concerned, ought to be regarded as a solid body. The radiation from the sun is, therefore, essentially not the radiation from an incandescent gas; it is the radiation from a glowing solid. This is the reason why the solar spectrum is of the continuous type.

Fig. 12.—Solar Spectra with Bright Lines and Dark Lines during Eclipse.
(Photographed by Captain Hills, R.E.)

By the kindness of Captain Hills, R.E., I am able to show a photograph (Fig. [12]) containing two spectra taken during a recent eclipse, which will serve as an excellent illustration of the different points which we have been discussing. It is, indeed, true that neither of the spectra, here referred to, belongs to nebulæ, whether genuine gaseous objects or not. Both of the spectra in Captain Hills’ picture are actually taken from the sun. The conditions under which these spectra were obtained make them, however, serve as excellent illustrations of the different types of spectra. We are to notice that the upper band, which contains what is called the “flash” spectrum, exhibits bright lines on a dark background. See, for instance, the two lines so very distinctly marked, which are indicated by the letters H and K. These lines are very characteristic of the solar spectrum, and it may be mentioned that they are indications of the presence of a well-known element. These lines prove that the sun contains calcium, the metal of which common lime is the oxide. It is, indeed, the presence of this substance in the sun which gives rise to these lines. We shall refer again to this subject in a later chapter.

As the upper of the two spectra exhibit H and K as white lines on a dark background, so the lower represents the same lines as dark objects on a white background. These photographs give illustrations of spectra of the two different classes which provide means of discriminating between a genuine nebula and an object which, though it looks like a nebula, is not itself gaseous.

Fig. 13.—The Nebula in the Pleiades (Exposure 10 hours).
(Photographed by Dr. Isaac Roberts, F.R.S.)

But, it will be asked, how can the spectra of the two distinct types both be obtained from the sun? The explanation of this point is an interesting one. The lower of the two is the ordinary solar spectrum; it is a continuous spectrum showing dark lines on a bright field. The upper spectrum, which shows bright lines on a dark field, is produced by a small part of the sun just at the moment when the eclipse is total. The circumstances in which that picture was secured will explain its character. The moon had completely covered that dazzling part of the sun which we ordinarily see, but a region of intensely glowing gaseous material in the sun’s atmosphere was too high above the surface to be completely hidden by the moon. The spectrum of this region, consisting of the characteristic bright gaseous lines, is here represented. The ordinary light of the sun being cut off, opportunity was thus afforded for the production of the spectrum of the light from the glowing gas, and we see this spectrum to be of the nebular type.

And now we may bring this chapter to a close by calling attention to the very important bearing which its facts have on the Nebular Theory. It is essential for us to see how far modern investigation and discovery have tended either to substantiate or refute that famous doctrine which traces the development of the solar system from a nebula. To do this it is necessary to contrast the knowledge of nebulæ, as it exists at present, with the knowledge of nebulæ as it existed in the days of Kant and Laplace and Herschel.

We assuredly do no injustice to Kant or to Laplace if we say that their actual knowledge of the nebulous contents of the heavens was vastly inferior to that possessed by Herschel. There is not a single astronomical observation of nebulæ recorded by either Kant or Laplace; it may be doubted whether either of them ever even saw a nebula. Their splendid contributions to science were made in directions far removed from those of the practical observer, who passes long hours of darkness in the scrutiny of the celestial bodies. Herschel, on the other hand, was pre-eminently an observer. His nights were spent in the most diligent practical observation of the heavens, and at all times the nebulæ were the objects which received the largest measure of his attention, with the result that the knowledge of nebulæ received the most extraordinary development from his labours. Earlier astronomers had no doubt observed nebulæ occasionally, but with their imperfect appliances only the brighter of these objects were discernible by them. The astonishing advance made by the observations of Herschel is only paralleled by the advance made a hundred years later by the photographs of Keeler.

But it must be remembered that though Herschel observed nebulæ, and discovered nebulæ, and discoursed on nebulæ in papers which to this day are classics in this important subject, yet not to the last day of his life could he have felt sure that he had ever seen a genuine nebula. He might have surmised, and he did surmise, that many of the objects he set down as nebulæ were actually gaseous objects, but he knew that many apparent nebulæ were in truth clusters of stars, and he had no means of knowing whether all so-called nebulæ might not belong to the same category.

It was not till nearly half a century after Sir William Herschel’s unrivalled career had closed that the spectroscope was invoked to decide finally on the nature of these mysterious objects. That decision, which has been of such transcendent importance in the study of the heavens, was not pronounced till 1864. In that year Sir William Huggins established the fundamental truth that the so-called nebulæ are not all star-clusters, but that the universe does contain objects which are most certainly gigantic volumes of incandescent gases.

This great achievement provided a complete answer to those who urged an objection, which seemed once very weighty, against the Nebular Theory. It must be admitted that before 1864 no one could have affirmed with confidence that any genuine nebula really existed. It was, therefore, impossible for the authors of the Nebular Theory to point to any object in the heavens which might have illustrated the great principles involved in the theory. The Nebular Theory required that in the beginning there should have been a gaseous nebula from which the solar system has been evolved. But the objector, who was pleased to contend that the gaseous nebula was a figment of the imagination, could never have been effectively silenced by Kant or Laplace or Herschel. It would have been useless for them to point to the Nebula in Orion, for the objector might say that it was only a cluster of stars, and at that time there would have been no way of confuting him.

The authors of the Nebular Theory had, in respect to this class of objector, a much more difficult task than falls to its modern advocate. The latter is able to deny in the most emphatic manner that a gaseous nebula is no more than an imaginary conception.

The famous discovery of Sir W. Huggins has removed the first great objection to the Nebular Theory.

CHAPTER V.
THE HEAT OF THE SUN.

The Sun to be first considered: its Evolution is in vigorous Progress—Considerations on Solar Heat—Size of the Sun—Waste of Sun-heat—Langley’s Illustration—Sun in Ancient Days—Problem Stated—The Solar Constant explained—Its Value determined—Estimate of Radiation from a Square Foot of the Sun—Illustrations of Solar Energy—Decline of Solar Energy—The Warehouse of Grain—White-hot Globe of Iron would Cool in Forty-eight Years—Sun’s Heat is not sustained by Combustion—Inadequacy of Combustion Demonstrated—Joule’s Unit—Energy of a Moving Body—Energy of a Body moving Five Miles a Second—Energy of the Earth due to its Motion.

IT will be convenient to consider different bodies in the solar system, and to study them with the special object of ascertaining what information they afford as to the great celestial evolution. We cannot hesitate as to which of the bodies should first claim our attention. Not on account of the predominant importance of our sun to the inhabitants of the earth, but rather because the sun is nearly a thousand times greater than the greatest of the planets, do we assign to the great luminary the first position in this discussion.

The sun is, indeed, especially instructive on the subject with which we are occupied. By reason of its great mass, the process of evolution takes place more slowly in the sun than in the earth or in any other planet. Evolution has, no doubt, largely transformed the sun from its primæval condition, but it has not yet produced a transformation so radical as that which the earth and the other planets have undergone. On this account the sun can give us information about the process of evolution which is not to be so easily obtained from any of the other heavenly bodies. The sun can still exhibit to us some vestiges, if we may so speak, of that great primæval nebula from which the whole system has sprung.

The heat of the sun is indeed one of the most astonishing conceptions which the study of Nature offers to us. Let me try to illustrate it. Think first of a perfect modern furnace in which even steel itself, having first attained a dazzling brilliance, can be further melted into a liquid that will run like water. Let us imagine the temperature of that liquid to be multiplied seven-fold, and then we shall obtain some conception of the fearful intensity of the heat which would be found in that wonderful celestial furnace the great sun in the heavens.

Ponder also upon the stupendous size of that orb, which glows at every point of its surface with the astonishing fervour that this illustration suggests. The earth on which we stand is a mighty globe; yet what are the dimensions of our earth in comparison with those of the sun? If we represent the earth by a grain of mustard seed, then on the same scale the sun should be represented by a cocoanut. We may perhaps obtain a more impressive conception of the proportions of the orb of day in the following manner. Look up at the moon which revolves round the heaven, describing as it does so majestic a track that it is generally at a distance of two hundred and forty thousand miles from the earth. Yet the sun is so large that if there were a hollow globe equally great, and the earth were placed at its centre, the entire orbit of the moon would lie completely within it.

Every portion of that stupendous desert of flame is pouring forth torrents of heat. It has, indeed, been estimated that the heat which issues from an area of two square feet on the sun would more than suffice, if it could be all utilised, to drive the engines of the largest Atlantic liner between Liverpool and New York.

This solar heat is scattered through space with boundless prodigality. No doubt the dwellers on the earth do receive a fair supply of sunbeams; but what is available for the use of mankind can be hardly more than an infinitesimal fraction of what the sun emits. We shall scarcely be so presumptuous as to suppose that the sun has been designed solely for the benefit of the poor humanity which needs light and warmth. The heat and light daily lavished by the sun would suffice to warm and to illuminate two thousand million globes, each as great as the earth. If, indeed, it were true that the only object of the sun’s existence was to cherish this immediate world of ours, then all we can say is that the sun carries on its business in a most outrageously wasteful manner. What would be thought of the prudence of one who, having been endowed with a fortune of ten million pounds, spent one single penny of that vast sum in a profitable manner and dissipated every other penny and every other pound of his fortune in aimless extravagance? But this is apparently the way in which the sun manages its affairs, so far as our earth is concerned. Out of every ten million pounds worth of heat issuing from the glorious orb of day, we on this earth secure one pennyworth, and all but that solitary pennyworth seems to be utterly squandered. We may say it certainly is squandered so far as humanity is concerned. What, indeed, its actual destination may be science is unable to tell.

And now for the great question as to how the sun’s heat is sustained. How is it that this career of tremendous prodigality has not ages ago been checked by absolute exhaustion? Every child knows that the fire on the hearth will go out unless coal be provided. The workman knows that his devouring furnace in the ironworks requires to be incessantly stoked with fresh supplies of fuel. How, then, comes it that the wonderful furnace on high can still continue, as it has continued for ages, to pour forth its amazing stores of heat without being exhausted?

Professor Langley has supplied us with an admirable illustration showing the amount of fuel which would be necessary, if indeed it were by successive additions of fuel that the sun’s heat was sustained. Suppose that all the coal-seams which underlie England and Scotland were made to yield up their stores; that the vast coalfields in America, Australia, China, and elsewhere were compelled to contribute every combustible particle they contained; suppose, in fact, that we extracted from this earth every ton of coal which it possesses in every isle and every continent; suppose that this mighty store of fuel, sufficient to supply all the wants of the earth for centuries, were to be accumulated, and that by some mighty effort that mass were to be hurled into the sun and were forthwith to be burnt to ashes; there can be no doubt that a stupendous quantity of heat would be produced. But what is that heat in comparison, we do not say with the heat of the sun, but with the daily expenditure of the sun’s heat? How long, think you, would the combustion of so vast a mass of fuel provide for the sun’s expenditure? We are giving deliberate expression to a scientific fact when we say that a conflagration which destroyed every particle of coal contained in this earth would not generate as much heat as the sun lavishes in the tenth part of every single second. During the few minutes that you have been reading these words a quantity of heat has gone for ever from the sun which is five thousand times as great as all the heat that ever has been or ever will be produced by the combustion of the coal that this earth has furnished.

But we have still another conception to introduce before we can appreciate the full significance of the sun’s extraordinary expenditure of heat and light. We have been thinking of the sun as it shines now; but as the sun shines to-day, so it has shone yesterday, and so it shone a hundred years ago, a thousand years ago; so it shone in the earliest dawn of history, so it shone during those still remoter periods when great animals flourished which have now vanished for ever; so the sun shone during those remote ages when life began to dawn on an earth which still was young. We do not, indeed, say that the intensity of the sunbeams has remained actually uniform throughout a period so vast; but there is every reason to believe that throughout these illimitable periods the sun has expended its radiance with the most lavish generosity.

A most important question is suggested by these considerations. The consequences of frightful extravagance are known to us all; we know that such conduct tends to bankruptcy and ruin; and certainly the expenditure of heat by the sun is the most magnificent extravagance of which our knowledge gives us any conception. Accordingly, the important question arises: As to how the consequences of such awful prodigality have been hitherto averted. How is it that the sun is still able to draw on its heat reserve, from year to year, from century to century, from æon to æon, ever squandering two thousand million times as much heat as that which genially warms our temperate regions, as that which draws forth the exuberant vegetation of the tropics or which rages in the desert of Sahara? That is the great problem to which our attention has to be given.

We must first ascertain, with such precision as the circumstances permit, the actual amount of heat which the sun pours forth in its daily radiation. The determination of this quantity has engaged the attention of many investigators, and the interpretation of their results is by no means free from difficulty. It is to be observed that what we are now seeking to ascertain is not exactly a question of temperature, but of something quite different. What we have to measure is a quantity of heat, which is to be expressed in the proper units for quantities of heat. The unit of heat which we shall employ is the quantity of heat necessary to raise one pound of water through one degree Fahrenheit.

The solar constant is the number of units of heat which fall, in one minute, on one square foot of a surface placed at right angles to the sun’s rays, and situated at the mean distance of the earth from the sun. We shall suppose that losses due to atmospheric absorption have been allowed for, so that the result will express the number of units of heat that would be received in one minute on a square foot turned directly to the sun, and at a distance of 93,000,000 miles.

Fig. 14.—The Sun (July 8th, 1892).
(Royal Observatory, Greenwich.)
(From the Royal Astronomical Society Series.)

This is a matter for determination by actual observation and measurement. Theory can do little more than suggest the precautions to be observed and discuss the actual figures which are obtained. There have been many different methods of making the observations, and the results are somewhat various, but the discrepancies are not greater than might be expected in an investigation of such difficulty. The mean value which has been arrived at is fourteen, and the fundamental fact with regard to the solar radiation which we are thus enabled to state is that an area of a square foot exposed at right angles to the solar rays, at a distance of 93 millions of miles, will in each minute receive from the sun as much heat as would raise one pound of water fourteen degrees Fahrenheit.

It follows that the total radiation from the sun must suffice to convey, in each minute, to the surface of a sphere whose radius is 93,000,000 miles, fourteen units of heat per square foot of that surface. This radiation comes from the surface of the sun. It is easily shown that the heat from each square foot on the sun will have to supply an area of 46,000 square feet at the distance of the earth. Hence the number of units of heat emerging each minute from a square foot on the sun’s surface must be about 640,000.

We can best realise what this statement implies by finding the amount of coal which would produce the same quantity of heat. It can be shown that the heat given out by each square foot of the solar surface in one minute will be equivalent to that produced in the combustion of forty-six pounds of coal. If the sun’s heat were sustained by combustion, every part of the sun’s surface as large as the grate of an ordinary furnace would have to be doing at least one hundred times as much heating as the most vigorous stoking could extract from any actual furnace.

The radiation of heat from a single square foot of the solar surface in the course of a year must, therefore, be equivalent to the heat generated in the combustion of 11,000 tons of the best coal. If we estimate the annual coal production of Great Britain at 250,000,000 tons, we find that the total heat which this coal can produce is not greater than the annual emission from a square of the sun’s surface of which each side is fifty yards. All the coal exported from England in a year does not give as much heat as the sun radiates in the same time from every patch on its surface which is as big as a croquet ground.

There is perhaps no greater question in the study of Nature than that which enquires how the sun’s heat is sustained so that the radiation is still dispensed with unstinted liberality. If we are asked how the sun can be fed so as to sustain this expenditure, we have to explain that the sun is not really fed. If, then, it receives no adequate supplies of energy from without, we have to admit that the sun must be getting exhausted.

I ought, indeed, to anticipate objection by at once making the admission that the sun does receive some small supply of energy from the meteors which are perennially drawn into it. The quantity of energy they yield is, however, insignificant in comparison with the solar expenditure of heat. We may return to this subject at a later period, and it need not now receive further attention.

We must deliberately face the fact that the energy of the sun is becoming exhausted. But the rate of exhaustion is so slow that it affords no prospect of inconvenience to humanity; it does not excite alarm. We grant that we are not able to observe by instrumental means any perceptible diminution of solar energy. Still, as we know that energy is being steadily dissipated from the sun, and that energy cannot be created from nothing, it is certain the decline is in progress. But the reserve of energy which the sun possesses, and which can be ultimately rendered available to sustain the radiation, is so enormous in comparison with the annual expenditure of energy, that myriads of centuries will have to elapse before there is any appreciable alteration in the effectiveness of the sun.

Let me illustrate the point by likening the sun to a grain warehouse, in which 2,500 tons of wheat can be accommodated. Let us suppose that the warehouse was quite full at the beginning, and that the wheat was to be gradually abstracted, but only at the rate of one grain each day. Let us further suppose that no more wheat is to be added to that already in the warehouse, and let us assume that the wheat thus stored away experiences no deterioration and no loss whatever except by the removal of one grain per diem. It is easy to see that very many centuries would have to elapse before the grain in that warehouse had decreased to any appreciable extent.

With a consumption at the rate of a single grain a day a ton of corn would last about four thousand years, and 2,500 tons of corn would accordingly last about ten million years. It follows, therefore, that if the grain in that store were consumed at the rate of only one grain per day the warehouse would not be emptied for ten million years.

Fig. 15.—I. Spectrum of the Sun.
II. Spectrum of Arcturus.
(Professor H. C. Lord.)

The quantity of heat, or rather the reserve of energy equivalent to heat, which still remains stored up in the sun bears to the quantity of heat which the sun radiates away in a single day a ratio something like that which a single grain of corn bears to 2,500 tons of corn.

The sun’s potential store of heat is no doubt very great, though not indefinitely great. That heat is beyond all doubt to be ultimately exhausted; but the reserve is so prodigious that for the myriads of years during which the sun has been subjected to human observation there has been no appreciable alteration in the efficiency of radiation.

It might be supposed that the sun was merely a white-hot globe cooling down, and that the solar radiation was to be explained in this way. But a little calculation will prove it to be utterly impossible that the heat of the great luminary could be so accounted for. A knowledge of the current expenditure of solar heat shows that if the sun had been a globe of iron at its fusing point, then at the present rate of radiation it would have sunk to the temperature of freezing water in forty-eight years.

Perhaps I ought here to explain a point which might otherwise cause misapprehension. For our ordinary sources of artificial heat we, of course, employ some form of combustion. Whenever combustion takes place there is chemical union between the carbon or other fuel, whatever it may be, and the oxygen of the atmosphere. A certain quantity of carbon enters into chemical union with a definite quantity of oxygen, and, as an incident in the process, a definite quantity of heat is liberated. So much coal, for instance, requires for complete combustion so much air, and, granted a sufficiency of air, the union of the carbon and hydrogen in the coal will give out a certain quantity of heat which may be conveniently expressed by the number of pounds of water which that heat would suffice to transform into steam. It is necessary to observe that there are definite numerical relations among these quantities. The quantity of heat that can be produced by the combustion of a pound of any particular substance will depend upon the nature of that substance.

As chemical combination is the main source of the artificial heat which we employ for innumerable purposes on the earth, it seems proper to consider whether it can be any form of chemical combination which constitutes the source of the heat which the sun radiates in such abundance. It is easy to show that the solar radiation cannot be thus sustained. The point to which I am now referring was very clearly illustrated by Helmholtz in a lecture he delivered many years ago on the origin of the planetary system.

To investigate whether the solar heat can be attributed to chemical combination, we shall assume for the moment that the sun is composed of those particular materials which would produce the utmost quantity of heat for a given weight; in other words, that the sun is formed of hydrogen and oxygen in quantities having the same ratio as that in which they should be united to form water. The quantity of heat generated by the union of known weights of oxygen and hydrogen has been ascertained, by experiments in the laboratory, to exceed that which can be generated by corresponding weights of any other materials. We can calculate how much of the sun’s mass, if thus constituted, would have to enter into combination every hour in order to generate as much heat as the hourly radiation of the sun. We need not here perform the actual calculation, but merely state the result, which is a very remarkable one. It shows that the heat arising from the supposed chemical action would not suffice to sustain the radiation of the sun at its present rate for more than 3,000 years. Thirty centuries is a long time, no doubt, yet still we must remember that it is no more than a part even of the period known to human history. If, indeed, it had been by combustion that the sun’s heat was produced, then from the beginning of the sun’s career as a luminous object to its final extinction and death could not be longer than 3,000 years, if we assumed that its radiation was to be uniformly that which it now dispenses.

But it may be said that we are dealing only with elements known to us and with which terrestrial chemists are familiar, and it may be urged that the sun possibly contains materials whose chemical union produces heat in much greater abundance than do the elements with which alone we are acquainted. But this argument cannot be sustained. One of the most important discoveries of the last century, the discovery which perhaps more than any other has tended to place the nebular theory in an impregnable position, is that which tells us that the elements of which the sun is composed are the same as the elements of which our earth is made. We shall have to refer to this in detail in a later chapter. We now only make this passing reference to it in order to dismiss the notion that there can be unknown substances in the sun whose heat of combustion would be sufficiently great to offer an explanation of the extraordinary abundance of solar radiation.

There is nothing more characteristic of the physical science of the century just closed than the famous discovery of the numerical relation which exists between heat and energy. We are indebted to the life-long labours of Joule, followed by those of many other investigators, for the accurate determination of the fundamental constant which is known as the mechanical equivalent of heat. Joule showed that the quantity of heat which would suffice to raise one pound of water through a single degree Fahrenheit was the precise equivalent of the quantity of energy which would suffice to raise 772 pounds through a height of one foot. It would be hard to say whether this remarkable principle has had a more profound effect on practical engineering or on the course of physical science. In practical engineering, the knowledge of the mechanical equivalent of heat will show the engineer the utmost amount of work that could by any conceivable apparatus be extracted from the heat potentially contained in a ton of coal. In the study of astronomy the application of the same principle will suffice to explain how the sun’s heat has been sustained for illimitable ages.

Fig. 16.—Brooks’ Comet and Meteor Trail.
(November 13th, 1893. Exposure 2 hours.)
(Photographed by Professor E. E. Barnard.)

It will be convenient to commence with a little calculation, which will provide us with a result very instructive when considering celestial phenomena in connection with energy. We have seen that the unit of heat—for so we term the quantity of heat necessary to raise a pound of water one degree—will suffice, when transformed into mechanical energy, to raise 772 pounds through a single foot. This would, of course, be precisely the same thing as to raise one pound through 772 feet. Suppose a pound weight were carried up 772 feet high and were then allowed to drop. The pound weight would gradually gather speed in its descent, and, at the moment when it was just reaching the earth, would be moving with a speed of about 224 feet a second. We may observe that the work which was done in raising the body to this height has been entirely expended in giving the body this particular velocity. A weight of one pound, moving with a speed of 224 feet a second, will therefore contain, in virtue of that motion, a quantity of energy precisely equivalent to the unit of heat.

It is a well-known principle in mechanics that if a body be dropped from any height, the velocity with which it would reach the ground is just the velocity with which the body should be projected upwards from the ground in order to re-ascend to the height from which it fell (the resistance of the air is here overlooked as not having any bearing upon the present argument). Thus we see that a weight, moving with a velocity of 224 feet per second, contains within itself, in virtue of its motion, energy adequate to make it ascend against gravity to the height of 772 feet. That is to say, this velocity in a body of a pound weight can do for the body precisely what the unit of heat can do for it; hence we say that in virtue of its movement the body contains a quantity of energy equal to the energy in the unit of heat.

Let us now carry our calculation a little further. If a pound of good coal be burned with a sufficient supply of oxygen, and if every precaution be taken so that no portion of the heat be wasted, it can be shown that the combustion of the coal is sufficient to produce 14,000 units of heat. In other words, the burning of one pound of coal ought to be able to raise 14,000 pounds of water one degree, or 140 pounds of water a hundred degrees, or 70 pounds of water two hundred degrees. I do not mean to say that efficiency like this will be attained in the actual circumstances of the combustion of coal in the fireplace. A pound of coal does, no doubt, contain sufficient heat to boil seven gallons of water; but it cannot be made to effect this, because the fireplace wastes in the most extravagant manner the heat which the coal produces, so that no more than a small fraction of that heat is generally rendered available. But in the cosmical operations with which we shall be concerned we consider the full efficiency of the heat; and so we take for the pound of coal its full theoretical equivalent, namely, 14,000 thermal units. Let us now find the quantity of energy expressed in foot-pounds[^[2]] to which this will correspond. It is obtained by multiplying 14,000 units of heat by 772, and we get as the result 10,808,000. That is to say, a pound of good coal, in virtue of the fact that it is combustible and will give out heat, contains a quantity of energy which is represented by ten or eleven million foot-pounds.

[2]. A foot-pound is the amount of energy required to raise a pound weight through a height of one foot.

We now approach the question in another way. Let us think of a piece of coal in rapid motion; if the coal weighed a pound, and if it were moving at 224 feet a second, then the energy it contains in consequence of that velocity would, as we have seen, correspond to one thermal unit. We have, however, to suppose that the piece of coal is moving with a speed much higher than that just stated; and here we should note that the energy which a moving body possesses, in virtue of its velocity, increases very rapidly when the speed of that body increases. If the velocity of a moving body be doubled, the energy that it possesses increases fourfold. If the velocity of the body be increased tenfold, then the energy that it possesses will be increased a hundredfold. More generally, we may say that the energy of a moving body is proportional to the square of the velocity with which the body is animated. Let us, then, suppose that the piece of coal, weighing one pound, is moving with a speed as swift as a shot from the finest piece of artillery, that is to say, with a speed of 2,240 feet a second; and as this figure is ten times 224, it shows us that the moving body will then possess, in virtue of its velocity, the equivalent of one hundred units of heat.

But we have to suppose a motion a good deal more rapid than that obtained by any artillery; we shall consider a speed rather more than ten times as fast. It is easy to calculate that if the piece of coal which weighs a pound is moving at the speed of five miles a second, the energy that it would possess in consequence of that motion would approximate to 14,000 thermal units. In other words, we come to the conclusion that any body moving with a velocity of five miles a second will possess, in virtue of that velocity, a quantity of energy just equal to the energy which an equally heavy piece of good coal could produce if burnt in oxygen, and if every portion of the heat were utilised.

It is quite true that the speed of five miles a second here supposed represents a velocity much in excess of any velocity with which we are acquainted in the course of ordinary experience. It is more than ten times as fast as the speed of a rifle bullet. But a velocity of five miles a second is not at all large when we consider the velocities of celestial bodies. We want this fact relating to the energy in a piece of coal to be remembered. We shall find it very instructive as our subject develops, and therefore we give some illustrations with reference to it.

The speed of the earth as it moves round the sun is more than eighteen miles a second—that is to say, it is three and a half times the critical speed of five miles. In virtue of this speed the earth has a corresponding quantity of energy. To find the equivalent of that energy it must, as already explained, be remembered that the energy of a moving body is proportional to the square of its velocity; it follows that the energy of the earth, due to its motion round the sun, must be almost twelve times as great as the energy of the earth would be if it moved at the rate of only five miles a second. But, we have already seen that a body with the velocity of five miles a second would, in virtue of that motion, be endowed with a quantity of energy equal to that which would be given out by the perfect combustion of an equal weight of coal. It follows, therefore, that this earth of ours, solely in consequence of the fact that it is moving in its orbit round the sun, is endowed with a quantity of energy twelve times as great as all the energy that would be given out in the combustion of a mass of coal equal to the earth in weight. This may seem an astonishing statement; but its truth is undoubted. If it should happen that the earth came into collision with another body by which its velocity was stopped, the principle of the conservation of energy tells us that this energy, which the earth has in consequence of its motion, must forthwith be transformed, and the form which it will assume is that of heat. Such a collision would generate as much heat as could be produced by the combustion of twelve globes of solid coal, each as heavy as the earth. We may indeed remark that the coal-seams in our earth’s crust contain, in virtue of the fact that they partake of the earth’s orbital motion, twelve times as much energy as will ever be produced by their combustion.

It can hardly be doubted that such collisions as we have here imagined do occasionally happen in some parts of space. Those remarkable new stars which from time to time break out derive, in all probability, their temporary lustre from collisions between bodies which were previously non-luminous. But we need not go so far as inter-stellar space for a striking illustration of the transformation of energy into heat. In the pleasing phenomena of shooting stars our own atmosphere provides us with beautiful illustrations of the same principle. The shooting star so happily caught on Professor Barnard’s plate (Fig. [16]) may be cited as an example.

CHAPTER VI.
HOW THE SUN’S HEAT IS MAINTAINED.

The Contraction of a Body—Helmholtz Explained Sun-heat—Change of a Mile every Eleven Years in the Sun’s Diameter—Effect of Contraction on Temperature—The Solar Constant—Limits to the Solar Shrinkage—Astronomers can Weigh the Sun—Density of the Sun—Heat Developed by the Falling Together of the Solar Materials—Contraction of Nebula to Form the Earth—Heat Produced in the Earth’s Contraction—Similar Calculation about the Sun—Earth and Sun Contrasted—Heat Produced in the Solar Contraction from an indefinitely Great Nebula—The Coal-Unit Employed—Calculation of the Heat given out by the Sun.

THE law which declares that a body which gives out heat must in general submit to a corresponding diminution in volume appears, so far as we can judge, to be one of those laws which have to be obeyed not alone by bodies on which we can experiment, but by bodies throughout the extent of the universe. The law which bids the mercury ascend the stem of the thermometer when the temperature rises, and descend when the temperature falls, affords the principle which explains some of the grandest phenomena of the heavens. Applied to the solar system it declares that as the sun, in dispensing its benefits to the earth day by day, has to pour forth heat, so in like manner must it be diminishing in bulk.

Assuming that this principle extends sufficiently widely through time and space, we shall venture to apply its consequences over the mighty spaces and periods required for celestial evolution. We disdain to notice the paltry centuries or mere thousands of years which include that infinitesimal trifle known as human history. Our time conceptions must undergo a vast extension.

It was Helmholtz who first explained by what agency the sun is able to continue its wonderful radiation of heat, notwithstanding that it receives no appreciable aid from chemical combination. Helmholtz pointed out that inasmuch as the sun is pouring out heat it must, like every other cooling body, contract. We ought not, indeed, to say every cooling body; it would be more correct to say, every body which is giving out heat, for the two things are not necessarily the same. Indeed, strange as it may appear, it would be quite possible that a mass of gas should be gaining in temperature even though it were losing heat all the time. At first this seems a paradox, but the paradox will be explained if we reflect upon the physical changes which the gas undergoes in consequence of its contraction.

Let us dwell for a moment on the remarkable statement that the sun is becoming gradually smaller. The reduction required to sustain the radiation corresponds to a diminution of the diameter by about a mile every eleven years. It may serve to impress upon us the fact of the sun’s shrinkage if we will remember that on that auspicious day when Queen Victoria came to the throne the sun had a diameter more than five miles greater than it had at the time when her long and glorious career was ended. The sun that shone on Palestine at the beginning of the present era must have had a diameter about one hundred and seventy miles greater than the sun which now shines on the Sea of Galilee. This process of reduction has been going on for ages, which from the human point of view we may practically describe as illimitable. The alteration in the sun’s diameter within the period covered by the records of man’s sway on this earth may be intrinsically large; it amounts no doubt to several hundreds of miles. But in comparison with the vast bulk of the sun this change in its magnitude is unimportant. A span of ten thousand years will certainly include all human history. Let us take a period which is four times as long. It is easy to calculate what the diameter of the sun must have been forty thousand years ago, or what the diameter of the sun is to become in the next forty thousand years. Calculated at the rate we have given, the alteration in the sun’s diameter in this period amounts to rather less than four thousand miles. This seems no doubt a huge alteration in the dimensions of the orb of day. We must, however, remember that at the present moment the diameter of the sun is about 863,000 miles, and that a loss of four thousand miles, or thereabouts, would still leave a sun with a diameter of 859,000 miles. There would not be much recognisable difference between two suns of these different dimensions. I think I may say that if we could imagine two suns in the sky at the same moment, which differed only in the circumstance that one had a diameter of 863,000 miles and the other a diameter of 859,000 miles, it would not be possible without careful telescopic measurement to tell which of the two was the larger.

After a contraction has taken place by loss of heat, the heat that still remains in the body is contained within a smaller volume than it had originally. The temperature depends not only on the actual quantity of heat that the mass of gas contains, but also on the volume through which that quantity of heat is diffused. If there be two equal weights of gas, and if they each have the same absolute quantity of heat, but if one of them occupies a larger volume than the other, then the temperature of the gas in the large volume will not be so high as the temperature of the gas in the smaller volume. This is indeed so much the case, that the reduction of volume by the loss of heat may sometimes have a greater effect in raising the temperature than the very loss of heat which produced the contraction has in depressing it. On the whole, therefore, a gain of temperature may be shown. This is what, indeed, happens not unfrequently in celestial bodies. The contraction having taken place, the lesser quantity of heat still shows to such advantage in the reduced volume of the body, that no decline of temperature will be perceptible. It may happen that simultaneously with the decrease of heat there is even an increase of temperature.

The principle under consideration shows that, though the sun is now giving out heat copiously, it does not necessarily follow that it must at the same time be sinking in temperature. As a matter of fact, physicists do not know what course the temperature of the sun is actually taking at this moment. The sun may now be precisely at the same temperature at which it stood a thousand years ago, or it may be cooler, or it may be hotter. In any case it is certain that the change of temperature per century is small, too small, in fact, to be decided in the present state of our knowledge. We cannot observe any change, and to estimate the change from mechanical principles would only be possible if we knew much more about the interior of the sun than we know at present.

We are forced to the conclusion that the energy of the sun, by which we mean either its actual heat or what is equivalent to heat, must be continually wasting. A thousand years ago there was more heat, or its equivalent, in the sun than there is at present. But the sun of a thousand years ago was larger than the sun that we now have, and the heat, or its equivalent, a thousand years ago may not have been so effective in sustaining the temperature of the bigger sun as the lesser quantity of heat is in sustaining the temperature of the sun at the present day. It will be noticed that the argument depends essentially on the alteration of the size of the sun. Of course if the orb of day had been no greater a thousand years ago than it is now, then the sun of those early days would not only have contained more heat than our present sun, but it must have shown that it did contain more heat. In other words, its temperature would then certainly have been greater than it is at present.

Thus we see the importance—so far as radiation is concerned—of the gradual shrinking of the sun. The great orb of day decreases, and its decrease has been estimated numerically. We cannot, indeed, determine the rate of decrease by actual telescopic measurement of the sun’s disc with the micrometer; observations extending over a period of thousands of years would be required for this purpose. But from knowing the daily expenditure of heat from the sun it is possible to calculate the amount by which it shrinks. We cannot conveniently explain the matter fully in these pages. Those who desire to see the calculation will find it in the Appendix. Suffice it to say here that the sun’s diameter diminishes about sixteen inches in every twenty-four hours. This is an important conclusion, for the rate of contraction of the solar diameter is one of the most significant magnitudes relating to the solar system.

It was Helmholtz who showed that the contraction of the sun’s diameter by sixteen inches a day is sufficient to account for the sustentation of the solar radiation. For immense periods of time the heat may be dispensed with practically unaltered liberality. The question then arises as to what time-limit may be assigned to the efficiency of our orb. Obviously the sun cannot go on contracting sixteen inches a day indefinitely. If that were the case, a certain number of millions of years would see it vanish altogether. The limit to the capacity of the sun to act as a dispenser of light and heat can be easily indicated. At present the sun, in its outer parts at all events, is strictly a vaporous body. The telescope shows us nothing resembling a solid or a liquid globe. The sun seems composed of gas in which clouds and vapours are suspended. In the sun’s centre the temperature is probably very much greater than any temperature which can be produced by artificial means; it would doubtless be sufficient not only to melt, but even to drive into vapour the most refractory materials. On the other hand, the enormous condensing pressure to which those materials are submitted by the stupendous mass of the sun will have the effect of keeping them together and of compressing them to such an extent that the density of the gas, if indeed we may call it gas, is probably as great as the density of any known matter. The fact is that the terms liquids, gases, and solids cease to retain intelligible distinctions when applied to materials under such pressure as would be found in the interior of the sun.

Astronomers can weigh the sun. It may well be imagined that this is a delicate and difficult operation. It can, however, be effected with but little margin of uncertainty, and the result is a striking one. It serves no useful purpose to express the sun’s weight as so many myriads of tons. It is more useful for our present purpose to set down the density of the sun, that is to say, the ratio of the weight of the orb, to that of a globe of water of the same size. This is the useful form in which to consider the weight of the sun. Astronomers are accustomed to think of the weight of our own earth in this same fashion, and the result shows that the earth is rather more than five times as heavy as a globe of water of the same size. We can best appreciate this by stating that if the earth were made of granite, and had throughout the density which we find granite to possess at the surface, our globe would be about three times as heavy as a globe of water of the same size. If, however, the earth had been entirely made of iron, it would be more than seven times as heavy as a globe of water of the same size. As the earth actually has a density of 5, it follows that our globe taken as a whole is heavier than a globe of granite of the same size, though not so heavy as a globe of iron.

In the matter of density there is a remarkable contrast between the sun and the earth. The sun’s density is much less than that of the earth. Of course it will be understood that the sun is actually very much heavier than our globe; it is indeed more than three hundred thousand times greater in weight. But the sun is about a million three hundred thousand times as big as the earth, and it follows from these figures that its density cannot be more than about a fourth of that of the earth. The result is that, at present, the sun is nearly half as heavy again as a globe of water the same size. We have used round numbers: the density of the sun is actually 1.4.

Fig. 17.—Argo and the Surrounding Stars and Nebulosity.
(Photographed by Sir David Gill, K.C.B.)

In the following manner we explain how heat is evolved in the contraction of the sun. In its early days the sun, or rather the materials which in their aggregate form now constitute the sun, were spread over an immense tract of space, millions of times greater than the present bulk of the sun. We see nebulosities even now in the heavens which may suggest what the primæval nebula may have been before the evolution had made much progress. Look for instance at Sir David Gill’s photograph of the Nebula in Argo in Fig. [17], or at the Trifid Nebula in Fig. [18]. We may, indeed, consider the primæval nebula to have been so vast that particles from the outside falling into the position of the present solar surface would acquire that velocity of three hundred and ninety miles a second which we know the attraction of the sun is capable of producing on an object which has fallen in from an indefinitely great distance. As these parts are gradually falling together at the centre, there will be an enormous quantity of heat developed from their concurrence. Supposing, for instance, that the materials of the sun were arranged in concentric spherical shells around the centre, and imagining these shells to be separated by long intervals, so that the whole material of the sun would be thus diffused over a vast extent, then every pound weight in the outermost shell, by the very fact of its sinking downwards to the present solar system, would acquire a speed of 390 miles a second, and this corresponds to as much energy as could be produced by the burning of three tons of coal. But be the fall ever so gentle, the great law of the conservation of energy tells us that for the same descent, however performed, the same quantity of heat must be given out. Each pound in the outer shell would therefore give out as much heat as three tons of coal. Every pound in the other shells, by gradual descent into the interior, would also render its corresponding contribution. It then becomes easily intelligible how, in consequence of the original diffusion of the materials of the sun over millions of times its present volume, a vast quantity of energy was available. As the sun contracted this energy was turned into radiant heat.

We may anticipate a future chapter so far as to assume that there was a time when even this solid earth of ours was a nebulous mass diffused through space. We are not concerned as to what the temperature of that nebulous mass may have been. We may suppose it to be any temperature we please. The point that we have now to consider is the quantity of heat which is generated by the contraction of the nebula. That heat is produced in the contraction will be plain from what has gone before. But we may also demonstrate it in a slightly different way. Let us take any two points in the nebula, P and Q. After the nebula has contracted the points which were originally at P and Q will be found at two other points, A and B. As the whole nebula in its original form was larger than the nebula after it has undergone its contraction, the distance P Q is generally greater than the distance A B. We may suppose the contraction to proceed uniformly, so that the same will be true of the distance between any other two particles. The distance between every pair of particles in the contracted nebula will be less than the distance between the same particles in the original nebula.

Fig. 18.—Trifid Nebula in Sagittarius (Lick Observatory, California).
(From the Royal Astronomical Society Series.)

If two attracting bodies, A and B, are to be moved further apart than they were originally, force must be applied and work must be done. We may measure the amount of that work in foot-pounds, and then, remembering that 772 foot-pounds of work are equivalent to the unit of heat, we may express the energy necessary to force the two particles to a greater distance asunder in the equivalent quantity of heat. If, therefore, we had to restore the nebula from the contracted state to the original state, this would involve a forcible enlargement of the distance A B between every two particles to its original value, P Q. Work would be required to do this in every case, and that work might, as we have explained, be expressed in terms of its equivalent heat value. Even though the temperature of the nebula is the same in its contracted state as in its original state, we see that a quantity of heat might be absorbed or rendered latent in forcing the nebula from one condition to the other. In other words, keeping the temperature of the nebula always constant, we should have to apply a large quantity of heat to change the nebula from its contracted form to its expanded form.

It is equally true that when the nebula is contracting, and when the distance between every two particles is lessening, the nebula must be giving out energy, because the total energy in the contracted state is less than it was in the expanded state. This energy is equivalent to heat. We need not here pause to consider by what actual process the heat is manifested; it suffices to say that the heat must, by one of the general laws of Nature, be produced in some form.

We are now able to make a numerical estimate. We shall suppose that the earth, or rather the materials which make the earth, existed originally as a large nebula distributed through illimitable space. The calculations show that the quantity of heat, generated by the condensation of those materials from their nebulous form into the condition which the earth now has, was enormously great. We need not express this quantity of heat in ordinary units. The unit we shall take is one more suited to the other dimensions involved. Let us suppose a globe of water as heavy as the earth. This globe would have to be five or six times as large as the earth. Next let us realise the quantity of heat that would be required to raise that globe of water from freezing point to boiling point. It can be proved that the heat, or its equivalent, which would be generated merely by the contraction of the nebula to form the earth, would be ninety times as great as the amount of heat which would suffice to raise a mass of water equal in weight to the earth from freezing point to boiling point.

We apply similar calculations to the case of the sun. Let us suppose that the great luminary was once diffused as a nebula over an exceedingly great area of space. It might at first be thought that the figures we have just given would answer the question. We might perhaps conjecture that the quantity of heat would be such as would raise a mass of water equal to the sun’s mass from freezing to boiling point ninety times over. But we should be very wrong in such a determination. The heat that is given out by the sun’s contraction is enormously greater than this estimate would represent, and we shall be prepared to admit this if we reflect on the following circumstances. A stone falling from an indefinitely great distance to the sun would acquire a speed of 390 miles a second by the time it reached the sun’s surface. A stone falling from an indefinitely great distance in space to the earth’s surface would, however, acquire a speed of not more than seven miles a second. The speed acquired by a body falling into the sun by the gravitation of the sun is, therefore, fifty-six times as great as the speed acquired by a body falling from infinity to the earth by the gravitation of the earth. As the energy of a moving body is proportional to the square of its velocity, we see that the energy with which the falling body would strike the sun, and the heat that it might consequently give forth, would be about three thousand times as great as the heat which would be the result of the fall of that body to the earth. We need not therefore be surprised that the drawing together of the elements to form the sun should be accompanied by the evolution of a quantity of heat which is enormously greater than the mere ratio of the masses of the earth and sun would have suggested.

There is another line of reasoning by which we may also illustrate the same important principle. Owing to the immense attraction possessed by the large mass of the sun, the weights of objects on that luminary would be very much greater than the weights of corresponding objects here. Indeed, a pound on the sun would be found by a spring-balance to weigh as much as twenty-seven pounds here. If the materials of the sun had to be distributed through space, each pound lifted a foot would require twenty-seven times the amount of work which would be necessary to lift a pound through a foot on the earth’s surface. It will thus be seen that not only the quantity of material that would have to be displaced is enormously greater in the sun than in the earth, but that the actual energy that would have to be applied per unit of mass from the sun would be many times as great as the quantity of energy that would have to be applied per unit of mass from the earth to effect a displacement through the same distance. To distribute the sun’s materials into a nebula we should therefore require the expenditure of a quantity of work far more than proportional to the mere mass of the sun. It follows that when the sun is contracting the quantity of work that it will give out, or, what comes to the same thing, the amount of heat that would be poured forth in consequence of the contraction per unit of mass of the sun will largely exceed the quantity of heat given out in the similar contraction of the earth per unit of mass of the earth.

These considerations will prepare us to accept the result given by accurate calculation. It has been shown that the heat which would be generated by the condensation of the sun from a nebula filling all space down to its present bulk is two hundred and seventy thousand times the amount of heat which would be required to raise the temperature of a mass of water equal to the sun from freezing point to boiling point.

This is a result of a most instructive character. The amount of heat that would be required to raise a pound of water from freezing point to boiling point would, speaking generally, be quite enough if applied to a pound of stone or iron to raise either of these masses to a red heat. If, therefore, we think of the sun as a mighty globe of stone or iron, the amount of heat that would be produced by the contraction of the sun from the primæval nebula would suffice to raise that globe of stone or iron from freezing point up to a red heat 270,000 times. This will give us some idea of the stupendous amount of heat which has been placed at the disposal of the solar system by the process of contraction of the sun. This contraction is still going on, and consequently the yield of heat which is the consequence of this contraction is still in progress, and the heat given out provides the annual supply necessary for the sustenance of our solar system.

There is one point which should be specially mentioned in connection with this argument. We have here supposed that the current supply of radiant heat from the sun is entirely in virtue of the sun’s contraction. That is to say, we suppose the sun’s temperature to be remaining unaltered. This is perhaps not strictly the case. There may be reason for believing that the temperature of the sun is increasing, though not to an appreciable extent.

It will be convenient to introduce a unit that will be on a scale adapted to our measurements. Let us think of a globe of coal as heavy as the sun. Now suppose adequate oxygen were supplied to burn that coal, a definite quantity of heat would be produced. There is no present necessity to evaluate this in the lesser units adapted for other purposes. In discussing the heat of the sun, we may use what we call the coal-unit, by which is to be understood the total quantity of heat that would be produced if a mass of coal equal to the sun in weight were burned in oxygen. It can be shown by calculations, which will be found in the Appendix, that in the shrinkage of the sun from an infinitely great extension through space down to its present bulk the contraction would develop the stupendous quantity of heat represented by 3,400 coal-units. It is also shown that one coal unit would be adequate to supply the sun’s radiation at its present rate for 2,800 years.

CHAPTER VII.
THE HISTORY OF THE SUN.

The Inconstant Sun—Representation of the Solar System at different Epochs—Primæval Density of the Sun—Illustration of Gas in Extreme Tenuity—Physical State of the Sun at that Period—The Sun was then a Nebula.

WE pointed out in the last chapter how, in consequence of its perennial loss of heat, the orb of day must be undergoing a gradual diminution in size. In the present chapter we are to set down the remarkable conclusions with respect to the early history of the sun to which we have been conducted by pursuing to its legitimate consequences the shrinkage which the sun had undergone in times past.

The outer circle in Fig. [19] represents the track in which our earth now revolves around the sun, and we are to understand that the radius of this circle is about ninety-three million miles. We must imagine that the innermost of the four circles represents the position of the sun. Along its track the earth revolves year after year; so it has revolved for centuries, so it has revolved since the days of the first monarch that ever held sway in Britain, so it has revolved during all the time over which history extends, so it has doubtless revolved for illimitable periods anterior to history. For an interval of time that no one presumes to define with any accuracy the earth has revolved in the same track round that sun in heaven which, during all those ages, has dispensed its benefits of light and heat for the sustenance of life on our globe.

Fig. 19.—To Illustrate the History of the Sun.
Present orbit of Earth.
Sun in times very much earlier still.
Sun in very early times.
Present Sun.

The sun appears constant during those few years in which man is allowed to strut his little hour. The size of the sun and the lustre of the sun has not appreciably altered. But the sun does not always remain the same. It has not always shone with the brightness and vigour with which it shines now; it will not continue for ever to dispense its benefits with the same liberality that it does at present. The sun is always in a state of change. It would not indeed be correct to refer to these changes as growths, in the same sense in which we speak of the growth in a tree. Decade after decade the tree waxes greater; but the sun, as we have already explained, does not increase with the time, for the change indeed lies the other way. It may well be that in this present era the sun is near its prime, in so far as its capacity to radiate warmth and brightness is concerned. It is, however, certain that the sun is not now so large as it was in ancient days. The diminution of the orb is still in progress. In these present days of its glorious splendour the orb of day is much larger than it will be in that gloomy old age which destiny assigns to it.

We have already shown how to give numerical precision to our facts. We have stated that the sun’s diameter is diminishing at the rate of one mile every eleven years. We have dwelt upon the remarkable significance of that shrinkage in accounting for the sustentation of the sun’s heat. We have now to call on this perennial diminution of the sun’s diameter to provide some information as to the early history of our luminary.

The innermost circle in our sketch is to suggest the sun as it is at present. Millions of years ago the orb of day was as large as I have indicated it by the circle with the words “sun in very early times.” It will, of course, be understood that we do not make any claim to precise representation of the magnitude of the orb. At a period much earlier still, the sun must have been larger still, and we venture so to depict it. We know the rate at which the sun is now contracting, and doubtless this rate has continued sensibly unaltered during thousands of years, and indeed we might say scores of thousands of years. But it would not be at all safe to assume that the annual rate of change in the sun’s radius has remained the same throughout excessively remote periods in its evolutionary history. What we do affirm is, that in the course of its evolution the sun must have been contracting continually, and we have been able to learn the particular rate of contraction characteristic of the present time. But though we are ignorant of the rate of contraction at very early epochs, yet the sun ever looms larger and larger in days earlier and still earlier. But in those early days the sun was not heavier, was not, indeed, quite so heavy as it is at present. For we remember that the sun is perennially adding thousands of tons to its bulk by the influx of meteors. Perhaps we ought to add that the gain of mass from the meteors may be to some extent compensated by the loss of substance which the sun not infrequently experiences if, as is sometimes supposed, it expels in some violent convulsion a mass of material which takes the form of a comet (Fig. [21]).

Let us now consider what the density of the sun must have been in those primæval days, say, for example, when the luminary had ten times the volume that it has at present. Even now, as already stated, it does not weigh half as much again as a globe of water of the same size, so that when it was ten times as big its density must have been only a small fraction of that of water. But we may take a stage still earlier. Let us think of a time—it was, perhaps, many scores of millions of years ago—when the sun was a thousand times as big as it is at present. The same quantity of matter which now constitutes the sun was then expanded over a volume a thousand times greater. A remarkable conclusion follows from this consideration. The air that we breathe has a density which is about the seven-hundredth part of that of water. Hence we see that at the time when the materials of the sun were expanded into a volume a thousand times as great as it is at present the density of the luminary must have been about equal to that of ordinary air. We refer, of course, in such statements to the average density of the sun. It will be remembered that the density of the sun cannot be uniform. The mutual attractions and pressures of the particles in the interior must make the density greater the nearer we approach to the centre.

We must push our argument further still. We have ascertained that the primæval sun could not have been a dense solid body like a ball of metal. It must have been more nearly represented by a ball of gas. There was a time when that collection of matter which now constitutes the sun was so big that a balloon of equal size, filled at ordinary pressure with the lightest of known gases, would contain within it a heavier weight than the sun. At this early period the sun must have been as light as an equal volume of hydrogen. The reasoning which has conducted us to this point remains still unimpaired. From that early period we may therefore look back to periods earlier still. We see that the sun must have been ever larger and larger, for the same quantity of material must have been ever more and more diffused. There was a time when the mean density of the sun must have been far less than that of the gas in any balloon.

We must not pause to consider intermediate stages. We shall look back at once to an excessively early period when the sun—or perhaps we ought rather to say the matter which in a more condensed form now constitutes the sun—was expanded throughout the volume of a globe whose radius was as great as the present distance from the sun to the earth. Have we not here truly an astonishing result, deduced as a necessary consequence from the fundamental laws of heat?

Fig. 20.—The Solar Corona (January 1st, 1899).
(Photographed during Eclipse by Professor W. H. Pickering.)

I need hardly say that the sun at that early date did not at all resemble the glorious orb to which we owe our very existence. The primæval sun must have been a totally different object, as we can easily imagine if we try to think that the sun’s materials then filled a volume twelve million times as great as they occupy at present. Instead of comparing such an object with the gases in our ordinary atmosphere, it should rather be likened to the residue left in an exhausted receiver after the resources of chemistry have been taxed to make as near an approach as possible to a perfect vacuum.