The Earth's Beginning

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Title: The Earth's Beginning
Author: Ball, Robert S. (Robert Stawell)
Language: English
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*** Start of this LibraryBlog Digital Book "The Earth's Beginning" ***

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.

------------------------------------------------------------------------

[Illustration: 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.

------------------------------------------------------------------------

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 10^{18}, and
think of a line a kilometre long. If that line were divided into 10^{18}
parts, each of those parts would represent the diameter of a corpuscle
of radium. If that line were multiplied by 10^{18}, 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

CHAPTER PAGE

I. —INTRODUCTION 1

II. —THE PROBLEM STATED 21

III. —THE FIRE-MIST 39

IV. —NEBULÆ—APPARENT AND REAL 52

V. —THE HEAT OF THE SUN 75

VI. —HOW THE SUN’S HEAT IS MAINTAINED 95

VII. —THE HISTORY OF THE SUN 112

VIII. —THE EARTH’S BEGINNING 122

IX. —EARTHQUAKES AND VOLCANOES 158

X. —SPIRAL AND PLANETARY NEBULÆ 191

XI. —THE UNERRING GUIDE 207

XII. —THE EVOLUTION OF THE SOLAR SYSTEM 246

XIII. —THE UNITY OF MATERIAL IN THE HEAVENS 261
AND THE EARTH

XIV. —THE FIRST CONCORD 294

XV. —THE SECOND CONCORD 308

XVI. —THE THIRD CONCORD 324

XVII. —OBJECTIONS TO THE NEBULAR THEORY 337

XVIII. —THE BEGINNING OF THE NEBULA 348

XIX. —CONCLUDING CHAPTER 361

APPENDICES 369

INDEX 382

------------------------------------------------------------------------

LIST OF ILLUSTRATIONS

FIG. PAGE

An English Sunset tinged by Krakatoa _Frontispiece_
(colour)

1. Immanuel Kant (from an old print) 7

2. A Faint Diffused Nebulosity 17

3. The Crab Nebula 19

4. Jupiter 25

5. Nebulous Region and Star-cluster 33

6. The Great Nebula in Orion 41

7. The Dumb-bell Nebula 45

8. The Crossley Reflector 49

9. The Cluster in Hercules 53

10. Spectra of the Sun and Capella 62

11. Spectrum of Nebula in Orion and Spectrum 64
of White Star

12. Solar Spectra with Bright Lines and Dark 69
Lines during Eclipse

13. The Nebulæ in the Pleiades 71

14. The Sun 81

15. I. Spectrum of the Sun. II. Spectrum of 85
Arcturus

16. Brooks’ Comet and Meteor Trail 89

17. Argus and the surrounding Stars and 103
Nebulosity

18. Trifid Nebula in Sagittarius 105

19. To illustrate the History of the Sun 113

20. Solar Corona 117

21. The Great Comet of 1882 119

22. Special Thermometer for use in Deep 129
Borings

23. At the Bottom of the Great Bore 140

24. Three consecutive Shells of the Earth’s 145
Crust

25. Earthquake Routes from Japan to the Isle 171
of Wight

Showing Localities of Earthquakes 175
(colour)

26. Showing Coasts invaded by the Great 179
Sea-waves from Krakatoa

The Early Stage of the Eruption of 180
Krakatoa (colour)

27. Spread of the Air-wave from Krakatoa to 183
the Antipodes

28. The great Spiral Nebula 193

29. How to find the great Spiral Nebula 196

30. A group of Nebulæ 199

31. A Ray Nebula 201

32. Portion of the Milky Way 205

33. A Spiral Nebula seen Edgewise 211

34. A foreshortened Spiral 212

35. Edge-view of a Spiral boldly shown 213

36. To illustrate Moment of Momentum 223

37. Saturn 233

38. The Ring Nebula in Lyra 249

39. Lunar Craters: Hyginus and Albategnius 255

40. A remarkable Spiral 257

41. A clearly-cut Spiral 259

42. The H and K Lines in the Photographic 276
Solar Spectrum

43. Spectrum of Comet showing Carbon Lines 290

The Solar Spectrum (colour) 290

44. Spectrum of the Sun during Eclipse 291

45. A Spiral presented Edgewise 296

46. The Plane of a Planet’s Orbit 298

47. A Right Angle divided into Ten Parts 301

48. Illustration of the Second Concord 309

49. Orbits of the Earth, Eros and Mars 313

50. I. A Natural System. II. An Unnatural 318
System

51. An elongated irregular Nebula 329

52. Two-branched Spiral 345

53. Cluster with Stars of the 17th Magnitude 353

54. Spectrum of Nova Persei (1901) 359

55. The Apteryx: a Wingless Bird of New 365
Zealand

56. Skeleton of the Apteryx, showing 366
Rudimentary Wings

57. Spirals in other Departments of Nature: 367
Foraminifer

58. Ditto ditto Nautilus 367

59. To illustrate a Theorem in the 369
Attraction of Gravitation

60. First Law of Motion exemplifies Constant 375
Moment of Momentum

61. A useful Geometrical Proposition 376

62. Acceleration of Moment of Momentum 376
equals Moment of Force

63. Moment of Momentum unaltered by 380
Collision

------------------------------------------------------------------------

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.

Footnote 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.”

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

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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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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.

Footnote 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.

[Illustration: 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.

[Illustration: 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.

[Illustration: 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?

[Illustration: 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.

We can give a familiar illustration of gas in a state of extreme
tenuity. Look at the beautiful incandescent light with which in these
days our buildings are illuminated. How brilliantly those little globes
shine! The globe has to be most carefully sealed against the outside
air. If there were the smallest opportunity for access, the air from
outside would rush in and the lamp would be destroyed. In the
preparation of such a lamp elaborate precautions have to be taken to
secure that the exhaustion of the air from the little globe shall be as
nearly perfect as possible. Of course it is impossible to remove all the
air. No known processes can produce a perfect vacuum. Some traces of gas
would remain after the air-pump had been applied even for hours.

We must now imagine a globe, not merely two inches in diameter like one
of these little lamps, but a globe 186,000,000 miles in diameter, a
globe so large that the earth’s orbit would just form a girdle round it.
Even if this globe had been exhausted, so that its density was only the
twelve-thousandth part of the ordinary atmospheric density, it would
still contain more material than is found in the sun in heaven. Thus our
reasoning has conducted us to the notion of an epoch when the sun—or
rather I should say the matter composing the sun—formed something
totally different from the orb which we know so well. The matter in that
very diffuse state would not dispense light and heat as a sun in the
sense in which we understand the word. However vast might be the store
of energy which it contained—a store indeed thousands of times greater
than our present sun possesses—yet it would hardly be possessed of the
power of effective radiation. It would assuredly not be able to warm and
light a world associated with it, in the same way as the sun now
provides so gloriously for our wants and comfort.

[Illustration: Fig. 21.—THE GREAT COMET OF 1882.
(_Photographed on November 7th, 1882, by Sir David Gill, K.C.B._)]

But it is certain that in those early days there was no earth to be
warmed and lighted. Our globe, even if it can be said to have existed at
all, was truly “without form and void.” At the time when the sun was
swollen into a great globe of gas or rarefied matter, the elementary
substances which were to form the future earth were in a condition
utterly different from that of our present globe. The history of this
earth itself involves another chapter of the argument. Let it suffice to
notice, for the present, that our reasoning has led us to a time when
the sun consisted only of a rarefied gaseous material, and let us give
to the matter in this condition the name which astronomers apply to any
object of a similar character wherever they may meet with it in the
universe. Suppose that we could observe through our telescopes at the
present moment an object in remote space which was like what the sun
must have been at that early stage of its existence which we have been
considering, I do not think that the object would be unfamiliar to
astronomers. There is, indeed, no doubt that there are many objects
visible at this moment, and nightly studied in our observatories, which
are formed of matter just in the same state as the sun was in those
early times. Examined with a good telescope, the object would seem like
a small stain of light on the black background of the sky. The observer
would at once call it a nebula. In these modern days he would probably
apply the spectroscope to it, and this instrument would assure him that
the object he was looking at was a mass of incandescent gas. Such an
object would in all probability not greatly differ from many nebulæ now
known to us.

This being so, why should we withhold from the sun of primitive days the
designation to which it seems to be so fully entitled? Why should we not
speak of it as a nebula? The application of the laws of heat has shown
that the great orb of day was once one of those numerous objects which
astronomers know as nebulæ, and perhaps it may not be too fanciful to
suppose that a trace of the primæval nebula still survives in what we
call the Solar Corona (Fig. 20).

------------------------------------------------------------------------

CHAPTER VIII.

THE EARTH’S BEGINNING.

The Earth to be Studied—A great Experiment—The Diamond Drill—A Boring
upwards of a Mile Deep—A Mechanical Feat—The Scientific Importance
of the Work—Increase of Temperature with the Depth—A special Form of
Thermometer—Taking the Temperature in the Boring—The Level of
Constant Temperature—The Rate of Increase of Temperature with the
Depth—One degree Fahrenheit for every Sixty-six Feet in
Depth—Temperatures at Depths above a Mile—Conclusions as to the Heat
at very great Depths—The Heat developed by Tidal Action—This will
not account for the Earth’s Internal Heat—The Earth must be
continually Cooling—Inferences from the incessant loss of Heat from
the Earth—The Earth’s Surface once Red-Hot, or Molten—The Earth must
have originated from a Nebula—The Earth’s Beginning.

IN the last chapter we endeavoured to ascertain what can be learned from
the radiation of the sun with regard to the history of the solar system.
In this chapter we shall not consider any body in the heavens, but the
condition of the earth itself. We have learned something of the history
of the solar system from the celestial bodies; we shall now learn
something about it in another way—from the condition of our globe at
depths far beneath our feet.

It will be convenient to commence by mentioning a remarkable experiment
which was made a few years ago. Though that experiment is of great
scientific interest, yet it was not designed with any scientific object
in view. Not less than £10,000 was expended on the enterprise, and
probably so large a sum has never been expended on a single experiment
of which the sole object was to add to scientific knowledge. In the
present case the immediate object in view was, of course, a commercial
one. There was, it may be presumed, reasonable expectation that the
great initial cost, and a handsome profit as well, would be returned as
the fruits of the enterprise. Whether the great experiment was
successful from the money-making point of view does not now concern us,
but it does concern us to know that the experiment was very successful
in the sense that it incidentally afforded scientific information of the
very highest value.

The experiment in question was made in Germany, at Schladebach, about
fifteen miles from Leipzig. It was undertaken in making a search for
coal. Some enterprising capitalists consulted the geologists as to
whether coal-seams were likely to be found in this locality. They were
assured that coal was there, though it must certainly be a very long way
down, and consequently the pit by which alone the seams could be worked
would have to be unusually deep. The capitalists were not daunted by
this consideration. But, before incurring the great expense of sinking
the shaft, they determined to make a preliminary search and verily the
actual presence of workable seams of useful fuel. They determined to
bore a hole down through the rocks deep enough to reach the coal, if it
could be reached. A boring for coal was, of course, by no means a
novelty; but there was an unprecedented degree of mechanical skill and
scientific acumen shown in this memorable boring near Leipzig. The
result of this enterprise was to make the deepest hole which, with
perhaps a single more recent exception not of so much scientific
interest, has ever been pierced through the crust of the earth. This
boring was merely a preliminary to the operations which would follow if
the experiment were successful in discovering coal. It was accordingly
only necessary to make a hole large enough to allow specimens of the
strata to be brought to the surface.

The instrument employed in sinking a hole of such a phenomenal depth
through solid rock is characteristic of modern enterprise. The boring
tool had a cutting edge of diamonds: for no other cutting implement is
at once hard enough and durable enough to advance steadily, yard by
yard, through the various rocks and minerals that are met with in the
descent through the earth’s crust. We might, perhaps, illustrate the
actual form of the tool as follows: imagine a piece of iron pipe, about
six inches in diameter, cut squarely across, with diamonds inserted
round its circular end, and we have a notion of the diamond drill. If
the drill be made to revolve when held vertically, with the diamonds in
contact with the rocks, the cutting will commence. As the rotation is
continued, the drill advances through the rocks, and a solid core of the
material will occupy the hollow of the pipe. We do not now enter into
any description of the many mechanical details; there are ingenious
contrivances for removing the _débris_ produced by the attrition of the
rocks as the diamonds cut their way, and provision is also made for
carefully raising the valuable core which, as it provides specimens of
the different strata pierced, will show the coal, if coal is ever
reached. There is, of course, an arrangement by which, as the first
length of drill becomes buried, successive lengths can be added, so as
to transmit the motion to the cutting edge and enable the tool to be
raised when necessary; in this manner one length of solid rock after
another is brought up for examination. These cores, when ranged in
series, give to the miner the information he requires as to the
different beds of rock through which the instrument has pierced in its
descent and as to the depths of the beds. A series of cores will
sometimes show astonishing variety in the material through which the
drill has passed. Here the tool will be seen passing through a bed of
hard limestone, and then entering a bed of soft shale; now the tool
bores through dense and hard masses of greenstone, anon it pierces, it
may be, a stratum of white marble; and finally the explorer may hope to
find his expectations realised by the arrival at the surface of a
cylinder of solid coal.

The famous boring to which we are now referring, though very deep, was
not large in diameter. As it descended the comparatively large tool
first employed was replaced by a succession of smaller tools, so that
the hole gradually tapered from the surface to the lowest point. At its
greatest depth the hole was indeed hardly larger than a man’s little
finger. It increased gradually all the way to the surface, where it was
large enough for a man’s arm to enter it easily.

How often do we find that the success which rewards mechanical
enterprise greatly transcends even the most sanguine estimate previously
formed! Without the actual experience which has been acquired, I do not
think anyone could have anticipated the extraordinary facilities which
the diamond drill has given in the operations of a deep boring. This
hole at Schladebach was, indeed, a wonderful success. It pierced deeper
than any previous excavation, deeper than any well, deeper than any coal
pit. From the surface of the ground, where the hole was some six inches
in diameter, down to the lowest point, where it was only as large as a
little finger, the vertical depth was not less than one mile and a
hundred and seventeen yards.

It is worth pondering for a moment on the extraordinary mechanical feat
which this represents. When the greatest depth was reached, the total
length of the series of boring rods from the surface where the machinery
was engaged in rotating the tool down to the cutting diamonds at the
lower end where the penetration was being effected, was as long as from
Piccadilly Circus to the top of Portland Place. If a hole of equal
length had been bored downwards from the top of Ben Nevis, it would have
reached the sea level and gone down 1,200 feet lower still. When the
foreman in charge wished to look at the tool to see whether it was
working satisfactorily, or whether any of the diamonds had got injured
or displaced, it was necessary to raise that tremendous series of rods.
Each one of them had to be lifted, had to be uncoupled, and had to be
laid aside. I need hardly say that such an operation was a very tedious
one. The collective weight of the working system of rods was about
twenty tons, and not less than ten hours’ hard work was required before
the tool was raised from the bottom to the surface. We may, I believe,
conclude that so much ingenuity and so much trouble was never before
expended on the act of boring a hole; but the results are full of
information on important problems of science.

I am not going to speak of the geological results of this exploration.
There is not the least doubt that the remarkable section of the earth’s
crust thus obtained is of much interest to geologists. Our object in now
alluding to this wonderful boring is, however, very different. Its
significance will be realised when we say that it gives us more full and
definite information about the internal heat of the earth than had ever
been obtained by any other experiment on the earth’s crust. No doubt
many previous observations of the internal heat of the globe were well
known to the investigators who feel an interest in these important
questions; but the exceptional depth of this boring, as well as the
exceptionally favourable conditions under which it was made, have
rendered the information derived from it of the utmost value to science.

We ought first to record our special obligation to the German engineer,
Captain Huyssen, who bored this wonderful hole. He was not only a highly
skilful mining engineer, diligent in the pursuit of his profession, but,
by the valuable scientific work he has done, he has shown himself to be
one of those cultivated and thoughtful students who love to avail
themselves of every opportunity of searching into Nature’s secrets. Our
thanks are due to him for the remarkable zeal with which he utilised the
exceptional opportunities for valuable scientific work that arose,
incidentally as it were, in connection with the work committed to him.

Of course, everybody knows that the temperature of the earth is found to
increase gradually as greater depths are reached. The rate at which the
increase takes place has been determined on many occasions. But when
opportunities have arisen for taking the temperature at considerable
depths below the earth’s surface, it has happened sometimes that the
observations have been complicated by circumstances which deprived them
of a good deal of their accuracy. If our object be to learn the law
connecting the earth’s temperature with the depth below the surface, it
is not sufficient to study the thermometric readings in different coal
pits. Throughout the workings in every pit there must be arrangements
for ventilation. The cool air has to be drawn down, and thus the
temperature indicated in the pit is forced below the temperature which
would really be found at that depth if external sources of change of
temperature were absent.

Captain Huyssen rightly deemed that the hole which he had pierced
presented exceptional opportunities for the study of the important
question of the earth’s internal temperature. Precautions had, of
course, to be observed. The hole, as might be expected, was filled with
water, and the water would tend, if its circulation were permitted, to
equalise the temperature at different depths. But the ingenious Captain
quickly found an efficient remedy for this source of inaccuracy. He
devised an arrangement, which I must not delay to describe, by which he
could place temporary plugs in the hole at any depths he might desire;
he then determined the temperature of the water in a short length, so
plugged above and below that the circulation was stopped, and
accordingly the water thus confined might be relied on to indicate the
temperatures of the strata which hold it.

[Illustration: Fig. 22.—SPECIAL THERMOMETER FOR USE IN DEEP BORINGS.]

The thermometer employed in an investigation of this sort is ingenious
though extremely simple. The ordinary maximum thermometer is not found
to be adapted for the purpose. The instrument (Fig. 22) employed in the
determination of underground temperatures is very much less complicated
and at the same time much more accurate. The contrivance is indeed so
worthy of notice that I do not like to pass it by without a few words.
The thermometer with which the temperature of the earth is ascertained
in such investigations is not like any ordinary thermometer. There is no
scale of degrees attached to it or engraved upon it, as we generally
find in such instruments. The instrument with which the temperature of
the deep hole was measured was merely a bulb of glass with a slender
capillary stem, the end of which was not closed. When it was about to be
lowered to test the temperature of the rocks at the lowest point to
which the drill had penetrated, the bulb and the tube were first filled
with mercury to the top, and brimming over. This simple apparatus was
attached to a long wire, by the aid of which it could be lowered down
this deep hole. Down it went till at last the thermometer reached the
bottom, which, as we have explained, it could not do until more than a
mile of wire had been paid out. The instrument was then left quietly
until it presently assumed the same temperature as the rocks about it.
There could be no interference by heat from other strata, as the
circulation of water was prevented by the plugging already referred to.
The temperature to which the thermometer had been exposed must,
therefore, have been precisely the temperature corresponding in that
particular locality to that particular depth below the earth’s surface.

As the thermometer descended, it passed through a succession of strata
of ever-increasing temperature. Consequently the mercury, which, it will
be remembered, had completely filled the instrument when it was at the
surface, began to expand according as it was exposed to greater
temperatures. As the mercury expanded, it must, of course, flow out of
the tube and be lost, because the tube had been already full. So long as
the mercury was gaining in temperature, more and more of it escaped from
the top of the tube, and the flow only ceased when the instrument was
resting at the bottom of the hole, and the mercury became as hot as the
surrounding rocks. No more mercury was then expelled, the tube, however,
remaining full to the brim. After allowing a sufficient time for the
temperature to settle definitely, the thermometer was raised to the
surface. As it ascended through the long bore the temperature
surrounding it steadily declined. With the fall in the temperature of
the mercury the volume of that liquid began to shrink; but the mercury
already expelled could not be recalled. When at last the instrument had
safely reached the surface, after its long journey down and up, and when
the mercury had regained the temperature of the air, the lessened
quantity that remained told the tale of the changes of temperature.

It is now easy to see how, even in the absence of an engraved scale on
the instrument, it is possible to determine, from the amount of mercury
remaining, the temperature to which the thermometer has been subjected
at the bottom of the boring. It is only necessary to place this
thermometer in a basin of cold water, and then gradually increase the
temperature by adding hot water. As the temperature increases the
mercury will, of course, rise, and the hotter the water the more nearly
will the mercury approach the top of the tube. At last, when the mercury
has just reached the top of the tube, and when it is just on the point
of overflowing, we may feel certain that the temperature of the water in
the basin has been raised to the same temperature as that to which the
instrument was subjected at the bottom of the boring. In each case the
temperature is just sufficient to expand the quantity of mercury
remaining in the instrument so as to make it fill precisely both bulb
and stem. When this critical condition is reached, it only remains to
dip a standard thermometer, furnished with the ordinary graduation, into
the hot water of the basin. Thus we learn the temperature of the basin,
thus we learn the temperature of the mercury in the thermometer, and
thus we determine the temperature at the bottom of the boring over a
mile deep.

I need not specify the details of the arrangements which enabled the
skilful engineer also to determine the temperature at various points of
the hole intermediate between the top and the bottom. In fact, taking
every precaution to secure accuracy, he made measurements of the
temperature at a succession of points about a hundred feet distant
throughout the whole depth. In each case he was careful, as I have
already indicated, to plug the hole above and below the thermometer, so
as to prevent the circulation of water in the vicinity of the
instrument. The thermometer, therefore, recorded the temperature of the
surrounding rocks without any disturbing element. Fifty-eight
measurements at equal distances from the surface to the greatest depths
were thus obtained.

We have now to discuss the instructive results to which we have been
conducted by this remarkable series of measurements. First let us notice
that there is much less variation in the subterranean temperatures than
in the temperatures on the earth’s surface. On the surface of the earth
we are accustomed to large fluctuations of temperature. We have, of
course, the diurnal fluctuations in temperature from day to night; we
have also the great seasonal fluctuations between summer and winter. But
below a certain depth in the ground the temperature becomes much more
equable. Whether the temperature on the surface be high or whether it be
low, the temperature of any particular point far beneath the surface
does not change to any appreciable extent. In Arctic regions the surface
of the earth may undergo violent seasonal changes of temperature, while
at a few feet below the surface the temperature, from one end of the
year to the other, may remain sensibly unaltered.

In deep and extensive caverns the temperature is sometimes found to
remain practically unaffected by the changes in the seasons. The Mammoth
Cave of Kentucky is a notable instance. The uniformity of the
temperature, as well as the mildness and dryness of the air, in those
wonderful subterranean vaults is such that many years ago a project was
formed to utilise the cavern as an abode for consumptive patients, for
whose cure, according to the belief then prevailing, an equable
temperature was above all things to be desired. Houses were indeed
actually built on the sandy floors of the cavern, and I believe they
were for some time tenanted by consumptive patients willing to try this
desperate remedy. The temperature may have been uniform and the air may
have been dry, but the intolerable gloom of such a residence entirely
neutralised any beneficial effects that might otherwise have accrued.
The ruins of the houses still remain to testify to the failure of the
experiment.

The heat received from the sun does not penetrate far into the earth’s
crust, and consequently the diurnal and even the seasonal changes of the
temperature at the surface produce less and less effect with every
increase of the depth. All such variations of temperature are confined
to within 100 feet of the surface. At the depth of about 100 feet a
fixed temperature of 52° Fahrenheit is reached, and this is true all
over the earth. It matters not whether the surface be hot or cold,
whether the latitude is tropical and the season is midsummer, whether
the latitude lie in the Arctic regions and the season be the awful
winter of iron-bound frost and total absence of sun—in all cases we find
that about 100 feet below the surface the temperature is 52°. With
sufficient accuracy we may say that this depth expresses the limit of
the penetration of the earth’s crust by sunbeams. The remarkable law
according to which the temperature changes below the depth of 100 feet
is wholly irrespective of the solar radiation.

The study of the internal heat of the earth may be said to begin below
the level of 100 feet, and the results that were obtained in the great
boring are extremely accordant. The deeper the hole, the hotter the
rocks; and Captain Huyssen found that for each sixty-six feet in descent
the temperature increased one degree Fahrenheit. To illustrate the
actual observations, let us take two particular cases. We have said that
the hole was one mile and 117 yards deep. Let us first suppose the
thermometer to be lowered 117 yards and then raised, after a due
observance of the precautions required to obtain an accurate result. The
temperature of the rocks at the depth of 117 yards is thus ascertained.
In the next observation let the thermometer be lowered from the surface
to the bottom of the hole, that is to say, exactly one mile below the
position which it occupied in the former experiment. The observations
indicate a temperature 80° Fahrenheit higher in the latter case than in
the former. We have thus ascertained a most important fact. We have
shown that the temperature of the crust of the earth at the depth of one
mile increases about 80°. This is at the rate of one degree every
sixty-six feet. I should just add, as a caution, that if we choose to
say the temperature increases one degree per sixty-six feet of descent,
we ought to suppose that we start from a point which is not higher than
that level of 100 feet above which as already explained, the temperature
of the rocks is more or less affected by solar heat.

We have described these particular observations in some detail because
they have been conducted under conditions far more favourable to
accuracy than have ever been available in any previous investigations of
the same kind. But now we shall omit further reference to this
particular undertaking near Leipzig. It is not alone in that particular
locality, not alone in Germany, not alone in Europe, not alone on the
surface of any continent, that this statement may be made. The statement
is one universally true so far as our whole earth is concerned. Wherever
we bore a hole through the earth’s crust, whether that hole be made in
the desert of Sahara or through the icebound coasts of Greenland, we
should find the general rule to obtain, that there is an increase of
temperature of about 80° for a mile of descent. This is true in every
continent, it is true in every island; and, though we cannot here go
into the evidence fully, there is not the least doubt that it is true
also under the floor of ocean. If beneath the bed of the Atlantic a hole
a mile deep were pierced, the temperature of the rocks at the bottom of
that hole would, it is believed, exceed by about 80° the temperature of
the rocks at the surface where the hole had its origin. We learn that at
the depth of a mile the temperature of the earth must generally be 80°
hotter than it is at the level of constant temperature near the surface.

It may perhaps help us to realise the significance of this statement if
we think of the following illustration. Let us imagine that the waters
of the ocean were removed from the earth. The ocean may in places be
five or six miles deep, but that is quite an inconsiderable quantity
when compared with the diameter of the earth. The change in the size of
the earth by the removal of all the water would not be greater,
proportionally, than the change produced in a wet football by simply
wiping it dry. Let us suppose that an outer layer of the earth’s
surface, a mile in thickness, was then to be peeled off. If we remember
that the diameter of the earth is 8,000 miles, we shall see that this
outer layer, whose removal we have supposed, does not bear to the whole
extent of the earth a ratio even as great as that which the skin of a
peach does to the fruit inside. But this much is certain, that if the
earth were so peeled there would be a wonderful difference in its
nature. For though practically of the same size as it is at present, it
would be so hot that it would be impossible to live upon it.

Next comes the very interesting question as to the temperature that
would be found at the bottom of a hole deeper still than that we have
been considering. Our curiosity as to the depths of the earth extends
much below the point to which Captain Huyssen drove down his diamond
drill. The trouble and the cost of still deeper exploration of the same
kind seem, however, to be actually prohibitive. To bore a hole two miles
deep would certainly cost a great deal more than twice the sum which
sufficed to bore a hole one mile deep. At a great depth each further
foot could only be won with not less difficulty and expense than a
dozen, or many dozen feet, at the surface. Mining enterprise does not at
present seem to contemplate actual workings at depths much over a mile,
so there does not seem much chance of any very much deeper boring being
attempted. We do not say that a hole two miles deep would be actually
impossible; it may well be wished that some millionaire could be induced
to try the experiment. We should greatly like to be able to lower a
thermometer down to a depth of two miles through the earth’s crust.

Seeing there is but little chance of our wish for such future
experiments being gratified, it is consolatory to find that actual
observations of this kind are not indispensable to the argument on which
we are to enter. Our argument can indeed be conducted a stage further,
even with our present information. The indications already obtained in
the hole one mile deep go a long way towards proving what the
temperature of a hole still deeper would be. We have already remarked
that it was part of Captain Huyssen’s scheme to obtain careful readings
of his thermometer at intervals of 100 feet from the surface to the
bottom of the hole. A study of these readings shows that the increase of
80° in a mile takes place uniformly at the rate of one degree for each
sixty-six feet of depth. As the temperature increases uniformly from the
surface down to the lowest point which our thermometers have reached, it
would be unreasonable to suppose that the rate of increase would be
found to suffer some abrupt change if it were possible to go a little
deeper. As the temperature rises 80° in the first mile, and as the rate
of increase is shown by the observations to be quite as large at the
bottom of the hole as it is at the top, we certainly shall not make any
very great mistake if we venture to assume that in the second mile the
temperature would also increase to an extent which will not be far from
80°. This inference from the observations leads to the remarkable
conclusion that at a depth of two miles the temperature of the earth
must be, we will not say exactly, but at all events not very far from,
160° higher than at the level of constant temperature about 100 feet
down.

As in the former case, we need not confine ourselves to any particular
locality in drawing this conclusion. The arguments apply not only to the
rocks underneath Leipzig, but to the rocks over every part of the globe,
whether on continents or islands, or even if forming the base of an
ocean. No one denies that the law of increase in temperature with the
depth must submit to some variation in accordance with local
circumstances. In essential features it may, however, be conceded that
the law is the same over all the earth. If we take 52° to be the
temperature of the level 100 feet down, which limits the seasonal
variations, and if we add that at two miles further down the temperature
is somewhere about 160° more, we come to the conclusion that at a depth
of a little over two miles the temperature of the rocks forming the
earth’s crust is about 212° Fahrenheit. Thus we draw the important
inference that if, the oceans having been removed, we were then to
remove from the earth’s surface a rind two miles thick—a thickness
which, it is to be observed, is only the two-thousandth part of the
earth’s radius—we should transform the earth into a globe which, while
it still retained appreciably the same size, would have such a
temperature that even the coolest spot would be as hot as boiling water.
This is indeed a remarkable result.

And now that we have gone so far, it is impossible for us to resist
making a further attempt to determine what the temperature of the
earth’s crust must be if we could send a thermometer still lower. A hole
one mile deep we have seen; I do not think we can hope to see a hole two
miles deep, but still it may not be absolutely impracticable; but a hole
of three or more miles deep we may safely regard as transcending present
possibilities in engineering enterprise. Are we therefore to be deprived
of all information as to the condition of our earth at depths exceeding
those already considered? Fortunately we can learn something. We are
assisted by certain laws of heat, and, though the evidence on which we
believe those laws is necessarily limited to the experience of Nature as
it comes within our observation, yet it is impossible to refuse assent
to the belief that the same laws will regulate the transmission of heat
in the crust of the earth two miles, three miles, or many miles beneath
our feet.

I represent, in the diagram shown in Fig. 23, three consecutive beds of
rock—A, B, and C—as they lie in the earth’s crust, a little more than a
mile beneath our feet. I shall suppose that the bed B is the very lowest
rock whose temperature was determined in the great boring. The drill has
passed completely through A, it has pierced to the middle of B, but it
has not entered C. The observations have shown that the temperature of
the stratum B exceeds that of the stratum A, and we further note that
this is a permanent condition—that is to say, B constantly remains
hotter than A. From this fact alone we can learn something as regards
the temperature of the stratum C which lies in contact with B. Of course
we are unable to observe the temperature of C directly, because by
hypothesis the boring tool has not entered that rock. We can, however,
prove, from the laws of the conduction of heat, that the temperature of
C must be greater than that of B; and this appears from the following
consideration.

[Illustration: Fig. 23.—AT THE BOTTOM OF THE GREAT BORE.]

It is plain that C must be either just the same temperature as B, or it
must be hotter than B, or it must be colder than B. If C were the same
temperature as B, then the law of conduction of heat tells us that no
heat would flow from one of these strata to the other. The laws of heat,
however, assure us that when two bodies at different temperatures are in
contact the heat will flow from the hotter of these bodies into the
colder, so long as the inequality of temperature is maintained. As B is
hotter than A, then heat must necessarily flow from B into A, and this
flow must tend to equalise the temperature in these strata, for B is
losing heat while none is flowing into it from C. Therefore B and A
could not continue to preserve indefinitely the different temperatures
which observation shows them to do. We are therefore forced to the
conclusion that B and C cannot be at the same temperature.

Next let us suppose that the temperature of the stratum B exceeded that
of C. Then, as A is colder than B, it appears that B would be lying
between two strata each having a temperature lower than itself. But
that, of course, cannot be a permanent arrangement, for the heat would
then escape from B on both sides. The laws of heat, therefore, tell us
that B could not possibly retain permanently a temperature above both A
and C. Observation, however, shows that the temperatures of A and B are
persistently unequal. We are therefore obliged to reject the supposition
that the temperature of C can be less than that of B.

We have thus demonstrated that the temperature of the stratum C cannot
be the same as that of B. We have also demonstrated that it cannot be
colder than B. We must therefore believe that C is hotter than B. This
proves that the stratum immediately beneath that stratum to which the
observations have extended must be hotter than it. Thus, though the
stratum below the bottom of the hole lies beyond the reach of our actual
observation, we have, nevertheless, been able to learn something with
regard to its temperature.

Having established this much, we can continue the same argument further;
indeed, it would seem that we can continue it indefinitely, so long as
there is a succession of such strata. Underneath the stratum C must lie
another stratum D. But we have shown that C must be hotter than B, and
precisely the same argument that has proved this will prove that D is
hotter than C. Underneath D comes the stratum E, and again the same
argument will apply. Inasmuch as D is hotter than C, it follows that E
must be hotter than D. These three strata, C, D, and E, are all beyond
the reach of the thermometer, we know nothing of their temperatures by
direct observation; but none the less is the argument, which we are
following strictly, applicable. Thus we obtain the important result that
in the crust of the earth the temperature must be always greater, the
greater the depth beneath the surface.

We have seen that the rate of increase of temperature with the depth is
about 80° for the first mile, and we deem it probable that the rate of
increase may be maintained at about the same for the second mile. But we
do not suppose that the rate of increase mile after mile will remain the
same at extremely great depths. It may perhaps be presumed that there
must be some increase of temperature all the way to the earth’s centre;
but the rate of increase per mile may change as the centre is
approached. The point of importance for our present argument is, that
the temperature of the earth must increase with the depth, though the
rate of increase is quite unknown to us at depths greatly beyond those
which the thermometer has reached. It is easy to see that the conditions
prevailing in the earth’s interior might greatly modify any conclusion
we should draw from observations near the surface. Our argument has been
based on the laws of heat, as we find them existing in matter on the
surface of the earth submitted to such ranges of different physical
conditions as can be dealt with in our laboratories; but at such
excessively high temperatures as may exist in the earth’s interior the
properties of matter may be widely different from the properties of
matter as known to us within the temperatures that we are able to
produce and control. The enormous pressure to which matter in the
interior of the earth must be subjected should also be mentioned in this
connection. It is wholly impossible to produce pressures by any
mechanical artifice which even distantly approach in intensity to that
awful force to which matter is subjected in the earth’s interior.

It may be instructive to consider a few facts with respect to this
question of pressure in the earth’s interior. A column of water 34½ feet
high gives, as everybody knows, a pressure of fifteen pounds on the
square inch. It will be quite accurate enough for our present purpose to
assume that the average density of rock is three times that of water:
the pressure of ten feet of rock would therefore produce the same
pressure as thirty feet of water, that is to say, fifteen pounds on the
square inch. The pressure due to the superincumbent weight of a mile of
rock would be more than three tons on the square inch. At the depth of
ten miles beneath the earth’s surface the pressure, amounting as it does
to over thirty tons on the square inch, would very nearly equal the
pressure produced on the inside of a 100-ton gun when the charge of
cordite has been exploded to drive the missile forth. This is indeed
about as large a pressure as can well be dealt with artificially, for we
know that the 100-ton gun has to be enormously strong if it is to resist
this pressure. But ten miles of rock is as nothing compared with the
thickness of rock that produces the pressures in the earth’s interior.
Even if a shell of rocks ten miles thick were removed from the surface
it would alter the diameter of our globe by no more than one
four-hundredth part. At the depth of about thirty miles from the surface
the pressure in the earth’s interior would amount to some 100 tons on
each square inch. With each increase in depth the pressure increases
enormously, though it may not be correct to say that the pressure is
proportional to the depth. A pressure of 1,000 tons on the square inch
must exist at a depth which is still quite small in comparison with the
radius of the earth.

We have not, and apparently cannot have, the least experimental
knowledge of the properties of matter at the moment when it is subjected
to pressure amounting to thousands of tons per square inch; still less
can we determine the behaviour of matter at that pressure of scores of
thousands of tons, to which much of the interior of the earth is at this
moment subjected. Professor Dewar, in his memorable researches, has
revealed to us the remarkable changes exhibited in the properties of
matter when that matter has been cooled to a temperature which lies in
the vicinity of absolute zero. We can, however, hardly hope that any
experiments will give us information as to the properties of matter when
heated to a temperature vastly transcending that which could ever be
produced in our most powerful electric furnaces, and at the same time
exposed to a pressure hundreds of times, or indeed we may say thousands
of times, greater than any pressure that has ever been produced
artificially by the action of the most violent explosive with which the
discoveries of chemistry have made us acquainted.

[Illustration: Fig. 24.—THREE CONSECUTIVE SHELLS OF THE EARTH’S CRUST.]

We really do not know how far the laws of heat, which have been employed
in showing that the temperature must increase as the depth increases,
can be considered as valid under the extreme condition to which matter
is subjected in the deep interior of our globe. The laws may be
profoundly modified. It suffices, fortunately for our present argument,
to say that, so far as observations have been possible, the temperature
does gradually increase with the depth, and that this increase must
still continue from stratum to stratum as greater depths are reached,
unless it should be found that by the excessive exaltation of
temperature and the vast intensity of pressure certain properties of
matter become so transformed as to render the laws of heat, as we know
them, inapplicable.

In subsequent chapters we shall have some further points to consider
with respect to the interior of the earth and its physical
characteristics, which are, however, not necessary for our present
argument. What we now desire to prove can be deduced from the
demonstrated fact that the earth’s temperature does steadily increase
from the level of constant temperature, 100 feet below the surface, down
to the greatest depth to which thermometers have ever been lowered. We
may presume that the same law holds at very much greater depths, even if
it does not hold all the way to the centre.

To make our argument clear, let us think of three different strata of
rock. This time, however, we shall suppose them to cover the whole
earth, and we shall consider them to lie within the first mile from the
surface; they will thus be well within the region explored by
observation (Fig. 24). We shall also regard them as shells of uniform
thickness, and it will be convenient to think of them as being so very
thin that we may consider any one of the shells called A to have
practically a uniform temperature. The next shell B immediately inside A
will have a slightly greater temperature, and be also regarded as
uniform, and the shell immediately inside that again will have a
temperature greater still. We shall call the innermost of the three
shells C, and C is hotter than the next outer shell B, while B is hotter
than A. The laws of heat tell us that as B and A are in contact, and
that as B is continually hotter than A, then B must be continuously
transmitting heat to A. In fact, B appears to be constantly endeavouring
to reduce itself to the temperature of A by sharing with A the excess of
temperature which it possesses. But if we consider the relation between
the shell B and the hotter shell C, immediately beneath it, we see that
precisely the same argument will show that B is constantly receiving
heat from C. We thus see that while B is continuously discharging heat
from its outside surface, it is as constantly receiving heat which
enters through its inside surface. Heat enters B from C, and heat passes
from B into A, so that B is in fact a channel through which heat passes
from C into A.

That which we have shown to take place in those three consecutive layers
in the earth’s crust must also take place in every three consecutive
layers. Each layer is continually receiving heat from the layer below,
and is as constantly communicating heat to the layer above. No doubt the
rocks are very bad conductors of heat, so that the transmission of heat
from layer to layer is a very slow process. But even if this flow of
heat be slow, it is incessant, so that in the course of ages large
quantities of heat are gradually transmitted from the earth’s interior,
and ultimately reach the level of constant temperature. There is
nothing, however, to impede their outward progress, so at last the heat
reaches the earth’s surface.

When the surface has been reached, then another law of heat declares
what must happen next. It is, of course, by conduction that the heat
passes from layer to layer in its outward progress, until it ultimately
gains the surface. At the surface the heat is then absolutely removed
from the solid earth either by the convection through the air or by
direct radiation into space.

I may here interrupt the argument for a moment to make quite clear a
point which might perhaps otherwise offer some difficulty to the reader.
When this outward flow of heat reaches the superficial layers it
becomes, of course, mixed up with the heat which has been absorbed by
the soil from the direct radiation of the sun, and this varies, of
course, with the hour of the day and with the season of the year. The
heat which steadily leaks from the interior has an effect on the rocks
near the surface, which is only infinitesimal in comparison with the
heat which they receive from periodic causes. We may, however, say that
whatever would be the temperature of the rock, so far as the periodic
causes are concerned, the actual temperature is always to some minute
extent increased by reason of the heat from the earth’s interior. The
argument is, perhaps, still clearer if, instead of attending to the
earth’s surface, we think only of that shell, some 100 feet down, which
marks the limit of the depth to which the seasonal and diurnal
variations of heat extend. The argument shows how the internal heat of
the earth, passing from shell to shell in the interior, reaches this
layer of constant temperature, and passing through it, enters into those
superficial strata of the earth which are exposed to the seasonal
variations. With what befalls that heat ultimately we need not now
concern ourselves; it suffices for our argument to show that there is a
current of heat outward across this level. It is a current which is
never reversed, and consequently must produce a never-ceasing drainage
from the heat with which it would seem that the interior of the earth is
so copiously provided.

Calculations have been made to ascertain how much heat passes annually
from the earth’s interior, across this surface of constant temperature,
out into the superficial regions from which in due course it becomes
lost by radiation. A convenient way of measuring a quantity of heat is
by the amount of ice it will melt, for of course a definite quantity of
heat is required to melt a definite quantity of ice. It has been
estimated by Professor J. D. Everett, F.R.S., that the amount of
internal heat escaping from our earth each year would be sufficient to
melt a shell of ice one-fifth of an inch thick over the whole surface of
the globe. We cannot indeed pretend that any determination of the actual
loss of heat which our earth experiences could be very precise.
Sufficient observations have not yet been obtained, for the operation is
so slow that an immense period would have to elapse before the total
quantity of heat lost would be sufficient to produce effects large
enough to be measured accurately. But now let us hasten to add that, for
the argument as to the nebular theory with which we are at present
concerned, it is not really material to know the precise rate at which
heat is lost. It is absolutely certain that a perennial leakage of heat
from the interior of the earth does take place. This fact, and not the
amount of that leakage, is the essential point.

And this loss, which is at present going on, has been going on
continually. Heat from the earth has been lost this year and last year;
it has been lost for hundreds of years and for thousands of years. Not
alone during the periods of human history has the earth’s heat been
declining. Even throughout those periods, those overwhelming periods
which geology has revealed to us, has this earth of ours been slowly
parting with its heat.

Let us pursue this reflection to its legitimate consequence. Whatever
may ultimately become of that heat, it is certain that once radiated
into space it is lost for ever so far as this globe is concerned. You
must not imagine that the warm beams of the sun possess any power of
replenishment by which they can restore to the earth the heat which it
has been squandering for unlimited ages; we have already explained that
the effect of the heat radiated to us from the sun is purely
superficial. Even amid the glories of the tropics, even in the burning
heat of the desert, the vertical sun produces no appreciable effects at
depths greater than this critical limit, which is about 100 feet below
the surface. The rigours of an Arctic winter have as little effect in
reducing the temperature of the rocks at that depth as the torrid heat
at the Equator has in raising it. The effect in each case is nothing.

The argument which we are here employing to deduce the nebulous origin
of our earth from the increase of temperature with increase in depth in
the earth’s crust must be cleared from an objection. It is necessary to
explain the matter fully, because it touches on a doctrine of very great
interest and importance.

That a rotating body should possess a quantity of energy in virtue of
its rotation will be familiar to anyone who has ever turned a grindstone
or watched the fly-wheel of an engine. A certain amount of work has to
be expended to set the heavy wheel into rotation, and when the machine
is called upon to do work it will yield up energy and its motion will
undergo a corresponding abatement. The heavy fly-wheel of the machine in
a rolling mill contains, in virtue of its motion, enough energy to
overcome the tremendous resistance of the materials submitted to it.
Once upon a time the earth revolved upon its axis in six hours, instead
of in the twenty-four hours which it now requires. At that time the
energy of the rotation must have been sixteenfold what it is at present.
This consideration shows that fifteen-sixteenths of the energy that the
earth originally possessed in its rotation has disappeared, and we want
to know what has become of it.

We are here entering upon a matter of some difficulty. It is connected
with that remarkable chapter in astronomy which describes the evolution
of the earth-moon system. The moon was originally a part of the earth,
for in very early times, when the earth was still in a plastic state, a
separation would seem to have taken place, by which a small piece broke
off to form the moon, which has been gradually revolving in an enlarging
orbit until it has attained the position it now occupies. A considerable
portion of the energy of the earth’s rotation has been applied to the
purpose of driving the moon out to its present path, but there is a
large remainder which cannot be so accounted for. It is well known that
the evolution of the moon has been a remarkable consequence of tidal
action. There are tides which sway to and fro in the waters on the
earth’s surface; there are tides in any molten or viscous matter that
the earth may contain, and there are even certain small tidal
displacements in the solid material of our globe. Tides of any kind will
generate friction, and friction produces heat, and the energy of the
earth’s rotation, which we have not been able to account for otherwise,
has been thus transformed into heat. Throughout the whole interior of
the earth heat has been produced by the tidal displacement of its parts.
The question therefore arises as to whether the internal heat of the
earth may not receive an adequate explanation from this tidal action,
which is certainly sufficient as to quantity. It is easy to calculate
what the total quantity of this tidal heat may have been. We know the
energy which the earth had when it rotated in six hours, and we know
that it now retains no more than a sixteenth of that amount. We know
also precisely how much was absorbed in the removal of the moon, and the
balance can be evaluated in heat. It can be shown, and the fact is a
very striking one, that the quantity of heat thus arising would be
sufficient to account many times over for the internal heat of the
earth. It might therefore be urged plausibly that the internal heat
which we actually find has had its origin in this way. And if this were
the case the argument which we are using in favour of the nebular origin
of the earth, would be, of course, invalidated.

We may state the issue in a slightly different manner, as follows. Heat
there is undoubtedly in the earth; that heat might have come from the
primæval nebula as we have supposed, and as in actual fact it did come.
But apparently it might have come from the tidal friction. Why then are
we entitled to reject the latter view, and say that the tidal friction
will not explain the internal heat, and why are we compelled to fall
back on the only other explanation?

Lord Kelvin suggested a test for deciding to which of these two sources
the earth’s internal heat was to be attributed. Professor G. H. Darwin
applied the test and decided the issue. We have dwelt upon the rate at
which the heat increases with the descent, this rate being about one
degree every sixty-six feet. Now the distribution of the heat, if it had
come from the tidal action, would be quite different from the
distribution which would result from the gradual efflux of heat from the
centre in the process of cooling. And, speaking quite generally, we may
surmise that the heat produced by tidal friction would be distributed
rather more towards the exterior of the earth than at its centre. We
might therefore reasonably expect that if the internal heat of the earth
arose from tidal friction it would be more uniformly distributed
throughout the globe, and there would not be so great a contrast between
the high temperature of the interior and the lesser temperatures near
the surface as there is when the heat distribution is merely the result
of cooling. It has been proved that if the internal heat had its origin
from the tidal friction, the rate of increase with the depth would be
totally different from what it is actually found to be. It would be
necessary to go down 2,000 feet to obtain an increase of one degree,
instead of only sixty-six feet, as is actually the case.

Hence we conclude that the increasing heat met with in descending
through the earth’s crust is not accounted for by tidal friction; it has
its origin in the other alternative, namely, from the cooling of the
primæval nebula. The heat which was undoubtedly produced by the tidal
friction has gradually become blended with the heat from the other, and,
as we must now say, the principal source. The facts with regard to the
rate of increase with depth thus show that, whatever the tides may have
done in producing internal heat, there has been another and a still more
potent cause in operation. The important conclusion for our present
purpose is that our argument may justly proceed without taking account
of the effect of tidal friction.

We are led by these considerations to a knowledge of a great
transformation in the nature of our globe which must have occurred in
the course of ages. We have seen that this earth is gradually losing
heat from its interior, and we have seen that this loss of heat is
incessant. From the fountains of heat, still so copious, in the interior
the supply is gradually dissipating. Now heat is only a form of energy,
and energy, like matter, cannot itself be created out of nothing. There
can be no creation of heat in our earth without a corresponding
expenditure of energy. If, therefore, the earth is radiating heat, then,
as there is no known or, indeed, conceivable source of energy by which
an equivalent can be restored, it follows that the earth must have less
internal heat now than it had at any earlier period. No doubt the
process of cooling is excessively slow. The earth has less internal heat
at present than it had a hundred years ago, but I do not suppose that
even in a thousand years, or perhaps in ten thousand years, there would
be any appreciable decline in the quantity of heat, so far as any
obvious manifestations of that heat are concerned. It is, however,
certain that the earth must have been hotter, even though there are not
any observations to which we can appeal to verify the statement; and as
our retrospect extends further and still further through the ages we see
that the globe must have been ever hotter and ever still hotter.
Whatever be the heat contained in our earth now, it must have contained
vastly more heat ten million years ago; how otherwise could the daily
leakage of heat for all those ten million years have been supplied? It
follows that there must have been much more heat somewhere in our earth
ten million years ago than there is at present, and the further our
retrospect extends the hotter do we find the earth to have been. There
was a time when the temperature of the earth’s surface must have been
warmed not alone by such sunbeams as fell upon it, but by the passage of
the heat from the interior.

No matter how early be the period which we consider, we find the same
causes to be in operation. There was a time when, owing to the internal
heat, the surface of the earth must have been as hot as boiling water.
The loss of heat by radiation must then have taken place much more
copiously than it does at present. The argument we are pursuing must
therefore have applied with even greater force in those early days.
There was a time when the materials at the surface of the earth must
have been intensely heated, when they must have even been red-hot. There
was a time when the earth’s surface must have had a temperature like
that of the lava as it issues from a volcano. There must have been a
time when the surface of the earth was not even solid, when indeed it
was a viscid liquid, and earlier still the liquid must have been more
and more incandescent. From that brilliant surface heat was vehemently
radiated. Each day the globe was hotter than on the succeeding day.
There is no break in the argument. We have to think of this glowing
globe passing through those phases through which we know that all matter
will pass if only we apply to it sufficient heat. The globe assumed the
liquid state from that state which is demanded by a temperature still
higher, the state in which the matter is actually in the form of vapour.
Even the most refractory substances will take the form of vapour at a
very high temperature.

Thus we are conducted to a remarkable conception of the condition in
which the materials now forming our solid earth must have been in the
exceedingly remote past. What is now our earth must once have been a
great quantity of heated vapour. It need hardly be said that in that
form the volume of the earth was much larger than the volume which the
earth has at present, while no doubt the mass of the earth then was even
less than the mass of the earth now, by reason of the meteoric matter
which has been drawn in by our globe.

But even when our earth was in this inflated state of vapour our
argument can be still maintained. Thus we see that the earth, or rather
the cloud of vapour which was ultimately to form the earth, is ever
growing larger and larger in our retrospect, ever becoming more and more
rarefied; and it may well have been that there was a time when the
materials of this earth occupied a volume thousands of times greater
than they do at present.

In a previous chapter we have seen how the sun was at one time in the
nebulous state, and now we have been led to a similar conclusion with
regard to the earth. At that time, of course, the sun was greatly in
excess of its present dimensions, and the earth was also greatly
swollen. The nebula which formed our sun, and the nebula which formed
our earth, were both so vast as to be confluent; they were indeed both
part of the same vast nebula.

Such has been the Earth’s Beginning so far as modern science can make it
clear to us. We have at least indicated the course which events must
have taken according to the laws of nature as we understand them. Many
of the details of the great evolution are no doubt unknown at present,
and perhaps must ever remain so. That the events which we have
endeavoured to describe do substantially represent the actual evolution
of our system is the famous Nebular Theory.

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CHAPTER IX.

EARTHQUAKES AND VOLCANOES.

Interior of the Earth—Illustration from Norway—Solids and
Liquids—Rigidity of the Interior of the Earth—Earthquakes,
how caused—Their Testimony as to the Rigidity of the
Earth—Delicate Instrument for Measuring Earthquake Tremors—The
Seismometer—Professor Milne’s Work in the Isle of Wight—Different
Earthquake Groups—Precursors and Echoes—Vibrations transmitted
through the Earth’s Centre—Earthquakes in England—Other Evidence of
the Earth’s Rigidity—Krakatoa, August 27th, 1883—The Sounds from
Krakatoa—The Diverging Waves—The Krakatoa Dust—The Hurricane
Overhead—Strange Signs in the Heavens—The Blood-red Skies.

IN this chapter we shall learn what we can as to the physical condition
of the interior of our earth so far as it may be reasonably inferred
from the facts of observation. We have already explained in the last
chapter that a very high temperature must be found at the depth of even
a small fraction of the earth’s radius, and we have pointed out that the
excessively high pressure characteristic of the earth’s interior must be
borne in mind in any consideration as to the condition of the matter
there found.

Let us take, for instance, that primary question in terrestrial physics,
as to whether the interior of the earth is liquid or solid. If we were
to judge merely from the temperatures reasonably believed to exist at a
depth of some twenty miles, and if we might overlook the question of
pressure, we should certainly say that the earth’s interior must be in a
fluid state. It seems at least certain that the temperatures to be found
at depths of two score miles, and still more at greater depths, must be
so high that the most refractory solids, whether metals or minerals,
would at once yield if we could subject them to such temperatures in our
laboratories. At such temperatures every metal would become fluid, even
if it were not transformed into a cloud of vapour. But none of our
laboratory experiments can tell us whether, under the pressure of
thousands of tons on the square inch, the application of any heat
whatever would be adequate to transform solids into liquids. It may
indeed be reasonably doubted whether the terms solids and liquids are
applicable, in the sense in which we understand them, to the materials
forming the interior of the earth.

It was my good fortune some years ago to enjoy a most interesting trip
to Norway, in company with a distinguished geologist. Under his guidance
I there saw evidence which demonstrates conclusively that, when
subjected to great pressure, solids, as we should call them, behave in a
manner which, if not that of actual liquids, resembles at all events in
some of its characteristics the behaviour of liquids. These rocks in
some places are conglomerates, of which the leading constituents are
water-worn pebbles of granite. These pebbles are of various sizes, from
marbles to paving-stones. In some parts of the country these granite
pebbles remain in the form which they acquired on the beach on which
they were rolled by the primæval ocean; in other parts of the same
interesting region the form of the pebbles has been greatly changed from
what it was originally. For in the course of geological periods, and
after the pebbles had become consolidated into the conglomerate, the
rock so formed had been in some cases submitted to enormous pressure.
This may have been lateral pressure, such as is found to have occurred
in many other places, where it has produced the well-known geological
phenomenon of strata crumpled into folds. In the present case, however,
it seemed more probable that it was the actual weight of the
superincumbent rocks, which once lay over these beds of conglomerate,
which produced the surprising transformation. It seems to be not at all
improbable that at one time these beds of conglomerate must have been
covered with strata of which the thickness is so great that it may
actually be estimated by miles. There has, however, been immense
denudation of the superficial rocks in this part, at all events, of
Norway, so that in the course of ages these strata, overlying the
conglomerate for ages, have been so far worn away, and indeed removed,
by the action of ice and the action of water that the conglomerate is
now exposed to view. It offers for our examination striking indications
of the enormous pressure to which it was subjected during the
incalculable ages of geological time.

The effect of this long continuance of great pressure upon the pebbles
of the conglomerate in certain parts of the country has been most
astonishing. The granite in the pebbles still retains its characteristic
crystalline structure; it has obviously not undergone anything that
could be described as fusion; yet under the influence of the two factors
of that pressure, namely, its intensity and its long continuance, the
granite pebbles have yielded. In some cases they are slightly elongated,
in others they are much elongated, while in yet others they are even
rolled out flat. At different places along the valley the various phases
of the transformation can be studied. We can find places where the
pebbles seem little altered, and then we can trace each stage until the
solid granite pebbles have, by the application of excessive pressure,
been compressed into thin sheets whose character it would not have been
easy to divine if it had not been possible to trace out their history.
These sheets lie close and parallel, so that the material thus produced
acquires some of the characteristics of slate. It splits easily along
the flattened sheets, and this rolled-out conglomerate is indeed
actually used as a substitute for slate, and in some places there are
houses roofed with the conglomerate which has been treated in this
extraordinary fashion.

This fact will illustrate a principle, already well known in the arts,
that many, if not all, solids may be made to flow like liquids if only
adequate pressure be applied. The making of lead tubes is a well-known
practical illustration of the same principle, for these tubes are simply
formed by forcing solid lead by the hydraulic press through a mould
which imparts the desired form.

If then a solid can be made to behave like a liquid, even with such
pressures as are within our control, how are we to suppose that the
solids would behave with such pressures as those to which they are
subjected in the interior of the earth? The fact is that the terms solid
and liquid, at least as we understand them, appear to have no physical
meaning with regard to bodies subjected to these stupendous pressures,
and this must be carefully borne in mind when we are discussing the
nature of the interior of the earth.

It must, however, be admitted that the interior of the earth in its
actual physical state seems to possess at least one of the most
important characteristics of a solid, for it seems to be intensely
rigid. We mean by this, that the material of the earth, or rather each
particle of that material, is very little inclined to move from its
position with reference to the adjacent particles by the application of
force. Possibly a liquid, such as water, might not behave very
differently in this respect from a solid such as cast iron, if each of
them were exposed to a pressure of scores of thousands of tons per
square inch, as are the materials which form the great bulk of the
earth. But, without speculating on these points, we are able to
demonstrate that the earth, as a whole, does exhibit extreme rigidity.
This is one of the most remarkable discoveries which has ever been made
with regard to the physics of our earth. The discovery that the earth is
so rigid is mainly due to Lord Kelvin.

We shall now mention the line of evidence which appears to prove, in the
simplest and most direct manner, the excessive rigidity of our earth. It
is derived from the study of earthquake phenomena, and we must endeavour
to set it forth with the completeness its importance deserves.

As to the immediate cause of earthquakes, there is no doubt considerable
difference of opinion. But I think it will not be doubted that an
earthquake is one of the consequences, though perhaps a remote one, of
the gradual loss of internal heat from the earth. As this terrestrial
heat is gradually declining, it follows from the law that we have
already so often had occasion to use that the bulk of the earth must be
shrinking. No doubt the diminution in the earth’s diameter, due to the
loss of heat must be excessively small, even in a long period of time.
The cause, however, is continually in operation, and accordingly the
crust of the earth has, from time to time, to be accommodated to the
fact that the whole globe is lessening. The circumference of our earth
at the Equator must be gradually declining; a certain length in that
circumference is lost each year. We may admit that loss to be a quantity
far too small to be measured by any observations as yet obtainable, but,
nevertheless, it is productive of phenomena so important that it cannot
be overlooked.

It follows from these considerations that the rocks which form the
earth’s crust over the surface of the continents and the islands, or
beneath the beds of ocean, must have a lessening acreage year by year.
These rocks must therefore submit to compression, either continuously or
from time to time, and the necessary yielding of the rocks will in
general take place in those regions where the materials of the earth’s
crust happen to have comparatively small powers of resistance. The acts
of compression will often, and perhaps generally, not proceed with
uniformity, but rather with small successive shifts, and even though the
displacements of the rocks in these shifts be actually very small, yet
the pressures to which the rocks are subjected are so vast that a very
small shift may correspond to a very great terrestrial disturbance.

Suppose, for instance, that there is a slight shift in the rocks on each
side of a crack, or fault, at a depth of ten miles. It must be
remembered that the pressure ten miles down would be about thirty-five
tons on the square inch. Even a slight displacement of one extensive
surface over another, the sides being pressed together with a force of
thirty-five tons on the square inch, would be an operation necessarily
accompanied by violence greatly exceeding that which we might expect
from so small a displacement if the forces concerned had been only of
more ordinary magnitude. On account of this great multiplication of the
intensity of the phenomenon, merely a small rearrangement of the rocks
in the crust of the earth, in pursuance of the necessary work of
accommodating its volume to the perpetual shrinkage, might produce an
excessively violent shock extending far and wide. The effect of such a
shock would be propagated in the form of waves through the globe, just
as a violent blow given at one end of a bar of iron by a hammer is
propagated through the bar in the form of waves. When the effect of this
internal adjustment reaches the earth’s surface, it will sometimes be
great enough to be perceptible in the shaking it gives that surface. The
shaking may be so violent that buildings may not be able to withstand
it. Such is the phenomenon of an earthquake.

Earthquakes have been made to yield testimony of the most striking
character with regard to the rigidity of the earth. The researches we
are now to describe are mainly due to Professor Milne, who, having
enjoyed the advantage of studying earthquakes in their natural home in
Japan, where are to be found some of the most earthquake-shaken regions
of this earth, has now transferred his observations of these phenomena
to the more peaceful regions of the Isle of Wight. But though the Isle
of Wight is perhaps one of the last places in the world to which anyone
who desired to experience violent earthquake shocks would be likely to
go, yet by the help of a beautiful apparatus Professor Milne is actually
able to witness important earthquakes that are happening all over the
world. He has a demonstration of these earthquakes in the indications of
an extremely sensitive instrument which he has erected in his home at
Shide.

When our earth is shaken by one of those occasional adjustments of the
crust which I have described, the wave that spreads like a pulsation
from the centre of agitation extends all over our globe and, indeed I
may say, is transmitted right through it. At the surface lying
immediately over the centre of disturbance there will be a violent
shock. In the surrounding country, and often over great distances, the
earthquake may also be powerful enough to produce destructive effects.
The convulsion may also be manifested over a far larger area of country
in a way which makes the shock to be felt, though the damage wrought may
not be appreciable. But beyond a limited distance from the centre of the
agitation the earthquake will produce no destructive effects upon
buildings, and will not even cause vibrations that would be appreciable
to ordinary observation.

This earth of ours may transmit from an earthquake pulses of a very
distinct and definite character, which are too weak to be perceived by
our unaided senses; but, just as the microscope will render objects
visible which are too minute to be perceived without this aid to the
ordinary vision, so these faint earth-pulses may be rendered perceptible
by the delicate indications of an instrument which perceives and records
tremors that would pass unnoticed by our ordinary observations. The
ingenious instrument for studying earthquakes is called a seismometer.
It marks on a revolving drum of paper the particulars of those
infinitesimal tremors by which the earth is almost daily agitated in one
place or another.

Let us suppose, for example, that an earthquake occurs in Japan, in
which much agitated country it is, I believe, estimated that no fewer
than one thousand earthquakes of varying degrees of intensity occur
annually in one district or another. Let us suppose that this earthquake
behaves as serious earthquakes usually do; that it knocks down buildings
and monuments, causes landslips, raises great waves in the sea and hurls
them as inundations on the land. We may also suppose that it issues
tragically in the loss of many lives and that there is a destruction of
much property, and that its energies in the acutely violent form extend
over, let us say, an area of a hundred square miles. Beyond that area of
greatest destruction such an earthquake would be felt over a great
extent of country as a shaking more or less vehement, and characteristic
rumbling sounds would be heard. But the intensity declines with the
distance, and we may feel confident that not even the faintest
indications of the earthquake would be perceptible by the unaided senses
at a thousand miles from its origin. A thousand miles is, however, less
than a fifth of the distance between Tokio and Shide, in the Isle of
Wight, measured in a great circle round the earth’s surface. The acutest
sense could not perceive the slightest indication of the convulsion in
Japan at even half the distance between these two places. But the earth
transmits so faithfully the undulations committed to its care that
though the intensity may have declined so as to be no longer perceptible
to the unaided sense, it is still possible that they may be shown
distinctly on the seismometer in Professor Milne’s laboratory, even
after a journey of five thousand miles. This instrument not only
announces that an earthquake has been in progress some little time
previously, but the recording pencil reproduces with marvellous fidelity
some actual details of the vibration. The movements of the line up and
down on the revolving drum of paper show how the convulsions succeed
each other, and their varying intensity. Thus Professor Milne is enabled
to set down some features of the earthquake long before the post brings
an account of the convulsion from the unhappy locality.

Professor Milne’s account of work in studying earthquakes has the charm
of a romance, even while it faithfully sets out the facts of Nature. I
have supposed the earthquake to take place in Japan; but we must observe
that the seismometer at Shide will also take account of considerable
earthquakes in whatever part of the world the disturbance may arise.
There are, for example, localities in the West Indies in which
earthquakes are by no means infrequent, though they may not be phenomena
of almost daily occurrence, as they are in Japan. Every considerable
earthquake, no matter where its centre may lie, produces in our whole
globe a vibration or a tingle which is sufficient to be manifested by
the delicate indications of the seismometer at Shide. Thus this
instrument, which in the morning may record an earthquake from Japan,
will in the afternoon of the same day delineate with equal fidelity an
earthquake from the opposite hemisphere in the neighbourhood of the
Caribbean Sea.

In each locality in which earthquakes are chronic it would seem as if
there must be some particularly weak spot in the earth some miles below
the surface. A shrinkage of the earth, in the course of the incessant
adjustment between the interior and the exterior, will take place by
occasional little jumps at this particular centre. The fact that there
is this weak spot at which small adjustments are possible may provide,
as it were, a safety-valve for other places in the same part of the
world. Instead of a general shrinking, the materials would be
sufficiently elastic and flexible to allow the shrinking for a very
large area to be done at this particular locality. In this way we may
explain the fact that immense tracts on the earth are practically free
from earthquakes of a serious character, while in the less fortunate
regions the earthquakes are more or less perennial.

The characteristics of an earthquake record, a _seismogram_, if we give
it the correct designation, depend on the distance of the origin from
the locality where the record is made. The length of the journey, as
might be expected, tells on the character of the inscription which the
earthquake waves make on the drum. If, for instance, the first
intimation of a large earthquake received at Shide precedes the second
by about thirty-five minutes, it may be concluded that the earthquake
has come from Japan.

In like manner the shocks, with their origin in the West Indies, will
proceed from their particular earthquake centre, and consequently all
the earthquakes from this source will possess a characteristic
resemblance. The Japan group of earthquakes will have, so to speak, a
family resemblance; and the Trinidad group of earthquakes, though quite
different from the Japan group, will also possess a family resemblance.
These features are faithfully transmitted by undulations through the
earth and round the earth; thus in due course they reach the Isle of
Wight, and they are reproduced by the pencil of the seismometer. The
different earthquakes of a family may differ in size, in intensity, and
undulation, but they will have the features appropriate to the
particular group from which they come. From long experience Professor
Milne has become so familiar with the lineaments of these earthquake
families, that in his study at Shide, as he looks at the indications of
his instrument, he is able to say, for example, “Here is an earthquake,
and it is a little earthquake from Japan;” then a little later, when a
new earthquake begins, he will say, “And here is a big earthquake from
Trinidad.”

Professor Milne’s apparatus has brought us remarkable information with
regard to the interior of the earth. The story which we have to tell is
really one of the most astonishing in physical science. Let us suppose
that an earthquake originates in Japan. We shall assume that the
earthquake is a vigorous one, capable of producing bold and definite
indications on the seismometer even in the Isle of Wight. It is to be
noted that this instrument is not content merely with a single version
of the story of that earthquake; it will indeed repeat that story twice
more. First of all, about a quarter of an hour after a shock has taken
place in Japan, the pencil of the seismometer commences to record. But
this record, though quite distinct, is not so boldly indicated as the
subsequent records of the same event which will presently be received.
It is to be regarded as a precursor. After the first record is completed
there is a pause of perhaps three-quarters of an hour, and then the
pencil of the seismometer commences again. It commences to give an
earthquake record, but it is obviously only a second version of the same
earthquake. For the ups and downs traced by the pencil are just the same
relatively as before. The picture given of the earthquake is, however,
on a much larger scale than the one that is first sent. The extent of
the shaking of the instrument in this second record is greater than in
the first, and all the details are more boldly drawn.

After the second diagram has been received, there is yet another pause,
which may be perhaps for half an hour. Then, by the same pencil, a third
and last version is conveyed to the seismometer. This diagram is not
quite so strong as the last, though stronger than the first; in it
again, however, the faithful pencil tells, with many a detail, what
happened in this earthquake at Japan.

We have first to explain how it occurs that there are three versions of
the event, for it need hardly be said that the same earthquake did not
take place three different times over. The point is indeed a beautiful
one. The explanation is so astonishing that we should hardly credit it
were it not established upon evidence that does not admit of a moment’s
question.

[Illustration: Fig. 25.—EARTHQUAKE ROUTES FROM JAPAN TO THE ISLE OF
WIGHT.]

In the adjoining diagram we represent the position of Japan at one side
of the earth, and the Isle of Wight at the other. When the earthquake
takes place at Japan it originates, as we have said, a series of
vibrations through our globe. We must here distinguish between the
rocks—I might almost say the comparatively pliant rocks—which form the
earth’s crust, and those which form the intensely rigid core of the
interior of our globe. The vibrations which carry the tidings of the
earthquake spread through the rocks on the surface, from the centre of
the disturbance, in gradually enlarging circles. We may liken the spread
of these vibrations to the ripples in a pool of water which diverge from
the spot where a raindrop has fallen, or to the remarkable air-waves
from Krakatoa, to which we shall presently refer. The vibrations
transmitted by the rocks on the surface, or on the floor of the ocean,
will carry the message all over the earth. As these rocks are flexible,
at all events by comparison with the earth’s interior, the vibrations
will be correspondingly large, and will travel with vigour over land and
under sea. In due time they reach the Isle of Wight, where they set the
pencil of the seismometer at work. But there are different ways round
the earth from Japan to the Isle of Wight. There is the most direct
route across Asia and Europe; there is also the route across the
Pacific, America, and the Atlantic. The vibrations will travel by both
routes, and the former is the shorter of the two. The vibrations which
take the first route through the crust of the earth’s surface are
travelling by the shorter distance; they consequently reach Shide first,
and render their version of what has happened. But the vibrations which,
starting from the centre of the disturbance, move through the earth’s
crust in an opposite direction will also in their due course of
expansion reach the Isle of Wight. They will have had a longer journey,
and will consequently be somewhat enfeebled, though they will still
retain the characteristics marking the particular earthquake centre from
which they arose.

We thus account for both the second and the third of the different
versions of the earthquake which are received at Shide. And now for the
first of the three versions. This is the one which is of special
interest to us at present. The original subterranean impulse was, as we
have seen, propagated through the rocks forming the earth’s crust. Part
of it, however, entered into the core forming the earth’s interior. The
earthquake had the power not only of shaking the earth’s crust all over,
but it produced the astonishing effect of setting the whole interior of
our globe into a tremble. There was not a single particle of our earth,
from centre to surface, which was not made to vibrate, in some degree,
in consequence of the earthquake. Certain of these vibrations, spreading
from the centre of disturbance, took a direct course to the Isle of
Wight, right through the globe. They consequently had a shorter journey
in travelling from Tokio to Shide than those which went round the
earth’s crust. The former travelled near the chord, while the latter
travelled on the arc. Even for this reason alone the internal vibrations
might be expected to accomplish their journey more rapidly than the
superficial movements. With the same velocity they would take a shorter
time for the journey. There is, however, another reason for the lesser
time taken by the internal vibrations. Not only is the journey shorter,
but the speed with which these vibrations travel through the solid earth
is much greater than the speed with which superficial vibrations travel
through the crust. It has been shown that the average velocity of these
vibrations when travelling through the centre of the earth is rather
more than ten miles a second. The velocity varies with the square root
of the depth, and near the surface it is scarcely two miles a second.

There are two points to be specially noticed. The vibrations, which,
passing through the earth’s interior with a high velocity, arrive as
precursors, make a faithful diagram, but only on a very small scale. We
say that these vibrations have but small amplitude. This shows that the
particles in the earth’s interior are not much displaced by the
earthquake, as compared with those on the earth’s crust, and this is one
indication of the effective rigidity of the earth. It is also to be
noted that the great speed with which the vibrations traverse the solid
earth is a consequence of the extreme rigidity of our globe. These
vibrations travel more rapidly through the earth than they would do
through a bar of solid steel. In other words, we have here a proof that,
under the influence of the tremendous pressures characteristic of the
earth’s interior, the material of which that earth is composed,
notwithstanding the high temperature to which it is raised, possesses a
rigidity which is practically greater than that of steel itself.

[Illustration: SHOWING LOCALITIES OF EARTHQUAKES]

This is perhaps the most striking testimony that can be borne to the
rigidity of our globe; but we must not imagine that we are dependent
solely upon the phenomena of earthquakes for the demonstration of this
important point; there are other proofs. It can be shown that the ebb
and flow of the tides on our coasts would be very different from that
which they actually are were it not that the earth behaves as a rigid
globe. It has also been demonstrated that certain astronomical phenomena
connected with the way in which the earth turns round on its axis would
not be the same as we actually find them to be if the earth were not
solid in its interior.

The result of these investigations is to show that, though this globe of
ours must be excessively hot inside, so hot indeed that at ordinary
pressures even the most refractory solids would be liquefied or
vaporised, yet under the influence of the pressure to which its
materials are subjected the behaviour of that globe is as that of the
most rigidly solid body.

Happily in this country we do not often experience earthquakes other
than delicate movements shown by the record of the seismometer. But
though most of us live our lives without ever having felt an earthquake
shock, yet earthquakes do sometimes make themselves felt in Great
Britain. The map we here give, which was drawn by Professor J. P.
O’Reilly, indicates the localities in England in which from time to time
earthquake shocks have been experienced.

The internal heat of the earth, derived from the primæval nebula, is in
no way more strikingly illustrated than by the phenomena of volcanoes.
We have shown in this chapter that there is no longer any reason to
believe that the earth is fluid in its interior. The evidence has proved
that, under the extraordinary pressure which prevails in the earth, the
materials in the central portions of our globe behave with the
characteristics of solids rather than of liquids. But though this
applies to the deep-seated regions of our globe, it need not universally
apply at the surface or within a moderate depth from the surface. When
the circumstances are such that the pressure is relaxed, then the heat
is permitted to exercise its property of transforming the solids into
liquids. Masses of matter near the earth’s crust are thus, in certain
circumstances, and in certain localities, transformed into the fluid or
viscid form. In that state they may issue from a volcano and flow in
sluggish currents as lava.

There has been much difference of opinion as to the immediate cause of
volcanic action, but there can be little doubt that the energy which is
manifested in a volcanic eruption has been originally derived in some
way from the contraction of the primæval nebula. The extraordinary
vehemence that a volcanic eruption sometimes attains may be specially
illustrated by the case of the great eruption of Krakatoa. It is,
indeed, believed that in the annals of our earth there has been no
record of a volcanic eruption so vast as that which bears the name of
this little island in far Eastern seas, ten thousand miles from our
shores.

Until the year 1883 few had ever heard of Krakatoa. It was unknown to
fame, as are hundreds of other gems of glorious vegetation set in
tropical waters. It was not inhabited, but the natives from the
surrounding shores of Sumatra and Java used occasionally to draw their
canoes up on its beach, while they roamed through the jungle in search
of the wild fruits that there abounded. Geographers in early days hardly
condescended to notice Krakatoa; the name of the island on their maps
would have been far longer than the island itself. It was known to the
mariner who navigated the Straits of Sunda, for it was marked on his
charts as one of the perils of the intricate navigation in those waters.
It was no doubt recorded that the locality had been once, or more than
once, the seat of an active volcano. In fact, the island seemed to owe
its existence to some frightful eruption of bygone days; but for a
couple of centuries there had been no fresh outbreak. It almost seemed
as if Krakatoa might be regarded as a volcano that had become extinct.
In this respect it would only be like many other similar objects all
over the globe, or the countless extinct volcanoes all over the moon.

In 1883 Krakatoa suddenly sprang into notoriety. Insignificant though it
had hitherto seemed, the little island was soon to compel by its tones
of thunder the whole world to pay it instant attention. It was to become
the scene of a volcanic outbreak so appalling that it is destined to be
remembered throughout the ages. In the spring of that year there were
symptoms that the volcanic powers in Krakatoa were once more about to
awake from the slumber that had endured for many generations. Notable
warnings were given. Earthquakes were felt, and deep rumblings proceeded
from the earth, showing that some disturbance was in preparation, and
that the old volcano was again to burst forth after its long period of
rest. At first the eruption did not threaten to be of any serious type;
in fact, the good people of Batavia, so far from being terrified at what
was in progress in Krakatoa, thought the display was such an attraction
that they chartered a steamer and went forth for a pleasant picnic to
the island. Many of us, I am sure, would have been delighted to have
been able to join the party who were to witness so interesting a
spectacle. With cautious steps the more venturesome of the excursion
party clambered up the sides of the volcano, guided by the sounds which
were issuing from its summit. There they beheld a vast column of steam
pouring forth with terrific noise from a profound opening about thirty
yards in width.

As the summer of this dread year advanced the vigour of Krakatoa
steadily increased, the noises became more and more vehement; these were
presently audible on shores ten miles distant, and then twenty miles
distant; and still those noises waxed louder and louder, until the great
thunders of the volcano, now so rapidly developing, astonished the
inhabitants that dwelt over an area at least as large as Great Britain.
And there were other symptoms of the approaching catastrophe. With each
successive convulsion a quantity of fine dust was projected aloft into
the clouds. The wind could not carry this dust away as rapidly as it was
hurled upwards by Krakatoa, and accordingly the atmosphere became
heavily charged with suspended particles. A pall of darkness thus hung
over the adjoining seas and islands. Such was the thickness and the
density of these atmospheric volumes of Krakatoa dust that, for a
hundred miles around, the darkness of midnight prevailed at midday. Then
the awful tragedy of Krakatoa took place. Many thousands of the
unfortunate inhabitants of the adjacent shores of Sumatra and Java were
destined never to behold the sun again. They were presently swept away
to destruction in an invasion of the shore by the tremendous waves with
which the seas surrounding Krakatoa were agitated.

Gradually the development of the volcanic energy proceeded, and
gradually the terror of the inhabitants of the surrounding coasts rose
to a climax. July had ended before the manifestations of Krakatoa had
attained their full violence. As the days of August passed by the spasms
of Krakatoa waxed more and more vehement. By the middle of that month
the panic was widespread, for the supreme catastrophe was at hand.

[Illustration: Fig. 26.—SHOWING COASTS INVADED BY THE GREAT SEA-WAVES
FROM KRAKATOA.
(_From the Royal Society’s Reports._)]

On the night of Sunday, August 26th, 1883, the blackness of the
dust-clouds, now much thicker than ever in the Straits of Sunda and
adjacent parts of Sumatra and Java, was only occasionally illumined by
lurid flashes from the volcano. The Krakatoan thunders were on the point
of attaining their complete development. At the town of Batavia, a
hundred miles distant, there was no quiet that night. The houses
trembled with the subterranean violence, and the windows rattled as if
heavy artillery were being discharged in the streets. And still these
efforts seemed to be only rehearsing for the supreme display. By ten
o’clock on the morning of Monday, August 27th, 1883, the rehearsals were
over and the performance began. An overture, consisting of two or three
introductory explosions, was succeeded by a frightful convulsion which
tore away a large part of the island of Krakatoa and scattered it to the
winds of heaven. In that final effort all records of previous explosions
on this earth were completely broken.

This supreme effort it was which produced the mightiest noise that, so
far as we can ascertain, has ever been heard on this globe. It must have
been indeed a loud noise which could travel from Krakatoa to Batavia and
preserve its vehemence over so great a distance; but we should form a
very inadequate conception of the energy of the eruption of Krakatoa if
we thought that its sounds were heard by those merely a hundred miles
off. This would be little indeed compared with what is recorded, on
testimony which it is impossible to doubt.

[Illustration: THE EARLY STAGE OF THE ERUPTION OF KRAKATOA.
(_From a Photograph taken on May 27th, 1883._)]

Westward from Krakatoa stretches the wide expanse of the Indian Ocean.
On the opposite side from the Straits of Sunda lies the island of
Rodriguez, the distance from Krakatoa being almost three thousand miles.
It has been proved by evidence which cannot be doubted that the booming
of the great volcano attracted the attention of an intelligent
coastguard on Rodriguez, who carefully noted the character of the sounds
and the time of their occurrence. He had heard them just four hours
after the actual explosion, for this is the time the sound occupied on
its journey.

We shall better realise the extraordinary vehemence of this tremendous
noise if we imagine a similar event to take place in localities more
known to most of us than are the far Eastern seas.

If Vesuvius were vigorous enough to thunder forth like Krakatoa, how
great would be the consternation of the world! Such a report might be
heard by King Edward at Windsor, and by the Czar of all the Russias at
Moscow. It would astonish the German Emperor and all his subjects. It
would penetrate to the seclusion of the Sultan at Constantinople. Nansen
would still have been within its reach when he was furthest north, near
the Pole. It would have extended to the sources of the Nile, near the
Equator. It would have been heard by Mohammedan pilgrims at Mecca. It
would have reached the ears of exiles in Siberia. No inhabitant of
Persia would have been beyond its range, while passengers on half the
liners crossing the Atlantic would also catch the mighty reverberation.

The subject is of such exceptional interest that I may venture on
another illustration. Let us suppose that a similar earth-shaking event
took place in a central position in the United States. Let us say, for
example, that an explosion occurred at Pike’s Peak as resonant as that
from Krakatoa. It would certainly startle not a little the inhabitants
of Colorado far and wide. The ears of dwellers in the neighbouring
States would receive a considerable shock. With lessening intensity the
sound would spread much further around—indeed, it might be heard all
over the United States. The sonorous waves would roll over to the
Atlantic coast, they would be heard on the shores of the Pacific.
Florida would not be too far to the south, nor Alaska too remote to the
north. If, indeed, we could believe that the sound would travel as
freely over the great continent as it did across the Indian Ocean, then
we may boldly assert that every ear in North America might listen to the
thunder from Pike’s Peak, if it rivalled Krakatoa. The reverberation
might even be audible by skin-clad Eskimos amid the snows of Greenland,
and by naked Indians sweltering on the Orinoco. Can we doubt that
Krakatoa made the greatest noise that has ever been recorded?

[Illustration: Fig. 27.—SPREAD OF THE AIR-WAVE FROM KRAKATOA TO THE
ANTIPODES.
(_From the Royal Society’s Reports._)]

Among the many other incidents connected with this explosion, I may
specially mention the wonderful system of divergent ripples that started
in our atmosphere from the point at which the eruption took place. I
have called them ripples, from the obvious resemblance which they bear
to the circular expanding ripples produced by raindrops which fall upon
the still surface of water. But it would be more correct to say that
these objects were a series of great undulations which started from
Krakatoa and spread forth in ever-enlarging circles through our
atmosphere. The initial impetus was so tremendous that these waves
spread for hundreds and thousands of miles. They diverged, in fact,
until they put a mighty girdle round the earth, on a great circle of
which Krakatoa was the pole. The atmospheric waves, with the whole earth
now well in their grasp, advanced into the opposite hemisphere. In their
further progress they had necessarily to form gradually contracting
circles, until at last they converged to a point in Central America, at
the very opposite point of the diameter of our earth, eight thousand
miles from Krakatoa. Thus the waves completely embraced the earth. Every
part of our atmosphere had been set into a tingle by the great eruption.
In Great Britain the waves passed over our heads, the air in our
streets, the air in our houses, trembled from the volcanic impulse. The
very oxygen supplying our lungs was responding also to the supreme
convulsion which took place ten thousand miles away. It is needless to
object that this could not have taken place because we did not feel it.
Self-registering barometers have enabled these waves to be followed
unmistakably all over the globe.

Such was the energy with which these vibrations were initiated at
Krakatoa, that even when the waves thus arising had converged to the
point diametrically opposite in South America their vigour was not yet
exhausted. The waves were then, strange to say, reflected back from
their point of convergence to retrace their steps to Krakatoa. Starting
from Central America, they again described a series of enlarging
circles, until they embraced the whole earth. Then, advancing into the
opposite hemisphere, they gradually contracted until they had regained
the Straits of Sunda, from which they had set forth about thirty-six
hours previously. Here was, indeed, a unique experience. The air-waves
had twice gone from end to end of this globe of ours. Even then the
atmosphere did not subside until, after some more oscillations of
gradually fading intensity, at last they became evanescent.

But, besides these phenomenal undulations, this mighty incident at
Krakatoa has taught us other lessons on the constitution of our
atmosphere. We previously knew little, or I might almost say nothing, as
to the conditions prevailing above the height of ten miles overhead. We
were almost altogether ignorant of what the wind might be at an altitude
of, let us say, twenty miles. It was Krakatoa which first gave us a
little information which was greatly wanted. How could we learn what
winds were blowing at a height four times as great as the loftiest
mountain on the earth, and twice as great as the loftiest altitude to
which a balloon has ever soared? We could neither see these winds nor
feel them. How, then, could we learn whether they really existed? No
doubt a straw will show the way the wind blows, but there are no straws
up there. There was nothing to render the winds perceptible until
Krakatoa came to our aid. Krakatoa drove into those winds prodigious
quantities of dust. Hundreds of cubic miles of air were thus deprived of
that invisibility which they had hitherto maintained. They were thus
compelled to disclose those movements about which, neither before nor
since, have we had any opportunity of learning.

With eyes full of astonishment men watched those vast volumes of
Krakatoa dust start on a tremendous journey. Westward the dust of
Krakatoa took its way. Of course, everyone knows the so-called
tradewinds on our earth’s surface, which blow steadily in fixed
directions, and which are of such service to the mariner. But there is
yet another constant wind. We cannot call it a trade-wind, for it never
has rendered, and never will render, any service to navigation. It was
first disclosed by Krakatoa. Before the occurrence of that eruption no
one had the slightest suspicion that far up aloft, twenty miles over our
heads, a mighty tempest is incessantly hurrying with a speed much
greater than that of the awful hurricane which once laid so large a part
of Calcutta on the ground, and slew so many of its inhabitants.
Fortunately for humanity, this new trade-wind does not come within less
than twenty miles of the earth’s surface. We are thus preserved from the
fearful destruction that its unintermittent blasts would produce, blasts
against which no tree could stand, and which would, in ten minutes, do
as much damage to a city as would the most violent earthquake. When this
great wind had become charged with the dust of Krakatoa, then, for the
first and, I may add, for the only time, it stood revealed to human
vision. Then it was seen that this wind circled round the earth in the
vicinity of the Equator, and completed its circuit in about thirteen
days.

Please observe the contrast between this wind of which we are now
speaking and the waves to which we have just referred. The waves were
merely undulations or vibrations produced by the blow which our
atmosphere received from the explosion of Krakatoa, and these waves were
propagated through the atmosphere much in the same way as sound waves
are propagated. Indeed, these waves moved with the same velocity as
sound. But the current of air of which we are now speaking was not
produced by Krakatoa; it existed from all time, before Krakatoa was ever
heard of, and it exists at the present moment, and will doubtless exist
as long as the earth’s meteorological arrangements remain as they are at
present. All that Krakatoa did was simply to provide the charges of dust
by which for one brief period this wind was made visible.

In the autumn of 1883 the newspapers were full of accounts of strange
appearances in the heavens. The letters containing these accounts poured
in upon us from residents in Ceylon; they came from residents in the
West Indies, and from other tropical places. All had the same tale to
tell. Sometimes experienced observers assured us that the sun looked
blue; sometimes we were told of the amazement with which people beheld
the moon draped in vivid green. Other accounts told of curious halos,
and, in short, of the signs in the sun, the moon, and the stars, which
were exceedingly unusual, even if we do not say that they were
absolutely unprecedented.

Those who wrote to tell of the strange hues that the sun manifested to
travellers in Ceylon, or to planters in Jamaica, never dreamt of
attributing the phenomena to Krakatoa, many thousands of miles away. In
fact, these observers knew nothing at the time of the Krakatoa eruption,
and probably few of them, if any, had ever heard that such a place
existed. It was only gradually that the belief grew that these,
phenomena were due to Krakatoa. But when the accounts were carefully
compared, and when the dates were studied at which the phenomena were
witnessed in the various localities, it was demonstrated that these
phenomena, notwithstanding their worldwide distribution, had certainly
arisen from the eruption in this little island in the Straits of Sunda.
It was most assuredly Krakatoa that painted the sun and the moon, and
produced the other strange and weird phenomena in the tropics.

After a little time we learned what had actually happened. The dust
manufactured by the supreme convulsion was whirled round the earth in
the mighty atmospheric current into which the volcano discharged it. As
the dust-cloud was swept along by this incomparable hurricane, it showed
its presence in the most glorious manner by decking the sun and the moon
in hues of unaccustomed splendour and beauty. The blue colour in the sky
under ordinary circumstances is due to particles in the air, and when
the ordinary motes of the sunbeam were reinforced by the introduction of
the myriads of motes produced by Krakatoa, even the sun itself sometimes
showed a blue tint. Thus the progress of the great dust-cloud was traced
out by the extraordinary sky effects it produced, and from the progress
of the dust-cloud we inferred the movements of the invisible air current
which carried it along. Nor need it be thought that the quantity of
material projected from Krakatoa should have been inadequate to produce
effects of this worldwide description. Imagine that the material which
was blown to the winds of heaven by the supreme convulsion of Krakatoa
could be all recovered and swept into one vast heap. Imagine that the
heap were to have its bulk measured by a vessel consisting of a cube one
mile long, one mile broad, and one mile deep; it has been estimated that
even this prodigious vessel would have to be filled to the brim at least
ten times before all the products of Krakatoa had been measured.

It was in the late autumn of 1883 that the marvellous series of
celestial phenomena connected with the great eruption began to be
displayed in Great Britain. Then it was that the glory of the ordinary
sunsets was enhanced by a splendour which has dwelt in the memory of all
those who were permitted to see them. The frontispiece of this volume
contains a view of the sunset as seen at Chelsea at 4.40 p.m. on
November 26th, 1883. The picture was painted from nature by Mr. W.
Ascroft, and is given in the great work on Krakatoa which was published
by the Royal Society. There is not the least doubt that it was the dust
from Krakatoa which produced the beauty of those sunsets, and so long as
that dust remained suspended in our atmosphere, so long were strange
signs to be witnessed in the heavenly bodies. But the dust which had
been borne with unparalleled violence from the interior of the volcano,
the dust which had been shot aloft by the vehemence of the eruption to
an altitude of twenty miles, the dust which had thus been whirled round
and round our earth for perhaps a dozen times or more in this air
current, which carried it round in less than a fortnight, was endowed
with no power to resist for ever the law of gravitation which bids it
fall to the earth. It therefore gradually sank downwards. Owing,
however, to the great height to which it had been driven, owing to the
impetuous nature of the current by which it was hurried along, and owing
to the exceedingly minute particles of which it was composed, the act of
sinking was greatly protracted. Not until two years after the original
explosion had all the particles with which the air was charged by the
great eruption finally subsided on the earth.

At first there were some who refused to believe that the glory of the
sunsets in London could possibly be due to a volcano in the Straits of
Sunda, at a distance from England which was but little short of that of
Australia. But the gorgeous phenomena in England were found to be
simultaneous with like phenomena in other places all round the earth.
Once again the comparison of dates and other circumstances proved that
Krakatoa was the cause of these exceptional and most interesting
appearances.

Nor was the incident without a historical parallel, for has not Tennyson
told us of the call to St. Telemachus—

“Had the fierce ashes of some fiery peak
Been hurl’d so high they ranged about the globe?
For day by day, thro’ many a blood-red eve,
In that four-hundredth summer after Christ,
The wrathful sunset glared....”

------------------------------------------------------------------------

CHAPTER X.

SPIRAL AND PLANETARY NEBULÆ.

A Substitute for History—Photograph of the Great Spiral taken at the
Lick Observatory—Solar System Relations Unimportant—Chaotic
Nebulæ—Lord Rosse’s Great Discovery—Dr. Roberts’ Photographs—The
Astonishing Discovery of Professor Keeler—The Perspective of the
Spirals—The Spiral Nebulæ are not Gaseous—The Spiral is a Nebula in
an advanced Stage of Development—Character of the Great Nebula in
Andromeda.

IN a great college in America a new educational experiment has been
tried with some success. Instead of the instruction in history which
students receive in most other institutions, an attempt has been made in
this college to give instruction in a very different manner, which it is
believed will not be of less educational value than the more ordinary
processes of teaching. In the course of study to which I am now
referring the student is invited to consider, not so much the history of
the development of the Constitution of one particular country, as to
make a broad survey of the different Constitutions under which the
several countries of the world are at this moment governed. The
promoters of this scheme believe that many of the intellectual
advantages which are ordinarily expected to be gained by the study of
the history of one country may be secured equally well by studying only
existing conditions, provided that attention is given to several
countries which have arrived at different stages of civilisation.

Without attempting to say how far the study of the existing
Constitutions of France and Germany, America and Australia, Turkey and
India, Morocco and Fiji, might be justly used to supersede the study of
English history, it may at least be urged that if we had no annals from
which history could be compiled it might be instructive to employ such a
substitute for historical studies as is here suggested. This is, indeed,
the course which we are compelled to take in our study of that great
chapter in earth-history which we are discussing in these pages. It is
obvious from the nature of the case that it can never be possible for us
to obtain direct testimony as to what occurred in the bringing together
of the materials of this globe. We must, therefore, look abroad through
the universe, and see whether we can find, from the study of other
systems at present in various stages of their evolution, illustrations
of the incidents which we may presume to have occurred in the early
stages of our own history.

If Kant had never lived, if Laplace had never announced his Nebular
Theory, if the discoveries of Sir William Herschel had not been made, I
still venture to think that a due consideration of the remarkable
photograph of the famous Great Spiral, which was obtained at the famous
Lick Observatory in California, would have suggested the high
probability of that doctrine which we describe as the Nebular Theory.

[Illustration: Fig. 28.—THE GREAT SPIRAL NEBULA (Lick Observatory).
(_From the Royal Astronomical Series._)]

If an artist thoroughly versed in the great facts of astronomy had been
commissioned to represent the nebular origin of our system as perfectly
as a highly cultivated yet disciplined imagination would permit, I do
not think he could have designed anything which could answer the purpose
more perfectly than does that picture which is now before us. We might
wish indeed that Kant and Laplace and Herschel could have lived to see
this marvellous natural illustration of their views, for photographs
were of course unthought of in those days, and, I need hardly say, that
for any one celestial nebula that could have been known in the times of
Laplace, hundreds are now within the reach of astronomers.

We entreat special attention to this picture which Nature has herself
given us, and which represents what we may not unreasonably conclude to
be a system in a state of formation. Let me say at once that our solar
system, however imposing it may be from our point of view, is but of
infinitesimal importance as compared with the system which is here in
the course of development. It is sometimes urged that it is difficult to
imagine how a system so large as ours could have been produced by
condensation from a primæval nebula. The best answer is found in the
fact that the Great Spiral now before us may be considered to exhibit at
this very moment a system in actual evolution, the central body of which
is certainly thousands of times, and not improbably millions of times,
greater than the sun, and of which the attending planets or other
revolving bodies, are framed on a scale immensely transcending that of
even Jupiter himself. The details of this remarkable nebula seem to
illustrate those particular features which had been previously assigned
to the primæval nebula of our system, long before any photograph was
available for the purpose of their study.

In the Great Nebula in Orion, to which we have already referred, as well
as in many other similar objects which we might also have adduced, the
nebulous material from which after long ages new systems may be the
result, was shown in an extremely chaotic state. It was little more than
an irregular stain of light on the sky. But in the picture of the Great
Spiral which is before us (Fig. 28) it is manifest that the evolution of
the system has reached an advanced stage; such considerable progress has
been made in the actual formation that the final form seems to be
shadowed forth. The luminosity is no longer diffused in a chaotic
condition; it has formed into spirals, and become much condensed at the
centre and somewhat condensed in other regions. As we now see it, the
object seems to represent a system much more advanced in its formation
than any of the other great nebulæ with which we have compared it. In
comparison with it the evolution of such an object as the Great Nebula
in Orion can hardly be said to have begun. But in the Great Spiral many
portions of the nebula have already become outlined into masses which,
though still far from resembling the planets in the solar system, have
at least made some approach thereto while the central portions are being
drawn together, just as we may conceive the great primæval fire-mist to
have drawn together in the actual formation of the sun.

The famous nebula which we are discussing, and which is generally known
as the Great Spiral, is found in the constellation of Canes Venatici,
very near the end star in the tail of the Great Bear, and one-fourth of
the way from it to Cor Caroli. It will be easy to find it from the
indication given in the adjoining Fig. 29. As a nebulous spot it is an
object which can be seen with any moderately good telescope, but to
detect those details which indicate the spiral structure demands an
instrument of first-class power. This object had indeed been studied by
many astronomers before Lord Rosse turned his colossal reflector upon
it. Then it was that the wonderful whirlpool structure was first
discovered, and thus the earliest spiral nebula became known.

[Illustration: Fig. 29.—HOW TO FIND THE GREAT SPIRAL NEBULA.]

In those days there were few telescopes of great power, and none of
those instruments appeared able to deal with this nebula sufficiently to
reveal its spiral character. The announcement of the discovery of the
spiral constitution of this object was therefore received with
incredulity by some astronomers, who believed, or professed to believe,
that the spiral lines of nebulous matter which Lord Rosse described so
faithfully, existed only in the imagination of the astronomer. Indeed,
in one notable instance, it was alleged that these features were to be
attributed to actual imperfections in the unrivalled telescope. The
incredulity widely prevalent in the middle of the last century about the
existence of the spiral nebulæ may be paralleled by the incredulity
about other discoveries in more recent years. When a highly skilled
observer, using an instrument of adequate power, and, it may be,
enjoying unequalled opportunities for good work, testifies to certain
discoveries; when he has employed in the verification of his
observations the skill and experience that years of practice have
procured for him, it is futile for those who have not the like
opportunities, either from the want of instruments of adequate power or
from climatic difficulties, to deny the truth of discoveries because
they are not able to verify them. It was absurd for astronomers to
refuse assent to the great discoveries of Lord Rosse simply because
instruments inferior to his would not show the spiral structure.

In due time, one astronomer after another began to admit that possibly
the remarkable form which Lord Rosse announced as characteristic of some
nebulæ might not be a mere figment of the imagination. The complete
vindication of Lord Rosse’s great discovery was not, however, attained
until that wonderful advance in the arts of astronomy when the
photographic plate was called in to supplement, or rather vastly to
extend, the powers of the eye. Dr. Isaac Roberts not only showed by a
magnificent photograph that the Great Spiral discovered by Lord Rosse
was just as Lord Rosse had described it, he not only showed that the
other spirals announced by Lord Rosse were equally entitled to the name,
but, with the newly acquired powers that the photographic plate placed
at his disposal, he was able to show that many other nebulæ, which had
been frequently observed and had even been sketched, possessed further
features too faint and delicate to be seen by any human eye, even with
the help of the most powerful telescope. These further features were
discovered because they came within the ken of the intensely acute
perception of the photographic plate. On the plate these features which
the camera showed, were added to those which the eye had already
perceived, and when these additions were made it was not infrequently
found that the nebula assumed the form of a spiral. But the most
remarkable circumstance has still to be added. Some of the plates
exposed by Dr. Roberts show clear and unmistakable photographs of spiral
nebulæ as exquisite in detail as the Great Spiral itself, but yet so
faint that they have never been seen by the eye in any telescope
whatever, though they could not elude the photographic plate. Thus, Dr.
Roberts not only confirmed in the most splendid manner that really great
discovery of the spiral nebulæ of which the honour belongs to Lord
Rosse, but the eminent photographic astronomer added many other spirals
of the greatest interest to the list of those objects which Lord Rosse
had himself given.

Though these discoveries placed the fact of the existence of spiral
nebulæ in an impregnable position, and though they greatly increased the
interest with which astronomers study such objects, yet another stop had
to be taken before the spiral nebula attained the position of
extraordinary importance as a celestial object which must now be
acknowledged to be its due.

[Illustration: Fig. 30.—A GROUP OF NEBULÆ (_Lord Rosse_). (3440, 3445 in
n.g.c.)
(_From the Scientific Transactions of the Royal Dublin Society._)]

We have already had occasion (page 67) to mention the marvellous
discoveries of nebulæ which the lamented Professor Keeler made with the
Crossley Reflector at the Lick Observatory. We have explained that his
discoveries have shown the number of nebulæ in the heavens to be
probably at least twenty times that which previous observations would
have authorised us in asserting. The mere announcement that 120,000 new
nebulæ were within the reach of a photographic plate attached to the
Crossley Reflector, would, by itself, have been a statement so
remarkable as to command the immediate attention of the scientific
world. But the interest of even this statement shrinks to unimportance
relatively to the further fact which Professor Keeler has added. I do
not know, in the annals of astronomy, a pronouncement of greater
interest, certainly none of more importance for our present purpose,
than the statement that of the 120,000 new nebulæ, at least half are
spirals. Here is indeed a stupendous revolution in our knowledge of the
celestial objects. Fifty years ago Lord Rosse announced the discovery of
a spiral nebula, and the existence of this spiral was doubted at first,
though it was gradually conceded at last. Now we have the announcement,
on the unchallenged evidence of the photographic plate itself, that to
all appearances there are at least 60,000 spiral nebulæ in the heavens.
It is, alas! too true that Professor Keeler did not live long enough to
enumerate all those nebulæ himself, and, indeed, they have not so far
been actually counted, but to those who will study Professor Keeler’s
papers, the evidence of the substantial accuracy of the statement is
incontestable.

[Illustration: Fig. 31.—A RAY NEBULA (_Lord Rosse_). (3628 in n.g.c.)
(_From the Scientific Transactions of the Royal Dublin Society._)]

And astonishing as this statement may be, we have still to add that, in
face of the actual facts, it may be regarded as even a moderate estimate
of the abundance of spirals in the universe. We must remember that a
spiral nebula is a flat object with long arms extending from it which
lie nearly in the same plane. If we are actually to see that such an
object is spiral, it is necessary for it to be turned squarely towards
the earth. If the object be too much foreshortened, it is quite plain
that we can hardly expect to detect its spiral character. It is also
obvious if the spiral happens to be turned edgeways towards us, that
then its spiral form cannot be seen; it would merely appear as what
astronomers often call a ray. In the enumeration of the spirals it is
therefore only possible for us to include those which happen to be so
far squarely turned towards the earth as to make their spiral character
unmistakable. We might, therefore, reasonably expect that the numbers of
spiral nebulæ actually counted would fall short of the reality. We know
that there are many nebulæ of a somewhat elliptical shape (Fig. 31).
There are also many nebulæ that look like long rays (Fig. 30). Those who
are familiar with the appearance of nebulæ in great telescopes will
recall at once the numerous spindle-shaped objects of this class. It can
hardly be doubted that many of the nebulæ, more or less oval in form,
and also these rays or the spindle-shaped objects so frequently seen in
good telescopes (Fig. 33) are in reality spiral nebulæ, which are turned
not squarely towards us, but which we are merely looking at more or less
edgewise, so that they have been foreshortened enough to hide their
peculiar structure (Figs. 34, 35). Taking these considerations into
account, it becomes obvious that the estimate of Professor Keeler as to
the number of spiral nebulæ in the heavens, vast as that estimate seems,
may still fall short of the truth. Thus we are led to one of the most
remarkable conclusions of modern astronomy, viz. that the spiral nebula,
next to a star itself, is the most characteristic object in the sidereal
heavens.

In treating of the nebulæ in Chapter IV. we explained those fundamental
features of the different spectra which make it possible to discriminate
with confidence between a nebula which is purely gaseous and a nebula
which cannot be so described. As the spiral nebulæ form a class
characterised among all the other nebulæ by the possession of a very
particular structure, it is interesting to enquire what evidence the
spectrum gives with regard to the nature of the material which enters
into the constitution of the nebulæ which belong to this strongly-marked
group. I do not mean to say that all the 60,000 spirals have been
examined with the spectroscope, but, as already explained on page 67, a
sufficient number have been examined to decide the question. We learn
from Professor Scheiner, a well-known authority on astronomical
spectroscopy, that the spectra of spirals are generally found to be
continuous; in other words, we learn that a spiral nebula is not
gaseous. It does not consist, like, for example, the nebula in Orion, of
vaporous matter in a state of incandescence.

A nebula or a nebulous-looking object which does not give a spectrum of
bright lines, but which does give a continuous spectrum, is not
infrequently set down as being merely a cluster of stars. This is
undoubtedly a true statement with regard to some of these nebulous
objects, but it is not true with regard to all. It is much more
reasonable to suppose that the greater part of the materials of the
spiral nebulæ, though certainly not in the form of gas, are still not
condensed into objects large enough to entitle them to be called stars.
It must be remembered that when an object of a gaseous nature has lost
heat by radiation, and has begun to draw itself together, the gas
condenses into particles which constitute small portions of liquid or
solid, just as the vapour of water in the atmosphere condenses into the
beads of water that form the clouds in our own sky. These small objects,
even if incandescent, would no longer radiate light with the
characteristics of a gaseous nebula. The light they would emit would be
of the same character as that dispensed from the particles of carbon in
the solar photosphere to which the sun owes its light. Radiation from
such a source would give light with a continuous spectrum, like that
from the sun or a star.

From the fact that the spectra of the spiral nebulæ are continuous, we
may infer that, though these nebulæ have reached an advanced stage in
their development, they have not always, and, perhaps, not generally,
attained to the stage in which condensation transformed them into a
cluster of actual stars. They have, however, reached a stage in their
progress towards those systems of large bodies that they are ultimately
to become. The character of its spectrum may show us that the spiral
nebula is not very young, that it has attained a considerable age in its
evolution as compared with other nebulæ which do not show the spiral
character and which have a gaseous spectrum. The importance of this
consideration will be made apparent in the next chapter, when we discuss
the dynamical conditions to which a spiral nebula must submit.

But there is no reason to doubt that some of the spiral nebulæ may be in
reality star-clusters, in which there are aggregations of myriads of
points, each justly entitled by its dimensions and its lustre to be
regarded as a real star. The great nebula in Andromeda seems to be a
greatly foreshortened spiral. This, at least, is the interpretation
which may perhaps be most reasonably given to Dr. Roberts’ famous
photograph of this splendid object. The spectrum of the Andromeda nebula
has been photographed by Scheiner after a protracted exposure of seven
and a half hours. That spectrum showed no trace of bright lines, thus
proving that there is no discernible incandescent gas in the nebula of
Andromeda. It gives practically a continuous spectrum, across which some
broad bands can be recognised. It was interesting to compare this
spectrum of the great nebula in Andromeda with the solar spectrum seen
by the same apparatus and under the same conditions. Professor Scheiner
announces that there was a remarkable coincidence between the two, and
he draws the inference that the stars which enter into the nebula in
Andromeda are stars of that particular type to which the sun belongs.

[Illustration: Fig. 32.—PORTION OF THE MILKY WAY (NEAR MESSIER II.).
(_Photographed by Professor E. E. Barnard._)
(_From the Royal Astronomical Society Series._)]

But we have now to point out how the recent study of nebulæ has afforded
a yet more striking confirmation of the nebular theory. Laplace showed
how a gradually condensing nebula might have formed a sun and a system
of planets. Had Laplace known of the spiral nebulæ he would, I doubt
not, have found in them the most striking illustration of the operation
of evolution on a gigantic scale. They would have provided him with
admirable arguments in support of the nebular theory. It is possible
that they might also have provided suggestions as to the details of the
evolution, which he had not anticipated. But Laplace did not know of
such objects, and we can only deplore the loss of the instructive
lessons which his incomparable genius would have derived from them.

We must, however, admit that the lessons as to the origin of the solar
system, derived from the spiral nebulæ, must be received with due
limitation. We may say at once that the _great_ spiral nebulæ do not
appear to be evolving into systems like the sun and planets; their work
is of a higher order of magnitude altogether. The great spiral nebulæ
seem to be more analogous to galaxies, like the Milky Way (Fig. 32),
than to solar systems. The spiral nebula instead of being described as a
system, should perhaps be described as a system of systems. If the solar
system were drawn to scale on the photograph of the Great Spiral (Fig.
28) the orbit of Neptune would not be larger than the smallest
recognisable dot.

------------------------------------------------------------------------

CHAPTER XI.

THE UNERRING GUIDE.

The Solar System—Orbits nearly Plane—Satellites, Saturn’s Ring, Spiral
Nebulæ—An Explanation of this Tendency of a System towards
Flatness—The Energy of a System—Loss of Energy by Collision and
Tidal Action—A System within a System—Movements of Translation and
Movements of Rotation—The General Law of Conservation of Moment of
Momentum—Illustrations of the Principle—The Conception of the
Principal Plane—The Utility of this principle arises from its
independence of Collisions or Friction—Nature does not do Things
infinitely Improbable—The Decline of Energy and the Preservation of
Moment of Momentum—Explanation of the Motions in one Plane and in
the same Direction—The Satellites of Uranus—The Rotation of
Uranus—Why the Orbits are not exactly in the same Plane—The
Evolution of a Nebula—The Inevitable Tendency towards the Spiral—The
Explanation of the Spiral.

WE have to consider in this chapter the light which the laws of
mathematics throw upon certain features which are possessed by a very
large number of celestial objects. Let us first describe, as clearly as
the circumstances will permit, the nature of these common features to
which we now refer, and of which mathematics will suggest the
explanation.

We shall begin with our solar system, in which the earth describes an
orbit around the sun. That orbit is contained within a plane, which
plane passes through the centre of the sun. We may neglect for the
present the earth’s occasional slight deviations from this plane which
are caused by the attractions of the other planets. If we consider the
other bodies of our system, such, for instance, as Venus or Jupiter, we
find that the orbit of Venus also lies in a plane, and that plane also
passes through the centre of the sun. The orbit of Jupiter is found to
be contained within a plane, and it, too, passes through the sun’s
centre. Each of the remaining planets in like manner is found to revolve
in an orbit which is contained in a plane, and all these planes have one
common point, that point being the centre of the sun.

It is a remarkable fact that the mutual inclinations are very small, so
that the several planes are nearly coincident. If we take the plane of
our earth’s orbit, which we call the ecliptic, as the standard, then the
greatest inclination of the orbit of any other important planet is seven
degrees, which is found in the case of Mercury. The inclinations to the
ecliptic of the planes of the orbits of a few of the asteroids are much
more considerable; to take an extreme case, the orbit of Pallas is
inclined at an angle of no less than thirty-four degrees. It must,
however, be remembered that the asteroids are very small objects, as the
collective masses of the five hundred which are at present known would
amount to no more than an unimportant fraction of the mass of one of the
great planets of our system. Three-fourths of the asteroids have
inclinations under ten degrees. We may, therefore, leave these bodies
out of consideration for the present, though we may find occasion to
refer to them again later on. Still less need we pay attention at
present to the comets, for though these bodies belong to our system, and
though they move in plane orbits, which like the orbits of the planets
pass through the centre of the sun, yet their orbits are inclined at
angles of very varying magnitudes. Indeed, we cannot detect any tendency
in the orbits of comets to approximate to the plane of the ecliptic. The
masses of comets are, however, inconsiderable in comparison with the
robust globes which form the planets, while the origin of comets has
been apparently so different from that of the planets, that we may leave
them out of consideration in our present argument. There is nothing in
the motion of either asteroids or comets to invalidate the general
proposition which affirms, that the planes of the orbits of the heaviest
and most important bodies in the solar system are very nearly
coincident.

Many of the planets are accompanied by satellites, and these satellites
revolve round the planets, just as the planet accompanied by its
satellites revolves round the sun. The orbit of each satellite is
contained within a plane, and that plane passes through the centre of
the planet to which it is appended. We thus have a system of planes
appropriate to the satellites, just as there is a system of planes
appropriate to the planets. The orbits of the satellites of each planet
are very nearly in the same plane, with notable exceptions in the cases
of Uranus and Neptune, which it will be necessary to consider at full
length later on. This plane is very nearly coincident with the planes in
which the planets themselves move. Omitting the exceptions, which are
unimportant as to magnitude, though otherwise extremely interesting and
instructive, the fundamental characteristic of the movements of the
principal bodies in our system is that their orbits are nearly parallel
to the same plane. We draw an average plane through these closely
adjacent planes and we term it the principal plane of our system. It is
not, indeed, coincident with the plane of the orbit of any one planet,
yet the actual plane of the orbit of every important planet, and of the
important satellites, lies exceedingly close to this principal plane.
This is a noteworthy circumstance in the arrangement of the planetary
system, and we expect that it must admit of some physical explanation.

When we look into the details of the planetary groups composing the
solar system, we find striking indications of the tendency of the orbits
of the bodies in each subordinate system to become adjusted to a plane.
The most striking instance is that exhibited by the Rings of Saturn. It
has been demonstrated that these wonderful rings are composed of myriads
of separate particles. Each of these particles follows an independent
orbit round Saturn. Each such orbit is contained in a plane, and all
these planes appear, so far as our observations go, to be absolutely
coincident. It is further to be noted that the plane, thus remarkably
related to the system of rings revolving around Saturn, is substantially
identical with the plane in which the satellites of Saturn themselves
revolve, and this plane again is inclined at an angle no greater than
twenty-eight degrees to the plane of the ecliptic, and close to that in
which Saturn itself revolves around the sun.

Overlooking, as we may for the present, the varieties in detail which
such natural phenomena present, we may say that the most noticeable
characteristic of the revolutions in the solar system is expressed by
the statement that they lie approximately in the same plane.

[Illustration: Fig. 33.—A SPIRAL NEBULA SEEN EDGEWISE (n.g.c. 3628; in
Leo).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]

We shall also find that this tendency of the movements in a system to
range themselves in orbits which lie in the same plane, is exhibited in
other parts of the universe. Let us consider from this point of view the
spiral nebulæ, those remarkable objects which, in the last chapter, we
have seen to be so numerous and so characteristic. It is obvious that a
spiral nebula must be a flat object. Its thickness is small in
comparison with its diameter. When a spiral nebula is looked at edgewise
(Fig. 45), then it seems long and thin, so much so that it presents the
appearance of a ray such as we have shown in Fig. 33, which represents a
type of object very familiar to those astronomers who are acquainted
with nebulæ. The characteristics of these objects seem consistent only
with the supposition that there is a tendency in the materials which
enter into a spiral nebula to adapt their movements to a particular
plane, just as there is a tendency for the objects in Saturn’s ring to
remain in a particular plane, and just as there has been a tendency
among the bodies belonging to the solar system themselves to revolve in
a particular plane. Remembering also that there seems excellent reason
to believe that spiral nebulæ exhibiting this characteristic are to be
reckoned in scores of thousands, it is evident that the fundamental
feature in which they all agree must be one of very great importance in
the universe.

[Illustration: Fig. 34.—A FORESHORTENED SPIRAL (n.g.c. 3198; in Ursa
Major).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]

[Illustration: Fig. 35.—EDGE VIEW OF A SPIRAL BOLDLY SHOWN (n.g.c. 4565;
in Coma Berenices).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]

We may mention yet one more illustration of the remarkable tendency, so
frequently exhibited by an organised system in space, to place its parts
ultimately in or near the same plane, or at all events, to assume a
shape of which one dimension is small in comparison with the two others.
We have, in the last chapter, referred to the Milky Way, and we have
alluded to the significance of the obvious fact that, however the mass
of stars which form the Milky Way may be arranged, they are so disposed
that the thickness of the mass is certainly much less than its two other
dimensions. Herschel’s famous illustration of a grindstone to represent
the shape of the Milky Way will serve to illustrate the form we are now
considering.

When we meet with a characteristic form so widely diffused through the
universe, exhibited not only in the systems attending on the single
planets, not only in the systems of planets which revolve round a single
sun, but also in that marvellous aggregation of innumerable suns which
we find in the Milky Way, and in scores of thousands of nebulæ in all
directions, at all distances, and apparently of every grade of
importance, we are tempted to ask whether there may not be some physical
explanation of a characteristic so universal and so remarkable.

Let us see whether mathematics can provide any suggestion as to the
cause of this tendency towards flatness which seems to affect those
systems in the universe which are sufficiently isolated to escape from
any large disturbance of their parts by outside interference. We must
begin by putting, as it were, the problem into shape, and by enumerating
certain conditions which, though they may not be absolutely fulfilled in
nature, are often so very nearly fulfilled that we make no appreciable
error by supposing them to be so.

Let us suppose that a myriad bodies of various sizes, shapes, materials
and masses, are launched in space in any order whatever, at any
distances from each other, and that they are started with very different
movements. Some may be going very fast, some going slowly, or not at
all; some may be moving up or down or to the right or to the left—there
may be, in fact, every variety in their distances and their velocities,
and in the directions in which they are started.

We assume that each pair of masses attract each other by the well-known
law of gravitation, which expresses that the force between any two
bodies is proportional directly to the product of their masses and
inversely to the square of their distance. We have one further
supposition to make, and it is an important one. We shall assume that
though each one of the bodies which we are considering is affecting all
the others, and is in turn affected by them, yet that they are subjected
to no appreciable disturbing influence from other bodies not included in
the system to which they belong. This may seem at first to make the
problem we are about to consider a purely imaginary one, such as could
only be applicable to systems different from those which are actually
presented to us in nature. It must be admitted that the condition we
have inferred can only be approximately fulfilled. But a little
consideration will show that the supposition is not an unreasonable one.
Take, for instance, the solar system, consisting of the sun, the
planets, and their satellites. Every one of these bodies attracts every
other body, and the movement of each of the bodies is produced by the
joint effects of the forces exerted upon it by all the others. Assuredly
this gives a problem quite difficult enough for all the resources that
are at our command. But in such investigations we omit altogether the
influence of the stars. Sirius, for example, does exercise some
attraction on the bodies of our system, but owing to its enormous
distance, in comparison with the distances in our solar system, the
effect of the disturbance of Sirius on the relative movements of the
planets is wholly inappreciable. Indeed, we may add that the
disturbances in the solar system produced by all the stars, even
including the myriads of the Milky Way, are absolutely negligible. The
movements in our solar system, so far as our observations reveal them,
are performed precisely as if all bodies of the universe foreign to the
solar system were non-existent. This consideration shows that in the
problem we are now to consider, we are introducing no unreasonable
element when we premise that the system whose movements we are to
investigate is to be regarded as free from appreciable disturbance by
any foreign influence.

To follow the fortunes of a system of bodies, large or small, starting
under any arbitrary conditions at the commencement, and then abandoned
to their mutual attractions, is a problem for the mathematician. It
certainly presents to him questions of very great difficulty, and many
of these he has to confess are insoluble; there are, however, certain
important laws which must be obeyed in all the vicissitudes of the
motion. There are certain theorems known to the mathematician which
apply to such a system, and it is these theorems which afford us most
interesting and instructive information. I am well aware that the
subject upon which I am about to enter is not a very easy one, but its
importance is such that I must make the effort to explain it.

Let me commence by describing what is meant when we speak of the energy
of a system. Take, first, the case of merely two bodies, and let us
suppose that they were initially at rest. The energy of a system of this
very simple type is represented by the quantity of work which could be
done by allowing these two bodies to come together. If, instead of being
in the beginning simply at rest, the bodies had each been in motion, the
energy of the system would be correspondingly greater. The energy of a
moving body, or its capacity of doing work in virtue of its movement, is
proportional jointly to its mass and to the square of its velocity. The
energy of the two moving bodies will therefore be represented by three
parts; first, there will be that due to their distance apart; secondly,
there will be that due to the velocity of one of them; and, thirdly,
there is that due to the velocity of the other. In the case of a number
of bodies, the energy will consist in the first place of a part which is
due to the separation of the bodies, and measured by the quantity of
work that would be produced if, in obedience to their mutual attraction,
all the bodies were allowed to come together into one mass. In the
second place, the bodies are to be supposed to have been originally
started with certain velocities, and the energy of each of the bodies,
in virtue of its motion, is to be measured by the product of one-half
its mass into the square of its velocity. The total energy of the system
consists, therefore, of the sum of the parts due to the velocities of
the bodies, and that which is due to their mutual separation.

If the bodies could really be perfectly rigid, unyielding masses, so
that they have no movements analogous to tides, and if their movements
be such that collisions will not take place among them, then the laws of
mechanics tell us that the quantity of energy in that system will remain
for ever unaltered. The velocities of the particles may vary, and the
mutual distances of the particles may vary, but those variations will be
always conducted, subject to the fundamental condition that if we
multiply the square of the velocity of each body by one-half its mass,
and add all those quantities together, and if we increase the sum thus
obtained by the quantity of energy equivalent to the separation of the
particles, the total amount thus obtained is constant. This is the
fundamental law of mechanics known as the conservation of energy.

For such material systems as the universe presents to us, the
conservation of energy, in the sense in which I have here expressed it,
will not be maintained; for the necessary conditions cannot be
fulfilled. Let us suppose that the incessant movements of the bodies in
the system, rushing about under the influence of their mutual
attractions, has at last been productive of a collision between two of
the bodies. We have already explained in Chapter VI. how in the
collision of two masses the energy which they possess in virtue of their
movements may be to a large extent transformed into heat; there is
consequently an immediate increase in the temperature of the bodies
concerned, and then follows the operation of that fundamental law of
heat, by which the excess of heat so arising will be radiated away. Some
of it will, no doubt, be intercepted by falling on other bodies in the
system, and the amount that might be thus possibly retained would, of
course, not be lost to the system. The bodies of the solar system at
least are so widely scattered, that the greater part of the heat would
certainly escape into space, and the corresponding quantity of energy
would be totally lost to the system. We may generally assume that a
collision among the bodies would be most certainly productive of a loss
of energy from the system.

No doubt collisions can hardly be expected to occur in a system
consisting of large, isolated bodies like the planets. Even in any
system of solid bodies collisions may be presumed to be infrequent in
comparison with the numbers of the bodies. But if, instead of a system
of few bodies of large mass, we have a gas or nebula composed of
innumerable atoms or molecules, the collisions would be by no means
infrequent, and every collision, in so far as it led to the production
of heat, would be productive of loss of energy by radiation from the
system.

It should also be added that, even independently of actual collisions,
there is, and must be, loss of energy in the system from other causes.
There are no absolutely rigid bodies known in nature, for the hardest
mineral or the toughest steel must yield to some extent when large
forces are applied to it, and as the bodies in the system are not mere
points or particles of inconsiderable dimensions, they will experience
stresses something like those to which our earth is subjected in that
action of the moon and sun which produces the tides. In consequence of
the influences of each body on the rest, there will be certain relative
changes in the parts of each body; there will be, as it were, tidal
movements in their liquid parts and even in their solid substance. These
tides will produce friction, and this will produce heat. This heat will
be radiated from the system, but the heat radiated corresponds to a
certain amount of energy; the energy is therefore lost to the system, so
that even without actual collisions we still find that energy must be
gradually lost to the system.

Thus we have been conducted to an important conclusion, which may be
stated in the following way. Let there be any system of bodies, subject
to their mutual attractions, and sufficiently isolated from the
disturbing influence of all bodies which do not belong to the system,
then the original energy with which that system is started must be
undergoing a continual decline. It must at least decline until such a
condition of the system has been reached that collisions are no longer
possible and that tidal influences have ceased. These conditions might
be fulfilled if all the bodies of the system coalesced into a single
mass.

As illustrations of the systems we are now considering, we may take the
sun and planets as a whole. A spiral nebula is a system in the present
sense, while perhaps the grandest illustration of all is provided by the
Milky Way.

It will be noted that we may have a system which is isolated so far as
our present argument is concerned, even while it forms a part of another
system of a higher order of magnitude. For instance, Saturn with his
rings and satellites is sufficiently isolated from the rest of the solar
system and the rest of the universe, to enable us to trace the
consequences of the gradual decline of energy in his attendant system.
The solar system in which Saturn appears merely as a unit, is itself
sufficiently isolated from the stars in the Milky Way to permit us to
study the decline of energy in the solar system, without considering the
action of those stars.

This general law of the decline of energy in an isolated system, is
supplemented by another law often known as the conservation of moment of
momentum. It may at first seem difficult to grasp the notion which this
law involves. The effort is, however, worth making, for the law in
question is of fundamental importance in the study of the mechanics of
the universe. In the Appendix will be found an investigation by
elementary geometry of the important mechanical principles which are
involved in this subject.

Whatever may have been the origin of the primæval nebula, and whatever
may have been the forces concerned in its production we may feel
confident that it was not originally at rest. We do not indeed know any
object which is at rest. Not one of the heavenly bodies is at rest,
nothing on earth is at rest, for even the molecules of rigid matter are
in rapid motion. Rest seems unknown in the universe. It would be,
therefore, infinitely improbable that a primæval nebula, whatever may
have been the agency by which it was started on that career which we are
considering, was initially in a condition of absolute rest. We assume
without hesitation that the nebula was to some extent in motion, and we
may feel assured that the motions were of a highly complicated
description. It is fortunate for us that our argument does not require
us to know the precise character of the movements, as such knowledge
would obviously be quite unattainable. We can, however, invoke the laws
of mechanics as an unerring guide. They will tell us not indeed
everything about those motions, but they will set forth certain
characteristics which the movements must have had, and these
characteristics suffice for our argument.

To illustrate the important principle on which we are now entering I
must mention the famous problem of three bodies which has engaged the
attention of the greatest mathematicians. Let there be a body A, and
another B, and another C. We shall suppose that these bodies are so
small that they may be regarded merely as points in comparison with the
distances by which they are separated. We shall suppose that they are
all moving in the same plane, and we shall suppose that each of them
attracts the others, but that except these attractions there are no
other forces in the system. To discover all about the motions of these
bodies is so difficult a problem that mathematicians have never been
able to solve it. But though we are not able to solve the problem
completely, we can learn something with regard to it.

We represent by arrows in Fig. 36 the directions in which A, B, and C
are moving at the moment. We choose any point O in the plane, and for
simplicity we have so drawn the figure that A, B, and C are forces
tending to turn round O in the same direction. The velocity of a body
multiplied into its mass is termed the _momentum_ of the body. Draw the
perpendicular from O to the direction in which the body A is moving,
then the product of this perpendicular and the momentum of A is called
the _moment of momentum_ of A around O. In like manner we form the
moment of momentum of B and C, and if we add them together we obtain the
total moment of momentum of the system.

We can now give expression to a great discovery which mathematicians
have made. No matter how complicated may be the movements of A, B, and
C; no matter to what extent these particles approximate or how widely
they separate; no matter what changes may occur in their velocities, or
even what actual collision may take place, the sum of the moments of
momentum must remain for ever unaltered. This most important principle
in dynamics is known as the conservation of moment of momentum.

Though I have only mentioned three particles, yet the same principle
will be true for any number. If it should happen that any of them are
turning round O in the opposite direction, then their moments of
momentum are to be taken as negative. In this case we add the moments
tending in one direction together; and then subtract all the opposite
moments. The remainder is the quantity which remains constant.

[Illustration: Fig. 36.—TO ILLUSTRATE MOMENT OF MOMENTUM.]

We may state this principle in a somewhat different manner as follows:
Let us consider a multitude of particles in a plane; let them be
severally started in any directions in the plane, and then be abandoned
to their mutual attractions, it being understood that there are no
forces produced by bodies external to the system; if we then choose any
point in the plane, and measure the areas described round that point by
the several moving bodies in one second, and if we multiply each of,
those areas by the mass of the corresponding body, then, if all the
bodies are moving in the same direction round the point, the sum of the
quantities so obtained is constant. It will be the same a hundred or a
thousand years hence as it is at the present moment, or as it was a
hundred or a thousand years ago. If any of the particles had been
turning round the point in the opposite direction, then the products
belonging to such particles are to be subtracted from the others instead
of added.

We have now to express in a still more general manner the important
principle that is here involved. Let us consider any system of
attracting particles, no matter what their masses or whether their
movements be restricted to a plane or not. Let us start them into motion
in any directions and with any initial velocities, and then abandon them
to the influence of their mutual attractions, withholding at the same
time the interference of any forces from bodies exterior to the system.
Draw any plane whatever, and let fall perpendiculars upon this plane
from the different particles of the system. It will be obvious that as
the particles move the feet of the perpendiculars must move in
correspondence with the particles from which the perpendiculars were let
fall. We may regard the foot of every perpendicular as the actual
position of a moving point, and it can be proved that if the mass of
each particle be multiplied into the area which the foot of its
perpendicular describes in a second round any point in the plane, and
then be added to the similar products from all the other particles, only
observing the proper precautions as to sign, the sum will remain
constant, _i.e._, in any other second the total quantity arrived at will
be exactly the same. This is a general law of dynamics. It is not a law
of merely approximate truth, it is a law true with absolute accuracy
during unlimited periods of time.

The actual value of the constant will depend both on the system and on
the plane. For a given system the constant will differ for the different
planes which may be drawn, and there will be some planes in which that
sum will be zero. In other words, in those planes the areas described by
the feet of the perpendiculars, multiplied by the masses of the
particles which are moving in one way, will be precisely equal to the
similar sum obtained from the particles moving in the opposite
direction.

But among all possible planes there is one of special significance in
its relation to the system. It is called the “principal plane,” and it
is characterised by the fact that the sum (with due attention to sign)
of the areas described each second by the feet of the perpendiculars,
multiplied into the masses of the corresponding particle, is greater
than the like magnitude for any other plane, and is thus a maximum. For
all planes parallel to this principal plane, the result will be, of
course, the same; it is the direction of the plane and not its absolute
situation that is material. We thus see that while this remarkable
quantity is constant in any plane, for all time, yet the actual value of
that constant depends upon the aspect of the plane; for some planes it
is zero, for others the constant has intermediate values, and there is
one plane for which the constant is a maximum. This is the principal
plane, and a knowledge of it is of vital importance in endeavouring to
understand the nebular theory. Nor are the principles under
consideration limited only to a system consisting of sun and planets;
they apply, with suitable modifications, to many other celestial systems
as well.

The instructive character of this dynamical principle will be seen when
we deduce its consequences. The term “moment of momentum” of a particle,
with reference to a certain point in a plane, expresses double the
product of the rate at which the area is described by the foot of the
perpendicular to this plane, multiplied by the mass of the particle. The
moment of momentum of the system, with reference to the principal plane,
is a maximum in comparison with all other planes; that moment of
momentum retains precisely the same value throughout all time, from the
first instant the system was started onwards. And it retains this value,
no matter what changes or disturbances may happen in the system,
provided only that the influence of external forces is withheld. Subject
to this condition, the transformations of the system may be any
whatever. The several bodies may be forced into wide changes of their
orbits, so that there may even be collisions among them; yet,
notwithstanding those collisions, and notwithstanding the violent
alterations which may be thus produced in the movements of the bodies,
the moment of momentum will not alter. No matter what tides may be
produced, even if those tides be so great as to produce disruption in
the masses and force the orbits to change their character radically, yet
the moment of momentum will be conserved without alteration.

It is essential to notice the fundamental difference between the
principle which has been called the conservation of energy in the
system, and the conservation of moment of momentum. We have pointed out
that when collisions take place, part of the energy due to motion is
transformed into heat, and energy in that form admits of radiation
through space, and thus becomes lost to the system, with the result that
the total energy declines. Even without actual collision, we have shown
how certain effects of tides, or other consequences of friction,
necessarily involve the squandering of energy with which the system was
originally endowed. A system started with a certain endowment of energy
may conserve that energy indefinitely, if all such actions as collisions
or frictions are absent. If collisions or frictions are present the
system will gradually dissipate energy. Our interpretation of the future
of such a system must always take account of this fundamental fact.

It is, of course, conceivable that the moment of momentum with which a
system was originally endowed might have happened to be zero. A system
of particles could be so constructed and so started on their movements
that their moment of momentum with regard to a certain plane should be
zero. It might happen that the moment of momentum of the system with
regard to a second plane, perpendicular to the former one, should be
also zero; and, finally, that the moment of momentum of the system with
regard to a third plane perpendicular to each of the other two, should
be also zero. If these three conditions were found to prevail at the
commencement, they would prevail throughout the movement, and, more
generally still, we may state that in such circumstances the moment of
momentum of the system would be zero about any plane whatever. There
would be no principal plane in such a system. We thus note that though
it is inconceivable that a group of mutually attracting bodies should be
started into movement without a suitable endowment of energy, it is yet
quite conceivable that a system could be started without having any
moment of momentum. And if at the beginning the system had no moment of
momentum, then no matter what may be the future vicissitudes of its
motion, no moment of momentum can ever be acquired by it to all
eternity, so long as the interference of external forces is excluded.

But having said this much as to the conceivability of the initiation of
a system with no moment of momentum, we now hasten to add that, so far
as Nature is actually concerned, this bare possibility may be set aside
as one which is infinitely improbable. Nature does not do things which
are infinitely improbable, and, therefore, we may affirm that all
material systems, with which we shall have to deal, do possess moment of
momentum. However the system may have originated, whatever may have been
the actions of forces by which it was brought into being, we may feel
assured that the system received at its initiation some endowment of
moment of momentum, as well as of energy. Hence we may conclude that
every such system as is presented to us in the infinite variety of
Nature, must stand in intimate relation to some particular plane, being
that which is known as the principal plane of moment of momentum. In our
effort to interpret Nature, the physical importance of this fact can
hardly be over-estimated.

In a future chapter we shall make some attempt to sketch the natural
operations by which individual systems have been started on their
careers. Postponing, then, such questions, we propose to deal now with
the phenomena which the principles of dynamics declare must accompany
the evolution of a system under the action of the exclusive attraction
of the various parts of that system for each other. The system commences
its career with a certain endowment of energy, with a certain endowment
of moment of momentum, and with a certain principal plane to which that
moment of momentum is specially related. In the course of the evolution
through which, in myriads of ages, the system is destined to pass, the
energy that it contains will undergo vast loss by dissipation. On the
other hand, the moment of momentum will never vary, and the position of
the principal plane will remain the same for all time. We have to
consider what features, connected with the evolution, may be attributed
to the operation of these dynamical laws. We have, in fact, to deduce
the consequences which seem to follow from the fact that, in consequence
of collisions, and in consequence of friction, an isolated system in
space must gradually part with its initial store of energy, but that,
notwithstanding any collisions and any friction, the total moment of
momentum of the system suffers no abatement.

As the system advances in development, we have to deal with a gradual
decline in the ratio of the original store of energy to the original
store of moment of momentum. And hence we must expect that a system will
ultimately tend towards a form in which, while preserving its moment of
momentum, it shall do so with such a distribution of the bodies of which
it consists as shall be compatible with a diminishing quantity of
energy. It is not hard to see that in the course of ages this tends, as
one consequence, to make the movements of each of the bodies in the
system ultimately approximate to movements in a plane.

Let us, for simplicity, begin with the case of three attracting
particles, A, B and C. Let B be started in any direction in the plane L,
and let A be started in an orbit round it, and in the same plane L. Now
let C be started into motion, in any direction, from some point also in
L. It is certain that the sum of the areas projected parallel to any
plane, which are described in a second by these three bodies, must be
constant, each of the areas being, as usual, multiplied by the mass of
the corresponding body. Let us specially consider the plane L in which
the motions of A and B already lie. It is on this plane that the area
described by C has to be projected. The essential point now to remember
is that the projected area is less than the actual area. It is plain
that if C has to describe a certain projected area in a certain time,
the velocity with which C has to move must be greater when C starts off
at an inclination to the plane than would have been necessary if C had
started in the plane, other things being the same. Thus we see that, if
the three bodies were all moving in the same plane, they could, speaking
generally, maintain more easily the requisite description of areas, that
is, the requisite moment of momentum with smaller velocities than if
they were moving in directions which were not so regulated; that is to
say, the moment of momentum can be kept up with less energy when the
particles move in the same plane.

In a more general manner we see that any system in which the bodies are
moving in the same plane will, for equal moment of momentum, require
less energy than it would have done had the bodies been moving in
directions which were not limited to a plane. Thus we are led to the
conclusion that the ultimate result of the collisions and the friction
and the tides, which are caused by the action of one particle on
another, is to make the movements tend towards the same plane.

In this dynamical principle we have in all probability a physical
explanation of that remarkable characteristic of celestial movements to
which we have referred. The solar system possesses less energy in
proportion to its moment of momentum than it would require to have if
the orbits of the important planets, instead of lying practically in the
same plane, were inclined at various angles. Whatever may have been the
original disposition of the materials forming the solar system, they
must once have contained much more energy than they have at present. The
moment of momentum in the principal plane, at the beginning, was not,
however, different from the moment of momentum that the system now
possesses. As the energy of the system gradually declined, the system
has gradually been compelled to adjust itself in such a manner that,
with the reduced quantity of energy, the requisite moment of momentum
shall still be preserved. This is the reason why, in the course of the
myriads of ages during which the solar system has been acquiring its
present form, the movements have gradually become nearly conformed to a
plane.

The operation of the principle, now before us, may be seen in a striking
manner in Saturn’s ring. (Fig. 37.) The particles constituting this
exquisite object, so far as observations have revealed them, seem to
present to us an almost absolutely plane movement. The fact that the
movements of the constituents of Saturn’s ring lie in a plane is
doubtless to be accounted for by the operation of the fundamental
dynamical principle to which we have referred. Saturn, in its great
motion round the luminary, is, of course, controlled by the sun, yet the
system attached to Saturn is so close to that globe as to be attracted
by the sun in a manner which need not here be distinguished from the
solar attraction on Saturn itself. It follows that the differential
action, so to speak, of the sun on Saturn, and on the myriad objects
which constitute its ring, may be disregarded. We are therefore
entitled, as already mentioned, to view Saturn and its system as an
isolated group, not acted upon by any forces exterior to the system. It
is therefore subject to the laws which declare that, though the energy
declines, the moment of momentum is to remain unaltered. This it is
which has apparently caused the extreme flatness of Saturn’s ring. The
energy of the rotation of that system has been expended until it might
seem that no more energy has been left than just suffices to preserve
the unalterable moment of momentum, under the most economical
conditions, so far as energy is concerned.

[Illustration: Fig. 37.—SATURN. Drawn by E. M. Antoniadi. (July 30th,
1899.)]

Let us suppose that one of the innumerable myriads of particles which
constitute the ring of Saturn were to forsake the plane in which it now
revolves, and move in an orbit inclined to the present plane. We shall
suppose that the original track of the orbit was a circle, and we shall
assume that in the new plane to which the motion is transferred the
motion is also circular. That particle will have still to do its share
of preserving the requisite total moment of momentum, for we are to
suppose that each of the other particles remains unaltered in its pace
and in the other circumstances of its motion. The aberrant particle will
describe, in a second, an area which, for the purpose of the present
calculation, must be projected upon the plane containing the other
particles. The area, when projected, must still be as large as the area
that the particle would have described if it had remained in the plane.
It is therefore necessary that the area swept over by the particle in
the inclined plane, in one second, shall be greater than the area which
sufficed in the original plane. This requires the circle in which the
particle revolves to be enlarged, and this necessitates that its energy
should be increased. In other words, while the moment of momentum was no
greater than before, the energy of the system would have to be greater.
We thus see that inasmuch as the particles forming the rings of Saturn
move in circles in the same plane, they require a smaller amount of
energy in the system to preserve the requisite moment of momentum than
would be required if they moved in circular orbits which were not in the
same plane. In such a system as Saturn’s ring, in which the particles
are excessively numerous and excessively close together, it may be
presumed that there may once have been sufficient collisions and
frictions among the particles to cause the exhaustion of energy to the
lowest point at which the moment of momentum would be sustained. In the
course of ages this has been accomplished by the remarkable adjustment
of the movements to that plane in which we now find them.

The importance of this subject is so great that we shall present the
matter in a somewhat different manner as follows: We shall simplify the
matter by regarding the orbits of the planets or other bodies as circles
The fact that these orbits are ellipses, which are, however, very nearly
circles, will not appreciably affect the argument.

Let us, then, suppose a single planet revolving round a fixed sun, in
the centre. The energy of this system has two parts. There is first the
energy due to the velocity of the planet, and this is found by taking
half the product of the mass of the planet and the square of its
velocity. The second part of the energy depends, as we have already
explained, on the distance of the planet from the sun. The planet
possesses energy on account of its situation, for the attraction of the
sun on the planet is capable of doing work. The further the planet is
from the sun the larger is the quantity of energy that it possesses from
this cause. On the other hand, the further the planet is from the sun
the smaller is its velocity, and the less is the quantity of energy that
it possesses of the first kind. We unite the two parts, and we find that
the net result may be expressed in the following manner: If a planet be
revolving in a circular path round the sun, then the total energy of
that system (apart from any rotation of the sun and planet on their
axes), when added to the reciprocal of the distance between the two
bodies, measured with a proper unit of length, is the same for all
distances of the same two bodies. This shows the connection between the
energy and the distance of the planet from the sun.

Thus we see that if the circle is enlarged the energy of the system
increases. The moment of momentum of the system is proportional to the
square root of the distance of the two bodies. If, therefore, the
distance of the two bodies is increased, the moment of momentum
increases also.

It will illustrate the application of the argument to take a particular
case in which a system of particles is revolving round a central sun in
circular orbits, all of which lie in the same plane. Let us suppose
that, while the moment of momentum of the system of particles is to
remain unaltered, one of the particles is to be shifted into a plane
which is inclined at an angle of 60° to the plane of the other orbits;
it can easily be seen that an area in the new plane, when projected down
into the original plane, will be reduced to half its amount. Hence, as
the moment of momentum of the whole system is to be kept up, it will be
necessary for the particle to have a moment of momentum in the circle
which it describes in the new plane which is double that which it had in
the original plane. It follows that the radius of the circle in the new
plane must be four times the radius of the circle which defined the
orbit of the particle in the old plane. The energy of the particle in
this orbit is therefore correspondingly greater, and thus the energy of
the whole system is increased. This illustrates how a system, in which
the circular orbits are in different planes, requires more energy for a
given moment of momentum than would suffice if the circular orbits had
all been in the same plane. So long as the orbits are in different
planes there will still remain a reserve of energy for possible
dissipation. But the dissipation is always in progress, and hence there
is an incessant tendency towards a flattening of the system by the
mutual actions of its parts.

It may help to elucidate this subject to state the matter as follows:
The more the system contracts, the faster it must generally revolve;
this is the universal law when disturbing influences are excluded. Take,
for instance, the sun, which is at this moment contracting on account of
its loss of heat. In consequence of that contraction it is essential
that the sun shall gradually turn faster round on its axis. At present
the sun requires twenty-five days, four hours and twenty-nine minutes
for each rotation. That period must certainly be diminishing, although
no doubt the rate of diminution is very slow. Indeed, it is too slow for
us to observe; nevertheless, some diminution must be in progress.
Applying the same principle to the primitive nebula, we see, that as the
contraction of the original volume proceeds, the speed with which the
several parts will rotate must increase.

The periodic times of the planets are here instructive. The materials
now forming Jupiter were situated towards the exterior of the nebula, so
that, as the nebula contracted, it tended to leave Jupiter behind. The
period in which Jupiter now revolves round the sun may give some notion
of the period of the rotation of the nebula at the time that it extended
so far as Jupiter. Subsequently to the formation, and the detachment of
Jupiter, a body which was henceforth no longer in contact with the
nebula, the latter proceeded further in its contraction. Passing over
the intermediate stages, we find the nebula contracting until it
extended no further than the line now marked by the earth’s orbit; the
speed with which the nebula was rotating must have been increasing all
the time, so that though the nebula required several years to go round
when it extended as far as Jupiter, only a fraction of that period was
necessary when it had reached the position indicated by the earth’s
track at the present time. Leaving the earth behind it, just as it had
previously left Jupiter, the nebula started on a still further
condensation. It drew in, until at last it reached a further stage by
contraction into the sun, which rotates in less than a month. Thus the
period of Jupiter namely, twelve years, the period of the earth, namely,
one year, and the period of the sun, namely, twenty-five days,
illustrate the successive accelerations of the rotation of the nebula in
the process of contraction. No doubt these statements must be received
with much qualification, but they will illustrate the nature of the
argument.

We may also here mention the satellites of Uranus, all the more so
because it has been frequently urged as an objection to the nebular
theory that the orbits of the satellites of Uranus lie in a plane which
is inclined at a very large angle; no less than 82° to the general plane
of the solar system. I shall refer in a later chapter to this subject,
and consider what explanation can be offered with regard to the great
inclination of this plane, which is one of the anomalies of our system.
For the present I merely draw attention to the fact that the movements
of all four satellites of Uranus do actually lie in the same plane,
though, as already indicated, it stands nearly at right angles to the
ecliptic.

Professor Newcomb has shown that the four satellites of Uranus revolve
in orbits which are almost exactly circular, and which, so far as
observation shows, are absolutely in the same plane. From our present
point of view this is a matter of much interest. Whatever may have been
the influence by which this plane departs so widely from the plane of
the ecliptic, it seems certain that it must be regarded as having acted
at a very early period in the evolution of the Uranian system; and when
this system had once started on its course of evolution, the operation
of that dynamical principle to which we have so often referred was
gradually brought to bear on the orbits of the satellites. We have here
another isolated case resembling that of Saturn and its rings. The
fundamental law ordained that the moment of momentum of Uranus and its
moons must remain constant, though the total quantity of energy in that
system should decline. In the course of ages this has led to the
adjustment of the orbits of the four satellites into the same plane.

I ought here to mention that the rotation of Uranus on its axis presents
a problem which has not yet been solved by telescopic observation. It is
extremely interesting to note that, as a rule, the axes on which the
important planets rotate are inclined at no great angles to the
principal plane of the solar system. The great distance of Uranus has,
however, prevented astronomers from studying the rotation of that planet
in the ordinary manner, by observation of the displacement of marks on
its surface. So far as telescopic observations are concerned, we are
therefore in ignorance as to the axis about which Uranus revolves. If,
following the analogy of Jupiter, or Saturn, or Mars, or the earth, the
rotation of Uranus was conducted about an axis, not greatly inclined
from the perpendicular to the ecliptic, then the rotation of Uranus
would be about an axis very far from perpendicular to the plane in which
its satellites revolve. The analogy of the other planets seems to
suggest that the rotation of a planet should be nearly perpendicular to
the plane in which its satellites revolve. As the question is one which
does not admit of being decided by observation, we may venture to remark
that the necessity for a declining ratio of energy to moment of momentum
in the Uranian system provides a suggestion. The moment of momentum of a
system, such as that of Uranus and its satellites, is derived partly
from the movements of the satellites and partly from the rotation of the
planet itself. From the illustrations we have already given, it is plain
that the requisite moment of momentum is compatible with a comparatively
small energy only when the system is so adjusted that the axis of
rotation of the planet is perpendicular to the plane in which the
satellites revolve, or in other words when the satellites revolve in the
plane of the equator of the planet. We do not expect that this condition
will be complied with to the fullest extent in any members of the solar
system. There is indeed an obvious exception; for the moon, in its
revolution about the earth, does not revolve exactly in the earth’s
equator. We might, however, expect that the tendency would be for the
movements to adjust themselves in this manner. It seems therefore likely
that the direction of the axis of Uranus is perpendicular, or nearly so,
to the plane of the movements of its satellites.

At this point we take occasion to answer an objection which may perhaps
be urged against the doctrine of moment of momentum as here applied. I
have shown that the tendency of this dynamical principle is to reduce
the movements towards one plane. It may be objected that if there is
this tendency, why is it that the movements have not all been brought
into the same plane exactly? This has been accomplished in the case of
the bodies forming Saturn’s ring, and perhaps in the satellites of
Uranus. But why is it that all the great planets of our solar system
have not been brought to revolve absolutely in the same plane?

We answer that the operations of the forces by which this adjustment is
effected are necessarily extremely slow. The process is still going on,
and it may ultimately reach completion. But it is to be particularly
observed that the nearer the approach is made to the final adjustment,
the slower must be the process of adjustment, and the less efficient are
the forces tending to bring it about. For the purpose of illustrating
this, we may estimate the efficiency of the forces in flattening down
the system in the following manner. Suppose that there are two circular
orbits at right angles to each other, and that we measure the efficiency
of the action tending to bring the planes to coincide by 100. When the
planes are at an angle of thirty degrees the efficiency is represented
by 50, and when the inclination is only five degrees the efficiency is
no more than 9, and the efficiency gradually lessens as the angle
declines. As the angles of inclination of the planes in the solar system
are so small, we see that the efficiency of the flattening operation in
the solar system must have dwindled correspondingly. Hence we need not
be surprised that the final reduction of the orbits into the same plane
has not yet been absolutely completed.

Certainly the most numerous, and perhaps the grandest, illustrations of
the operation of the great natural principles we have been considering
are to be found in the case of the spiral nebulæ. The characteristic
appearance of these objects demands special explanation, and it is to
dynamics we must look for that explanation.

As to the original cause of a nebula we shall have something to say in a
future chapter. At present we are only considering how, when a nebula
has come into existence, the action of known dynamical principles will
mould that nebula into form. As an illustration of a nebula, in what we
may describe as its comparatively primitive shape, we may take the Great
Nebula in Orion. This stupendous mass of vaguely diffused vapour may
probably be regarded as in an early stage when contrasted with the
spirals. We have already shown how the spectroscopic evidence
demonstrates that the famous nebula is actually a gaseous object. It
stands thus in marked contrast with many other nebulæ which, by not
yielding a gaseous spectrum, seem to inform us that they are objects
which have advanced to a further stage in their development than such
masses of mere glowing gas as are found in the splendid object in Orion.

The development of a nebula must from dynamical principles proceed along
the lines that we have already indicated. We shall assume that the
nebula is sufficiently isolated from surrounding objects in space as to
be practically free from disturbing influences produced by these
objects. We shall therefore suppose that the evolution of the nebula
proceeds solely in consequence of the mutual attractions of its various
parts. In its original formation the nebula receives a certain endowment
of energy and a certain endowment of moment of momentum; the mere fact
that we see the nebula, the fact that it radiates light, shows that it
must be expending energy, and the decline of the energy will proceed
continuously from the formation of the object. The laws of dynamics
assure us that no matter what may be the losses of energy which the
nebula suffers through radiation or through the collisions of its
particles, or through their tidal actions, or in any way whatever from
their mutual actions, the moment of momentum must remain unchanged.

As the ages roll by, the nebula must gradually come to dispose itself,
so that the moment of momentum shall be maintained, notwithstanding that
the energy may have wasted away to no more than a fraction of its
original amount. Originally there was, of course, one plane, in which
the moment of momentum was a maximum. It is what we have called the
principal plane of the system, and the evolution tends in the direction
of making the nebula gradually settle down towards this plane. We have
seen that the moment of momentum can be sustained with the utmost
economy of energy by adjusting the movements of the particles so that
they all take place in orbits parallel to this plane, and the mutual
attractions of the several parts will gradually tend to bring the planes
of the different orbits into coincidence. Every collision between two
atoms, every ray of light sent forth, conduce to the final result. Hence
it is that the nebula gradually tends to the form of a flat plane. This
is the first point to be noticed in the formation of a spiral nebula.

But there is a further consideration. As the nebula radiates its light
and its heat, and thus loses its energy, it must be undergoing continual
contraction. Concurrently with its gradual assumption of a flat form,
the nebula is also becoming smaller. Here again that fundamental
conception of the conservation of moment of momentum will give us
important information. If the nebula contracts, that is to say, if each
of its particles draws in closer to the centre, the orbits of each of
its particles will be reduced. But the quantity of areas to be described
each second must be kept up. We have pointed out that it is infinitely
improbable the system should have been started without any moment of
momentum, and this condition of affairs being infinitely improbable, we
dismiss any thought of its occurrence. As the particles settle towards
the plane, the areas swept out by the movements to the right, and those
areas swept out by the movements to the left, will not be identical;
there will therefore be a balance on one side, and that balance must be
maintained without the slightest alteration throughout all time. As the
particles get closer together, and as their orbits lessen, it will
necessarily happen that the velocities of the particles must increase,
for not otherwise can the fundamental principle of the constant moment
of momentum be maintained. And as the system gets smaller and smaller,
by contraction from an original widely diffused nebulosity, like,
perhaps, the nebula in Orion, down to a spiral nebula which may occupy
not a thousandth or a millionth part of the original volume, the areas
will be kept up by currents of particles moving in the two opposite ways
around a central point. As the contraction proceeds, the opposing
particles will occasionally collide, and consequently the tendency will
be for the predominant side to assert itself more and more, until at
last we may expect a condition to be reached in which all the movements
will take place in one direction, and when the sum of the areas
described in a second, by each of the particles, multiplied by their
respective masses, will represent the original endowment of moment of
momentum. Thus we find that the whole object becomes ultimately
possessed of a movement of rotation.

The same argument will show that the inner parts of the nebula will
revolve more rapidly than those in the exterior. Thus we find the
whirlpool structure produced, and thus we obtain an explanation, not
only of the flatness of the nebula, but also of the spiral form which it
possesses. It is not too much to say that the operation of the causes we
have specified, if external influence be withheld, tends ultimately to
produce the spiral, whatever may have been the original form of the
object. No longer, therefore, need we feel any hesitation in believing
the assurance of Professor Keeler that out of the one hundred and twenty
thousand nebulæ, at least one-half must be spirals. We have found in
dynamics an explanation of that remarkable type of object which we have
now reason to think is one of the great fundamental forms of nature.

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CHAPTER XII.

THE EVOLUTION OF THE SOLAR SYSTEM.

The Primæval Nebula—A Planetary Nebula—The Progress of its
Evolution—Unsymmetrical Contraction—Centres of Condensation—The Form
ultimately assumed—Difference between Small Bodies and Large—Earth
and Sun—Acceleration of Velocities—Formation of the Subordinate
Systems—Special Circumstances in the case of the Earth and Moon—Vast
Scale of the Spirals—Spectra of the Spiral Nebulæ.

WE shall consider in this chapter what we believe to have been the
history of that splendid system, formed by the planets under the
presiding control of the sun. The ground over which we have already
passed will prepare us for the famous doctrine that the sun, the planets
and their satellites, together with the other bodies which form the
group we call the solar system, have originated from the contraction of
a primæval nebula.

As the ages rolled by, this great primæval nebula began to undergo
modification. In accordance with the universal law which we find obeyed
in our laboratories, and which we have reason to believe must be equally
obeyed throughout the whole extent of space, this nebula, if warmer than
the surrounding space, must begin to radiate forth its heat. We are to
assume that the nebula does not receive heat from other bodies, adequate
to compensate for that which it dissipates by radiation. There is thus a
loss of heat and consequently the nebula must begin to contract. Its
material must gradually draw together, and must do so under the
operation of those fundamental laws which we have explained in the last
chapter.

The contraction, or rather the condensation, of the material would of
course generally be greatest at the central portion of the nebula. This
is especially noticeable in the photograph of the great spiral already
referred to. But in addition to this special condensation at the centre,
the concentration takes place also, though in a lesser degree, at many
other points throughout the whole extent of the glowing mass. Each
centre of condensation which in this way becomes established tends
continually to increase. In consequence of this law, as the great nebula
contracted and as the great bulk of the material drew in towards the
centre, there were isolated regions in the nebula which became
subordinate centres of condensation. Perhaps in the primæval nebula,
from which the solar system originated, there were half-a-dozen or more
of these centres that were of conspicuous importance, while a much
larger number of small points were also distinguished from the
surrounding nebula. (Figs. 40 and 41.) And still the contraction went
on. The heat, or rather the energy with which the nebula had been
originally charged, was still being dissipated by radiation. We give no
estimate of the myriads of years that each stage of the mighty process
must have occupied. The tendency of the transformation was, however,
always in one direction. It did at last result in a great increase of
the density of the substance of the nebula, both in the central regions
as well as in the subordinate parts. In due time this increase in
density had reached such a point that the materials in the condensing
centres could be no longer described as retaining the gaseous form.

But though heat was incessantly being radiated from the great nebula, it
did not necessarily follow that the nebula was itself losing
temperature. This is a seeming paradox to which we have already had
occasion to refer in Chapter VI. We need not now further refer to it
than to remember that, in speaking of the loss of heat from the nebula,
it would sometimes not be correct to describe the operation as that of
cooling. Up to a certain stage in the condensation, the loss of heat
leads rather to an augmentation of temperature than to its decline.

We are thus led to see how the laws of heat, after being in action on
the primitive nebula for a period of illimitable ages, have at last
effected a marvellous transformation. That nebula has condensed into a
vast central mass with a number of associated subordinate portions. We
may suppose that the original nebula in the course of time does
practically disappear. It is absorbed by the attraction of those
ponderous centres which have gradually developed throughout its extent.

The large central body, and perhaps some of the other bodies thus
evolved, are at first of so high a temperature that a copious radiation
of heat still goes forth from the system. As they discharge their stores
of heat, the smaller bodies show the effects of loss of heat more
rapidly than those which are larger. It is indeed obvious that a small
body must cool more rapidly than a big one. It is sufficient to note
that the cooling takes place from the surface, and that the bigger the
body the larger the quantity of material that it contains for each unit
of superficial area. If the radius of a sphere be doubled, its volume is
increased eightfold, while its surface is only increased fourfold.

[Illustration: Fig. 38.—THE RING NEBULA IN LYRA (Lick Observatory).
(_From the Royal Astronomical Society Series._)]

Let us now concentrate our attention on two of the bodies which, after
immense ages, have been formed from the condensation of the primæval
nebula. Let one of the two bodies be that central object, which
preponderates so enormously that its mass is a thousandfold that of all
the others taken together. Let the other be one of the smaller bodies.
As it parts with its heat, the smaller body, which has originally
condensed from the nebula, will assume some of the features of a mass of
molten liquid. From the liquid condition, the body will pass with
comparative rapidity into a solid state, at least on its outer parts.
The exterior of this body will therefore become solid while the interior
is still at an excessively high temperature. The outer material, which
has assumed the solid form, is constituted of the elements with which we
are acquainted, and is in the form of what the geologist would class as
the igneous rocks, of which granite is the best known example. The shell
of hard rocks outside encloses the material which is still heated and
molten inside. Such a crust would certainly be an extremely bad
conductor of heat. The internal heat is therefore greatly obstructed in
its passage outwards to the surface. The internal heat may consequently
be preserved in the interior of the body for an enormously protracted
period, a period perhaps comparable with those immense ages which the
evolution of the body from the primæval nebula has demanded. The smaller
body may have thus attained a condition in which the temperature
reigning on its surface is regulated chiefly by the external conditions
of the space around, while the internal parts are still highly charged
with the primitive heat from the original nebula.

The great central mass, which we may regard as thousands of times
greater than that of the subordinate body, cools much more slowly. The
cooling of this great mass is so enormously protracted in comparison
with that of the smaller body that it is quite conceivable the central
mass may continue to glow with intense fervour for immense ages after
the smaller body has become covered with hard rock.

It will, I hope, be clear that the two bodies to which I am here
alluding are not merely imaginary objects. The small body, which has so
far cooled down that its surface has lost all indication of internal
heat, is of course our earth. The great central mass which still glows
with intense fervour is the sun. Such is in outline the origin of the
sun and the earth as suggested by the nebular theory.

What we have said of the formation of the earth will equally apply to
the evolution of other detached portions of the primitive nebula. There
may be several of these, and they may vary greatly in size. The smaller
they are the more rapidly in general will the superabundant heat be
radiated away, and the sooner will the surface of that planet acquire
the temperature which is determined by the surrounding conditions. There
are, however, many modifying circumstances.

It is essential to notice that the primæval nebula must have had some
initial moment of momentum, unless we are to assume the occurrence of
that which is infinitely improbable. It would have been infinitely
improbable for the system not to have had some moment of momentum
originally. As the evolution proceeds, and as the energy is expended,
while this original endowment of moment of momentum is preserved, we
find, as explained in the last chapter, the system gradually settling
down into proximity to a plane, and gradually acquiring a uniform
direction of revolution. Hence we see that each of the subordinate
masses which ultimately consolidate to form a planet have a motion of
revolution around the central body. In like manner the central body
itself rotates, and all these motions are performed in the same
direction.

In addition to the revolutions of the planets around the sun, there are
other motions which can be accounted for as consequences of the
contraction of the nebula. We now refer to that central portion which is
to form the sun, and consider, in the first instance, only one of the
subordinate portions which is to form a planet. As these two bodies form
part of the same nebulous mass they will to a certain extent rotate
together as one piece. If any body is rotating as a whole, every part of
that body is also in actual rotation. We shall refer to this again later
on; but for the present it is sufficient to observe that as the planet
was originally continuous with the sun, it had a motion of rotation
besides its motion of revolution, and it revolved round its own axis in
a period equal to that of its revolution round the sun. In the beginning
the rotation of the planet was therefore an exceedingly slow movement.
But it became subsequently accelerated. For we have already explained
that each planet is by itself subjected to the law of the conservation
of moment of momentum. As each planet assumes a separate existence, it
draws to itself its share of the moment of momentum, and that must be
strictly preserved. But the planet, or rather the materials which are to
form the future planet, are all the time shrinking; they are drawing
more closely together. If, therefore, the area which each particle of
the planet describes when multiplied by the mass of that particle and
added to the similar products arising from all the other particles, is
to remain constant, it becomes necessary that just as the orbits of
these particles diminish in size, so must the speed at which they
revolve increase. We thus find that there is a tendency in the planet to
accelerate its rotation. And thus we see that a time will come when the
planet, having assumed an independent existence, will be found rotating
round its axis with a velocity which must be considered high in
comparison with the angular velocity which the planet had while it still
formed part of the original nebula.

As the planets have been evolved so as to describe their several orbits
around the sun, so in like manner the smaller systems of satellites have
been so evolved as to describe their orbits round the several planets
that are their respective primaries. When a planet, or rather the
materials which were drawing together to form a planet, had acquired a
predominant attraction for the parts of the primæval nebula in their
locality, a portion of the nebulous material became specially associated
with the planet. As the planet with this nebulous material became
separated from the central contracting sun, or became, as it were, left
behind while the sun was drawing into itself the material which
surrounded it the planet and its associated nebula underwent on a
miniature scale an evolution similar to that which had already taken
place in the formation of the sun and the planets as a whole. In this
manner secondary systems seem sometimes to have had their origin.

We should, however, say that though what we have here indicated appears
to explain fully the evolution of some of the systems, such, for
instance, as that of Jupiter and his four moons, or Saturn and his eight
or nine, the circumstances with regard to the earth and the moon are
such as to require a very different explanation of the origin of our
satellite. In the first place we may notice that the great mass of the
moon, in comparison with the earth, is a wholly exceptional feature in
the relations between the planets and their satellites in the other
parts of the system. In no other instance does the mass of a satellite
bear to the mass of the planet a ratio anything like so great as the
ratio of our moon to the earth. The moon has a mass which is about
one-eightieth of the mass of the earth, while even the largest of
Jupiter’s satellites has not one ten-thousandth part of the mass of the
planet itself. The evolution of the earth and moon system has been
brought about in a manner very different from that of the evolution of
the other systems of satellites. We do not here enter into any
discussion of the matter. We merely remind the reader that it is now
known, mainly by the researches of Professor G. H. Darwin, that in all
probability the moon was originally part of the earth, and that a
partition having occurred while the materials of the earth and moon were
still in a plastic state, a small portion broke away to form the moon,
leaving behind the greater mass to form the earth. Then, under the
influence of tides, which may agitate a mass of molten rock, as the moon
was once (Fig. 39), just as they may agitate an ocean, the moon was
forced away, and was ultimately conducted to its present orbit.

[Illustration: Fig. 39.—LUNAR CRATERS: HYGINUS AND ALBATEGNIUS.
(_Photographed by MM. Loewy and Puiseux._)]

It was at first tempting to imagine that a theory which accounted so
satisfactorily for the evolution of the moon from the earth might also
account in a similar manner for the evolution of the earth from the sun.
Had this been the case, it is needless to say that the principles we now
accept in the nebular theory would have needed large modification, if
not actual abandonment. A close examination into the actual statistics
brings forcibly before us the exceptional character of the earth-moon
system. It can be demonstrated that the earth could not have been
evolved from the sun in the same manner as there is every reason to
believe that the moon has been evolved from the earth. The evolution of
the satellites of Jupiter has proceeded along lines quite different from
those of the evolution of the moon from the earth, so that we may,
perhaps, find in the evolution of the satellites of Jupiter an
illustration in miniature of the way in which the planets themselves
have been evolved in relation to the sun.

We must not forget that the only spiral nebulæ which lie within the
reach of our powers of observation, whether telescopic or photographic,
appear to be objects of enormously greater cosmical magnificence than
was that primæval nebula from which so insignificant an object as the
solar system has sprung. The great spirals, so far as we can tell at
present, appear to be thousands of times, or even millions of times,
greater in area than the solar system. At this point, however, we must
speak with special caution, having due regard to the paucity of our
knowledge of a most important element. Astronomers must confess that no
efforts which have yet been made to determine the dimensions of a nebula
have been crowned with success. We have not any precise idea as to what
the distance of the great spiral might be. We generally take for granted
that these nebulæ are at distances comparable with the distances of the
stars. On this assumption we estimate that the spiral nebulæ must
transcend enormously the dimensions of the primæval nebula from which
the solar system has sprung. The spiral nebulæ that have so far come
within our observation seem to be objects of an order of magnitude
altogether higher than a solar system. They seem to be engaged on the
majestic function of evolving systems of stars like the Milky Way,
rather than on the inconsiderable task of producing a system which
concerns only a single star and not a galaxy.

[Illustration: Fig. 40.—A REMARKABLE SPIRAL (n.g.c. 628; in Pisces).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]

The spiral form of structure is one in which Nature seems to delight. We
find it in the organic world allied with objects of the greatest
interest and beauty. The ammonite, a magnificent spiral shell sometimes
exceeding three feet in diameter, belongs to a type which dominated the
waters of the globe in secondary times, and which still survives in the
nautilus. The same form is reproduced in minute creations totally
different from ammonites in their zoological relations. Among the
exquisite foraminifera which the microscopist knows so well may be found
most delicate and beautiful spirals. Just as we see every range of
spiral in the animal world, from an organism invisible to the naked eye,
up to an ammonite a yard or more across, so it would seem that there are
spiral nebulæ ranging from such vast objects as the great spiral in
Canes Venatici down to such relatively minute spirals as those whose
humble function it is to develop a solar system. It is no more than a
reasonable supposition that the great spirals in the heavens are
probably only the more majestic objects of an extremely numerous class.
The smaller objects of this type—among which we might expect to find
nebulæ like, in size and importance, to the primæval nebula of our
system—are so small that they have not yet been recognised.

It should at this stage be mentioned that several curious small
planetary nebulæ have in these modern days been discovered by their
peculiar spectra. If the nebulous character of these most interesting
objects had not been accidentally disclosed by characteristic lines in
their spectra, these undoubted nebulæ would each have been classified
merely as stars. This fact will lead us to the surmise that there must
be myriads of nebulæ in the heavens, too small to come within the range
of our telescopes or of our most sensitive photographic plates. Suppose
that a facsimile of the primæval nebula of our system, precisely
corresponding with it in size and identical with it in every detail,
were at the present moment located in space, but at a distance from our
standpoint, as great as the distance of, let us say, the great spiral;
it seems certain that this nebula, even though it contained the
materials for a huge sun and a potential system of mighty planets, if
not actually invisible to us here, would in all probability demand the
best powers of our instruments to reveal it, and then it would be
classed not as a nebula at all but as a star of perhaps the 12th or
15th, or even smaller magnitude.

[Illustration: Fig. 41.—A CLEARLY CUT SPIRAL (n.g.c. 4321; in Coma
Berenices).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]

It is to be remembered that the class of minute planetary nebulæ make
themselves known solely by the fact that they exhibit the bright line
indicative of gaseous spectra. If these objects (though still nebulæ)
had not displayed gaseous spectra, it is certain they would have escaped
detection, at least by the process which has actually proved so
successful. The continuous band of light which they would then have
presented could not be discriminated from the band of light from a star.
It is therefore not improbable that among the star-like bodies which
have been represented on our photographs, there may be some which are
really minute spiral nebulæ. In general a star is a minute point of
light which no augmentation of telescopic power and no magnification
will show otherwise than as a point, granted only good optical
conditions and good opportunity so far as the atmosphere is concerned.
It has, however, been occasionally noted that certain so-called stars
are not mere points of light; they do possess what is described as a
disc. It is not at all impossible that the objects so referred to are
spiral nebulæ. We may describe them as formed on a small scale in
comparison with the great spiral or the nebula in Andromeda. But the
smallness here referred to is only relative. They are in all probability
quite as vast as the primæval spiral nebula from which the solar system
has been evolved, though not so large as those curious ring-shaped
nebulæ of which the most celebrated example lies in the constellation
Lyra (Fig. 38).

Such is an outline of what we believe to have been the history of our
solar system. We have already given the evidence derived from the laws
of heat. We have now to consider the evidence which has been derived
from the constitution of the system itself. We shall see how strongly it
supports the belief that the origin of sun and planets has been such as
the nebular theory suggests.

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CHAPTER XIII.

THE UNITY OF MATERIAL IN THE HEAVENS AND THE EARTH.

Clouds—Fire-Mist—Vapour of Platinum—Components of Chalk—Constituents of
the Primæval Fire-Mist—Objections—Origin of the Mist—Remarkable
Discovery of the Century—Analysis of the Sun—Spectroscopic
Analysis—Simplicity of Solar Chemistry—Potassium—A Drop of Water—The
Solar Elements—Calcium—The Most Important Lines in the Solar
Spectrum—Photograph of the Sun—Carbon in the Solar Clouds—Function
of Carbon—Bunsen’s Burner Illustrates Carbon in the Sun—Carbon
Vapours in the Sun—The Supposed Limit to our Knowledge of the
Heavens—Characteristics of Spectroscopic Work—Bearing on the Nebular
Theory.

IN considering how the formation of our solar system was brought about,
we naturally first enquire as to the material of which this superb
scheme is constructed. What were the materials already to hand from
which, in pursuance of the laws of Nature, the solar system was evolved?

See the robust and solid nature of this earth of ours, and the robust
and solid nature of the moon and the planets. It might at first sight be
concluded that the primitive materials of our earth had also been in the
solid state. But such is not the case. The primitive material of the
solar system was not solid, it was not even liquid. What we may describe
as the mother-substance of the universe must have been of quite a
different nature; we can give an illustration of the physical character
of that substance.

The lover of Nature delights to look at the mountains and the trees, the
lakes and the rivers. But he will not confine his regard merely to the
objects on the earth’s surface. He, no less than the artist and the
poet, delights to gaze at that enchanting scenery which, day by day, is
displayed in infinite beauty overhead; that scenery which is not wholly
withheld even from observers whose lives may be passed amid the busy
haunts of men, that scenery which is so often displayed on fine days at
all seasons. We are alluding to those clouds which add the charm of
infinite variety to the sky above us.

It is necessary for us now to think of matter when it possesses neither
the density of a solid, nor the qualities of a liquid, but rather when
it has that delicate texture which the clouds exhibit. The primæval
material from which the solar system has been evolved is of a texture
somewhat similar to that of the clouds. This primæval material is
neither solid nor liquid; it is what we may describe as vapour.

But having pointed to the clouds in our own sky as illustrating, in a
sense, the texture of this original mother-substance of the solar
system, we can carry the analogy no further. Those dark and threatening
masses which forbode the thunderstorm, or those beautiful fleecy clouds
which enhance the loveliness of a summer’s day, are, of course, merely
the vapours of water. But the vapours in the mother-substance from which
systems have been evolved were by no means the vapours of water. They
were vapours of a very different character—vapours that suggest the
abodes of Pluto rather than the gentle rain that blesses the earth. In
the mother-substance of the solar system vapours of a great variety of
substances were blended. For in the potent laboratory of Nature every
substance, be it a metal or any other element, or any compound, no
matter how refractory, will, under suitable circumstances, be dissolved
into vapour.

Take, for instance, such a material as platinum. Could anything be less
like a vapour than this silvery metal? We know that platinum is the
densest of all the elements. We know that platinum, more effectually
than other metals, resists liquefaction from the application of heat. No
ordinary furnace can fuse platinum; yet in another way we can overcome
the resistance of this metal. The electric arc, when suitably managed,
yields a temperature higher than that of any furnace. Let the electric
current spring from one pole of platinum to another, and a brilliant arc
of light is produced by the glowing gas, which is characteristic of
platinum. The light dispensed from that arc is different from the light
that would be radiated if the poles were of any material other than
platinum. Some of the platinum has not alone been melted, it has
actually been turned into vapour by the overpowering heat to which it
has been subjected. Thus the solidity of this substance, which resists
so stubbornly the action of lower temperatures, can be overcome, and the
very densest of all metals is dissolved into wisps of vapour.

We choose the case of platinum as an illustration because it is a
substance exceptionally dense and exceptionally refractory. If platinum
can be vaporised, there is not much difficulty in seeing that other
elements must be capable of being vaporised also. In fact, given such
heat as is found abundantly in natural sources, there is no known
element, or combination of elements, which will not assume the form of
gas or vapour or cloud.

At the temperature of the sun a drop of water would be forthwith
resolved into its component gases of oxygen and hydrogen. In like manner
a piece of chalk, if exposed to the sun, would be speedily transformed;
it would first be heated red-hot and then white-hot; it is, indeed,
white-hot chalk that gives us that limelight which we know so well. But
the heat of the sun is far greater than the temperature of the
incandescent lime. The lime would not only be heated white-hot by
contact with solar heat, but still further stages would be reached. It
would suffer decomposition. It would break up into three different
elements: there would be the metal which we call calcium, there would be
oxygen, and there would be carbon. Owing to the tremendous temperature
of the sun the metal would not remain in the metallic form; it would not
be even in a liquid form; it would become a gas. The elements which
unite to form this chalk would be not only decomposed, but they would be
vaporised. What is thus stated about the drop of water and the chalk
may, so far as we know, be stated equally with regard to any other
compounds. It matters not how close may be the chemical association in
which the elements are joined: no matter how successfully those
compounds may resist the decomposition under the conditions ordinarily
prevailing on earth, they have to yield under the overwhelming trial to
which the sun would subject them. Though there are many elements in the
solar chemistry, there are no compounds. At the exalted temperature to
which they are exposed in the sun the elements are indisposed for union
with the other elements there met with, and which are at the same
temperature. In these circumstances, they successfully resist all
alliances.

Until the last few years no elements were known in our terrestrial
experience which possessed at ordinary temperatures the same qualities
of resolute isolation which all elements seem to display at extreme
temperatures. The famous discovery of argon, and of other strange gases
associated with argon in the atmosphere and elsewhere, has revealed, to
the astonishment of chemists and to the great extension of knowledge,
that we have with us here elements which resist all solicitations to
enter into chemical union with other substances. It is doubtless in
consequence of this absolute refusal to unite that, in spite of their
abundance and their wide distribution, these elements have eluded
detection for centuries. To the astronomer argon is both interesting and
instructive. It shows us an element which possesses, at the ordinary
temperatures of the surface of the earth, a property which is true of
all elements when subjected to such temperatures as are found in the
sun.

Think of the rocks which form the earth’s crust and of the minerals
which lie far below. Think of the soil which lies on its surface, of the
forests which that soil supports, and the crops which it brings forth.
Think of the waters of the ocean, and the ice of the Poles. Think of the
objects of every kind on this globe. Think of the stone walls of a great
building, of the iron used to give it strength, of the slates which
cover it, and of the timber which forms its floors; think of the
innumerable other materials which have gone towards its construction;
think even of the elementary substances which go to form the bodies of
animals, of the lime in their bones, and of the carbon which is so
intimately associated with life itself. The nebular theory declares that
those materials have not always been in the condition in which we now
see them; that there was a time in which they were so hot that they were
not in the solid state; they were not even in the fluid state, but were
all in rolling volumes of glowing vapour which formed the great primæval
fire-cloud.

We must understand the composite nature of the primitive fire-mist from
which our solar system originated. Let me illustrate the matter thus: We
shall suppose that a heterogeneous collection of substances is brought
together, the items of which may be somewhat as follows: let there be
many tons of iron and barrels of lime, some pieces of timber, and
cargoes of flint; let there be lead and tin and zinc, and many other
metals, from which copper and silver and several of the rarest metals
must not be excluded; let there be innumerable loads of clay, which
shall represent aluminium and silicon, and hogsheads of sea-water to
supply oxygen, hydrogen, and sodium. There should be also, I need hardly
add, many other elements; but there is no occasion to mention more;
indeed, it would be impossible to give a list which would be complete.

Suppose that this diverse material is submitted to a heat as intense as
the most perfect furnace can make it. Let the heat be indeed as great as
that which we can get from the electric arc, or even greater still. Let
us suppose this heat to be raised to such a point that, not only have
the most refractory metals been transformed into vapour, but the
elements which were closely in combination have also been rent asunder.
This we know will happen when compound substances are raised to a very
high temperature. We shall suppose that the heat has been sufficient to
separate each particle of water into its constituent atoms of oxygen and
hydrogen; we shall suppose that the heat has been sufficient to
decompose even lime itself into its constituent parts, and exhibit them
in the form of vapour. The heat is to be so great that even carbon
itself, the most refractory of substances, has had to yield, so that
after passing through a stage of dazzling incandescence it has melted
and ultimately dissolved into vapour. Next let us suppose that these
several vapours are blended, though we need not assume that the separate
elements are diffused uniformly throughout all parts of the cloud. Let
us suppose that these bodies, which contributed to form the nebula, have
been employed in amounts, not to be measured in tons, or in hundreds of
tons, but in a thousand millions of millions of millions of millions of
tons. Let the mass of vapour thus arising be expanded freely through
open space. Let it extend over a region which is to measure hundreds of
thousands of millions of miles in length and breadth and depth. Then the
doctrine of the earth’s beginning, which we are striving to unfold in
these lectures, declares that in a fire-mist such as is here outlined
the solar system had its origin.

Various objections may occur to the thoughtful reader when asked to
accept such statements. We must do our best to meet these objections.
The evidence we submit must be of an indirect or circumstantial kind.
Direct testimony on such a subject is from the nature of the case
impossible. The actual fire-mist in which our system had its origin is a
mist no longer. The material that forms the solid earth beneath our feet
did once, we verily believe, float in the great primæval fire-mist. Of
course we cannot show you that mist. Darwin could not show the original
monkeys from which it would seem the human race has descended; none the
less do most of us believe that our descent has really taken the line
that Darwin’s theory indicates.

In connection with this subject, as with most others, it is easy to ask
questions which, I think we may say, no one can answer with any
confidence. It may, for instance, be asked how this vast fire-mist came
into existence. If it arose from heat, how did that heat happen to be
present? Why was all the material in the state of vapour? What, in
short, was the origin of that great primæval nebula? Here we must admit
that we have proposed questions to which it is impossible for us to do
more than suggest answers. As to what brought the mist into existence,
as to whence the materials came, and as to whence the energy was derived
which has been gradually expended ever since, we do not know anything,
and, so far as I can see, we have no means of knowing. Conjectures on
the subject are not wanting, of course, and in a later chapter we shall
discuss what may be said on this matter.

I have shown you to some extent our reasons for believing that our solar
system did originate in a fire-mist And even if we are not able to
explain how the mist itself arose, yet we do not admit that our argument
as to the origin of our system is thereby invalidated. That such a
fire-mist as the solar system required did once exist, must surely be
regarded as not at all improbable so long as we can point to the
analogous nebulæ or fire-mists which exist at the present moment, and
which we see with our telescopes. Many of these are millions of times as
great as the comparatively small fire-mist that would have evolved into
our solar system.

A question has sometimes been asked as to the most important discovery
in astronomy which has been made in the century that has just closed.
If, by the most important discovery, we mean that which has most widely
extended our knowledge of the Universe, I do not think there need be
much hesitation in stating the answer. It seems to me beyond doubt that
the most astonishing discovery of the last century in regard to the
heavenly bodies is that which has revealed the elementary substances of
which the orbs of heaven are composed. This discovery is the more
interesting and instructive because it has taught us that the materials
of the sun, of the stars, and of the nebulæ are essentially the elements
of which our own earth is formed, and with which chemists had already
become well acquainted.

We know, of course, that this earth, no matter how various may be the
rocks and minerals which form its crust, and how infinite the variety of
objects, organic and inorganic, which diversify its surface, is really
formed from different combinations of about eighty different elements.
There are gases like oxygen and hydrogen, there are other substances
like carbon and sulphur, and there are metals like iron and copper.
These elements are sometimes met with in their free or uncombined state,
like oxygen in the atmosphere, or like gold in Klondike. More frequently
they are found in combination, and in such combinations the characters
of the constituent elements are sometimes completely transformed. A
deadly gas and a curious metal, which burns as it floats on water, most
certainly renounce their special characters when they unite to form the
salt on our breakfast-table. Who would have guessed, if the chemist had
not told him, that in every wheelbarrowful of ordinary earth there are
pounds of silvery aluminium, and that marble is largely composed of an
extremely rare metal, which but few people have ever seen?

Until the middle of the century just completed it seemed utterly
impossible to form any notion as to the substances actually present in
the sun. How could anyone possibly discern them by the resources of the
older chemists? It might well have been doubted whether the elements of
which the sun was made were the elements of which our earth was formed,
and with which ordinary chemistry had made us familiar. Just as the
animals and plants which met the gaze of the discoverers when they
landed in the New World were essentially different from those in the Old
World, so it might have been supposed, with good share of reason, that
this great solar orb, ninety-three million miles distant, would be
composed of elements totally different from those with which dwellers on
the earth had been permitted to become acquainted.

This great discovery of the last century revealed to us the character of
the elements which constitute the sun. It also added the astonishing
information that they are essentially the same elements as those of
which our earth itself and all which it contains are formed.

If any one had asked in the early years of the century what those
elements were which entered into the composition of the sun, the
question would have been deemed a silly one; it would have been regarded
as hopelessly beyond the possibility of solution, and it would have been
as little likely to receive an answer as the questions people sometimes
ask now as to the possible inhabitants on Mars.

But about the middle of the century a new era dawned; the wonderful
method of spectroscopic analysis was discovered, and it became possible
to examine the chemistry of the sun. The most important result was to
show that the elements which enter into the composition of the sun are
the same elements which enter into the composition of the earth. The
student of the solar chemistry enjoys, however, one advantage over the
terrestrial chemist, if it be an advantage to have his science
simplified to the utmost extent. Chemistry would, however, lose its
chief interest if all the elements remained as obstinately neutral as
argon, and disdained alliance with all other elements. It would seem
that those elements which most eagerly enter into combination here, and
which resist with such vehemence our efforts to divorce them, must
renounce all chemical union when exposed to the tremendous temperature
of the sun.

Those elements which unite with the utmost eagerness at ordinary
temperatures, seem to become indifferent to each other when subjected to
the extremes of heat and cold. Potassium unites fiercely with oxygen in
the most familiar of all chemical experiments. Potassium is indeed a
strange metal, for it is of such small density that a piece cast on a
basin of water will float like a chip of wood. It has such avidity for
oxygen that it will decompose the water to wrench the molecules of
oxygen from those of hydrogen. The union of the metal with the gas
generates such heat that the strange substance bursts into flame. This
is what takes place at the ordinary temperatures in the well-known
experiment of the chemical lecture-table. But at extreme temperatures
the greed of potassium for oxygen abates, if it does not vanish
altogether. In those excessively low temperatures at which Professor
Dewar experiments chemical affinities languish. He has reduced oxygen to
a liquid, and he tells us that “a berg of silvery potassium might float
for ever untarnished on an ocean of liquid oxygen.” At the excessively
high temperature of the electric arc the oxygen and the potassium, whose
union has been accomplished with such vehemence, cease to possess
affinity, and they separate again.

The solar chemistry seems to know no combination. If a drop of water
were transferred to the sun and subjected to the heat of the solar
surface, it must immediately undergo decomposition. That which was a
drop of water here would not remain a drop of water there; it would be
at once resolved into its component elements of oxygen and hydrogen. The
considerations just given greatly simplify the search for the particular
bodies which are at present in the sun. We have only to test for the
presence of each of eighty elements. We have not to take account of the
thousands of chemical combinations of which these elements are
susceptible under terrestrial conditions.

We are specially indebted to the late Professor Henry Rowland, of
Baltimore, for a profound study of the solar spectrum. In his great work
he enumerates thirty-six elements present in the sun, and the number may
be increased now by at least two. Eight elements he classes as doubtful,
fifteen are set down as absent from the solar spectrum, and several had
not been tried. Iron stands foremost among all the solar elements, so
far as the number of its lines are concerned. No fewer than 2,000 lines
in the spectrum of the sun are attributed to this element. At the other
end of the list lead is found. There is only one line apparently due to
this metal. Carbon is represented by about 200 lines, and calcium by
about 75. If, however, we test the significance of lines not by their
number, but by their intensity, then iron no longer heads the list, its
place being taken by calcium (Fig. 42). Among the elements which Rowland
sets down as not contributing any recognisable lines to the solar
spectrum we may mention arsenic and sulphur, phosphorus, mercury, and
gold.

Of the more prominent solar elements there are two or three of such
special importance that we pause to give them a little consideration.
Who does not remember the delight of the first occasion in childhood
when he was permitted to peep into a bird’s-nest and there see a group
of eggs, often so exquisitely marked or so delicately tinted? How
beautiful they seemed as they lay in their cosy receptacle concealed
with so much cunning! Among other delightful recollections of early
youth many will recall a ramble by the sea-shore. We may suppose the
tide had retreated, and with other objects left by the sea on the
gleaming sand a little cowrie shell is found. How enchanted we were with
our prize! How we looked at the curious marks on its lips, and the
inimitable beauty of its tints!

The shell of the hedge-sparrow and the shell cast up by the sea have
another quality in common besides their beauty. They have both been
fabricated from the same material. Lime is of course the substance from
which the bird, by some subtle art of physiology, forms those exquisite
walls by which the vital part of the egg is protected. The soft organism
that once dwelt in the cowrie was endowed with some power by which it
extracted from the waters of the ocean the lime with which it gradually
built an inimitable shell. Is it an exaggeration to say that this
particular element calcium, this element so excessively abundant and so
rarely seen, seems to enjoy some peculiar distinction by association
with exquisite grace and beauty? The white marble wrought to an
unparalleled loveliness by the genius of a Phidias or a Canova is but a
form of lime. So is the ivory on which the Japanese artist works with
such delicacy and refinement. Whether as coral in a Pacific island, as a
pearl in a necklace or as a stone in the Parthenon, lime seems often
privileged to form the material basis of beauty in nature and beauty in
art.

Though lime in its different forms, in the rocks of the earth or the
waters of the ocean, is one of the most ordinary substances met with on
our globe, yet calcium, the essential element which goes to the
composition of lime, is, as we have already said, not by any means a
familiar body, and not many of us, I imagine, can ever have seen it.
Chemistry teaches that lime is the result of a union in definite
proportions between oxygen gas and the very shy metal, calcium. This
metal is never found in nature unless in such intimate chemical union
with some other element like oxygen or chlorine, that its characteristic
features are altogether obscured, and would indeed never be suspected
from the mere appearance of the results of the union. To see the metal
calcium you must visit a chemical laboratory where, by electrical
decomposition or other ingenious process, this elusive element can be
induced to part temporarily from its union with the oxygen or other body
for which it has so eager an affinity, and to which it returns with such
alacrity. Though calcium is certainly a metal, it is very unlike the
more familiar metals such as gold or silver, copper or iron. A coin
might conceivably be formed out of calcium, but it would have no
stability like the coins of the well-known metals. Calcium has such an
unconquerable desire to unite with oxygen that the unstable metal will
speedily grasp from the surrounding air the vital element. Unless
special precautions are taken to withhold from the calcium the air, or
other source from whence it could obtain oxygen, the union will most
certainly take place, and the calcium will resume the stable form of
lime. Thus it happens that though this earth contains incalculable
billions of tons of calcium in its various combinations, yet calcium
itself is almost unknown except to the chemist.

It is plain that calcium plays a part of tremendous significance on this
earth. I do not say that it is the most important of all the elements.
It would indeed seem impossible to assign that distinction to any
particular element. Many are, of course, of vital importance, though
there are, no doubt, certain of the rarer elements with which this earth
could perhaps dispense without being to any appreciable extent different
from what it is at present. I do not know that we should be specially
inconvenienced or feel any appreciable want unsatisfied, if, let us say,
the element lanthanum were to be struck out of existence; and there are
perhaps certain other rare bodies among the known eighty elements, about
which the same remark might be made.

[Illustration: Fig. 42.—THE H. AND K. LINES IN THE PHOTOGRAPHIC SOLAR
SPECTRUM (Higgs).]

But without calcium there would neither be fertile soil for plants nor
bones for animals, and consequently a world, inhabited in the same
manner as our present globe, would be clearly impossible. There may be
lowly organisms on this earth to which calcium is of no appreciable
consequence, and it is of course conceivable that a world of living
types could be constructed without the aid of that particular element
which is to us so indispensable. But a world without calcium would be
radically different from that world which we know, so that we are
disposed to feel special interest in the important modern discovery that
this same element, calcium, is abundantly distributed throughout the
universe. The boldest and most striking features in the photograph of
the solar spectrum are those due to calcium (Figs. 42 and 44).

In the solar spectrum are two very broad, very dark, and very
conspicuous lines, known as H and K. In every photograph of that portion
of the solar spectrum which, lying beyond the extreme violet, is
invisible to our eyes, though intensely active on the photographic
plate, these lines stand forth so boldly as to arrest the attention more
than any other features of the spectrum. It had been known that these
lines were due to calcium, but there were certain difficulties connected
with their interpretation. Some recent beautiful researches by Sir
William and Lady Huggins have cleared away all doubt. It is now certain
that the presence of these lines in the spectrum demonstrates that that
remarkable element which is the essential feature of lime on this earth
is also found in the sun. We have also to note that these same lines
have been detected in the photographic spectra of many other bodies in
widely different regions of space. Thus we establish the interesting
result that this particular element which plays a part so remarkable on
our earth is not restricted to our globe, but is diffused far and wide
throughout the universe.

Perhaps the most astonishing discovery made in modern times about the
sun is connected with the wonderful element, helium. So long ago as 1868
Sir Norman Lockyer discovered, during an eclipse, that the light of the
sun contained evidence of the presence in that orb of some element which
was then totally unknown to chemists. This new body was not unnaturally
named the sun-element, or helium. But more than a quarter of a century
had to elapse before any chemist could enjoy the opportunity of
experimenting directly upon helium. No labour could prepare the smallest
particle of this substance, no money could purchase it, for at that time
no specimen of the element was known to exist nearer than the sun,
ninety-three million miles distant. But in 1895 an astonishing discovery
was made by Professor Ramsay. He was examining a rare piece of mineral
from Norway. From this mineral, clevite, the Professor extracted a
little gas which was to him and to all other chemists quite unknown. But
on applying the spectroscope to examine the character of the light which
this gas emitted when submitted to the electric current, it yielded, to
their amazement, the characteristic light of helium. Thus was the
sun-element at last shown to be a terrestrial body, though no doubt a
rare one. The circumstances that I have mentioned make helium for ever
famous among the constituents of the universe. It will never be
forgotten that though from henceforth it may be regarded as a
terrestrial body, yet it was first discovered, not in the earth beneath
our feet, but in the far-distant sun.

In a previous picture (Fig. 14) we showed a photograph of a part of the
sun’s surface; this striking view displays those glowing clouds from
which the sun dispenses its light and heat. These clouds form a
comparatively thin stratum around the sun, the interior of which is very
much darker. The layer of clouds is so thin that it may perhaps be
likened to the delicate skin of a peach in comparison with the luscious
interior. It is in these dazzling white clouds that we find the source
of the sun’s brightness. Were those clouds removed, though the sun’s
diameter would not be appreciably reduced, yet its unparalleled lustre
would be at once lessened. We use the expression “clouds” in speaking of
these objects, for clouds they certainly are, in the sense of being
aggregates of innumerable myriads of minute beads of some substance; but
those solar clouds are very unlike the clouds of our own sky, in so far
as the material of which they are made is concerned. The solar clouds
are not little beads of water; they are little beads of white-hot
material so dazzlingly bright as to radiate forth the characteristic
brilliance and splendour of the sun. The solar clouds drift to and fro;
they are occasionally the sport of terrific hurricanes; they are
sometimes driven away from limited areas, and in their absence we see
merely the black interior of the solar globe, which we call a sun-spot.
Now comes the important question as to the material present in these
clouds which confers on the sun its ability to radiate forth such
abundant light and heat.

The profound truth already stated, that the solar elements are the same
as the terrestrial elements, greatly simplifies the search for that
particular element which forms those solar clouds. As the sun is made of
substances already known to us by terrestrial chemistry, and as there
are no chemical compounds to embarrass us, the choice of the possible
constituents of those solar clouds becomes narrowed to the list of
elements experimented on in our laboratories.

We owe to Dr. G. Johnstone Stoney, F.R.S., the discovery of the
particular element which forms those fire-clouds in the sun, and confers
on the presiding body of the solar system the power of being so useful
to the planets which owe it allegiance. Carbon is the element in
question. I need hardly add that carbon is well known as one of the most
commonplace and one of the most remarkable substances in Nature. A piece
of coke differs from a piece of pure carbon only by the ash which the
coke leaves behind when burned. Timber is principally composed of this
same element, and when the timber is transformed into charcoal but
little more than the carbon remains. Carbon is indeed everywhere
present. It is, as we have mentioned, one of the elements which enter
into the composition of a piece of chalk. Carbon is in the earth beneath
our feet; it is in the air above us. Carbon is one of the chief
ingredients in our food, and it is by carbon that the heat of the body
is sustained. Indeed, this remarkable element is intimately connected
with life in every phase. Every organic substance contains carbon, and
it courses with the blood in our veins. It assumes the widest variety of
forms, renders the greatest diversity of services, and appears in the
most widely different places. Carbon is indeed of a protean character,
and there is a beautiful symbol of the unique position which it occupies
in the scheme of Nature (Fig. 43). Carbon is associated not alone with
articles of daily utility and of plenteous abundance, but it is carbon
which forms the most exquisite gems “of purest ray serene.” The diamond
is, of course, merely a specimen of carbon of absolute purity and in
crystalline form. Great as is the importance of carbon on this earth, it
is spread far more widely; it is not confined merely to the earth, for
carbon abounds on other bodies in space. The most important functions of
carbon in the universe are not those it renders on this earth. It was
shown by Dr. Stoney that this same wonderful substance is indeed a solar
element of vast utility. It is carbon which forms the glowing solar
clouds to which our very life owes its origin.

In the incandescent lamp the brilliant light is produced by a glowing
filament of carbon, and one reason why we employ this element in the
electric lamp, instead of any other, may be easily stated. If we tried
to make one of these lamps with an iron wire, we should find that when
the electric current is turned on and begins to flow through the wire,
the wire will, in accordance with a well-known law, become warm, then
hot, red-hot, and white-hot; but even when white-hot the wire will not
glow with the brightness that we expect from one of these lamps. Ere a
sufficient temperature can be reached the iron will have yielded, it
will have melted into drops of liquid, continuity will be broken, the
circuit will be interrupted, and the lamp destroyed. We should not have
been much more successful if instead of iron we had tried any other
metal. Even a platinum wire, though it will admit of being raised to a
much higher temperature than a wire of iron or a wire of steel, cannot
remain in the solid condition at the temperature which would be
necessary if the requisite incandescence is to be produced.

There is no known metal, and perhaps no substance whatever, which has so
high a temperature of fusion as carbon. A filament of carbon, alone
among the available elements, will remain continuous and unfused while
transmitting a current intense enough to produce that dazzling
brilliance which is expected from the incandescent lamp. This is the
reason why this particular element carbon is an indispensable material
for the electrician.

Modern research has now demonstrated that just as we employ carbon as
the immediate agent for producing our beautiful artificial light, so the
sun uses precisely the same element as the agent of its light and
heat-giving power. In the extraordinary fervour which prevails in the
interior of the sun all substances of every description must submit to
be melted, nay, even to be driven into vapour. An iron poker, for
instance, would vanish into iron vapour if submitted to this appalling
solar furnace. Even carbon itself is unable to remain solid when
subjected to the intense heat prevailing in the inner parts of the sun.
At that heat carbon must assume the form of gas or vapour, just as iron
or the other substances which yield more readily to the application of
heat.

By the help of a simple experiment we may illustrate the significance of
the carbon vapours in the solar economy. Let us take a Bunsen burner, in
which the air and gas are freely mingled before they enter into
combustion. If the air and the gas be properly proportioned, the
combustion is so perfect that though a great deal of heat is produced
there is but little light. The gas burned in this experiment ought to be
the ordinary gas of our mains, which depends for its illuminating power
on the circumstance that the hydrogen, of which the gas is chiefly
composed, is largely charged with carbon. The illuminating power of the
gas may indeed be measured by its available richness in carbon. As it
enters the burner the carbon is itself in a gaseous form. This is not,
of course, on account of a high temperature. The carbon of the coal-gas
is in chemical union with hydrogen, and the result is in the form of
invisible gases. It is these composite gases, blended with large volumes
of ordinary hydrogen, which form the illuminating gas of our mains.

In the Bunsen burner the admission of a proper proportion of air, which
becomes thoroughly mixed with the coal gas, produces perfect combustion.
In the act of burning, the oxygen of the air unites immediately with the
gas; it combines with the hydrogen to form watery vapour, and it
combines with the carbon to form gases which are the well-understood
products of combustion.

Suppose, now, we cut off the supply of air from the Bunsen burner, which
can be done in a moment by placing the hand over the ring of holes at
the bottom at which the air is admitted. Immediately a change takes
place in the combustion. In place of the steady, hardly visible, but
intensely hot flame which we had before, we have now a very much larger
flame which makes a bright and flickering flare that lights up the room.
If we re-admit the air at the bottom of the burner the light goes down
instantly; the small, pale flame replaces it, and again the perfect
combustion gives out intense heat at the expense of the light.

The remarkable change in the character of a gas-flame produced by
admitting air to mix with the gas before combustion is, of course,
easily explained. The chemical action takes place with much greater
facility under these circumstances. The union of the carbon in the coal
gas with the oxygen then takes place so thoroughly and instantaneously
that the carbon never seems to have abandoned the gaseous form even for
a moment in the course of the transformation. But in the case where air
is not permitted to mingle with the gas, the supply of oxygen to unite
with the incandescent gases can only be obtained from the exterior of
the flame. The consequence is that the glowing gas charged with carbon
vapour is chilled to some extent by contact with the cold air. It
therefore seems as if the union of the hydrogen with the oxygen
permitted the particles of carbon in the flame to resume their solid
form for a moment. But in that solid form these particles, being at a
high temperature, have a wonderful efficiency for radiation, and
consequently brilliance is conferred upon the light. Most of the
particles of carbon speedily unite with the surrounding oxygen, and
re-enter the gaseous state in a different combination. Some of them,
however, may escape this fate, in which case they assume the undesirable
form of smoke. The Bunsen lamp can thus be made to give an illustration
of the fact that when carbon vapours receive a chill, the immediate
effect of the chill is to transform the carbon from the gaseous form to
myriads of particles in the liquid, or more probably in the solid form.
In the latter state the carbon possesses a power of radiation greatly in
excess of that which it possessed in the gaseous state, even though the
gas may have been at a much higher temperature than the white-hot solid
particles.

We can now apply these principles to the explanation of the marvellous
radiation of light and heat from the great orb of day. The buoyancy of
the carbon vapours is one of their most remarkable characteristics; they
tend to soar upwards through the solar atmosphere until they attain an
elevation considerably over that of many of the other materials in the
heated vapours surrounding the great luminary. We may illustrate what
happens to these carbon vapours by considering the analogous case
presented in the formation of ordinary clouds in our own skins. It is
true, no doubt, that terrestrial clouds are composed of material very
different from that which enters into the solar clouds. Terrestrial
clouds of course arise in this way; the generous warmth of the sun
evaporates water from the great oceans, and transforms it into vapour.
This vapour ascends through our atmosphere, not at first as a visible
cloud, but in the form of an invisible vapour. It is gradually diffused
throughout the upper air, until at last particles of water, but recently
withdrawn from the oceans, attain an altitude of a mile or more above
the surface of the earth. A transformation then awaits this aqueous
vapour. In the coldness of those elevated regions the water can no
longer remain in the form of vapour. The laws of heat require that it
shall revert to the liquid state. In obedience to this law the vapour
collects into liquid beads, and it is these liquid beads, associated in
countless myriads, which form the clouds we know so well. The same
phenomenon of cloud-production is witnessed on a smaller scale in the
formation of the visible puffs which issue from the funnel of a
locomotive. We generally describe these rolling white volumes as steam;
but this language is hardly correct. Steam, properly so called, is truly
as invisible as the air itself; it is only after the steam has done its
work and is discharged into the atmosphere, and there receives a chill,
that it becomes suddenly transformed from the purely gaseous state into
clustering masses of microscopic spheres of water, and thus becomes
visible.

We can now understand the transformation of these buoyant carbon vapours
which soar upwards in the sun. They attain an elevation at which the
fearful intensity of the solar heat has been so far abated by the cold
of outer space that the carbon gas is not permitted to remain any longer
in the form of gas; it must return to the liquid or to the solid state.
In the first stage on this return the carbon gas becomes transformed,
just in the same way as watery vapour ascending from the earth becomes
transformed into the fleecy cloud. Under the influence of its fall in
temperature the carbon vapour collects into a clustering host of little
beads of carbon. This is the origin of the glorious solar clouds. Each
particle of carbon in that magnificent radiant surface has a
temperature, and consequently a power of radiation, probably exceeding
that with which the filament of carbon glows in the incandescent
electric arc. When we consider that millions of millions of square miles
on our luminary are covered with clouds, of which every particle is so
intensely bright, we shall perhaps be able to form some idea of that
inimitable splendour which even across the awful gulf of ninety-three
million miles transmits the indescribable glory of daylight.

We are perhaps at present living rather too close to the period itself
to be able to appreciate to its full extent the greatness of that
characteristic discovery made in astronomy during the century just
closed, to which the present chapter relates. In the early part of the
last century it might have been said—indeed, by a certain very
distinguished philosopher it actually was said—that a limit could be
laid down bounding the possibilities of our knowledge of the heavenly
bodies. It was admitted that we might study the movements of the
different orbs in vastly greater detail than had been hitherto
attempted, and that we might calculate the forces to which those orbs
were submitted. With the help of mathematical analysis we might pursue
the consequences of these forces to their remote ramifications; we might
determine where the various orbs were situated at inimitably remote
periods in the past. We might calculate the positions which they shall
attain at epochs to be reached in the illimitably remote future; we
might discover innumerable new stars and worlds; and we might map down
and survey the distant parts of the universe. We might even sound the
depths of space and determine the distances of the more remote celestial
bodies, much more distant than any of those which have already yielded
their secrets; we might measure the dimensions of those bodies and
determine their weights; we might add scores or hundreds to the list of
the known planets; we might multiply many times the number of known
nebulæ and star-clusters; we might make measurements of many thousands
of double stars; we might essay the sublime task of forming an inventory
of the stars of the universe and compiling a catalogue in which the
stars and their positions would be recorded in their millions; but, said
the philosopher to whom I have referred, though you might accomplish all
this, and much more in the same direction, yet there is a well-marked
limit to your possible achievements; you can, he said, never expect to
discover the actual chemical elements of which the heavenly bodies are
composed. Nobody could dispute the reasonableness of this statement at
the time he made it; indeed, it seemed to be a necessary deduction from
our knowledge of the arts of chemistry, as those arts were understood
before the middle of the last century.

In the prosecution of his researches by the older method, the chemist
could no doubt discover the different elements of which the body was
formed. That is to say, his art enabled him to accomplish this task,
provided one very essential and fundamental condition could be complied
with. However accomplished the chemist of fifty years ago might have
been, he would assuredly have thought that he was being mocked if asked
to determine the composition of a body which was 93,000,000 miles away
from him. The very idea of forming an analysis under such conditions
would have been scouted as preposterous. He would naturally ask that a
specimen of the body should be delivered into his hands, a specimen
which he could take into his laboratory, pulverise in his mortars, place
in his test-tubes, treat with his re-agents, or examine with his
blowpipe. Only by such methods was it then thought possible to obtain an
analysis and discover the elements from which any given substance was
formed.

For in the early part of this century the splendid method of spectrum
analysis, that method which has revealed to us so many of the secrets of
Nature, had not yet come into being. When that memorable event took
place it was at once perceived that the spectroscope required no actual
contact with the object to be tested, but only asked to receive some of
the rays of light which that object dispersed when sufficiently heated.
It was obvious that this new method must be capable of an enormously
enlarged application. The flame producing the vapour might be at one end
of the room, while the spectroscope testing the elements in that vapour
might be at the other end. This new and beautiful optical instrument
could analyse an object at a distance of a hundred feet. But if
applicable at a distance of a hundred feet, why not at a hundred yards,
or a hundred miles, or a hundred million miles? Why might the method not
be used if the source of light were as far as the sun, or as far as a
star, or even as far as the remotest nebula, whose faint gleam on the
sky is all that the mightiest telescope can show.

Presently another great advance was recorded. As the study of this
subject progressed, it was soon found that a spectrum visible to the
human eye was not always indispensable for the success of the analysis.
The photographic plate, which so frequently replaces the eye in other
classes of observation, has also been used to replace the eye in the use
of the spectroscope. A picture has thus been obtained showing the
characteristic lines in the spectrum of a celestial object. That object
may have been sunk in space to a distance so tremendous that even though
the light travelled at a pace sufficient to complete seven circuits of
our earth in each second of time, yet the rays from the object in
question may have been travelling for centuries before they reached our
instrument.

However the rays of light may have become weakened in the course of that
journey, they still faithfully preserve the credentials of their origin.
At last the light is decomposed in the spectroscope, and the several
rays, which have been so closely commingled in their long voyage of
myriads of miles, are now for the first time forced to pursue different
tracks; they thus reach their different destinations on the photographic
plate, and they there engrave their characteristic inscriptions. Nature
in this operation imparts for our instruction a message which it is our
business to interpret. It is true that these inscriptions are not always
easily deciphered; many of them have not yet been understood. A portion
of the solar spectrum showing many of the lines in the visible region is
represented in the accompanying plate.

[Illustration: Fig. 43.—SPECTRUM OF COMET SHOWING CARBON LINES.
(_Sir W. Huggins, K.C.B._)]

Considering the insignificance of our earth when viewed in comparison
with the millions of other orbs in the universe, considering also the
stupendous distances by which the earth is separated from innumerable
globes which are very much greater, it is certainly not a little
astonishing to learn that the elements from which the various bodies in
the universe have been composed are practically the same elements as
those of which our earth is built. Is not this a weighty piece of
evidence in favour of the theory that earth, sun, and planets are all
portions of the same primæval nebula in which these elements were
blended?

[Illustration: THE SOLAR SPECTRUM.]

We do not, of course, mean to affirm that the great primæval nebula was
homogeneous throughout its vast extent. The waters of ocean are not
strictly the same in all places; even the atmosphere is not absolutely
uniform. Nature does not like homogeneity. The original nebula, we may
well believe, was irregular in form, and denser in some places than in
others. We do not suppose that if we could procure a sample of nebula in
one place and another sample from the same nebula, but in a different
place, say a hundred million miles distant, the two would show an
identity of chemical composition; two samples of rock from different
parts of the same quarry will not always be identical. But we may be
assured that, in general, whatever elements are present in the nebula
will be widely dispersed through its extent. If from different parts of
the nebula two globes are formed by condensation, though we should not
affirm, and though in fact we could not believe, that those globes would
be of identical composition, yet we should reasonably expect that the
elementary bodies which entered into their composition would be in
substantial agreement. If one element, say iron, was abundant in one
globe, we should expect that iron would not be absent from the other.
Thus the elements represented in one body should be essentially those
which were represented in the other.

[Illustration: Fig. 44.—SPECTRUM OF SUN DURING ECLIPSE.
THE TWO CHIEF LINES ARE DUE TO CALCIUM.
(_Evershed._)]

It is obvious that if the sun and the earth—to confine our attention
solely to those two bodies—had originated from the primæval nebula, they
would bear with them, as a mark of their common origin, a resemblance in
the elementary bodies of which they were composed. When Laplace framed
his theory, he had not, he could not have had, the slightest notion as
to the particular elements in the sun. For anything he could tell, those
elements might be absolutely different from the elements in the earth.
Yet, even without information on this critical point, the evidence for
the nebular theory appeared to him so cogent that he gave it the
sanction of his name.

It cannot be denied that if spectroscopic analysis had demonstrated that
the elements in the sun were totally different from the elements in the
earth a serious blow would have been dealt to the nebular theory. The
collateral evidence, strong as it undoubtedly is, might hardly have
withstood so damaging an admission. If, on the other hand, we find, as
we actually have found, that the elements in the sun and the elements in
the earth are practically identical, we obtain the most striking
corroboration of the truth of the nebular theory. Had Kant and Laplace
been aware of this most significant fact, they would probably have cited
it as most important testimony. They would have pointed out that the
iron so abundant in the earth beneath our feet is also abundant in the
sun overhead. They would, I doubt not, if they had known it, have dwelt
upon the circumstance that with that element, carbon, which enters into
every organic body on this earth, our sun is also richly supplied, and
they would have hardly failed to allude to the wide distribution in
space of calcium, hydrogen, and many other well-known elements.

Laplace mainly based his belief in the nebular theory on some remarkable
deductions from the theory of probabilities. To the consideration of
these we proceed in the next three chapters. We may, however, remark at
the outset that if the evidence derived from probabilities seemed
satisfactory to Laplace one hundred years ago, this same line of
evidence, strengthened as it has been by recent discoveries, is
enormously more weighty, at the present day.

------------------------------------------------------------------------

CHAPTER XIV.

THE FIRST CONCORD.

Certain Remarkable Coincidences—The Plane of Movement of a
Planet—Consideration of Planes of Several Planetary Orbits—A
Characteristic of the Actual Planetary Motions not to be Explained
by Chance—The First Concord—The Planes not at Random—A Division of
the Right Angle—Statement of the Coincidences—An Illustration by
Parable—The Cause of the Coincidences—The Argument Strengthened by
the Asteroids—An Explanation by the Nebular Theory.

IN the present chapter, and in the two chapters which are to follow, I
propose to give an outline of those arguments in favour of the nebular
theory which are presented by certain remarkable coincidences observed
in the movements of the bodies of our solar system. There are, indeed,
certain features in the movements of the planets which would seem so
inexplicable if the arrangement of the system had taken place by chance,
that it is impossible not to seek for some physical explanation. We have
already had occasion to refer in previous chapters to the movements of
the bodies of our system. It will be our object at present to show that
it is hardly conceivable that the movements could have acquired the
peculiar characteristics they possess unless the solar system has itself
had an origin such as that which the nebular theory assigns.

The argument on which we are to enter is, it must be confessed, somewhat
subtle, but its cogency is irresistible. For this argument we are
indebted to one of the great founders of the nebular theory. It was
given by Kant himself in his famous essay.

We will commence with a preliminary point which relates to elementary
mechanics. It may, however, help to clear up a difficult point in our
argument if I now state some well-known principles in a manner specially
adapted for our present purpose.

Let us think of two bodies, A and S, and, for the sake of clearness, we
may suppose that each of these bodies is a perfect sphere. We might
think of them as billiard balls, or balls of stone, or balls of iron. We
shall, however, suppose them to be formed of material which is perfectly
rigid. They may be of any size whatever, large or small, equal or
unequal. One of them may be no greater than a grain of mustard-seed, and
the other may be as large as the moon or the earth or the sun. Let us
further suppose that there is no other body in the universe by which the
mutual attraction of the two bodies we are considering can be interfered
with. If these two bodies are abandoned to their mutual attraction, let
us now see what the laws of mechanics assure us must necessarily happen.

[Illustration: Fig. 45.—A SPIRAL PRESENTED EDGEWISE (n.g.c. 4631; in
Coma Berenices).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]

Let A and S be simply released from initial positions of absolute rest.
In these circumstances, the two points will start off towards each
other. The time that must elapse before the two bodies collide will
depend upon circumstances. The greater the initial distance between the
two balls, their sizes being the same, the longer must be the interval
before they come together. The relation between the distance separating
the bodies and the time that must elapse before they meet may be
illustrated in this way. Suppose that two balls, both starting from rest
at a certain distance, should take a year to come together by their
mutual attraction, then we know that if the distance of the two balls
had been four times as great eight years would have to elapse before the
two balls collided. If the distances were nine times as great then
twenty-seven years would elapse before the balls collided, and generally
the squares of the times would increase as the cubes of the distances.
In such statements we are supposing that the radii of the balls are
inconsiderable in comparison with the distances apart from which they
are started. The time occupied in the journey must also generally depend
on the masses of the two bodies, or, to speak more precisely, on the sum
of the masses of the two bodies. If the two balls each weighed five
hundred tons, then they would take precisely the same time to rush
together as would two balls of one ton and nine hundred and ninety-nine
tons respectively, provided the distances between the centres of the two
balls had been the same in each case. If the united masses of the two
bodies amounted to four thousand tons, then they would meet in half the
time that would have been required if their united masses were one
thousand tons, it being understood that in each case they started with
the same initial distance between the centres.

Instead of simply releasing the two bodies A and S so that neither of
them shall have any impulse tending to make it swerve from the line
directly joining them, let us now suppose that we give one of the
bodies. A, a slight push sideways. The question will be somewhat simpler
if we think of S as very massive, while A is relatively small. If, for
instance, S be as heavy as a cannon-ball, while A is no heavier than a
grain of shot, then we may consider that S remains practically at rest
during the movement. The small pull which A is able to give will produce
no more than an inappreciable effect on S. If the two bodies come
together, A will practically do all the moving.

[Illustration: Fig. 46.—THE PLANE OF A PLANET’S ORBIT.]

We represent the movement in the adjoining figure. If A is started off
with an initial velocity in the direction A T, the attraction of S will,
however, make itself felt, even though A cannot move directly towards S.
The body will not be allowed to travel along A T; it will be forced to
swerve by the attraction of S; it will move from P to Q, gradually
getting nearer to S. To enter into the details of the movement would
require rather more calculation than it would be convenient to give
here. Even though S is much more massive than A, we may suppose that the
path which A follows is so great that the diameter of the globe S is
quite insignificant in comparison with the diameter of the orbit which
the smaller body describes. We shall thus regard both A and S as
particles, and Kepler’s well-known law, to which we so often refer,
tells us that A will revolve around S in that beautiful figure which the
mathematician calls an ellipse. For our present purpose we are
particularly to observe that the movement is restricted to a plane. The
plane in which A moves depends entirely on the direction in which it was
first started. The body will always continue to move in the same plane
as that in which its motion originally commenced. This plane is
determined by the point S and the straight line in which A was
originally projected. It is essential for our argument to note that A
will never swerve from its plane so long as there are not other forces
in action beside those arising from the mutual attractions of A and S.
The ordinary perturbations of one body by the action of others need not
here concern us.

The case we have supposed will, of course, include that of the movement
of a planet round the sun. The planet is small and represented by the
body A, which revolves round the great body S, which stands for the sun.
However the motion of the planet may actually have originated, it moves
just as if it had received a certain initial impulse, in consequence of
which it started into motion, and thus defined a certain plane, to which
for all time its motion would be restricted.

So far we have spoken of only a single planet; let us now suppose that a
second planet, B, is also to move in revolution about the same sun. This
planet may be as great as A, or bigger, or smaller, but we shall still
assume that both planets are inconsiderable in comparison with S. We may
assume that B revolves at the same distance as A, or it may be nearer,
or further. The orbit of B might also have been in the same plane as A,
or—and here is the important point—it might have been in a plane
inclined at any angle whatever to the orbit of A. The two planes might,
indeed, have been perpendicular. No matter how varied may be the
circumstances of the two planets, the sun would accept the control of
each of them; each would be guided in its own orbit, whether that orbit
be a circle, or whether it be an ellipse of any eccentricity whatever.
So far as the attraction of the sun is concerned, each of these planets
would remain for ever in the same plane as that in which it originally
started. Let us now suppose a third planet to be added. Here again we
may assume every variety in the conditions of mass and distance. We may
also assume that the plane which contains the orbit of this third planet
is inclined at any angle whatever to the planes of the preceding
planets. In the same way we may add a fourth planet, and a fifth; and in
order to parallel the actual circumstance of our solar system, so far as
its more important members are concerned, we may add a sixth, and a
seventh, and an eighth. The planes of these orbits are subjected to a
single condition only. Each one of them passes through the centre of the
sun. If this requirement is fulfilled, the planes may be in other
respects as different as possible.

In the actual solar system the circumstances are, however, very
different from what we have represented in this imaginary solar system.
It is the most obvious characteristic of the tracks of Jupiter and
Venus, and the other planets belonging to the sun, that the planes in
which they respectively move coincide very nearly with the plane in
which the earth revolves. We must suppose all the orbits of our
imaginary system to be flattened down, nearly into a plane, before we
can transform the imaginary system of planets I have described into the
semblance of an actual solar system.

If the orbits of the planets had been arranged in planes which were
placed at random, we may presume they would have been inclined at very
varied angles. As they are not so disposed, we may conclude that the
planes have not been put down at random; we must conclude that there has
been some cause in action which, if we may so describe it, has
superintended the planes of these orbits and ordained that they should
be placed in a very particular manner.

Two planets’ orbits might conceivably coincide or be perpendicular, or
they might contain any intermediate angle. The plane of the second
planet might be inclined to the first at an angle containing any number
of degrees. To make some numerical estimate of the matter, we proceed as
follows: If we divide the right angle into ten parts of nine degrees
each (Fig. 47), then the inclination of the two planes might, for
example, lie between O° and 9°, or between 18° and 27°, or between 45°
and 54°, or between 81° and 90°, or in any one of the ten divisions. Let
us think of the orbit of Jupiter. Then the inclination of the plane in
which it moves to the plane in which the earth moves must fall into one
of the ten divisions. As a matter of fact, it does fall into the angle
between 0° and 9°.

[Illustration: Fig. 47.—A RIGHT ANGLE DIVIDED INTO TEN PARTS.]

But now let us consider a second planet, for example Venus. If the orbit
of Venus were to be placed at random, its inclination might with equal
probability lie in any one of the ten divisions, each of nine degrees,
into which we have divided the right angle. It would be just as likely
to lie between forty-five and fifty-four, or between seventy-two and
eighty-one, as in any other division. But we find another curious
coincidence. It was already remarkable that the plane of Jupiter’s orbit
should have been included in the first angle of nine degrees from the
orbit of the earth. It is therefore specially noteworthy to find that
the planet Venus follows the same law, though each one of the ten
angular divisions was equally available.

The coincidences we have mentioned, remarkable as they are, represent
only the first of the series. What has been said with respect to the
positions of the orbits of Jupiter and Venus may be repeated with regard
to the orbits of Mercury and Mars, Saturn, Uranus, and Neptune. If the
tracks of these planets had been placed merely at random, their
inclinations would have been equally likely to fall into any of the ten
divisions. As a matter of fact, they all agree in choosing that one
particular division which is adjacent to the track of the earth. If the
orbits of the planets had indeed been arranged fortuitously, it is
almost inconceivable that such coincidences could have occurred. Let me
illustrate the matter by the following little parable.

There were seven classes in a school, and there were ten boys in each
class. There was one boy named Smith in the first class, but only one.
There was also one Smith, but only one, in each of the other classes.
The others were named Brown, Jones, Robinson, etc. An old boy, named
Captain Smith, who had gone out to Australia many years before, came
back to visit his old school. He had succeeded well in the world, and he
wanted to do something generous for the boys at the place of which he
had such kindly recollections. He determined to give a plum-cake to one
boy in each class; and the fortunate boy was to be chosen by lot. The
ten boys in each class were to draw, and each successful boy was to be
sent in to Captain Smith to receive his cake.

The Captain sat at a table, and the seven winners were shown in to
receive their prizes. “What is your name?” he said to the boy in the
first class, as he shook hands with him. “Smith,” replied the boy. “Dear
me,” said the Captain, “how odd that our names should be the same. Never
mind, it’s a good name. Here’s your cake. Good-bye, Smith.” Then up came
the boy from the second class. “What is your name?” said the Captain.
“Smith, sir,” was the reply. “Dear me,” said the visitor. “This is very
singular. It is indeed a very curious coincidence that two Smiths should
have succeeded. Were you really chosen by drawing lots?” “Yes, sir,”
said the boy. “Then are all the boys in your class named Smith?” “No,
sir; I’m the only one of that name in the ten.” “Well,” said the
Captain, “it really is most curious. I never heard anything so
extraordinary as that two namesakes of my own should happen to be the
winners. Now then for the boy from class three.” A cheerful youth
advanced with a smile. “Well, at all events,” said the good-natured old
boy, “your name is not Smith?” “Oh, but it is,” said the youth. The
gallant Captain jumped up, and declared that there must have been some
tremendous imposition. Either the whole school consisted of Smiths, or
they called themselves Smiths, or they had picked out the Smiths. The
four remaining boys, still expecting their cakes, here burst out
laughing. “What are your names?” shouted the donor. “Smith!” “Smith!!”
“Smith!!!” “Smith!!!!” were the astounding replies. The good man could
stand this no longer. He sent for the schoolmaster, and said, “I
particularly requested that you would choose a boy drawn by lot from
each of your seven classes, but you have not done so. You have merely
picked out my namesakes and sent them up for the cakes.” But the master
replied, “No, I assure you, they have been honestly chosen by lot. Nine
black beans and one white bean were placed in a bag; each class of ten
then drew in succession, and in each class it happened that the boy
named Smith drew the white bean.”

“But,” said the visitor, “this is not credible. Only once in ten million
times would all the seven Smiths have drawn the white beans if left
solely to chance. And do you mean to tell me that what can happen only
once out of ten million times did actually happen on this occasion—the
only occasion in my life on which I have attempted such a thing? I don’t
believe the drawing was made fairly by lot. There must have been some
interference with the operation of chance. I insist on having the lots
drawn again under my own inspection.” “Yes, yes,” shouted all the other
boys. But all the successful Smiths roared out, “No.” They did not feel
at all desirous of another trial. They knew enough of the theory of
probabilities to be aware that they might wait till another ten million
fortunate old boys came back to the school before they would have such
luck again. The situation came to a deadlock. The Captain protested that
some fraud had been perpetrated, and in spite of their assurances he
would not believe them. The seven Smiths declared they had won their
cakes honestly, and that they would not surrender them. The Captain was
getting furious, the boys were on the point of rebellion, when the
schoolmaster’s wife, alarmed by the tumult, came on the scene. She asked
what was the cause of the disturbance. It was explained to her, and then
Captain Smith added that by mathematical probabilities it was almost
inconceivable that the only seven Smiths in the school should have been
chosen. The gracious lady replied that she knew nothing, and cared as
little, about the theory of probabilities, but she did care greatly that
the school should not be thrown into tumult. “There is only one solution
of this difficulty,” she added. “It is that you forthwith provide cakes,
not only for the seven Smiths, but for every one of the boys in the
school.” This resolute pronouncement was received with shouts of
approval. The Captain, with a somewhat rueful countenance, acknowledged
that it only remained for him to comply. He returned, shortly
afterwards, to his gold-diggings in Australia, there to meditate during
his leisure on this remarkable illustration of the theory of
probabilities.

This parable illustrates the improbability of such arrangements as we
find in the planets having originated by chance. The chances against
their having thus occurred are 10,000,000 to 1. Hence we find it
reasonable to come to the conclusion that the arrangement, by which the
planets move round the sun in planes which are nearly coincident, cannot
have originated by chance. There must have been some cause which
produced this special disposition. We have, therefore, to search for
some common cause which must have operated on all the planets. As the
planets are at present absolutely separated from each other, it is
impossible for us to conceive a common cause acting upon them in their
present condition. The cause must have operated at some primæval time,
before the planets assumed the separate individual existence that they
now have.

We have spoken so far of the great planets only, and we have seen how
the probability stands. We should also remark that there are also nearly
500 small planets, or asteroids, as they are more generally called.
Among them are, no doubt, a few whose orbits have inclinations to the
ecliptic larger than those of the great planets. The great majority of
the asteroids revolve, however, very close to that remarkable plane with
which the orbits of the great planets so nearly coincide. Every one of
these asteroids increases the improbability that the planes of the
orbits could have been arranged as we find them, without some special
disposing cause. It is not possible or necessary to write down the exact
figures. The probability is absolutely overwhelming against such an
arrangement being found if the orbits of the planets had been decided by
chance, and chance alone.

We may feel confident that there must have been some particular
circumstances accompanying the formation of the solar system which
rendered it absolutely necessary for the orbits of the planets to
possess this particular characteristic. We have pointed out in Chapter
XII. that the nebular theory offers such an explanation, and we do not
know of any other natural explanation which would be worthy of serious
attention. Indeed, we may say that no other such explanation has ever
been offered.

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CHAPTER XV.

THE SECOND CONCORD.

Another Remarkable Coincidence in the Solar System—The Second
Concord—The Direction of the Movements of the Great Planets—The
Movement of Ceres—Yet Another Planet—Discovery of Eros—The Nearest
Neighbour of the Earth—Throwing Heads and Tails—A Calculation of the
Chances—The Numerical Strength of the Argument—An Illustration of
the Probability of the Origin of the Solar System from the
Nebula—The Explanation of the Second Concord offered by the Nebular
Theory—The Relation of Energy and Moment of Momentum—Different
Systems Illustrated—That all the Movements should be in the same
Direction is a Consequence of Evolution from the Primæval Nebula.

WE have seen in the last chapter that there is a very remarkable
concordance in the positions of the planes of the orbits of the planets,
and we have shown that this concordance finds a natural historical
explanation in the nebular origin of our system. We have now to consider
another striking concord in the movements of the planets in their
several orbits, and this also furnishes us with important evidence as to
the truth of the nebular theory. The argument on which we are now to
enter is one which specially appealed to Laplace, and was put forward by
him as the main foundation of the nebular theory.

[Illustration: Fig. 48.—ILLUSTRATION OF THE SECOND CONCORD.]

In the adjoining Fig. 48 we have a diagram of a portion of the solar
system. We shall regard the movements as somewhat simplified. The sun is
supposed to be at the centre, turning round once every twenty-five days,
on an axis which is supposed to be perpendicular to the plane of the
paper. We may also for our present purpose assume that the orbits of the
earth and the other planets lie in this same plane.

In the first place we observe that the earth might have gone round its
track in either direction so far as the welfare of mankind is concerned.
The succession of day and night, and the due changes of the seasons,
could have been equally well secured whichever be the direction in which
the earth revolves. We do, however, most certainly find that the
direction in which the earth revolves round the sun is the same as the
direction in which the sun rotates on its axis. This is the first
coincidence.

We may now consider other planets. Look, for instance, at the orbit of
Jupiter. It seems obvious that Jupiter might have been made to revolve
round the sun either one way or the other; indeed, it will be remembered
that though Kepler’s laws indicate so particularly the shape of the
track in which the planet revolves, and prescribe so beautifully the way
in which the planet must moderate or accelerate its velocity at the
different parts of its track, yet they are quite silent as to the
direction in which the planets shall revolve in that track. If we could
imagine a planet to be stopped to have its velocity reversed, and then
to be started in a precisely opposite direction, it would still continue
to describe precisely the same path; it would still obey Kepler’s laws
with unfailing accuracy, so far as our present argument is concerned,
and the velocity which it would have at each point of the track would be
quite the same whether the planet were going one way or whether it was
going the other. It is therefore equally possible for Jupiter to pursue
his actual track by going round the sun in the same direction as the
earth, or by going in the opposite direction. But we actually find that
Jupiter does take the same direction as the earth, and this, as we have
already seen, is the direction in which the sun rotates. Here we have
the second coincidence.

We now take another planet; for example, Mars. Again we affirm that Mars
could have moved in either direction, but, as a matter of fact, it
pursues the same direction as Jupiter and the earth. In the orbital
movement of Saturn we have the fourth coincidence of the same kind, and
we have a fifth in the case of Mercury, and a sixth in Venus, a seventh
in Uranus, and an eighth in Neptune. The seven great planets and the
earth all revolve around the sun, not only in orbits which are very
nearly in the same plane, but they also revolve in the same direction.

The coincidences we have pointed out with regard to the movements of the
great planets of our system may be also observed with regard to the
numerous bodies of asteroids. On the first night of the century just
closed, the 1st of January, 1801, the first of the asteroids, now known
as Ceres, was discovered. This was a small planet, not a thousandth part
of the bulk of one of the older planets, and visible, of course, only in
the telescope. Like the older planets, it was found to obey Kepler’s
laws; but this we might have foreseen, because Kepler’s laws depend upon
the attraction of gravitation, and must apply to any planet, whatever
its size. When, therefore, the new planet was found, and its track was
known, it was of much interest to see whether the planet in moving round
that track observed the same direction in which all the older planets
had agreed to travel, or whether it moved in the opposite direction. In
the orbit of Ceres we have a repetition of the coincidence which has
been noticed in each of the other planets. The new planets, like all the
rest, move round the sun in the same direction as the sun rotates on its
axis. The discovery of this first asteroid was quickly followed by other
similar discoveries; each of the new planets described, of course, an
ellipse, and the directions which these planets followed in their
movements round the sun were in absolute harmony with those of the older
planets.

But, besides the great planets and the asteroids properly so called,
there is yet another planet, Eros. Its testimony is of special value,
inasmuch as it seems to stand apart from all other bodies in the solar
system, and with, of course, the exception of the moon, it is the
earth’s nearest neighbour. But whatever may be the exceptional features
of Eros, however it may differ from the great planets and the asteroids
already known, yet Eros makes no exception to the law which we have
found to be obeyed by all the other planets. It also revolves round the
sun in the same direction as all the planets revolve, in the same
direction as the rotation of the sun (Fig. 49).

We may pause at this moment to make a calculation as to the
improbability that the sun, the earth, the seven great planets, and
Ceres, numbering altogether ten, should move round in the same direction
if their movements had been left to chance. This will show what we can
reasonably infer from this concord in their movements. The theory of
probabilities will again enlighten a difficult subject.

There are only two possible directions for the motion of a planet in its
orbit. It must move like the hands of a watch, or it must move in the
opposite direction. The planet must move one way or the other, just as a
penny must always fall head or tail.

[Illustration: Fig. 49.—ORBITS OF EARTH, EROS AND MARS.]

We may illustrate this remarkable coincidence in the following manner:
Suppose we take ten coins in the hand, and toss them all up together and
let them fall on the table; in the vast majority of cases in which the
experiment may be tried, there would be some heads and some tails; they
would not all be heads. But it is, of course, not impossible that the
coins should all turn up heads. We should, however, deem it a very
remarkable circumstance if it happened: yet it would certainly not be
more remarkable than that the ten celestial movements should all take
place in the same direction, unless, indeed, it should turn out that
there is some sound physical cause which imposes on the planets of the
solar system an obligation, restricting their movements round the sun to
the same direction as that in which the sun itself rotates.

It will be useful to study the matter numerically; and the rules of
probabilities will enable us to do so, as we may see by the following
illustration: We deem the captain of a cricket team fortunate when he
wins the toss for innings. We should deem him lucky indeed if he won it
three times in successive matches. If he won it five times running, his
luck would be phenomenal; while, if it was stated that he won it ten
times consecutively, we should consider the statement well-nigh
incredible. For it is easy to calculate that the chances against such an
occurrence are one thousand and twenty-four to one. In like manner we
may say, that for nine planets and the sun all to go round in the same
direction would be indeed surprising if the arrangement of the planets
had been determined by chance; there are more than a thousand chances to
one against such an occurrence.

But Ceres was only the earliest of many other similar discoveries. And
as each asteroid was successively brought to light, it became most
interesting to test whether it followed the rest of the planets in that
wonderful unanimity in the direction of their movements of revolution,
or whether it made a new departure by going in the opposite direction.
No such exception has ever yet been observed. Let us take, then, ten
more planets, in addition to those we have already considered, so that
we have now nineteen planets all revolving in the same direction as the
sun rotates. It is easy to compute the improbability that these twenty
movements should all be in the same direction, if, indeed, it were by
chance that their directions had been determined. It is the same problem
as the following: What is the chance that twenty coins, taken together
in the hand and tossed into the air at once, shall all alight with their
heads uppermost? We have seen that the chances against this occurrence,
if there were ten coins, is about a thousand to one. It can easily be
shown that if there were twenty coins the chances against the occurrence
would be a million to one. We thus see that, even with no more than
nineteen planets and the sun, there is a million to one against a
unanimity in the directions of the movements, if the determination of
the motions was made by chance. We may, however, express the result in a
different manner, which is more to the purpose of our argument. There
are a million chances to one in favour of the supposition that the
disposition of the movements of the planets has not been the result of
chance; or we may say that there are a million chances to one in favour
of the supposition that some physical agent has caused the unanimity.

We can add almost any desired amount of numerical strength to the
argument. The discoveries of minor planets went on with ever-increasing
success through the whole of the last century. When ten more had been
found, and when each one was shown to obey the same invisible guide as
to the direction in which it should pursue its elliptic orbit, the
chances in favour of some physical cause for the unanimity became
multiplied by yet another thousand. The probability then stood at a
thousand millions to one. As the years rolled by, asteroids were found
in ever-increasing abundance. Sometimes a single astronomer discovered
two, and sometimes even more than two, on a single night. In the course
of a lifetime a diligent astronomer has placed fifty discoveries of
asteroids, or even more than fifty, on his record. By combined efforts
the tale of the asteroids has now approached five hundred, and out of
that huge number of independent planetary bodies there is not one single
dissentient in the direction of its motion. Without any exception
whatever, they all perform their revolutions in the same direction as
the sun rotates at the centre. When this great host is considered, the
numerical strength of the argument would require about 150 figures for
expression. Each new asteroid simply doubled the strength of the
argument as it stood before.

Professor J. J. Thomson recently discovered that there are corpuscles of
matter very much smaller than atoms. Let us think of one of these
corpuscles, of which many millions would be required to make the
smallest grain of sand which would just be visible under a microscope.
Think, on the other hand, of a sphere extending through space to so vast
a distance that every star in the Milky Way will be contained within its
compass. Then the number of those corpuscles which would be required to
fill that sphere is still far too small to represent the hugeness of the
improbability that all the five hundred planetary bodies should revolve
in the same direction, if chance, and chance alone, had guided the
direction which each planet was to pursue in moving round its orbit.

The mere statement of these facts is sufficient to show that some
physical agent must have caused this marvellous concord in the movements
of the solar system. How the argument would have stood if there had been
even a single dissentient it is not necessary to consider, for there is
no dissentient No reasonable person will deny that these facts impose an
obligation to search for the physical explanation of this feature in the
planetary movements.

As in the last chapter, where we were dealing with the positions of the
planes of the orbits, there can here be no hesitation as to the true
cause of this most striking characteristic of the planetary movements.
The nebular theory is at once ready with an explanation, as has been
already indicated in Chapter XI. The primæval nebula, endowed in the
beginning with a certain amount of moment of momentum, has been
gradually contracting. It has been gradually expending its energy, as we
have already had occasion to explain; but the moment of momentum has
remained undiminished. And from this it can be shown that the dynamical
principles guiding the evolution of the nebula must ultimately refuse
permission for any planet to revolve in opposition to the general
movement. This point is a very interesting one, and as it is of very
great importance in connection with our system, I must give it some
further illustration and explanation.

The two figures that are shown in Fig. 50 represent two imaginary
systems. We have a sun in each, and we have two planets in each. The sun
is marked with the letter S, and the two planets are designated by A and
B. For simplicity I have represented the orbits as circles, and for the
same reason I have left out the rest of the planets; we shall also
suppose the orbits of the two planets that are involved to lie exactly
in the same plane. In the two systems that I have here supposed, the two
suns are to be of the same weight, the planet A in one system is of
equal mass to the planet A in the other; and the planets B in the two
systems are also equal. It is also assumed that the orbit of A in one
diagram shall be the same as the orbit of A in the other, and that the
orbit of B in one shall be precisely the same as the orbit of B in the
other. The sun rotates in precisely the same manner in both, and takes
the same time for each rotation. A, in one system, goes round in the
same time that A does in the other; and B, in one system, goes round in
the same time that B does in the other. There is, therefore, a perfect
resemblance between the two systems I have here supposed in every point
but one. I have indicated, as usual, the movements of the bodies by
arrows, and, while in one of the systems the sun and A and B all go
round in the same direction, in the other system the sun and A go round,
no doubt, in the same direction, but the direction of B is opposite. We
are not, in this illustration, considering the rotations of the planets
on their axes. That will be dealt with in the next chapter.

[Illustration: Fig. 50.—I. A NATURAL SYSTEM ON THE LEFT.
II. AN UNNATURAL SYSTEM ON THE RIGHT.]

There can be no doubt that either of these two systems would be possible
for thousands of revolutions. There is nothing whatever to prevent A and
B from being started in the same direction round the sun as in the first
figure, or with A in one direction and B in the opposite direction, as
in the second figure. It is equally conceivable that, while A and B
revolve in the same direction, both should be opposite to that of the
sun. But one system is permanent, and the other is not.

For, as a matter of fact, we do not find in Nature such an arrangement
as that in the second figure, or as that in which both the planets
revolve in opposite directions to the sun’s rotation; what we do find
is, that the planets go round in the same direction as the sun. And the
explanation is undoubtedly connected with the important principle
already illustrated, namely, that natural systems are in a condition in
which the total quantity of energy undergoes continuous reduction in
comparison with the moment of momentum.

In the arrangements made in the two figures, it will be recollected that
the masses of the three bodies were respectively the same, and also
their distances apart, and their velocities. As the energy depends only
on the masses, the distances, and the velocities, the energies of the
two systems must be identical. But the moment of momentum of the two
systems is very different, for while in the one case the sum of the
moments of momentum of the sun’s rotation and that of the planet A,
which is going in the same direction, are to be _increased_ by the
moment of momentum of B, the same is not the case in the other system.
The moment of momentum of the sun and of A conspire, no doubt, and must
be added together; but as B is revolving in the opposite direction, the
moment of momentum of this planet has to be subtracted before we obtain
the nett moment of momentum of the system. Hence, we perceive a
remarkable difference between the two systems; for, though in each the
total energy is the same, yet in the latter case the moment of momentum
is smaller than in the former.

It has been pointed out that the effect of the mutual actions of the
different bodies of a system is to lessen, in course of time, the total
quantity of energy that they receive in the beginning, while it is not
in the power of the mutual actions of the particles of the system to
affect the sum total of the moment of momentum. Hence we see that, so
long as the system is isolated from external interference, the tendency
must ever be towards the reduction of the quantity of energy to as low a
point as may be compatible with the preservation of the necessary amount
of moment of momentum. The first of the two systems given in Fig. 50 is
much more in conformity with this principle than the second. The moment
of momentum in the former case must be nearly as large as could be
obtained by any other disposition of the matter forming it, with the
same amount of energy. But in the second diagram the moment of momentum
is much less, though the energy is the same. It follows that the energy
of this system might be largely reduced, for if accompanied by a
suitable rearrangement of the planets the reduced amount of moment of
momentum might be easily provided for. We thus see that this system is
not one to which the evolution of a material arrangement would
ultimately tend. It is, therefore, not to be expected in Nature, and we
do not find it. Of course, the same would be equally true if, instead of
having merely two planets, as I have here supposed for the sake of
illustration, the planets were much more numerous. The operation of the
causes we have been considering will show that, in the evolution of such
a system, there will be a tendency for the planets to revolve in the
same direction.

It is easy to see how, in the contraction of the original nebula, there
must have been a strong influence to check and efface any movements
antagonistic to the general direction of the rotation of the nebula. If
particles revolve in a direction opposite to the current pursued by the
majority of particles, there would be collisions and frictions, and
these collisions and frictions will, of course, find expression in the
production of equivalent quantities of heat. That heat will, in due
course, be radiated away at the expense of the energy of the system, and
consequently, so long as any contrary movements exist, there will be an
exceptional loss of energy from this cause. Thus the energy would
incessantly tend to decline. As the shrinking of the body proceeded
while the moment of momentum would have to be sustained, this would
incessantly tend more and more to require from all the particles a
movement in the same direction.

The second concord of the planetary system, which is implied in the fact
that all the planets go round in the same direction, need not therefore
surprise us. It is a consequence, an inevitable consequence, of the
evolution of that system from the great primæval nebula. We have seen
that it would be excessively improbable that even nine or ten planets
should revolve round the sun in the same direction, if the directions of
their movements had been merely decided by chance. We have seen that the
movements of the hosts of planets, which actually form our system, would
be inconceivable, unless there were some reason for those movements. The
chances against such an arrangement having arisen without some
predisposing cause is so vast that, even if the chances were infinite,
the case would be hardly strengthened. But once we grant that the system
originated from the contraction of the primæval nebula, dynamics offers
ready aid, and the difficulty vanishes. Not only do we see most
excellent reasons why all the planets should revolve in the same
direction; we are also provided with illustrations of similar evolutions
in progress in other parts of the universe; we learn that the evolving
nebula, however erratic may have been its primitive motion, whatever
cross currents may have agitated it in the early phases of a possibly
violent origin, will ultimately attain a rotation uniform in direction.
As the evolution proceeds, the various parts of the nebula draw together
to form the planets of the future system, and the planets retain the
movement possessed by their component particles. Thus we see that the
nebular theory not only extricates us from the difficulty of trying to
explain something which seemed almost infinitely improbable, but it also
shows why no other disposition of the motions than that which we
actually find could be expected. The nebular theory explains to us why
there is no exception to that fundamental law in the solar system which
declares that the orbits of the planets shall all be followed in the
same direction.

This wonderful agreement in the movements of the planets, which we have
called the second concord, thus affords us striking evidence of the
general truth of the nebular theory. But there is yet a third concord in
the solar system which, like the other two, lends wonderful
corroboration to the sublime doctrine of Kant and Laplace. This we shall
consider in the next chapter.

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CHAPTER XVI.

THE THIRD CONCORD.

Rotations of the Planets on their Axes.—The Older Planets—No Information
about Uranus or Neptune or the Asteroids—The Speed of Rotation is
Arbitrary so far as Kepler’s Laws are concerned—The Third Concord—A
Remarkable Unanimity—Kant’s Argument—Illustration of the Rotation of
the Moon on its Axis—How the Nebular Theory explains the
Rotation—The Moon’s Evolution—Special Action of Tides—The Evolution
of the other Satellites—The case of Mars—Jupiter and Saturn as
Miniatures of the Solar System—Uranus and Neptune offer
Difficulties.

WE have seen in the last chapter how the rotation of the sun beat time,
as it were, for the planets, by giving to them an indication of the
direction in which the revolutions round the sun should be performed,
and we have observed with what marvellous unanimity the planets follow
the precept thus given. We have now to consider yet another concord,
which has perhaps not the great numerical strength of that last
considered, but is, nevertheless, worthy of our most special attention.
The earth revolves about an axis which is not very far from being
perpendicular to the principal plane to which the movements of the solar
system are related. From a dynamical point of view it would, of course,
have been equally possible for the earth to revolve on its axis in the
same direction as the rotation of the sun, or in the opposite direction.
There is nothing so far as the welfare of man is concerned to make one
direction of rotation preferable to the other, but, as a matter of fact,
the earth does turn round in the same way as the sun turns.

Jupiter also turns on its axis, and Jupiter again, like the earth, might
turn either with the sun or it might turn in the opposite direction.
Here, again, we find a unanimity between the earth and Jupiter; they
both turn in the same direction, and that is the direction in which the
sun rotates. The same may be said of Mars, and the same may be said of
Saturn. In the case of the planets Mercury and Venus we cannot speak
with equal definiteness on the subject of their rotations about their
axes. The circumstances of these planets are such that there are great
difficulties attending the exact telescopic determination of their
periods of rotation. The widest variations appear in the periods which
have been assigned. It has, for instance, been believed that Venus
rotates in a period not greatly differing from the period of twenty-four
hours in which our earth revolves. But it has been lately supposed that
the period of Venus is very much longer, and is in fact no less than
seven months, which is, indeed, that of the revolution of Venus about
the sun. According to this view, Venus rotates round the sun in a period
equal to its revolution. If this be so, then Venus constantly turns the
same face to the sun, and the movement of the planet would thus resemble
the movement of the moon around the earth. As a matter of observation,
the question must still be considered unsettled, though there are sound
dynamical reasons for believing that the long period is much more
probable than the short one. We do not now enter into this question, or
into the still more difficult matter of the rotation of Mercury; it
suffices to say that whichever period be adopted for either of these
planets is really not material to our present argument. In both cases it
has never been doubted that the direction of the rotation of the planets
is the same as the direction in which Jupiter and Mars and the earth
rotate, these being also the same as the direction of the solar
rotation.

As to the rotations of Uranus and Neptune about their respective axes,
the telescope can show us nothing. The remoteness of both these planets
is such that we are unable to discern objects on their discs with the
definiteness that would be required if we desired to watch their
rotations. We have also no information as to the rotation of the several
asteroids. No one, I think, will doubt that each of these small planets,
equally with the large planets, does rotate about its axis; but it is
impossible for us to say so from actual knowledge.

But undoubtedly the five old planets, Mercury, Venus, Mars, Jupiter, and
Saturn, as well as the earth, all rotate in the same direction as the
sun. Each planet might rotate twice as fast, or half as fast, as it does
at present. They might all rotate in the opposite direction from that in
which they do now, or some of them might go in one direction, and some
in the other, with every variety in their diurnal periods, while the
primary condition of Kepler’s Laws would have still been complied with.
We may also note that the _direction_ in which the rotation takes place
seems quite immaterial so far as the welfare of the inhabitants on these
planets is concerned.

The fact that the planets and the sun have this third concord demands
special attention. The chance that the earth should rotate in the same
direction as the sun is, of course, expressed by one-half. It is easy to
show, that out of sixty-four possible arrangements of the directions of
rotation of the five planets and the earth, there would be only one in
which all the movements coincided with the direction of the rotation of
the sun. If, therefore, it had been by chance that the direction of
these motions was determined, then Nature would have taken a course of
which the probability was only one sixty-fourth. No doubt this figure is
by no means so large as those which expressed the probabilities of the
other planetary concords; it is, however, quite sufficient to convince
us that the direction of the rotation of the planets on their axes has
not been determined merely by the operation of chance.

We are to see if there is any physical agent by which the planets have
been forced to turn round in the same direction. And here comes in one
of those subtle points which the metaphysical genius of Kant suggested.
Let us take any two planets—say, for instance, the earth and Jupiter—and
let us endeavour to see what the nature of the agent must have been
which has operated on these planets so as to make them both rotate in
the same direction. Kant urged that there must have been some material
agent working on the materials in Jupiter, and some material agent
working on those of the earth, and that to produce the like effect in
each planet there must have been at one time a material connection
existing between that body which is now Jupiter and that body which is
now the earth. In like manner Kant saw this material connection existing
between the other planets and the sun, and thus he was led to see that
the whole material of our solar system must once have formed a more or
less continuous object. The argument is a delicate one, but it seems
certainly true that in the present arrangement of the orbits it is
impossible for us to conceive how, with intervals of empty space between
the tracks of the planets, a common influence can have been exerted so
as to give them all rotations in the same direction.

The nebular theory at once supplies the explanation of the unanimity in
the rotation of the planets, just as it supplied the explanation of the
unanimity in the directions of their revolutions. To explain the
rotation of a planet on its axis, let us imagine that one portion of the
contracting nebula has acquired exceptional density. In virtue of its
superior attraction it absorbs more and more material from the adjacent
parts of the nebula, and this will ultimately be consolidated into the
planet, though in its initial stages this contracting matter will remain
part of the nebula. We have shown that the law which decrees that the
moment of momentum must remain constant will require that, after a
certain advance in the contraction, all the parts of the nebula shall
rotate in the same direction. Thus we find that the sun, or rather the
parts of the nebula that are to form the sun, and the parts that are to
form the planets are all turning round together.

[Illustration: Fig. 51.—AN ELONGATED IRREGULAR NEBULA
(n.g.c. 6992; in Cygnus). (_Dr. W. E. Wilson, F.R.S._)
(_From the Astronomical and Physical Researches at Daramona
Observatory._)]

At this point we may consider a geometrical principle which, though
really quite simple, is not always easily understood. It has indeed
presented considerable difficulty to many people. Suppose that an
ordinary card is laid on a flat board, and that, with a bradawl, a hole
is made through the card into the board. The hole may be at the centre,
or at one of the corners, or a little way in from one of the edges, or
in any other position whatever on the card. Now suppose that a postage
stamp is stuck upon the card anywhere, and that the card is then moved
around the bradawl. How are we to describe the motion of that postage
stamp? It would certainly be revolving around the bradawl; but this
motion we may consider as composed of two others. At any instant we may
accurately represent the movement of the postage stamp by considering
that its centre was moving in a direction perpendicular to the line
joining that centre to the hole made by the bradawl, and that it also
had a rotation around its centre, the period of that rotation being just
the same as the time the card would take to go round the bradawl. Thus
we see that the movement of the postage stamp contains at any moment a
movement of translation and a movement of rotation.

We may illustrate the case we have supposed by the movement of the moon
around the earth. If the centre of the earth be considered to be at the
centre of rotation the moon may be considered to be in the position of
the postage stamp. As our satellite revolves, the same side of the moon
is continually turned towards the earth, but this is due to the fact
that the moon, at each moment, really possesses two movements, namely, a
movement of translation of its centre, in a direction perpendicular to
the line from the moon’s centre to the earth’s centre, coupled with a
slow rotation of the moon round its axis.

The contracting nebula we may liken to our piece of cardboard, the stamp
will represent the spot in which the nebulous material has contracted to
form the planet, and the position of the bradawl is the centre of the
sun. As we have seen by our illustration, the nebulous planet is endowed
with a certain movement of rotation, the period of its rotation on its
axis being equal to that of its revolution around the centre; and it is
important also to notice that both these movements take place in the
same direction.

Thus we see from the nebular theory how the primæval nebula, in the
course of its contraction, originated a planet, and how that planet was
also endowed with a movement of rotation; its period of rotation being
originally equal to the period of rotation of the whole nebula. This
explains how the planet, or rather the materials which are to form the
future planet, derived from the nebula their movement of rotation, which
must have been extremely slow in the beginning. As the contraction
continued, the materials of the gradually growing globe drew themselves
together, and tended to become separate from the surrounding nebula. At
length the time arrived when the planet became sufficiently isolated
from the rest of the nebula to permit the conservation of moment of
momentum to be applied to it individually. Thus, though the rotation was
at first excessively slow, yet, as the contraction proceeded, and as the
parts of the forming planet drew themselves closer together, in
consequence of their mutual attractions, it became necessary that the
speed with which these parts accomplished their revolutions should be
accelerated. At last, when the planet had become consolidated, and when
consequently the mutual distances of the several particles constituting
the planet had been reduced to but a fraction of what those distances
were originally, the speed of the planet’s rotation had become
enormously increased. In this manner we learn how, from the very slow
rotation which the nebulous material had at first, a solid planet may be
made to rotate on its axis as rapidly as the planets in the solar system
do to-day.

We thus find that the third concord, namely, the agreement in the
directions of the planets’ rotations, is a further strong corroboration
of the nebular theory. The unanimity of all these various movements is
the dominant characteristic of the solar system.

But this third concord, derived from the rotation of the planets, may be
yet further strengthened. The movements of the satellites, which
accompany so many of the planets, must also find their explanation from
the primæval nebula. The circumstances of the satellites are, however,
different in the different cases.

As regards the moon, the theory of its evolution is now well known,
mainly by the researches of Professor George Darwin. In the moon there
appear to have been causes at work of a somewhat special kind. We must
just refer to what is well known with regard to the history of the moon.
Here, again, we observe the importance of the principles of the
conservation of moment of momentum. As the moon raises tides on the
ocean surrounding the earth, and as those tides flow around the globe,
they cause friction, and that friction involves, as we have so often
pointed out, the loss of energy to the system. Thus, the energy of the
earth-moon system must be declining, while the moment of momentum
remains constant. Now there are only two sources from which the energy
can be derived. One of those sources is that due to the rotation of the
earth on its axis. The other is due to the moon, and consists of two
parts, namely, the energy arising from the velocity of the moon in its
orbit, and the energy due to the distance by which the earth is
separated from the moon. As the moon’s velocity depends upon its
distance, we cannot view these two portions as independent. They are
connected together, and we associate them into one. So that we say the
total energy of the earth-moon system consists partly of that due to the
rotation of the earth on its axis, and partly of that due to the
revolution of the moon around the earth. It might also seem that we
ought to add to this the energy due to the rotation of the moon around
its own axis; but this is too inconsiderable to need attention. In the
first place, the moon is so small that even if it rotated as rapidly as
the earth the energy due to the rotation would not be important. Seeing,
however, that the moon has for the rotation on its axis a period of
between twenty-seven and twenty-eight days, its velocity of rotation is
so small that, for this reason also, the energy of rotation would be
inconsiderable. We are, therefore, amply justified in omitting from our
present consideration the energy due to the rotation of the moon on its
axis.

The energy of the earth-moon system is on the decline: the lost energy
might conceivably be drawn from the rotation of the earth, or it might
be drawn from the revolution of the moon, or it might be drawn from both
If it were drawn from the revolution of the moon, that would imply that
the moon would lose some of its speed or some of its distance, or in any
case that the moon would get nearer to the earth and revolve more
slowly, the speed of the earth being on this supposition unaltered. In
this case, the moment of momentum of the earth would remain the same as
before, while the moment of momentum of the moon would be lessened; the
total moment of momentum would therefore have decreased, but this we
have seen to be impossible. It therefore follows that the energy
withdrawn from the earth-moon system is not to be obtained at the
expense of the revolution of the moon.

The energy must therefore be obtained at the expense of the rotation of
the earth on its axis. But if this be the case, the speed with which the
earth rotates must be diminished; that is to say, the length of the day
must be increased. And if the speed of the earth’s rotation be reduced,
that means that the amount of moment of momentum contributed by the
earth is lessened. But the total quantity of moment of momentum must be
sustained, and this can only be done by making the moon go further away
and describe a larger orbit. We thus see that in consequence of the
tides the length of the day must be increasing, and the moon must be
gradually retreating. Thus we find that at earlier periods the moon’s
distance from the earth must have been less than it is at present, and
the further we look back through remote periods the less do we find the
distance between the earth and the moon. Thus we see that there must
have been a time when the moon or the materials of the moon were in
actual contact with the materials of the earth. In fact, it seems quite
possible that the moon may have been a portion of the earth, broken off
at some very early period, while the earth was still in a liquid state,
if indeed it had condensed to even that extent. Thus the revolution of
the moon round the earth is hardly to be used as an argument in favour
of the nebular hypothesis. The moon is indeed a consequence of the
earth’s rotation.

The satellites of Mars offer conditions of a very different kind, though
here, again, tidal influences have been so important, that it is perhaps
questions relating to tides that are illustrated by these satellites
rather than the nebular theory.

A remarkable circumstance may be noted with regard to the movements of
the satellites of Mars. The inner satellite has a period of about seven
and a half hours, which is not a third of the period that the planet
itself takes to go round on its axis. This leads to a somewhat curious
consequence. The tides raised on Mars by this inner satellite would
certainly tend rather to accelerate the rotation of the planet than to
retard it; for these tides must course round the planet in the direction
of its rotation, but with a speed in excess of that rotation. Any tidal
friction, so far as this satellite is concerned, will tend to augment
the velocity of the planet’s rotation, just as in the opposite case,
where the moon raises tides on the earth, it is the lagging of the tides
behind the movement due to the rotation that acts as a brake, and tends
to check that speed. If, therefore. Mars is accelerated by this
satellite, it will do more than its original share of the moment of
momentum of the Martian system; it is therefore imperative that the
satellite shall do less. Accordingly, we find that this satellite must
go in towards the planet. No doubt this effect is much complicated by
the influence of the other satellite of the same planet, but the
illustration may suffice to show that if the satellites of the earth and
Mars do not convey to us much direct evidence with regard to the nebular
theory, this is largely because the effect of the tides has been a
preponderating influence. The Martian system as we now see it has
acquired its characteristic features by tidal influence, so that the
more simple influences which would immediately illustrate the nebular
theory have become hidden.

As to the satellites of Jupiter and Saturn, the circumstances are again
quite different from those that we find in the earth and in Mars. There
is little more to be said with regard to them than that everything that
they present to us is consistent with the indications of the nebular
theory. The evolution in each case has been a reproduction in miniature
of the evolution of the solar system.

But the satellites of Uranus and Neptune present, it must be admitted,
the greatest stumbling block to the acceptance of the nebular theory.
Both as to the directions in which they move and as to the planes in
which their orbits lie, it must be admitted that the satellites of
Uranus are distinctly at variance with what the nebular theory would
suggest. The consideration of this subject will be found in the next
chapter.

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CHAPTER XVII.

OBJECTIONS TO THE NEBULAR THEORY.

There are Difficulties in the Nebular Theory—The General Conformity of
the Movements—Details of the Uranian Movements—The Anomaly in the
Satellite of Neptune—Where the Difficulty Lies—The Fundamental
Principle which Dynamics Offers for our Guidance—The Immense
Contrast between the Nebula in its Original Form and its Final
Form—Energy that could be Obtained by a rearrangement of our
System—Probable Nature of the Present Change in the Plane of the
Orbits of the Satellites of Uranus—The Similar Explanation in the
Case of Neptune.

NO one will deny that there are points in connection with the nebular
theory which present difficulties which to some seem important. We shall
endeavour to estimate the significance of these difficulties in this
chapter. They are certain anomalous phenomena presented by the planets
Uranus and Neptune.

The satellites which attend upon the planets exhibit a general
conformity with those movements of the planets themselves on which we
have dwelt in Chapters XIV., XV., XVI. The planes in which the orbits of
the satellites are contained are usually not much inclined to the plane
of the ecliptic, and the directions in which the satellites revolve also
agree with the general direction of the planetary movement. We find
these conditions in the one satellite of the earth, in the two
satellites of Mars, in the five satellites of Jupiter, in the eight or
nine satellites of Saturn; but, when we come to Uranus and Neptune, the
two outermost planets, we observe a striking but most instructive
violation of the laws which we have found so consistently prevailing in
the other parts of the solar system.

Let me first mention the special circumstances of Uranus. It is now
known that this planet has four satellites. Of these, Titania and Oberon
were both discovered by Sir William Herschel on January 11th, 1787. The
two remaining satellites, named Ariel and Umbriel, were not discovered
for more than half a century later by Mr. Lassell, on October 24th,
1851. It is, however, just possible that they were previously seen by
Sir William Herschel.

The innermost of the four satellites, Ariel, accomplishes a revolution
in a day and a half, Umbriel goes round in four days and three hours,
Titania in eight days and seventeen hours, and Oberon in thirteen days
and eleven hours. We have already mentioned how the investigations of
Newcomb show that these four satellites of Uranus revolve in the same
direction and in the same plane; but this plane, instead of lying in or
near the ecliptic, is very nearly perpendicular thereto, the actual
angle being eighty-three degrees. This is one of the features in which
the satellites of Uranus are in startling disobedience to the laws which
have been so rigidly observed in most other parts of the system. But
there is also a second anomaly. The direction in which the satellites
move, when projected on the plane of the ecliptic, is found to be
opposite to the universal direction in which all the other movements in
the solar system are performed. Of course the fact that the plane of the
orbits of the satellites lies so nearly at right angles to the plane of
the ecliptic detracts somewhat from the significance of this
circumstance. If the two planes were absolutely at right angles, there
would be, of course, no projection at all, and, in the actual
circumstances, the moment of momentum, when projected, loses
nineteen-twentieths of its amount. It follows that in the actual
position of the plane the abnormal direction in which the satellites are
moving is not very material.

It must be admitted that, in the position of the plane of their orbits
and the direction of their movements, the satellites of Uranus are in
contrast to what a hasty consideration of the nebular theory might have
led us to expect. If the orbits of those satellites had all lain close
to the plane of the ecliptic, and if the direction in which the
satellites revolved had also conspired with that of the revolution of
Uranus round the sun, and with all the other hundreds of movements which
are in the same direction, there can be no doubt that we should in this
place have been appealing to the satellites of Uranus as confirmatory
evidence of the truth of the nebular theory. The fact that they move in
a manner so totally at variance with what might have been expected
cannot therefore be overlooked.

Neptune, the outermost planet of our system, presents us also with
difficulties of an analogous character. So far as the orbit of Neptune
itself is concerned, it agrees entirely with the general planetary
convention; the inclination of that orbit to the plane of the ecliptic
is no more than six degrees, and the direction in which the outermost
planet revolves round the frontier of our system is not different from
the directions in which all the other planets revolve. We know nothing
about the axis of rotation of Neptune except that it may be reasonably
presumed to be in the same plane as the movement of its satellite. On
October 10th, 1846, Lassell, with the help of his great telescope,
suspected the existence of a satellite to Neptune, and he announced it
definitely on July 7th, 1847. We are indebted to Newcomb for a careful
investigation of the orbit of this satellite. It moves in a track which
is practically circular, and it requires about five days and twenty-one
hours to accomplish each revolution. Its inclination to the ecliptic is
not so anomalous as in the case of Uranus, the inclination being in this
case not more than thirty-five degrees. This is not much greater than
the inclinations of the orbits of some of the asteroids, and it might
have passed without much comment had it not been for the circumstance
that the direction of motion of the satellite in this track is
antagonistic to all the other movements in the solar system. This is
indeed a more startling fact in some respects than the movements of the
satellites of Uranus, for, as we pointed out, the plane of the orbits of
the satellites of Uranus is so nearly perpendicular to the plane of the
ecliptic that the direction of the movement could not be held to be of
much significance. The satellite of Neptune, having an orbital
inclination barely more than a third of a right angle, exhibits a
retrograde movement which is in some respects the most anomalous feature
in the solar system.

These circumstances connected with the satellites of Uranus and Neptune
have been sometimes brought forward as arguments against the nebular
theory. What Laplace would have said to them we can only conjecture,
for, at the time he brought out his theory, Neptune was entirely
unknown, and none of the satellites of Uranus had been observed. But it
has sometimes been urged that the movements of these two systems are
inconsistent with the principles of the nebular theory, and that,
therefore, the nebular theory must be abandoned. I have no desire to
minimise the difficulties, but I think the considerations to which I now
invite attention may help to lessen them even if they do not altogether
remove them. I trust, at least, we may be able to show that even those
anomalous movements are not incompatible with the acceptance of the
account of the origin of our solar system given by the nebular theory.

The primæval nebula may be regarded as chaotic in its earliest stages;
perhaps it was like the nebulous wisps in Fig. 51. It was chaotic in the
arrangement of the material of which it is formed, and in the movements
of that material. Before a disorganised nebula can become evolved into a
nebula with any definite form like that in Fig. 52, or into anything
resembling a solar system, an immense period of time must elapse, and
during that time the operation of the laws of dynamics gradually
impresses certain well-marked features on the nebula, and disposes it to
assume an orderly form. We have explained that no matter how the nebula
originated, or no matter what may have been the irregularities in its
extent or distribution, and no matter how diverse may have been the
agitations of its various parts, the principles of dynamics assure us
that each such nebula must, for all time, stand in some special relation
to a certain particular plane. The moment of momentum which the nebula
has with respect to this plane, exceeds the moment of momentum that it
has with respect to any other plane. We have pointed out how,
notwithstanding the vicissitudes and transformations to which, in the
course of illimitable ages, the nebula must submit, its moment of
momentum relatively to this plane will remain absolutely unaltered. We
have shown how the energy of the nebula becomes gradually exhausted. The
collisions between various particles, the frictions that will
necessarily arise, and the actions which we may sufficiently describe by
saying that they are of a tidal character, will all result in the
transformation of energy into heat. This heat is radiated away and lost,
and there is a corresponding decline in the energy of the system. To
preserve its moment of momentum unaltered in the course of ages,
notwithstanding the continuous reduction of energy, the materials of the
nebula will ever find themselves more and more approximating to the
plane, and will ever find themselves more and more compelled to revolve
in the same direction. If the original size of the nebula be compared
with the area of the Atlantic Ocean, the condensed form which the nebula
may ultimately assume may be no larger than a coral island. If the nett
moment of momentum, diffused over the space as large as the ocean, has
still to be preserved in the space as large as the island, we need not
be surprised that the spin of the system in its condensed form is its
dominating characteristic.

In the evolution of our solar system from the primæval nebula, this
operation of reducing the movements to the same plane and of requiring
that all the movements shall take place in the same direction, having
had play for unmeasured ages, has in the main accomplished its end. All
the important bodies of the system do go round in the same direction;
that much, at least, has been attained. All of them also go round in
planes which are nearly coincident, but, as we have already noted, they
are not yet absolutely coincident. The greatest planets have, however,
very nearly become reconciled, so far as the planes of their orbits are
concerned, to the condition which dynamics imposes. The same is true of
the rotation of the sun on its axis. That axis is inclined at an angle
of eighty-three degrees to the plane of the ecliptic, so that the sun’s
equator would have to be shifted only through an angle no greater than
seven degrees, if it were to be placed in the plane in which it should
be situated, if the condition of the smallest quantity of energy for a
given amount of moment of momentum was to be realised. We find a greater
discrepancy in the plane of the earth’s equator. This is inclined by
about twenty-three degrees to the plane of the ecliptic. Here there is
some energy which might yet be expended without a diminution of the
amount of moment of momentum in the system; for if the earth’s axis were
to be made perpendicular to the plane of the ecliptic, then the velocity
of rotation of the earth about its axis might undergo a corresponding
abatement, and yet keep up the requisite moment of momentum. We thus see
that even with the older planets the conditions which would be enforced,
if the moment of momentum was to be sustained with the least quantity of
energy, are not absolutely complied with; which simply means that there
has not yet been time enough for our system to arrive at the perfect
state, to which it must be approximating.

If we have found that in the rotations of the earth and of the sun, and
in the revolutions of the planets round the sun, the conditions
ultimately aimed at have not yet been reached, why should we feel
surprised that in the outer planets of our system, Uranus and Neptune,
the conditions which evolution tends to produce have not yet been fully
attained? That the operation of the conservation of moment of momentum
is in progress in the internal economy of the Uranian system, we have
already had occasion to explain in Chapter XI. The fact which Newcomb
demonstrated, that the four satellites revolve in the same plane, can
only be accounted for by the supposition that in that system the
conservation of moment of momentum, with declining energy, has gradually
imposed this condition on the system belonging to Uranus. With reference
to the position of the plane of the satellites, in the case of Uranus
and Neptune, we would say, that though at present their arrangement
appears anomalous, it will probably not always remain so. The fact that
the satellites of Uranus are in a plane nearly perpendicular to the
plane of the ecliptic really implies that there is a certain amount of
energy still disposable in our system, if by readjustment of the plane
of the Uranian satellites the necessary moment of momentum in the system
is still preserved.

[Illustration: Fig. 52.—TWO-BRANCHED SPIRAL (n.g.c. 7479; in Pegasus).
(_Lick Observatory._)]

The laws of dynamics tell us that the orbits of planets must be
gradually, if with excessive slowness, tending still further to the same
plane. In this process energy can be expended by the system, while the
moment of momentum is unabated. We can at least suggest what seems to be
at this moment in progress in the system belonging to Uranus. It will
readily be admitted that there may be a difficulty in seeing how the
movement of a planet, which is going in the wrong direction, could be
stopped and turned into the right direction. But we need not suppose
that so violent a change as this would imply is to be expected in our
system. We are quite accustomed to find the planes of the orbits of all
planets in gradual movement. The plane containing the orbits of the four
satellites of Uranus is at this moment probably moving gradually
upwards. It will in due course become actually at right angles to the
ecliptic, and we may then reasonably assume that it will advance further
in the same direction. At the moment the right angle is passed, this
continuous movement will have the effect of changing the directions of
the satellites’ movement from retrograde to direct. The present anomaly
will then tend to become evanescent, for, as the exhaustion of the
energy continues, the planes of the satellites of Uranus will gradually
come into conformity with the plane of the ecliptic.

We make no doubt that there may be a similar explanation of the
movements of the satellite of Neptune. The inclination of the plane of
the orbit of the satellite to the ecliptic is probably now increasing.
It will ultimately come to be at right angles thereto, and then the next
advance of the plane will convert, by a continuous action, the
retrograde motion of the satellite, at present so disconcerting, into a
direct motion. The change of the plane will still continue until it,
too, may ultimately coalesce with the ecliptic.

The fact appears to be, that though an enormous quantity of energy must
have been lost by radiation from our system during the illimitable ages
through which the evolution has been running its course, the disposable
energy is not yet quite exhausted. There are certain adjustments in our
system which may still be made and which will allow of yet further
radiation of energy, while still preserving sufficient to keep up the
necessary moment of momentum. It seems obvious that the system is
tending towards a condition in which the planes of all the orbits shall
be coincident, and in which all the directions shall be absolutely
unanimous. If we were at once to alter the system by moving all the
orbits into the plane of the ecliptic, but making no change in the
dimensions of those orbits, or the velocities concerned; if we were also
to adjust the rotations of the earth, as well as of the other planets,
so that all the axes of rotation should be perpendicular to the plane of
the ecliptic; if we were to turn the plane of the satellites of Uranus
through that angle of 97°, which would suffice at the same time to bring
it into coincidence with the ecliptic, and lay the movements of the
satellites in the right direction; if we were also to turn the orbit of
the satellite of Neptune through 145°, thus bringing that orbit to
coincide with the plane of the ecliptic, in such a manner that the
direction of the movement of the satellite of Neptune conspired with all
the other movements of the system, then this rearrangement of the system
would increase the moment of momentum, while the quantity of energy was
not altered. But this is the same thing as saying that some energy yet
remains to be disposed of, while the system still preserves the
requisite moment of momentum.

The conclusion we come to may be thus expressed: the movements of the
satellites of Uranus and Neptune do not disprove the nebular hypothesis.
They rather illustrate the fact that the great evolution which has
wrought the solar system into form has not yet finished its work; it is
still in progress. The work is very nearly done, and when that work
shall have been completed, the satellites of Uranus and Neptune will no
longer be dissociated from the general concord.

------------------------------------------------------------------------

CHAPTER XVIII.

THE BEGINNING OF THE NEBULA.

Nebula not of Infinite Duration—8,300 Coal-Units was the Total Energy
of the System—460 Miles a Second—Solar Nebula from a
Collision—What we Know as to the Colliding Bodies—Probability of
Celestial Collisions—Multitudes of Dark Objects—New Star in
Perseus—Characteristics of New Stars—Incandescent Hydrogen—The
Ruby in the Spectrum—Photographs of the Spectrum—Rarity of a
Collision on a Scale Adequate to a Solar System.

WHATEVER may have been the antiquity of the actual elements that formed
the primæval nebula from which the solar system has been evolved, the
nebula itself has certainly not been of infinite duration. The question
then arises as to what has been the origin of the nebula as such, or
rather by what agency the material from which the nebula was formed
underwent so radical a transformation from its previous condition as to
be changed into that glowing object which we have considered so
frequently in this book. We have to explain how, by the operation of
natural causes, a dark body can be transformed into a glowing nebula.

Let us first estimate what the quantity of energy in that system is. The
sun has been pouring forth heat for inimitable ages, and will doubtless
continue to pour forth heat for millions of years to come. But the
destiny which awaits the sun, though it may be protracted, yet cannot be
averted. The sun will go on pouring forth its heat and gradually
shrinking. The time will come at last when the radius of the sun will
have appreciably decreased, and when once it has assumed a density
corresponding to a solid state its history as a radiant globe will be
approaching its close. A period of insignificant extent, a century or
less, will then suffice for that solid globe to cool down so as to be no
longer an efficient source of light and heat. We shall assume that when
the sun has ultimately become solid and cold, and when it is no longer
the life and light of our system, it will have attained a mean density
of 21.5, which we have chosen because that is the density of platinum,
the heaviest substance known. In all probability the solar density will
never become so great as this, but to include the most extreme case in
our argument I am making the assumption in the form stated. We are now
to estimate what will have been the total energy that the sun has
radiated from the moment when as an indefinitely great nebula it first
began to radiate at all, down to that moment in the future when, having
shrunk to the density of platinum, and having parted with all its heat,
the solar radiation is at an end.

In the beginning of the evolutionary history the sun was a nebula, which
we have supposed to extend in every direction to an indefinitely great
distance. The system has resulted from the contraction of that nebula,
and the energy liberated in that contraction has supplied the sun’s
radiation. We calculate (_see_ Appendix) the energy that would be given
out in the contraction of a nebula whose materials were originally at
infinity, and which ultimately coalesced to form a cold, solid globe of
the density of platinum, and as heavy as the sun. There is no object in
attempting to express this quantity of energy in foot-pounds—the figures
would convey no distinct impression—we shall employ the coal-unit
explained in Chapter VI. We imagine a globe of coal the weight of the
sun; then, if that globe of coal were adequately supplied with oxygen,
it would, on combustion, give out a certain amount of heat, which is a
convenient unit for our measurements. It is demonstrated that the
quantity of energy given out by the contraction of the nebula from
infinity, to this globe of the density of platinum, would be about equal
to the quantity of energy which would be produced by the combustion of
8,300 globes of coal as heavy as the sun, an adequate contribution of
oxygen being supposed to be supplied. This expresses the original
endowment of energy in the solar system, or rather a major limit to that
endowment; it shows that the solar system can never have developed more
energy by contraction than that which could be produced by the
combustion of 8,300 globes of coal as heavy as the sun. We may mention
that of this great endowment of energy an amount which is rather less
than half (3,400) has been already expended, so that rather more than
half of the sun’s career as a radiant globe may yet have to be run.

We can also express the total energy of the solar system in a different
manner. We shall consider what must be the velocity of the sun, so that
the energy that it will possess, in virtue of that velocity, shall be
equal to the energy which could be produced by the combustion of 8,300
globes of coal of the same weight. This calculation is very much
simplified by making use of a principle which we have already stated and
applied in Chapter V. We have shown that if a piece of coal be animated
with a velocity of five miles a second, the energy it possesses in
virtue of that motion is equal to the energy produced by the coal in the
act of combustion. If a body were moving at the rate of, let us say, 100
miles a second—its speed being then twenty times as great as the
particular speed just mentioned—its energy, which depends on the square
of the velocity, would be 400 times as much as would be produced by the
burning of a piece of coal equal to it in weight. We can easily
calculate that if the sun were moving at a speed of 460 miles a second,
it would possess, in virtue of its motion, as much energy as would be
generated by the contraction of the primæval nebula from infinity down
to a globe of the density of platinum.

It is thus easy to form a supposition as to how the nebula constituting
our solar system may have come into being; most probably it originated
in this way. Let us suppose that two masses, either dark or bright,
either hot or of the temperature of space, or the temperature of frozen
air, were moving with speeds of 460 miles a second. No doubt the
velocities we are here postulating are very high velocities, but they
are not unprecedentedly high. We know of stars which at this present
moment move quite as fast, so that there is nothing unreasonable in our
supposition so far as the velocities are concerned. Let us suppose that
each of these bodies had a mass which is half that of our present solar
system. If these two bodies dashed into collision, when moving from
opposite directions, the effect of the blow would be to transform the
energy into heat. That heat would be so great that it would be
sufficient not alone to render these globes red-hot and white-hot, but
even to fuse them—nay, further, to drive them into vapour, even to a
vapour which might expand to an enormously great distance. In other
words, it is quite conceivable that a collision of two such masses as we
have here supposed might be adequate to the formation of a nebula such
as that one which in the lapse of indefinite ages has shaped itself into
the solar system.

Before the collision, which resulted in the formation of the nebula,
each of these bodies, or rather their centres of gravity, would be
moving in what may be regarded for the moment as straight lines, and a
plane through those two straight lines will be a plane which for ever
afterwards will stand in important relation to the system. It will be,
in fact, that principal plane of which we have so often spoken.

As those two bodies met they would possess a certain moment of momentum,
and this moment of momentum would remain for ever unaltered, no matter
what may be the future vicissitudes of the system.

For the sake of simplicity in describing what has occurred, we have
spoken as if the two bodies were of equal mass, and, moving with equal
velocities from opposite points of the heavens, dashed into collision.
But what actually happens cannot have been quite so symmetrical. There
is one feature in the solar system which absolutely proves that the
collision cannot have taken place precisely in the way we have laid
down. If it had happened that two equal masses had been hurled into
collision with equal velocities from precisely opposite directions, then
there could have been no resultant moment of momentum. From the
principle of the conservation of moment of momentum, we can see that, if
absent in the beginning, it could never originate later. As, however, we
have a large moment of momentum in the movements of the planets and the
sun, it is certain that the collision cannot have taken place in a
manner quite so simple.

[Illustration: Fig. 53.—CLUSTER WITH STARS OF 17TH MAGNITUDE
(n.g.c. 6705; in Antinous).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]

The probabilities of the case show that it is almost infinitely unlikely
that two bodies of equal dimensions, and moving with equal velocities in
opposite directions, should come squarely into collision. It would be
much more likely that the bodies should be not of the same size, not
moving with the same velocity, and should collide partially rather than
squarely. The collision may have been, in fact, little more than a
graze. The probabilities of the case are such as to show that what
actually occurred was a collision between two unequal masses, which were
moving in directions inclined to each other and with different
velocities. It is easy to show that, granted sufficiently great
velocities, an impact which fell far short of direct collision might
still produce enough heat to transform the whole solar system into
vapour.

The circumstances which would naturally accompany so transcendent an
incident will also go far to account for a difficulty which has been
often felt with regard to the evolution of the system from a nebula.
Were such a collision to take place we should certainly not expect that
the resulting nebulous mass, the product of a shock of such stupendous
violence, would be a homogeneous or symmetrical object. Portions of the
colliding body would become more highly heated than others; portions of
the bodies would not be so completely transformed into vapour as would
other parts. There would thus be differences in the nebula at the
different parts of its mass. This non-homogeneity would be connected
with the formation and growth of planets in the different parts of the
nebula.

There is another circumstance connected with the movement of the sun
which should here be mentioned. It is well known that the sun has a
velocity which carries it on through space at the rate of half a million
miles a day. In this movement the whole solar system, of course,
participates. This movement of translation of our system must also be a
result of the movements of the two original colliding masses. These two
masses imparted to the system, which resulted from their union, both the
lineal velocity with which it advances through space, and also that
moment of momentum which is of such vast importance in the theory.

A consideration of the probabilities of the case make it quite certain
that the celestial bodies we see are as nothing compared with the dark
bodies we do not see. The stars we see are moving, and the natural
assumption is that the dark objects with which the heavens teem are also
in motion. We shall, under these conditions, not feel any insuperable
difficulty in the supposition that collisions between different bodies
in the heavens may have taken place from time to time. We remember that
these bodies are moving in all directions, and at extremely high
velocities. We are quite willing to grant the excessive improbability
that any two bodies particularly specified should come into collision.
Within view of our telescopes we have, however, a hundred millions of
stars, and if we multiply that figure even by millions, it will still,
we may well suppose, not be too large to express the number of bodies
which, though contained within the region of space ranged over by our
telescopes, are still totally invisible. In these circumstances, we may
admit that occasional collisions are not impossible. Please note the
strength which the argument derives from the enormous increase in our
estimate of the number of bodies, when we include the dark objects as
well as the stars. If we were asked whether it would ever be possible
for two bright stars to come into collision, we might well hesitate
about the answer. We know, of course, that the stars have proper
motions; we know, too, that the stars, in this respect unlike the
planets, have no definite directions of movement under the control of a
supreme co-ordinating attraction. Some stars move to the right, and some
to the left, some one way and some another; but even still,
notwithstanding their great number, the extent of space is such that the
stars keep widely apart, and thus collisions can hardly be expected to
take place, unless perhaps in a cluster such as that shown in Fig. 53.
We have no reason to think that a collision between two actual bright
stars was the origin of the primæval nebula of our system. But when we
reflect that the stars, properly so called, are but the visible members
of an enormously greater host of objects, then the possibilities of
occasional collision between a pair of these incomparably more abundant
dark bodies seems to merit our close attention. We are not by any means
claiming that such collisions occur frequently. But what we do say is,
that if, as we believe, these bodies are to be reckoned in many millions
of millions, then it does sometimes happen that two of them, moving
about in space, will approach together sufficiently to give rise to a
collision. It was from some such collision that we believe the nebula
took its rise from which the solar system originated.

We have the best reason for knowing that celestial collisions do
sometimes occur. It will be in the recollection of the readers of this
chapter that in February, 1901, the astronomical world was startled by
the announcement of the outbreak of a new star in Perseus. A photograph
of that part of the heavens had been taken a few days before. There were
the ordinary stars, such as existed from time immemorial, and such as
have been represented on the numerous maps in which the stars are
faithfully set down. But, on February 22nd, Dr. Anderson, already famous
by similar discoveries, noticed that the constellation of Perseus
contained a star which he had not seen before. Instantly the
astronomical world was apprised by telegraph that a new star had
appeared in Perseus, and forthwith most diligent attention was paid to
its observation. Photographs then obtained show the stars that had been
seen there before, with the addition of the new star that had suddenly
come into view. For a few nights after its discovery the object
increased in lustre, until it attained a brightness as great as that of
Capella or Vega. But in this state it did not long remain. This
brilliant object began to wane. Presently it could not be classed as a
star of the first magnitude, nor yet of the second, and then it ran down
until a little below the third, and even below the fourth. In the
subsequent decline of the star there were several curious oscillations.
On one night the star might be seen, the next night it would be hardly
discerned, while the night after it had again risen considerably. But,
notwithstanding such temporary rallies, the brightness, on the whole,
declined, until at last the star dwindled to the dimensions of a small
point of light, scarcely distinguishable with the naked eye. The decline
was apparently not so rapid as the increase, but nevertheless from the
first moment of its appearance to the last was not longer than a few
weeks.

This new star in Perseus established, in one sense, a record. For the
star was brighter than any new star which had been noticed since the
days of accurate astronomical observations. Not indeed for three
centuries had a star of such lustre sprung into existence. But a
temporary star, such as this was, has been by no means an infrequent
occurrence. Many such have been recorded. Those who have been acquainted
with astronomical matters for thirty years will recollect four or five
such stars. In each of them the general character was somewhat the same.
There was a sudden outbreak, and then a gradual decline. The questions
have sometimes arisen as to whether the outbreak of such an object is
really the temporary exaltation of a star which was previously visible,
or whether it ought not to be regarded as the creation of a totally new
star. In some cases it does seem possible that a new star may have been
partly, at all events, due to a large increase of brightness of some
star which had been known before. In the case of Nova Persei, however,
we have the best authority that this is not the case. Professor
Pickering, the distinguished astronomer of Harvard College Observatory,
happened to photograph the region in which Nova Persei appeared a few
days before the outbreak took place. He tells us that there is not the
least indication on his photograph of the presence of a star in that
region.

[Illustration: Fig. 54.—SPECTRUM OF NOVA PERSEI (1901).
(_Photographed with the 40 in. Yerkes Telescope by Mr. Ferdinand
Ellerman._)]

The spectrum of Nova Persei, in an instrument of sufficient power,
appeared a truly magnificent object. Like other stellar spectra, it
displayed the long line of light marked with the hues of the rainbow,
but it was unlike the spectra of ordinary stars in respect of the
enormous enhancements of the brightness at various parts of this
spectrum. For instance, at one end of the long coloured band a brilliant
ruby line glowed with a lustre that would at once attract attention, and
demonstrated that the object under view must be something totally
different from ordinary stars. This superb feature is one of the lines
of hydrogen. The presence of that line showed that m the source from
which the light came there must have been a remarkable outbreak of
incandescent hydrogen gas. At various points along the spectrum there
were other beautiful bright lines which, in each case, must have been
due to glowing gas. Here we have the evidence of the spectrum telling us
in unmistakable language that there were features in this star wholly
unlike the features found in any ordinary star. It is impossible to
dissociate these facts from the history of the star. Much of what we
have said with regard to the spectrum of Nova Persei might be repeated
with regard to the spectrum of the other temporary stars which, from
time to time, have burst forth. In each case the spectrum characteristic
of an ordinary star is present, but superadded to it are bright lines
which indicate that some great convulsion has taken place, a convulsion
by which vast volumes of gas have been rendered incandescent. In Fig. 54
we show the spectrum of Nova Persei on five dates, from February 27th to
March 28th, 1901. These photographs were taken by Mr. Ferdinand Ellerman
with the great telescope of the Yerkes Observatory. They show in the
clearest manner the bright lines indicating the incandescent gases.

We have pointed out the high probability that among the millions and
millions of bodies in the universe it may now and then happen that a
collision takes place. Have we not also explained how the heat generated
in virtue of such a collision might be sufficient, and, indeed, much
more than sufficient, to raise the masses of the two colliding bodies to
a state of vivid incandescence? A collision affords the simplest
explanation of the sudden outbreak of the star, and also accounts for
the remarkable spectrum which the star exhibits.

------------------------------------------------------------------------

CHAPTER XIX.

CONCLUDING CHAPTER.

Comprehensiveness of the Nebular Theory—Illustration—Huxley and the
Origin of Species—Rudimentary Organs—The Apteryx—Its Evanescent
Wings—The Skeleton—An Historical Explanation—Application of the Same
Method to the Nebular Theory—The Internal Heat of the Earth—The Lady
Psyche.

IT is not difficult to show that the nebular theory occupies a unique
position among other speculations of the human intellect. It is so
comprehensive that almost every conceivable topic will bear some
relation to it. Perhaps I may venture to give a rather curious
illustration of this fact, which was told me many years ago by one who
attended a course of lectures by an eminent Professor in the medical
faculty at, let us say, Vienna. The subject of the course was the no
doubt highly important, but possibly not generally interesting, subject
of “inflammation.” I think I am right in saying that the course had to
last for six months, because the subject was to be treated with
characteristic breadth and profundity. At all events, I distinctly
remember that the learned Professor commenced his long series of
professional discourses with an account of the nebular theory, and from
that starting point he gradually evolved the sequence of events which
ultimately culminated in—inflammation!

It may be remembered that in the year 1880, Professor Huxley delivered
at the Royal Institution a famous lecture which he termed “The Coming of
Age of the Origin of Species.” Among the many remarkable and forcible
illustrations which this lecture contained, I recall one which brought
before the audience, in the most convincing manner, the truth of the
great Darwinian Theory of Evolution. Huxley pointed out how the
discoveries in Biology, during the twenty-one years which immediately
succeeded the publication of the “Origin of Species,” had been so
numerous and so important, and had a bearing so remarkable on the great
evolutionary theory, that even if the Darwinian Theory had not been
formed to explain the facts of Nature, as they were known at the time
when Darwin published his immortal book, the same theory would have had
to be formed, were it only to explain the additional facts which had
come to light since the great theory itself had been first given to the
world.

I believe we may use similar language with regard to the nebular theory
and its great founders, Kant, Laplace, and Herschel. If the facts which
were known to these philosophers led them to adopt in one form or
another that view of the Origin of the Universe which the nebular theory
suggests, how stands the theory now in the light of the additional facts
that have been since disclosed? If we merely took the discoveries which
have been made since the last of the three great philosophers passed
away, it might well be maintained that a nebular theory would be
demanded to account for the facts brought to light, in the interval.

The argument on which the nebular theory of the solar system is founded
has other parallels with that wonderful doctrine of Natural Selection by
which Darwin revealed the history of life on our globe. It not
unfrequently happens that an animal has in its organisation some
rudiments of a structure which is obviously of no use to the animal in
his present mode of life, and would be unintelligible if we supposed the
animal to have been created as he is. A curious instance of a
rudimentary structure is furnished in the apteryx, the famous wingless
bird which still lives in New Zealand.

The arrival of civilisation in New Zealand seems likely to be
accompanied with fatal results, so far as the unfortunate apteryx is
concerned. Weasels and other fierce enemies have been introduced, with
which this quaint bird of antiquity is unable to cope. The apteryx is
defenceless against such foes. Nature had not endowed it with weapons
wherewith to fight, for it had, apparently, no serious adversaries until
these importations appeared in its island home. Unlike the ostrich, the
apteryx has neither strength to fight his enemies, nor speed to run away
from them, though, like the ostrich, it has no wings for flight; indeed,
the apteryx has no wings at all. As its name signifies the apteryx is
the wingless bird. Living specimens are still to be seen in the
Zoological Gardens. The special point to notice is that, though he has
no wings whatever, still there are small rudimentary wing-bones which
can be easily seen. You need not be afraid to put your hand on the
apteryx, and feel the puny little remnants of wings (Fig. 55).

If, having seen the bird in the Zoological Gardens, you go to the
Natural History Museum, you will there find a skeleton of the apteryx
(Fig. 56). Look near the ribs in the photograph, and there you will see
those poor little wing-bones—wing-bones where there never was a wing.
From our present point of view these wings are, however, more
interesting and instructive than the most perfect wings of an eagle or a
carrier-pigeon. Those wings in the apteryx may be incapable of flight,
but they are full of instruction to the lover of Nature. As it is
certain that they are absolutely of no use whatever to the bird, we may
well ask, why are they there? They are not there to give assistance to
the bird in his struggle for life; they cannot help him to escape from
his enemies or to procure his food; they cannot help him to tend and
nurture the young one which is hatched from the egg; they can help him
in no way. The explanation of those ineffectual wings is historical.
Those bones are present in the apteryx simply because that bird has come
down by a long line of descent from birds which were endowed with
genuine wings, with wings which enabled them to fly like rooks or
partridges.

[Illustration: Fig. 55.—THE APTERYX: A WINGLESS BIRD OF NEW ZEALAND.]

[Illustration: Fig. 56.—SKELETON OF THE APTERYX, SHOWING RUDIMENTARY
WINGS.]

But if this be the explanation, how has it come to pass that the wings
have dwindled to useless little bones? We cannot of course feel certain
of the reason, but it seems possible to make surmises. In early times
winged birds flew over the sea into New Zealand, and found it a country
of abundance, as many other immigrants have done in later times. It may
have been that the food in New Zealand was so plentiful that the wants
of the birds could be readily supplied, without the necessity for
ranging over large tracts. It may have been that the newly arrived birds
found that they had few or no enemies in New Zealand, from which flight
would be necessary as a means of escape. It may possibly have been both
causes together, and doubtless there must have been other causes as
well. The fact is, however, certain, that in the course of long
generations this bird gradually lost the power of flight. Natural
selection decrees that an organ which has ceased to serve a useful
purpose shall deteriorate in the course of generations. If the wings had
become needless in the search for food, unnecessary for escape from
enemies, and useless for protection of its young, they would certainly
tend towards disappearance. The organism finds it uneconomical to
maintain the nutrition of a structure which discharges no useful end.
The wings, in such circumstances, would be an encumbrance rather than an
aid, and so we may readily conjecture that, in accordance with this
well-known principle, the wings gradually declined, until they ceased to
be useful organs, so that now merely a few rudimentary bones remain to
show that the bird’s ancestors had once been as other birds. Whatever
may have been the cause, it seems certain that in the course of
thousands of years, or it may be in scores of thousands of years, these
birds lost the power of flight; thus they gradually ceased to have
wings, and these little bones are all that now remain to render it
almost certain that, if we could learn what this bird’s ancestry has
been, we should find that it was descended from a bird which had useful
wings and vigorous flight. Whenever we find an organ which is obviously
rudimentary, or of no use to its possessor in its present form, Darwin
has taught us to look for an historical explanation. Let us see if we
cannot apply this principle to the illustration of the nebular theory.

[Illustration: SPIRALS IN OTHER DEPARTMENTS OF NATURE.
Fig. 57.—FORAMINIFER.
Fig. 58.—NAUTILUS.]

We liken the internal heat of the earth to the rudimentary wing-bones of
the apteryx. In each case we find a survival devoid of much
significance, unless in regard to its historical interpretation. But
that historical significance can hardly be over-estimated. Unimportant
as the wing-bones may be, they admit of explanation only on the
supposition that the apteryx was descended from a winged ancestor.
Unimportant as the internal heat, still lingering in our globe, may
seem, it admits of explanation only on the supposition that the earth
has had the origin which the nebular theory suggests.

That the earth’s beginning has been substantially in accordance with the
great Nebular Theory is, I believe, now very generally admitted. But the
only authority I shall cite in illustration of this final statement is
the Lady Psyche, who commences her exquisite address to her “patient
range of pupils” with the words:—

“This world was once a fluid haze of light,
Till toward the centre set the starry tides,
And eddied into suns, that wheeling, cast
The planets;”

------------------------------------------------------------------------

APPENDICES.

-------

I.—ON THE HEAT GIVEN OUT IN THE CONTRACTION OF THE NEBULA.

§ 1. FUNDAMENTAL THEOREMS IN THE ATTRACTION OF GRAVITATION.

The first theorem to be proved is as follows:—

_The attraction of a thin homogeneous spherical shell on any point in
its interior vanishes._

[Illustration: Fig. 59.]

Take any point P within the sphere. Let this be the vertex of a cone
produced both ways, but with a very small vertical angle, so that the
small areas S and S´, in which the two parts of the cone cut the sphere,
may be regarded as planes. Draw the tangent planes at S and S´. Let the
plane of the paper pass through P and be perpendicular to both these
tangent planes. Let O P O´ be one of the generators of the cone, and let
fall P Q perpendicular to the tangent plane at O, and P Q´ perpendicular
to the tangent plane at O´. The volume of the cone with the vertex at P
and the base S is ⅓ P Q × S, and the other part of the cone has the
volume ⅓ P Q´ × S´.

As the vertical angles of the cones are small, their volumes will, in
the limit, be in the ratio of O P^3 to O´ P^3, and accordingly ⅓ P Q · S
÷ ⅓ P Q´ · S´ = P O^3 ÷ O´ P^3. But from the figure P Q ÷ P Q´ = P O ÷ P
O´, and hence S ÷ O P^2 = S´ ÷ O´ P^2.

As the shell is uniform, the masses of the parts cut out by the cones
are respectively proportional to S and S´. Hence we see that the
attractions of S and S´ on P will neutralise. The same must be true for
every such cone through P, and accordingly the total attraction of the
shell on a particle inside is zero.

The second fundamental theorem is as follows:—

_A thin spherical homogeneous shell produces the same attraction at an
external point as if its entire mass were concentrated at the centre of
the sphere._

This is another famous theorem due to Newton. He gives a beautiful
geometrical proof in Section XII. of the first book of the “Principia.”
We shall here take it for granted, and we shall consequently assume
that—

_The attraction by the law of gravitation of a homogeneous sphere on an
external point is the same as if the entire mass of the sphere were
concentrated at its centre._

§ 2. ON THE ENERGY BETWEEN TWO ATTRACTING MASSES.

Let _m_ and _m´_ be two attracting bodies supposed to be small in
comparison with their distance _x_. Let the force between them be ε _m
m´_ ÷ _x_^2 when ε is the force between two unit masses at unit
distance. It is required to find the energy necessary to separate them
to infinity, it being supposed that they start from an initial distance
_a_. The energy required is obtained by integrating between the limits
infinity and _a_, and is consequently ε _m_ _m´_ ÷ _a_.

§ 3. ON THE ENERGY GIVEN OUT IN THE CONTRACTION OF THE NEBULA.

We assume that the nebula is contracting symmetrically, so that at any
moment it is a homogeneous sphere. We shall consider the shell which
lies between the two spheres of radii, _r_ + _dr_ and _r_ respectively.

Let M´ be the mass of the nebula contained within the sphere of radius
_r_, and let _d_M´ be the mass of the shell just defined. Then it
follows from § 1 that the condensation of the shell will have been
effected by the attraction of the mass M´ solely. The exterior parts of
the nebula can have had no effect, for the outer part has always been in
symmetrical spherical shells exterior to _d_M´, and the attraction of
these is zero. We see from § 2 that the contraction of _d_M´ from
infinity, until it forms a shell with radius _r_, represents a quantity
of energy,

(ε M´_d_M´)/_r_ ;

for it is obvious that the energy involved in the contraction of the
whole shell is the sum of the energies corresponding to its several
parts.

If M be the total mass and _a_ the radius of the nebula always supposed
homogeneous

M´ = M (_r_^3/_a_^3),

and therefore

_d_M´ = 3 M (_r_^2/_a_^3) _dr_.

Hence the work done in the contraction is

(ε/_r_) M (_r_^3/_a_^3) · 3 M (_r_^2/_a_^3) _dr_ = (3 ε/_a_^6) M^2 _r_^4
_dr_.

Integrating, therefore, the total work of contraction is

⅗ (ε M^2/_a_)

At the present moment a mass of 1 lb. at the surface of the sun would
weigh 27 lbs. if tested by a spring balance. Hence

ε M/_a_^2 = 27.

With this substitution we find the expression for the foot-pounds of
work corresponding to the contraction of the nebula from infinity to a
sphere of radius _a_ to be,

⅗ · 27 _a_ M = 16 _a_ M very nearly.

Hence we have the following fundamental theorem due to Helmholtz, which
is the basis of the theory of sun heat.

_If the sun he regarded as a homogeneous sphere of mass_ M _pounds and
radius a feet, then the foot-pounds of energy rendered available for sun
heat by the contraction of the solar material from, an infinite distance
is_ 16 a M.

§ 4. EVALUATION OF THE SUN HEAT GIVEN OUT IN CONTRACTION.

The number of foot-pounds of work given out in the contraction from
infinity is 16 _a_ M. As 772 foot-pounds are equal to one unit of heat,
_i.e._ to the quantity of heat necessary to raise 1 lb. of water 1°
Fahrenheit, we see that 772 M is the work required to raise a mass of
water equal to the mass of the sun through 1° Fahrenheit. Hence the
number of globes of water, each equal to the sun in mass, which would be
raised 1° Fahrenheit by the total heat arising from the contraction, is

(16 _a_)/772,

but _a_, the radius of the sun in feet, is 2,280,000,000, and hence we
have the following theorem:—

_The energy liberated in the contraction of the sun from infinity to its
present dimensions would, if turned into heat, suffice to raise
47,000,000 globes of water, each having the same mass as the sun,
through 1° Fahr._

It is found by experiment that 1 lb. of good coal may develop 14,000
units of heat, and is therefore equivalent to 14,000 × 772 foot-pounds
of work. A mass of coal equal to the sun would therefore (granted oxygen
enough) be equivalent to 14,000 × 772 × M foot-pounds of work. But we
have

(16 _a_ M) 16 × 2,280,000,000
–––––––––––––– = ––––––––––––––– = 3,400.
14,000 × 772 × M 14,000 × 772

Hence we see that

_The energy liberated in the contraction of the sun from infinity to its
present dimensions, is as great as could be produced by the combustion
of 3,400 globes of coal, each as heavy as the sun._

We may speak of 3,400 in this case as the coal equivalent.

§ 5. ON THE FURTHER CONTRACTION OF THE SUN AND THE HEAT THAT MAY THUS BE
GIVEN OUT.

Let us suppose the sun contracts to the radius _r_, and then, as already
proved, § 3, the energy it gives out is

⅗ (ε M^2)/_r_,

but we have

ε M/_a_^2 = 27,

whence on contraction to the radius _r_ the total energy given out from
the commencement is

16 M (_a_^2/_r_)

The average density of the sun at present is 1.4. Let us suppose it
condenses until it has a density ρ.

_r_^3 ÷ _a_^3 = 1.4 ÷ ρ,

whence the energy becomes

14 _a_ M · ∛ρ;

but the coal equivalent of 16 _a_ M has been found in § 4 to be 3,400,
and hence the coal equivalent in this case is

3,000 ∛ρ.

If we take ρ to be the density of platinum (21.5), we get a coal
equivalent 8,300. This, therefore, seems to represent a major limit to
the quantity of heat which can be obtained from the condensation of the
nebula from infinity into a sun of the utmost density.

§ 6. ON THE PRESENT EMISSION OF SUN HEAT.

According to Scheiner, “Strahlung und Temperatur der Sonne, Leipzig,
1899,” the value of the solar constant, _i.e._ the number of cubic
centimetres of water which would be raised 1° Centigrade by the quantity
of sun heat which, if there were no atmospheric absorption, would fall
perpendicularly on a square centimetre, at the earth’s mean distance
from the sun, is between 3.5 and 4.0. If we take the mean value, we have
(translated into British units), the following statement:—

_If at a point in space, distant from the sun by the earth’s mean
distance, one square foot was exposed perpendicularly to the solar rays,
then the sun heat that would fall upon it in one minute would raise one
pound of water 14° Fahr._

This shows that the solar energy emitted daily amounts to

700,000,000,000 × 4 π _a_^2 foot-pounds.

§ 7. ON THE DAILY CONTRACTION OF THE SUN NECESSARY TO SUPPLY THE PRESENT
EXPENDITURE OF HEAT.

We have seen that at the radius _r_ the energy is

16 M (_a_^2/_r_).

Hence for a change _dr_ it is

–16 M (_a_^2/_r_^2) _dr_.

At its present size, accordingly, the energy given out by a shrinkage
_dr_ is

16 M _dr_.

One cubic foot of the sun averages 87 pounds, so that

M = 4/3 π _a_^3 × 87

16 M _dr_ = 464 × 4 π _a_^3 _dr_.

We have to equate this to the expression in the last article, and we get

_dr_ = 700,000,000,000/(464 _a_) = .65.

This is the shrinkage of the sun’s radius expressed in feet. Hence the
daily reduction of the sun’s _diameter_ is 16 inches.

One coal equivalent possesses energy represented by M × 14,000 × 772.
Hence we can calculate that one coal equivalent would supply the solar
radiation at its present rate for about 2,800 years.

II.—THE CONSERVATION OF MOMENT OF MOMENTUM.

We give here an elementary investigation of the fundamental dynamical
principle which has been of such importance throughout this volume.

§ 8. CASE WHERE THERE ARE NO FORCES.

Newton’s first law of motion tells us that a particle in motion if
unacted upon by force, will move continuously in a straight line without
change of velocity.

Let A_{0}, Fig. 60, be the position of the particle at any moment. Let
A_{1} be its position after the time _t_; A_{2} be the position at the
time 2_t_; A_{3} be the position at the time 3_t_, and so on.

Then the first law of motion tells us that the distances A_{0} A_{1},
A_{1} A_{2}, A_{2} A_{3}, A_{3} A_{4}, must form parts of the same
straight line and must be all equal.

If lines O A_{0}, O A_{1}, O A_{2}, etc., be drawn from any fixed point
0, then the areas of the triangles O A_{0} A_{1}, O A_{1} A_{2}, O A_{2}
A_{3}, 0 A_{3} A_{4}, will be all equal. For each area is one-half the
product of the base of the triangle into the perpendicular O T from O on
A_{0} A_{1}, and, as the bases of all the triangles are equal, it
follows that their areas are equal.

Thus we learn that a particle moving without the action of force will
describe around any fixed point O equal areas in equal times.

[Illustration: Fig. 60.—FIRST LAW OF MOTION EXEMPLIFIES CONSTANT MOMENT
OF MOMENTUM.]

The product of the mass of the particle and its velocity is termed the
momentum. If the momentum be multiplied by O T the product is termed the
moment of momentum around O. We have in this case the simplest example
of the important principle known as the conservation of moment of
momentum.

The moment of momentum of a system of particles moving in a plane is
defined to be the excess of the sum of the moments of momentum of those
particles which tend round O in one direction, over the sum of the
moments of momentum of those particles which tend round O in the
opposite direction.

If we deem those moments in one direction round O as positive, and those
in the other direction as negative, then we may say that the moment of
momentum of a system of particles moving in a plane is the algebraical
sum of the several moments of momentum of each of the particles.

§ 9. A GEOMETRICAL PROPOSITION.

The following theorem in elementary geometry will be required:—

[Illustration: Fig. 61.—A USEFUL GEOMETRICAL PROPOSITION.]

Let A B and A C be adjacent sides of a parallelogram, Fig. 61, of which
A D is the diagonal, and let O be any point in its plane. Then the area
O A C is the difference of the areas O A D and O A B.

Draw D Q and C P parallel to O A. Then O A D = O A Q, whence O A D – O A
B = O B Q = O A P = O A C.

§ 10. RELATION BETWEEN THE CHANGE OF MOMENT OF MOMENTUM AND THE FORCE
ACTING ON THE PARTICLE.

[Illustration: Fig. 62.—ACCELERATION OF MOMENT OF MOMENTUM EQUALS MOMENT
OF FORCE.]

Let A_{1} and A_{2}, Fig. 62, be two adjacent points on the path of the
particle, and let A_{1} Q and A_{2} R be the tangents at those points.
Let S Q represent the velocity of the particle at A_{1}, and SR the
velocity of the particle at A_{2}. Then Q R represents both in magnitude
and direction the change in velocity due to the force F, which we
suppose constant both in magnitude and direction, while the particle
moves from A_{1} to A_{2} in the small time _t_; we have also Q R = F
_t_ ÷ _m_.

Complete the parallelogram S Q R U, and let fall O P_{1}, O P_{2}, O T
perpendiculars from O on S Q, S R, S U respectively. Since S Q is the
velocity of the particle when at A_{1} the moment of momentum is _m_ O
P_{1} × S Q; when the particle is at A_{2} the moment of momentum is _m_
O P_{2} × S R. Whence the difference of the moments of momentum at A_{1}
and A_{2} is _m_ (O P_{2} × S R - O P_{1} × S Q) = 2 _m_ (O S R - O S Q)
= 2 _m_ O S U = _m_ O T × S U = _m_ O T. Q R = F _t_ × O T. But in the
limit S coincides with A_{1} and A_{2}, and we see that the gain in
moment of momentum is _t_ times the moment of the force around O. Hence
we deduce the following fundamental theorem, in which, by the expression
acceleration of moment of momentum, we mean the rate at which the moment
of momentum increases:—

_If a particle under the action of force describes a plane orbit, then
the acceleration of the moment of momentum around any point in the plane
is equal to the moment of the force around the point._

If the force is constantly directed to a fixed point, then the moment of
the force about this point is always zero. Hence the acceleration of the
moment of momentum around this point is zero, and the moment of momentum
is constant. Thus we have Kepler’s law of the description of equal areas
in equal times, and we learn that the velocity is inversely proportional
to the perpendicular on the tangent.

§ 11. IF TWO OR MORE FORCES ACT ON A POINT, THEN THE ACCELERATION OF THE
MOMENT OF MOMENTUM, DUE TO THE RESULTANT OF THESE FORCES, IS EQUAL TO
THE ALGEBRAIC SUM OF THE MOMENTS OF MOMENTUM DUE TO THE ACTION OF THE
SEVERAL COMPONENTS.

Let A D, Fig. 61, be a force, and A C and A B its two components. Then,
since O A D = O A B + O A C, we see that the moment of A D around O is
equal to the sum of the moments of its components. Hence we easily infer
that if a force be resolved into several components the moment of that
force around a point is equal to the algebraical sum of the moments of
its several components.

The acceleration of the moment of momentum around O, due to the
resultant of a number of forces, is equal to the moment of that
resultant around O. But, as we have just shown, this is equal to the sum
of the moments of the separate forces, and hence the theorem is proved.

§ 12. IF ANY NUMBER OF PARTICLES BE MOVING IN A PLANE, AND IF THEY ARE
NOT SUBJECTED TO ANY FORCES SAVE THOSE WHICH ARISE FROM THEIR MUTUAL
ACTIONS, THEN THE ALGEBRAIC SUM OF THEIR MOMENTS OF MOMENTUM ROUND ANY
POINT IS CONSTANT.

This important theorem is deduced from the fact stated in the third law
of motion, that action and reaction are equal and opposite. Let us take
any two particles; then, the acceleration of the moment of momentum of
one of them, A, by the action of the other, B, will be the moment of the
force between them. The acceleration of the moment of momentum of B by
the action of A will be the same moment, but with an opposite sign.
Hence the total acceleration of the moment of momentum of the system by
the mutual action of A and B is zero. In like manner we dispose of every
other pair of actions, and thus, as the total acceleration of the moment
of momentum is zero, it follows that the moment of momentum of the
system itself must be constant.

This fundamental principle is also known as the doctrine of the
conservation of areas. It may be stated in the following manner:—

_If a system of particles are moving in a plane under the influence of
their mutual actions only, the algebraic sum of the areas swept out
around a point, each multiplied by the mass of the particle, is directly
proportional to the time._

§ 13. IF A PARTICLE OF MASS _m_, IS MOVING IN SPACE UNDER THE ACTION OF
ANY FORCE F, THEN THE PROJECTION OF THAT PARTICLE ON ANY FIXED PLANE
WILL MOVE AS IF IT WERE A PARTICLE OF MASS _m_ ACTED UPON BY THAT
COMPONENT OF F WHICH IS PARALLEL TO THE PLANE.

This is evident from the consideration that the acceleration of the
particle parallel to the plane must be proportional to this component of
F.

Let us now suppose a system of particles moving in space under their
mutual actions. The projections of these particles on a plane will move
as if they were the particles themselves subjected to the action of
forces which are the projections of the actual forces on the same plane,
and as the reactions between any two particles are equal and opposite,
the projections of those reactions on the plane are equal and opposite.
Hence the proof already given of the constancy of the moments of
momentum of a plane system, will apply equally to prove the constancy of
the moments of momentum of the projections of the particles on the
plane. Hence we have the following important theorem:—

_Let a system of particles be moving in space under the action of forces
internal to the system only. Let any plane be taken, and any point in
that plane, and let the momentum of each particle be projected into the
plane, then the algebraic sum of the moments of these projections around
the point is constant._

§ 14. ON THE PRINCIPAL PLANE OF A SYSTEM.

Let us suppose a system of particles moving under the influence of their
mutual actions. Let O be any point, and draw any plane L through O. Then
the moment of momentum of the system around the point O and projected
into the plane L is constant. Let us call it S. If another plane, L´,
had been drawn through O, the similar moment with regard to L´ is S´.
Thus for each plane through O there will be a corresponding value of S.
We have now to show that one plane can be drawn through O, such that the
value of S is greater than it is for any other plane. This is the
principal plane of the system.

If _v_ be the velocity of a particle, then in a small time _t_ it moves
over the distance _v t_. If _p_ be the perpendicular from O on the
tangent to the motion, then the area of the triangle swept round O in
the time _t_ is ½ _p v t_, and we see that the momentum is proportional
to the mass of the particle multiplied into the area swept over in the
time _t_. The quantity S will, therefore, be proportional to the sum of
the projections of the areas in L, swept over in the time _t_, each
increased in the proportion of the mass of the particle. It is easily
seen that the projection of an area in one plane on another is obtained
by multiplying the original area by the cosine of the angle between the
two planes. For if the area be divided into thin strips by lines
parallel to the line of intersection of the planes, then in the
projection of these strips the lengths are unchanged, while the breadths
are altered by being multiplied by the cosine of the angle between the
two planes. If, therefore, we mark off on the normal to a plane L a
length _h_ proportional to any area in that plane, then the projection
of this area on any other plane L´ may be measured by the projection of
_h_ on the normal to L´.

[Illustration: Fig. 63.—MOMENT OF MOMENTUM UNALTERED BY COLLISION.]

To determine the moment of momentum resolved in any plane we therefore
proceed as follows: Draw a plane through O, and the tangent to the path
of one of the particles, and mark off on the normal drawn through O to
this plane a length _l_ proportional to the moment of momentum. Repeat
the same process for each of the other particles with lengths _l´_,
_l″_, etc., on their several normals. Suppose that _l_, _l´_, _l″_
represent forces acting at O, and determine their resultant R. Then R,
resolved along any other direction, will give the component of moment of
momentum in the plane to which that direction is normal. In any plane
which passes through R the component of moment of momentum is zero. The
plane perpendicular to R contains the maximum projection of moment of
momentum. This is the principal plane of the system which we have seen
to be of such importance in connection with the nebular theory.

§ 15. COLLISIONS.

The conservation of moment of momentum remains true in a system, even
though there may have been actual collisions between the several parts.
This is included in the proof already given, for collisions are among
the mutual actions referred to. It may, however, be instructive to give
a direct proof of a particular case.

Let two particles collide when meeting in the directions A P and B P
(Fig. 63) respectively. Whether the particles be elastic or inelastic is
quite immaterial, for in both cases the action and reaction must be
equal and opposite, and take place along some line P Q. The action on
the particle moving along A P will give to it an acceleration of moment
of momentum which is equal to the moment of the action around O. The
acceleration of the moment of momentum coming along B P will be equal
and opposite. Thus the total acceleration of the moment of momentum is
zero. Hence the collision has no effect on the total moment of momentum.

§ 16. FRICTION AND TIDES.

We have shown that such actions as collisions cannot affect the moment
of momentum of the system, neither can it be affected by friction of one
body on another. Here, as in the former case, the actions and reactions
are equal and opposite, and consequently the accelerations of moment of
momentum are zero. Nor is it possible for any tidal action to affect the
total moment of momentum of the system. Every such action must be
composed of the effects of one particle in the system on another, and as
this must invariably produce an equal and opposite reaction the total
moment of momentum is unaltered.

------------------------------------------------------------------------

INDEX.

Acceleration of moment of momentum, 377

Aldebaran, 27, 28

Anderson, Dr., 356

Andromeda, Great Nebula in, 43, 204

Antinous, Cluster of stars in, 353

Apteryx, Rudimentary wing-bones of, 364, 366

——, Skeleton of, 364, 366

——, The, 363, 365

Arcturus, Spectrum of, 85

Argon, 265

Argus and surrounding stars, 103

Ariel, 338

Boring, The great, 123

Brooks’ comet, 89

Bunsen burner, The, 283

Butterfly and the oak-tree, The, 15

Calcium, 274

Capella, Spectrum of, 61–64

Carbon, 280

Ceres, 311

Change of moment of momentum, 375

Cluster, Nebulous region round a, 33

Clusters of stars, 53–60, 203

—— —— of 17th magnitude, 353

Coal-unit, 110

Collisions, 219, 380

——, Cause of formation of nebulæ, 356

Comets, 37

Comet, Brooks’, 89

—— of 1882, 119

——, Spectrum of, 290

Common, Dr. A. A., 44

Concord, The first, 294–307

——, The second, 308–323

——, The third, 324–336

Conglomerates, 159

Conservation of moment of momentum, 374

Corona of the sun, 117

Crab nebula, The, 19, 44

Crossley Reflector, The, 45, 46, 48, 49, 50, 67, 199

Cygnus, Nebula in, 329

Dark bodies in universe, 355

Darwin, Professor G. H., 153, 254, 332

Darwinian theory, 10, 268, 362

Dewar, Professor, 144, 272

Diurnal motion, The, 21

Dumb-bell nebula, 43, 44, 45, 46, 50, 74, 195

Dust from Krakatoa, 185

Earth, Heat in interior of, 134, 367

——, ——, Cause of, 153

——, History of, 122–157, 251

——, Rigidity of, 162

Earth-moon system, 253, 332

Earthquakes, 158–190

—— in England, 175

——, Routes of, 171

Emission of sun heat, 373

Energy between two attracting masses, 370

—— given out in contraction of nebula, 370

—— of a system, 216, 235

Equivalent of heat, 88

Eros, 312

Evaluation of sun heat given out in contraction, 371

Everett, Professor, 149

Fire-mist, The, 268

“Flash” spectrum, 70

Foot-pound, 91

Foraminifera, 367

Friction and tides, 381

Gas in rarefaction, 118

H and K lines, 70, 276

Heat, Cause of, 153

——, Equivalent of, 88

—— given out in contraction of nebula, 369

—— in interior of the earth, 134, 367

——, Unit of, 80, 89

Helium, 277

Helmholtz, 86, 96, 100

Hercules, Star-cluster in, 52, 53, 56, 57, 59

Herschel, Sir William, 4, 11, 72, 73, 74

Huggins, Sir W., 60, 61, 63, 65

Huxley, Professor, and Darwinian theory, 362

Huyssen, Captain, 127

Hydrogen in spectrum of Nova Persei, 358

“Inflammation” and nebular theory, 361

Joule’s equivalent of heat, 88

Jupiter, 23, 25, 26, 29, 208, 237, 310, 327

K and H lines, 70, 276

Kant, Immanuel, 4, 5, 72, 73, 74, 327

Keeler, Professor, 45–48, 67, 73, 199, 200, 202, 245

Kelvin, Lord, 153, 162

Krakatoa, 176–189

Langley, Professor, 78

Laplace, 4, 72, 73, 74, 206

Lassell, Mr., 338, 340

Lick Observatory, 41, 43, 44, 45

Lockyer, Sir Norman, 277

Lyra, Ring nebula in, 249

Mars, 25, 26, 27, 28, 29, 311, 341, 349

——, Satellites of, 341

_Mécanique Céleste_, 5, 8

Mercury, 23, 25, 26, 29, 208

Meteors, 37

Milky Way, 205, 206, 214, 220

Milne, Professor, 165

Moment of momentum, 222, 226, 240, 352

—— ——, Acceleration of, 377

—— ——, Change of, 375

—— ——, Conservation of, 374

Momentum, Moment of, 222, 220, 240, 352

Monoceros, Nebulous region round a cluster in, 33

Moon, Origin of, 254

——, Surface of, 255

Nautilus, The, 367

Nebula, Contraction of, Heat given out in, 369

——, ——, Energy given out in, 370

—— in Orion, The great, 40, 41, 42, 44, 46, 50, 74, 195, 242

—— ——, ——, Spectrum of, 63, 64, 65

——, The great spiral, 192, 193

Nebulæ, 40, 41, 43, 45, 47, 50, 57, 58, 66, 67, 71, 73, 105, 120, 157,
191–206, 242, 247, 249, 256, 257, 258, 259, 296, 329, 345, 348–360

——, Development of, 242

——, Discovery of, 11

——, Number of, 67, 200

Nebular anecdote, 362

—— Theory, The, 2, 3, 72, 74, 157, 205, 266, 292, 307, 323, 328, 331,
337–347, 362, 368

Nebulosity, Faint diffused, in Perseus, 17

Neptune, 37

——, Satellites of, 330, 340

Newcomb, Professor, 238

Norway, Conglomerates in, 159

Nova Persei, 358

—— ——, Spectrum of, 358, 359, 360

Oak-tree and the butterfly, The, 15

Oberon, 338

Orbits of the planets, 208

Orion, 22

Orion, Great nebula in, 40, 41, 42, 44, 46, 50, 74, 195, 242

——, Spectrum of, 63, 64, 65

Pegasus, Nebula in, 47, 345

Perseus, A faint diffused nebulosity in, 17

——, New star in, 356

Photosphere, The, 69

Pickering, Professor, 358

“Plane, Principal,” The, 225, 352, 379

Planetary system, The, 37, 208

Planets, 22, 26, 28

——, Movement of, 35, 311

——, Orbits of, 208, 298

——, Rotation of, on their axes, 325

Platinum, 263

Pleiades, 22

——, Nebulae in, 71

Potassium, 272

“Plane, Principal” The, 225, 352, 379

Probabilities, Theory of, 305

Radiation of sun’s heat, 82

Ramsay, Professor, 278

Ray nebulæ, 201, 211

Rigidity of the earth, 162

Ring nebula in Lyra, The, 249

Roberts, Dr. Isaac, 198

Rosse, Lord, 57, 196–201

Rowland, Prof. Henry, 273

Sagittarius, Nebula in, 105

Satellites, 37, 209

Saturn, 25, 26, 29, 220, 233

——, Dweller in, and the Sirian, 14

——, Ring of, 210, 220, 231, 232, 233, 234

Scheiner, Professor, 202, 204

Seismometer, The, 165

Sirian, The, and the dweller in Saturn, 14

Sirius, 215, 216

Smiths, The parable of the, 303

Solar system, 36, 207

——, Energy of, 350

——, Evolution of, 20, 246–260, 349

——, Origin of, 351

Solar system, Scale of, 29, 30, 31

Spectra, Continuous, 68, 203

——, Discontinuous, 68

Spectroscope, The, 60, 271

Spiral form in Nature, 256, 257

Spiral nebula, The great, 192, 193, 247

Spiral nebulæ, 191–206, 211, 212, 213, 220, 243, 247, 256, 257, 258,
259, 296, 345

Star-clusters, 53–60

Star, Spectrum of, 64

Stars distinguished from planets, 28, 29

Stoney, Dr. G. Johnstone, 279

Sun compared with the planets, 26, 29

——, Corona of, 117

——, Contraction of, 99, 373

——, Density of, 102, 115

——, Heat of, 75–94, 95–111, 371, 372, 373

——, History of, 112–121, 251

——, Nebulous part of, 121

——, Spectrum of, 61, 62, 69, 70, 85, 273

——, Surface of, 278

——, Velocity of, 354

——, Weight of, 101

Sun heat, given out in contraction, Evaluation of, 371, 372

——, Present emission of, 373

Sunsets, The Krakatoa, 189

_Système du Monde_, 8

Thermometer for testing the heat of the earth’s interior, 129

Thomson, Prof. J. J., 316

Tides and friction, 381

Titania, 338

Umbriel, 338

Unit of heat, 80, 89

Uranus, 37, 238, 239
——, Satellites of, 238, 338

Venus, 23, 25, 26, 29, 208, 325

Volcanoes, 158–190

Voltaire, Fable of, 14

Waves caused by Krakatoa earth quake, 179, 182, 183

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● Transcriber’s Notes:
○ The raised dot (·), used to indicate multiplication, was confused
with the decimal point in several numbers. The raised dot has been
changed to the decimal point in numbers and the raised dot used
only for multiplication.
○ In places where “×” was used for multiplication, it was left as
the author wrote it.
○ Missing or obscured punctuation was silently corrected.
○ Typographical errors were silently corrected.
○ Inconsistent spelling and hyphenation were made consistent only
when a predominant form was found in this book.
○ Superscripts are used to indicate numbers raised to a power. In
this plain text document, they are represented by characters like
this: “P^3” or “10^{18}”, i.e. P cubed or 10 to the 18th power.
○ Variables in formulæ sometimes use subscripts, which look like
this: “A_{0}”. This would be read “A sub 0”.
○ Text that was in italics is enclosed by underscores (_italics_).

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