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<body>
<div>*** START OF THE PROJECT GUTENBERG EBOOK 59080 ***</div>
<div class='figcenter id001'>
<img src='images/cover.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>The cover image was created by the transcriber and is placed in the public domain.</span></p>
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<div class='pbb'>
<hr class='pb c000' />
</div>
<div>
<span class='pageno' id='Page_I'>I</span>
<h1 class='c001'>THE EARTH’S BEGINNING</h1>
</div>
<div class='pbb'>
<hr class='pb c002' />
</div>
<p class='c003'><span class='pageno' id='Page_II'>II</span> </p>
<div class='box'>
<div class='nf-center-c0'>
<div class='nf-center'>
<div><i>WORKS BY</i></div>
<div class='c000'>SIR ROBERT S. BALL,</div>
<div class='c000'>M.A., LL.D., F.R.S.</div>
</div>
</div>
<p class='c004'>THE STORY OF THE HEAVENS.</p>
<p class='c005'>With 24 Coloured Plates and Numerous
Illustrations. New Edition. 10s. 6d.</p>
<p class='c003'>THE EARTH’S BEGINNING.</p>
<p class='c005'>With 4 Coloured Plates and Numerous
Illustrations. New Edition. 7s. 6d.</p>
<p class='c003'>THE STORY OF THE SUN.</p>
<p class='c005'>With 11 Full Page Coloured and other Plates
and Numerous Illustrations. 7s. 6d.</p>
<p class='c003'>STAR-LAND.</p>
<p class='c005'>Being Talks with Young People about the
Wonders of the Heavens With Rembrandt
Frontispiece and 94 Illustrations in Text.
7s. 6d.</p>
<div class='nf-center-c0'>
<div class='nf-center c006'>
<div>CASSELL & COMPANY, <span class='sc'>Limited</span>, <i>London,</i></div>
<div><i>New York, Toronto & Melbourne</i>.</div>
</div>
</div>
</div>
<div class='pbb'>
<hr class='pb c002' />
</div>
<div id='i004' class='figcenter id001'>
<span class='pageno' id='Page_IV'>IV</span>
<img src='images/i004.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>AN ENGLISH SUNSET TINGED BY KRAKATOA.<br />(<i>From a Drawing made at Chelsea at 4.40 p.m. on Nov. 26th, 1883, by Mr. W. Ascroft.</i>)</span></p>
</div>
</div>
<div class='pbb'>
<hr class='pb c000' />
</div>
<div class='nf-center-c0'>
<div class='nf-center c002'>
<div><span class='pageno' id='Page_V'>V</span><span class='c007'>THE</span></div>
<div><span class='c008'><span class='sc'>Earth’s Beginning</span></span></div>
<div class='c006'>BY</div>
<div><span class='c008'>SIR ROBERT S. BALL, <span class='fss'>M.A.</span>, <span class='fss'>LL.D.</span>, <span class='fss'>F.R.S.</span></span></div>
<div class='c000'>Lowndean Professor of Astronomy and Geometry in the University of Cambridge,</div>
<div>Author of “Star-Land,” “The Story of the Heavens,”</div>
<div>etc. etc.</div>
<div class='c006'><span class='c009'>WITH FOUR COLOURED PLATES AND</span></div>
<div><span class='c009'>NUMEROUS ILLUSTRATIONS</span></div>
<div class='c006'>NEW EDITION</div>
<div class='c006'><span class='c010'>CASSELL AND COMPANY, LIMITED</span></div>
<div>LONDON, NEW YORK, TORONTO AND MELBOURNE</div>
<div>MCMIX</div>
</div>
</div>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='nf-center-c0'>
<div class='nf-center c002'>
<div><span class='pageno' id='Page_VI'>VI</span>First Edition <i>October 1901</i>.</div>
<div><i>Reprinted December 1901, 1903.</i></div>
<div>Enlarged Edition 1909.</div>
<div class='c011'>ALL RIGHTS RESERVED</div>
</div>
</div>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_v'>v</span>
<h2 class='c012'>FOREWORD</h2>
</div>
<p class='c013'><span class='sc'>Since</span> 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.</p>
<p class='c004'>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.</p>
<p class='c004'>But from the evidence of geology it must now be
<span class='pageno' id='Page_vi'>vi</span>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.</p>
<p class='c004'>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 <i>fresh</i> 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 <i>fresh</i> 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.</p>
<p class='c004'>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
<span class='pageno' id='Page_vii'>vii</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_viii'>viii</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>The researches of Professor Sir J. J. Thomson
have shown how corpuscles of matter are sometimes
moving with velocities enormously greater than those
<span class='pageno' id='Page_ix'>ix</span>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<sup>18</sup>, and think of a line a kilometre long.
If that line were divided into 10<sup>18</sup> parts, each of those
parts would represent the diameter of a corpuscle of
radium. If that line were multiplied by 10<sup>18</sup>, 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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_x'>x</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_xi'>xi</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div class='c014'>R. S. B.</div>
<p class='c004'><i>May 1, 1909.</i></p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_xiii'>xiii</span>
<h2 class='c012'>CONTENTS</h2>
</div>
<table class='table0' summary=''>
<colgroup>
<col width='15%' />
<col width='75%' />
<col width='9%' />
</colgroup>
<tr>
<td class='c015'><span class='small'><span class='sc'>Chapter</span></span></td>
<td class='c016'> </td>
<td class='c017'><span class='small'><span class='sc'>Page</span></span></td>
</tr>
<tr>
<td class='c015'>I.</td>
<td class='c016'>—<span class='sc'>Introduction</span></td>
<td class='c017'><a href='#ch01'>1</a></td>
</tr>
<tr>
<td class='c015'>II.</td>
<td class='c016'>—<span class='sc'>The Problem Stated</span></td>
<td class='c017'><a href='#ch02'>21</a></td>
</tr>
<tr>
<td class='c015'>III.</td>
<td class='c016'>—<span class='sc'>The Fire-mist</span></td>
<td class='c017'><a href='#ch03'>39</a></td>
</tr>
<tr>
<td class='c015'>IV.</td>
<td class='c016'>—<span class='sc'>Nebulæ—Apparent and Real</span></td>
<td class='c017'><a href='#ch04'>52</a></td>
</tr>
<tr>
<td class='c015'>V.</td>
<td class='c016'>—<span class='sc'>The Heat of the Sun</span></td>
<td class='c017'><a href='#ch05'>75</a></td>
</tr>
<tr>
<td class='c015'>VI.</td>
<td class='c016'>—<span class='sc'>How the Sun’s Heat is Maintained</span></td>
<td class='c017'><a href='#ch06'>95</a></td>
</tr>
<tr>
<td class='c015'>VII.</td>
<td class='c016'>—<span class='sc'>The History of the Sun</span></td>
<td class='c017'><a href='#ch07'>112</a></td>
</tr>
<tr>
<td class='c015'>VIII.</td>
<td class='c016'>—<span class='sc'>The Earth’s Beginning</span></td>
<td class='c017'><a href='#ch08'>122</a></td>
</tr>
<tr>
<td class='c015'>IX.</td>
<td class='c016'>—<span class='sc'>Earthquakes and Volcanoes</span></td>
<td class='c017'><a href='#ch09'>158</a></td>
</tr>
<tr>
<td class='c015'>X.</td>
<td class='c016'>—<span class='sc'>Spiral and Planetary Nebulæ</span></td>
<td class='c017'><a href='#ch10'>191</a></td>
</tr>
<tr>
<td class='c015'>XI.</td>
<td class='c016'>—<span class='sc'>The Unerring Guide</span></td>
<td class='c017'><a href='#ch11'>207</a></td>
</tr>
<tr>
<td class='c015'>XII.</td>
<td class='c016'>—<span class='sc'>The Evolution of the Solar System</span></td>
<td class='c017'><a href='#ch12'>246</a></td>
</tr>
<tr>
<td class='c015'>XIII.</td>
<td class='c016'>—<span class='sc'>The Unity of Material in the Heavens and the Earth</span></td>
<td class='c017'><a href='#ch13'>261</a></td>
</tr>
<tr>
<td class='c015'>XIV.</td>
<td class='c016'>—<span class='sc'>The First Concord</span></td>
<td class='c017'><a href='#ch14'>294</a></td>
</tr>
<tr>
<td class='c015'>XV.</td>
<td class='c016'>—<span class='sc'>The Second Concord</span></td>
<td class='c017'><a href='#ch15'>308</a></td>
</tr>
<tr>
<td class='c015'>XVI.</td>
<td class='c016'>—<span class='sc'>The Third Concord</span></td>
<td class='c017'><a href='#ch16'>324</a></td>
</tr>
<tr>
<td class='c015'>XVII.</td>
<td class='c016'>—<span class='sc'>Objections to the Nebular Theory</span></td>
<td class='c017'><a href='#ch17'>337</a></td>
</tr>
<tr>
<td class='c015'>XVIII.</td>
<td class='c016'>—<span class='sc'>The Beginning of the Nebula</span></td>
<td class='c017'><a href='#ch18'>348</a></td>
</tr>
<tr>
<td class='c015'>XIX.</td>
<td class='c016'>—<span class='sc'>Concluding Chapter</span></td>
<td class='c017'><a href='#ch19'>361</a></td>
</tr>
<tr><td> </td></tr>
<tr>
<td class='c015'> </td>
<td class='c016'><span class='sc'>Appendices</span></td>
<td class='c017'><a href='#appx'>369</a></td>
</tr>
<tr><td> </td></tr>
<tr>
<td class='c015'> </td>
<td class='c016'><span class='sc'>Index</span></td>
<td class='c017'><a href='#idx'>382</a></td>
</tr>
</table>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_xv'>xv</span>
<h2 class='c012'>LIST OF ILLUSTRATIONS</h2>
</div>
<table class='table1' summary=''>
<colgroup>
<col width='9%' />
<col width='72%' />
<col width='18%' />
</colgroup>
<tr>
<td class='c015'><span class='small'><span class='sc'>Fig.</span></span></td>
<td class='c016'> </td>
<td class='c017'><span class='small'><span class='sc'>Page</span></span></td>
</tr>
<tr>
<td class='c015'> </td>
<td class='c016'>An English Sunset tinged by Krakatoa (colour)</td>
<td class='c017'><a href='#i004'><i>Frontispiece</i></a></td>
</tr>
<tr>
<td class='c015'>1.</td>
<td class='c016'>Immanuel Kant (from an old print)</td>
<td class='c017'><a href='#i007'>7</a></td>
</tr>
<tr>
<td class='c015'>2.</td>
<td class='c016'>A Faint Diffused Nebulosity</td>
<td class='c017'><a href='#i017'>17</a></td>
</tr>
<tr>
<td class='c015'>3.</td>
<td class='c016'>The Crab Nebula</td>
<td class='c017'><a href='#i019'>19</a></td>
</tr>
<tr>
<td class='c015'>4.</td>
<td class='c016'>Jupiter</td>
<td class='c017'><a href='#i025'>25</a></td>
</tr>
<tr>
<td class='c015'>5.</td>
<td class='c016'>Nebulous Region and Star-cluster</td>
<td class='c017'><a href='#i033'>33</a></td>
</tr>
<tr>
<td class='c015'>6.</td>
<td class='c016'>The Great Nebula in Orion</td>
<td class='c017'><a href='#i041'>41</a></td>
</tr>
<tr>
<td class='c015'>7.</td>
<td class='c016'>The Dumb-bell Nebula</td>
<td class='c017'><a href='#i045'>45</a></td>
</tr>
<tr>
<td class='c015'>8.</td>
<td class='c016'>The Crossley Reflector</td>
<td class='c017'><a href='#i049'>49</a></td>
</tr>
<tr>
<td class='c015'>9.</td>
<td class='c016'>The Cluster in Hercules</td>
<td class='c017'><a href='#i053'>53</a></td>
</tr>
<tr>
<td class='c015'>10.</td>
<td class='c016'>Spectra of the Sun and Capella</td>
<td class='c017'><a href='#i062'>62</a></td>
</tr>
<tr>
<td class='c015'>11.</td>
<td class='c016'>Spectrum of Nebula in Orion and Spectrum of White Star</td>
<td class='c017'><a href='#i064'>64</a></td>
</tr>
<tr>
<td class='c015'>12.</td>
<td class='c016'>Solar Spectra with Bright Lines and Dark Lines during Eclipse</td>
<td class='c017'><a href='#i069'>69</a></td>
</tr>
<tr>
<td class='c015'>13.</td>
<td class='c016'>The Nebulæ in the Pleiades</td>
<td class='c017'><a href='#i071'>71</a></td>
</tr>
<tr>
<td class='c015'>14.</td>
<td class='c016'>The Sun</td>
<td class='c017'><a href='#i081'>81</a></td>
</tr>
<tr>
<td class='c015'>15.</td>
<td class='c016'>I. Spectrum of the Sun. II. Spectrum of Arcturus</td>
<td class='c017'><a href='#i085'>85</a></td>
</tr>
<tr>
<td class='c015'>16.</td>
<td class='c016'>Brooks’ Comet and Meteor Trail</td>
<td class='c017'><a href='#i089'>89</a></td>
</tr>
<tr>
<td class='c015'>17.</td>
<td class='c016'>Argus and the surrounding Stars and Nebulosity</td>
<td class='c017'><a href='#i103'>103</a></td>
</tr>
<tr>
<td class='c015'>18.</td>
<td class='c016'>Trifid Nebula in Sagittarius</td>
<td class='c017'><a href='#i105'>105</a></td>
</tr>
<tr>
<td class='c015'>19.</td>
<td class='c016'>To illustrate the History of the Sun</td>
<td class='c017'><a href='#i113'>113</a></td>
</tr>
<tr>
<td class='c015'>20.</td>
<td class='c016'>Solar Corona</td>
<td class='c017'><a href='#i117'>117</a></td>
</tr>
<tr>
<td class='c015'>21.</td>
<td class='c016'>The Great Comet of 1882</td>
<td class='c017'><a href='#i119'>119</a></td>
</tr>
<tr>
<td class='c015'>22.</td>
<td class='c016'>Special Thermometer for use in Deep Borings</td>
<td class='c017'><a href='#i129'>129</a></td>
</tr>
<tr>
<td class='c015'>23.</td>
<td class='c016'>At the Bottom of the Great Bore</td>
<td class='c017'><a href='#i140'>140</a></td>
</tr>
<tr>
<td class='c015'>24.</td>
<td class='c016'>Three consecutive Shells of the Earth’s Crust</td>
<td class='c017'><a href='#i145'>145</a></td>
</tr>
<tr>
<td class='c015'>25.</td>
<td class='c016'>Earthquake Routes from Japan to the Isle of Wight</td>
<td class='c017'><a href='#i171'>171</a></td>
</tr>
<tr>
<td class='c015'> </td>
<td class='c016'>Showing Localities of Earthquakes (colour)</td>
<td class='c017'><a href='#i174'>175</a></td>
</tr>
<tr>
<td class='c015'>26.</td>
<td class='c016'>Showing Coasts invaded by the Great Sea-waves from Krakatoa</td>
<td class='c017'><a href='#i179'>179</a></td>
</tr>
<tr>
<td class='c015'> </td>
<td class='c016'>The Early Stage of the Eruption of Krakatoa (colour)</td>
<td class='c017'><a href='#i180'>180</a></td>
</tr>
<tr>
<td class='c015'>27.</td>
<td class='c016'>Spread of the Air-wave from Krakatoa to the Antipodes</td>
<td class='c017'><a href='#i183'>183</a></td>
</tr>
<tr>
<td class='c015'><span class='pageno' id='Page_xvi'>xvi</span>28.</td>
<td class='c016'>The great Spiral Nebula</td>
<td class='c017'><a href='#i193'>193</a></td>
</tr>
<tr>
<td class='c015'>29.</td>
<td class='c016'>How to find the great Spiral Nebula</td>
<td class='c017'><a href='#i196'>196</a></td>
</tr>
<tr>
<td class='c015'>30.</td>
<td class='c016'>A group of Nebulæ</td>
<td class='c017'><a href='#i199'>199</a></td>
</tr>
<tr>
<td class='c015'>31.</td>
<td class='c016'>A Ray Nebula</td>
<td class='c017'><a href='#i201'>201</a></td>
</tr>
<tr>
<td class='c015'>32.</td>
<td class='c016'>Portion of the Milky Way</td>
<td class='c017'><a href='#i205'>205</a></td>
</tr>
<tr>
<td class='c015'>33.</td>
<td class='c016'>A Spiral Nebula seen Edgewise</td>
<td class='c017'><a href='#i211'>211</a></td>
</tr>
<tr>
<td class='c015'>34.</td>
<td class='c016'>A foreshortened Spiral</td>
<td class='c017'><a href='#i212'>212</a></td>
</tr>
<tr>
<td class='c015'>35.</td>
<td class='c016'>Edge-view of a Spiral boldly shown</td>
<td class='c017'><a href='#i213'>213</a></td>
</tr>
<tr>
<td class='c015'>36.</td>
<td class='c016'>To illustrate Moment of Momentum</td>
<td class='c017'><a href='#i223'>223</a></td>
</tr>
<tr>
<td class='c015'>37.</td>
<td class='c016'>Saturn</td>
<td class='c017'><a href='#i233'>233</a></td>
</tr>
<tr>
<td class='c015'>38.</td>
<td class='c016'>The Ring Nebula in Lyra</td>
<td class='c017'><a href='#i249'>249</a></td>
</tr>
<tr>
<td class='c015'>39.</td>
<td class='c016'>Lunar Craters: Hyginus and Albategnius</td>
<td class='c017'><a href='#i255'>255</a></td>
</tr>
<tr>
<td class='c015'>40.</td>
<td class='c016'>A remarkable Spiral</td>
<td class='c017'><a href='#i257'>257</a></td>
</tr>
<tr>
<td class='c015'>41.</td>
<td class='c016'>A clearly-cut Spiral</td>
<td class='c017'><a href='#i259'>259</a></td>
</tr>
<tr>
<td class='c015'>42.</td>
<td class='c016'>The H and K Lines in the Photographic Solar Spectrum</td>
<td class='c017'><a href='#i276'>276</a></td>
</tr>
<tr>
<td class='c015'>43.</td>
<td class='c016'>Spectrum of Comet showing Carbon Lines</td>
<td class='c017'><a href='#i290'>290</a></td>
</tr>
<tr>
<td class='c015'> </td>
<td class='c016'>The Solar Spectrum (colour)</td>
<td class='c017'><a href='#i290a'>290</a></td>
</tr>
<tr>
<td class='c015'>44.</td>
<td class='c016'>Spectrum of the Sun during Eclipse</td>
<td class='c017'><a href='#i291'>291</a></td>
</tr>
<tr>
<td class='c015'>45.</td>
<td class='c016'>A Spiral presented Edgewise</td>
<td class='c017'><a href='#i296'>296</a></td>
</tr>
<tr>
<td class='c015'>46.</td>
<td class='c016'>The Plane of a Planet’s Orbit</td>
<td class='c017'><a href='#i298'>298</a></td>
</tr>
<tr>
<td class='c015'>47.</td>
<td class='c016'>A Right Angle divided into Ten Parts</td>
<td class='c017'><a href='#i301'>301</a></td>
</tr>
<tr>
<td class='c015'>48.</td>
<td class='c016'>Illustration of the Second Concord</td>
<td class='c017'><a href='#i309'>309</a></td>
</tr>
<tr>
<td class='c015'>49.</td>
<td class='c016'>Orbits of the Earth, Eros and Mars</td>
<td class='c017'><a href='#i313'>313</a></td>
</tr>
<tr>
<td class='c015'>50.</td>
<td class='c016'>I. A Natural System. II. An Unnatural System</td>
<td class='c017'><a href='#i318'>318</a></td>
</tr>
<tr>
<td class='c015'>51.</td>
<td class='c016'>An elongated irregular Nebula</td>
<td class='c017'><a href='#i329'>329</a></td>
</tr>
<tr>
<td class='c015'>52.</td>
<td class='c016'>Two-branched Spiral</td>
<td class='c017'><a href='#i345'>345</a></td>
</tr>
<tr>
<td class='c015'>53.</td>
<td class='c016'>Cluster with Stars of the 17th Magnitude</td>
<td class='c017'><a href='#i353'>353</a></td>
</tr>
<tr>
<td class='c015'>54.</td>
<td class='c016'>Spectrum of Nova Persei (1901)</td>
<td class='c017'><a href='#i359'>359</a></td>
</tr>
<tr>
<td class='c015'>55.</td>
<td class='c016'>The Apteryx: a Wingless Bird of New Zealand</td>
<td class='c017'><a href='#i365'>365</a></td>
</tr>
<tr>
<td class='c015'>56.</td>
<td class='c016'>Skeleton of the Apteryx, showing Rudimentary Wings</td>
<td class='c017'><a href='#i366'>366</a></td>
</tr>
<tr>
<td class='c015'>57.</td>
<td class='c016'>Spirals in other Departments of Nature: Foraminifer</td>
<td class='c017'><a href='#i367'>367</a></td>
</tr>
<tr>
<td class='c015'>58.</td>
<td class='c016'>Ditto ditto Nautilus</td>
<td class='c017'><a href='#i367'>367</a></td>
</tr>
<tr>
<td class='c015'>59.</td>
<td class='c016'>To illustrate a Theorem in the Attraction of Gravitation</td>
<td class='c017'><a href='#i369'>369</a></td>
</tr>
<tr>
<td class='c015'>60.</td>
<td class='c016'>First Law of Motion exemplifies Constant Moment of Momentum</td>
<td class='c017'><a href='#i375'>375</a></td>
</tr>
<tr>
<td class='c015'>61.</td>
<td class='c016'>A useful Geometrical Proposition</td>
<td class='c017'><a href='#i376a'>376</a></td>
</tr>
<tr>
<td class='c015'>62.</td>
<td class='c016'>Acceleration of Moment of Momentum equals Moment of Force</td>
<td class='c017'><a href='#i376b'>376</a></td>
</tr>
<tr>
<td class='c015'>63.</td>
<td class='c016'>Moment of Momentum unaltered by Collision</td>
<td class='c017'><a href='#i380'>380</a></td>
</tr>
</table>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='nf-center-c0'>
<div class='nf-center c002'>
<div><span class='pageno' id='Page_1'>1</span><span class='c010'>THE EARTH’S BEGINNING.</span></div>
</div>
</div>
<div class='chapter'>
<h2 id='ch01' class='c012'>CHAPTER I.<br /> <br /><span class='small'>INTRODUCTION.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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
<span class='pageno' id='Page_2'>2</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_3'>3</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_4'>4</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_5'>5</span>of the movements of the heavenly bodies, publishing
the results in his immortal work, <i>Mécanique Céleste</i>;
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.</p>
<p class='c004'>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
<span class='pageno' id='Page_6'>6</span>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.</p>
<p class='c004'>Kant’s famous work with which we are now concerned
appeared in 1755.<a id='r1' /><a href='#f1' class='c019'><sup>[1]</sup></a> 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
<span class='pageno' id='Page_8'>8</span>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.</p>
<div class='footnote c020' id='f1'>
<p class='c021'><span class='label'><a href='#r1'>1</a>. </span>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.”</p>
</div>
<div id='i007' class='figcenter id002'>
<img src='images/i007.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>IMMANUEL KANT.<br />(<i>From an old Print.</i>)</span></p>
</div>
</div>
<p class='c004'>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.</p>
<p class='c004'>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 <i>Mécanique Céleste</i>
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 <i>Système du Monde</i>, 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.</p>
<p class='c004'>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
<span class='pageno' id='Page_9'>9</span>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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_10'>10</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_11'>11</span>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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_12'>12</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_13'>13</span>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
<span class='pageno' id='Page_14'>14</span>prior—to the time when that marvellous thing
which we call life first came into being.</p>
<p class='c004'>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
<span class='pageno' id='Page_15'>15</span>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.”</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_16'>16</span>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.</p>
<div id='i017' class='figcenter id003'>
<img src='images/i017.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 2.—<span class='sc'>A Faint Diffused Nebulosity</span> (n.g.c. 1499; in Perseus).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_18'>18</span>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.</p>
<p class='c004'>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.</p>
<div id='i019' class='figcenter id001'>
<img src='images/i019.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 3.—<span class='sc'>The Crab Nebula</span> (n.g.c. 1952; in Taurus).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_19'>19</span>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.</p>
<p class='c004'><span class='pageno' id='Page_20'>20</span>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.</p>
<p class='c004'>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—</p>
<div class='lg-container-b c022'>
<div class='linegroup'>
<div class='group'>
<div class='line'>“A thousand ages in Thy sight</div>
<div class='line in3'>Are like an evening gone,</div>
<div class='line in1'>Short as the watch that ends the night,</div>
<div class='line in3'>Before the rising sun.”</div>
</div>
</div>
</div>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_21'>21</span>
<h2 id='ch02' class='c012'>CHAPTER II.<br /> <br /><span class='small'>THE PROBLEM STATED.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_655 c013'>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.</p>
<p class='c004'>Except this great diurnal motion, the vast majority
<span class='pageno' id='Page_22'>22</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_23'>23</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>Thus the astronomers of the earliest ages pointed
to the five planets and the sun and the moon as the
<span class='pageno' id='Page_24'>24</span>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.</p>
<div id='i025' class='figcenter id001'>
<span class='pageno' id='Page_25'>25</span>
<img src='images/i025.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 4.—<span class='sc'>Jupiter</span> (May 30th, 1899, 10h. 9.5m.; g.m.t.).<br />(E. M. Antoniadi.)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_26'>26</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_27'>27</span>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?</p>
<p class='c004'>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
<span class='pageno' id='Page_28'>28</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>We are now enabled to place the scheme of things
<span class='pageno' id='Page_29'>29</span>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.</p>
<p class='c004'>We have thus obtained a plan of the solar
system; but now we should like to indicate the
<span class='pageno' id='Page_30'>30</span>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.</p>
<p class='c004'>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.
<span class='pageno' id='Page_31'>31</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_32'>32</span>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
<span class='pageno' id='Page_34'>34</span>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.</p>
<div id='i033' class='figcenter id004'>
<img src='images/i033.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 5.—<span class='sc'>Nebulous Region and Star-Cluster</span><br />(n.g.c. 2237-9 in Monoceros).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_35'>35</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_36'>36</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_37'>37</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_38'>38</span>the sun is an isolated object in the universe; it is but
as a grain of sand in the extent of infinite space.</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_39'>39</span>
<h2 id='ch03' class='c012'>CHAPTER III.<br /> <br /><span class='small'>THE FIRE-MIST.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_40'>40</span>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.</p>
<p class='c004'>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.</p>
<div id='i041' class='figcenter id001'>
<img src='images/i041.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 6.—<span class='sc'>The Great Nebula in Orion</span> (Lick Observatory, California).<br />(<i>From the Royal Astronomical Society Series.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_41'>41</span>around. We give in Fig. <a href='#i041'>6</a> 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
<span class='pageno' id='Page_42'>42</span>sensitiveness of the plate, show more and more the
extent of the nebula.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_43'>43</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_44'>44</span>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.</p>
<p class='c004'>We have chosen the Dumb-bell (Fig. <a href='#i045'>7</a>) 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. <a href='#i019'>3</a>)
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.</p>
<p class='c004'>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.</p>
<p class='c004'>Many years ago Dr. A. A. Common, the distinguished
English astronomer, constructed an exquisite reflecting
telescope of three feet aperture (Fig. <a href='#i049'>8</a>). 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
<span class='pageno' id='Page_45'>45</span>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.</p>
<div id='i045' class='figcenter id001'>
<img src='images/i045.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 7.—<span class='sc'>The Dumb-bell Nebula</span> (Lick Observatory, California).<br />(<i>From the Royal Astronomical Society Series.</i>)</span></p>
</div>
</div>
<p class='c004'><span class='pageno' id='Page_46'>46</span>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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_47'>47</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_48'>48</span>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.</p>
<p class='c004'>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.</p>
<div id='i049' class='figcenter id005'>
<img src='images/i049.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 8.—<span class='sc'>The Crossley Reflector (Constructed by Dr. A. A.<br />Common F.R.S. and now at the Lick Observatory).</span></span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_50'>50</span>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.</p>
<p class='c004'>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. <a href='#i033'>5</a> we can
pass to other nebulæ in which we see a certain advance
being made in the process by which the nebula is
<span class='pageno' id='Page_51'>51</span>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_52'>52</span>
<h2 id='ch04' class='c012'>CHAPTER IV.<br /> <br /><span class='small'>NEBULÆ—APPARENT AND REAL.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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
<span class='pageno' id='Page_53'>53</span>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.</p>
<div id='i053' class='figcenter id006'>
<img src='images/i053.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 9.—<span class='sc'>The Cluster in Hercules.</span><br />(<i>Photographed by Dr. W. E. Wilson, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'><span class='pageno' id='Page_54'>54</span>In Fig. <a href='#i053'>9</a> 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.</p>
<p class='c004'>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
<span class='pageno' id='Page_55'>55</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>Our immediate concern, however, with the globular
star-clusters relates to a point hardly of such refinement
<span class='pageno' id='Page_56'>56</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_57'>57</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_58'>58</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_59'>59</span>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.</p>
<p class='c004'>It is easy to illustrate the question at issue by the
help of the photograph of the Cluster in Hercules in
Fig. <a href='#i053'>9</a>. 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.</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_60'>60</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_61'>61</span>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.</p>
<p class='c004'>I give, in the adjoining figure (Fig. <a href='#i062'>10</a>), 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.</p>
<div id='i062' class='figcenter id001'>
<span class='pageno' id='Page_62'>62</span>
<img src='images/i062.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 10.—<span class='sc'>Sun and Capella.</span><br />Sun above. Capella below.<br />(<i>Sir William and Lady Huggins</i>.)</span></p>
</div>
</div>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_63'>63</span>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.</p>
<p class='c004'>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.</p>
<div id='i064' class='figcenter id001'>
<img src='images/i064.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 11.—<span class='sc'>Spectrum of Nebula in Orion and<br />Spectrum of a White Star.</span><br />(<i>Sir William Huggins, K.C.B.</i>)</span></p>
</div>
</div>
<p class='c004'>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. <a href='#i064'>11</a>), 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
<span class='pageno' id='Page_64'>64</span>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.</p>
<p class='c004'><span class='pageno' id='Page_65'>65</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_66'>66</span>band of light so faint that the dark lines, even if they
are there, are not distinguishable.</p>
<p class='c004'>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. <a href='#i064'>11</a>, 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.</p>
<p class='c004'>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
<span class='pageno' id='Page_67'>67</span>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.</p>
<p class='c004'>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 <i>spiral</i> 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.</p>
<p class='c004'>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. <a href='#i071'>13</a>) is an example.</p>
<p class='c004'><span class='pageno' id='Page_68'>68</span>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.</p>
<p class='c004'><span class='pageno' id='Page_69'>69</span>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.</p>
<div id='i069' class='figcenter id001'>
<img src='images/i069.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 12.—<span class='sc'>Solar Spectra with Bright Lines and Dark Lines during Eclipse.</span><br />(<i>Photographed by Captain Hills, R.E.</i>)</span></p>
</div>
</div>
<p class='c004'>By the kindness of Captain Hills, R.E., I am able
to show a photograph (Fig. <a href='#i069'>12</a>) containing two spectra
taken during a recent eclipse, which will serve as an
excellent illustration of the different points which we
<span class='pageno' id='Page_70'>70</span>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.</p>
<p class='c004'>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.</p>
<div id='i071' class='figcenter id007'>
<img src='images/i071.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 13.—<span class='sc'>The Nebula in the Pleiades</span> (Exposure 10 hours).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_72'>72</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_73'>73</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_74'>74</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>The famous discovery of Sir W. Huggins has removed
the first great objection to the Nebular Theory.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_75'>75</span>
<h2 id='ch05' class='c012'>CHAPTER V.<br /> <br /><span class='small'>THE HEAT OF THE SUN.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>The sun is, indeed, especially instructive on the
<span class='pageno' id='Page_76'>76</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_77'>77</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_78'>78</span>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.</p>
<p class='c004'>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?</p>
<p class='c004'>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
<span class='pageno' id='Page_79'>79</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_80'>80</span>illimitable periods the sun has expended its radiance
with the most lavish generosity.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>The <i>solar constant</i> is the number of units of heat
<span class='pageno' id='Page_81'>81</span>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.</p>
<div id='i081' class='figcenter id001'>
<img src='images/i081.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 14.—<span class='sc'>The Sun</span> (July 8th, 1892).<br />(Royal Observatory, Greenwich.)<br />(<i>From the Royal Astronomical Society Series.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_82'>82</span>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 <i>fourteen</i>, 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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_83'>83</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.
<span class='pageno' id='Page_84'>84</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div id='i085' class='figcenter id001'>
<span class='pageno' id='Page_85'>85</span>
<img src='images/i085.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 15.—<span class='sc'>I. Spectrum of the Sun.</span><br /><span class='sc'>II. Spectrum of Arcturus.</span><br />(<i>Professor H. C. Lord.</i>)</span></p>
</div>
</div>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_86'>86</span>it would have sunk to the temperature of freezing
water in forty-eight years.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_87'>87</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_88'>88</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_89'>89</span>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.</p>
<div id='i089' class='figcenter id001'>
<img src='images/i089.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 16.—<span class='sc'>Brooks’ Comet and Meteor Trail.</span><br />(November 13th, 1893. Exposure 2 hours.)<br />(<i>Photographed by Professor E. E. Barnard.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_90'>90</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_91'>91</span>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<a id='r2' /><a href='#f2' class='c019'><sup>[2]</sup></a> 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.</p>
<div class='footnote c020' id='f2'>
<p class='c021'><span class='label'><a href='#r2'>2</a>. </span>A foot-pound is the amount of energy required to raise a pound
weight through a height of one foot.</p>
</div>
<p class='c004'>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
<span class='pageno' id='Page_92'>92</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_93'>93</span>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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_94'>94</span>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.</p>
<p class='c004'>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. <a href='#i089'>16</a>) may be cited
as an example.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_95'>95</span>
<h2 id='ch06' class='c012'>CHAPTER VI.<br /> <br /><span class='small'>HOW THE SUN’S HEAT IS MAINTAINED.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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
<span class='pageno' id='Page_96'>96</span>by day, has to pour forth heat, so in like manner
must it be diminishing in bulk.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_97'>97</span>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
<span class='pageno' id='Page_98'>98</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_99'>99</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_100'>100</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_101'>101</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_102'>102</span>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.</p>
<p class='c004'>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.</p>
<div id='i103' class='figcenter id001'>
<img src='images/i103.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 17.—<span class='sc'>Argo and the Surrounding Stars and Nebulosity.</span><br />(<i>Photographed by Sir David Gill, K.C.B.</i>)</span></p>
</div>
</div>
<p class='c004'>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. <a href='#i103'>17</a>, or at the Trifid Nebula
in Fig. <a href='#i105'>18</a>. 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
<span class='pageno' id='Page_103'>103</span>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
<span class='pageno' id='Page_104'>104</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_105'>105</span>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.</p>
<div id='i105' class='figcenter id001'>
<img src='images/i105.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 18.—<span class='sc'>Trifid Nebula in Sagittarius</span> (Lick Observatory, California).<br />(<i>From the Royal Astronomical Society Series.</i>)</span></p>
</div>
</div>
<p class='c004'>If two attracting bodies, A and B, are to be moved
<span class='pageno' id='Page_106'>106</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>We are now able to make a numerical estimate.
<span class='pageno' id='Page_107'>107</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_108'>108</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_109'>109</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_110'>110</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<i>coal-unit</i>, by which is to be understood the total
quantity of heat that would be produced if a mass
<span class='pageno' id='Page_111'>111</span>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_112'>112</span>
<h2 id='ch07' class='c012'>CHAPTER VII.<br /> <br /><span class='small'>THE HISTORY OF THE SUN.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>The outer circle in Fig. <a href='#i113'>19</a> 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
<span class='pageno' id='Page_113'>113</span>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.</p>
<div id='i113' class='figcenter id001'>
<img src='images/i113.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 19.—<span class='sc'>To Illustrate the History of the Sun.</span><br />Present orbit of Earth.<br />Sun in times very much earlier still.<br />Sun in very early times.<br />Present Sun.</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_114'>114</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_115'>115</span>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. <a href='#i119'>21</a>).</p>
<p class='c004'>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
<span class='pageno' id='Page_116'>116</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_117'>117</span>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?</p>
<div id='i117' class='figcenter id001'>
<img src='images/i117.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 20.—<span class='sc'>The Solar Corona</span> (January 1st, 1899).<br />(<i>Photographed during Eclipse by Professor W. H. Pickering.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_118'>118</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_119'>119</span>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.</p>
<div id='i119' class='figcenter id001'>
<img src='images/i119.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 21.—<span class='sc'>The Great Comet of 1882.</span><br />(<i>Photographed on November 7th, 1882, by Sir David Gill, K.C.B.</i>)</span></p>
</div>
</div>
<p class='c004'>But it is certain that in those early days there was
no earth to be warmed and lighted. Our globe, even if
<span class='pageno' id='Page_120'>120</span>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.</p>
<p class='c004'>This being so, why should we withhold from the sun
of primitive days the designation to which it seems to
<span class='pageno' id='Page_121'>121</span>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. <a href='#i117'>20</a>).</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_122'>122</span>
<h2 id='ch08' class='c012'>CHAPTER VIII.<br /> <br /><span class='small'>THE EARTH’S BEGINNING.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>It will be convenient to commence by mentioning
a remarkable experiment which was made a few years
<span class='pageno' id='Page_123'>123</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_124'>124</span>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.</p>
<p class='c004'>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 <i>débris</i> produced by the
attrition of the rocks as the diamonds cut their way,
and provision is also made for carefully raising the
<span class='pageno' id='Page_125'>125</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>How often do we find that the success which
rewards mechanical enterprise greatly transcends even
the most sanguine estimate previously formed! Without
<span class='pageno' id='Page_126'>126</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_127'>127</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_128'>128</span>arose, incidentally as it were, in connection with the
work committed to him.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_129'>129</span>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.</p>
<div id='i129' class='figright id008'>
<img src='images/i129.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 22.—<span class='sc'>Special<br />Thermometer<br />for Use in<br />Deep Borings.</span></span></p>
</div>
</div>
<p class='c004'>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. <a href='#i129'>22</a>)
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
<span class='pageno' id='Page_130'>130</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_131'>131</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_132'>132</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>In deep and extensive caverns the temperature is
sometimes found to remain practically unaffected by
<span class='pageno' id='Page_133'>133</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_134'>134</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_135'>135</span>as already explained, the temperature of the rocks
is more or less affected by solar heat.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_136'>136</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_137'>137</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_138'>138</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_139'>139</span>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.</p>
<p class='c004'>I represent, in the diagram shown in Fig. <a href='#i140'>23</a>, 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
<span class='pageno' id='Page_140'>140</span>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.</p>
<div id='i140' class='figcenter id001'>
<img src='images/i140.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 23.—<span class='sc'>At the Bottom of the<br />Great Bore.</span></span></p>
</div>
</div>
<p class='c004'>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.</p>
<p class='c004'>Next let us suppose that the temperature of the
<span class='pageno' id='Page_141'>141</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_142'>142</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_143'>143</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_144'>144</span>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.</p>
<p class='c004'>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.</p>
<div id='i145' class='figcenter id001'>
<img src='images/i145.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 24.—<span class='sc'>Three Consecutive Shells of the Earth’s Crust.</span></span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_145'>145</span>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
<span class='pageno' id='Page_146'>146</span>pressure certain properties of matter become so transformed
as to render the laws of heat, as we know
them, inapplicable.</p>
<p class='c004'>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.</p>
<p class='c004'>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. <a href='#i145'>24</a>). 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
<span class='pageno' id='Page_147'>147</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_148'>148</span>then absolutely removed from the solid earth either
by the convection through the air or by direct radiation
into space.</p>
<p class='c004'>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
<span class='pageno' id='Page_149'>149</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>And this loss, which is at present going on, has
been going on continually. Heat from the earth has
<span class='pageno' id='Page_150'>150</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>That a rotating body should possess a quantity
<span class='pageno' id='Page_151'>151</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_152'>152</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_153'>153</span>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?</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_154'>154</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_155'>155</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_156'>156</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_157'>157</span>been that there was a time when the materials of this
earth occupied a volume thousands of times greater
than they do at present.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_158'>158</span>
<h2 id='ch09' class='c012'>CHAPTER IX.<br /> <br /><span class='small'>EARTHQUAKES AND VOLCANOES.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_159'>159</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_160'>160</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_161'>161</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_162'>162</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>As to the immediate cause of earthquakes, there is
no doubt considerable difference of opinion. But I think
<span class='pageno' id='Page_163'>163</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_164'>164</span>which the rocks are subjected are so vast that a very
small shift may correspond to a very great terrestrial
disturbance.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_165'>165</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>This earth of ours may transmit from an earthquake
<span class='pageno' id='Page_166'>166</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_167'>167</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_168'>168</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>The characteristics of an earthquake record, a <i>seismogram</i>,
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.
<span class='pageno' id='Page_169'>169</span>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.</p>
<p class='c004'>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.”</p>
<p class='c004'>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,
<span class='pageno' id='Page_170'>170</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>We have first to explain how it occurs that there
are three versions of the event, for it need hardly
<span class='pageno' id='Page_171'>171</span>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.</p>
<div id='i171' class='figcenter id001'>
<img src='images/i171.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 25.—<span class='sc'>Earthquake Routes from Japan to the Isle of Wight.</span></span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_172'>172</span>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.</p>
<p class='c004'>We thus account for both the second and the
<span class='pageno' id='Page_173'>173</span>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
<span class='pageno' id='Page_174'>174</span>varies with the square root of the depth, and near the
surface it is scarcely two miles a second.</p>
<p class='c004'>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.</p>
<div id='i174' class='figcenter id009'>
<img src='images/i174.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>SHOWING LOCALITIES OF EARTHQUAKES</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_175'>175</span>would not be the same as we actually find them to
be if the earth were not solid in its interior.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_176'>176</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_177'>177</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_178'>178</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_180'>180</span>was widespread, for the supreme catastrophe was at
hand.</p>
<div id='i179' class='figcenter id001'>
<img src='images/i179.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 26.—<span class='sc'>Showing Coasts invaded by the Great Sea-waves from Krakatoa.</span><br />(<i>From the Royal Society’s Reports.</i>)</span></p>
</div>
</div>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div id='i180' class='figcenter id010'>
<img src='images/i180.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>THE EARLY STAGE OF THE ERUPTION OF KRAKATOA.<br />(<i>From a Photograph taken on May 27th, 1883.</i>)</span></p>
</div>
</div>
<p class='c004'><span class='pageno' id='Page_181'>181</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_182'>182</span>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?</p>
<div id='i183' class='figcenter id001'>
<img src='images/i183.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 27.—<span class='sc'>Spread of the Air-wave from Krakatoa to the Antipodes.</span><br />(<i>From the Royal Society’s Reports.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_184'>184</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_185'>185</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_186'>186</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_187'>187</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_188'>188</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_189'>189</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_190'>190</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>Nor was the incident without a historical parallel,
for has not Tennyson told us of the call to St.
Telemachus—</p>
<div class='lg-container-b c022'>
<div class='linegroup'>
<div class='group'>
<div class='line'>“Had the fierce ashes of some fiery peak</div>
<div class='line in1'>Been hurl’d so high they ranged about the globe?</div>
<div class='line in1'>For day by day, thro’ many a blood-red eve,</div>
<div class='line in1'>In that four-hundredth summer after Christ,</div>
<div class='line in1'>The wrathful sunset glared....”</div>
</div>
</div>
</div>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_191'>191</span>
<h2 id='ch10' class='c012'>CHAPTER X.<br /> <br /><span class='small'>SPIRAL AND PLANETARY NEBULÆ.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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
<span class='pageno' id='Page_192'>192</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div id='i193' class='figcenter id011'>
<span class='pageno' id='Page_193'>193</span>
<img src='images/i193.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 28.—<span class='sc'>The Great Spiral Nebula</span> (Lick Observatory).<br />(<i>From the Royal Astronomical Series.</i>)</span></p>
</div>
</div>
<p class='c004'><span class='pageno' id='Page_194'>194</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_195'>195</span>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.</p>
<p class='c004'>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. <a href='#i193'>28</a>)
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.</p>
<p class='c004'>The famous nebula which we are discussing, and
<span class='pageno' id='Page_196'>196</span>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. <a href='#i196'>29</a>. 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.</p>
<div id='i196' class='figcenter id001'>
<img src='images/i196.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 29.—<span class='sc'>How to Find the Great Spiral Nebula.</span></span></p>
</div>
</div>
<p class='c004'>In those days there were few telescopes of great
power, and none of those instruments appeared able
<span class='pageno' id='Page_197'>197</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_198'>198</span>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.</p>
<p class='c004'>Though these discoveries placed the fact of the existence
of spiral nebulæ in an impregnable position, and
<span class='pageno' id='Page_199'>199</span>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.</p>
<div id='i199' class='figcenter id001'>
<img src='images/i199.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 30.—<span class='sc'>A Group of Nebulæ</span> (<i>Lord Rosse</i>).<br />(3440, 3445 in n.g.c.)<br />(<i>From the Scientific Transactions of the Royal Dublin Society.</i>)</span></p>
</div>
</div>
<p class='c004'>We have already had occasion (page <a href='#Page_67'>67</a>) 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
<span class='pageno' id='Page_200'>200</span>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.</p>
<div id='i201' class='figcenter id001'>
<img src='images/i201.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 31.—<span class='sc'>A Ray Nebula</span> (<i>Lord Rosse</i>).<br />(3628 in n.g.c.)<br />(<i>From the Scientific Transactions of the Royal Dublin Society.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_201'>201</span>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. <a href='#i201'>31</a>). There are also
many nebulæ that look like long rays (Fig. <a href='#i199'>30</a>). 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
<span class='pageno' id='Page_202'>202</span>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. <a href='#i211'>33</a>)
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.
<a href='#i212'>34</a>, <a href='#i213'>35</a>). 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.</p>
<p class='c004'>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 <a href='#Page_67'>67</a>, 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
<span class='pageno' id='Page_203'>203</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_204'>204</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_205'>205</span>nebula in Andromeda are stars of that particular
type to which the sun belongs.</p>
<div id='i205' class='figcenter id012'>
<img src='images/i205.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 32.—<span class='sc'>Portion of the Milky Way (near Messier II.).</span><br />(<i>Photographed by Professor E. E. Barnard.</i>)<br />(<i>From the Royal Astronomical Society Series.</i>)</span></p>
</div>
</div>
<p class='c004'>But we have now to point out how the recent study
of nebulæ has afforded a yet more striking confirmation
<span class='pageno' id='Page_206'>206</span>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.</p>
<p class='c004'>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 <i>great</i> 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. <a href='#i205'>32</a>), 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. <a href='#i193'>28</a>) the orbit of Neptune would
not be larger than the smallest recognisable dot.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_207'>207</span>
<h2 id='ch11' class='c012'>CHAPTER XI.<br /> <br /><span class='small'>THE UNERRING GUIDE.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_208'>208</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_209'>209</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_210'>210</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div id='i211' class='figcenter id001'>
<span class='pageno' id='Page_211'>211</span>
<img src='images/i211.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 33.—<span class='sc'>A Spiral Nebula Seen Edgewise</span> (n.g.c. 3628; in Leo).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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. <a href='#i296'>45</a>), then it seems long and thin, so much so
that it presents the appearance of a ray such as we have
shown in Fig. <a href='#i211'>33</a>, which represents a type of object
<span class='pageno' id='Page_212'>212</span>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
<span class='pageno' id='Page_213'>213</span>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.</p>
<div id='i212' class='figcenter id001'>
<img src='images/i212.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 34.—<span class='sc'>A foreshortened Spiral</span> (n.g.c. 3198; in Ursa Major).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<div id='i213' class='figcenter id001'>
<img src='images/i213.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 35.—<span class='sc'>Edge-View of a Spiral boldly shown</span> (n.g.c. 4565;<br />in Coma Berenices).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_214'>214</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_215'>215</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_216'>216</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>Let me commence by describing what is meant
when we speak of the energy of a system. Take, first,
<span class='pageno' id='Page_217'>217</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_218'>218</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_219'>219</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_220'>220</span>actual collisions we still find that energy must be
gradually lost to the system.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>This general law of the decline of energy in an
<span class='pageno' id='Page_221'>221</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>To illustrate the important principle on which we
<span class='pageno' id='Page_222'>222</span>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.</p>
<p class='c004'>We represent by arrows in Fig. <a href='#i223'>36</a> 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 <i>momentum</i>
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 <i>moment of momentum</i> 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.</p>
<p class='c004'>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
<span class='pageno' id='Page_223'>223</span>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.</p>
<p class='c004'>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.</p>
<div id='i223' class='figcenter id001'>
<img src='images/i223.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 36.—<span class='sc'>To illustrate Moment of<br />Momentum.</span></span></p>
</div>
</div>
<p class='c004'>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,
<span class='pageno' id='Page_224'>224</span>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.</p>
<p class='c004'>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>i.e.</i>, 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
<span class='pageno' id='Page_225'>225</span>truth, it is a law true with absolute accuracy during
unlimited periods of time.</p>
<p class='c004'>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.</p>
<p class='c004'>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;
<span class='pageno' id='Page_226'>226</span>they apply, with suitable modifications, to many other
celestial systems as well.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_227'>227</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_228'>228</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_229'>229</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_230'>230</span>of each of the bodies in the system ultimately approximate
to movements in a plane.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_231'>231</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>The operation of the principle, now before us, may
be seen in a striking manner in Saturn’s ring. (Fig. <a href='#i233'>37</a>.)
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
<span class='pageno' id='Page_232'>232</span>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.</p>
<div id='i233' class='figcenter id001'>
<img src='images/i233.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 37.—<span class='sc'>Saturn.</span> Drawn by E. M. Antoniadi. (July 30th, 1899.)</span></p>
</div>
</div>
<p class='c004'>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,
<span class='pageno' id='Page_234'>234</span>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.</p>
<p class='c004'>The importance of this subject is so great that we
shall present the matter in a somewhat different manner
<span class='pageno' id='Page_235'>235</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_236'>236</span>distance of the two bodies is increased, the moment of
momentum increases also.</p>
<p class='c004'>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.</p>
<p class='c004'>It may help to elucidate this subject to state the
matter as follows: The more the system contracts,
<span class='pageno' id='Page_237'>237</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_238'>238</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_239'>239</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_240'>240</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_241'>241</span>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?</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_242'>242</span>explanation, and it is to dynamics we must look for that
explanation.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_243'>243</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_244'>244</span>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
<span class='pageno' id='Page_245'>245</span>of moment of momentum. Thus we find that the
whole object becomes ultimately possessed of a movement
of rotation.</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_246'>246</span>
<h2 id='ch12' class='c012'>CHAPTER XII.<br /> <br /><span class='small'>THE EVOLUTION OF THE SOLAR SYSTEM.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_247'>247</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_248'>248</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_249'>249</span>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.</p>
<div id='i249' class='figcenter id001'>
<img src='images/i249.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 38.—<span class='sc'>The Ring Nebula in Lyra</span> (Lick Observatory).<br />(<i>From the Royal Astronomical Society Series.</i>)</span></p>
</div>
</div>
<p class='c004'>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,
<span class='pageno' id='Page_250'>250</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_251'>251</span>in outline the origin of the sun and the earth as suggested
by the nebular theory.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_252'>252</span>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
<span class='pageno' id='Page_253'>253</span>velocity which the planet had while it still formed part
of the original nebula.</p>
<p class='c004'>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.</p>
<p class='c004'>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.
<span class='pageno' id='Page_254'>254</span>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. <a href='#i255'>39</a>), just as they may agitate an ocean,
the moon was forced away, and was ultimately conducted
to its present orbit.</p>
<div id='i255' class='figcenter id013'>
<img src='images/i255.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 39.—<span class='sc'>Lunar Craters: Hyginus and Albategnius.</span><br />(<i>Photographed by MM. Loewy and Puiseux.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_255'>255</span>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
<span class='pageno' id='Page_256'>256</span>which the planets themselves have been evolved in
relation to the sun.</p>
<p class='c004'>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.</p>
<div id='i257' class='figcenter id001'>
<img src='images/i257.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 40.—<span class='sc'>A remarkable Spiral</span> (n.g.c. 628; in Pisces).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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.
<span class='pageno' id='Page_257'>257</span>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
<span class='pageno' id='Page_258'>258</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_259'>259</span>as a star of perhaps the 12th or 15th, or even smaller
magnitude.</p>
<div id='i259' class='figcenter id001'>
<img src='images/i259.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 41.—<span class='sc'>A clearly-cut Spiral</span> (n.g.c. 4321; in Coma Berenices).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_260'>260</span>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. <a href='#i249'>38</a>).</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_261'>261</span>
<h2 id='ch13' class='c012'>CHAPTER XIII.<br /> <br /><span class='small'>THE UNITY OF MATERIAL IN THE HEAVENS AND THE EARTH.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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?</p>
<p class='c004'>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
<span class='pageno' id='Page_262'>262</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_263'>263</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>We choose the case of platinum as an illustration
because it is a substance exceptionally dense and
exceptionally refractory. If platinum can be vaporised,
<span class='pageno' id='Page_264'>264</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_265'>265</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_266'>266</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>Suppose that this diverse material is submitted to a
heat as intense as the most perfect furnace can make it.
<span class='pageno' id='Page_267'>267</span>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.</p>
<p class='c004'>Various objections may occur to the thoughtful
<span class='pageno' id='Page_268'>268</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_269'>269</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_270'>270</span>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?</p>
<p class='c004'>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.</p>
<p class='c004'>This great discovery of the last century revealed
<span class='pageno' id='Page_271'>271</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>Those elements which unite with the utmost eagerness
at ordinary temperatures, seem to become indifferent
<span class='pageno' id='Page_272'>272</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_273'>273</span>combinations of which these elements are susceptible
under terrestrial conditions.</p>
<p class='c004'>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. <a href='#i276'>42</a>). 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.</p>
<p class='c004'>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
<span class='pageno' id='Page_274'>274</span>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!</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_275'>275</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_276'>276</span>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.</p>
<div id='i276' class='figcenter id001'>
<img src='images/i276.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 42.—<span class='sc'>The H. and K. Lines in the Photographic Solar<br />Spectrum</span> (Higgs).</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_277'>277</span>the photograph of the solar spectrum are those due
to calcium (Figs. 42 and 44).</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_278'>278</span>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.</p>
<p class='c004'>In a previous picture (Fig. <a href='#i081'>14</a>) 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
<span class='pageno' id='Page_279'>279</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_280'>280</span>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. <a href='#i290'>43</a>). 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
<span class='pageno' id='Page_281'>281</span>is carbon which forms the glowing solar clouds to which
our very life owes its origin.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>Modern research has now demonstrated that just as
we employ carbon as the immediate agent for producing
<span class='pageno' id='Page_282'>282</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'><span class='pageno' id='Page_283'>283</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_284'>284</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_285'>285</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_286'>286</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_287'>287</span>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.</p>
<p class='c004'>In the prosecution of his researches by the older
method, the chemist could no doubt discover the different
<span class='pageno' id='Page_288'>288</span>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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_289'>289</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_290'>290</span>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.</p>
<div id='i290' class='figcenter id001'>
<img src='images/i290.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 43.—<span class='sc'>Spectrum of Comet showing Carbon Lines.</span><br />(<i>Sir W. Huggins, K.C.B.</i>)</span></p>
</div>
</div>
<p class='c004'>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?</p>
<div id='i290a' class='figcenter id001'>
<img src='images/i290a.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>THE SOLAR SPECTRUM.</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_291'>291</span>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
<span class='pageno' id='Page_292'>292</span>body should be essentially those which were represented
in the other.</p>
<div id='i291' class='figcenter id001'>
<img src='images/i291.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 44.—<span class='sc'>Spectrum of Sun during Eclipse. The Two<br />Chief Lines are due to Calcium.</span><br />(<i>Evershed.</i>)</span></p>
</div>
</div>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_293'>293</span>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.</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_294'>294</span>
<h2 id='ch14' class='c012'>CHAPTER XIV.<br /> <br /><span class='small'>THE FIRST CONCORD.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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
<span class='pageno' id='Page_295'>295</span>system has itself had an origin such as that which
the nebular theory assigns.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div id='i296' class='figcenter id001'>
<img src='images/i296.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 45.—<span class='sc'>A Spiral presented Edgewise</span> (n.g.c. 4631; in Coma Berenices).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_296'>296</span>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
<span class='pageno' id='Page_297'>297</span>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.</p>
<p class='c004'>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.</p>
<div id='i298' class='figleft id014'>
<span class='pageno' id='Page_298'>298</span>
<img src='images/i298.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 46.—<span class='sc'>The Plane of a Planet’s<br />Orbit.</span></span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_299'>299</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_300'>300</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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;
<span class='pageno' id='Page_301'>301</span>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.</p>
<p class='c004'>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. <a href='#i301'>47</a>), 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°.</p>
<div id='i301' class='figcenter id001'>
<img src='images/i301.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 47.—<span class='sc'>A Right Angle Divided into Ten Parts.</span></span></p>
</div>
</div>
<p class='c004'><span class='pageno' id='Page_302'>302</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_303'>303</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_304'>304</span>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.”</p>
<p class='c004'>“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
<span class='pageno' id='Page_305'>305</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_306'>306</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_307'>307</span>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_308'>308</span>
<h2 id='ch15' class='c012'>CHAPTER XV.<br /> <br /><span class='small'>THE SECOND CONCORD.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<div id='i309' class='figcenter id015'>
<span class='pageno' id='Page_309'>309</span>
<img src='images/i309.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 48.—<span class='sc'>Illustration of the Second Concord.</span></span></p>
</div>
</div>
<p class='c004'>In the adjoining Fig. <a href='#i309'>48</a> 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.</p>
<p class='c004'>In the first place we observe that the earth
<span class='pageno' id='Page_310'>310</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_311'>311</span>have already seen, is the direction in which the sun
rotates. Here we have the second coincidence.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_312'>312</span>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.</p>
<p class='c004'>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. <a href='#i313'>49</a>).</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div id='i313' class='figcenter id001'>
<span class='pageno' id='Page_313'>313</span>
<img src='images/i313.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 49.—<span class='sc'>Orbits of Earth, Eros and Mars.</span></span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_314'>314</span>their movements round the sun to the same direction
as that in which the sun itself rotates.</p>
<p class='c004'>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.</p>
<p class='c004'>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.
<span class='pageno' id='Page_315'>315</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_316'>316</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_317'>317</span>person will deny that these facts impose an obligation to
search for the physical explanation of this feature in
the planetary movements.</p>
<p class='c004'>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.</p>
<p class='c004'>The two figures that are shown in Fig. <a href='#i318'>50</a> 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.
<span class='pageno' id='Page_318'>318</span>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.</p>
<div id='i318' class='figcenter id001'>
<img src='images/i318.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 50.—I. <span class='sc'>A Natural System on the Left.</span><br />II. <span class='sc'>An Unnatural System on the Right.</span></span></p>
</div>
</div>
<p class='c004'>There can be no doubt that either of these two
<span class='pageno' id='Page_319'>319</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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 <i>increased</i> 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
<span class='pageno' id='Page_320'>320</span>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.</p>
<p class='c004'>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. <a href='#i318'>50</a> 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
<span class='pageno' id='Page_321'>321</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_322'>322</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_323'>323</span>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_324'>324</span>
<h2 id='ch16' class='c012'>CHAPTER XVI.<br /> <br /><span class='small'>THE THIRD CONCORD.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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
<span class='pageno' id='Page_325'>325</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_326'>326</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<i>direction</i> in which the rotation takes place seems quite
immaterial so far as the welfare of the inhabitants on
these planets is concerned.</p>
<p class='c004'><span class='pageno' id='Page_327'>327</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_328'>328</span>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.</p>
<p class='c004'>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.</p>
<div id='i329' class='figcenter id016'>
<img src='images/i329.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 51.—<span class='sc'>An elongated irregular Nebula</span> (n.g.c. 6992; in Cygnus).<br />(<i>Dr. W. E. Wilson, F.R.S.</i>)<br />(<i>From the Astronomical and Physical Researches at Daramona Observatory.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_330'>330</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>The contracting nebula we may liken to our piece
<span class='pageno' id='Page_331'>331</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_332'>332</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_333'>333</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_334'>334</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_335'>335</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_336'>336</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_337'>337</span>
<h2 id='ch17' class='c012'>CHAPTER XVII.<br /> <br /><span class='small'>OBJECTIONS TO THE NEBULAR THEORY.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>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
<a href='#ch14'>XIV.</a>, <a href='#ch15'>XV.</a>, <a href='#ch16'>XVI.</a> 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
<span class='pageno' id='Page_338'>338</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_339'>339</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_340'>340</span>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.</p>
<p class='c004'>These circumstances connected with the satellites
of Uranus and Neptune have been sometimes brought
forward as arguments against the nebular theory.
<span class='pageno' id='Page_341'>341</span>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.</p>
<p class='c004'>The primæval nebula may be regarded as chaotic in
its earliest stages; perhaps it was like the nebulous
wisps in Fig. <a href='#i329'>51</a>. 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. <a href='#i345'>52</a>, 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
<span class='pageno' id='Page_342'>342</span>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.</p>
<p class='c004'>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,
<span class='pageno' id='Page_343'>343</span>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.</p>
<p class='c004'><span class='pageno' id='Page_344'>344</span>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.</p>
<div id='i345' class='figcenter id010'>
<img src='images/i345.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 52.—<span class='sc'>Two-branched Spiral</span> (n.g.c. 7479; in Pegasus).<br />(<i>Lick Observatory.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_345'>345</span>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
<span class='pageno' id='Page_346'>346</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_347'>347</span>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.</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_348'>348</span>
<h2 id='ch18' class='c012'>CHAPTER XVIII.<br /> <br /><span class='small'>THE BEGINNING OF THE NEBULA.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_349'>349</span>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.</p>
<p class='c004'>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 (<i>see</i>
Appendix) the energy that would be given out in
<span class='pageno' id='Page_350'>350</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_351'>351</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_352'>352</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_353'>353</span>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.</p>
<div id='i353' class='figcenter id001'>
<img src='images/i353.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 53.—<span class='sc'>Cluster with Stars of 17th Magnitude</span> (n.g.c. 6705; in<br />Antinous).<br />(<i>Photographed by Dr. Isaac Roberts, F.R.S.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_354'>354</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_355'>355</span>through space, and also that moment of momentum
which is of such vast importance in the theory.</p>
<p class='c004'>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
<span class='pageno' id='Page_356'>356</span>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. <a href='#i353'>53</a>. 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.</p>
<p class='c004'>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
<span class='pageno' id='Page_357'>357</span>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_358'>358</span>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.</p>
<div id='i359' class='figcenter id017'>
<img src='images/i359.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 54.—<span class='sc'>Spectrum of Nova Persei</span> (1901).<br />(<i>Photographed with the 40 in. Yerkes Telescope by Mr. Ferdinand Ellerman.</i>)</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_359'>359</span>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
<span class='pageno' id='Page_360'>360</span>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. <a href='#i359'>54</a> 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.</p>
<p class='c004'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_361'>361</span>
<h2 id='ch19' class='c012'>CHAPTER XIX.<br /> <br /><span class='small'>CONCLUDING CHAPTER.</span></h2>
</div>
<p class='c018'>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.</p>
<p class='drop-capa0_3_0_65 c013'>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
<span class='pageno' id='Page_362'>362</span>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!</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_363'>363</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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
<span class='pageno' id='Page_364'>364</span>your hand on the apteryx, and feel the puny little
remnants of wings (Fig. <a href='#i365'>55</a>).</p>
<p class='c004'>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. <a href='#i366'>56</a>). 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.</p>
<div id='i365' class='figcenter id001'>
<img src='images/i365.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 55.—<span class='sc'>The Apteryx: A Wingless Bird of New Zealand.</span></span></p>
</div>
</div>
<div id='i366' class='figcenter id001'>
<img src='images/i366.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 56.—<span class='sc'>Skeleton of the Apteryx, showing Rudimentary Wings.</span></span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_365'>365</span>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
<span class='pageno' id='Page_366'>366</span>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
<span class='pageno' id='Page_367'>367</span>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.</p>
<div id='i367' class='figcenter id001'>
<img src='images/i367.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 57.—<span class='sc'>Foraminifer.</span></span><br /><span class='small'>Fig. 58.—<span class='sc'>Nautilus.</span></span><br /><span class='small'><span class='sc'>Spirals in other Departments of Nature.</span></span></p>
</div>
</div>
<p class='c003'>We liken the internal heat of the earth to the
rudimentary wing-bones of the apteryx. In each case
<span class='pageno' id='Page_368'>368</span>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.</p>
<p class='c004'>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:—</p>
<div class='lg-container-b c022'>
<div class='linegroup'>
<div class='group'>
<div class='line in4'>“This world was once a fluid haze of light,</div>
<div class='line'>Till toward the centre set the starry tides,</div>
<div class='line'>And eddied into suns, that wheeling, cast</div>
<div class='line'>The planets;”</div>
</div>
</div>
</div>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_369'>369</span>
<h2 id='appx' class='c012'>APPENDICES.</h2>
</div>
<hr class='c023' />
<h3 class='c024'>I.—ON THE HEAT GIVEN OUT IN THE CONTRACTION OF THE NEBULA.</h3>
<h4 id='s01' class='c025'>§ 1. <span class='sc'>Fundamental Theorems in the Attraction of Gravitation.</span></h4>
<p class='c026'>The first theorem to be proved is as follows:—</p>
<p class='c004'><i>The attraction of a thin homogeneous spherical shell on any
point in its interior vanishes.</i></p>
<div id='i369' class='figright id018'>
<img src='images/i369.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 59.</span></p>
</div>
</div>
<p class='c004'>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
<span class='pageno' id='Page_370'>370</span>⅓ P Q × S, and the other part of the cone has the volume
⅓ P Q´ × S´.</p>
<p class='c004'>As the vertical angles of the cones are small, their volumes
will, in the limit, be in the ratio of O P<sup>3</sup> to O´ P<sup>3</sup>, and accordingly
⅓ P Q · S ÷ ⅓ P Q´ · S´ = P O<sup>3</sup> ÷ O´ P<sup>3</sup>. But from the figure P Q ÷
P Q´ = P O ÷ P O´, and hence S ÷ O P<sup>2</sup> = S´ ÷ O´ P<sup>2</sup>.</p>
<p class='c004'>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.</p>
<p class='c004'>The second fundamental theorem is as follows:—</p>
<p class='c004'><i>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.</i></p>
<p class='c004'>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—</p>
<p class='c004'><i>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.</i></p>
<h4 id='s02' class='c027'>§ 2. <span class='sc'>On the Energy between Two Attracting Masses.</span></h4>
<p class='c026'>Let <i>m</i> and <i>m´</i> be two attracting bodies supposed to be small
in comparison with their distance <i>x</i>. Let the force between
them be ε <i>m m´</i> ÷ <i>x</i><sup>2</sup> 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 <i>a</i>. The energy required is obtained
by integrating between the limits infinity and <i>a</i>, and is consequently
ε <i>m</i> <i>m´</i> ÷ <i>a</i>.</p>
<h4 id='s03' class='c027'>§ 3. <span class='sc'>On the Energy Given Out in the Contraction of the Nebula.</span></h4>
<p class='c026'>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,
<i>r</i> + <i>dr</i> and <i>r</i> respectively.</p>
<p class='c004'>Let M´ be the mass of the nebula contained within the sphere
of radius <i>r</i>, and let <i>d</i>M´ be the mass of the shell just defined.
Then it follows from <a href='#s01'>§ 1</a> that the condensation of the shell will
<span class='pageno' id='Page_371'>371</span>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 <i>d</i>M´, and the attraction of these is zero. We see
from <a href='#s02'>§ 2</a> that the contraction of <i>d</i>M´ from infinity, until it
forms a shell with radius <i>r</i>, represents a quantity of energy,</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div>(ε M´<i>d</i>M´)/<i>r</i> ;</div>
</div>
</div>
<p class='c021'>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.</p>
<p class='c004'>If M be the total mass and <i>a</i> the radius of the nebula always
supposed homogeneous</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div>M´ = M (<i>r</i><sup>3</sup>/<i>a</i><sup>3</sup>),</div>
</div>
</div>
<p class='c021'>and therefore</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div><i>d</i>M´ = 3 M (<i>r</i><sup>2</sup>/<i>a</i><sup>3</sup>) <i>dr</i>.</div>
</div>
</div>
<p class='c021'>Hence the work done in the contraction is</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>(ε/<i>r</i>) M (<i>r</i><sup>3</sup>/<i>a</i><sup>3</sup>) · 3 M (<i>r</i><sup>2</sup>/<i>a</i><sup>3</sup>) <i>dr</i> = (3 ε/<i>a</i><sup>6</sup>) M<sup>2</sup> <i>r</i><sup>4</sup> <i>dr</i>.</div>
</div>
</div>
<p class='c021'>Integrating, therefore, the total work of contraction is</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>⅗ (ε M<sup>2</sup>/<i>a</i>)</div>
</div>
</div>
<p class='c004'>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</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div>ε M/<i>a</i><sup>2</sup> = 27.</div>
</div>
</div>
<p class='c021'>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 <i>a</i> to be,</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>⅗ · 27 <i>a</i> M = 16 <i>a</i> M very nearly.</div>
</div>
</div>
<p class='c021'>Hence we have the following fundamental theorem due to
Helmholtz, which is the basis of the theory of sun heat.</p>
<p class='c004'><i>If the sun he regarded as a homogeneous sphere of mass</i>
M <i>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</i> 16 a M.</p>
<h4 id='s04' class='c027'>§ 4. <span class='sc'>Evaluation of the Sun Heat Given Out in Contraction.</span></h4>
<p class='c026'>The number of foot-pounds of work given out in the contraction
from infinity is 16 <i>a</i> M. As 772 foot-pounds are equal to
<span class='pageno' id='Page_372'>372</span>one unit of heat, <i>i.e.</i> 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</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div>(16 <i>a</i>)/772,</div>
</div>
</div>
<p class='c021'>but <i>a</i>, the radius of the sun in feet, is 2,280,000,000, and hence we
have the following theorem:—</p>
<p class='c004'><i>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.</i></p>
<p class='c004'>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</p>
<div class='mono'>
<p class='c004'> (16 <i>a</i> M) 16 × 2,280,000,000<br />
———————————————— = —————————————————— = 3,400.<br />
14,000 × 772 × M 14,000 × 772</p>
</div>
<p class='c021'>Hence we see that</p>
<p class='c004'><i>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.</i></p>
<p class='c004'>We may speak of 3,400 in this case as the coal equivalent.</p>
<h4 class='c027'>§ 5. <span class='sc'>On the Further Contraction of the Sun and the Heat that may thus be Given Out.</span></h4>
<p class='c026'>Let us suppose the sun contracts to the radius <i>r</i>, and then, as
already proved, <a href='#s03'>§ 3</a>, the energy it gives out is</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div>⅗ (ε M<sup>2</sup>)/<i>r</i>,</div>
</div>
</div>
<p class='c021'>but we have</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>ε M/<i>a</i><sup>2</sup> = 27,</div>
</div>
</div>
<p class='c021'>whence on contraction to the radius <i>r</i> the total energy given out
from the commencement is</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>16 M (<i>a</i><sup>2</sup>/<i>r</i>)</div>
</div>
</div>
<p class='c004'><span class='pageno' id='Page_373'>373</span>The average density of the sun at present is 1.4. Let us
suppose it condenses until it has a density ρ.</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div><i>r</i><sup>3</sup> ÷ <i>a</i><sup>3</sup> = 1.4 ÷ ρ,</div>
</div>
</div>
<p class='c021'>whence the energy becomes</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>14 <i>a</i> M · ∛ρ;</div>
</div>
</div>
<p class='c021'>but the coal equivalent of 16 <i>a</i> M has been found in <a href='#s04'>§ 4</a> to be
3,400, and hence the coal equivalent in this case is</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>3,000 ∛ρ.</div>
</div>
</div>
<p class='c004'>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.</p>
<h4 class='c027'>§ 6. <span class='sc'>On the Present Emission of Sun Heat.</span></h4>
<p class='c026'>According to Scheiner, “Strahlung und Temperatur der Sonne,
Leipzig, 1899,” the value of the solar constant, <i>i.e.</i> 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:—</p>
<p class='c004'><i>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.</i></p>
<p class='c004'>This shows that the solar energy emitted daily amounts to</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div>700,000,000,000 × 4 π <i>a</i><sup>2</sup> foot-pounds.</div>
</div>
</div>
<h4 class='c027'>§ 7. <span class='sc'>On the Daily Contraction of the Sun Necessary to Supply the Present Expenditure of Heat.</span></h4>
<p class='c026'>We have seen that at the radius <i>r</i> the energy is</p>
<div class='nf-center-c0'>
<div class='nf-center'>
<div>16 M (<i>a</i><sup>2</sup>/<i>r</i>).</div>
</div>
</div>
<p class='c021'>Hence for a change <i>dr</i> it is</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>–16 M (<i>a</i><sup>2</sup>/<i>r</i><sup>2</sup>) <i>dr</i>.</div>
</div>
</div>
<p class='c021'>At its present size, accordingly, the energy given out by a
shrinkage <i>dr</i> is</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>16 M <i>dr</i>.</div>
</div>
</div>
<p class='c021'><span class='pageno' id='Page_374'>374</span>One cubic foot of the sun averages 87 pounds, so that</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div>M = <span class='c028'><sup>4</sup></span>⁄<span class='small'><sub>3</sub></span> π <i>a</i><sup>3</sup> × 87</div>
<div class='c000'>16 M <i>dr</i> = 464 × 4 π <i>a</i><sup>3</sup> <i>dr</i>.</div>
</div>
</div>
<p class='c021'>We have to equate this to the expression in the last article, and
we get</p>
<div class='nf-center-c1'>
<div class='nf-center'>
<div><i>dr</i> = 700,000,000,000/(464 <i>a</i>) = .65.</div>
</div>
</div>
<p class='c021'>This is the shrinkage of the sun’s radius expressed in feet. Hence
the daily reduction of the sun’s <i>diameter</i> is 16 inches.</p>
<p class='c004'>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.</p>
<h3 class='c024'>II.—THE CONSERVATION OF MOMENT OF MOMENTUM.</h3>
<p class='c026'>We give here an elementary investigation of the fundamental
dynamical principle which has been of such importance throughout
this volume.</p>
<h4 class='c027'>§ 8. <span class='sc'>Case where there are no forces.</span></h4>
<p class='c026'>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.</p>
<p class='c004'>Let A<sub>0</sub>, Fig. <a href='#i375'>60</a>, be the position of the particle at any moment.
Let A<sub>1</sub> be its position after the time <i>t</i>; A<sub>2</sub> be the position at
the time 2<i>t</i>; A<sub>3</sub> be the position at the time 3<i>t</i>, and so on.</p>
<p class='c004'>Then the first law of motion tells us that the distances
A<sub>0</sub> A<sub>1</sub>, A<sub>1</sub> A<sub>2</sub>, A<sub>2</sub> A<sub>3</sub>, A<sub>3</sub> A<sub>4</sub>, must form parts of the same straight
line and must be all equal.</p>
<p class='c004'>If lines O A<sub>0</sub>, O A<sub>1</sub>, O A<sub>2</sub>, etc., be drawn from any fixed point
0, then the areas of the triangles O A<sub>0</sub> A<sub>1</sub>, O A<sub>1</sub> A<sub>2</sub>, O A<sub>2</sub> A<sub>3</sub>,
0 A<sub>3</sub> A<sub>4</sub>, 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<sub>0</sub> A<sub>1</sub>, and, as the bases of all the triangles are equal, it follows
that their areas are equal.</p>
<p class='c004'>Thus we learn that a particle moving without the action of
force will describe around any fixed point O equal areas in
equal times.</p>
<div id='i375' class='figright id014'>
<img src='images/i375.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 60.—<span class='sc'>First Law of Motion exemplifies<br />Constant Moment of Momentum.</span></span></p>
</div>
</div>
<p class='c004'>The product of the mass of the particle and its velocity is
termed the momentum. If the momentum be multiplied by
<span class='pageno' id='Page_375'>375</span>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.</p>
<p class='c004'>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.</p>
<p class='c004'>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.</p>
<h4 class='c027'>§ 9. <span class='sc'>A Geometrical Proposition.</span></h4>
<p class='c026'>The following theorem in elementary geometry will be
required:—</p>
<div id='i376a' class='figcenter id001'>
<img src='images/i376a.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 61.—<span class='sc'>A Useful Geometrical Proposition.</span></span></p>
</div>
</div>
<p class='c004'>Let A B and A C be adjacent sides of a parallelogram, Fig. <a href='#i376a'>61</a>,
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.</p>
<p class='c004'>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.</p>
<h4 class='c027'>§ 10. <span class='sc'>Relation Between the Change of Moment of Momentum and the Force Acting on the Particle.</span></h4>
<div id='i376b' class='figcenter id001'>
<img src='images/i376b.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 62.—<span class='sc'>Acceleration of Moment of Momentum equals Moment of Force.</span></span></p>
</div>
</div>
<p class='c026'>Let A<sub>1</sub> and A<sub>2</sub>, Fig. <a href='#i376b'>62</a>, be two adjacent points on the path of the
particle, and let A<sub>1</sub> Q and A<sub>2</sub> R be the tangents at those points.
<span class='pageno' id='Page_376'>376</span>Let S Q represent the velocity of the particle at A<sub>1</sub>, and SR the
velocity of the particle at A<sub>2</sub>. 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<sub>1</sub> to A<sub>2</sub> in the small time <i>t</i>; we
have also Q R = F <i>t</i> ÷ <i>m</i>.</p>
<p class='c004'>Complete the parallelogram S Q R U, and let fall O P<sub>1</sub>, O P<sub>2</sub>,
<span class='pageno' id='Page_377'>377</span>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<sub>1</sub> the moment of
momentum is <i>m</i> O P<sub>1</sub> × S Q; when the particle is at A<sub>2</sub> the
moment of momentum is <i>m</i> O P<sub>2</sub> × S R. Whence the difference
of the moments of momentum at A<sub>1</sub> and A<sub>2</sub> is <i>m</i> (O P<sub>2</sub> × S R -
O P<sub>1</sub> × S Q) = 2 <i>m</i> (O S R - O S Q) = 2 <i>m</i> O S U = <i>m</i> O T ×
S U = <i>m</i> O T. Q R = F <i>t</i> × O T. But in the limit S coincides
with A<sub>1</sub> and A<sub>2</sub>, and we see that the gain in moment of momentum
is <i>t</i> 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:—</p>
<p class='c004'><i>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.</i></p>
<p class='c004'>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.</p>
<h4 class='c027'>§ 11. <span class='sc'>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.</span></h4>
<p class='c026'>Let A D, Fig. <a href='#i376a'>61</a>, 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.</p>
<p class='c004'>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.</p>
<div>
<span class='pageno' id='Page_378'>378</span>
<h4 class='c027'>§ 12. <span class='sc'>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.</span></h4>
</div>
<p class='c026'>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.</p>
<p class='c004'>This fundamental principle is also known as the doctrine of
the conservation of areas. It may be stated in the following
manner:—</p>
<p class='c004'><i>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.</i></p>
<h4 class='c027'>§ 13. <span class='sc'>If a Particle of Mass</span> <i>m</i>, <span class='sc'>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</span> <i>m</i> <span class='sc'>Acted upon by that Component of F which is Parallel to the Plane</span>.</h4>
<p class='c026'>This is evident from the consideration that the acceleration
of the particle parallel to the plane must be proportional to
this component of F.</p>
<p class='c004'>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
<span class='pageno' id='Page_379'>379</span>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:—</p>
<p class='c004'><i>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.</i></p>
<h4 class='c027'>§ 14. <span class='sc'>On the Principal Plane of a System.</span></h4>
<p class='c026'>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.</p>
<p class='c004'>If <i>v</i> be the velocity of a particle, then in a small time <i>t</i> it
moves over the distance <i>v t</i>. If <i>p</i> be the perpendicular from O
on the tangent to the motion, then the area of the triangle
swept round O in the time <i>t</i> is ½ <i>p v t</i>, and we see that the
momentum is proportional to the mass of the particle multiplied
into the area swept over in the time <i>t</i>. The quantity S will, therefore,
be proportional to the sum of the projections of the areas in
L, swept over in the time <i>t</i>, 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 <i>h</i> proportional to any area in that plane, then the
<span class='pageno' id='Page_380'>380</span>projection of this area on
any other plane L´ may
be measured by the projection
of <i>h</i> on the normal
to L´.</p>
<div id='i380' class='figright id018'>
<img src='images/i380.jpg' alt='' class='ig001' />
<div class='ic001'>
<p><span class='small'>Fig. 63.—<span class='sc'>Moment of Momentum unaltered<br />by Collision.</span></span></p>
</div>
</div>
<p class='c004'>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 <i>l</i> proportional
to the moment of
momentum. Repeat the
same process for each of the other particles with lengths <i>l´</i>, <i>l″</i>,
etc., on their several normals. Suppose that <i>l</i>, <i>l´</i>, <i>l″</i> 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.</p>
<h4 class='c027'>§ 15. <span class='sc'>Collisions.</span></h4>
<p class='c026'>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.</p>
<p class='c004'>Let two particles collide when meeting in the directions A P
and B P (Fig. <a href='#i380'>63</a>) 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
<span class='pageno' id='Page_381'>381</span>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.</p>
<h4 class='c027'>§ 16. <span class='sc'>Friction and Tides.</span></h4>
<p class='c026'>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.</p>
<div class='pbb'>
<hr class='pb c006' />
</div>
<div class='chapter'>
<span class='pageno' id='Page_382'>382</span>
<h2 id='idx' class='c012'>INDEX.</h2>
</div>
<ul class='index c006'>
<li class='c029'>Acceleration of moment of momentum, <a href='#Page_377'>377</a></li>
<li class='c029'>Aldebaran, <a href='#Page_27'>27</a>, <a href='#Page_28'>28</a></li>
<li class='c029'>Anderson, Dr., <a href='#Page_356'>356</a></li>
<li class='c029'>Andromeda, Great Nebula in, <a href='#Page_43'>43</a>, <a href='#Page_204'>204</a></li>
<li class='c029'>Antinous, Cluster of stars in, <a href='#Page_353'>353</a></li>
<li class='c029'>Apteryx, Rudimentary wing-bones of, <a href='#Page_364'>364</a>, <a href='#Page_366'>366</a></li>
<li class='c029'>——, Skeleton of, <a href='#Page_364'>364</a>, <a href='#Page_366'>366</a></li>
<li class='c029'>——, The, <a href='#Page_363'>363</a>, <a href='#Page_365'>365</a></li>
<li class='c029'>Arcturus, Spectrum of, <a href='#Page_85'>85</a></li>
<li class='c029'>Argon, <a href='#Page_265'>265</a></li>
<li class='c029'>Argus and surrounding stars, <a href='#Page_103'>103</a></li>
<li class='c029'>Ariel, <a href='#Page_338'>338</a></li>
<li class='c006'>Boring, The great, <a href='#Page_123'>123</a></li>
<li class='c029'>Brooks’ comet, <a href='#Page_89'>89</a></li>
<li class='c029'>Bunsen burner, The, <a href='#Page_283'>283</a></li>
<li class='c029'>Butterfly and the oak-tree, The, <a href='#Page_15'>15</a></li>
<li class='c006'>Calcium, <a href='#Page_274'>274</a></li>
<li class='c029'>Capella, Spectrum of, <a href='#Page_61'>61</a>–<a href='#Page_64'>64</a></li>
<li class='c029'>Carbon, <a href='#Page_280'>280</a></li>
<li class='c029'>Ceres, <a href='#Page_311'>311</a></li>
<li class='c029'>Change of moment of momentum, <a href='#Page_375'>375</a></li>
<li class='c029'>Cluster, Nebulous region round a, <a href='#i033'>33</a></li>
<li class='c029'>Clusters of stars, <a href='#Page_53'>53</a>–<a href='#Page_60'>60</a>, <a href='#Page_203'>203</a></li>
<li class='c029'>—— —— of 17th magnitude, <a href='#Page_353'>353</a></li>
<li class='c029'>Coal-unit, <a href='#Page_110'>110</a></li>
<li class='c029'>Collisions, <a href='#Page_219'>219</a>, <a href='#Page_380'>380</a></li>
<li class='c029'>——, Cause of formation of nebulæ, <a href='#Page_356'>356</a></li>
<li class='c029'>Comets, <a href='#Page_37'>37</a></li>
<li class='c029'>Comet, Brooks’, <a href='#Page_89'>89</a></li>
<li class='c029'>—— of 1882, <a href='#Page_119'>119</a></li>
<li class='c029'>——, Spectrum of, <a href='#Page_290'>290</a></li>
<li class='c029'>Common, Dr. A. A., <a href='#Page_44'>44</a></li>
<li class='c029'>Concord, The first, <a href='#Page_294'>294</a>–<a href='#Page_307'>307</a></li>
<li class='c029'>——, The second, <a href='#Page_308'>308</a>–<a href='#Page_323'>323</a></li>
<li class='c029'>——, The third, <a href='#Page_324'>324</a>–<a href='#Page_336'>336</a></li>
<li class='c029'>Conglomerates, <a href='#Page_159'>159</a></li>
<li class='c029'>Conservation of moment of momentum, <a href='#Page_374'>374</a></li>
<li class='c029'>Corona of the sun, <a href='#Page_117'>117</a></li>
<li class='c029'>Crab nebula, The, <a href='#Page_19'>19</a>, <a href='#Page_44'>44</a></li>
<li class='c029'>Crossley Reflector, The, <a href='#Page_45'>45</a>, <a href='#Page_46'>46</a>, <a href='#Page_48'>48</a>, <a href='#i049'>49</a>, <a href='#Page_50'>50</a>, <a href='#Page_67'>67</a>, <a href='#Page_199'>199</a></li>
<li class='c029'>Cygnus, Nebula in, <a href='#i329'>329</a></li>
<li class='c006'>Dark bodies in universe, <a href='#Page_355'>355</a></li>
<li class='c029'>Darwin, Professor G. H., <a href='#Page_153'>153</a>, <a href='#Page_254'>254</a>, <a href='#Page_332'>332</a></li>
<li class='c029'>Darwinian theory, <a href='#Page_10'>10</a>, <a href='#Page_268'>268</a>, <a href='#Page_362'>362</a></li>
<li class='c029'>Dewar, Professor, <a href='#Page_144'>144</a>, <a href='#Page_272'>272</a></li>
<li class='c029'>Diurnal motion, The, <a href='#Page_21'>21</a></li>
<li class='c029'>Dumb-bell nebula, <a href='#Page_43'>43</a>, <a href='#Page_44'>44</a>, <a href='#Page_45'>45</a>, <a href='#Page_46'>46</a>, <a href='#Page_50'>50</a>, <a href='#Page_74'>74</a>, <a href='#Page_195'>195</a></li>
<li class='c029'>Dust from Krakatoa, <a href='#Page_185'>185</a></li>
<li class='c006'>Earth, Heat in interior of, <a href='#Page_134'>134</a>, <a href='#Page_367'>367</a></li>
<li class='c029'>——, ——, Cause of, <a href='#Page_153'>153</a></li>
<li class='c029'>——, History of, <a href='#Page_122'>122</a>–<a href='#Page_157'>157</a>, <a href='#Page_251'>251</a></li>
<li class='c029'>——, Rigidity of, <a href='#Page_162'>162</a></li>
<li class='c029'>Earth-moon system, <a href='#Page_253'>253</a>, <a href='#Page_332'>332</a></li>
<li class='c029'>Earthquakes, <a href='#Page_158'>158</a>–<a href='#Page_190'>190</a></li>
<li class='c029'>—— in England, <a href='#i174'>175</a></li>
<li class='c029'>——, Routes of, <a href='#Page_171'>171</a></li>
<li class='c029'>Emission of sun heat, <a href='#Page_373'>373</a></li>
<li class='c029'>Energy between two attracting masses, <a href='#Page_370'>370</a></li>
<li class='c029'>—— given out in contraction of nebula, <a href='#Page_370'>370</a></li>
<li class='c029'>—— of a system, <a href='#Page_216'>216</a>, <a href='#Page_235'>235</a></li>
<li class='c029'>Equivalent of heat, <a href='#Page_88'>88</a></li>
<li class='c029'>Eros, <a href='#Page_312'>312</a></li>
<li class='c029'>Evaluation of sun heat given out in contraction, <a href='#Page_371'>371</a></li>
<li class='c029'>Everett, Professor, <a href='#Page_149'>149</a></li>
<li class='c006'>Fire-mist, The, <a href='#Page_268'>268</a></li>
<li class='c029'>“Flash” spectrum, <a href='#Page_70'>70</a></li>
<li class='c029'><span class='pageno' id='Page_383'>383</span>Foot-pound, <a href='#Page_91'>91</a></li>
<li class='c029'>Foraminifera, <a href='#Page_367'>367</a></li>
<li class='c029'>Friction and tides, <a href='#Page_381'>381</a></li>
<li class='c006'>Gas in rarefaction, <a href='#Page_118'>118</a></li>
<li class='c006'>H and K lines, <a href='#Page_70'>70</a>, <a href='#Page_276'>276</a></li>
<li class='c029'>Heat, Cause of, <a href='#Page_153'>153</a></li>
<li class='c029'>——, Equivalent of, <a href='#Page_88'>88</a></li>
<li class='c029'>—— given out in contraction of nebula, <a href='#Page_369'>369</a></li>
<li class='c029'>—— in interior of the earth, <a href='#Page_134'>134</a>, <a href='#Page_367'>367</a></li>
<li class='c029'>——, Unit of, <a href='#Page_80'>80</a>, <a href='#Page_89'>89</a></li>
<li class='c029'>Helium, <a href='#Page_277'>277</a></li>
<li class='c029'>Helmholtz, <a href='#Page_86'>86</a>, <a href='#Page_96'>96</a>, <a href='#Page_100'>100</a></li>
<li class='c029'>Hercules, Star-cluster in, <a href='#Page_52'>52</a>, <a href='#Page_53'>53</a>, <a href='#Page_56'>56</a>, <a href='#Page_57'>57</a>, <a href='#Page_59'>59</a></li>
<li class='c029'>Herschel, Sir William, <a href='#Page_4'>4</a>, <a href='#Page_11'>11</a>, <a href='#Page_72'>72</a>, <a href='#Page_73'>73</a>, <a href='#Page_74'>74</a></li>
<li class='c029'>Huggins, Sir W., <a href='#Page_60'>60</a>, <a href='#Page_61'>61</a>, <a href='#Page_63'>63</a>, <a href='#Page_65'>65</a></li>
<li class='c029'>Huxley, Professor, and Darwinian theory, <a href='#Page_362'>362</a></li>
<li class='c029'>Huyssen, Captain, <a href='#Page_127'>127</a></li>
<li class='c029'>Hydrogen in spectrum of Nova Persei, <a href='#Page_358'>358</a></li>
<li class='c006'>“Inflammation” and nebular theory, <a href='#Page_361'>361</a></li>
<li class='c006'>Joule’s equivalent of heat, <a href='#Page_88'>88</a></li>
<li class='c029'>Jupiter, <a href='#Page_23'>23</a>, <a href='#Page_25'>25</a>, <a href='#Page_26'>26</a>, <a href='#Page_29'>29</a>, <a href='#Page_208'>208</a>, <a href='#i233'>237</a>, <a href='#Page_310'>310</a>, <a href='#Page_327'>327</a></li>
<li class='c006'>K and H lines, <a href='#Page_70'>70</a>, <a href='#Page_276'>276</a></li>
<li class='c029'>Kant, Immanuel, <a href='#Page_4'>4</a>, <a href='#Page_5'>5</a>, <a href='#Page_72'>72</a>, <a href='#Page_73'>73</a>, <a href='#Page_74'>74</a>, <a href='#Page_327'>327</a></li>
<li class='c029'>Keeler, Professor, <a href='#Page_45'>45</a>–<a href='#Page_48'>48</a>, <a href='#Page_67'>67</a>, <a href='#Page_73'>73</a>, <a href='#Page_199'>199</a>, <a href='#Page_200'>200</a>, <a href='#Page_202'>202</a>, <a href='#Page_245'>245</a></li>
<li class='c029'>Kelvin, Lord, <a href='#Page_153'>153</a>, <a href='#Page_162'>162</a></li>
<li class='c029'>Krakatoa, <a href='#Page_176'>176</a>–<a href='#Page_189'>189</a></li>
<li class='c006'>Langley, Professor, <a href='#Page_78'>78</a></li>
<li class='c029'>Laplace, <a href='#Page_4'>4</a>, <a href='#Page_72'>72</a>, <a href='#Page_73'>73</a>, <a href='#Page_74'>74</a>, <a href='#Page_206'>206</a></li>
<li class='c029'>Lassell, Mr., <a href='#Page_338'>338</a>, <a href='#Page_340'>340</a></li>
<li class='c029'>Lick Observatory, <a href='#Page_41'>41</a>, <a href='#Page_43'>43</a>, <a href='#Page_44'>44</a>, <a href='#Page_45'>45</a></li>
<li class='c029'>Lockyer, Sir Norman, <a href='#Page_277'>277</a></li>
<li class='c029'>Lyra, Ring nebula in, <a href='#Page_249'>249</a></li>
<li class='c006'>Mars, <a href='#Page_25'>25</a>, <a href='#Page_26'>26</a>, <a href='#Page_27'>27</a>, <a href='#Page_28'>28</a>, <a href='#Page_29'>29</a>, <a href='#Page_311'>311</a>, <a href='#Page_341'>341</a>, <a href='#Page_349'>349</a></li>
<li class='c029'>——, Satellites of, <a href='#Page_341'>341</a></li>
<li class='c029'><i>Mécanique Céleste</i>, <a href='#Page_5'>5</a>, <a href='#Page_8'>8</a></li>
<li class='c029'>Mercury, <a href='#Page_23'>23</a>, <a href='#Page_25'>25</a>, <a href='#Page_26'>26</a>, <a href='#Page_29'>29</a>, <a href='#Page_208'>208</a></li>
<li class='c029'>Meteors, <a href='#Page_37'>37</a></li>
<li class='c029'>Milky Way, <a href='#Page_205'>205</a>, <a href='#Page_206'>206</a>, <a href='#Page_214'>214</a>, <a href='#Page_220'>220</a></li>
<li class='c029'>Milne, Professor, <a href='#Page_165'>165</a></li>
<li class='c029'>Moment of momentum, <a href='#Page_222'>222</a>, <a href='#Page_226'>226</a>, <a href='#Page_240'>240</a>, <a href='#Page_352'>352</a></li>
<li class='c029'>—— ——, Acceleration of, <a href='#Page_377'>377</a></li>
<li class='c029'>—— ——, Change of, <a href='#Page_375'>375</a></li>
<li class='c029'>—— ——, Conservation of, <a href='#Page_374'>374</a></li>
<li class='c029'>Momentum, Moment of, <a href='#Page_222'>222</a>, <a href='#Page_220'>220</a>, <a href='#Page_240'>240</a>, <a href='#Page_352'>352</a></li>
<li class='c029'>Monoceros, Nebulous region round a cluster in, <a href='#i033'>33</a></li>
<li class='c029'>Moon, Origin of, <a href='#Page_254'>254</a></li>
<li class='c029'>——, Surface of, <a href='#Page_255'>255</a></li>
<li class='c006'>Nautilus, The, <a href='#Page_367'>367</a></li>
<li class='c029'>Nebula, Contraction of, Heat given out in, <a href='#Page_369'>369</a></li>
<li class='c029'>——, ——, Energy given out in, <a href='#Page_370'>370</a></li>
<li class='c029'>—— in Orion, The great, <a href='#Page_40'>40</a>, <a href='#Page_41'>41</a>, <a href='#Page_42'>42</a>, <a href='#Page_44'>44</a>, <a href='#Page_46'>46</a>, <a href='#Page_50'>50</a>, <a href='#Page_74'>74</a>, <a href='#Page_195'>195</a>, <a href='#Page_242'>242</a></li>
<li class='c029'>—— ——, ——, Spectrum of, <a href='#Page_63'>63</a>, <a href='#Page_64'>64</a>, <a href='#Page_65'>65</a></li>
<li class='c029'>——, The great spiral, <a href='#Page_192'>192</a>, <a href='#Page_193'>193</a></li>
<li class='c029'>Nebulæ, <a href='#Page_40'>40</a>, <a href='#Page_41'>41</a>, <a href='#Page_43'>43</a>, <a href='#Page_45'>45</a>, <a href='#Page_47'>47</a>, <a href='#Page_50'>50</a>, <a href='#Page_57'>57</a>, <a href='#Page_58'>58</a>, <a href='#Page_66'>66</a>, <a href='#Page_67'>67</a>, <a href='#i071'>71</a>, <a href='#Page_73'>73</a>, <a href='#Page_105'>105</a>, <a href='#Page_120'>120</a>, <a href='#Page_157'>157</a>, <a href='#Page_191'>191</a>–<a href='#Page_206'>206</a>, <a href='#Page_242'>242</a>, <a href='#Page_247'>247</a>, <a href='#Page_249'>249</a>, <a href='#Page_256'>256</a>, <a href='#Page_257'>257</a>, <a href='#Page_258'>258</a>, <a href='#Page_259'>259</a>, <a href='#i296'>296</a>, <a href='#i329'>329</a>, <a href='#Page_345'>345</a>, <a href='#Page_348'>348</a>–<a href='#Page_360'>360</a></li>
<li class='c029'>——, Development of, <a href='#Page_242'>242</a></li>
<li class='c029'>——, Discovery of, <a href='#Page_11'>11</a></li>
<li class='c029'>——, Number of, <a href='#Page_67'>67</a>, <a href='#Page_200'>200</a></li>
<li class='c029'>Nebular anecdote, <a href='#Page_362'>362</a></li>
<li class='c029'>—— Theory, The, <a href='#Page_2'>2</a>, <a href='#Page_3'>3</a>, <a href='#Page_72'>72</a>, <a href='#Page_74'>74</a>, <a href='#Page_157'>157</a>, <a href='#Page_205'>205</a>, <a href='#Page_266'>266</a>, <a href='#Page_292'>292</a>, <a href='#Page_307'>307</a>, <a href='#Page_323'>323</a>, <a href='#i329'>328</a>, <a href='#Page_331'>331</a>, <a href='#Page_337'>337</a>–<a href='#Page_347'>347</a>, <a href='#Page_362'>362</a>, <a href='#Page_368'>368</a></li>
<li class='c029'>Nebulosity, Faint diffused, in Perseus, <a href='#i017'>17</a></li>
<li class='c029'>Neptune, <a href='#Page_37'>37</a></li>
<li class='c029'>——, Satellites of, <a href='#Page_330'>330</a>, <a href='#Page_340'>340</a></li>
<li class='c029'>Newcomb, Professor, <a href='#Page_238'>238</a></li>
<li class='c029'>Norway, Conglomerates in, <a href='#Page_159'>159</a></li>
<li class='c029'>Nova Persei, <a href='#Page_358'>358</a></li>
<li class='c029'>—— ——, Spectrum of, <a href='#Page_358'>358</a>, <a href='#Page_359'>359</a>, <a href='#Page_360'>360</a></li>
<li class='c006'>Oak-tree and the butterfly, The, <a href='#Page_15'>15</a></li>
<li class='c029'>Oberon, <a href='#Page_338'>338</a></li>
<li class='c029'>Orbits of the planets, <a href='#Page_208'>208</a></li>
<li class='c029'>Orion, <a href='#Page_22'>22</a></li>
<li class='c029'><span class='pageno' id='Page_384'>384</span>Orion, Great nebula in, <a href='#Page_40'>40</a>, <a href='#Page_41'>41</a>, <a href='#Page_42'>42</a>, <a href='#Page_44'>44</a>, <a href='#Page_46'>46</a>, <a href='#Page_50'>50</a>, <a href='#Page_74'>74</a>, <a href='#Page_195'>195</a>, <a href='#Page_242'>242</a></li>
<li class='c029'>——, Spectrum of, <a href='#Page_63'>63</a>, <a href='#Page_64'>64</a>, <a href='#Page_65'>65</a></li>
<li class='c006'>Pegasus, Nebula in, <a href='#Page_47'>47</a>, <a href='#Page_345'>345</a></li>
<li class='c029'>Perseus, A faint diffused nebulosity in, <a href='#i017'>17</a></li>
<li class='c029'>——, New star in, <a href='#Page_356'>356</a></li>
<li class='c029'>Photosphere, The, <a href='#Page_69'>69</a></li>
<li class='c029'>Pickering, Professor, <a href='#Page_358'>358</a></li>
<li class='c029'>“Plane, Principal,” The, <a href='#Page_225'>225</a>, <a href='#Page_352'>352</a>, <a href='#Page_379'>379</a></li>
<li class='c029'>Planetary system, The, <a href='#Page_37'>37</a>, <a href='#Page_208'>208</a></li>
<li class='c029'>Planets, <a href='#Page_22'>22</a>, <a href='#Page_26'>26</a>, <a href='#Page_28'>28</a></li>
<li class='c029'>——, Movement of, <a href='#Page_35'>35</a>, <a href='#Page_311'>311</a></li>
<li class='c029'>——, Orbits of, <a href='#Page_208'>208</a>, <a href='#Page_298'>298</a></li>
<li class='c029'>——, Rotation of, on their axes, <a href='#Page_325'>325</a></li>
<li class='c029'>Platinum, <a href='#Page_263'>263</a></li>
<li class='c029'>Pleiades, <a href='#Page_22'>22</a></li>
<li class='c029'>——, Nebulae in, <a href='#i071'>71</a></li>
<li class='c029'>Potassium, <a href='#Page_272'>272</a></li>
<li class='c029'>“Plane, Principal” The, <a href='#Page_225'>225</a>, <a href='#Page_352'>352</a>, <a href='#Page_379'>379</a></li>
<li class='c029'>Probabilities, Theory of, <a href='#Page_305'>305</a></li>
<li class='c006'>Radiation of sun’s heat, <a href='#Page_82'>82</a></li>
<li class='c029'>Ramsay, Professor, <a href='#Page_278'>278</a></li>
<li class='c029'>Ray nebulæ, <a href='#Page_201'>201</a>, <a href='#Page_211'>211</a></li>
<li class='c029'>Rigidity of the earth, <a href='#Page_162'>162</a></li>
<li class='c029'>Ring nebula in Lyra, The, <a href='#Page_249'>249</a></li>
<li class='c029'>Roberts, Dr. Isaac, <a href='#Page_198'>198</a></li>
<li class='c029'>Rosse, Lord, <a href='#Page_57'>57</a>, <a href='#Page_196'>196</a>–<a href='#Page_201'>201</a></li>
<li class='c029'>Rowland, Prof. Henry, <a href='#Page_273'>273</a></li>
<li class='c006'>Sagittarius, Nebula in, <a href='#Page_105'>105</a></li>
<li class='c029'>Satellites, <a href='#Page_37'>37</a>, <a href='#Page_209'>209</a></li>
<li class='c029'>Saturn, <a href='#Page_25'>25</a>, <a href='#Page_26'>26</a>, <a href='#Page_29'>29</a>, <a href='#Page_220'>220</a>, <a href='#i233'>233</a></li>
<li class='c029'>——, Dweller in, and the Sirian, <a href='#Page_14'>14</a></li>
<li class='c029'>——, Ring of, <a href='#Page_210'>210</a>, <a href='#Page_220'>220</a>, <a href='#Page_231'>231</a>, <a href='#Page_232'>232</a>, <a href='#i233'>233</a>, <a href='#Page_234'>234</a></li>
<li class='c029'>Scheiner, Professor, <a href='#Page_202'>202</a>, <a href='#Page_204'>204</a></li>
<li class='c029'>Seismometer, The, <a href='#Page_165'>165</a></li>
<li class='c029'>Sirian, The, and the dweller in Saturn, <a href='#Page_14'>14</a></li>
<li class='c029'>Sirius, <a href='#Page_215'>215</a>, <a href='#Page_216'>216</a></li>
<li class='c029'>Smiths, The parable of the, <a href='#Page_303'>303</a></li>
<li class='c029'>Solar system, <a href='#Page_36'>36</a>, <a href='#Page_207'>207</a></li>
<li class='c029'>——, Energy of, <a href='#Page_350'>350</a></li>
<li class='c029'>——, Evolution of, <a href='#Page_20'>20</a>, <a href='#Page_246'>246</a>–<a href='#Page_260'>260</a>, <a href='#Page_349'>349</a></li>
<li class='c029'>——, Origin of, <a href='#Page_351'>351</a></li>
<li class='c029'>Solar system, Scale of, <a href='#Page_29'>29</a>, <a href='#Page_30'>30</a>, <a href='#Page_31'>31</a></li>
<li class='c029'>Spectra, Continuous, <a href='#Page_68'>68</a>, <a href='#Page_203'>203</a></li>
<li class='c029'>——, Discontinuous, <a href='#Page_68'>68</a></li>
<li class='c029'>Spectroscope, The, <a href='#Page_60'>60</a>, <a href='#Page_271'>271</a></li>
<li class='c029'>Spiral form in Nature, <a href='#Page_256'>256</a>, <a href='#Page_257'>257</a></li>
<li class='c029'>Spiral nebula, The great, <a href='#Page_192'>192</a>, <a href='#Page_193'>193</a>, <a href='#Page_247'>247</a></li>
<li class='c029'>Spiral nebulæ, <a href='#Page_191'>191</a>–<a href='#Page_206'>206</a>, <a href='#Page_211'>211</a>, <a href='#Page_212'>212</a>, <a href='#Page_213'>213</a>, <a href='#Page_220'>220</a>, <a href='#Page_243'>243</a>, <a href='#Page_247'>247</a>, <a href='#Page_256'>256</a>, <a href='#Page_257'>257</a>, <a href='#Page_258'>258</a>, <a href='#Page_259'>259</a>, <a href='#i296'>296</a>, <a href='#Page_345'>345</a></li>
<li class='c029'>Star-clusters, <a href='#Page_53'>53</a>–<a href='#Page_60'>60</a></li>
<li class='c029'>Star, Spectrum of, <a href='#Page_64'>64</a></li>
<li class='c029'>Stars distinguished from planets, <a href='#Page_28'>28</a>, <a href='#Page_29'>29</a></li>
<li class='c029'>Stoney, Dr. G. Johnstone, <a href='#Page_279'>279</a></li>
<li class='c029'>Sun compared with the planets, <a href='#Page_26'>26</a>, <a href='#Page_29'>29</a></li>
<li class='c029'>——, Corona of, <a href='#Page_117'>117</a></li>
<li class='c029'>——, Contraction of, <a href='#Page_99'>99</a>, <a href='#Page_373'>373</a></li>
<li class='c029'>——, Density of, <a href='#Page_102'>102</a>, <a href='#Page_115'>115</a></li>
<li class='c029'>——, Heat of, <a href='#Page_75'>75</a>–<a href='#Page_94'>94</a>, <a href='#Page_95'>95</a>–<a href='#Page_111'>111</a>, <a href='#Page_371'>371</a>, <a href='#Page_372'>372</a>, <a href='#Page_373'>373</a></li>
<li class='c029'>——, History of, <a href='#Page_112'>112</a>–<a href='#Page_121'>121</a>, <a href='#Page_251'>251</a></li>
<li class='c029'>——, Nebulous part of, <a href='#Page_121'>121</a></li>
<li class='c029'>——, Spectrum of, <a href='#Page_61'>61</a>, <a href='#Page_62'>62</a>, <a href='#Page_69'>69</a>, <a href='#Page_70'>70</a>, <a href='#Page_85'>85</a>, <a href='#Page_273'>273</a></li>
<li class='c029'>——, Surface of, <a href='#Page_278'>278</a></li>
<li class='c029'>——, Velocity of, <a href='#Page_354'>354</a></li>
<li class='c029'>——, Weight of, <a href='#Page_101'>101</a></li>
<li class='c029'>Sun heat, given out in contraction, Evaluation of, <a href='#Page_371'>371</a>, <a href='#Page_372'>372</a></li>
<li class='c029'>——, Present emission of, <a href='#Page_373'>373</a></li>
<li class='c029'>Sunsets, The Krakatoa, <a href='#Page_189'>189</a></li>
<li class='c029'><i>Système du Monde</i>, <a href='#Page_8'>8</a></li>
<li class='c006'>Thermometer for testing the heat of the earth’s interior, <a href='#Page_129'>129</a></li>
<li class='c029'>Thomson, Prof. J. J., <a href='#Page_316'>316</a></li>
<li class='c029'>Tides and friction, <a href='#Page_381'>381</a></li>
<li class='c029'>Titania, <a href='#Page_338'>338</a></li>
<li class='c006'>Umbriel, <a href='#Page_338'>338</a></li>
<li class='c029'>Unit of heat, <a href='#Page_80'>80</a>, <a href='#Page_89'>89</a></li>
<li class='c029'>Uranus, <a href='#Page_37'>37</a>, <a href='#Page_238'>238</a>, <a href='#Page_239'>239</a></li>
<li class='c029'>——, Satellites of, <a href='#Page_238'>238</a>, <a href='#Page_338'>338</a></li>
<li class='c006'>Venus, <a href='#Page_23'>23</a>, <a href='#Page_25'>25</a>, <a href='#Page_26'>26</a>, <a href='#Page_29'>29</a>, <a href='#Page_208'>208</a>, <a href='#Page_325'>325</a></li>
<li class='c029'>Volcanoes, <a href='#Page_158'>158</a>–<a href='#Page_190'>190</a></li>
<li class='c029'>Voltaire, Fable of, <a href='#Page_14'>14</a></li>
<li class='c006'>Waves caused by Krakatoa earth quake, <a href='#i179'>179</a>, <a href='#Page_182'>182</a>, <a href='#i183'>183</a></li>
</ul>
<hr class='c030' />
<div class='nf-center-c0'>
<div class='nf-center'>
<div><span class='sc'>Printed by Cassell & Company, Limited, La Belle Sauvage, London, E.C.</span></div>
<div>20.509</div>
</div>
</div>
<div class='pbb'>
<hr class='pb c006' />
</div>
<p class='c004'> </p>
<div class='tnbox'>
<ul class='ul_1 c006'>
<li>Transcriber’s Notes:
<ul class='ul_2'>
<li>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.
</li>
<li>In places where “×” was used for multiplication, it was left as the author wrote it.
</li>
<li>Missing or obscured punctuation was silently corrected.
</li>
<li>Typographical errors were silently corrected.
</li>
<li>Inconsistent spelling and hyphenation were made consistent only when a predominant
form was found in this book.
</li>
</ul>
</li>
</ul>
</div>
<p class='c004'> </p>
<div>*** END OF THE PROJECT GUTENBERG EBOOK 59080 ***</div>
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