success by Dr. Croll in his book "Climate and Time."
A brief and partial explanation of the matter may be given, because
it is a point of some interest and is also one of fair simplicity.
Every one knows that the climatic conditions of winter and summer
are inverted in the two hemispheres, and that at present the sun is
nearest to us in our (northern) winter. In other words, the earth's
axis is inclined so as to tilt its north pole away from the sun at
perihelion, or when the earth is at the part of its elliptic orbit
nearest the sun's focus; and to tilt it towards the sun at
aphelion. The result of this present state of things is to diminish
the intensity of the average northern winter and of the average
northern summer, and on the other hand to aggravate the extremes of
temperature in the southern hemisphere; all other things being
equal. Of course other things are not equal, and the distribution
of land and sea is a still more powerful climatic agent than is the
three million miles or so extra nearness of the sun. But it is
supposed that the Antarctic ice-cap is larger than the northern,
and increased summer radiation with increased winter cold would
account for this.
But the present state of things did not always obtain. The conical
movement of the earth's axis (now known by a curious perversion of
phrase as "precession") will in the course of 13,000 years or so
cause the tilt to be precisely opposite, and then we shall have the
more extreme winters and summers instead of the southern
hemisphere.
If the change were to occur now, it might not be overpowering,
because now the excentricity is moderate. But if it happened some
time back, when the excentricity was much greater, a decidedly
different arrangement of climate may have resulted. There is no
need to say _if_ it happened some time back: it did happen, and
accordingly an agent for affecting the distribution of mean
temperature on the earth is to hand; though whether it is
sufficient to achieve all that has been observed by geologists is a
matter of opinion.
Once more, the whole diversity of the seasons depends on the tilt
of the earth's axis, the 23 deg. by which it is inclined to a
perpendicular to the orbital plane; and this obliquity or tilt is
subject to slow fluctuations. Hence there will come eras when all
causes combine to produce a maximum extremity of seasons in the
northern hemisphere, and other eras when it is the southern
hemisphere which is subject to extremes.
But a grander problem still awaited solution--nothing less than the fate
of the whole solar system. Here are a number of bodies of various sizes
circulating at various rates round one central body, all attracted by
it, and all attracting each other, the whole abandoned to the free play
of the force of gravitation: what will be the end of it all? Will they
ultimately approach and fall into the sun, or will they recede further
and further from him, into the cold of space? There is a third possible
alternative: may they not alternately approach and recede from him, so
as on the whole to maintain a fair approximation to their present
distances, without great and violent extremes of temperature either way?
If any one planet of the system were to fall into the sun, more
especially if it were a big one like Jupiter or Saturn, the heat
produced would be so terrific that life on this earth would be
destroyed, even at its present distance; so that we are personally
interested in the behaviour of the other planets as well as in the
behaviour of our own.
The result of the portentously difficult and profoundly interesting
investigation, here sketched in barest outline, is that the solar system
is stable: that is to say, that if disturbed a little it will oscillate
and return to its old state; whereas if it were unstable the slightest
disturbance would tend to accumulate, and would sooner or later bring
about a catastrophe. A hanging pendulum is stable, and oscillates about
a mean position; its motion is periodic. A top-heavy load balanced on a
point is unstable. All the changes of the solar system are periodic,
_i.e._ they repeat themselves at regular intervals, and they never
exceed a certain moderate amount.
The period is something enormous. They will not have gone through all
their changes until a period of 2,000,000 years has elapsed. This is
the period of the planetary oscillation: "a great pendulum of eternity
which beats ages as our pendulums beat seconds." Enormous it seems; and
yet we have reason to believe that the earth has existed through many
such periods.
The two laws of stability discovered and stated by Lagrange and
Laplace I can state, though they may be difficult to understand:--
Represent the masses of the several planets by m_1, m_2, &c.; their
mean distances from the sun (or radii vectores) by r_1, r_2, &c.;
the excentricities of their orbits by e_1, e_2, &c.; and the
obliquity of the planes of these orbits, reckoned from a single
plane of reference or "invariable plane," by [theta]_1, [theta]_2,
&c.; then all these quantities (except m) are liable to
fluctuate; but, however much they change, an increase for one
planet will be accompanied by a decrease for some others; so that,
taking all the planets into account, the sum of a set of terms like
these, m_1e_1^2 [square root]r_1 + m_2e_2^2 [square root]r_2
+ &c., will remain always the same. This is summed up briefly in
the following statement:
[Sigma](me^2 [square root]r) = constant.
That is one law, and the other is like it, but with inclination of
orbit instead of excentricity, viz.:
[Sigma](m[theta]^2 [square root]r) = constant.
The value of each of these two constants can at any time be
calculated. At present their values are small. Hence they always
were and always will be small; being, in fact, invariable. Hence
neither _e_ nor _r_ nor [theta] can ever become infinite, nor can
their average value for the system ever become zero.
The planets may share the given amount of total excentricity and
obliquity in various proportions between themselves; but even if it were
all piled on to one planet it would not be very excessive, unless the
planet were so small a one as Mercury; and it would be most improbable
that one planet should ever have all the excentricity of the solar
system heaped upon itself. The earth, therefore, never has been, nor
ever will be, enormously nearer the sun than it is at present: nor can
it ever get very much further off. Its changes are small and are
periodic--an increase is followed by a decrease, like the swing of a
pendulum.
The above two laws have been called the Magna Charta of the solar
system, and were long supposed to guarantee its absolute permanence. So
far as the theory of gravitation carries us, they do guarantee its
permanence; but something more remains to be said on the subject in a
future lecture (XVIII).
And now, finally, we come to a sublime speculation, thrown out by
Laplace, not as the result of profound calculation, like the results
hitherto mentioned, not following certainly from the theory of
gravitation, or from any other known theory, and therefore not to be
accepted as more than a brilliant hypothesis, to be confirmed or
rejected as our knowledge extends. This speculation is the "Nebular
hypothesis." Since the time of Laplace the nebular hypothesis has had
ups and downs of credence, sometimes being largely believed in,
sometimes being almost ignored. At the present time it holds the field
with perhaps greater probability of ultimate triumph than has ever
before seemed to belong to it--far greater than belonged to it when
first propounded.
It had been previously stated clearly and well by the philosopher Kant,
who was intensely interested in "the starry heavens" as well as in the
"mind of man," and who shewed in connexion with astronomy also a most
surprising genius. The hypothesis ought by rights perhaps to be known
rather by his name than by that of Laplace.
The data on which it was founded are these:--Every motion in the solar
system known at that time took place in one direction, and in one
direction only. Thus the planets revolve round the sun, all going the
same way round; moons revolve round the planets, still maintaining the
same direction of rotation, and all the bodies that were known to rotate
on their own axis did so with still the same kind of spin. Moreover,
all these motions take place in or near a single plane. The ancients
knew that sun moon and planets all keep near to the ecliptic, within a
belt known as the zodiac: none strays away into other parts of the sky.
Satellites also, and rings, are arranged in or near the same plane; and
the plane of diurnal spin, or equator of the different bodies, is but
slightly tilted.
Now all this could not be the result of chance. What could have caused
it? Is there any connection or common ancestry possible, to account for
this strange family likeness? There is no connection now, but there may
have been once. Must have been, we may almost say. It is as though they
had once been parts of one great mass rotating as a whole; for if such a
rotating mass broke up, its parts would retain its direction of
rotation. But such a mass, filling all space as far as or beyond Saturn,
although containing the materials of the whole solar system in itself,
must have been of very rare consistency. Occupying so much bulk it could
not have been solid, nor yet liquid, but it might have been gaseous.
Are there any such gigantic rotating masses of gas in the heaven now?
Certainly there are; there are the nebulae. Some of the nebulae are now
known to be gaseous, and some of them at least are in a state of
rotation. Laplace could not have known this for certain, but he
suspected it. The first distinctly spiral nebula was discovered by the
telescope of Lord Rosse; and quite recently a splendid photograph of the
great Andromeda nebula, by our townsman, Mr. Isaac Roberts, reveals what
was quite unsuspected--and makes it clear that this prodigious mass also
is in a state of extensive and majestic whirl.
Very well, then, put this problem:--A vast mass of rotating gas is left
to itself to cool for ages and to condense as it cools: how will it
behave? A difficult mathematical problem, worthy of being attacked
to-day; not yet at all adequately treated. There are those who believe
that by the complete treatment of such a problem all the history of the
solar system could be evolved.
[Illustration: FIG. 80.--Lord Rosse's drawing of the spiral nebula in
Canes Venatici, with the stub marks of the draughtsman unduly emphasised
into features by the engraver.]
Laplace pictured to himself this mass shrinking and thereby whirling
more and more rapidly. A spinning body shrinking in size and retaining
its original amount of rotation, as it will unless a brake is applied,
must spin more and more rapidly as it shrinks. It has what
mathematicians call a constant moment of momentum; and what it loses in
leverage, as it shrinks, it gains in speed. The mass is held together by
gravitation, every particle attracting every other particle; but since
all the particles are describing curved paths, they will tend to fly off
tangentially, and only a small excess of the gravitation force over the
centrifugal is left to pull the particles in, and slowly to concentrate
the nebula. The mutual gravitation of the parts is opposed by the
centrifugal force of the whirl. At length a point is reached where the
two forces balance. A portion outside a certain line will be in
equilibrium; it will be left behind, and the rest must contract without
it. A ring is formed, and away goes the inner nucleus contracting
further and further towards a centre. After a time another ring will be
left behind in the same way, and so on. What happens to these rings?
They rotate with the motion they possess when thrown or shrunk off; but
will they remain rings? If perfectly regular they may; if there be any
irregularity they are liable to break up. They will break into one or
two or more large masses, which are ultimately very likely to collide
and become one. The revolving body so formed is still a rotating gaseous
mass; and it will go on shrinking and cooling and throwing off rings,
like the larger nucleus by which it has been abandoned. As any nucleus
gets smaller, its rate of rotation increases, and so the rings last
thrown off will be spinning faster than those thrown off earliest. The
final nucleus or residual central body will be rotating fastest of all.
The nucleus of the whole original mass we now see shrunk up into what we
call the sun, which is spinning on its axis once every twenty-five days.
The rings successively thrown off by it are now the planets--some large,
some small--those last thrown off rotating round him comparatively
quickly, those outside much more slowly. The rings thrown off by the
planetary gaseous masses as they contracted have now become satellites;
except one ring which has remained without breaking up, and is to be
seen rotating round Saturn still.
One other similar ring, an abortive attempt at a planet, is also left
round the sun (the zone of asteroids).
Such, crudely and baldly, is the famous nebular hypothesis of Laplace.
It was first stated, as has been said above, by the philosopher Kant,
but it was elaborated into much fuller detail by the greatest of French
mathematicians and astronomers.
The contracting masses will condense and generate great quantities of
heat by their own shrinkage; they will at a certain stage condense to
liquid, and after a time will begin to cool and congeal with a
superficial crust, which will get thicker and thicker; but for ages they
will remain hot, even after they have become thoroughly solid. The small
ones will cool fastest; the big ones will retain their heat for an
immense time. Bullets cool quickly, cannon-balls take hours or days to
cool, planets take millions of years. Our moon may be nearly cold, but
the earth is still warm--indeed, very hot inside. Jupiter is believed by
some observers still to glow with a dull red heat; and the high
temperature of the much larger and still liquid mass of the sun is
apparent to everybody. Not till it begins to scum over will it be
perceptibly cooler.
[Illustration: FIG. 81.--Saturn.]
Many things are now known concerning heat which were not known to
Laplace (in the above paragraph they are only hinted at), and these
confirm and strengthen the general features of his hypothesis in a
striking way; so do the most recent telescopic discoveries. But fresh
possibilities have now occurred to us, tidal phenomena are seen to have
an influence then wholly unsuspected, and it will be in a modified and
amplified form that the philosopher of next century will still hold to
the main features of this famous old Nebular Hypothesis respecting the
origin of the sun and planets--the Evolution of the solar system.
NOTES TO LECTURE XII
The subject of stellar astronomy was first opened up by Sir William
Herschel, the greatest observing astronomer.
_Frederick William Herschel_ was born in Hanover in 1738, and brought up
as a musician. Came to England in 1756. First saw a telescope in 1773.
Made a great many himself, and began a survey of the heavens. His sister
Caroline, born in 1750, came to England in 1772, and became his devoted
assistant to the end of his life. Uranus discovered in 1781. Music
finally abandoned next year, and the 40-foot telescope begun. Discovered
two moons of Saturn and two of Uranus. Reviewed, described, and gauged
all the visible heavens. Discovered and catalogued 2,500 nebulae and 806
double stars. Speculated concerning the Milky Way, the nebulosity of
stars, the origin and growth of solar systems. Discovered that the stars
were in motion, not fixed, and that the sun as one of them was
journeying towards a point in the constellation Hercules. Died in 1822,
eighty-four years old. Caroline Herschel discovered eight comets, and
lived on to the age of ninety-eight.
LECTURE XII
HERSCHEL AND THE MOTION OF THE FIXED STARS
We may admit, I think, that, with a few notable exceptions, the work of
the great men we have been recently considering was rather to complete
and round off the work of Newton, than to strike out new and original
lines.
This was the whole tendency of eighteenth century astronomy. It appeared
to be getting into an adult and uninteresting stage, wherein everything
could be calculated and predicted. Labour and ingenuity, and a severe
mathematical training, were necessary to work out the remote
consequences of known laws, but nothing fresh seemed likely to turn up.
Consequently men's minds began turning in other directions, and we find
chemistry and optics largely studied by some of the greatest minds,
instead of astronomy.
But before the century closed there was destined to arise one remarkable
exception--a man who was comparatively ignorant of that which had been
done before--a man unversed in mathematics and the intricacies of
science, but who possessed such a real and genuine enthusiasm and love
of Nature that he overcame the force of adverse circumstances, and
entering the territory of astronomy by a by-path, struck out a new line
for himself, and infused into the science a healthy spirit of fresh life
and activity.
This man was William Herschel.
"The rise of Herschel," says Miss Clerke, "is the one conspicuous
anomaly in the otherwise somewhat quiet and prosy eighteenth century. It
proved decisive of the course of events in the nineteenth. It was
unexplained by anything that had gone before, yet all that came after
hinged upon it. It gave a new direction to effort; it lent a fresh
impulse to thought. It opened a channel for the widespread public
interest which was gathering towards astronomical subjects to flow in."
Herschel was born at Hanover in 1738, the son of an oboe player in a
military regiment. The father was a good musician, and a cultivated man.
The mother was a German _Frau_ of the period, a strong, active,
business-like woman, of strong character and profound ignorance. Herself
unable to write, she set her face against learning and all new-fangled
notions. The education of the sons she could not altogether control,
though she lamented over it, but the education of her two daughters she
strictly limited to cooking, sewing, and household management. These,
however, she taught them well.
It was a large family, and William was the fourth child. We need only
remember the names of his younger brother Alexander, and of his much
younger sister Caroline.
They were all very musical--the youngest boy was once raised upon a
table to play the violin at a public performance. The girls were
forbidden to learn music by their mother, but their father sometimes
taught them a little on the sly. Alexander was besides an ingenious
mechanician.
At the age of seventeen, William became oboist to the Hanoverian Guards,
shortly before the regiment was ordered to England. Two years later he
removed himself from the regiment, with the approval of his parents,
though probably without the approbation or consent of the commanding
officer, by whom such removal would be regarded as simple desertion,
which indeed it was; and George III. long afterwards handed him an
official pardon for it.
At the age of nineteen, he was thus launched in England with an outfit
of some French, Latin, and English, picked up by himself; some skill in
playing the hautboy, the violin, and the organ, as taught by his father;
and some good linen and clothing, and an immense stock of energy,
provided by his mother.
He lived as musical instructor to one or two militia bands in Yorkshire,
and for three years we hear no more than this of him. But, at the end of
that time, a noted organist, Dr. Miller, of Durham, who had heard his
playing, proposed that he should come and live with him and play at
concerts, which he was very glad to do. He next obtained the post of
organist at Halifax; and some four or five years later he was invited to
become organist at the Octagon Chapel in Bath, and soon led the musical
life of that then very fashionable place.
About this time he went on a short visit to his family at Hanover, by
all of whom he was very much beloved, especially by his young sister
Caroline, who always regarded him as specially her own brother. It is
rather pitiful, however, to find that her domestic occupations still
unfairly repressed and blighted her life. She says:--
"Of the joys and pleasures which all felt at this long-wished-for
meeting with my--let me say my dearest--brother, but a small
portion could fall to my share; for with my constant attendance at
church and school, besides the time I was employed in doing the
drudgery of the scullery, it was but seldom I could make one in the
group when the family were assembled together."
While at Bath he wrote many musical pieces--glees, anthems, chants,
pieces for the harp, and an orchestral symphony. He taught a large
number of pupils, and lived a hard and successful life. After fourteen
hours or so spent in teaching and playing, he would retire at night to
instruct his mind with a study of mathematics, optics, Italian, or
Greek, in all of which he managed to make some progress. He also about
this time fell in with some book on astronomy.
In 1763 his father was struck with paralysis, and two years later he
died.
William then proposed that Alexander should come over from Hanover and
join him at Bath, which was done. Next they wanted to rescue their
sister Caroline from her humdrum existence, but this was a more
difficult matter. Caroline's journal gives an account of her life at
this time that is instructive. Here are a few extracts from it:--
"My father wished to give me something like a polished education,
but my mother was particularly determined that it should be a
rough, but at the same time a useful one; and nothing further she
thought was necessary but to send me two or three months to a
sempstress to be taught to make household linen....
"My mother would not consent to my being taught French, ... so all
my father could do for me was to indulge me (and please himself)
sometimes with a short lesson on the violin, when my mother was
either in good humour or out of the way.... She had cause for
wishing me not to know more than was necessary for being useful in
the family; for it was her certain belief that my brother William
would have returned to his country, and my eldest brother not have
looked so high, if they had had a little less learning."
However, seven years after the death of their father, William went over
to Germany and returned to England in triumph, bringing Caroline with
him: she being then twenty-two.
So now began a busy life in Bath. For Caroline the work must have been
tremendous. For, besides having to learn singing, she had to learn
English. She had, moreover, to keep accounts and do the marketing.
When the season at Bath was over, she hoped to get rather more of her
brother William's society; but he was deep in optics and astronomy, used
to sleep with the books under his pillow, read them during meals, and
scarcely ever thought of anything else.
He was determined to see for himself all the astronomical wonders; and
there being a small Gregorian reflector in one of the shops, he hired
it. But he was not satisfied with this, and contemplated making a
telescope 20 feet long. He wrote to opticians inquiring the price of a
mirror suitable, but found there were none so large, and that even the
smaller ones were beyond his means. Nothing daunted, he determined to
make some for himself. Alexander entered into his plans: tools, hones,
polishers, and all sorts of rubbish were imported into the house, to the
sister's dismay, who says:--
[Illustration: FIG. 82.--Principle of Newtonian reflector.]