THE PROBLEM STATED.
The Great Diurnal Motion—The Distinction between Stars and Planets—The
Earth no more than a Planet—Relation of the Stars to the Solar
System—Contrast between Aldebaran and Mars—Illustration of
Star-distances—The Celestial Perspective—Illustration of an
Attractive Force—Instructive Experiments—The Globe and the Tennis
Ball—The Law of Gravitation—The Focal Ellipse—The Solar System as it
is now Known—Statement of the Great Problem before us.
WHEN we raise our eyes to the heavens on a clear night, thousands of
bright objects claim our attention. We observe that all these objects
move as if they were fastened to the inside of an invisible sphere. They
are seen gradually ascending from the east, passing across the south,
and in due course sinking towards the west. The sun and the moon, as
well as all the other bodies, alike participate in this great diurnal
movement. The whole scheme of celestial objects seems to turn around the
two points in the heavens that we call the Poles, and so far as the pole
in the northern hemisphere is concerned, its position is most
conveniently indicated by the proximity of the well-known Pole Star.
Except this great diurnal motion, the vast majority of the bodies on the
celestial sphere have no other movement easily recognisable, and
certainly none which it is necessary for us to consider at present. The
groups in which the stars have been arranged by the poetical imagination
of the ancients exist to-day, as they have existed during all the ages
since they were first recognised, without any noticeable alteration in
their lineaments. The stately belt of Orion is seen to-night as Job
beheld it thousands of years ago; the stars in the Pleiades have not
altered their positions, relatively to the adjacent stars nor their
arrangement among themselves, since the time when astronomers in early
Greece observed them. All the bodies which form these groups are
therefore known as fixed stars.
But besides the fixed stars, which exist in many thousands, and, of
course, the sun and the moon, there are other celestial objects, so few
in number as to be counted on the fingers of one hand, which are in no
sense fixed stars. It is quite true that these wandering bodies, or
planets, as they are generally designated, bear a certain resemblance to
the fixed stars. In each case the star or the planet appears as a bright
point, like many other bright points in the heavens, and star and planet
both participate in the general diurnal motion. But a little attention
will show that while the stars, properly so called, retain their
relative places for months and years and centuries, the planets change
their places so rapidly that in the course of a few nights it is quite
easy to see, even without the aid of any instrument, that they have
independent motion.
We may compare the movements of these bodies to the movement of the
moon, which nightly shifts her place over a long track in the sky; and
although we are not able to see the stars in the vicinity of the sun,
inasmuch as the brilliant light of the orb quenches the feeble radiance
from such stars, there is no doubt that, did we see them, the sun itself
would seem to move relatively to the stars, just as does the moon and
just as do the planets.
The fundamental distinction between stars and planets was noticed by
acute observers of Nature in the very earliest times. The names of the
planets come to us as survivals from the time when the sun, the moon,
and the stars were objects of worship, and they come to us bearing the
names of the deities of which these moving globes were regarded as the
symbols. But it was not the movements of the planets alone which called
for the notice of the early observers of the skies. The brightness and
certain other features peculiar to them also attracted the attention of
the primitive astronomers. They could not fail to observe that when the
beautiful planet Venus was placed so as to be seen to the greatest
advantage, her orb was far brighter than any other object in the host of
heaven, the sun and the moon both of course excepted. It was also
obvious that Jupiter at its best exceeded the stars in lustre, and
sometimes approached even to that of Venus itself. Though Mercury was
generally so close to the sun as to be invisible among its beams, yet on
the rare occasions when that planet was seen, just after sunset or just
before sunrise, its lustre was such as to mark it out as one of the
remarkable bodies in the heavens.
Thus the astronomers of the earliest ages pointed to the five planets
and the sun and the moon as the seven wandering stars. The diligent
attention of the learned of every subsequent period was given to the
discovery of the character of their movements. The problems that these
motions presented were, however, so difficult that not until after the
lapse of thousands of years did their nature become understood. The
supreme importance of the earth appeared so obvious to the early
astronomers that it did not at first occur to them to assign to our
earth a position which would reduce it to the same class as any of the
celestial bodies. The obviously great size of our globe, the fact that
to the uninstructed senses the earth seemed to be at rest, while the
other bodies seemed to be in motion, and many other analogous
circumstances, appeared to show that the earth must be a body totally
different from the other objects distributed around us in space. It was
only by slow degrees, and after much observation and reflection, and not
a little controversy, that at last the true nature of our system was
detected. Those who have been brought up from childhood in full
knowledge of the rotation of the earth and of the other fundamental
facts relating to the celestial sphere, will often find it difficult to
realise the way such problems must have presented themselves to the
observers of old, who believed, as for centuries men did believe, that
the earth was a plane of indefinite extent fixed in space, and that the
sun and the planets, the moon and the stars, were relatively small
bodies whose movements must be accounted for as best they could be,
consistently with the fixity and flatness of the earth.
[Illustration: Fig. 4.—JUPITER (May 30th, 1899, 10h. 9.5m.; g.m.t.).
(E. M. Antoniadi.)]
But at last it began to be seen that the earth must be relegated to a
position infinitely less important than that which the untutored
imagination assigned to it. It was found that the earth was not an
indefinite plane; it was rather a globe poised in space, without direct
material support from any other body. It was found that the earth was
turning round on its axis: while instead of the sun revolving around the
earth, it was much more correct to say that the earth revolved around
the sun. The astonishing truth was then disclosed that the five planets,
Jupiter and Saturn, Mercury, Venus and Mars, stood in a remarkable
relation to the earth. For as each of these planets was found to revolve
round the sun, and as the earth also revolved round the sun, the assumed
difference in character between the earth and the planets tended to
vanish altogether. There was in fact no essential difference. If indeed
the earth was smaller than Jupiter and Saturn, yet it was considerably
greater and heavier than Mars or Mercury, and it was almost exactly the
same size and weight as Venus. There was clearly nothing in the question
of bulk to indicate any marked difference between our earth and the
planets. It was also observed that there was no distinction to be drawn
between the way in which the earth revolved round the sun and the
movements of the planets. No doubt the earth is not so near the sun as
Mercury; it is not so near the sun as even Venus; on the other hand the
sun is nearer the earth than Mars, while Jupiter is a long way further
off than Mars, and Saturn is even beyond Jupiter again. It is these
considerations which justify us in regarding our earth as one of the
planets. We have also to note the overwhelming magnitude of the sun in
comparison with any one of the planets. It will suffice to give a single
illustration. The sun is more than a thousand times as massive as
Jupiter, and Jupiter is the greatest of the planets. This latter noble
globe is in fact greater than all the rest of the planets put together.
But before we can fully realise the circumstances of the solar system,
it will be necessary to see how the stars, properly so called, enter
into the scheme of things celestial. The stars look so like the planets
that it has not infrequently happened that even an experienced
astronomer has mistaken one for the other. The planet Mars is often very
like the star Aldebaran, and there are not a few first-magnitude stars
which on a superficial view closely resemble Saturn. But how great is
the intrinsic difference between a star and a planet! In the first place
we have to note that every planet is a dark object like this earth of
ours, possessing no light of its own, and dependent entirely on the sun
for the supply of light by which it is illumined. But a star is totally
different. The star is not a dark object, but is really an object which
is in itself intensely luminous and brilliant; the star is in fact a
sun-like body. How then, it may well be asked, does a star like
Aldebaran, which is indeed a sun-like body, and in all probability is
quite as large and quite as brilliant as the sun itself, bear even a
superficial resemblance to an object like Mars, which would not be
visible at all were it not for the illumination with which the beams
from the sun endow it?
The explanation of this striking resemblance is to be sought in the
relative distances of the two objects. A light which is near to the eye
may produce an effect quite as great as a very much stronger light which
is further away. The intensity of a light varies inversely as the square
of the distance. If the distance of a light from the eye be doubled,
then the intensity of that light is reduced to one-fourth. Now Aldebaran
as a sun-like body emits light which is literally millions of times as
great as the gleam of sunshine which starts back to us after reflection
from Mars; but Aldebaran is, let us say, a million times as far away
from us as Mars, and this being so, the light from Aldebaran would come
to us with only a million-millionth part of the intensity that it would
have if the star were at the same distance as the planet. There can be
no doubt that if Aldebaran were merely at the same distance from the
earth as Mars, then Aldebaran would dispense lustre like a splendid sun.
By moving Aldebaran further off its light, or rather the light that
arrives at the earth, will gradually decrease until by the time that the
star is a million times as far as Mars, the light that it sends us is
about equal to that of Mars. If it were removed further still, the light
that it would send us would become less than that which we receive from
Mars, and if still more remote, Aldebaran might cease to be visible
altogether.
This illustration will suffice to explain the fundamental difference
between planets and stars, notwithstanding the fact that the two classes
of bodies bear to each other a resemblance which is extremely
remarkable, even if it must be described as being in a sense accidental.
But we now know that all of the thousands of stars are to be regarded as
brilliant suns, some of which may not be so far off as Aldebaran, though
doubtless some are very much further. The actual distances are
immaterial, for the essential point to notice is that the five planets
are distinguished from the stars, not merely by the fact that they are
moving, while the stars are at rest, but by the circumstance that the
planets are comparatively close to each other and close to the sun,
while the stars are at distances millions of times as great as the
distances which the planets are from each other and from the sun.
We are now enabled to place the scheme of things celestial in its proper
perspective. I shall suppose that at a point in a field in the centre of
England, somewhere near Leamington, let us say, we drive in a peg to
represent the sun. Let us draw a circle with that peg as centre, a yard
being the radius, and let that circle represent the track in which the
earth goes round the sun. I do not indeed say that the orbit of the
earth is exactly a circle, and the actual shape of that orbit we may
have to refer to later. As, however, the apparent size of the sun does
not greatly alter with the seasons, it is evident that the track which
our earth pursues cannot be very different from a circular path. Inside
this circle which we have drawn with a yard radius, we shall put two
smaller circles which are to represent the path in which Venus moves,
and the path in which Mercury moves. Outside the path of the earth we
shall draw another circle with a radius of five yards; this will be the
highway along which the majestic Jupiter wends his way. Inside the path
of Jupiter we shall put a circle which will represent the track of Mars,
and outside the path of Jupiter a circle with ten yards as radius will
represent the track of Saturn. In each of these circles we shall suppose
the corresponding planet to revolve, and the time of revolution will of
course be greater the further the planet is from the sun. To complete
one of its circuits the earth will require a year, Jupiter twelve years,
while Saturn, which in the ancient astronomy moved on the frontier of
the solar system, will need thirty years to accomplish its mighty
journey.
We have thus obtained a plan of the solar system; but now we should like
to indicate the positions which some of the stars are to occupy on the
same scale. Let us, to begin with, see where the very nearest fixed star
is to be placed. We may suppose that the field at the centre of England,
in which our little diagram has been constructed, is a large one, so
that we can represent the places of objects which are ten or twenty
times as far from the sun as Saturn. It is, however, certain that no
actual field would be large enough to contain within its bounds the
points which would faithfully represent the positions of even the
nearest fixed stars. The whole county of Warwick would not be nearly big
enough for this purpose; indeed we may say that the whole of England, or
indeed of the United Kingdom, would not be sufficiently extensive. If we
represented the star at its true relative distance, it could not be put
down anywhere within the bounds of the United Kingdom; the nearest
object of this kind would have to be far away out on the continent of
Europe, or far away out on the Atlantic Ocean, far away down near the
equator, or far away up near the pole. This illustration will at all
events give some notion of the isolated position of the sun, with the
planets revolving around it, in relation to the rest of the host of
heaven.
We thus learn that the real scheme of the universe is widely different
from that which a superficial glance at the heavens would lead us to
expect. We are now able to put our system into its proper perspective.
We are to think of the universe as consisting of a myriad suns, each
sun, however, being so far from the other suns that viewed from any one
of its neighbours it appears only of star-like insignificance. Let us
fix our attention on one of these suns in space, and imagine that around
it, and comparatively close to it, there are a number of small particles
in revolution, the particles being illumined by the light and warmed by
the heat of the central body to which they are attached. Viewed from one
of those particles, the sun to which they belong would doubtless appear
as a great and glorious orb, while a glance from one of these particles
to any of the other myriad suns in space will show these orbs reduced to
mere points of stellar light by reason of their enormous distance. This
sun and the particles around it, by which of course we shall understand
the planets, constitute what we know as the solar system. This
illustration may suffice to show the isolation of our system in space,
and that isolation is due to the vast distances by which the sun and its
attendant worlds are separated from the myriads of other bodies which
form the sidereal heavens. We must next, so far as our present subject
requires it, consider the laws according to which the planets belonging
to that system revolve around the sun.
Let us think first of a single one of these bodies which, as is most
natural, we shall take to be the earth itself, and now let us consider
by what agency the movement of the earth around the sun is guided along
the path which so closely resembles a circle. It must, of course, be
borne in mind that there can be no direct material connection between
the two bodies; there is no physical bond uniting the earth to the sun.
It is, however, certain that some influence proceeding from the sun does
really control the motion. We may perhaps illustrate what takes place in
the following manner. Here is a globe, and here in my hand I hold a
tennis ball, which is attached to a silken thread, the other end of the
thread being attached to the ceiling. The tennis ball is to hang so that
both globe and ball are about the same height from the floor. We put the
globe directly underneath the point on the ceiling from which the silken
thread hangs. If I draw the tennis ball aside and simply release it,
then of course everybody knows what happens—it is hardly necessary to
try the experiment—the tennis ball falls at once towards the globe and
strikes it. We may, if we please, regard that tendency of the tennis
ball towards the globe as a sort of attraction which the globe exercises
upon the ball. I must, however, say that this is not a strictly accurate
version of what actually takes place. The attraction of the earth for
the tennis ball is of course largely neutralised by the support given by
the silk thread. There is thus only a slight outstanding component of
gravitation acting on the ball, and this component, which is virtually
the effective force on the ball, tends to draw the ball directly towards
the globe. For the purpose of our illustration we may neglect the direct
attraction of the earth altogether; we may omit all thought of the
tension of the silken thread. If there were indeed no attraction from
the earth, the tennis ball might remain poised in space without falling;
and if it were then attracted by the globe it would fly towards the
globe just as we actually see it do. We are therefore justified in
regarding the movement of the tennis ball as equivalent to that which
would be produced if an attractive virtue resided in the globe by which
it pulled the tennis ball. We may also imagine that the globe attracts
the tennis ball in all its positions; for whatever be the point at which
the ball is released it starts off straight towards the globe. This is
our first experiment in which, having withdrawn the ball, it is merely
released without receiving an initial impulse to one side.
[Illustration: Fig. 5.—NEBULOUS REGION AND STAR-CLUSTER
(n.g.c. 2237-9 in Monoceros).
(_Photographed by Dr. Isaac Roberts, F.R.S._)]
Let us now try a different experiment. We withdraw the ball, and,
instead of merely releasing it quietly and allowing it to drop directly
to the globe, we give it a little throw sideways, perpendicular to the
line joining it to the centre of the globe. If we start it with the
proper speed, which a few trials will indicate, the ball can be made
actually to move in a circle round the globe. If the initial speed be
somewhat different, the path in which the tennis ball moves will not be
a circle; it will rather be an ellipse of some form. Even if the speed
be correct the orbit will always be an ellipse if the direction of the
initial throw be not perpendicular to the line joining the ball to the
centre of the globe. We can make the ball describe a very long ellipse
or an ellipse which differs but little from a circle. But I would ask
you to note particularly that, no matter how we may start the tennis
ball into motion, it will, so long as it passes clear of the globe, move
in an ellipse of some kind; but in making this statement we assume that
a circle is a particular form of the ellipse.
And now for the lesson which we are to learn from this experiment,
which, as it is so easily performed, I would wish everyone to try for
himself. We have in this simple device an illustration of the movement
of a planet around the sun. We see that this tennis ball can be made to
move in a circle round the globe, and that as it performs this circular
movement the globe is all the time attracting the ball towards it. Thus
we illustrate the important law that when one body moves round another
in a circular path this movement takes place in consequence of a force
of attraction constantly exerted between the large body in the centre
and the body revolving round it.
The principle here involved will provide the explanation of the
movements of the planets round the sun. Each of the planets revolves
round the sun in an orbit which is approximately circular, and each of
the planets performs that movement because it is continually attracted
by the sun. It is, however, necessary to add that there is a fundamental
difference between the attraction of the sun for the planets and the
attraction which the globe appeared to exert on the tennis ball in our
experiment. The difference relates to the character of the forces in the
two cases. If the tennis ball be drawn but a very small distance from
the globe, the attraction between the two bodies is very slight. If the
tennis ball be drawn to a greater distance from the globe, the
attraction is increased correspondingly; and, indeed, in this experiment
the attraction between the two bodies increases with the distance, and
is said to be proportional to the distance.
But the case is very different in that particular kind of attraction by
which the sun controls the movements of the planets. This attraction of
gravitation, as it is called, also depends on the distance between the
two bodies. But the attraction does not increase when the distance of
the two bodies increases, for the change lies the other way. The
attraction, in fact, diminishes more rapidly than the distance
increases. If the distance between the sun and a planet be doubled, then
the attraction between the two bodies is only a fourth of what the
attraction was between the two bodies in the former case. This
difference between the law of attraction as it exists in the solar
system and the law of attraction which is exemplified in our little
experiment produces a remarkable contrast in the resulting movements.
The orbit in each case is, no doubt, an ellipse, but in the case of the
tennis ball revolving round the globe the ellipse is so circumstanced
that the fixed attracting body stood at its centre, while in the case of
a planet revolving round the sun the conditions are not so simple. The
sun does not stand in the centre of the ellipse. The sun is placed at
that remarkable point of the ellipse so dear to the heart of the
geometer, which he calls the focus.
The solar system consists, first, of the great regulating orb, the sun;
then of the planets, each of which revolves in its own track round the
sun; each of these tracks is an ellipse, and all these ellipses have
this in common, that a focus in each is identical with the centre of the
sun. In other respects the ellipses may be quite different. To begin
with, they are not in the same plane, though it is most important to
notice, as we shall have to discuss more fully hereafter, that these
planes are not very much separated. The dimensions of the ellipses vary,
of course, for the different planets, and the periods that the planets
require for their several revolutions are also widely different in the
cases of the different bodies; for the greater the diameter of a
planet’s orbit, the longer is the time required for that planet to
complete a single journey round the sun. The sun presiding at the common
focus of the orbits while governing the planets by its attraction, at
the same time that it illumines them with its light and warms them by
its rays, gives the conception of the solar system.
But the planetary system I have here indicated is merely that system as
known to the ancients. It is very imperfect from the standpoint of our
present knowledge. The solar system as we now know it, when telescopes
have been applied with such marvellous diligence and success to the
discovery of new bodies, is a system of much greater complexity. To the
five old planets have been added two new and majestic planets—Uranus and
Neptune—which revolve outside the track of Saturn. Hundreds of smaller
planets, invisible to the unaided eye, the asteroids as they are called,
also describe their ellipses round the presiding luminary. And then just
as the sun controls the planets revolving round it, so do many of the
planets themselves preside over subordinate systems of revolving globes.
Our earth has a single attendant, the moon, which, under the guidance of
the earth’s attraction, performs its monthly journey; Jupiter has its
five moons, while Mars has two, and Saturn eight or nine, besides his
incomparable system of rings, and we must also add that Uranus has four
satellites and Neptune one. To complete the tale of bodies in the solar
system, we should add many thousands of comets, not to mention their
more humble associates the meteors, which swarm in countless myriads.
Finally, we are to remember that this elaborate system associated with
the sun is an isolated object in the universe; it is but as a grain of
sand in the extent of infinite space.
As we contemplate a system so wonderful, the question naturally arises,
How came that system into being? We have to consider whether the laws of
nature as we know them afford any rational explanation of the manner in
which this system came into existence, any rational explanation of how
the sun came to shine, how the earth had its beginning, how the planets
came to revolve round the sun, and to rotate on their own axes. We have
to seek for a rational explanation of the rings of Saturn, and of the
satellites by which so many planets are attended. We have to show that a
satisfactory explanation of these remarkable phenomena is forthcoming,
and that it is provided by the famous doctrine of evolution, which it is
the object of these lectures to discuss.
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