THE SECOND CONCORD.
Another Remarkable Coincidence in the Solar System—The Second
Concord—The Direction of the Movements of the Great Planets—The
Movement of Ceres—Yet Another Planet—Discovery of Eros—The Nearest
Neighbour of the Earth—Throwing Heads and Tails—A Calculation of the
Chances—The Numerical Strength of the Argument—An Illustration of
the Probability of the Origin of the Solar System from the
Nebula—The Explanation of the Second Concord offered by the Nebular
Theory—The Relation of Energy and Moment of Momentum—Different
Systems Illustrated—That all the Movements should be in the same
Direction is a Consequence of Evolution from the Primæval Nebula.
WE have seen in the last chapter that there is a very remarkable
concordance in the positions of the planes of the orbits of the planets,
and we have shown that this concordance finds a natural historical
explanation in the nebular origin of our system. We have now to consider
another striking concord in the movements of the planets in their
several orbits, and this also furnishes us with important evidence as to
the truth of the nebular theory. The argument on which we are now to
enter is one which specially appealed to Laplace, and was put forward by
him as the main foundation of the nebular theory.
[Illustration: Fig. 48.—ILLUSTRATION OF THE SECOND CONCORD.]
In the adjoining Fig. 48 we have a diagram of a portion of the solar
system. We shall regard the movements as somewhat simplified. The sun is
supposed to be at the centre, turning round once every twenty-five days,
on an axis which is supposed to be perpendicular to the plane of the
paper. We may also for our present purpose assume that the orbits of the
earth and the other planets lie in this same plane.
In the first place we observe that the earth might have gone round its
track in either direction so far as the welfare of mankind is concerned.
The succession of day and night, and the due changes of the seasons,
could have been equally well secured whichever be the direction in which
the earth revolves. We do, however, most certainly find that the
direction in which the earth revolves round the sun is the same as the
direction in which the sun rotates on its axis. This is the first
coincidence.
We may now consider other planets. Look, for instance, at the orbit of
Jupiter. It seems obvious that Jupiter might have been made to revolve
round the sun either one way or the other; indeed, it will be remembered
that though Kepler’s laws indicate so particularly the shape of the
track in which the planet revolves, and prescribe so beautifully the way
in which the planet must moderate or accelerate its velocity at the
different parts of its track, yet they are quite silent as to the
direction in which the planets shall revolve in that track. If we could
imagine a planet to be stopped to have its velocity reversed, and then
to be started in a precisely opposite direction, it would still continue
to describe precisely the same path; it would still obey Kepler’s laws
with unfailing accuracy, so far as our present argument is concerned,
and the velocity which it would have at each point of the track would be
quite the same whether the planet were going one way or whether it was
going the other. It is therefore equally possible for Jupiter to pursue
his actual track by going round the sun in the same direction as the
earth, or by going in the opposite direction. But we actually find that
Jupiter does take the same direction as the earth, and this, as we have
already seen, is the direction in which the sun rotates. Here we have
the second coincidence.
We now take another planet; for example, Mars. Again we affirm that Mars
could have moved in either direction, but, as a matter of fact, it
pursues the same direction as Jupiter and the earth. In the orbital
movement of Saturn we have the fourth coincidence of the same kind, and
we have a fifth in the case of Mercury, and a sixth in Venus, a seventh
in Uranus, and an eighth in Neptune. The seven great planets and the
earth all revolve around the sun, not only in orbits which are very
nearly in the same plane, but they also revolve in the same direction.
The coincidences we have pointed out with regard to the movements of the
great planets of our system may be also observed with regard to the
numerous bodies of asteroids. On the first night of the century just
closed, the 1st of January, 1801, the first of the asteroids, now known
as Ceres, was discovered. This was a small planet, not a thousandth part
of the bulk of one of the older planets, and visible, of course, only in
the telescope. Like the older planets, it was found to obey Kepler’s
laws; but this we might have foreseen, because Kepler’s laws depend upon
the attraction of gravitation, and must apply to any planet, whatever
its size. When, therefore, the new planet was found, and its track was
known, it was of much interest to see whether the planet in moving round
that track observed the same direction in which all the older planets
had agreed to travel, or whether it moved in the opposite direction. In
the orbit of Ceres we have a repetition of the coincidence which has
been noticed in each of the other planets. The new planets, like all the
rest, move round the sun in the same direction as the sun rotates on its
axis. The discovery of this first asteroid was quickly followed by other
similar discoveries; each of the new planets described, of course, an
ellipse, and the directions which these planets followed in their
movements round the sun were in absolute harmony with those of the older
planets.
But, besides the great planets and the asteroids properly so called,
there is yet another planet, Eros. Its testimony is of special value,
inasmuch as it seems to stand apart from all other bodies in the solar
system, and with, of course, the exception of the moon, it is the
earth’s nearest neighbour. But whatever may be the exceptional features
of Eros, however it may differ from the great planets and the asteroids
already known, yet Eros makes no exception to the law which we have
found to be obeyed by all the other planets. It also revolves round the
sun in the same direction as all the planets revolve, in the same
direction as the rotation of the sun (Fig. 49).
We may pause at this moment to make a calculation as to the
improbability that the sun, the earth, the seven great planets, and
Ceres, numbering altogether ten, should move round in the same direction
if their movements had been left to chance. This will show what we can
reasonably infer from this concord in their movements. The theory of
probabilities will again enlighten a difficult subject.
There are only two possible directions for the motion of a planet in its
orbit. It must move like the hands of a watch, or it must move in the
opposite direction. The planet must move one way or the other, just as a
penny must always fall head or tail.
[Illustration: Fig. 49.—ORBITS OF EARTH, EROS AND MARS.]
We may illustrate this remarkable coincidence in the following manner:
Suppose we take ten coins in the hand, and toss them all up together and
let them fall on the table; in the vast majority of cases in which the
experiment may be tried, there would be some heads and some tails; they
would not all be heads. But it is, of course, not impossible that the
coins should all turn up heads. We should, however, deem it a very
remarkable circumstance if it happened: yet it would certainly not be
more remarkable than that the ten celestial movements should all take
place in the same direction, unless, indeed, it should turn out that
there is some sound physical cause which imposes on the planets of the
solar system an obligation, restricting their movements round the sun to
the same direction as that in which the sun itself rotates.
It will be useful to study the matter numerically; and the rules of
probabilities will enable us to do so, as we may see by the following
illustration: We deem the captain of a cricket team fortunate when he
wins the toss for innings. We should deem him lucky indeed if he won it
three times in successive matches. If he won it five times running, his
luck would be phenomenal; while, if it was stated that he won it ten
times consecutively, we should consider the statement well-nigh
incredible. For it is easy to calculate that the chances against such an
occurrence are one thousand and twenty-four to one. In like manner we
may say, that for nine planets and the sun all to go round in the same
direction would be indeed surprising if the arrangement of the planets
had been determined by chance; there are more than a thousand chances to
one against such an occurrence.
But Ceres was only the earliest of many other similar discoveries. And
as each asteroid was successively brought to light, it became most
interesting to test whether it followed the rest of the planets in that
wonderful unanimity in the direction of their movements of revolution,
or whether it made a new departure by going in the opposite direction.
No such exception has ever yet been observed. Let us take, then, ten
more planets, in addition to those we have already considered, so that
we have now nineteen planets all revolving in the same direction as the
sun rotates. It is easy to compute the improbability that these twenty
movements should all be in the same direction, if, indeed, it were by
chance that their directions had been determined. It is the same problem
as the following: What is the chance that twenty coins, taken together
in the hand and tossed into the air at once, shall all alight with their
heads uppermost? We have seen that the chances against this occurrence,
if there were ten coins, is about a thousand to one. It can easily be
shown that if there were twenty coins the chances against the occurrence
would be a million to one. We thus see that, even with no more than
nineteen planets and the sun, there is a million to one against a
unanimity in the directions of the movements, if the determination of
the motions was made by chance. We may, however, express the result in a
different manner, which is more to the purpose of our argument. There
are a million chances to one in favour of the supposition that the
disposition of the movements of the planets has not been the result of
chance; or we may say that there are a million chances to one in favour
of the supposition that some physical agent has caused the unanimity.
We can add almost any desired amount of numerical strength to the
argument. The discoveries of minor planets went on with ever-increasing
success through the whole of the last century. When ten more had been
found, and when each one was shown to obey the same invisible guide as
to the direction in which it should pursue its elliptic orbit, the
chances in favour of some physical cause for the unanimity became
multiplied by yet another thousand. The probability then stood at a
thousand millions to one. As the years rolled by, asteroids were found
in ever-increasing abundance. Sometimes a single astronomer discovered
two, and sometimes even more than two, on a single night. In the course
of a lifetime a diligent astronomer has placed fifty discoveries of
asteroids, or even more than fifty, on his record. By combined efforts
the tale of the asteroids has now approached five hundred, and out of
that huge number of independent planetary bodies there is not one single
dissentient in the direction of its motion. Without any exception
whatever, they all perform their revolutions in the same direction as
the sun rotates at the centre. When this great host is considered, the
numerical strength of the argument would require about 150 figures for
expression. Each new asteroid simply doubled the strength of the
argument as it stood before.
Professor J. J. Thomson recently discovered that there are corpuscles of
matter very much smaller than atoms. Let us think of one of these
corpuscles, of which many millions would be required to make the
smallest grain of sand which would just be visible under a microscope.
Think, on the other hand, of a sphere extending through space to so vast
a distance that every star in the Milky Way will be contained within its
compass. Then the number of those corpuscles which would be required to
fill that sphere is still far too small to represent the hugeness of the
improbability that all the five hundred planetary bodies should revolve
in the same direction, if chance, and chance alone, had guided the
direction which each planet was to pursue in moving round its orbit.
The mere statement of these facts is sufficient to show that some
physical agent must have caused this marvellous concord in the movements
of the solar system. How the argument would have stood if there had been
even a single dissentient it is not necessary to consider, for there is
no dissentient No reasonable person will deny that these facts impose an
obligation to search for the physical explanation of this feature in the
planetary movements.
As in the last chapter, where we were dealing with the positions of the
planes of the orbits, there can here be no hesitation as to the true
cause of this most striking characteristic of the planetary movements.
The nebular theory is at once ready with an explanation, as has been
already indicated in Chapter XI. The primæval nebula, endowed in the
beginning with a certain amount of moment of momentum, has been
gradually contracting. It has been gradually expending its energy, as we
have already had occasion to explain; but the moment of momentum has
remained undiminished. And from this it can be shown that the dynamical
principles guiding the evolution of the nebula must ultimately refuse
permission for any planet to revolve in opposition to the general
movement. This point is a very interesting one, and as it is of very
great importance in connection with our system, I must give it some
further illustration and explanation.
The two figures that are shown in Fig. 50 represent two imaginary
systems. We have a sun in each, and we have two planets in each. The sun
is marked with the letter S, and the two planets are designated by A and
B. For simplicity I have represented the orbits as circles, and for the
same reason I have left out the rest of the planets; we shall also
suppose the orbits of the two planets that are involved to lie exactly
in the same plane. In the two systems that I have here supposed, the two
suns are to be of the same weight, the planet A in one system is of
equal mass to the planet A in the other; and the planets B in the two
systems are also equal. It is also assumed that the orbit of A in one
diagram shall be the same as the orbit of A in the other, and that the
orbit of B in one shall be precisely the same as the orbit of B in the
other. The sun rotates in precisely the same manner in both, and takes
the same time for each rotation. A, in one system, goes round in the
same time that A does in the other; and B, in one system, goes round in
the same time that B does in the other. There is, therefore, a perfect
resemblance between the two systems I have here supposed in every point
but one. I have indicated, as usual, the movements of the bodies by
arrows, and, while in one of the systems the sun and A and B all go
round in the same direction, in the other system the sun and A go round,
no doubt, in the same direction, but the direction of B is opposite. We
are not, in this illustration, considering the rotations of the planets
on their axes. That will be dealt with in the next chapter.
[Illustration: Fig. 50.—I. A NATURAL SYSTEM ON THE LEFT.
II. AN UNNATURAL SYSTEM ON THE RIGHT.]
There can be no doubt that either of these two systems would be possible
for thousands of revolutions. There is nothing whatever to prevent A and
B from being started in the same direction round the sun as in the first
figure, or with A in one direction and B in the opposite direction, as
in the second figure. It is equally conceivable that, while A and B
revolve in the same direction, both should be opposite to that of the
sun. But one system is permanent, and the other is not.
For, as a matter of fact, we do not find in Nature such an arrangement
as that in the second figure, or as that in which both the planets
revolve in opposite directions to the sun’s rotation; what we do find
is, that the planets go round in the same direction as the sun. And the
explanation is undoubtedly connected with the important principle
already illustrated, namely, that natural systems are in a condition in
which the total quantity of energy undergoes continuous reduction in
comparison with the moment of momentum.
In the arrangements made in the two figures, it will be recollected that
the masses of the three bodies were respectively the same, and also
their distances apart, and their velocities. As the energy depends only
on the masses, the distances, and the velocities, the energies of the
two systems must be identical. But the moment of momentum of the two
systems is very different, for while in the one case the sum of the
moments of momentum of the sun’s rotation and that of the planet A,
which is going in the same direction, are to be _increased_ by the
moment of momentum of B, the same is not the case in the other system.
The moment of momentum of the sun and of A conspire, no doubt, and must
be added together; but as B is revolving in the opposite direction, the
moment of momentum of this planet has to be subtracted before we obtain
the nett moment of momentum of the system. Hence, we perceive a
remarkable difference between the two systems; for, though in each the
total energy is the same, yet in the latter case the moment of momentum
is smaller than in the former.
It has been pointed out that the effect of the mutual actions of the
different bodies of a system is to lessen, in course of time, the total
quantity of energy that they receive in the beginning, while it is not
in the power of the mutual actions of the particles of the system to
affect the sum total of the moment of momentum. Hence we see that, so
long as the system is isolated from external interference, the tendency
must ever be towards the reduction of the quantity of energy to as low a
point as may be compatible with the preservation of the necessary amount
of moment of momentum. The first of the two systems given in Fig. 50 is
much more in conformity with this principle than the second. The moment
of momentum in the former case must be nearly as large as could be
obtained by any other disposition of the matter forming it, with the
same amount of energy. But in the second diagram the moment of momentum
is much less, though the energy is the same. It follows that the energy
of this system might be largely reduced, for if accompanied by a
suitable rearrangement of the planets the reduced amount of moment of
momentum might be easily provided for. We thus see that this system is
not one to which the evolution of a material arrangement would
ultimately tend. It is, therefore, not to be expected in Nature, and we
do not find it. Of course, the same would be equally true if, instead of
having merely two planets, as I have here supposed for the sake of
illustration, the planets were much more numerous. The operation of the
causes we have been considering will show that, in the evolution of such
a system, there will be a tendency for the planets to revolve in the
same direction.
It is easy to see how, in the contraction of the original nebula, there
must have been a strong influence to check and efface any movements
antagonistic to the general direction of the rotation of the nebula. If
particles revolve in a direction opposite to the current pursued by the
majority of particles, there would be collisions and frictions, and
these collisions and frictions will, of course, find expression in the
production of equivalent quantities of heat. That heat will, in due
course, be radiated away at the expense of the energy of the system, and
consequently, so long as any contrary movements exist, there will be an
exceptional loss of energy from this cause. Thus the energy would
incessantly tend to decline. As the shrinking of the body proceeded
while the moment of momentum would have to be sustained, this would
incessantly tend more and more to require from all the particles a
movement in the same direction.
The second concord of the planetary system, which is implied in the fact
that all the planets go round in the same direction, need not therefore
surprise us. It is a consequence, an inevitable consequence, of the
evolution of that system from the great primæval nebula. We have seen
that it would be excessively improbable that even nine or ten planets
should revolve round the sun in the same direction, if the directions of
their movements had been merely decided by chance. We have seen that the
movements of the hosts of planets, which actually form our system, would
be inconceivable, unless there were some reason for those movements. The
chances against such an arrangement having arisen without some
predisposing cause is so vast that, even if the chances were infinite,
the case would be hardly strengthened. But once we grant that the system
originated from the contraction of the primæval nebula, dynamics offers
ready aid, and the difficulty vanishes. Not only do we see most
excellent reasons why all the planets should revolve in the same
direction; we are also provided with illustrations of similar evolutions
in progress in other parts of the universe; we learn that the evolving
nebula, however erratic may have been its primitive motion, whatever
cross currents may have agitated it in the early phases of a possibly
violent origin, will ultimately attain a rotation uniform in direction.
As the evolution proceeds, the various parts of the nebula draw together
to form the planets of the future system, and the planets retain the
movement possessed by their component particles. Thus we see that the
nebular theory not only extricates us from the difficulty of trying to
explain something which seemed almost infinitely improbable, but it also
shows why no other disposition of the motions than that which we
actually find could be expected. The nebular theory explains to us why
there is no exception to that fundamental law in the solar system which
declares that the orbits of the planets shall all be followed in the
same direction.
This wonderful agreement in the movements of the planets, which we have
called the second concord, thus affords us striking evidence of the
general truth of the nebular theory. But there is yet a third concord in
the solar system which, like the other two, lends wonderful
corroboration to the sublime doctrine of Kant and Laplace. This we shall
consider in the next chapter.
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