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distance being equal, to the mass of each planet. In accordance with the
laws of Kepler, which relate to the whole interior of our system, the
same theory applies to the connection between the satellites and their
planets.
Newton thought it necessary to complete his demonstration by pre-
senting it in an inverse manner; that is, by determining a priori the
planetary motions which must result from such a dynamic law. The
process brought him back, as it must do, to Kepler s laws. Besides fur-
nishing some means of simplifying the study of these motions, this labour
proved that, whereas, by Kepler s laws, the orbit might have had more
figures than one, the ellipse was the only one possible under the Newtonian
law.
It was once a great perplexity to some people, which others could
not satisfactorily explain, that when the planet is travelling towards its
aphelion we cannot say that it tends towards the sun. But the difficulty
arose out of the use of inappropriate language. The question is, not
186/Auguste Comte
whether the planet is nearer to the sun than it lately was, but whether it
is nearer than it would have been without the force that sends it forward.
It is always tending towards the sun to the utmost that is allowed by the
other force to which it is subjected. The orbit is always concave towards
the sun; and it would evidently have been insurmountable if the trajec-
tory could have been convex. In the same way, when a bomb ascends,
its weight is not suspended or reversed: it always tends towards the
earth, and is, in fact, falling towards it more rapidly every moment, even
if ascending, because it is every moment further below the point at which
it would have been but for the action of the earth upon it; and its trajec-
tory is always concave to the ground.
I have thus far carefully avoided giving any name to the tendency of
the planets. towards the sun, and of the satellites towards the planets. To
call it attraction would be misleading; and we, in truth, can know noth-
ing of its nature. All that we know is that these bodies are connected,
and that their effect upon each other is mathematically calculable. It is
by quite another property of Newton s great discovery that this effect is
explained, in the true sense of the word, that is, comprehended from its
conformity with the ordinary phenomena which gravity continually pro-
duces on the surface of our globe. Let us now see what this property of
the discovery is.
We owe a great deal to the moon. If the earth had no satellite, we
might calculate the celestial motions by the rules of dynamics, but we
could not connect them with those which are under our immediate ob-
servation. It is the moon which affords this connection by enabling us to
establish the identity of its tendency towards the earth with weight, prop-
erly so called; and from this knowledge we have risen to the view that
the mutual action of the heavenly bodies is nothing else than weight
properly generalized; or, putting it the other way, that weight is only a
particular case of the general action. The case of the moon is suscep-
tible of the most precise testing. The data are known; and by dynamical
analysis, the intensity of the action of the earth upon the moon is exactly
ascertainable. We have only to suppose the moon close to the earth, with
the due increase of this intensity, inversely to the square of the distance,
and compare it with the intensity of weight on the earth, as manifest to
us by the fall of bodies, or by the pendulum. A coincidence between the
two amounts to proof; and we have, in fact, mathematical demonstra-
tion of it. It was in pursuing this method of proof that Newton evinced
that philosophical severity which we find so interesting in the anecdote
Positive Philosophy/187
of his long delay because he could not establish the coincidence, while
confident that he had discovered the fact. He failed for want of an accu-
rate measurement of a degree on the earth s surface; and he put aside
this important part of his great, conception till Picard s measurement of
the earth enabled him to establish his demonstration.
The identity of weight and the moon s tendency towards the earth
places the whole of celestial mechanics in a new light. It shows us the
motions of the stars as exactly like that of projectiles which we have
under our immediate observation. If we could start our projectiles with
a sufficient and continuous force, we should, except for the resistance
of the air, find them the models of the planetary system: or, in other
words, astronomy has become to us an artillery problem simplified by
the absence of a resisting medium, but complicated by the variety and
plurality of weights. If our observation of weight on our globe has
helped us to a knowledge of planetary relations, our celestial observa-
tions have in turn taught us the law of the variation of weight, impercep-
tible in terrestrial phenomena. Men had always conceived weight to be
an inalterable property of bodies, finding that no metamorphosis, not
even from life to death, made any change in the weight of a body,
while it remained entire. This was the one particular in which men might
suppose they had found the Absolute. In a moment, the Newtonian dem-
onstration overthrew this fast-rooted notion, and showed that weight
was a relative quality, not under the circumstances in which it had
hitherto been observed, but under the new one, the position of the ob-
served body in the system, its distance from the centre of the earth.
The human mind could hardly have sought out this fact directly: but,
once revealed in the course of astronomical study, the verification easily
followed, and experiments on our globe, in the vertical direction, and
yet more in the horizontal, have established the reality of the law, by
experiments too delicate, from the necessity of the case, to be appre-
ciable, if we had not known beforehand what differences must be found
to exist. It is to express briefly the identity between weight and the ac-
celerating force of the planets that the happy term Gravitation has been
devised. This term has every merit. It expresses a simple fact, without
any reference to the nature or cause of this universal action. It affords
the only explanation which positive science admits; that is, the connec-
tion between certain less known facts and other better, known facts. [ Pobierz całość w formacie PDF ]

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