reas is
uniform, that point and no other must be the centre of all the
force there is. If there be no force, as in Fig. 59, well and good,
but if there be any force however small not directed towards _S_,
then the rate of description of areas about _S_ cannot be uniform.
Kepler, however, says that the rate of description of areas of each
planet about the sun is, by Tycho's observations, uniform; hence
the sun is the centre of all the force that acts on them, and there
is no other force, not even friction. That is the moral of Kepler's
second law.

We may also see from it that gravity does not travel like light, so
as to take time on its journey from sun to planet; for, if it did,
there would be a sort of aberration, and the force on its arrival
could no longer be accurately directed to the centre of the sun.
(See _Nature_, vol. xlvi., p. 497.) It is a matter for accuracy of
observation, therefore, to decide whether the minutest trace of
such deviation can be detected, _i.e._ within what limits of
accuracy Kepler's second law is now known to be obeyed.

I will content myself by saying that the limits are extremely
narrow. [Reference may be made also to p. 208.]

Thus then it became clear to Newton that the whole solar system depended
on a central force emanating from the sun, and varying inversely with
the square of the distance from him: for by that hypothesis all the laws
of Kepler concerning these motions were completely accounted for; and,
in fact, the laws necessitated the hypothesis and established it as a
theory.

Similarly the satellites of Jupiter were controlled by a force emanating
from Jupiter and varying according to the same law. And again our moon
must be controlled by a force from the earth, decreasing with the
distance according to the same law.

Grant this hypothetical attracting force pulling the planets towards
the sun, pulling the moon towards the earth, and the whole mechanism of
the solar system is beautifully explained.

If only one could be sure there was such a force! It was one thing to
calculate out what the effects of such a force would be: it was another
to be able to put one's finger upon it and say, this is the force that
actually exists and is known to exist. We must picture him meditating in
his garden on this want--an attractive force towards the earth.

If only such an attractive forc