THE MOON’S MOTIONS.

69

around centres slightly differing in attractive energy;Jupiter , for instance, around a centre equal in mass toJupiter and the sun; Saturn round a centre equal inmass to Saturn and the sun; and so on. The result ofthis consideration is that, instead of finding the frac-tion constant for the solar system, we find

that this fraction calculated for the different planets(1) Mercury, (2) Venus, (3) Earth , and so on, givesresults respectively proportional to—(1) the sun’s massadded to Mercury ’s, (2) the sun’s mass added toVenus ’s, (3) the sun’s mass added to the earth’s, andso on.*

* The law thus interpreted is applicable to all cases where differ-ent bodies revolve around a common centre. But it also admitsof being generalized for different bodies travelling round differentcentres. Thus extended, it runs as follows :—

If a body of mass m revolves round a centre of mass M intime P, and at a mean distance I), and another body of mass m'•revolves round another centre of mass M' in time P', and at amean distance D', then

D 3 D ' 3

P 2 (M + m) ~ P ' 2 (M' + m')

This general law, almost as simple, be it observed, as Kepler’s thirdlaw, is extremely important. It may be regarded as the fundamentallaw of the celestial motions. It presents the influence of gravity asa bond associating the motions of all the orbs in the universe,whether of double suns around each other, or of primary planetsaround suns, or of secondary planets around their primaries. It isa law absolutely universal (so far as is known), and strictly exact,excepting in so far as perturbations come into operation to affectlt; ; and as perturbations have very little effect on mean periods°f revolution, the exactness of the law is scarcely affected in thisWa y. It is a wonderful thought that we can by means of such alaw associate the motions of bodies, which to ordinary apprehen-