divided by the square of the time of revolution
of the satellite. The quotient is a number which is proportional to the
mass of the planet. The rule applies to the motion of the moon round
the earth and of the planets round the sun. If we divide the cube of
the earth's distance from the sun, say 93,000,000 miles, by the square
of 365 1/4, the days in a year, we shall get a certain quotient. Let us
call this number the sun-quotient. Then, if we divide the cube of the
moon's distance from the earth by the square of its time of revolution,
we shall get another quotient, which we may call the earth-quotient.
The sun-quotient will come out about 330,000 times as large as the
earth-quotient. Hence it is concluded that the mass of the sun is
330,000 times that of the earth; that it would take this number of
earths to make a body as heavy as the sun.

I give this calculation to illustrate the principle; it must not be
supposed that the astronomer proceeds exactly in this way and has only
this simple calculation to make. In the case of the moon and earth, the
motion and distance of the former vary in consequence of the attraction
of the sun, so that their actual distance apart is a changing quantity.
So what the astronomer actually does is to find the attraction of the
earth by observing the length of a pendulum which beats seconds in
various latitudes. Then, by very delicate mathematical processes, he
can find with great exactness what would be the time of revolution of a
small satellite at any given distance from the earth, and thus can get
the earth-quotient.

But, as I have already pointed out, we must, in the case of the
planets, find the quotient in question by means of the satellites; and
it happens, fortunately, that the motions of these bodies are much less
changed by the attraction of the sun than is the motion of the moon.
Thus, when we make the computation for the outer satellite of Mars, we
find the quotient to be 1/3093500 that of the sun-quotient. Hence we
conclude that the mass of Mars is 1/3093500 that of the sun. By the
corresponding quotient, the mass of Jupiter is found to be about 1/1047
that of the sun, Saturn 1/3500, Uranus 1/22700, Neptune 1/19500.

We have set forth only the great principle on which the astronomer has
proceeded for the purpose in question. The law of gravitation is at the
bottom of all his work. The effects of this law require mathematical
processes which it has taken two hundred years