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 to
bring to their present state, and which are still far from
perfect. The measurement of the distance of a satellite is not a
job to be done in an evening; it requires patient labor extending
through months and years, and then is not as exact as the
astronomer would wish. He does the best he can, and must be
satisfied with that.