Page:Popular Astronomy - Airy - 1881.djvu/283

Rh seconds, say six or eight. We compute what would be the amount of perturbations if the planet Mars were as big, or half as big, as the earth, and we alter the supposition till we find a mass which will produce perturbations equal to those which we observe. Thus we go through a process which is one of trial and error. In this manner the masses of Mars and Venus are determined. That of Mars is not very certain; that of Venus is more certain both because it produces larger perturbations of the earth, and because its attraction tends to produce a continual change in the plane of the ecliptic, which in many years amounts to a very sensible quantity. The mass of Mercury is still very uncertain; lately attempts have been made to deduce it from the perturbations which Mercury produces in the motion of one of the comets.

There is, however, one mass which is more important than the others, and that is the mass of the moon. There are several methods by which the mass of the moon is determined. In speaking of the precession of the equinoxes and nutation, I pointed out that lunar nutation is, in fact, an inequality of lunar precession, connected with it by a certain proportion which is known from the theoretical investigation. Therefore, as we can observe the amount of lunar nutation, we can, by taking the proportion backwards, compute the annual amount of lunar precession; and we can observe the whole annual precession produced by both the sun and the moon; and, subtracting the lunar part, there remains the part due to the sun. Thus we have got ths proportion of lunar precession to solar precession. Now, you may remember, that on a former occasion, I went through the steps of a calculation, showing how, if we assumed the proportion of the moon's mass to the sun's mass,