But, as before noticed, the largest part of the nutationj depends, not on the place of the moon in its orbit, but on the position of the orbit, that is, on the node of the orbit. Supposing the moon's orbit circular, imagine the mass of the moon to be distributed in a ring all round its orbit. If this ring were simply to revolve in its own plane, the pre cession and nutation produced by it in the earth, though materially altered in quantity, would be of the same sort as before, and iu both cases very small. But suppose the ring to shift its position, as does the moon's orbit, its nodes slowly regressing at the rate of a revolution in eighteen years. This shifting of the position of the ring will of course produce an alteration in the phenomena, and the substitution of the moon revolving in a shifting orbit in place of this ring must now be made. That the effect of the change of the orbit should be greater than that of the planet itself in a fixed orbit ought not to be surprising, since there is no d priori reason why it should be either greater or less.
Throughout the solar system there is no action of one planet upon a second, without a corresponding action of the second upon the first.
The protuberance of the earth, by which the planets produce preces sion and nutation, attracts those planets, and slightly varies their motion. In the case of the moon, sensible irregularities, both in longitude and Latitude, amounting at the maximum to about 7" in each, were found by Mayer, before Laplace showed them to be the consequences of the earth's protuberance. These inequalities may be made the means of calculating the amount of that protuberance, or, as it is technically called, the ellipticity of the earth : and it is a fact not a little remarkable, that the amount of this ellipticity, as calculated from its effect upon the moon's longitude, agrees with the same, as calculated from its latitude, better than actual measurements of the earth generally agree with one another, while both agree very nearly with the best of the latter. This sort of result had been anticipated as to quality by Newton, who showed that the motion of the equi noxes, being retrograde, proves the earth to be protuberant at the equator, and that if it had been protuberant at the poles (as many then thought was the case), the precession would have been in the contrary direction.