by the small body B upon the large body A; and both A and B will be disturbed; but A will not be disturbed so much as B, because its mass is greater. In the computations of perturbations, for instance the perturbations of Saturn by Jupiter, it is necessary to consider that Jupiter attracts the sun according to the same law, (as regards the motion produced in it,) by which it attracts Saturn; else the computed disturbance of Saturn would not at all answer to the observed disturbance. If, then, the sun attracts Jupiter and a comet (when at equal distances from the sun) so as to produce the same motion in them, this shows that the mechanical pull upon Jupiter is greater than the mechanical pull upon the comet in the same proportion in which the mass of Jupiter is greater than the mass of the comet; and therefore, (considering the reciprocal mechanical actions upon the sun as equal to the mechanical actions of the sun upon them,) Jupiter's pull upon the sun is greater than the comet's pull upon the sun in the same proportion as their masses; and the movements which they produce are in the same ratio. I may add that the same principle is involved in every investigation relating to the figure of the earth. Assuming this principle then, I shall proceed to compare the attractions which the sun and the earth would exert upon a body at equal distances from them.
In former computations in this lecture, I found that in Figure 56, the earth draws the moon through 10·963 miles in one hour, the moon being at the distance of 238,800 miles from the earth; and in Figure 57, that the sun draws the earth through 24·402 miles in one hour, the earth being at the distance of 95,000,000 miles from the sun. In order to make these attractions comparable, we must reduce them
