proportion of the weight of M to the weight of E; or so that if E and M were like two balls fastened upon the ends of a rod, they would balance at G. Then investigation shows that the motion of the earth may be almost exactly represented by saying that the point G travels round the sun in an ellipse, describing areas proportional to the times, (according to Kepler's laws), and that the earth E revolves round the point G in a month, being always on the side opposite to the moon.
Consequently, the direction in which the earth would be seen from the sun (and therefore the direction in which the sun is seen from the earth) depends in a certain degree on the distance EG. And therefore, if we observe the sun regularly, and if we compute where we ought to see the sun, according to Kepler's laws, the difference between these two directions will be the angle EGG; and knowing the distance CG, we can then compute the length of EG, and the proportion which it bears to GM; and this proportion, as I have said, is the same as the proportion of the mass of the moon to the mass of the earth.
A fourth method of determining the mass of the moon depends upon an accurate estimation of the force of gravity at the earth's surface. We know the moon's distance very accurately, and we know the earth's attraction at the earth's surface (that is, gravity) very accurately; and therefore we know the earth's attraction on the moon accurately. But the force which thus acts on the moon makes it revolve, not round E, in Figure 65, but round G. Now, in Figure 56, from a knowledge of the distance EM, and taking MN to be that proportion of the orbit which is described in one hour, we found the length of the line mN through which the earth's attraction pulls the moon in one hour. Here in Figure 65, we have the
