water nearest to it from the earth, and attracts the earth from the water which is farthest from the moon.
Still these forces undergo some very peculiar modifications in their actions which produce the lunar and solar tides, which in many cases alter them in proportions slightly different. Thus their tidal effects are nearly but not exactly in the proportion of their difference of attractions, of which I have spoken; but with proper investigation it is possible to find, from their tidal effects, the proportion of their differences of attraction. And when this is found, we have obtained a proportion of differences of attraction which are exactly the same as the differences of attraction concerned in producing precession (of which I have already spoken); and, from knowing this proportion, and knowing the distances of the sun and moon, we can, in the same way, find the proportions of the masses of the sun and moon.
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Fig. 65.
The third method is this. In Figure 65, suppose C to be the sun, E the earth, M the moon. I have spoken continually of the sun's attraction upon the earth and of the earth's revolution round the sun, as if the sun were the only body whose attraction influenced in a material degree the earth's movement. But in reality the moon also acts in a very sensible degree upon the earth. And the immediate effect upon the motion of the earth is found by proper investigation to be the following. Draw a line from E to M, and in this line take the point G, which is called the "centre of gravity," so that the proportion of EG to GM is the same as the
