we might find the proportion of the lunar precession to the solar precession. By going backward through the same steps, knowing the proportion of lunar precession to solar precession, we may find the proportion of the moon's mass to the sun's mass.
There is a second method by which the mass of the moon may be obtained, from the proportion which its effect (depending upon the difference of its attractions upon different parts of the earth) bears to the sun's effect (depending upon a similar difference); and that is, by comparing the tides at different times, Everybody knows that the tides follow the moon generally but not entirely. They do not follow the time of the moon's meridian passage by the same interval at all times; and they are much larger shortly after new moon and full moon than at other times. From a careful examination of all the phenomena of tides, it appears that they may be most accurately represented by the combination of two independent tides, the larger produced by the moon, and the smaller produced by the sun; that at spring tides these two tides are added together, and make a very large tide; but that at neap-tides the high water produced by the sun is combined with the low water produced by the moon, and the low water produced by the sun is combined with the high water produced by the moon, and thus a small tide is produced.
By comparing the spring-tides with the neap-tides, we can find the proportion of the effect produced by the moon to that produced by the sun. Now, the tides are produced, not by the whole attraction of the moon and the sun upon the water, but by the difference between their attraction upon the water and their attraction upon the mass of the earth, by which difference the moon (and similarly the sun) attracts the
