The moon’s mean distance is 59.96435 equatorial radii of the earth, which radius is, according to Sir John Herschel, 20.923.713 feet. Her mean distance as derived from the parallax is not to be considered the radius vector of the orbit, inasmuch as the earth also describes a small orbit around the common centre of gravity of the earth and moon; neither is radius vector to be considered as her distance from this common centre; for the attracting power is in the centre of the earth. But the mean distance of the moon moving around a movable centre, is to the same mean distance when the centre of attraction is fixed, as the sum of the masses of the two bodies, to the first of two mean proportionals between this sum and the largest of the two bodies inversely. (Vid. Prin. Prop. 60 Lib. Prim.) The ratio of the masses being as above 80 to 1 the mean proportional sought is 80.666 and in this ratio must the moon’s mean distance be diminished to get the force of gravity at the moon. Therefore as 81 is to 80.666, so is 59.96435 to 59.71657 for the moon’s distance in equatorial radii of the earth. Multiply this last by 20.923.713 to bring the semi-diameter of the lunar orbit into feet = 1.249.492.373, and this by 6.283185, the ratio of the circumference to the radius, gives 7.850.791.736 feet, for the mean circumference of the lunar orbit.
Further, the mean sidereal period of the moon is 2360591 seconds and the 1 ⁄ 2360591th part of 7.850.791.736 is the arc the moon describes in one second = 3325.77381 feet, the square of which divided by the diameter of the orbit, gives the fall of the moon from the tangent or versed size of that arc. =
This fraction is, however, too small, as the ablatitious action of the sun diminishes the attraction of the earth on the moon, in the ratio of
We have found the fall of a body at the surface of the earth, considered as a sphere, 16.1067 feet per second, and the force of gravity diminishes as the squares of the distances increases. The polar diameter of the earth is set down as 7899.170 miles, and the equatorial diameter 7925.648 miles; therefore, the mean diameter is 7916.189 miles.[36] So that, reckoning in mean radii of the earth, the moon’s distance is 59.787925, which squared, is equal to 3574.595975805625. At one mean radius distance, that is, at the surface, the force of gravity, or fall per second, is as above, 16.1067 feet. Divide this by the square of the distance, it is
As there must be a similar effect produced by the radial stream of every vortex, the masses of all the planets will appear too small, as derived from their gravitating force; and the inertia of the sun will also be greater than his apparent mass; and if, in addition to this, there be a portion of these masses latent, we shall have an ample explanation of the connection between the planetary densities and distances. We must therefore inquire what is the particular law of force which governs the radial stream of the solar vortex. It will be necessary to enter into this question a little more in detail than our limits will justify; but it is the resisting influence of the ether, and its consequences, which will appear to present a vulnerable point in the present theory, and to be incompatible with the perfection of astronomical science.