Page:Popular Astronomy - Airy - 1881.djvu/236

222 through, which the earth's attraction draws the moon in one second.

Now at a place on the earth's surface, which is 3,959 miles from the earth's centre, it is found by experiment, that a stone falls 193 inches in one second. And it is found (by a difficult mathematical investigation), that if our theory is true in this respect, "that the attraction of the stone to the earth is produced by the attraction to every particle of the earth," (see page 175,) then the attraction of the whole earth (considered to be a sphere) will be the same as if the whole matter of the earth were collected at its centre. Thus the question upon which the explanation of the moon's motion by gravitation must depend is this: the earth's attraction at the distance of 3,959 miles draws a body 193 inches in one second, and the earth's attraction at the distance of 238,800 miles draws the moon 0.0536 inch in one second. Are these effects of the earth's attraction inversely as the squares of the distances? They are, almost exactly. To make them exactly so, the space through which the earth draws the moon should be 0.05305 inch. Now it is found (by a process which I cannot hope fully to explain to you) that the two circumstances which I mentioned, namely the moon's action on the earth and the sun's disturbing force, do exactly explain this small difference; so that it is certain that the attraction of the earth which causes a stone to fall, and the attraction of the earth which bends the moon's path from a straight line to a circle, are really the same attraction, only diminished for the moon in the inverse proportion of the square of her distance.

I have used, for the time through which I compare the attracting power of the earth in the two cases