Page:Popular Astronomy - Airy - 1881.djvu/142

128 millions of miles from the sun, and that Venus is only thirty-six millions of miles from the sun. With the latter supposition (in which the distances are in the same proportion as in the former) we should find that Venus will appear to go just as much to the right or to the left of the sun as with the former. And, therefore, when we find that the apparent motions, computed on the supposition that the distances of the earth and Venus from the sun are respectively one hundred and seventy-two millions of miles, do agree with those which are really observed, we cannot tell whether the real distances are one hundred and seventy-two millions of miles, or fifty and thirty-six millions, or any other number; all that we know is, that they must be in that proportion. It is important to observe that this was the foundation of the third of Kepler's laws, and that he knew, as well as we do at the present time, what is the proportion of the distance of Venus from the sun to the distance of the earth from the sun, although he had not the slightest knowledge of the absolute distance of the earth from the sun.

I shall now proceed with the mention of the mechanical laws of orbital motion. In the first place, I shall take into consideration the general effects of attraction, or force; in which expression by the word force I mean pressure producing an effect on the motion of bodies that are free. Suppose we drop a stone from our hand, or from a high building, everybody knows that it begins to fall with a very small velocity, and that it gains velocity as it falls. If I were to drop a stone from my hand at the height of a foot from the floor, it would fall lightly; but if I were to drop it from the height of a hundred feet, it would fall with a great shock. It is therefore evident that