Page:Popular Astronomy - Airy - 1881.djvu/146

132 will agree with me, that half a man's life would be well spent in mastering them.

Kepler's third law is this: that if we compare the orbits of the different planets, the squares of the periodic times are in the same proportion as the cubes of the mean distances from the sun. This, also, is in conformity with the result of the theory of attraction following the law of the inverse square of the distance. I suppose there is no science in the world in which such important laws have been first discovered independently from observation only, and which have afterwards been shown to be the result of one grand principle of theory.

I next endeavoured to point out to you how it is that planets do not entirely depart from the sun. It has been wondered by some persons that, when the planets approach to the sun, they are not compelled by its attractive force to fall into the sun; and when they go away from the sun, it has been wondered that they do not go quite away from the sun's influence. I endeavoured to give you a notion of the mechanical causes which produced that alteration in the velocity of the planets, which is in fact embodied in that law of Kepler's, which states that a planet describes, by the lines connecting it with the sun, equal areas in equal times. In introducing that matter, I said, that the curvature of the orbit of a planet, in the same manner as a curvature of the path of a cannon ball, depends not only upon the force which pulls the planet or the ball so as to curve its orbit, but also upon the amount of velocity with which it is; moving. Therefore, in order to ascertain what is the curvature of an orbit, we must consider not only the amount of the sun's attraction at any part of it, but also what is the amount of velocity with which the