CH. xxxil. LEVERRIER'S ANALYSIS. 313 



ton (see p. 148), that not only does the sun attract the 

 planets, and the planets the sun, but that every planet 

 attracts every other planet in the solar system. Now, as 

 no two planets revolve round the sun in the same time, 

 they are constantly changing their positions with regard to 

 each other, just as, for example, the short and long hands 

 of a clock are sometimes near together and sometimes far 

 apart : only in the case of the planets it is as if there were 

 eight hands moving, all at different rates, and these rates do 

 not bear an even proportion to each other. Moreover, the 

 planets do not move all upon one flat surface, like the face 

 of a clock, but their orbits are in various planes, and these 

 planes themselves are subject to irregular motions. Lastly, 

 each planet moves in an ellipse, and these ellipses vary in 

 different ways. From this it arises that the planets cross 

 each other's paths at very varying intervals, and are inces- 

 santly assuming different positions with regard to each other. 

 Now, as the attraction of two bodies becomes stronger as 

 they approach each other, it is clear that as the positions of 

 the planets vary, their mutual attractions vary too, and the 

 task which Leverrier set himself was, to calculate all these 

 attractions and thus to discover the mass of each planet 

 by the effect which it has upon the other planets, and the 

 effect they have upon it. 



As our earth is one of the planets, the first thing was to 

 find out by the apparent motion of the sun, what is the real 

 path of our earth and how it is affected by all the others, 

 and from this to go on to each of the planets in turn. But 

 it must be remembered that no two planets can be studied 

 as if they were alone in the heavens ; on the contrary, they 

 are never free from the attractions of all the other six, whose 

 positions are constantly changing, so that the movements cross 

 and re-cross each other like the waves of a troubled sea. 



