CH. xxxi. ORBITS OF JUPITER AND SATURN. 279 



times on the other. This balancing movement is called 

 the libration of the moon. 



Laplace works out the Long Inequality of Jupiter 

 and Saturn, 1774-1783. The next calculation about the 

 planets was made by Laplace, and is more difficult to under- 

 stand. You will remember that Newton showed that every 

 planet attracts every other planet, and lias some effect upon 

 its path round the sun. Now it had been found, by com- 

 paring old astronomical tables with later ones, that these 

 different attractions had altered some of the ellipses in 

 which the planets move ; and both Lagrange and a cele- 

 brated mathematician named Euler had tried to calculate 

 these changes and find out whether the planets would ever 

 come back into trueir old places. Laplace, however, carried 

 the calculation farther than either Lagrange or Euler had 

 done, and he showed that the whole machinery does work 

 round in the course of a long period. Only two planets, 

 Jupiter and Saturn, did not seem to follow this general law, 

 but behaved in a very eccentric manner ; for it appeared 

 that during the seventeenth century Jupiter had been 

 moving more quickly every year and Saturn more slowly. 

 If this went on, it was clear that Jupiter would draw nearer 

 to the sun, and at last fall into it, while Saturn would go 

 farther off, and disappear entirely from our system, and 

 this would upset the balance of our planets, and might lead 

 eventually to our being all drawn into the sun. 



This was a very serious question, and it was a grand step 

 when Laplace answered it, and showed that there was 

 nothing to fear, for that, odd as their movements appear, 

 these two planets really obey the law of gravitation, and 

 will return to their old places like the other planets after an 

 immensely long period. He showed that their irregularity 

 arises from the fact that Jupiter travels two-and-a-half times 



