2?o EIGHTEENTH CENTURY. PT. in. 



when Laplace answered it, and showed that there was no- 

 thing to fear, for that, odd as their movements appeared, 

 these two planets really obeyed the law of gravitation, and 

 would 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 

 round the sun while Saturn travels once, and on this account 

 Jupiter is always catching Saturn up, so that the two planets 

 are often near together, or in conjunction, as it is called. 

 When this happens, they pull each other so strongly that 

 they are drawn each out of its proper path. If they always 

 met in the same places, and so were pulled in exactly the 

 same direction, they would never right themselves again ; 

 but as Jupiter does not quite make three rounds while Saturn 

 makes one, their points of meeting vary a little each time, 

 and this brings them round at last to their old positions. 

 Laplace's calculation of this movement is called the long 

 inequality of Jupiter and Saturn. 



Laplace also discovered the reason why the moon goes on 

 for a long time moving more and more quickly round our 

 earth, and then gradually more and more slowly. This pro- 

 blem, which is too long to examine here, was the last which 

 remained to complete the proof that Newton's theory of 

 gravitation would account for all the movements of the 

 heavenly bodies. 



lagrange proves the Stability of the Orbits of the 

 Planets, 1776. And now, in the year 1776, came Lagrange's 

 great conclusion. He and Laplace had worked hand in hand, 

 proving more and more at every step how beautifully all the 

 heavenly bodies move in order, so that an equal balance is 

 preserved between them all. At last Lagrange, taking up 

 all the known facts and uniting them in one grand mathe- 



