2 8o EIGHTEENTH CENTURY. PT. IIL 



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

 Jupiter is always overtaking Saturn, so that the two pin nets 

 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 posi- 

 tions. 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 

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

 winch 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 La- 

 grange's great conclusion. He and Laplace had worked hand 

 in hand, proving more and more at every step how beauti- 

 fully 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 mathematical problem, proved that whatever 

 might be the changes, and they are almost infinite, caused 

 by all the attractions of the different planets on each other, 

 yet in the course of long ages every part of the solar 

 system remains stable. Each planet has its appointed road 

 along which it travels, through many twists and turnings, 

 but from which it cannot escape, for the grand force of 



