NEWTON S PRINCIPIA. 121 



being the masses of the satellites, and M that of the 

 planets. Now, in the case of Jupiter = 



77l 



and TF are somewhat greater; but the greatest of the 



m iii I 



four factors ^ = only. But in the case of the 



earth this factor amounts to about ; so that 5 r and 



oU 



8 v become sensible ; and will be so, even if, in 

 stead of ^rr, we take the factor ^T_ which is more 



correct.* 



When Laplace began his celebrated investigations of 

 the orbits of Jupiter and Saturn, he found that, on substi 

 tuting numerical values for the quantities in the expres 

 sion of the mean movement of the one body as influenced 

 by the action of the other, the sums destroyed one ano 

 ther, and left the whole effect of this disturbing force equal 

 to nothing, or the mean motion of neither planet at all 

 affected by the other. The formulas could be in each case 

 reduced to terms only involving two co-efficients ; and these 

 destroyed one another, f He soon found that the same 

 principle applies to all the heavenly bodies ; that their 

 mean motions and mean distances (the great axis of their 

 orbits) are not affected by any changes other than those 

 which occur within limited periods of time ; that conse 

 quently the length of the solar year is precisely the same 

 at any one period of time, as it was at a period so far 

 distant as to enable the changes which are produced 

 within those moderate limits to be effected. This impor 

 tant proposition he demonstrated upon the supposition, 



* Mec. Cel. iv. vL ch. 10. 30. 



f Ibid, livvii. ch. 7 ; liv. xv. ch. 1. 



