174 HISTORY OF PHYSICAL ASTRONOMY. 



the satellites of Jupiter and Saturn are attracted as 

 the primaries are ; in the same manner, and with 

 the same forces. If this were not so, it is shown 

 that these attendant bodies could not accompany 

 the principal ones in the regular manner in which 

 they do. All those bodies at equal distances from 

 the sun would be equally attracted. 



But the complexity which must occur in tracing 

 the results of this principle will easily be seen. The 

 satellite and the primary, though nearly at the same 

 distance, and in the same direction, from the sun, 

 are not exactly so. Moreover the difference of the 

 distances and of the directions is perpetually chang- 

 ing ; and if the motion of the satellite be elliptical, 

 the cycle of change is long and intricate : on this 

 account alone the effects of the sun's action will 

 inevitably follow cycles as long and as perplexed as 

 those of the positions. But on another account 

 they will be still more complicated ; for in the con- 

 tinued action of a force, the effect which takes place 

 at first, modifies and alters the effect afterwards. 

 The result at any moment is the sum of the results 

 in preceding instants: and since the terms, in this 

 series of instantaneous effects, follow very complex 

 rules, the sums of such series will be, it might be 

 expected, utterly incapable of being reduced to any 

 manageable degree of simplicity. 



It certainly does not appear that any one but 

 Newton could make any impression on this pro- 

 blem, or course of problems. No one for sixty years 



