IX. 



OX FORCES OF ATTRACTION TO SEVERAL CENTRES. 



FORCES INVERSELY AS THE DISTANCE. 



1. IT is to be lamented that Sir I. Newton did not treat the 

 problem of forces directed to more fixed points than one, as 

 to two such points, either in the same or different planes 

 from the body acted on. This is the fundamental point in 

 considering disturbing forces when the centres are not fixed, 

 which makes the problem more complicated and difficult. 

 It is, however, sufficiently so even where the centres are 

 fixed. 



2. That the subject must have attracted Ms attention there 

 can be no doubt. He had gone so much into the more 

 difficult inquiries respecting disturbing forces that he must 

 have fully considered the somewhat simpler, what may be 

 termed the fundamental, case of fixed centres. Indeed, a 

 paper communicated to the Eoyal Society in 1769 {Phil. Trans. 

 p. 74) contains a demonstration by W. Jones, an intimate 

 friend of Newton, of a proposition on this subject, which 

 Machin had immediately after Sir Isaac's death given to the 

 translator of the Principia. Machin had observed on the 

 want of some investigation of the motion of forces directed to 

 two centres, as required to explain the motions of planet and 

 satellite, which gravitate to different centres, in a word the 

 problem of the Three Bodies. The proposition of Machin 

 and Jones goes but a very little way to supply the defect 

 complained of. It is confined to the case of the line joining 

 the two centres being in different planes from the line of 



