PHYSICAL ASTRONOMY. 267 



centres, appears to have been first suggested by 

 MACLAURIN, Fluxions, $470. It has been very 

 useful in the solution of the problem of The three 

 bodies. 



265. Let S be the Sun, (fig. 26.), and P 

 and P' two planets referred to the plane of 

 the ecliptic, each by three rectangular co-ordi- 

 nates, PQ, QR, RS, and PQ', Q'R', R'S, pa- 

 rallel to the three axes SO, SN, NM : let 

 SR = x, RQ = y, PQ = z. Let all the forces 

 that draw P in the direction of SM, or in a line 

 parallel to #, whether arising from the action of 

 the Sun S, or the Planet P', be denoted by F j 

 all those in the direction of SN Q"r# by F ; and 

 those in the direction of SO or z, by F" ; and 







let t be the momentary increment or fluxion of 

 the time ; then 



# = F> 



y = F x t* 9 and 



For from the principles of Dynamics, (1. 100.) 



7? 



F x = v v ; and (1. J 56.) v = 



