[ 'S ] 



that is, half the greateft force, when the fun is at the grcateft 

 diftance from the nodes. 



Now to compute the force of the fun to produce the anti- 

 cipation of the nodes of a fiagle moon at A, the nodes of the 

 orbit being in quadrature ; the force of the fun = fcs; the 



quantity of matter in the moon is = i. Then g : b : : fc s : ~ 



the fpsce defcribed in i" ; and 2/ (the circumference of a 

 circle whofe radius is unity, or the diftance of the moon from 



the earth") : •?6o^ : : : -260 x = the angle defcribed iu 



I" by the pl.ine of the orbit of a folitary moon in fyzige. 



Ano by a-procefs exadly fimilar to that, ufed before in the 

 cafe of a rigid annulus, it may be iliewn, that the mean force 

 of the fun to difturb the moon, conftantly in fyzige, is but 

 half its force when at the greateft diftance from the nodes. 



It follows therefore, from what has been demonftrated, that 

 the greateft force of the fun to move the annulus. in the di- 

 reftion PO^A is equal to its greateft force to move the plane 

 of the moon's orbit, the moon being conftantly in fyzige, and 

 that the mean force in both cafes is half the greateft force ; 

 confequently the mean force of the fun to move the plane of 

 the annulus in the dii-edlion P Q A is equal to its mean force 

 to move the plane of a folitary moon in .fyzige, in the fame 



diredion. 



