i 225 ] 



the error in the mean motion of the apfides of the lunar orbit, by. 

 neglefling the excentricity, is only 8 feconds in a revolution. 



In the lunar orbit referred to the ecliptic, the perturbing force 

 in the diredion of the radius vedor is expreffed by a fundion of 

 that radius vedor, and of the angular diftance of the moon from the 

 fun; and the perturbing force in a diredion perp; to the radius 

 vedor, is expreffed by another fundion of the fame quantities. 

 The former force in its mean quantity is expreffed by a fundion 

 of the radius vedor only. The mean quantity of the latter = 0. It 

 has therefore been often imagined, that the mean motion of the 

 lunar apogee might be inveftigated,by confidering the moon.aded up- 

 on by a centripetal force, expreffed by a fundion of the diftance only,. 

 The arguments for this opinion are certainly plaufible, but have by 

 no means the weight of demonftration. The refultfhevsfs, thatfuch 

 an opinion refts upon no folid foundation.. It does not appear to 

 be poffible to inveftigate the mean motion of the lunar apfides, ex- 

 cept from the general expreffions of the forces in diredion of the 

 radius vedot and in the diredion perp. thereto. 



Prop* 



