i 
517 
lative elliptic motion, with respect to that centre of gravity, 
are then contained in the following differential equation, which 
takes the place of the equation (5) : 
d?y _m+m' +m” 
ol rae 
Indeed, when we come to consider the small disturbing 
forces which belong to the second group, and which depend on 
the inverse fourth power of the sun’s distance, the correspond- 
ing terms of the development of the first member of the formula 
(6) are then, for greater accuracy, to be multiplied by the 
(33) 
m! . : . 
ml? which expresses the ratio of the difference to 
fraction ~— 
m 
the sum of the masses of the earth and moon. But if we neglect, 
for the present, those small disturbing terms, we may regard 
__ that formula (6) as accurate, without as yet neglecting anything 
on account of smallness of eccentricities or of inclinations ; and 
even without assuming any knowledge of the smallness of the 
moon’s mass, as compared with the mass of the earth; y still 
denoting, as just stated, the elliptic vector of the sun. And 
thus, if the moon’s geocentric vector 3 be changed to the sum 
(+6, where the term 6( is supposed to depend on the dis- 
turbing force, and to give a product which may be neglected 
when it is multiplied by or into the expression for that force, 
we shall have the following approximate differential equation, 
_by developing the disturbed or altered tractor (8+ 83), and 
confining ourselves to the first power of of : 
PUB a Ah OF 
dA GR si * 
em (38 + 38-88 B) + 7™ 1B +37 By) (84) 
2(— p?)! Y)? 
The disturbance 83 of the moon’s geocentric vector is thus 
exhibited as giving rise to an alteration dp((3) in the corres- 
ponding tractor ((3), which alteration is analogous to a dis- 
