lv 
Consider a system of three attracting masses, m, m‘, m’”, 
with their corresponding vectors, a, a’, a”; and make for 
abridgment a’ — a = 3, and a” — a = y; we shall have, 
by (1), for the differential equations of motion of these three 
masses, referred to an arbitrary origin of veetors, the following : 
4 
a m’ andl tie 7 
e-=BVCR) ven) | 
(a+ PB) _ m m’ ' 
, @ “Bv(—B) * @-nvVi-@-v} f ( 
(a+ a+ y) _ m m’ 
a y= 7) * G=BVI-G-PT 
which give, for the internal or relative motions of m’ and m” 
about m, the equations : . . 
dp m+m . (B= yy": Ri i 
d= By(=B) 7” iG DIT VAS 
Ee a soe ioral 
d? ~ yV¥(—7) T= ae @—-By} v¥(— BP’) 
If we suppress the terms multiplied by m” in the first of 
these equations (14), or the terms multiplied by m’ in the 
second of those equations, we get the differential equation of 
motion of a binary system, under a form, from which it was 
shown to the Academy last summer, that the laws of Kepler 
can “be deduced. If we take account of the terms thus sup- 
pressed, we have, at least in theory, the means of obtaining the 
perturbations. 
Let m be the earth, m’ the moon, m” the sun; then B 
andy will be the geocentric vectors of the moon and sun ; and 
the laws of the disturbed motion of our satellite will be con- 
tained in the two equations (14), but especially in the first of 
these equations. By the principles of the present calculus we 
(14) 
have the developments, 
fs 5). = yt y By, + x By By” “3 (15) 
and 
War) {Br t78 , OV  BrtaB 
Vi-o-BF oy ails 
+++3 (16) 
