es 
. we 
“ . 
points) about the former,—as consequences of the general 
equation (1) : 
dB m+m’ ais 2AM YD y— ; 
BB Bea Ve 
Did ERE rhode Be po 
fn o-wT vB © 
It was remarked, that by regarding m, m/, m’, as repre- 
senting respectively the masses of the earth, moon, and sun, 
B and y become the geocentric vectors of the two latter bodies ; 
and that thus the laws of the disturbed motion of our satellite 
are contained in the two equations (4) and (5),—but especially 
in the first of those equations (the second serving chiefly to 
express the laws of the sun’s relative motion). 
The part of this equation (4), which is independent of the 
sun’s mass m”, is of the form (2), and contains the laws of the 
undisturbed elliptic motion of the moon ; the remainder is the 
disturbing part of the equation, and contains the laws of the 
chief lunar perturbations. A commencement was made of the 
development of this disturbing part, according to ascending 
powers of the vector of the moon, and descending powers of 
the vector of the sun; and an approximate expression was 
thereby obtained, which may be written thus : 
pice hBrk 3h Lovo 2? —| = (B+ 3 y~"By) 
"bat Ta er 
There was also given a geometrical interpretation of this 
result, corresponding to a certain decomposition of the sun’s 
disturbing force into two others, of which the greater is triple 
of the less, while the angle between them is bisected by the 
geocentric vector of the sun; and the lesser of these two com- 
ponent forces is in the direction of the moon’s geocentric vec- 
tor prolonged, so that it is an ablatitious force, which was 
shown to be one of nearly constant amount. 
Although the foregoing formule may be found in the Appen- 
2y¥2 
509 
