380 
MR. LUBBOCK’S RESEARCHES 
a, m , raa 
4 fVb 
m a 
(jj is the mass of the sun + the mass of the disturbed planet, which is not of 
course the same for both, but the difference may be neglected in the planetary 
theory. 
Laplace determines the arbitrary quantity f, upon the hypothesis that the 
coefficient of the argument sin (n (1 + k) t -f s — in the expression for the 
longitude equals zero. According to the received theory of the moon, the true 
longitude is expressed in a series of angles consisting of various combinations 
of the quantities t, x, y and z, and their multiples and no others ; and in this 
theory the angle t + z occupies the place of the argument n t + s — nr p so 
that omitting s which accompanies t, 
= 1 + r 0 + e (1 +/) cos (cn/-sr) + ej t cos (n t — n, t + c i n / 1 — sr,) 
— = 1 + r 1/0 + e t {\ +/') cos (c f n / 1 — Tn t ) + e// cos (n ( t — n t + c n t — er) 
r. 
c ; = 1 ?H^Lb S)l = 1 nearly 
4 P, a i 
n ; (c ( — 1 ) = n & ( = 0 nearly 
m ( a 3 
* c and g are determined by quadratic equations, 
nearly. 
