380 
ME. LUBBOCK’S RESEARCHES 
(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 -f- k) t + 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 + £ — so 
that omitting e which accompanies t, 
— = 1 + r 0 + e (1 +/) cos (cni-sr) + ej t cos (nf-n^+c^f- tz,) 
r 
^ — 1 + r 1/0 + e ( (1 +/') cos (c' n ( t — ct,) + e//cos (n ( t — n t + c n t — zs) 
r, 
n ; (c, — 1) = n k l — 0 nearly 
* c and g are determined by quadratic equations. 
= 1- m1 a b 3 i nearlv. 
3,1 
