GOG 
MR. LUBBOCK’S RESEARCHES 
Thus 
i=i+»^(i + 4)-3.(i+4*) 
[ 0 ] [ 2 ] 
cos x — — e 4 cos 2 x + — cos 3 x + — cos 4 x 
o o b 
[ 3 ] 
[ 20 ] 
[35] 
ji (?j— n,) + 3 h j | (1 + 3 
£ ~) r 22 r i0 
r, 1 2 (i n + 3n) a p a 5 dR„ 2 _ n 
16 / ~ + iCn-n,) + 3n " 22 + “chT “ ° 
If i? be considered as a function of r, A' and s, we have 
d J? _ r d 1? dr' d R d A' d R d s 
d7 ” 17“ rd^ d A' dy Ts d~y 
4^7 = 7 — 7. (1 — 4 e-) cos 2 y + y e cos O — 2 y) — y e cos (x + 2 y) 
r d y 2 2 
[62] [65] [ 66 ] 
q I ^ 
— —ye 2 cos (2 £ — 2 ?/) + — ye 2 cos (2x + 2y) 
8 8 
["] 
[78] 
l *' 
-j— = — y(l — 4 e 2 ) sin 2 y + y e sin (x — 2y) — 3 y e sin (x + 2 ?/) 
[62] [65] [66] 
— ^ y e- sin (2 x + 2y) 
[78] 
— = (1 — e~) sin y + esin (x — y) + e sin (x + y) + -g-sin (2x — y) + — e 2 sin (2 x + y) 
[146] [149] [150] [161] 
If R be considered as a function of r, X' and s , 
[162] 
d R _d R d X' d R d s 
dy dX'dy ds dy 
^ = — i R as before, and the expression for ^ (in this case) is given for the 
Lunar Theory, Phil. Trans. 1832, p. 6. 
The multiplications required may be effected by means of the following 
d A' 
Table. In the terms multiplied by —, the coefficient of R is to be taken with 
a positive sign when its index is found in the upper line, and with a negative in 
the contrary case. In the terms multiplied by the coefficient of ^ is 
to be taken with a negative sign when the index is found in the upper line, and 
with a positive when in the lower. 
