213] 
IN THE LUNAR THEORY. 
317 
which, substituting for cos 4 -|-t its value 1 — + i 7 (t7 4 ~ & c -> and developing to the 
fourth order, gives 
_ a 
4 
e 2 + 
+ ‘f-eV 2 + 
e' 4 — i 7 2 + f 7 2 e ~ + f 7 2 e ' 2 + 
which, in fact, agrees with the value given supra. I have only referred to this term 
in order to make the reduction. 
Arg. 8, Lubbock’s coefficient is 
-1 (1 - i e 2 + f e'~ - f 7 2 ) e 2 
the exterior sign should be + instead of —. The term is given with the correct sign, 
Pontecoulant, Arg. 2. 
Arg. 18, Lubbock’s coefficient is 
- ¥ (1 -1 e 2 - -W- e' 2 - i 7 2 ) cos 4 i c 
which, developed to y 2 , would be 
I make it 
The remaining differences are 
No. of 
Arg. 
Lubbock. 
Lubbock’s coefficient. 
Coefficient from Development supra. 
58 
+ p-ee' 3 
64 
- 8 i5 ee , 
6 4 
59 
+ ^e' 4 
64 
— — e' 4 
3 2 
60 
_^453 /4 
128 
r 599 /4 
64 ' 
6t 
—— e' 4 
3 2 
*62 
-§( r - f