316 
ON THE DEVELOPMENT OF THE DISTURBING FUNCTION 
[213 
il (continued) = in' -, 4 multiplied into 
Lubbock. 
Pontécoulant. 
Arguments. 
Nos. 
Arguments. 
Nos. 
64 
cos 
3 T + 1 2 £ 
122 
59 - 39 
Shg 
w i 
1 
3T- f-f 
123 
29 ~ 4 9' 
16 
3 T + è + 
124 
49-2(j 
16 
3 T— ¿ + 1' 
I2 5 
29-29' 
* + 3 <G — 3 G' 
10 
3 T + 
126 
49- 49 
64 
3 T - 2 é' 
127 
59-5 9' 
+ ^-e' 2 
64 
3 T + 2 
128 
3 9- 9' 
I 
+¥<* 
3 T ~ 2 V 
129 
9-39' 
+ C-3C' 
where the abbreviation rev. denotes that the argument to which it is attached has 
its sign reversed in the third column of arguments : thus Arg. 63 (Lubbock), it is 
- (2t - 277) which is equal to 2g' + 2<0'. As the formula contains only cosines, there 
is, of course, no change in the sign of the coefficient. 
On comparing with Lubbock’s value, I find some differences, which are as follows :— 
It will be recollected that R (Lubbock) = - to' ï - il, so that the signs of the 
coefficients of ÎÎ are to be reversed in order to deduce the corresponding coefficients 
QS 
of R. The Nos. refer to Lubbock’s arguments, and the exterior factor to' —^ or to' ^ 
is disregarded^). 
Arg. 1. Lubbock’s coefficient (viz. the coefficient in R) is 
e' 2 + ff e 4 + -\ 5 - e 2 e'‘ 
TF 
e 4 +1% 
a-' 
a' 2 / 
COS' 
1 I have been favoured with a note from Sir J. W. Lubbock, confirming my values of the coefficients 
for the arguments 8, 18, 58, 101 and 123.—Added 15th Feb. 1859, A. C.