318 
ON THE DEVELOPMENT OF THE DISTURBINO FUNCTION &C. 
[213 
No. of 
Arg. 
Lubbock. 
Lubbock’s coefficient. 
Coefficient from Development suprà. 
*63 
~i( I + 
95 
e 2 
32 
96 
2 7 2 / 2 
—z y e “ 
2 7 2 '2 
3 2 y G 
*101 
- g (i + 3 e 2 + 3 e' 2 - ^ y 2 ) 
-l( I + 2e ‘ +2e " ! -jr) 
II5 
- 15 v ! 
I28 y 
-ÎS/ 
3 2 
123 
22Z , 
- —T- e e 
ID 
22K . 
+ -f-ee, 
16 
The greater part of the discordant terms do not occur in Pontécoulant’s develop 
ment, which is not carried so far, and the only differences which I find in the 
coefficients of Pontécoulant’s R (= 12) are, as regards the arguments 18, 57, 70, corre 
sponding respectively to Lubbock’s arguments 62, 63, 101, included in the preceding 
table, and for which Pontécoulant’s coefficients, correcting for the change of sign, 
correspond with those given by Lubbock. But I see no room for a mistake in the 
preceding investigation as regards the coefficients of these three terms; the terms in 
i) of the coefficients of 62 and 63 are simply the quantity (f t — f rf), which forms 
the exterior factor of i2 ;i and H 4 respectively, and which, putting for rf and rj 4 , their 
values, is equal to | (1 — y 3 ) y 2 , and as regards the coefficient of 101, the portion 
1 q- 2 e 2 + 2e' 2 of this coefficient is obtained by the mere multiplication of the factors 
l + 2e 2 —&c. and 1 + 2e' 2 set opposite to p+<D and 0g' — tj' respectively in the table 
for O,;. 
2, Stone Buildings, W.C., 7th July, 1858.