198 
SIR G. H. DARWIN ON THE 
On picking out the numerical coefficients of the several terms in (eE) 2 as given in 
(14) or (15), we see that 
3 a el ue) 2 = IKii) + JKiiiL + lizl + + JLliiL 1 
r/a v ,2 (1+X) 2 l2.5r 3 2 3 .5.7r 5 2 2 .5V 5 2 4 .3.7r 7 2tff7V 
Observe that 
P 
F 
k 2 sin 2 y sin 2 /3 
. (ii)'. . (iii)' . . (v)' . . (iv)' . . (vi)'. 
= c 2 , and write 
3 /c 2 sin 2 y 
(iii) 
3 Psin 2 
2 2 .5r 2 k 2 
, 5 K 2 sin 2 y r Ni 9 /c 2 sin 2 y , 
? (vi) 
<j = 
• • • (iii/.(v)'.(iv)' . . . 
Then we have 
(e£) s = (i„p,y ( -^,[T 3 (y_2«=- 2c ») + A 5 . «■ 
(vi)' 
(27). 
L 5 (^26»2c») + L. <rc! 
• ( 28 ). 
The terms in V denoted (eE) 1 and ( VV) do not contain a, b, c, and their 
differentials with respect to a, ft are zero; also, after omission of the terms in f*, 
(vv) is reduced to 
(vv) = (Ivrpa 3 ) 2 
^ 3 
Hence 
(i+xy 
• -roH- 
3 4(H = C^TpXjj,' 
X 
c/a 
311 4 ( vv ) = o 
10 1 a« db ° 0 J 
3\2 
Now 
c/ft v1 ~ fT+xpL ro 
cb ca ac 
a 
^=-Ip. 1 WQ. 1 W = -|a 1 >, 
c §£ = -l»-w ©■("•) = -|a.- 
Since i// is homogeneous of degree —1 in a, b, c, the sum of these three is equal to 
— 1, so that 
+ + = jfkxfj. 
