856 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
§ 26. Secular change in the obliquity ancl diurnal rotation of the planet, when the 
satellite moves in an eccentric orbit. 
The method of treating this problem will be the same as that of § 12, to which the 
reader is referred. 
In the complete development of the disturbing function y —f would occur wherever 
the F’s and G’s occur, but never with the H’s. 
If we put y— 1 in (284), we have 
dW dW 
de' 
2t 2 
5 ( 1 — v) 12 
■XE^(x). 
(295) 
Where % means summation for i, ii, iii, iv. 
This result follows from the fact that in all the E-terms of W, e and —' enter in 
the form le -\-mzx' , where 2. 
In the F x -terms f enters in the form and is of the opposite sign from l-\-m ; in 
the F x -terms it enters in the form and is of the same sign as l-\-m ; in the G x -terms 
it enters in the form f, and is of the opposite sign from l + m ; in the G x -terms it 
enters in the form f, and is of the same sign as l-\-m. 
Hence as far as regards the E-terms of W, we have 
in the F x -terms 
in the F x -terms 
in the G x -terms 
iii the G x -terms 
in the H-terms 
In the J-terms of W, f enters with coefficient 2 in the F x - and F x -terms, and with 
the coefficient 1 in the G x - and G x -terms, and is always of the same sign as the 
corresponding lag. 
Hence for the J-terms 
dW /dW dW\ 
df [d£* dgf 
Where % means summation for the cases where x is zero and both upper and lower 
i and ii. 
From this we have 
