860 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
The Variation is another lunar inequality of slightly less importance than the Evec- 
tion ; but it may be observed that the Evection was only of any importance because 
its argument involved the lunar perigee, and its coefficient the eccentricity. Now 
neither of these conditions are fulfilled in the case of the Variation. Moreover in the 
retrospective integration the coefficients will degrade far more rapidly than those of 
the evectional terms, because they will depend on (/2'/i2) 4 . Hence the secular effects 
of the variational tides will not be given, though of course it would be easy to find 
them if they were required. 
VI. 
INTEGRATION FOR CHANGES IN THE ECCENTRICITY OF THE ORBIT. 
§ 28. Integration in the case of small viscosity. 
By (291-2), we have approximately 
Therefore 
k dt 
log y=\ L sin 4f - (1 + V^)[cos i— IfX] 
y 
\ C §=k sm 4f v(l + 27^)[cos i-\] 
. .d. Ill— 44A sec i 
= — 1 — 7 ~ sec i approximately 
£ z n 
The last transformation assumes that X or fl/n is small compared with unity; this 
will be the case in the retrospective integration for a long way back. 
Then as a first approximation we have 
V=Vot 11 
Therefore 
r| 
j -fyd logr)=\ 1 ( V —rj Q )=—\ 1 r ]o (l-g u ) approximately 
And for a second approximation 
= 3 Ao(1-A)-U2 0 
(303) 
The integral in this expression is very small, and therefore to evaluate it we may 
