784 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
Also tlie equation of tidal reaction (151) is 
1 r* . 
7 "t:= o sin 4L 
lc dt * (j 1 
(185) 
Dividing one by the other and putting t 3 =t 0 2 P 12 , we have 
and integrating, 
— 1 ~b 
n n ^. Jen, 
'(i-O+Afr 
OL 
vo 
(1-P) 
(186) 
This is the equation of conservation of moment of momentum of the moon-earth 
system, as modified by solar tidal friction. From it we obtain n in terms of £. 
§15. On the secular changes of the constants of integration. 
It is often found difficult on first reading a long analytical investigation to trace the 
general method amidst the mass of detail, and it is only at the end that the ruling 
idea is perceived ; in such circumstances it has often appeared to me that a preliminary 
sketch would be of great service to the reader. I shall act on this idea here, and 
consider some simple equations analogous to those to be treated. 
Let the equations be 
dz 
dt= a y> 
dy 
dt 
-= —CLZ 
If a be constant, the solution is obviously 
z=L cos (ai+m), y— — L sin (a£-}-m) 
Now suppose a to be slowly varying; put therefore a-\-aft for a, and treat a, a as 
constants. 
Then 
dz , dy , 
— = a.y-\-aty, — — — clz — <xtz 
dt J dt 
Differentiating 
