780 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
Therefore 
'in rfW,' 
n 2 d x ' i d'k' _ 
-= — sin g+i sin (N—xjj+g )} 
When the moon is tide-raiser and the snn disturber, this becomes 
cos (iV—1/»)) sin 2g.(169) 
When the sun is tide-raiser and the moon disturber, this becomes 
—\i sin 2 o' 
(170) 
Then collecting results from (166-7-9, 170), we have by (18), 
di 
,l dt = ^ i+J ' C0S 
— (sin 4f L -{- sin 2g : — sin 2g) —— sin 2g 
5 9 
T . TT 
— sin 4f—— sin 2g 
9 
9 
1 
> ■ (^1) 
J 
This gives the additional terms due to bodily tides in the equation for di/dt, viz.: 
the third of (133). 
If the viscosity be small 
w 
here 
sin 4f x + sin 2g 1 — sin 2g= sin 4f(l —2\) ~1 
1 
sm 2g 
sin 4f 
n 
n 
J 
■ ( 172 ) 
Also we have from (160-2-4-8) to the present order of approximation, 
and by symmetry, 
Therefore by (18) 
^/ T2 --lsin4f 
d X '/ 9“ 2bUl4±1 
d W /H 2 _ 
d X '/ 9“"" 2 
1 sin 4f 
dn _ } 
dt 2 
T~' a rj- * 
— sin 4f, +— sin 4f 
a 1 a 
(173) 
