498 MR, Gr. H. DARWIN ON THE PRECESSION OF A VISCOUS SPHEROID, 
The parts of — and — which arise from the attraction of the sun on the solar tides 
1 dt at 
may he at once written down by symmetry, and \ y =—may be considered as a small 
ox 
fraction to be neglected compared with unity. Thus we have 
— sin 4e 4P0 ^ 
dt “tf-BAo 4 * 
dt 
(81) 
Lastly as to the terms due to the combined action of the two disturbing bodies, it 
was remarked that they only involved e and e, which are independent of the orbital 
motions. 
Thus by (33) we have 
di »m, _ 1 • , i t)/~\ 
——= — — — sm 4 e.j-FU 
dt N g» 0 4 c 
dN m 
sin 4e.4^ 2 
dt %n Q 
. . . . (82) 
Then collecting results from the last three sets of equations and substituting cos i 
and sin i for P and Q, and — for \, we have 
n 
di 1 sin 4e 
dt N jpt 0 
dN ^_, sin 4e 
p sm ^ cos i 
9 | o 
T+ V —77 — 
2/2 
-r- sec % 
n 
dt 
5«o 
n 
(1 —sin 3 ^)(t 3 +t / 2 )+-|tt / sin 3 i—-P cos i 
, i sin 4e . J ft 
/i-w= h —— cos ^ t'I 1 — — sec i 
W 
9"o 
n 
(83) 
These are the simultaneous equations which are to be solved. 
Subject to the special hypothesis regarding the relationship between the retarda- 
2/2 
tions of the several tides, and except for the neglect of a term — -rg sec i in the 
first of them, and of ——by 2 cos i in the second, they are rigorously true. 
OX 
We will first change the independent variable in the first two equations from t to £ 
