EQUILIBRIUM OF ROTATING MASSES OF FLUID. 
403 
With these values of the It s and As, I find 
22 4^+' -1 4= ‘8718 ; 22 -■ + -— y ,: A* = 1 *3949; f (-]' 
L3005 % ~ 1 2-8542 W 
i- 1 
•00829, 
•01701 
the summations, of course, stopping with i =5. 
Applying these in (71), we have, when 
. n 1 + -02891 _ , _ ’ T ' 1 +-0664 
^ = 7, 1 + A = 1 - --. 0088() = 1 -0380; or, when /3 = }, 1 + A = , _ 
whence 
3^)2 
f e = = -08839 X 1-0380 = *09175. 
47r -13608 x 1-0877 -1481 
•0195 
= 1-0877, 
Thus the angular velocity of the system has been found. 
Next we have 
W 
1 o 
= -001434. 
■00309 
Introducing this into (48) and (64) with the previously found values of the A’sand p’s, 
h. 2 + A 
4 = '0183, m 2 
•0428 
•00145, 1 
•0032 
1 4 = -0306, 
•0720 
m q 
•00145, 
■0032 
4 — -0460, = -00145, 
{> ; and hence ■{ 
•1089 
•0032 
4 = -0646, m 5 = -00145, 
•1541 
•0032 J 
l 
1-0776, 
1-1806 
l h -f 4 = 1-1318, 
1-3100 
K + 4 = 1-2019, 
1-4808 
h. + 4 = 1-2887. 
1-6965 
By taking the differences of h + l, we may conclude that 
K + 4—i ’fio? 
1-96 
and this sixth harmonic term will now be included. 
It appears from the values of the m’s that the harmonics of the type Shy + 3 are 
practically negligible, excepting the term Shr 4 , and that in that we may neglect the 
part depending on m 2 . 
Now, if r denotes the radius-vector due to the rotation, and Sr the increase of 
radius-vector due to the mutual influence of the two masses, we have 
8?’ 
a 
= -1191 + -0309 + -0100 ~ + -0035 yf + *0013 ~ + 
•2008 r -0637 r -0252 r -0108 5 -0048 
. . ( 77 ) 
