OF ROTATING COMPRESSIBLE MASSES. 
191 
On multiplying equations (141) and (142) by 18, 1, and adding, we obtain, with 
the help of the relations of § 36, 
18 
■R'-(y-2)LV1 
1 
3S' — (y—2) ( 2m'a 2 + L'c 2 ) 
a 12 
4 ^ 
« 8 c 4 
2 L 
6 a & 
(145) 
Equations (142) to (144), treated in a similar manner, give 
3S' — (y — 2) ( 2m'a 2 + LV) 
a 8 c 4 
+ 3 
3T / -( y -2) (NV + 2mV)~ 
« 4 c 8 
2 m 
r3T'-(y-2)(NV + 2m'c 2 )] 
1 1 £ 
ru'-(y —2) N'c 2 1 
« 4 c 8 
T It) 
c 12 
6 ac 
2 N 
0 c s ’ 
4,.4 > 
(146) 
(147) 
These equations, taken with one other, suffice to determine R', S', T', U'. For 
additional equation we shall use equation (141). 
The values of j\ and k x have already been given. For 5 h x I find, by direct 
computation from formula (134), 
5 h x = 0'00152R' —0'01345S' + 0‘03926T' —0‘03813U', 
so that equation (141) reduces to 
-6 
TF-(y-2)L V 
a 
+ 0'00152R'-0'01345S' + 0'03926T'-0'03183U' 
- 0'02214 (y-2)-0'02347. 
Solving the system of four equations (145) to (148), I find 
R/-( y -2) LV = q'04794 —0'04309 (y — 2), 
a 
12 
—— ( 2 | m a ' + N ^) = 04894 —0'2573 (y-2), 
ac 
3F-(y-2) (NV + 2 m'c-) _ 0 4388-0'6707 (y-2), 
a 4 c 
p/_( y 2 ) N V = q- 2605-0'5077 (y-2), 
leading to the values 
R' = 0'41 55 —17799 (y —2), 
3S' = 04894 -14585 (y-2), 
3T v = 0'0506 -04124 (y-2), 
U' = 0'00346 — 0'0375 (y — 2). J 
2 C 2 
(exact solution). 
(148) 
(149) 
