OF ROTATING COMPRESSIBLE MASSES. 
1 93 
The smallness of the last two terms of course measures the closeness of' the 
approximation (130). 
Equation (151) now reduces to 
-e 
r' —2 (y —2) pa 2 
^8 
a 
+ 0'010972r / -0 064324s , + 0 , 094925t / 
= -0*00843 + 0-00310 (y-2). 
On solving equations (152) to (154) directly, I find 
r -— 2 { V~- ] l’ ,r = 0-02074-0-01055 (y-2), 
2s' —2 (y —2) ( ra 2 + pc 2 ) _ 
a i c i 
-0-07096 + 0-08440 (y-2), 
t' —2 (y — 2) rc 2 
= -0-14008-0-02813 (y-2), 
whence the values of r', s', t' are 
r' = 0-08755 -0T0962 (y-2),' 
s'= — 0"01727 +0*04871 (y —2), ^ (exact solution), 
t' = -0-007862 + 0-02511 (y-2). . 
This may be compared with Approximation A, namely, 
r' = 2 (y-2 )p 
a 
4 A a 
abc 6 
—, &c.. 
(154) 
(155) 
which leads to the approximate values 
r' = 0-06590 -0-06509 (y-2), 
s' = — 0"00728 +0"02815 (y — 2), ^(Approximation A), 
t'= —0-007929 + 0"02669 (y-2). ^ 
The percentage error is large, although the absolute error in the coefficients is 
fairly small. This will be readily understood on noticing that under Approximation B, 
r', s' and t' would vanish altogether. 
39. Finally equating coefficients of w 2 and z 2 in equation (140) and making use of 
the relation k 9 = —2 k 8 , we obtain 
, 2u' ! • , 8k s , « 
K — T e = ljs + ~r 
a abc 
o/j 2v ~ i • 16& s 
(156) 
(157) 
