192 
MR. J. H. JEANS ON THE CONFIGURATIONS 
This may be compared with the approximation expressed by equation (130), which 
gives 
R' - ( y -2)LV-4-£i — 
' abc 6 
= 0-3981 -17691 (y-2), 
1 
3S' = (y-2)(2mV+L'c 2 )-^3& 2 — = 0'2013 -l'4659 (y-2) 
3T' = ( y -2)(NV+2mV)- -f-3jfc 3 — = 0'0452 -0'4090(y-2) 
, (Approxima- 
r tion A) . (150) 
abc ' 6 
u ' = ( y -2)NV-^*.f 
= 0-00355-0-0381 (y-2). 
The error of Approximation A is now something like 5 per cent, in the terms 
independent of (y —2), and there is also an additional small error of less than 1 per 
cent, in the terms containing (y—2). 
38. We pass now to the discussion of terms of degree 4. Equating coefficients of 
w i , tv 2 z 3 , and 2 4 in equation (140) gives 
3 K-e 
r' — 2 (y — 2 ) pa 2 
_ 3 j 2 
8 abc 
-24 hz-e 
2s'—2 (y —2) ( ra 2 +pc 2 ) 
a*c* 
Sk 6 
8 abc ’ 
Slu-6 
V —2 (y — 2) rc 
2-1 8 h + 
8 abc 
(151) 
Following the method of the last section, the last two equations may be replaced 
by 
r' —2 (y — 2) pet, 1 
4 - 
a 8 
i 
2s / —2 (y —2) (m 2 + pc 2 ) 
a*c* 
2s' — 2 (y — 2) (ra 2 +pc 2 ) 
4 4 
a c 
4-3 
t' — (y — 2) rc 2 
2 2 p 
6 a* ' 
2 r 
0c 4 ‘ 
(152) 
(153) 
The three equations (151) to (153) determine r', s' and t'. The values of 4 kjabc 
and of 3j 2 have already been given. For 3 h 2 I obtain by direct computation from 
formula (135) 
3 h, = 0‘010972r' —0'064324s' + 0'094925t' 
+ 0'0103lR/ —0'0Q7283S' —0'04422T' + 0'32343U', 
which, on inserting the exact solution (149) for It', S', T', U', becomes 
3 ho = 0‘010972r' —0'064324s'+ 0‘094925t' + 0'0017 9 — 0’00166 (y-2). 
