90 
MR. J. H. JEANS OX THE EQUILIBRIUM 
+ >?" = ¥- ^HoV + 
Using- the series which have already V)een obtained for 1^,/ and (equations (89) 
and (90)), we obtain 
y r _ .1.^,4 I A^2 I 2 . 15 . I I 
sO 16V U ijV t 54 ^ * • • • 
We can now evaluate that part of the right-hand side of equation (99) which does 
not contain or cIq. 
t l 2 .5 .5,,-3 _ 
Si (.64’? 48) — 
W^e have 
— 3^ 
2 5 2 1 
- + 
- 0 4: V 
_ i.i 2_5„a 1 
3 2 ^ m 
_ 6 7 5„4 
3 7 5.^2 
—-tru^ 
- 3 - 2 -V — 
625 
6 2 5 
1 2 
(^1 + >?) = 
I iilA 4 _ _l_ 
8 -^ d- 1-2 + 54^0 -h 
18U + • • • ’ 
10,625 
r-.) 0 r • • • ) 
i 
34;375 
216 r • ’ 
3125 
By addition the sum of the terms in question is found to be 
4375 
4 J .„4 _ _ 1 _ _ 1 _ 
iVO T- 36 m 
547?- 
+ . . . 
Lastly, we have 
f (So& + -I Sjfo) = + (2<4 + iiO V + lihr' 
+ (— d~ ~ 2 A“^ 2 ) + • ■ • 
Collecting tlie various series, we find as tlie form assumed by equation (99), 
o 
6 r? 
^5 
'27 r]^ 
'.00 
+ (2cC + -|- 5 -§ 2 ,) y) + -if So + (”■ 2cUo + V ^ + • • • ) 
1 oi-r: 
= nv^-nrf + w+^.+ ■ ■ • 
+ (L (tIV^ + lb?" + “54~ + 24^2+ • • 
+ c/o + t -b ^ 
+ <^0 • 
Equating the coefficients of the various powers of yj, we obtain 
1 = fa + \i^U ’ 
— br^^j, + + ^5^2 — ~ ill “b a^h + 4^2 > 
— ~ 'hh + = ‘Vu + + 3^4 “b 
2 000U BO.] 8 O;; 37 — 43 7 5 i .o OOOU I 115. a 
--o“4"3“^<'j. — 2 7 ^^2 — 2 7^2 4^—2 — 5 4 > ' 2 4 3 ^4 I 2 7 ^*2 • 
Solving, we obtain in succession. 
