370 Prof. D. N. Mallik on 
.'. from (3) and (5) we get 
C m . 
= JCI-^)"" 1 [»Dl: I 1 + (2m-2-n) { I)£ + (n-m + 2)1^, } 
+ (m-l)(m-2-n)D^] .... («) 
Multiplying (4) by (2m — 2) and (6) by m and subtracting, 
we get 
i* m m 
(m-2)J(l-/r') 2 D:^=2(m-l)(l-^) 2 D^ 
+jn(»+«i-l)(n-fl»+2)f(l-/* 2 )r- 1 D*_ 2 rf/t 
(w + m-l)(»-m + 2) ^n»»-^ , 
+ -" ~2 'JT. «^ 
and •> 
jV<^ = fp„^ 
in„ (Phil. Mag. Oct. 1907). 
n + 1 
We accordingly have 
{ r m dp=%£=$ir . (0) + 2,» (»+'»-i)("-"»+2) . 5L=3 D " ( o) 
Jx m r m — 2 m ~ lK J (m — 2) m — 4 "*-' 
+ . . . 
In order to evaluate D^.^O) &c, we proceed as follows: — 
Let 1 
* " V1-2m/j + /j 
Then 1 oi.uri 
p=(l-2/**+P) 
or dy 7 , 
=srp, 
and tT?/ _^;?i 
rfT, 
dfi r dfjf ' 
