168 
MR. W. M. HICKS OH THE STEADY MOTION AND 
and 
du C —c 
dn a 
Hence the A have to be determined from 
2 a 
f{y)—— (2A 0 —A^P^+AqP'oCOSv—^{(A* — A„ +1 )P'„ +1 — (A,,^ — AJP'^jcosm; 
(c-cy 
Suppose now 
f( v ) = 
C-cV 
a. m cos mv 
Then, writing for the present (A„—A, l _ 1 )P / w _ 1 P'„=a? w 
x n+ j—ar* = 0 | n>m 
.... =0 
Hence for 
and 
or 
Therefore 
whence 
ry> __ ryi -- yJ 
- /q -L i) 
x n+1 —x n = 0~1 n<m 
x %——|— AqP'qP'j=0 
= 0 J where aJ 0 =A 0 P' 0 P' 1 
!> 
n>m -\-1 x n =x m+1 
n<m x m =x n =0 
_2a« m p, 
Xm+ 1 - 
*„=^"P', . (»>m) 
x„=0 
(n<m) 
A.-A -i=^pTj^ (»>»») 
A„—A^_!=0 
(n<m> 1) 
A„=A„,+^T'J" -A” («> m ) 
V r=m+l -V ) A r—i 
A„=A 1 =2A C 
(n<m) 
