168 Proceedings of the Koyal Society of Edinburgh. [Sess. 
^ 4) ^ + If) + + Im,) 
+ 2(</, +/, - i j-i + + (g, - h + «i) 
+ (/4 + n, - ,»3)5^ - + (c, + ,g(g - 1^) = 0 , 
d(f) 
Z(2M+^l + m 
+ 2^ 
a/io a/> 
4 - n 
^9-2 ?/i' 
+ d 
81^ 8m^ 
+ 2(/o + nij - ^^4)^ + (^3 + ^6 ~ + ^1^ + (^'^3 + ^^2 “^4^^ 
(iii) From the coefficients of |jg , , ^^3 , ^^3 , 
* ’if. ft) * <2 *S) 
+ (». + », -/.)^ + (.«, + 1, - ’h)f^ - 2',^ + (<•, * '>l(^ - 1^) - 0 • 
K# +|-h+€f +#)+”#+?) 
\ a^^g a^j^/ va/^g a/j^/ ^<73 ac^y \a/g a^^j^y 
+ 2 (/< 3 +/i-. 3 f 4 .^g + (/-. + %-/ 3 )|- 2 ^ 3 | 
+ bfl + if, + m, - + ( 6 , + - 1 ) = 0 , 
+ 2<-i|^ + (<73 +/i - + (;/4 + »i - h)^ - 2/»|f 
i4 ^ 2i) ^ It) " ”(lt ^ ^It) ^ “^(It ^ ^) 
+ 2(^3 + + (73 + + <^,g - 2mfd 
+ + + d^^~ + ~ ^ • 
8^ ^8v 
8i 
