296 PROFESSOR A. G. GREENHILL ON THE 



' '-- ; < (26) , 

 . (27 , 



We now find, as in 41, writing f for fKf, 



dn 2 /_ a- s s __ 1 (m 



o 2 C ' " ' 



a 







and then, from the relation 



* v/26 + 1 - a 2 + v/1 - a* v/2fc 1 + a 2 



-"a 2 - v/1 -^ 



dn_(2n + 1 ) / N,,, 

 dn/ * D,, 



(30), 



writing c for a 2 , and putting 



1 +c) = B 2 (31), 





- c 2 ) + & (& 3 - <?) (2b~ - 1 - c 2 ) 



E 7 ,= // + -2W, - - Vc* - < (3 + r- 1 ) // - 6V + c (1 + c 2 ) 6 + c 4 



= (/^ _ p)a (ft-: + ( .o) + /w . ( fte _ 1} (2 ft 3 _ j _ c3)) 



o 

 and F 7 is obtained from E 7 by changing c into c. 



47. ^ = 16, v = K +/KV, /= ! 3 8 ^, 



and now the condition 



s (a,) - ,s (4r) = y ( S] - * 3 ,. s 2 - Ss ) = C n (l) 



s 

 reduces to 



a = b (2), 



