290 PROFESSOR A. G. GREENHILL ON THE 



1 



*7i = - - . 



Then, in 28, 



= a? _ 4 _ i ' 



- (18)- 



43. ,z = 28, r = K + - , r = 1, 3, 5, 9, 11, 13. 



D 7 - cN 7 = (1). 



a N 7 + D 7 , 2 v 



6"N 7 -D 7 



A change of b into h changes v into 13'\ 



Now, with 1 2/u = p, pa. in (I m) ft, 8pm = (l /r) (e + l), 



2/1 vl / e + 1 V 3/) - 1 e + 1 



D 7 = m' ( I - ) { /> ( - 2 -) ^- -3- 



= I m e (i _ , n )J { _ ^ + e (e _ 1} {t + e} (3) ; 



and changing p into p, 



N 7 = i- r (1 - /u) 2 { - p* - e (e - 1 ) p + *} (4). 



op (e-l) + 6(6-p a ) = (6). 



Snhstituting for /) and e in terms of a and b, and cancelling a factor (a 3 6' 2 ) 3 , 

 there results 



ab* + (i + a - a- - 3a ;i ) // - a s (l + - -Ja 3 - a 3 ) = (7), 



a quadratic for 6 + . 



To obtain a rational expression for C, we put 



a 3 - 6* = a s (l -a)c 2 (8), 



and now the relation (7) becomes 



(aV + a) 2 -(l +a)*c 2 = (9), 



