250 PROFESSOR A. G. GREEN HILL ON THE 



III. w = w s , s (far) = s (&) 3 ) = s. A = c 2 , s, = a 3 , * 2 = .& 2 (9), 



-- , ,- 

 j S 3 ) (s, 3 ) a 2 (a 



a 



1 f 3 _ 1 _-- 4 db_v/ll 8 (l 2m) } , * 



/c' 2 sn 2 /K" " /c' 2 cn 2 /K' " 2 



* 



cn2/K' = C , dn2/K' = 6 , sn (1 - 2/) K' = ^ (12). 



a o 



A. fourth case, where 1 8(1 2m) a. is negative and , /> imaginary, need not be 

 discussed here. 



The Weierstrassian Sigma Functions of the Division-values (Theilwerthe) can now 

 he expressed in terms of the Jacobian Theta and Eta Functions by the relations on 

 p. 52 of SCHWARZ, ' Formeln der elliptischen Functionen,' so that 



^ = 4n+2, t ,= K + ^ T (13), 



e K/ 



-- ^{(*, - ^ ("* -- *,)} ar*X-Wi (14), 



H 2K/ 



- = ^{(*, - , 3 ) ( a - 3 )} r*x-5ss (15); 



2K ' 



2n+ 1 7/ x -ix-r4r, 2K' 



00 ^v/^-^^X us 2n+i 



(16). 

 a m 



(17), 

 (18), 



(19), 



(20). 



a m 



