786 
ME. A. E. FORSYTH ON THE THETA-FUNCTIONS, 
IV. Cayley, (a) “ A Memoir on the Double 0-Functions,” ‘ Crelle,’ 
t. lxxxv. (1878), p. 214 ; 
(0) “On the Double 0-Functions,” ‘Crelle/ t. lxxxvii. (1879), 
p. 74; 
(y) “On the Addition of the Double 0-Functions,” ‘Crelle,’ 
t. lxxxviii. (1880), p. 74. 
For (ii.) I. Rosenhain. “ Memoire sur les fonctions de deux variables et a 
quatre periodes,” Mem. des Sav. Etr., t. xi, p. 361. This obtained 
the prize given by the Paris Academy of Sciences in 1846. 
II. Gopel. “ Theorise transcendentium Abelianarmn primi ordinis adum- 
bratio levis,” ‘ Crelle,’ t. xxxv. (1847), p. 277. 
III. Weierstrass. “Zur Theorie der Abelschen Functionen,” ‘Crelle,’ 
t. xlvii. (1854), p. 289 ; also t. lii. (1856), p. 285. 
IV. Riemann. “Theorie der Abelschen Functionen,” ‘ Crelle,’ t. liv.; Ges. 
Werke, p. 81. 
V. Cayley. “A Memoir on the Single and Double Theta-Functions,” 
Phil. Trans., 1881. 
VI. Brioschi. “ La relazione di Gopel per funzioni iperellittiche d’ordine 
qualunque,” Ann. di Mat., t. x. (1881). 
For (iii.) I. Hermite. “ Sur la theorie de la transformation des fonctions 
Abeliennes,” Comptes Rendus, t. xl. (1855). 
II. Konigsberger. (a) “ Ueber die Transformation der Abelschen Func¬ 
tionen erster Ordnung,” ‘Crelle,’ t. lxiv., p. 17 (1865). In this 
occurs part of the addition theorem ; 
(/3) “ Ueber die Transformation des zweiten Grades fur die 
Abelschen Functionen erster Ordnung,” ‘Crelle,’ t. lxvii. (1866), 
p. 58; a continuation of which, dealing with the modular equations, 
occurs in the Math. Ann., t. i. (1869), p. 163. 
For (iv.) I. Kummer. “ Ueber die algebraische Strahlen-systeme,” Berl. Abh. 
(1866). 
II. Cayley, (a) “On the Double 0-Functions in connexion with a 16- 
nodal Quartic Surface,” ‘ Crelle,’ t. lxxxiii. (1877), p. 210 ; 
(/3) “ On the 16-nodal Quartic Surface,” ‘ Crelle,’ t. lxxxiv. 
(1878), p. 238. 
III. Borchardt. “ Ueber die Darstellung der Kummerschen Flache 
vierter Ordnung mit sechzehn Knotenpunkten durch die Gopelsche 
biquadratische Relation zwische vier Theta-functionen mit zwei 
Variabeln,” ‘Crelle,’ t. lxxxiii. (1877), p. 234. 
IV. Weber. “ Ueber die Kummersche Flache vierter Ordnung,” ‘ Crelle,’ 
t. lxxxiv. (1878), p. 332. 
