662] 
157 
[661 
tion of x. We 
21 depends upon 
nuch as may be 
af the constants 
nplification may 
c. The proper 
- 2bd — 2cd, 
662. 
>e expressed as 
the differential 
is necessary to 
that O differs 
A, B, G, D, Ü, 
$il) 2 = n 2 Jf(8 w ) 2 
: 2) (8u) 2 , which 
ON THE DOUBLE ©-FUNCTIONS IN CONNEXION WITH A 
16-NOD AL QUARTIC SURFACE. 
[From the Journal für die reine und angewandte Mathematik (Crelle), t. lxxxiii. (1877), 
pp. 210—219.] 
I have before me Göpel’s memoir, “ Theoriae transcendentium Abelianarum primi 
ordinis adumbratio levis,” Crelle’s Journal, t. xxxv. (1847), pp. 277—312. Writing 
P u P,, P s , etc., in place of his P', P", P'", etc., also a, ß, y, 8, X', Y', Z', W, in 
place of his t, u, v, w, T, U, V, W, the system of 16 equations (given p. 287) is 
(1) 
P 2 = 
= («> 
-ß, 
- 7> 
«) 
(A', 
u, 
A', 
W), 
(4) 
Px 2 = 
= (a, 
ß, 
~ 75 
- 8) 
(A', 
T, 
A', 
W), 
(9) 
Pi-- 
= («» 
-ß, 
7’ 
-8) 
(A', 
Y\ 
A', 
w% 
(12) 
Pi- 
= («» 
ß, 
7, 
8) 
(A', 
Y', 
A', 
W'), 
(3) 
Q 2 - 
= 0®, 
- a, 
-s, 
7) 
(A', 
Y, 
A', 
w% 
(2) 
Qi 2 -- 
= (ß, 
a, 
-3, 
- 7) 
(A', 
Y', 
A', 
W'), 
(ID 
Qi-- 
= 0®, 
- a, 
3, 
- 7) 
(A', 
Y', 
A', 
W'), 
(10) 
Qa z 
= 08, 
a, 
3, 
7) 
(A', 
Y', 
A', 
W'), 
(13) 
P 2 = 
= (y, 
-8, 
- a, 
A 
(A', 
Y', 
A', 
W'\ 
(16) 
R>- 
= (7> 
8, 
-A 
(A', 
Y\ 
A', 
W'), 
( 5 ) 
R.X- 
= (7 5 
-3, 
a, 
- ß) 
(A', 
Y', 
A', 
W'), 
(8) 
R-X- 
= (7 > 
3, 
a, 
A 
(A', 
Y', 
A', 
W'), 
(15) 
S* -- 
= (8, 
- 7> 
-Ä 
«) 
(A', 
Y\ 
A', 
W), 
(14) 
$* = 
= (8, 
7> 
-A 
- «) 
(A', 
Y\ 
A', 
W'), 
U) 
S 2 2 -- 
= (3, 
~ 7) 
A 
- a) 
(A', 
Y', 
A', 
W), 
(6) 
s 3 2 -- 
= (», 
7> 
/3, 
A 
(A', 
Y', 
A', 
wy, 
)r of the form 
rs of the like 
hat, neglecting