As from (73) follows 
ORE ey = a FE ee ee (74) 
we find with the aid of (76) and (77) 
(a,,4,,-+4,,4,,) ¢ = (A—a,,A,,) « = A(l—A’) « = 
elden abo «4, GIN 
(4,241, +4534.) ¥ = (Aarden) y= ALA) y = 
=a aoa ae NE 
In this way we have expressed z and y as functions of + with 
the aid of the function ¢. It is now still our task to determine § 
as function of rt. Let us now put in 
9%? = u? — 36u? + 324 (1—A’) u 
(see 4th comm. p. 1016) 
(78) 
Benten BOs So, lr alst 1 (70) 
we then find 
EIS OU 
vd — —_— » — —— 
3 27 
By applying the ordinary notation 
143A? 9A7—1 
Ak a7 oa (80) 
we then find 
v= P(t} 9,5 9s) 
1 
=£6[/ pinot peels) 
B ae 1 
Ba pring) C8) 
Before transforming the p-function of Weirrsrrass we wish to 
remind the readers that the roots of # == 0 are 
u, == 0, u, = 18(1+A), u, = 18 (1—A), 
and 
so that 
so that for the roots of v —= 0 (see (79)) we find 
1 . 143) 1—3À 
v, = -- — =-— nn 
ape <3 Gai. gunn’ RTG 
We shall now investigate the relative value of these roots in the 
three cases: II (+ 1CWA<+o), IV (+1 >4>0), VI (Az il) 
(see 4t» comm. p. 1014). 
Case II: +-1cActo 
1* 
