10 
R, Sz 
ik v-plane 
0 
ie +K Ry 
ico 
| R, plane of 
VIS nT 
sn(v) 64 
+ik 
S3 <—— Rp 
== CO > CO 
S; 
S; 
Ry _ioo 
Fig. 1 
1—A A—1 dn (v) 
1 = 6 4 -= 62 DET ; the quotient — — assumes in those 
2 2 sn (v) 
points successively the values 0, 0, +k’, Eik. The corresponding 
values of » are congruent (mod. 2K and 27K’) with K+ 7K’, 0, 
K and 7K’. (see fig. 1). 
Case IVa. Point O lies in the domain between the hyperbola 
and the asymptotes. The points R,, R,,.S,,S,, 7, and 7, are all real; 
T, and 7, lie both on the same side of the polar line of O as O 
itself. We shall assume that the polar line intersects that branch on 
which 7, lies. The order of the singular points is then S,, R, , 7,, R,, 
SR Tets 
us), ie 
Che. walvesl 10; ey ker L=6{ 4S v6 oa 
) ) 
— 
correspond resp. to the values of 0, oo, +1 and +f for 0)’ 
sn (YP 
thus to the ‚values of » which are congruent (mod. 2K and 27k") 
resp. with 7’, 0, K and A -+ 1K’. (see fig. 2). 
. 
