Fig. 3. 
Case Vla. Point O lies on the concave side of the hyperbola: 
S,, S,, 7, and 7, are real, A, and R, are imaginary. Let 7, be 
“the point of intersection of the diameter through O lying on the 
same side of the polar line as O itself. 
v-plane 
Loo cn(v) 
plane of —_-———_ 
sn(p).dn(v) 
he A 
1+in! li)! 
The values ==, Tris (A 2 a ee 
ait 
correspond here respectively to the values 0, oo, + toa and 
ae 
thus to the values of » which are 
afl iN en(v) 
bel ee type 
i Li)’ sn(v) .dn(v) 
congruent (mod. 2K and K+7K’) with K,0, 4 (A+37K’), + (Kik! 
(see fig. 4). 
Case VIb. Point O lies outside the ellipse; A, R,, 7, and 7, 
are real, S, and S, are imaginary. The point of intersection 7, may 
lie on the same side of the polar line as O itself. 
For the particular values of J and the corresponding values of 
vp we can refer to Vla. (see fig. 5). 
