178 Transactio7is of the Royal Society of South Africa. 
1 
3. 
(Kg. 3.) 
Modular surface obtained by rotating a rectangular hyperbola about 
an asymptote. 
Stream lines given by — 
sin 2d = constant, 
a family of rectangular hyper- 
bolas asymptotic to the real and 
imaginary axes. Origin an 
infinite point. 
Note the infinite curvature 
at origin. 
4. (i.) w^k{z + a)z{z — b) 
(Fig. 4), 
where a and b are real and 
positive. 
[In the model constructed — 
Fig. 3. 
k = -02, a = 5, 6 = 10, 
unit of length a centimetre.] 
Modular surface rises from three 
zeros, and tends to a paraboloid of 
revolution of the third degree at 
infinity. 
Stream lines might be found by 
method (3), but more easily plotted 
by method (1). They tend to Ber- 
noulli's lemniscates at infinity, as in 
Fig. 6. 
(ii.) w^k(z^ + cc^) {z -b). 
(Fig. 5.) 
[In models constructed — Fig. 4. 
A; = -01, a = 4:JS, b = 12, 
.6., three zeros at angular points of equilateral triangle.] 
