180 Transactions of the Boyal Society of South Africa. 
6. iD=eK (Fig. 8.) 
Modular surface cylindrical, with generators parallel to imaginary axis. 
Vertical section the exponential 
curve. 
Stream lines best found by 
method (2), by solving — 
dy 
giving— 
^r + c = log (+ sin^/), 
a system of curves asymptotic to — 
Fig. 8. 
2(; = cos z. 
(Fig. 9.) 
[In model constructed, unit of length = 3 centimetres.] 
Here— 
W = ^ (cosh 2y + cos 2x). 
Modular surface rises from in- 
finite row of zeros — 
and rapidly tends to become cylin- 
drical, with generators parallel to 
real axis. 
Vertical section through real axis 
gives cos X, with lower parts in- 
vertedj and is shown in upper part 
of figure. 
Vertical sections through imagi- 
nary axis and parallel to it at dis- 
tance ^TT give cosh y and sinh y respectively, and are shown by thick and 
dotted lines in lower part of figure. 
Fig. 9. 
