( 629 ) 
If we consider how the region of divergence G3 is formed, that 
is in what way the u-circle is represented in the z-plane by the 
equation 
1— (l—w u) 
2 ae ae a ssl, 
we then come to the-eonclusion that for each point « within the 
eirele or on the circumference of the circle only one point « of Go is 
found and reversely. So Gg is a region simply connected, enclosing 
T=e and divided from the region of convergence G, by a closed 
eurve not cutting itself, passing through «= 1 and enclosing the 
origin. Evidently the curve les symmetrically with respect to the axis 
of the real quantities. We now extend the circle unity in the #-plane 
and consider how on account of that the image of this circle extends 
in the z-plane, 
oe : ; ; 
As long as |u| is < 7 still a single point # remains belonging 
‘ 
to one point wv and reversely. So the rim in the u-plane between the 
5 ier. 
circles with the radii 1 and — is represented point for point on an 
u 
annular region G," surrounded entirely on the outer side by Gs. On 
the inner side Gj’ is closed in by the representation of the circle 
1 ; A Ld 8 
lul = —, a curve still passing round the origin and with an angular 
u | 
point in the point «=. The angle is directed towards #=—=0 and 
has the value of /a (fig. 7). So of the z-plane remains after deduc- 
Biga: 
tion of the regions Gs and G," another part, the region Gj’ containing 
the origin and extending in the direction of the real axis from 
N 
LTS EN 
en APE 
