( 720 ) 
So there is certainly a domain or a set of domains G, common 
to all the inner domains of the corves Uk, and to the boundary of G 
belong all points of the limit set X of the Uk s } which are not points 
zero, thus also all points of X, which are points zero, as the latter are 
limit points of the former ones. So the boundary of G is identical 
to the limit set of the u; c ’s, is therefore coherent and identical to 
its outer circumference , whilst abroad from the points zero it consists 
of tangent curves to the vector distribution, which on account of the 
existence of the domain g can show nowhere in a non-singular point 
the character mentioned in theorem 1 sub 3. 
We shall now show that a tangent curve r' belonging to the boun¬ 
dary of G cannot have the property of r, that its pursuing or 
recurring branch converges spirally to the boundary of a domain or 
set of domains G'. 
We should then namely be able to form, in the same way as was 
done above and in the first communication for r, also for r' a closed 
curve u’k consisting of a geodetic arc ^ i fi tjb and an arc tp' of r', 
joining the same two points K! and H r . And there would exist arcs 
of r which would converge uniformly to <p' from the same side, e.g. 
from the inner side of u\. But when pursuing such an arc tp of r 
situated in sufficient vicinity of <jp', we should never be able to return 
between tp and q>'. 
As furthermore in the case considered here, that the pursuing branch 
of r lies in the inner domain of u lf it is also excluded, that r' 
reaches the boundary of y, only one form remains possible for /, 
namely that of an arc of simple curve, starting from a point zero, 
and stopping at a point zero. (For the rest these two end points can 
very well be identical). 
Of such tangent curves there can be in the boundary of G at 
most two, which possess the same end points, when these end points 
are ditferent; but there can be an infinite number, which are closed 
in the same point zero. Of these however there are only a finite 
number, of which the extent surpasses an arbitrarily assumed finite 
limit. For, each of these contributes to G a domain with an area, 
which surpasses a certain finite value. 
The curves r' whose extent surpasses a certain finite limit are run 
along by a u k of sufficient high index in the same order, as they 
succeed each other on the outer circumference of G. From this 
ensues that for all curves the pursuing sense belongs to the same 
sense of circuit of the outer circumference of G. 
