(82 
By the skeleton arc R,P,F, we understand the arc of simple 
curve obtained by following from Zè, first the path R,P,, then 
recurring W, up to its point of intersection with D,/’, and finally 
following this path to /. 
This skeleton arc /’,P,#,, its image /,p,r,, and its counterimage 
F,x,0, meet neither each other, nor the path w. Farthermore F,77,9, 
cuts neither the path D,/,, nor its image d,/,, f,p,7, cuts neither 
the path D,F,, nor its counterimage d,r,, and /,P,h, cuts neither 
the path d,r,, nor the path ¢, /,. 
The arcs P,F, and 0,7, we join by an arc of simple curve K,L,, 
belonging to an approximating polygonal line .,(r, >> 1), and abroad 
from its endpoints cutting neither the skeleton ares R,P,F,, 0,7,F, 
N 
and 7,7; 7,, nor the“ paths 2, D;K), die, and dpy,\ Nori ows 
image kl 
The ares 7,y, and zr‚r, we join by an arc of simple curve A, H., 
belonging to an approximating polygonal line P.(r >>r, and t >r,), 
and abroad from its endpoints cutting neither the paths £,G, and 
D,F,, nor their images ¢,y, and d,f,, nor the skeleton arcs 2, PG, 
ot Omron RPF, and r,p, f,, nor the joining arcs ALA 
and k,J,. 
Out of H,H, and straight paths drawn from there to p we finally 
construct skeleton ares in the same way as above out of A,Z,. 
We have now built up a simple closed curve P,K,/,2,H,H,7, 
L,K,P,R,R,P,, and, after addition of the image :27,9,7,p, of the are 
P,R,R,P, drawn splintered in the figure, a second simple closed 
curve %,H,H,2,L,K,P,l,k,p.7,9,%,. These two closed curves have 
the arc 2,H,H,2,L,K,P, in common, and this arc has for both 
closed curves the same inner side, so that it is not separated 
from the infmite by the two completing ares P,R,R,PK,L,2, and 
Pe To Hs. 
The first closed curve we represent by ©, and it is our aim to 
find the total angular variation of the transformation vector for a 
positive circuit of €. 
To this end we can during the description of the are P, A, La, 1, H,a, 
substitute in the curve described by the endpoint of the transforma- 
tion vector for each image skeleton are a path are according to the 
method of $ 2, with the restriction that here we are always in the 
case 1st of that §. After that substitution the curve described by the 
vector endpoint passes nowhere outside €, whilst its first and its 
last point have remained the same, and the total angular variation 
of the vector has not changed. 
