( 804 ) 



A^' resp. t't ; the segment cat off trom t resp. m' by ^'^ we represent 

 b}^ x\ resp. n' ; the part of t contained between the endpoints of 

 ''^\ and ''^.V^ we represent bj t' . The arcs r', f\ \p',, t' ^\, ijl form 

 together a polygon '^' ; 1 lies outside this polygon. For the lengths 

 of the transformation vector and of the inverse transformation vector 

 inside ^P' there exists a certain minimum /.. Let / be a quantity 



smaller thaii (n and smaller than — ir. then we take care to choose 



./' 8 



f so small that 



^1,^1,1 1 1 



0_ Old .J_j Oj OiJ 



We divide ^^'^ and 'p'^ into segments in which the distance of the 

 endpoints lies between — /and — ƒ, and the distance of two arbitrary 



8 



3 



points is smaller than — ƒ. From the points separating these segments 



we draw to 7 -\- c -\- r' -j- r" rectilinear paths whose lengths lie 



1 3 



between — f and — f, but among ihese paths we retain only those 



whose endpoints do not lie on r, r' or r". These remaining paths 

 determine together with ?/;', in', r\, and t\ skeleton arcs lying 

 against ^^.V^ and ^X''^, and not meeting their counterimage skeleton 

 arcs, whilst these counterimage skeleton arcs can meet neither /• nor r'. 

 The last point of intersection with 'P', of the counterimage skeleton 

 arc s separating Q' from the infinite, we represent by L ; the image 

 of L we represent by L', the image of s by s\ the first point of 

 intersection of r with '^V by E, the image of E by E' . 



A), s' is separated by s from the infinite. 

 Our aim is to find the total angular varia- 

 tion («1 of the inverse transformation vector 

 for a positive circuit of the polygon ^', 

 and we represent by Xi the total angle 

 described by the inverse transformation 

 ".^ vector from P' to L' along ^' ; by -/z the 

 total angular variation of a nowhere 

 vanishing vector of which the origin runs 

 from P' to L' along ^' , and the endpoint 

 as a continuous function of the origin 

 from P to L along path arcs nowhere 

 passing outside ^', constructed according 

 FiR-. la. 



