( 301 ) 



An arc of simple curve joining two points of the ciiciimference 



of ff, and for the rest not meeting y, will be called a .skeleton arc. 



We surround q by a fundamental series of polygons ^P^, ^^/Pj,... 



approximating rf ^^ distances s„ e^. f.,, ( f/,+i <^ ^ 8/, J . The side 



of the largest square whose inner domain lies between ^P„ and ff , 

 we represent by en; for indefinitely increasing n we find thai e,, 

 converges to zero. 



Each polygon '^t we divide into segments in which the distance 

 of (he endpoints lies between 4?/,, and 12?/,, and the distance of two 

 arbitrary points does not exceed 24g/, , and we draw from the points 

 which separate these segments, to ff paths <^ 2f/, not intersecting 

 each other, and cutting each polygon '^„ (n > k) only once. Each 

 two of these paths which immediately succeed each other, form 

 together with the segment of % connecting them a skeleton arc. 



We first suppose that the Schnitt S^ is not determined by an 

 accessible point, and we choose on a fundamental series ofpol^^gons 

 ^^«1 , *^a., , • . • a fundamental series of skeleton arcs .s\^ ,Sa^, . . . , not 

 intersecting each other, converging to a single point P, and all 

 containing between their endpoints the Schnitt aSj . The arc of ^j, 

 belonging to .'>'y. we shall represent by (j^ • 



We then construct an arc of simple curve b ending in P, inter- 

 secting each element s^ of a certain fundamental series s^^ , s-„ , . . . 



(contained in the series of the .sv ) once and onlv once in a point 



Pz of Oz , and passing there from the outside of ö-- to its inner 



/> ^ /' 'p 



side. The part of b contained between P^ , and P- we represent 



I- iJ—\ -p t- 



by bz , the part of ^Pr preceding resp. following qz , and lying inside 



6'r _ , by tz^ resp. Vz . Then it is impossible that as well the part 



of tz lying to the right of bz , as the part oïvz lying to the left of 



bz , converge to zero; for, in that case P would be an accessible point. 



So out of the series of the tp we can select such a fundamental 

 series /i^ , /?j , . . . (preceded in the series of the r^ successively by the 

 elements )\ ,Y^,-- ■), and determine to that series such a quantitj' c 

 that for each [i^j is attained on e. g. the part of t^s lying to the right 



of 6^5 a maximum distance > 32c from P by a certain point (3,2 



whilst neither óy , nor s^ , nor b^s reach a distance > c from P, 



and fy as well as e^ are <' c. 



Then on r^g lies a point R^^ which can be joined with Q^s inside 



21* 



