321 



Theorem 4 shows that B eaiiiiot be elliptical, hence B is 

 parabolical or hyperbolical. In the former case the points .4' and ^" 

 would {theorem 8) prescribe opposite directions for the cuspidal 

 branches departing from B-. a contradiction. 



Remains the case that B is hyperbolical. Let a be the tangent al 

 B in «. Now A' and A" prescribe opposite directions for that branch 

 of the loop in the tangent plane of 7i, which has a for tangent, 

 (the loops trail behind and cannot switch round discontinuously). 

 Hence once more a contradiction is obtained. 



CORRIGENDUM. 



In the tirst communication on this subject page 103 line 1 and 2, 

 for: "twodimensional continuum" read "closed twodimensional 

 continuum". * 



