923 
F* meet everywhere from the same side of a. Suppose a carries a 
point P, such that the branches meeting on a at P are connected 
on both sides of a. Then there exists a plane through P, not con- 
taining a and in which P is double point. The reasoning used for 
the second case (p. 921) again reduces this to a contradiction. Hence 
every point (F4) of a is internal to an interval along which the 
sectors meet from the same side of «. The note at the bottom of 
the preceding page completes the demonstration. 
Along a triple line in @ the sectors obviously meet everywhere 
from opposite sides of a. 
$ 2. In this $ we intend to give some corrections and additions 
to comm. 3 (p. 736—748). 
p. 740 and 741. The reasoning sub II (p. 740) is incomplete and 
starting at line 3 (p. 741) to be replaced by the following: Let d, 
turning round c, converge towards a, first from one and then from 
the other side. In both cases the loop of the curve in d contracts 
towards A, for if the loops converged towards a finite segment of 
a, then each of the converging planes would contain 3 branches, 
with only one common point (A) and breadths larger than some 
finite constant. These would converge towards a single linesegment 
in the limiting plane, which circumstance contradicts the assumption 
that #* is a twodimensional continnum. Hence only the principal 
branches of the enrve in d converge towards a. 
We consider a certain plane d. Let AP, AQ and AR be the 
branches departing in d on the same side of c, AQ really being the 
middle one. The two semilines in which A divides a, are connected 
on that same side of. « by a sector which crosses d along the 
branches AP, AQ and AR successively. If d converges from the 
one side towards «, the outside branch on the side of AP converges 
towards a and turning d in the opposite direction, the branch corre- 
sponding to AQ merges in a. In both cases this is a principal branch 
and as one of the outside branches belongs to the loop, there must 
somewhere be a change from principal branch to loop branch, and 
this means a degeneration. This contradicts the assumption that a 
is the only line of #* through A. 
p. 743 line 11 says: “If A is the only limiting point, then the 
contracting ovals would give to A the character of a point of a 
twodimensional continuum’. Here it has been overlooked that A does 
not belong to the contracting region, defined by the ovals on F°, 
but to these ovals themselves. This necessitates further consideration 
60* 
