(GEN ) 
points, and inner arcs, consists of ares (not closed sets of points), 
which we shall call outer arcs of ka resp. k',. Between the end- 
points of an inner are of £, runs an outer are of #,, and inversely. 
Each inner are of /:, encloses with the corresponding outer arc 
of k', a domain lying inside /, and inside 4’,, thus outside yz. 
Each inner are of 4’, encloses with the corresponding outer are 
of k, a domain lying outside /% and outside #,, thus likewise 
outside y,. To this however ove inner are of £', forms an exception: 
it encloses with the corresponding outer are of 4; a domain con- 
taining the inner domain of #£, and also the domain yz. 
We shall now run along the boundary of y, in opposite direction 
of the hands, starting somewhere on that special inner are of &’z: in 
this way the row of dividing points and dividing ares, or, as we shall 
call it, the row of elements of y. gets a first and a last element. 
Accordingly. in fig. 1. (which is special in as far as the elements 
appear only as dividing points and only in finite number) the elements 
are numbered from 1 to 8. 
We look upon all those dividing points and dividing ares as 
elements of 4, and we determine their images on /. After that we 
suppose each outer are to be laid along the corresponding inner are 
by a continuous one-one representation ; in this way all the images 
of the elements of y find their places on its boundary and we inves- 
tigate for each element of y,, whether when describing the boundary of 
ya in the opposite direction of the hands we find it gaining or losing 
on its image on #',*). (That a dividing are as a whole gains or as 
a whole loses, follows from the absence of an invariant point). To 
an element of the first species we assign the sign d; to one of the 
second species the sign p. These signs are unequivocally determined, 
except in the case, that all the elements should have to have the 
same sign, for which we can then take either p or d. 
We divide this row of elements into a succession of groups as 
extensive as possible, containing each only equal signs ; then before 
the first and after the last element of each group &, and 4’, lie out- 
side each other during ares, whose extension does not fall below a 
certain minimum. 
If such a group lies between two inner arcs of the same curve, 
1) True, the difference in argument between an element and its image is deter- 
mined only save an entire number of circuils; however a fixed choice for one 
of the elements includes a fixed choice for all. We can arrange that difference 
to be for all elements in absolute value smaller than a circuit; this is possible 
either in one or in two ways. In the first case is determined unequivocally, which 
elements gain on their images and which lose. In the second case they may be 
regarded arbitrarily as all gaining or as all losing on their images. 
