il PRE 
but now that g(w) has the pole a and log (L—x) is multiform, the 
mark can not fall below 1: |a |. The circle G, can here really 
be divided into two parts G' and G’). In the outer rim G") (fig. 2) 
the mark varies between 1 and 1 : fa f; in the inner part G'j,a 
| Ie 1 : 
circle with centre — EE and en: the mark is everywhere 
a— i am <a 
es, |e et 
Ga 
If we wish to calculate log (1 — x) for x = e@%, we must bring a 
circle through the points #(P), 0(O) and + 1(A) and assume the 
centre M of the are OP as the centre of the region Gj. The mark 
of the series is then as low as possible and equal to 
MP Q el 
MAT 14+ @?+1—2¢ cos 6° 
The point a(P) is now situated just on the boundary of G", 
and G';. So for instance for 2 = — 2 we shall assume the centre 
M of G, in x» =—1, ie. we shall put a =2 and the mark of 
the series wil be 4. Indeed we find in this supposition 
B | (ll ee 1 1 
a ( 1)m _os -- 
lon Si See es Se ar En 
a m=1 M 2m =o (2k-++1)22k+1 OT 
a series, bearing distinctly the mark 3. 
