asymptote u’ =— B on the left, and when 2 <0, or Tr <0, it is 
limited by a vertical asymptote u’ = + Con the right. 
As the real domain never extends beyond w'=— Band w= + C, 
dz . ve 
the slope gaar Hever become negative, and the quantities wv and 
au 
/ 
wu’ are simultaneously maximum and minimum, 
When 6 has a small positive value, u’ = — @ orv’ = O answers 
0 3 : ; 
to v= — oru=log == — A, which is a rather large negative 
 a—o “ a—o 
quantity. So for ¢ > 0 or B<O there exists an inferior limit 
2=A(—- S—wunm) for z, corresponding to u’ = — o@, consequently 
a horizontal asymptote below. 
When rt has a small negative value, vw =-+ © or v’ = + » cor- 
+ Tr (‘ +t 
; OF wi 109 
large positive quantity. So for +< 0 or y > 0 there exists a superior 
limit z=A(+ 7’—u,) for z, corresponding to u' = + oo, conse- 
quently a horizontal asymptote above. 
From (10) we find | 
en ae OS Ae Ie) (14) 
—tv' +(a—o) —tv' + (4— 0) (a—o) (yo'+1) 
and so conclude that in the real domain v—v’ has the sign of 
tT’ +0. 
When + and o are both positive, we have always v'<v or 
wu’ <u, so that the erroneous curve (w',z) has for equal z a smaller 
u than the true straight line. The curve is as it were generated by 
shifting (and deforming) the true line to the left. 
When o and rt are both negative, we have everywhere v' << v or 
u' <u, so that the erroneous curve (w',z) is as it were generated 
by shifting to the right. | 
responds to v = 
et 
) = + 7’, which is a rather 
0 
When o and rv have opposite signs, there is a real point, v’ = zo 
for which v’ =v and consequently wu’ =u. Then the erroneous 
T 
When o >0 and +< 0, we have u’ <u, or.v—v’ > 0, for 
Kij 
curve cuts the true straight line in a point u’ = u = log (— : ) =d; 
6 * . . . 
v’ << —-, or u’ <A. Then at the left of u’ =A the provisional 
T 
curve (w’,2) is on the left side of the true straight line and to the 
right of wu’ = A it is on the right side of this line. 
When «o < 0 and 'r > 0, we- have w'-< u, orv—v' > 0 or 
