540 
0 
t’ +0 >0 for v’ >—-—or wu’ > A. The disposition is then the 
T 
inverse of that of the last case. 
When o=0O, or B=0, we have B=om, S= ws A = — oo. So, 
the left and lower asymptotes being at infinity, also the point of 
intersection A is at infinite distance to the left. 
When t=O or y=0, we have C=om, T=o and A Jo. 
Now the right and upper asymptotes are at infinity, the point A 
being at infinite distance to the right. 
We now consider the curvature and the point of inflexion. For this latter 
l*z oa 
: —= 0 holds, or — yv?+f=0, or o'= + ze — ae Ne) : 
du’ Y t(a +1) 
The point of inflexion is real when o and r, the errors in «,' and w,/, 
have opposite signs. 
Lz 
When 6: >'0, 7 <0; of p> 0, y > 0) twe thave aa 
U 
EBR WI [Ys so that left of the point of inflexion the curve 
fi 
is convex downward. 
For the slope 4 of the inflexion tangent we find 
3 
2 day Ze 
lz / 4 ase he 
as i = 4 — ded 
du’ ahd @ 
7 
2 — Ais 
3 3 1 +83 
(exe ea 1) ee 
¥ y 
2 
d 
When 0 <0, r>0, or B< 0, 7 <0, we have = 
u 
3 
‘ t . 
TOE We > WE so that the curve is convex downward to the 
a 
right of the point of inflexion. 
To find the slope 2 of the inflexion tangent we put 
== 0 YET 
and so obtain: 
B, 
MLB, ai 
i) ee ome Ys aye Bi el 
"V5 
du’ 
a F's ee 
t= C7 B's n 122 
(5e) Dt 1) : Pay Ags 
When o=—0O, or 8==0, the point of inflexion lies to the left at 
infinity and its inflexion asymptote is parallel with the true straight line. 
When t=O or y=0O, the point of inflexion lies to the right at 
