( 699 ) 
with a continuous course. We shall here chiefly consider the pro- 
jection on the 7’, «-plane. This projection will possess a lowest and 
a highest point, and be enclosed on the right and on the left between 
a minimum and a maximum value of 2, which two values of « are 
the same as those between which the v,2-projection is enclosed. But 
the highest and the lowest point of the 7’-projection is no special 
point in the v,v-projection. Only in this v,2-projection the points 
2 
d 
mentioned have the property that a line er =0 and also a line 
Vv 
aw : ENE eis ; 
i touches this v,v-projection at the minimum or the maximum 
x 
temperature. At all temperatures between this minimum and this 
maximum temperature the v,v-projection is intersected by a line 
dp B dp f 
—— = 0 in two points, and also by a line —- == 0. But this contact 
dv? dx? 
can take place e.g. for the minimum temperature in a point that 
lies either on the left or on the right of the point in which v has 
the minimum value, and even, but in special cases, exactly in that 
ae? | 
point. So the quantity a, en be both positive and negative for the 
& 
point in which 7’ is maximum. 
This holds also for the point where 7’ is maximum, but generally 
the first mentioned point is of greater importance. 
dv 
If for this first-mentioned point a is positive, this is also the case 
Hij 
dee rde 
with 7 for the point in which —=0 touches the closed curve, 
& v 
dp  d*w dv d? 
; ———_ + —— = 0, th anti 
and as EEP UE ST ‚the quantity en 
will be negative in the 
3 
point in which 7’ is minimum. In the same way the quantity ER 
& 
d 
is positive, and is positive for that point because also the line 
U 
a? d? 
uae 0 touches, and so men 
da” dax? 
dw dv 
be bata k 
Ido © and the contact takes 
d? 
place in such a way that the whole closed curve lies inside Te =0, 
av 
If the minimum temperature should just happen to be in the point 
dv 
of the closed curve where ao eu we have at the same time 
ax 
