( 386 ) 
If we put e.g. T=2 7,, which is the case for air that is cooled 
somewhat below 0° centigrade, we find for the value of v for the 
maximum cooling 2,25, and for the value of v for a cooling = 0 
Dit 
an amount = iG b. For 7 =T;, these values have decreased to 
8 27 
5/.b and — 0. 
25 
By elimination of 7 we find for the locus of the points of maxi- 
mum cooling in the p,v diagram: 
a 2v—3b 
| a er Te 
b v 
1 
If we put —=g (density), we find the parabola : 
v 
. 
TRE 02), 
Pp 5 ( Q 3b 0) 
Ed 
21 
which yields p=0 for g=0 and for o= — 5 The maximum 
J 
Er 1 ; a 
value of p, which is found for GEE equal to sp Or to 
9p, For air (which we treat here for simplicity’s sake as a 
single substance) this minimum pressure amounts to 9 X 39 = 351 
atmospheres. 
To the existence of such a parabola for the points, where pv has 
a minimum value, has been concluded by BELTRAMI from the obser- 
vations concerning pv of AMAGAT. 
For the points, for which the cooling = 0, we find: 
Pinson 
or 
a 
PT De (2 v—b 0?) 
So also a parabola in the p, g diagram. 
By elimination of vj, we get a relation between pj, and 7), which 
has the following form : 
val Vga 
En 1 — ie ae 
wi den 27 T, 27 Ty 
