We find the maximum value of p, at 7= 83 7,, and as has been 
mentioned before, it is equal to 9 p,. So for air 9 X 39 = 351. 
For T=2 7, we find p; = 304 atmospheres, and for 
es Ty pi = 100 = 
The constant value which has been chosen in the apparatus of 
LINDE, may be considered as an arithmetical mean of the most ad- 
vantageous pressure at the beginning and that at the end of the process. 
But at the same time we may conclude from the circumstance 
that pj is a function of 7), that an apparatus, which would work 
theoretically perfectly, should be able to regulate the pressure pi 
according to the temperature which reigns in the inner spiral. 
The numeric values of the pressure, and the limits of the tem- 
perature which have been found, will be different according to the 
equation of state which is used. But though we cannot warrant the 
absolute accuracy of the numeric values in consequence of the in- 
accuracies of the equation of state, yet we may prove, that from 
every equation of state, which properly accounts for the course of 
the product pv, as found experimentally, the existence of a pressure, 
for which the cooling is equal to 0, follows, and so also the existence 
of a pressure, for which the cooling has a maximum value. For as 
long as prvi <P2v, the resulting external work will promote 
cooling. This influence is greatest for a pressure, at which pie, has 
a minimum value. If p, 7 is again equal to pv, the cooling has 
the same value as it has in case of perfectly free expansion. But 
if the pressure is still higher, »;% rises above py vs, and approaches 
infinitely to a limiting value which is oo, so that every cooling 
which would be the immediate result of free expansion, may be 
neutralized by that of pj vj — pov). Only if we should assume also 
an infinite value for the cooling caused by free expansion, the above 
reasoning would not be convincing. But then, nobody will assume this. 
We may represent the maximum cooling in the following simple 
form: ’ 
7 7 2 218 - 26 ( b \ 
ae eae m Cp b vi 
or 
Pr Beh orn re, 4 ies 7, )2 
To ce oar aa a 27, J 
or 
28* 
