( 388 ) 
From this we find at 7, = 2 7, the value 55°. 
Properly speaking we ought to subtract a certain amount from 
this 55°, because the opposed pz may not be neglected. Let us put 
it at 0,265 x 20. Then we may at 7; =2T, put the cooling at 
50°, if the opposed pressure amounts to 20 atm. and p, has the most 
advantageous value. According to the approximating formula we should 
find somewhat more than 75°. 
For decreasing values of 7; the maximum value increases, as 
EE ae 
a7 anf increases wit js 
= we write: 
Pyle RIS 5 At 4 
T= Dy Cp l 27 zn 
ip r 5 fe Sle 
it appears that if 7 hes the same value, ED has also the same 
x % 
value for all gases for which me, has the same value, and this is 
the case for all those whose molecules contain two ate: 
If we write: 
mC, (Ly mia He ah Fie a 2 
TC 27 iP 
mn 
1 NE 
we conclude, that at the same value of a the heat annihilated by 
1 
x 
the expansion is for all substances an equal fraction of 7, of Tj, 
and so of the vis viva of the progressive motion. 
It need scarcely be observed that if the expansion could have 
taken place in an adiabatic way, the cooling would have been much 
more considerable. 
From the equation of state: 
(rr) (aaa, 
follows for the course of the isentropic line: 
Cp aoe 
in which # represents the value of eS at infinite rarefaction. 
Cy 
By elimination of p we find T(v — b)*-1= 05. 
