( 380 ) 
temperature of the gas falls. For a small difference in pressure of 
the gas before the tap and the gas behind the tap the amount has 
been determined by the experiments of KELVIN and JouLE. They 
represent the cooling 7;—T, for air in the empiric formula: 
Ting LE 
7? 
By means of the equation of state we calculate for this cooling |), 
again on the supposition that p,; and ps are small: 
shin we 2 273 2a » ) ( 
ae ee tee ee 
In this formula p,; and p, are expressed in atmospheres, m is the 
molecular weight, c, the specific heat at a constant pressure for the 
gas in a rarefied state. 
If in the equation of state a is a function of the temperature, 
and is to be represented by a , we should find, if 7; and 7 
do not differ much, and p, and pg are small: 
2 273 r 273 \2 7 
7; — To = — E a( == ) =— D| (pari) 2 
m Cp 71) % 
It is still doubtful, which of those two formulae better represents 
the observations of KerLVIN and Joure. It is remarkable how dif- 
ferent a value we find for this cooling, as for everything which 
relates to quantities of heat, if a is a function of the temperature. 
The accurate knowledge of this process has of late proved to be 
more necessary than before, as LINDE has applied this process for 
obtaining very low temperatures and as in LiNpe's apparatus this 
way of expansion is made use of to obtain liquid air. 
Let us represent the energy per unity of weight of the gas under 
the pressure p, by «,- Let the specific volume be vj, and the tem- 
perature 7}. For the gas under the pressure py we represent these 
quantities by &, 2, Jp. Then the process is represented by the 
formula : 
Endpin Pet =&& en esas (gs eine eee) 
or 
1) Die Continuität ete, Ite Auflage Seite 123. 
