M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 359° 
whence 
and consequently 
Rdt mr 
OS ee Cae Or 
“dev Pap 
The function C by which the logarithm of the pressure in the 
value of Q is multiplied is, as we see, of great importance; it is inde- 
pendent of the nature of the gases, and is a function of the temperature 
alone; it is essentially positive, and serves as a measure of the maximum 
quantity of action developed by the heat. 
We have seen that of the four quantities Q, 4 p, and v, two being 
known, the other two follow from them ; they ought therefore to be 
united together by two equations; one of them, 
pr= R (267 ae t), 
results from the combined laws of Mariotte and Gay-Lussac. The 
equation 
Q=R (B—C lg p), 
deduced from our theory, is the second. However, the numerical dex 
termination of the alterations produced in the gases, when the volume 
and the pressure are varied in an arbitrary manner, requires a know- 
ledge of the functions B and C. 
We shall see upon another occasion that a value approaching to ‘te 
function C may be obtained through a considerable extent of the ther- 
mometrical scale; besides, being determined for one gas it will be de- 
termined for all. As to the function B, it may vary in different gases; 
however, it is probable that it is the same for all the simple gases: that 
they all have the same capacity for heat, is at least the apparent result 
of the indications of experiment. 
Let us refurn to the equation 
Q=R (B—C logp). 
ea will compress a gas oceupy ing the volume v, under the pressure 
p, until the volume becomes v', and allow it to cool till the tempera- 
ture sinks to the same point. Let p’ be the new value of the pressure; 
let Q’ be the new value of Q; we shall have 
= 2) 
Q—Q=RC log = RC log 5. 
The function C being the same for all the gases, it is evident that 
equal volumes of all the elastic fluids, taken at the same temperature 
and under the same pressure, being compressed or expanded by the same 
_ fraction of their volume, disengage or absorb the same absolute quantity 
_ of heat. This law M. Dulong has deduced from direct experiment. - 
