376 M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 
We thus see that ¢ (pv) is given by a series of terms, each of which 
is obtained by means of the preceding one, by differentiating it in re- 
spect to v, multiplying by the ratio ah and integrating the result in 
P ying by aT g 8 
dv 
ee 
respect of p. Thefirst term of this series being / dT, it is evident that 
dv 
the value of ¢ may be easily obtained ; substituting this value in the 
equation (1), we have for the expression of the general integral of the 
partial differential equation 
dQdT_ dQdT _ C 
dudp dpdv 
the formula 
Q=F(T)—C dp 
Se 
dv 
aT dp 
cae i dp 4 pyF 
Se aafF 
‘dv 
aT dT dp 
dp d dp d == 
a Seen ae d 
+90 ot ofthe ae f 2 
we eas eS v 
v dv 
+. 
This equation gives the law of the specific calorics, and of the heat 
disengaged by the variations of the volume and of the pressure of all 
the substances of nature, when the relation which exists between the 
temperature, the volume, and the pressure is known. 
