M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 367 
+ 
(a 
dQ Ot? NEON ON as 
dQ= ne i aa dv dp TN 
(7) 
| 
such is the quantity of heat consumed in the production of the effect 
that we have just calculated. The effect produced by a quantity of heat 
equal to unity will therefore be 
dT 
4G) dio dO dT 
It will be shown, as in the case of the gases, that this effect produced, 
is the largest which it is possible to realize; and as all the substances of 
nature may be employed, in the manner that has just been indicated, 
to produce this maximum effect, it is necessarily the same for all. 
When this theory has been applied specially to the gases, we have 
called = the coefficient of d T in the expression of this maximum quan- 
tity of action; the equation therefore of all thesubstances of nature, solid, 
liquid, or gaseous, will be 
in which C is a function of the temperature which is the same for all. 
For the gases we have 
T = — 267 + 4 pr, 
whence we deduce 
The preceding equation applied to the gases takes therefore the 
form ; 
dQ dQ _ as q 
Vide —Pdp — RC=F(p,v): 
it is the equation at which we have already arrived, and of which the 
_ integral is 
; Q=R(B— Clogp); 
that of the general equation 
1s of the form 
Q= F(T) —C¢@,); 
_ F(T) is an arbitrary function of the temperature, and ¢ (p, v) a parti- 
cular function satisfying the equation 
