M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 375 
1000° to 2000° higher than that of the boilers, there is an enormous 
loss of vis viva in the passage of the heat from the furnace into the 
boiler. It is therefore only from the employment of caloric at high 
temperatures, and from the discovery of agents proper to realize its 
motive force, that important improvements may be expected in the art 
of utilizing the mechanical power of heat. 
NOTE. 
The integral of the general equation 
dQ dT _dQdT _ Cc 
CREP CARD igre 
is, as we have seen, 
seen) OO gi prayey vs wets tee). we CN) 
F (T) is an arbitrary function of the temperature T, varying from one 
body to another; C is a function of the temperature which is the same 
for all the substances of nature, and ¢ (p, v) is a particular function of 
p, and of v satisfying the equation 
Ta es FAT ah, he Lk 
This function @ may be determined in the following manner. Let 
dp 
9= faT+¢, 
dv 
be substituted in the equation (2), it will be 
dT dg? adTda¢v aT a [at 
Saree: 
Ras ap PEt “a 
: 4? GT if itte 
SSS v 
du 
¢" satisfying the equation 
‘ pee eT dg aT ea tee’ par 
dv dp dpdv dp ree P ata fi’ 
v 
we shall have equally 
dT aT 
be ie: d 
d d <f 
