366 M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 
from T to T + dT, we bring it successively into contact with the se- 
cond, the third, and the (x +1)th of these sources, until it has ac- 
quired the temperature of each of them. When, on the contrary, the 
volume v of the body being increased by d v, we wish to give it the tem- 
perature T, we bring it successively into contact with the mth, the 
(n — 1)th, and the first of these sources, until it has acquired the tem- 
perature of each of them. We then return to these sources the heat 
that has been borrowed from them in the first part of the operation; for 
it is not necessary to attend to the differences of an order of inferior mag- 
nitude, arising from changes that may have been produced in the speci- 
fic caloric of the body, in consequence of the variations of v and Q. 
Nothing therefore will have been lost or gained by any of these 
sources, excepting always the source of which the temperature is T+ dT, 
which will have lost the heat necessary to elevate the temperature of the 
body upon which we are operating from T + ae to T+dT, 
and the source maintained at the temperature T, which will have ac- 
quired the heat necessary to reduce the temperature of the same body 
from T ad 
n 
tities of heat may be neglected. 
We see, therefore, that when the body in question, (its temperature 
being thus reduced to T,) is brought into contact with the source of 
heat B, the heat communicated to it from the source A will be all it 
has gained from the commencement of the operation. In consequence 
of the reduction of its volume in contact with the body B, it will be found 
at its original volume and temperature; the quantities Q and P will 
therefore have re-assumed their primitive value; it is therefore certain 
that all the heat borrowed from the source A, and nothing but that heat, 
will have been given to the body B. 
Whence it results that the effect produced, 
dvd T 
dT 
dg 
is owing to the transmission of the heat absorbed by the body subjected 
to the experiment during its contact with the source A, and which has 
afterwards flowed into the source B. 
_ The temperature having remained constant during the contact with 
the source A, it follows that the variations dp and dv of the pressure 
and the volume are connected by the relation 
aT dT 
at —__dv= 
dp es dv.” p 
These variations dp and dv occasion a variation in the absolute quan- 
tity of heat Q, the expression of which is . 
to T. If we suppose x to be infinitely great, these quan- 
