M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 351 
source A during its dilatation in contact with it in the first part of the 
process. Let then the volume of gas be A H, and the corresponding 
pressure H K: the gas in this state contains the same absolute quan- 
tity of heat that it did at the moment of commencing the process, when 
it occupied the volume A B under the pressure C B. If therefore 
we remove the body B and continue to compress the gas in an inclosure 
impermeable to heat, until the volume A H is reduced to the volume 
A B, its temperature will successively increase by the evolution of the 
latent caloric, which the compression converts into sensible caloric. 
The pressure will increase in a corresponding ratio; and when the 
volume shall be reduced to A B, the temperature will become T, and 
the pressure B C. In fact, the successive states which the same weight 
of gas experiences are characterized by the volume, the pressure, the 
temperature, and the absolute quantity of caloric which it contains: two 
of these four quantities being known, the other two become known as 
consequences of the former ; thus in the case in question the absolute 
quantity of heat and the volume having become what they were at the 
beginning of the process, we may be certain that the temperature and 
pressure will also be the same as before. Consequently, the unknown 
law according to which the pressure will vary when the volume of 
gas is reduced in its inclosure impermeable to heat, will be represented 
by a curve K C, which will pass through the point C, and in which 
the abscisses always represent the volumes, and the ordinates the 
pressures. 
However, the reduction of the gaseous volume from A G to A B will 
have consumed a quantity of mechanical action which, for the reasons 
we have stated above, will be represented by the two mixtilinear trape- 
ziums F G H K and K H BC. [If we subtract from these two trape- 
ziums the two first, C B D E and E D G F, which represent the quan- 
tity of action during the dilatation of the gas, the difference, which will 
be equal to the sort of curvilinear parallelogram C E F K, will represent 
_ the quantity of action developed in the circle of operations which we have 
just described, and after the completion of which the gas will be pre- 
cisely in the same state in which it was originally. Still, however, the 
entire quantity of heat furnished by the body A to the gas during its di- 
latation by contact with it, passes into the body B during the condensa- 
tion of the gas, which takes place by contact with it. 
- Here, then, we have mechanical force developed by the passage of 
_ aloric from a hot to a cold body, and this transfer is effected without 
_ the contact of bodies of different temperatures. 
_ + The inverse operation is equally possible: thus,we take the same volume 
‘ of gas A B at the temperature T and under the pressure B C, inclose 
_ it in an envelope impermeable to heat, and dilate it until its tempera- 
ture, gradually diminishing, becomes equal to #; we continue the dilatas 
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