M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 851 



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 \olume 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 unknowri 

 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 B C. 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 

 caloric 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 t ; we continue the dilata* 



