M.CLAPEYRON ON THE MOTIVE POWER OF HEAT. 349 
production of the mechanical force is attended by the passage of a part 
of the heat which is developed by combustion in the furnace, the tem- 
perature of which is very high, into the water in the condenser, the tem: 
perature of which is much lower. 
Reciprocally, it is always possible to render the passage of caloric from 
a hot to a cold body useful for the production of a mechanical force : 
to obtain this it is sufficient to construct a machine resembling an ordi- 
nary steam-engine, in which the heated body serves to produce steam 
and the cold one to condense it. It results from this that there is a loss 
of vis viva, of mechanical force, or of quantity of action, whenever im- 
mediate contact takes place between two bodies of different tempera- 
tures, and heat passes from the one into the other without traversing 
an intermediate body ; therefore in every machine intended to make ef- 
ficient the motive force developed by heat, there is a loss of power when- 
ever a direct communication of heat takes place between bodies of dif- 
ferent temperatures, and consequently the maximum of the effect pro- 
duced cannot be obtained but by means of a machine in which only 
bodies of equal temperature are brought into contact. Now the know- 
ledge we possess of the theory of gases and vapours shows the possibi- 
lity of attaining this object. 
Let us, then, suppose two bodies retained, one at a temperature T, 
and another at an inferior temperature ¢; such, for example, as the sides 
of a steam-boiler, in which the heat developed by combustion constantly 
supplies the place of that which the steam produced carries away ; and 
the condenser of the common atmospheric engine, in which a current of 
cold water removes, every moment, both the heat which the steam loses in 
condensing, and that which belongs to its proper temperature. For the 
sake of simplicity we will call the first body A and the second B. 
Let us now take any gas whatever, at the temperature T, and bring it 
into contact with the’source of heat A, representing its volume v» by the 
absciss A B, and its pressure by the ordinate C B (fig 1). 
If the gas is inclosed in an extensible vessel, and which is allowed to 
extend in a void space in which it cannot lose heat either by radiation or 
by contact, the source of heat A will supply it, from moment to moment, 
with the quantity of caloric which its increase of volume renders latent, 
and it will preserve the same temperature T. Its pressure, on the con- 
trary, will diminish according to the law of Mariotte. The law of this 
variation may be represented by a curve C E, of which the volumes will 
be the abscisses, and the corresponding pressures the ordinates. 
Supposing the dilatation of the gas to continue until the volume A B 
has become A D, and that the pressure corresponding to this new vo- 
lume is D E, the gas during its dilatation will have developed a quan- 
__ tity of mechanical action, which will have for its value the integral of the 
_ product of the pressure by the differential of the volume,. and which 
: 2B 2 
