M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 369 
M. Dulong has shown that the air, and all the other gases taken at 
the temperature of 0°, and under the pressure 0"-76 of mercury, when 
compressed by “= of their volume, disengage a quantity of heat, ca- 
pable of elevating the same volume of atmospheric air by 0°421. 
Suppose that we operate upon a kilogramme of air occupying a 
volume v = 0°770 of a cubic metre, under the pressure of the atmo- 
sphere p, equivalent to 10230 kilogrammes upon a square metre; we 
have 
pv=R (267 + 4), 
and 
Q=R(B—Clogp). 
If a variation be suddenly effected in v by an infinitely small quan- 
tity dv, without there being any variation in the absolute quantity of 
heat Q, we shall have 
pdv+vdp=Rdi, 
Bie Boh Sond Vi. ode 
and 
or preferably 
dt,, (dB dC dp _ R (Rdt—pdv\ __Rdt—pdv 
— | SS — ee ee — eid 
unt a: 8p Ge) = Fag ) O67 + ¢ 
a dC 
Now R er log P) being the partial differential of Q in re- 
spect of ¢, . ae constant, is nothing else than the specific caloric 
of the air at a constant pressure; it is the number of unities of heat ne- 
cessary to elevate a kilogramme of air under atmospheric pressure by 
one degree; we have therefore 
R (a 7 log p) = = 0-267. 
Then substituting — = for dv, and 0421 for dt, we arrive lastly at 
1 
— — 14). 
(C 
This is the maximum effect producible by a quantity of heat, equal to 
that which would elevate by 1° a kilogramme of water taken at zero, 
passing from a body maintained at 1° to a body maintained at 0° It 
is expressed in kilogrammes raised one metre high. 
_ Having the value of C, which corresponds to ¢ = 0, it is interesting 
to know, setting out from this point, whether C increases or decreases, 
and in what proportion. An experiment of MM. De Laroche and Bé- 
rard upon the variations experienced by the specific caloric of the air, 
