M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 365 
body by a quantity 6c, in such a manner that all the heat developed 
by the diminution of volume may be absorbed by the body B, and the 
temperature remain equal to its primitive value T. The volume V also 
again becoming the same as it was at the commencement of the opera- 
tion, it is certain that the pressure will return to its primitive value 6 d, 
as will also the absolute quantity of heat Q. 
If we now connect the four points f, g, e, d by right lines we shall form 
a quadrilateral figure, the area of which will measure the quantity of 
action developed during the operation described. Now it is easy to see 
that fg and de are two elements infinitely near, described upon two 
curves infinitely near, the equations of which will be T + dT = const. 
and T = const. They ought therefore to be considered as parallel ; the 
two ordinates which terminate the quadrilateral figure in the other di- 
rection being also parallel, the figure is parallelogrammical, and mea- 
sures be X df. 
Now fd is nothing but the increase experienced by the pressure p, 
the volume v remaining constant, and T becoming T + dT. We have 
therefore 
_ dp 
df= ape b 
whence 
tea] 
fd= TT d T. 
dp 
And be being the increase of volume dv 
EP ET 
SdXbe= ar 
dp 
It only remains to determine the heat consumed in the production of 
this quantity of mechanical action. 
_ We have first raised the temperature of the body subjected to expe- 
_riment by the quantity dT without changing its primitive volume v; 
_ afterwards, when it had become v + dv, we have lowered its tempera- 
ture by the same quantity d T without varying its primitive volume 
-¥+dv. Now it may easily be seen that this double Operation can 
be effected without loss of heat; let us suppose that 2 being a number 
indefinitely great, the interval of temperature dT be divided into a 
number 2 of new intervals cae and that we have + 1 sources of 
heat maintained at the ere T,; TF we es 
ap Se UG™ and T +47. 
To raise the temperature of the body upon which we are operating 
2c2 
