M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 373 



would conduce to the determination of several other important elements 

 of the theory of heat, with regard to which we know nothing, or have 

 arrived by our experiments at very insufficient approximations only. 

 In this number may be included the heat disengaged by the compression 

 of solid or liquid bodies ; the theory that we have enunciated enables 

 us to determine it numerically for all the values of the temperature for 

 which the function C is known in a manner sufficiently exact, that is to 

 say, from t = to t = 224°. 



We have seen that the heat disengaged by the augmentation of 

 pressure dp is equal to the dilatation by the heat of the body subjected 

 to experiment, multiplied by C. With regard to the air taken at zeroi, 

 the quantity of heat disengaged may be directly deduced from the ex- 

 periments upon sound in the following manner. 



M. Dulong has shown that a compression of ^ raises the tempera- 

 ture of a volume of air taken at zero by 0°-42I. Now the 0-267 unity 

 of heat necessary to elevate a kilogramme of air taken at zero under a 

 constant pressure by 1°, are equal to the heat necessary to maintain the 

 temperature of the gas dilated by — - of its volume at zero, above the 

 heat necessary to elevate the dilated volume, maintained constant, by 

 1°^; the last is equal to — — of the first ; their sum is therefore equal 



to the first multiplied by 1 + _A^ ; the former therefore, that is the 

 heat necessary to maintain the temperature of 1 kil. of air, dilated by 

 — of its volume, at zero, is equal to (0-267) = (l + /^ Y or to 

 0-07911. 



We arrive at the same results by the application of the formula 

 Q = R (B - C log jo), 



whence 



f/Q = RC— , 



putting C = ^, and observing that a diminution of volume of — 



corresponds to an increase of pressure equal to ^ of an atmosphere. 



Knowing the quantity of heat disengaged from gases by compression, 

 to ascertain that which a similar pressure would disengage from any 

 substance whatever, from iron for example, we write the proportion : 

 0-0791 1 of heat disengaged by a volume of air equal to 0-77 of a cubic 

 metre, subjected to an increase of pressure equal to — of an at- 



