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 O^'TS 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 jo, equivalent to 10230 kilogrammes upon a square metre; we 

 have 



pv = R (267 + 0' 

 and 



Q = R(B-Clogjo). 

 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 = lldt, 

 and 



= R(i^-\ogpi^\dt-RC^, 

 \dt ^^ dt ) p 



or preferably 



^r/'^— log <^C\_j^c?j9_ R /Rdt — pdv\_ Rdt—pdv 

 C V*^^ ^^ dt ) p p\ V ) 261 + t 



Now R { — -rr~ log j9 J being the partial differential of Q in re- 

 spect of t, p remaining 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 



\d-t-d-t''^P)='''^^^' 



Then substituting — - — for dv, and 0*421 for dt, we arrive lastly at 



— = 1*41. 

 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 fi'om this point, whether C increases or decreases, 



and in what proportion. An experiment of MM. De Laroche and Be- 



vard upon the variations experienced by the specific caloric of the air, 



