8 Mr. W. J. M. Rankiue ow the Mechanical Effect of Heat 



So that if Kv be the dynamical specific heat of the body at con- 

 stant volume, the final cooling efibct is 



If the substance were a perfect gas, then 



and the first integral would be null. But no existing gas is 



dV . P 



perfect, and -7- is always greater than — . I have therefore, in 



the first instance, calculated for the pressures and temperatures in 

 yoiu* experiments the values of the first term of the above for- 

 mula (which represents, in fact, the heat expended in overcoming 

 the cohesion of the gas) according to the formulae which I deduced 

 in 1819 from the experiments of M. Regnault; and so far as I 

 have gone, the result has been that the first teim of the above 

 equation always exceeds the actual cooling by a fraction of a 

 decree. These two quantities vary in a similar manner; that is 

 to say, they both increase with increased pressure, and diminish 

 rapidfly with increased temperature. 



The excess of the calculated cooling by cohesion above the 

 actual cooling, if freed from the effbcts of errors, would represent 

 the second term of the above equation, and afibrd the means of 

 computing the value of the constant /c ; but it is both too small 

 and too irregular in its amount to serve for this purpose further 

 than to show that k has probably some value, but certainly a 

 veiy small one. 



I would now suggest to you the advantage of using carbonic 

 acid gas in some future experiments, because it is a definite 

 chemical compound, and therefore not subject to variation in its 

 properties; and also because in it the effect of cohesion is greater 

 than in atmospheric air, and capable of being calculated with 

 greater precision. The formula representing the pressure of 

 carbonic acid in terms of its volume and temperature is very 

 simple, and agrees very closely with Regnault's experiments. It 

 is of this form : 



£_ D jr /Dy /a \ 

 P.- Do To \Dj'\r V- 



To is the absolute temperature of melting ice, Dg the theoretical 

 density in the state of perfect gas at the absolute temperature 



