and the Laws regarding the Nature of Heat, 19 



If it be desired to calculate the specific heat of the gas, not by 

 the unit of weight_, but by the method more in use, the unit of 

 volume, say at the temperature ^q and the pressure jOq, it is only 

 necessary to divide c and c' by Vq. Let these quotients be ex- 

 pressed by y and y, and we obtain ^>^ s-^' 



In this last expression nothing appears which is dependent on 

 the peculiar nature of the gas ; the difference of the specific heats 

 reckoned according to the unit of volume is therefore the same 

 for all gases. This proposition has been deduced by Clapeyron 

 from the theory of Carnot ; but the constant found above .is 

 not given by the difference d —c, the expression found for it 

 having still the form of a function of the temperature. 



Dividing both sides of equation (11.) by 7, we obtain 



wherein k is set for shortness' sake in the place of — . This is 



equal to the quotient - ; and through the theoretic labours of 



Laplace on the transmission of sound through air, has attained 

 a peculiar interest in science. The excess of this quotient above 

 unity in the case of different gases is therefore inversely propor- 

 tional to their specific heats, reckoned according to the unit of 

 volume when the latter is constant. This proposition has been 

 proved experimentally by Dulong* to be so nearly correct, that 

 its theoretic probability induced him to assume its entire truth, 

 and to use it in an inverse manner in calculating the specific 

 heat of various gases, the value of k being first deduced from 

 observation. It must, however, be remarked, that the propo- 

 sition is theoretically safe only so far as the law of M. and G. 

 holds good ; which, as regards the various gases examined by 

 Dulong, was not always the case to a sufficient degree of accuracy. 

 Let us suppose that the specific heat c of the gases by constant 

 volume is constant, which we have already stated to be very pro- 

 bable ; this will also be the case when the pressure is constant, 



c 

 and hence the quotient of both specific heats — =k must be also 



constant. This proposition, which Poisson, in agreement with 

 the experiments of Gay-Lussac and Welter, has assumed to be 

 correct, and made the basis of his investigations on the tension 



* Ann. de Chim. et de Phys,, xli. ; and Pogg. Ann., xvi. 

 C3 



