Dr. Schroedcr van der Kolk on Gases, 1 25 



stant J*, or the mechanical equivalent of heat, is then (c, —c) J = P —, 



in which a is the coefficient of expansion fori , b the density, and;; 

 the pressure. This formula could not, however, be used in the 

 present case. For, in the first place, an ideal gas is supposed in 

 the formula, whereas the experiments refer to air. The changes 

 which pressure and temperature produce in the value of k — that 

 is, the deviations from Mariotte and Gay-Lussac's law — had to 

 be taken into account. In the second place, the formula was 

 not applicable, because the first member gives the difference of the 

 specific heat, the second the work done, and because both these 

 magnitudes are only equal in case Mayer's assumption is appli- 

 cable, that the gas performs no internal work, which with air is 

 by no means the case. The formula 



is, on the other hand, universally valid, and therefore can be 



used. For this case the differential quotients -r- and --r were 



dk dk P a 



changed into a function of -y- and — , by which is obtained the 



dp ar J 



formula 



For atmospheric air, c, is known from Regnault's experiments, 



c . dk 



— from the velocity of sound, k and -y- from the formula) prc- 



c . . P dk 



viously obtained. The determination of -j- presented, however, 



CIT 



some difficulty. The values of k at 4° and 100° are indeed 

 known ; but the supposition that k changes regularly with the 

 temperature is untenable, because all gases at lower pressure 

 and higher temperature approximate to ideal gases, which in 

 this case would be impossible. But the divergent numbers 



specific heat under constant volume by the letter c, and under constant 

 pressure by c v Clausius, ' Memoirs on the Mechanical Theory of Heat,' 

 p. 291. 



* I have here kept to the English notation, as the letter A occurs further 

 on with a different meaning. 



t Zeuner, Grundziige der mechanischen Warmefheoric, p. 177. 



