280 M. Achille Cazin on Internal Work in Gases. 



I do not think that the thermal effects at present in question 

 can be studied very exactly by means of the thermometer. The 

 inevitable action of the sides, alone, prevents entire exactness. 



M. Hirn has given in one of his last memoirs some very simple 

 formula?, by means of which we can solve the problems before 

 us*. I tried to apply them; but the results to which they lead 

 differ from those which I have given. 



Following the method invented by M. Hirn, and which is 

 applied in the memoir quoted to the vapours of water, of bichlo- 

 ride of carbon, of sulphide of carbon, of alcohol, and of ether, I 

 calculated a formula for carbonic acid, 



T 



a±-b(^Y. (15) 



But I have not found for the constants a> b, B values which 

 made the formula agree sufficiently with the Table on page 272. 

 If an agreement between them were established, that formula 

 would take the place of the formula of Mr. Rankine, and, intro- 

 duced into the preceding equations, would solve our problems. 

 For example, in the problem of § I., formula (5) would give 



_ Afog (\ 1\ 



The calculations which I have made in the second problem 

 indicate that it is very distinct from the first. Id order that the 

 mechanical and thermal effects might be the same in these two 

 problems, it would be necessary that 



and this equality seems to me impossible. The contradiction 

 may very likely be only apparent between the results at which I 

 have arrived and those of M. Hirn. It is not in the spirit of 

 criticism that I refer to it here. Seeking to resolve those ques- 

 tions which have been already treated by my excellent friend, 

 by means of a method differing from his, I meet with differences 

 which may be explained by the inexactness of the numerical 

 data. The importance of formula (15), which M. Hirn has 

 used with advantage in the study of vapours, imposed on me 

 the comparison of the two methods ; and I have made it in the 

 hope that it may contribute to the elucidation of a delicate ques- 

 tion of thermodynamics. 



* G. A. Hirn, " Memoire sur la Thermodynamique," Ann. de Chim. et 

 de Phys. May 1867, p. 91. 



