44 K. D. Kraevitch on an Approximate Law of the 

 This last equation passes into (6) if it be assumed that 



, c — Ci / , m N mr 



log ^ 0+ AD ( g To + m ) + ADT =a > 



AD^+AD"^' 



C — Gi 



AD 



= 7. 



The difference between the equations (5) and (6) is that the 

 former does not contain any arbitrary magnitudes, as we 

 shall prove subsequently ; while equation (6) contains three 

 arbitrary magnitudes, which Messrs. Bertrand and Dupre* 

 endeavour to so choose for each vapour individually that the 

 formula may best accord with the results of experiment. 

 Hence equation (6) is an empirical one, while equation (5) 

 should be regarded as one based upon theory. In order to 

 convince ourselves of this, let us consider the magnitudes 

 which enter into the second portion of equation (5). The 

 specific heats c and e x of substances in a liquid and vaporous 

 state can be determined with more or less accuracy by expe- 

 riment. A is the thermal coefficient of work, we take it as 



equal to j~~ ; D is a constant quantity for every substance 



when it occurs as a perfect gas. It is not difficult to prove 

 that 



Ar ._ 848-7 



AU -425P' 

 or nearly ~ 



= P ; 



P is the molecular weight of the vapour. The magnitudes 

 T , r , and p correspond to that state of a vapour when it 

 is entirely subject to the laws of Boyle and Gay-Lussac. 

 If we have the means of determining the temperature 

 which corresponds to this state of a vapour, then T , and 

 consequently r and p Qy become perfectly definite quantities. 

 I shall afterwards give two methods, controlling each other, 

 by means of which it is possible to find such a temperature 

 for any substance if only it exists, and if there be a sufficient 

 number of observations on the vapour-pressure of the substance. 

 Thus equation (5) contains no arbitrary magnitudes ; and in 

 this it differs from all the formulas which have been found by 



* TMorie Mecanique de la Chaleur par Athauase Dupre. 1869. 



