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



2. Before applying equation (5) to various liquids we will 

 investigate its properties. The equation may be given in 

 another simpler form, more convenient for calculation. To 



do this let us resolve log ~f into a series in powers of — ^ — , 



and cast aside the members higher than the second power. 

 In this manner we shall have, instead of equation (5), the 

 following : — 



^ Po -2AD' m \ T J + ADVT T/' ' (5) 



This equation serves only in the case when the fraction 



T— T 



— =—9 is small, and when, consequently, the temperature T is 



not too far removed from T ; the results given by it will be 

 particularly near to those of experiment if c — Ci be small. I 

 have applied this equation to bisulphide of carbon [12]* in 

 order to form an idea of its accuracy, and found that the 

 simplified equation (5') and the complete equation (5) give 

 similar, or very nearly similar, results. 



Experiments have shown that the difference c — c x is ex- 

 ceedingly small, compared to the heat of vaporization, for 

 all investigated substances. Therefore the first member of 

 the equation may be neglected, and we shall have 



, p mr / 1 1 \ 



Whence a formula analogous to that of Roche f can be easily 

 obtained by integration, 



p='aet\+mt, 



a, a, and m are arbitrary constants. By choosing them in 

 the most advantageous manner Regnault obtained a formula 

 which amply satisfied the results of observation, and which 

 was hardly less satisfactory than Biot's formula with Rye 



arbitrary coefficients. The nearer . * approaches to zero 



the better does formula (r) agree with the results of experi- 

 ment. Among the substances for which I made calculations 

 there was one, namely ethyl bromide [14], for which c — c\ 

 closely equalled zero. I calculated its vapour-pressure 

 according to formula (r). Thus Roche's formula has a 



* The figures placed in brackets refer to the numbers of the sections in 

 this paper. 



f Memoir es de VAcad. des Sci. t. xxi, p. 685, 



