Variation in the Pressure of Saturated Vapours. 39 



of saturation depends, not only on the temperature, bnt also 

 on a number of other circumstances: on the properties of 

 the liquid (coefficient of expansion, latent heat of vaporization, 

 specific heat, &c), and of the vapour (coefficient of expansion, 

 specific heat, molecular weight, &c). In the present stage of 

 science it would be well to search for even an approximate 

 dependence between vapour-pressure and other thermal quan- 

 tities, and there is no necessity to limit this dependence to a 

 function of temperature ; and it might be deemed a consider- 

 able scientific success were an expression found for the pressure 

 of a vapour in a state of saturation, in dependence upon any 

 thermal quantity whatever. The finding of such a dependence 

 is naturally easier than that of a precise function, and one, espe- 

 cially, of temperature only "*. Such approximate inexact laws 

 and formulae would serve as guiding clues for further re- 

 searches and for the discovery of more exact laws. 



In this paper it is my object to show that the pressure of a 

 vapour is in a somewhat simple, although only approximate, 

 dependence upon other observable quantities ; or, in other 

 words, if certain quantities are known, corresponding to a 

 definite temperature, having a special significance, then it is 

 possible to calculate with sufficient accuracy the vapour- 

 pressure for temperatures near to it, and approximately also 

 for temperatures far removed. 



1. Let us imagine a kilogramme of a liquid at a tempera- 

 ture of vaporization t under a pressure p, and let us convert 

 it by two methods into vapour saturating a space, at a tem- 

 perature t + dt and under a pressure p-\-dp, and calculate 

 each time the increase of internal energy in the material. 



(a) Let us increase the pressure p on the liquid by dp\ and 

 heat it to the new boiling-point t + dt, corresponding to the 

 new pressure. The internal energy of the substance will then 

 increase by cdt, where c is an amount of heat which is slightly 

 less than the specific heat of the liquid. In the case of a small 

 external pressure we can neglect this difference, because the 

 coefficient of expansion and specific volume of the liquid, upon 

 which the amount of heat consumed in external work depends, 

 are exceedingly small. This difference only becomes significant 



* I have written more fully on the importance of researches of this 

 kind in my papers, {i Remarks on Van der Waals' Formula " (Journal of 

 the Russian Physieo-Chemical Society, vol. xix.), "On the Dependence 

 of the Latent Heat of Vaporization upon other Factors " (Idem, xxi.), 

 and in the Hepertoriu?n der Physik (vol. xxvi. p. 589). 



t The internal energy of a liquid then decreases, hut so slightly that 

 we do not take it into consideration. 



