4|4 VAN DER WAALS ON THE CONTINUITY 



Neglecting the effect of attraction, I find that the effect of the impulsive 

 repulsion reduces the equation of Clausius to the form 



where tr is the density of the molecules and p the mean density of the medium. 



The form of this equation is quite different from that of M. Van der 

 Waala, though it indicates the effect of the impulsive force in increasing the 

 pressure. It takes no account of the attractive force, a full discussion of which 

 \\.iiild carry us into considerable difficulties. 



At a constant temperature the effect of the attractive virial is to diminish 

 the pressure by a quantity varying as the square of the density, as long as 

 the encounters of the molecules are, on the whole, between two at a time, 

 and not between three or more. The effect of the attraction in deflecting the 

 paths of the molecules is to make the number of molecules which at any given 

 instant are at distances between r and r + dr of each other greater than the 

 number in an equal volume at a greater distance in the proportion of the 

 velocities corresponding to these distances. As the temperature rises, the volume 

 being constant, the ratio of these velocities approaches to unity, so that the 

 distribution of molecules according to distance becomes more uniform, and the 

 virial is thus diminished. 



If there is a virial arising from repulsive forces acting through a finite 

 distance, a rise of temperature will increase the amount of this kind of virial. 



Hence a rise of temperature at constant volume will produce a greater 

 increase of pressure than that given by the law of Charles. 



The isothermal lines at higher temperatures will exhibit less of the dimi- 

 nution of pressure due to attraction, and as the density increases will shew 

 more of the increase of pressure due to repulsion. 



I must not, however, while taking exception to part of the work of 

 M. Van der Waals, forget to add that to him alone are due the suggestions 

 which led me to examine the theory of virial more carefully in order to explore 

 the continuity of the liquid and the gaseous states. 



I cannot now enter into the comparison of his theoretical results with the 

 experiments of Andrews, but I would call attention to the able manner in 

 which he expounds the theory of capillarity, and to the remarkable phenomena 

 of the surface-tension of gases which he tells (p. 38) has been observed by 



