126 Mr. W. Sutherland on the 



by a function involving three constants, so that his equation 

 takes the complicated form 



__£ = _1 AT-"-B 



ET v-a (v + /3f 



Sarrau (Comptes Rendus, ci.) has modified the form of 

 Clausius's equation for C0 2 , and introduced another constant e, 

 thus : — 



RT Ke~ T 



P v-a (v + j3) 2 '' 



but even this form, he finds, fails to represent the behaviour 

 of C0 2 when its volume is reduced to less than ^J ff of the 

 normal volume, which at the lower temperatures (40° C.) 

 corresponds to a pressure of about 80 metres of mercury, while 

 Amagat's experiments extend to 320 metres. 



The last formula to be mentioned is that of Dr. Walter 

 (Wiedemann's Ann. xvi. 1882) — 



(p+/)w~*-l*Ii 



where e is the base of the natural logarithms and /3 and / are 

 functions of the temperature, left undefined. In a somewhat 

 similar manner to Yan der Waals, he argues, to give a meaning 



to his term e v , that it represents a correction which it is 

 necessary to make in the equation of the virial on account of 

 the mutual impenetrability of the molecules. And this brings 

 us to an important point. The equation of the virial does not 

 require any correction. It expresses a perfectly general 

 dynamical theorem as to the relation between the mean trans- 

 latory kinetic energy of any system of bodies in stationary 

 motion and the forces at play among them, and applies as 

 rigorously to a system of extended bodies as to a system of 

 ideal extensionless particles. When the equation of the virial 

 is applied to a number of molecules of a gas confined in vessel 

 of volume v, \pv represents the virial of the pressure applied 

 all over the surface, and is perfectly independent of what 

 mechanical arrangement there may be inside to influence the 

 number of collisions, so long as the motion is stationary. The 

 ideas of Van der Waals and Dr. Walter affect profoundly the 

 interpretation which is to be given to a characteristic equation, 

 and, if proved by their application to be correct, would upset 

 the kinetic theory. 



H. A. Lorentz (Wiedemann's Ann. xii.), accepting Yan der 

 Waals's equation as an empirically good one, suggests (but 

 does not press the suggestion) that at low densities the term 



