626 Mr. Bernard Cavanagh on 



square, this " virial " represents also the potential energy of 

 all the electrostatic forces. 



Milner then gives a thermodynamic demonstration * 

 supporting his application of the Virial theorem " to the 

 complex phenomenon which the osmotic pressure of an 

 electrolyte undoubtedly is." But this demonstration is open 

 to grave doubts, for it depends on treating the solute thermo- 

 dynamically as an independent system, whose " external 

 pressure " is the osmotic pressure of the solution, and also 

 on regarding K, the dielectric constant of the medium, as 

 independent of temperature. 



Of course, neither of these can possibly be strictly 

 permissible, but also one cannot, a priori, assume even 

 approximate validity as regards the conclusions to which 

 they may lead. 



Using the general molecular-thermodynamic method 

 developed in this paper, we shall, by means of a simple 

 example, reach the conclusion that this application of the 

 Virial theorem cannot be, in any general sense, valid. 



The Non-validity of the " Virial" Equation for Osmotic 

 Pressure. 



Consider a solution of a binary electrolyte, containing 

 c gram-molecules of electrolyte per gram of solvent. 



Suppose the " virial " per gram-molecule of electrolyte to 

 be given by 



Rm'<j* . ■ (65) 



where u' is independent of c. 

 n 



Then c being ^ we have 



to Mr 



U = M u + 2nu — nUu'c? 



= M mo + 2rau-RM u'c*,. . . . (66) 



where u is a mean value for the two ions f , 



Assuming, further, that owing to the smallness of the ex- 

 ternal pressure the general terms in V can be neglected in 

 comparison with that in U, we shall write 



V=Mpt7 + 2wt> J (67) 



* Loc. cit. xxv. p. 748. 



t The discussion of the possibility of distinguishing the thermo- 

 dynamic properties of the complementary ions of an electrolyte is 

 reserved for a later paper. 



