606 Mr. Bernard Cavanagh on 



Moreover, dyt! = — , 



where r is the shortest distance between the wires. 



The expression for fi can accordingly be expressed in the 

 following symbolical form : — 



We have 



[jV£v]p>)=(p+f 1 ^+...)p»w 



But ('e , V?.(p)tp=fon(i* + p)dp; 



(;P bW ^=( p+ |!^4,..)p b (0) 



i. e. 



° r n(n + iy dp ~ l/"^' ' ^\dfi 



Hence 



M = M - 



^W u(n + l)df* ' c{> ' 



since I P,,-^- 1 ' ) =0. 



-(J) 



, &c. 



L XXIII. Molecular Thermodynamics. I. /??/ Bernard 

 A. M. Cavanagh, I?. A, Balliol College, Oxford *. 



I. The General Condensed Phase. 



FT1HE treatment of the thermodynamics of solutions given 

 J_ by Planck f for the simple limiting case of extreme 

 dilution appears io be capable of extension to the general 

 case. Planck himself, indeed, suggested J the expansion of 

 the specific Total-Energy and Volume of the solution, in 

 integral powers of the various concentrations. But for 

 general applicability this assumption of integral powers would 

 appear to be quite unnecessarily arbitrary and narrow. 



We have, in general, for the Total-Energy and Volume 

 per unit quantity of solution, functions F x and F 2 (say) of 

 the various concentrations, which will involve parameters 

 dependent on Temperature and Pressure. 



Now it would seem that the minimum assumption required 



* Communicated by Dr. J. W. Nicholson, F.R.S. 

 f 'Thermodynamics' (Trans. Ogg) 1917, Chap, v, 

 + Ibid. p. 225. 



