154 Mr. Gr. von Kaufmann on the Theory of Corresponding 

 Again, the vapour-pressure formula of Nernst * 



Hp= - gj + ¥ log T ~ E T+lo « A ' 



gives the very simple reduced equation 



Q+- — 

 7r . e =u 



Here \ = er /R 2 is the specific constant of zero dimension. 



Another instance is found in the 4-constant state-equation 

 of Clausius, whose reduced form was given above (6), and is 

 used in the subsequent calculation. 



Part II. 



Calculation of the complete conditions of Liquid-vapour 

 coexistence from the State-equations of van der Waals, 

 D. Berthelot, and Clausius. 



The problem of calculating the equations connecting 

 temperature, pressure, and coexisting volumes in the two- 

 phase system, from the (p, v, T) state-equation for the 

 homogeneous substance, has received very little attention 

 hitherto. Theoretically, it is solved through the thermo- 

 dynamic equation first given by Maxwell (Heat), and by 

 Clausius : 



p.'dv=p(v 1 — v 2 ), 



J" 



together with the state-equation applied to each of the 

 coexisting volumes : 



F(p, vu T)=0, 



F(p,v lt 1)^=0. 



These three equations suffice to give any one of the 

 quantities p, v l9 v 2 < T in terms of any other one. In practice,, 

 the solution of these equations offers some difficulty, and 

 leads to somewhat complicated results, even with such simple 

 equations as that of van der Waals. This circumstance, 

 together with the fact that all the well-known state-equations 

 are known to be inaccurate at temperatures below the critical 

 point, probably accounts for the long neglect of a theoretically 

 very interesting problem. 



A partial solution has been given by P. Bitter f, who, 

 working with the critical reduced equation of van der Waals, 



* ' Applications of Thermodynamics to Chemistry ' (1907), p. 66. 

 t Wiener Berichte, cxi. p. 1046 (1902). 



