146 Mr. G. von Kaufman a on the Theory of Corresponding 



Roughly we could take 



C = -5, C'="75, andA = -25, 

 so that 



/( OT )=i+«i-^)- I/3 - 



If the radius of the tube be a, the total current I, and the 

 specific resistance <r, the total potential difference required 



= — 5 (L-f ah), where k is about *8217. 

 ira 1 



The normal current at the open end is approximately 



X. On the General Theory of Corresponding States, and 

 the Thermodynamic State- Equation. By George VON 

 Kaufmann *. 



Part I. 



Analysis and generalization of the Theory of Corresponding 

 States, and a new method of obtaining the Reduced State- 

 Equation. 



THE Theory of Corresponding States has its origin in the 

 famous equation of van der Waals, which was deduced 

 as a closer approximation to the state-equation of real gases 

 from certain assumptions in the kinetic molecular theory of 

 gases. Van der Waals' equation 



(/H-^) (-/*)= J.T • . . . (1) 



contains three specific constants, and three variables of 

 different dimensions, measured in independent units, Van 

 der Waals showed by simple algebraic calculation that by 

 introducing the quantities plp^n', vjv k =(f>', T/T^=^, where 

 p k , v k9 T k are the critical values, a, y3, and R/M are elimi- 

 nated, and the equation 



(t'+ ^)(3f-l) = W .... (2) 



is obtained, which is identical for all substances. On this 

 "Reduced Equation" was built up the whole of the extensive 

 and far-reaching theory of Corresponding States. 



* Communicated by Prof. W. J. Pope, F.R.S. 



