800 On the Abnormality of Strong Electrolytes. 



required to separate the ion from its partner ; and he states 

 that the number of ions which satisfy this condition is given 

 by the expression 



N«-*«, (A) 



in which N is the total number of ions, Jc the gas constant for 

 a single molecule, and t the absolute temperature. The latter 

 statement is we believe fallacious : for, according to a well- 

 known result in the kinetic theory of gases, the number of 

 molecules which have a velocity in excess of c is 



■nm. 





m being the mass of a molecule and c its velocity. 



On changing the variable 

 becomes 



/ wig 



from c tox = \/ --7- this number 



=£■ 1 x 2 e~ x2 dx, 



ir* Jx 



2N _ t2 2N 



7T-2 Tj-2 



«-- 



which, after integration by parts, assumes the form 



t I e~ x ~dx. 



*- 



In terms of the probability integral defined by 



2 C™ 

 er£x=~\ e-'^dx 



this number becomes 



N (j|V-^+erf x<\ (B) 



( Vide Jeans, ' The Dynamical Theory of Gases,' 2nd ed. 

 pp. 34, 35.) 



A 

 However, ^- * n expression (A) is equal to x^ 2 , and there- 



fore the number of free ions as estimated by Ghosh is 



N^-0 2 . ....... (C) 



Now, the number of free ions divided by the total number 



of ions is — ? P- being the molecular conductivity at dilution v, 



