the Inertia of Electric Convection. 233 



Introducing the current-density 



tsNg^+Ufl), 



and the weight p of dissociated molecules per unit volume, 

 which is related to the other quantities used by the equation 



p = $"(»*! + m 2 ) = Na^ (ax + « 2 ) , 



we obtain for the energy of ionic motion 



2r 2 |> L (wi-fw 2 ) s 





If Mi refers to the kation, the ratio w 2 / M i + M 2 is Hittorfs 

 constant deduced from the migration of ions. Denoting this 

 by n we have finally 



a?(a x (l — nY + a 2 n 2 ). 



P 



Taking for instance nitrate of silver, for which n = *53, 

 a! = 108, a 2 = 62, the energy of ionic motion per unit volume 

 and unit current becomes equal to 3*8 x 10~~ 5 /p, where p is 

 the number of grams of nitrate of silver per c.c. of water. 

 Hertz gives in the paper quoted for the same salt the number 

 7*8 x 10~ 5 , which is nearly double the value I find. As Hertz 

 does not indicate his method of calculation, it is not now 

 possible to trace the discrepancy, unless there is some slip in 

 the above reasoning. 



,In order to discuss the possibility of an experimental veri- 

 fication of the increase in self-induction due to electric inertia, 

 we may consider two narrow tubes placed side by side. If 

 the tubes have an internal diameter of 1 mm., their axes 

 might be placed 2 mm. apart and the coefficient of self- 

 induction would in that case be equal to 6'6 per cm. of the 

 double conductor. The ionic inertia would increase the value 

 by 7'6xlO~ 5 /pA, which is nearly equal to 1 if p=='01. 

 The increase in self-induction amounts therefore to about 

 15 per cent., but the whole quantity is so small that it could 

 not be measured very accurately. 



When the dilution of the electrolyte becomes great, the 

 ionic inertia may become considerable. Thus in the case of 

 the purest water obtained by Kohlrausch,he estimates that there 

 was '08 mg. of dissociated hvdrogen per cubic metre. This 

 gives p = 7'2 xlO- 10 . 



In order to avoid making any assumption as to the quantity 

 n, we may substitute that value for it which gives the smallest 



Phil. Mag. S. 6. Vol. 1, No. 2. Feb. 1901. R 



