Electric Inertia and t he Inertia of Electric Convection . 227 



gradient in the positive column, we are again led to conclude 

 that the ionization does not arise principally from collision?. 

 It has been found, in some cases, that the force per centi- 

 metre in the positive column is almost independent of the 

 current strength, so that the velocities of the ions would be 

 the same for different currents, and the rate of recombination 

 would be proportional to the square of the current. The rate 

 of production of ions by collisions would be proportional to 

 the current, and the new ions thus produced would not com- 

 pensate for the loss due to recombination. Thesa and other 

 considerations show that it is impossible to infer from pheno- 

 mena connected with discharge-tubes that any ionization is 

 produced by collisions when the force is as small as 30 volts 

 per centimetre. 



The results which we have obtained show that for a large 

 range of forces, the positive ions do not contribute to the 

 generation of ions, but it is probable that positive ions would 

 produce ionization in stronger fields. 



XVIII. On Electric Inertia and the Inertia of Electric Con- 

 vection. By Arthur Schuster, F.R.S., Professor of 

 Physics at Owens College, Manchester*. 



1. /^kUK calculations of self-induction are based on the 

 V-/ assumption that the currents which traverse a con- 

 ductor fill it continuously, the flow being treated as that of an 

 incompressible liquid. The assumption is generally recognized 

 not to hold in the case of electrolytes, where electricity is con- 

 veyed by a number of irregularly distributed ions. In the 

 immediate neighbourhood of such an ion, the magnetic field will 

 be many times greater than that calculated on the supposition 

 of continuous distribution, and hence the total magnetic energy 

 is underestimated. What is universally recognized in the case 

 of electrolytes must also be conceded when the current is con- 

 veyed by a gas, and the idea is gaining ground that even in 

 solid conductors the current consists of moving positive and 

 negative electrons. 



It is the object of this paper, to calculate the additional 

 terms which become necessary for the evaluation of self- 

 induction, and to discuss the possible cases in which the cor- 

 rections may affect experimental results. 



2. I begin by calculating the total energy of a number of 



electrically charged, equidistant particles, placed in a straight 



row and all moving with the same speed (u). If the charge 



(if) of each particle is taken to be spread uniformly over a 



* Communicated by the Physical Society : read Dec. 14, 1900. 



