234 ^, Prof. A. Schuster on Electric Inertia and 

 value to (A. This is found to be w = a 1 /(a 1 +a 2 ), so that if 

 a 1= 2, a 2 =16, a 2 = 108 x 10~ 10 , ^==7*2 X 10" 10 , 



The energy of straight parallel currents close together as 

 in the above example would therefore in this case be almost 

 entirely due to the ionic motion, but it will appear in § 9 that 

 the chances of experimental verification are not very great, as 

 long as an increase in the value of /x. is accompanied by a cor- 

 responding increase in the resistance. 



8. The case of gases presents several features of special 

 interest. The effect of inertia on the deflection of the cathode 

 ray has already been alluded to, and the fact that in the positive 

 portion of the discharge, the current is conveyed by a com- 

 paratively slow diffusion of molecules has been proved by me 

 in 1885 *. In the positive part of the discharge the number 

 of ions is proportional to the current, as follows from HittorPs 

 experiments. To make an estimate of the inertia involved 

 in the diffusion, I take as an example one of my experiments 

 for which I have calculated approximately the ratio of the 

 number of ions to the total number of molecules as 1*2 X 10~ 6 

 at a pressure of J mm., at which the density of nitrogen is 

 5 x 10 — 7 . The quantity called p above is in this case 10~ 13 , 

 and taking aj = a 2 = 7, 



A6 = 49xl0 13 a 2 = 5'4xl0 6 . 



This value holds for a current-density of 1*5 X 10 " 4 , and will 

 be inversely proportional to the current-density. 



The electric energy of convection in gases may therefore 

 be very large and exceed many times the magnetic inertia 

 calculated on the usual hypothesis. As an example I take a 

 circular tube of radius r bent into the form of a circle of 

 radius R, and as a first approximation we may take the 

 expression 



L = 4ttE (log — -1-75); 



the electric energy of convection per unit current is fiR/r 2 , 

 so that the total energy per unit current becomes 



^ + 4^(108^-1-75)]. 



With r=l, It = 10 the numerical value of the second term 



* Bakerian Lecture, pp. 548, 550. 



