230 Prof. A. Schuster on Electric Inertia and 



will be positive and tend to diminish the negative term in 

 (3). They will also be small and of the same order of magni- 

 tude as other quantities we neglect. It serves no useful 

 purpose therefore to calculate them out in detail. If A is 

 the area of the cross-section, the number of electrons spread 

 over it will be An 2 , so that the total correction to the mag- 

 netic energy becomes 



1 \6a a J 



If d is large compared with a the second term may be 

 neglected. In that case, writing i for the current-density 

 n s uq, and N for n ;i which represents the number of electrons 

 in unit volume, we obtain for the correcting term per unit 

 volume of the conductor 



toil* 

 where /j, stands for 2/3aN. 



The flow of electricity will behave, therefore, as if it had 

 inertia, the apparent mass for unit current-density and unit 

 volume being /j,. The dimension of //,, as pointed out by 

 Hertz, is the same as that of a surface. 



We may conveniently use the expression " electric inertia" 

 for the quantity jul ; the energy due to electric inertia is the 

 energy of the magnetic field due to the moving electrons over 

 and above that which is calculated in the usual way. 



5. The investigation has been restricted to the case of a 

 number of electrons moving in one direction, with the same 

 speed and keeping the same equal distances from each other, 

 but the result holds more generally. The magnetic field 

 established by a positive electron moving in one direction is 

 the same as that of a negative electron moving with the same 

 speed in the opposite direction. Superposing on our system 

 of one kind, a second one carrying opposite electricity in the 

 opposite direction, N being the number of electrons of each 

 kind and Az'i, Ai 2 the currents conveyed in the two directions, 

 the energy per unit volume becomes 



(*'i 2 + vO/3N« 

 or 



r l = 



ii+'h 



(ii + i 2 )* 3Na' 



The assumption that two sets of electrons move so as to 

 keep equal relative distances is not of course satisfied. The 

 change in the relative distance will increase the mutual energy 

 between the electrons, but the increase will be of the order 

 of magnitude which we have neglected, and the term we have 



