the Inertia of Electric Convection, 235 



is 34, and this term is therefore quite insignificant compared 

 with the first. A coil might be made of a good many windings 

 still leaving the inertia of convection great compared to the 

 magnetic inertia. In any problem in which the self-induction 

 of gases has to be calculated, the ordinary methods would give 

 erroneous results. 



9. The general equations of electric motion will be altered 

 by the introduction of the inertia, whether it be the inertia 

 of the electron or, as in the case of liquids or gases, the 

 inertia of the ion. 



If E represents the component of electric force in any one 

 direction, and u the flow in the same direction, the ordinary 

 equations of electric motion are 



pu 



= E 



with two other equations giving the components in two other 

 directions, p being the resistivity of the medium. If, however, 

 the electric flow possess inertia, the electric forces will be 

 doing work in increasing the energy of convection, the rate 

 of doing work per unit volume being fjuuii. Hence the 

 .complete equation will be 



pu-\-fjbic = ^j. 



In the case of conductors, we may put 



a|t being the electrostatic potential and F the X component of 

 the vector potential, and introducing the conductivity k for 

 1/p, the equation becomes 



/dF _,dyjr\ du 



U + \Tt+dxr K »-dt = °> 

 or, as V 2 F=— 47rw, 



with the corresponding equations for the other components 

 of the vector potential. The electrostatic potential disappears 

 in the usual way by introducing the components of magnetic 

 induction (a, b, c) for those of vector potential, the typical 

 equation in that case being 



i7rK< Jt = ( 1+Kli 7t}^ a ' 



R2 



