Self-induction of Wires. 123 



of a certain fundamental equation. That I should have been 

 able to arrive at the most general form, taking into account 

 intrinsic magnetization, as well as not confining myself to 

 media homogeneous and isotropic as regards the three quan- 

 tities conductivity, inductivity, and dielectric capacity, in a 

 simple and direct manner, without any volume-integrations or 

 complications, arose from my method of treating the general 

 equations. I here sketch out the scheme, in the form I give it. 

 Let Hx be the magnetic force and F the current. (Thick 

 letters here for vectors. The later investigation is wholly 

 scalar.) Then, " curl " denoting the well-known rotatory 

 operator, Maxwell's fundamental current equation is 



cnrl H 1 =4irr, (1) 



and is his definition of electric current in terms of magnetic 

 force. It necessitates closure of the electric current, and, at 

 a surface, tangential continuity of H x and normal continuity of 

 T. The electric current may be conductive, or the variation 

 of the elastic "displacement," say 



r=c + i. 



C being the conduction-current, D the displacement, linear 

 functions of the electric force E, thus 



C = &E l3 D = cE 1 /4tt; 



h being the conductivity, and c the dielectric capacity (or c/Att 

 the condenser-capacity per unit volume). Equation (1) thus 

 connects the electric and the magnetic forces one way. But 

 this is not enough to make a complete system. A second 

 relation between Ej and Hi is wanted. 



Maxwell's second relation is his equation of electric force 

 in terms of two highly artificial quantities, a vector and a 

 scalar potential, say A and P, thus 



E 1= -A-VP, (2) 



ignoring impressed force for the present. From A we get 

 down to Hi again, thus, 



curl A = B, 



B being the magnetic induction, and jn the inductivity. (Here 

 we ignore intrinsic magnetization.) 



The equation (2) is arrived at through a rather complex 

 investigation. From these equations are deduced the general 

 equations of electromagnetic disturbances in vol. ii. art. 783. 

 They contain both A and P. One or other of them must go 

 before we can practically work them, which are, independently 



