496 Displacement Currents [CH. xvn 



current at any point which is produced by the motion of electric charges, and 

 let this be measured in electromagnetic units. Let /, g, h be the compo- 

 nents of displacement (or polarisation) at this point, this being supposed 

 measured in electrostatic units. Let any closed surface be taken, and let 

 /, m, n be the direction-cosines of the outward normal to any element dS of 

 the surface. Then if E is the total charge of electricity enclosed by this 

 surface, we have, by Gauss' Theorem, 



E ..................... (522). 



Let us suppose that there are C electrostatic units of charge in one 



electromagnetic unit. Then the total charge of electricity enclosed by the 



-p 



surface, measured in electromagnetic units, is -^ , and the rate at which this 







quantity increases is measured by the total inward flow of electricity across 

 the surface S, these currents of electricity being measured also in electro- 

 magnetic units. Thus we have 



(523). 



7 -P 



Substituting for =- its value, as found by differentiation of equation 

 dt 



(522), we obtain 



Now u, v, iv are the components of the conduction current, while 



1 df 1 do 1 dh , T i 



n j* > r>j+> n 777 are tne com P onen ts of the displacement current, both 



dt O dt ttt 



currents being measured in electromagnetic units. Thus 



Idf Idg Idh 



are the components of Maxwell's " total current " and equation (524) expresses 

 that the total current is a solenoidal vector (cf. 177) the fundamental fact 

 upon which Maxwell's theory is based. 



571. The hypothesis upon which the theory proceeds is, as we have 

 already said, that the work done in taking a magnetic pole round any closed 

 circuit is equal to 4?r times the total flow of current through the circuit, 

 this current being measured in electromagnetic units. As in 533, this is 

 expressed by the equation 



dx dy dz 

 OL-T- + p-/- + r y- T - 

 ds ^ ds ' ds 



