Maxwell. 285 



in this the architecture of his system was displayed, stripped of 

 the scaffolding by aid of which it had been first erected. 



As the equations employed were for the most part the same 

 as had been set forth in the previous investigation, they need 

 only be briefly recapitulated. The magnetic induction juH, being 

 a circuital vector, may be expressed in terms of a vector-potential 



A by the equation 



luiK = curl A. 



The electric displacement D is connected with the volume- 

 density p of free electric charge by the electrostatic equation 



div D = p. 



The principle of conservation of electricity yields the equation 

 div i = - dp/dt, 



where i denotes the conduction-current. 



The law of induction of currents namely, that the total 

 electromotive force in any circuit is proportional to the rate of 

 decrease of the number of lines of magnetic induction which 

 pass through it may be written 



- curl E = /LtH ; 



from which it follows that the electric force E must be expressible 



in the form 



E = - A + grad i//, 



where ^ denotes some scalar function. The quantities A and ;// 

 which occur in this equation are not as yet completely deter- 

 minate ; for the equation by which A is defined in terms of the 

 magnetic induction specifies only the circuital part of A ; and as 

 the irrotational part of A is thus indeterminate, it is evident 

 that \p also must be indeterminate. Maxwell decided the matter 

 by assuming* A to be a circuital vector ; thus 



divA = 0, 

 and therefore div E = - 



* This is the effect of the introduction of (F 1 , G', H'} in 98 of the memoir ; 

 cf. also Maxwell's Treitise on Electricity and Magnetism, 616. 



