10 



Mr. A. Schuster's Electrical Notes. 



which a constant electromotive force is distributed over a 

 finite surface. 



Any one attempting the solution of such a problem would 

 probably be led into the same difficulties which I encountered, 

 and although he would doubtless soon get over them, the 

 following discussion may save him some trouble. 



I begin by writing down the well-known equations refer- 

 ring to the Vector Potential in Maxwell's form, taking in the 

 first place the magnetic permeability as constant. 



F, G, H being the components of the vector potential, 

 u, v, iv those of the current, we have 



Airu 

 or, writing 



dy \ dx dy / dz \ dz dx ) ' 



dy 



0) 



dx dy 



47T?/ = 



rfj 



V 2 F, 



(2) 



with similar equations for v and w. 

 Putting 





Maxwell concludes that 



F = F' 



dy 



dx 

 dz 



(S) 



(4) 



(5) 



This conclusion is not, however, justified. The second 

 terms on the right-hand side of equations (5) disappear 

 altogether from equations (1). If therefore F/ G', H' are 

 solutions of (1), the value of % is not restricted to that given 



