415 



The force witli wliich the field acts on unit of electric charge is 

 given by 



f=d + -[v.h] (5) 



c 



and there is a corresponding force 



g = h-i[w.d]. . . . . . . (6) 



c 



acting on unit of magnetic charge. 



Remarks on the fundamental equations. 



J. In order to simplify the mathematical treatment all quantities 

 occurring in the equations are considered as continuous functions 

 of the coordinates. 



2. We shall suppose that, while points of an element of volume 

 move with the velocity V varying from point to point, the electric 

 charge of the element remains constant, so that the density ^ changes 

 in the inverse latio as the size of the element. We shall make a 

 similar assumption concerning the magnetic charge. By these assump- 

 tions Ihe distributions, both of the electric current d -|- ^ v and of 

 the magnetic current h -[- ^t W are made to be solenoidal, as they 

 must be if equations (3) and (4) shall be true. 



3. For the sake of generality we have introduced different symbols 

 V and w for the velocities of the electric and the magnetic charges. 

 These charges may be imagined as penetrating each other and 

 having independent motions. 



§ 3. The fundamental equations form a consistent system and 

 are in good agreement with ideas and theorems which physicists 

 would be very unwilling to give up. 



The force acting on the electric and the magnetic charges con- 

 tained in an element of volume, taken per unit of volume, is 

 given by 



1 1 

 ^f + jugrzr^d 4- f*h H [9 V. h] [fiw- d] 



c c 



and for the ,?>component of this force one finds after some trans- 

 formations 



dX:, dXy dXj dGx 



gfx i f* gx = 



dx dy dz dt 



where 



Proceedings Royal Acad. Amsterdam. Vol. XXV. 



27 



