

A DYNAMICAL THEOKY OF THE ELECTROMAGNETIC FIELD. 539 



Coefficients of Induction for Two Circuits. 



(26) In the electromagnetic field the values of L, M, N depend on the 

 distribution of the magnetic effects due to the two circuits, and this distri- 

 bution depends only on the form and relative position of the circuits. Hence 

 L, M, N are quantities depending on the form and relative position of the 

 circuits, and are subject to variation with the motion of the conductors. It will 

 be presently seen that L, M, N are geometrical quantities of the nature of lines, 

 that is, of one dimension in space ; L depends on the form of the first conductor, 

 which we shall call A, N on that of the second, which we shall call B, and 

 M on the relative position of A and B, 



(27) Let be the electromotive force acting on A, 'x the strength of the 

 current, and R the resistance, then Rx will be the resisting force. In steady 

 currents the electromotive force just balances the resisting force, but in variable 

 currents the resultant force Rx is expended in increasing the "electro- 

 magnetic momentum," using the word momentum merely to express that which 

 is generated by a force acting during a time, that is, a velocity existing in a 

 body. 



In the case of electric currents, the force in action is not ordinary 

 mechanical force, at least we are not as yet able to measure it as common force, 

 but we call it electromotive force, and the body moved is not merely the 

 electricity in the conductor, but something outside the conductor, and capable 

 of being affected by other conductors in the neighbourhood carrying currents. 

 In this it resembles rather the reduced momentum of a driving-point of a 

 machine as influenced by its mechanical connexions, than that of a simple 

 moving body like a cannon ball, or water in a tube. 



Electromagnetic Relations of two Conducting Circuits. 



(28) In the case of two conducting circuits, A and B, we shall assume 

 that the electromagnetic momentum belonging to A is 



Lx + My, 



and that belonging to B, Mx + Ny, 



where L, M, N correspond to the same quantities in the dynamical illustration, 

 except that they are supposed to be capable of variation when the conductors 

 A or B are moved. 



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