534 A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



the same field with a magnet, I shew the distribution of its equipotential 

 magnetic surfaces, cutting the lines of force at right angles. 



In order to bring these results within the power of symbolical calculation, 

 I then express them in the form of the General Equations of the Electro- 

 magnetic Field. These equations express 



(A) The relation between electric displacement, true conduction, and the 

 total current, compounded of both. 



(B) The relation between the lines of magnetic force and the inductive 

 coefficients of a circuit, as already deduced from the laws of induction. 



(C) The relation between the strength of a current and its magnetic effects, 

 according to the electromagnetic system of measurement. 



(D) The value of the electromotive force in a body, as arising from the 

 motion of the body in the field, the alteration of the field itself, and 

 the variation of electric potential from one part of the field to 

 another. 



(E) The relation between electric displacement, and the electromotive force 

 which produces it. 



(F) The relation between an electric current, and the electromotive force 

 which produces it. 



(G) The relation between the amount of free electricity at any point, and 

 the electric displacements in the neighbourhood. 



(H) The relation between the increase or diminution of free electricity and 

 the electric currents in the neighbourhood. 



There are twenty of these equations in all, involving twenty variable 

 quantities. 



(19) I then express in terms of these quantities the intrinsic energy of 

 the Electromagnetic Field as depending partly on its magnetic and partly on 

 its electric polarization at every point. 



From this I determine the mechanical force acting, 1st, on a moveable con- 

 ductor carrying an electric current ; 2ndly, on a magnetic pole ; 3rdly, on an 

 electrified body. 



The last result, namely, the mechanical force acting on an electrified body, 

 /ives rise to an independent method of electrical measurement founded on its 



