532 Prof. J. C. Maxwell on a Dynamical Theory [Dec. 8, 



of magnetic force. Professor W. Thomson* has shown that this pheno- 

 menon cannot be explained without admitting that there is motion of the 

 luminiferous medium in the neighbourhood of magnets and currents. 



The phenomena of electromotive force seem also to indicate the elasticity 

 or tenacity of the medium. When the state of the field is being altered by 

 the introduction or motion of currents or magnets, every part of the field 

 experiences a force, which, if the medium in that part of the field is a con- 

 ductor, produces a current. If the medium is an electrolyte, and the elec- 

 tromotive force is strong enough, the components of the electrolyte are 

 separated in spite of their chemical affinity, and carried in opposite direc- 

 tions. If the medium is a dielectric, all its parts are put into a state of 

 electric polarization, a state in which the opposite sides of every such part 

 are oppositely electrified, and this to an extent proportioned to the intensity 

 of the electromotive force which causes the polarization. If the intensity 

 of this polarization is increased beyond a certain limit, the electric tenacity 

 of the medium gives way, and there is a spark or " disruptive discharge." 



Thus the action of electromotive force on a dielectric produces an elec- 

 tric displacement within it, and in this way stores up energy which will re- 

 appear when the dielectric is relieved from this state of constraint. 



A dynamical theory of the Electromagnetic Field must therefore assume 

 that, wherever magnetic effects occur, therels matter in motion, and that, 

 wherever electromotive force is exerted, there is a medium in a state of con- 

 straint ; so that the medium must be regarded as the recipient of two kinds 

 of energy— the actual energy of the magnetic motion, and the potential 

 energy of the electric displacement. According to this theory we look for 

 the explanation of electric and magnetic phenomena to the mutual actions 

 between the medium and the electrified or magnetic bodies, and not to any 

 direct action between those bodies themselves. 



In the case of an electric current flowing in a circuit A, we know that 

 the magnetic action at every point of the field depends on its position rela- 

 tive to A, and is proportional to the strength of the current. If there is 

 another circuit B in the field, the magnetic effects due to B are simply 

 added to those due to A, according to the well-known law of composition 

 of forces, velocities, &c. According to our theory, the motion of every part 

 of the medium depends partly on the strength of the current in A, and 

 partly on that in B, and when these are given the whole is determined. 

 The mechanical conditions therefore are those of a system of bodies con- 

 nected with two driving-points A and B, in which we may determine the 

 relation between the motions of A and B, and the forces acting on them, by 

 purely dynamical principles. It is shown that in this case we may find two 

 quantities, namely, the '^reduced momentum" of the system referred to A 

 and to B, each of which is a linear function of the velocities of A and B. 

 The effect of the force on A is to increase the momentum of the system 

 * Proceedings of the Royal Society June 1856 and June 1861. 



