1895.] of the Electric and Luminiferous Medium. 225 



represent electrification. It has been pointed out by von Helmholtz 

 and others, that the abstract dynamical analysis given in his Treatise 

 does not really lead to these equations when all the terms are retained ; 

 this later analysis proceeds, in fact, by the use of current-elements, 

 which form an imperfect representation, in that they give no account 

 of the genesis of the current by electric separation in the element of 

 volume of the conductor. 



The ponderomotive force (X, Y, Z) is at right angles to the direc- 

 tion of the true current, and is precisely that of Ampere in the ordi- 

 nary cases where the difference between the true current and the 

 total current is inappreciable. It differs from Maxwell's result in 

 involving true current instead of total current ; that is, the forcive 

 tends to move an element of a material body, but there is no such 

 forcive tending to move an element of the free tether itself. In this 

 respect it differs also from the hypothesis underlying von Helmholtz'x 

 recent treatment of the relations of moving matter to aether. 



When we treat of a single electron, (a, 6, c) is the flow of the aether 

 where it is situated. When we treat of an element of volume with 

 its contained electrons, (a, b, c) becomes the smoothed out, or averaged, 

 flow of the aether in the element of volume ; it is circuital because 

 the aether is incompressible, and thus it represents the magnetic 

 induction of Maxwell. 



When magnetic polarization of the medium contributes to the 

 forcive, it is necessary to divide (a, b, c) into two parts, one part 

 (a, /3, 7) contributed by the medium as a whole, and independent of 

 the surroundings of the element, and the other representing the effect 

 of the polarization in the immediate neighbourhood ; the former part 

 is, of course, the magnetic force of Maxwell. Similar considerations 

 apply as regards the electric force in a polarized dielectric ; it is 

 clearly proper to define it so as to correspond to magnetic induction, 

 not to magnetic force. It is then shown from the direct considera- 

 tion of the orbital motions of electrons, that there is, in addition to 

 the electrodynamic force on the element of volume of the material 

 medium, a magnetic force derived from a potential function 

 ^*c(a 2 + /3 2 -j-7 2 ), and a force of electric origin derived from a potential 

 (K l)/87rc 2 . (P 2 + Q 2 + R 3 ). If the element carries an electric charge 

 of density /, there is also the force p(P, Q, R). In addition to these 

 latter forces on the polarized element, there are also stresses due to 

 interaction between neighbouring parts, in which are to be found the 

 main explanation of the phenomena of electrostriction and magneto- 

 striction. 



As an example of these ponderomotive forces, the mechanical pressure 

 produced by radiation is examined later ou, with a result half that of 

 Maxwell when the light is incident on an opaque body, and which 

 gives pressures on the two sides of the interface each equal to Maxwell's 



R 2 



