lunations of a Moving Material Medium, cj-c. 369 



It is to be observed that this effective current satisfies the condi- 

 tion of incompressible flow,* which by definition (or rather by the 

 aethereal constitution) is necessarily satisfied by the total current 

 (u, v, w) of the previous memoirs ; for the additional terms which 

 represent the magnetism clearly satisfy the stream relation. f The 

 remainder of the scheme of electrodynamic relations is established as 

 in the previous memoirs. Thus (F, G, H) now representing simply 

 j(^i> ^i> Wi)r -1 ^T, which satisfies the stream relation dFldx + dGldy + 

 dH/dz = because (u it v-^ Wi) is a stream vector, we deduce an 

 electric force (P, Q, R) acting on the electrons, where 



also an aefchereal force (P', Q', R') straining the aether, where 

 P' = -lire 3 - 1 / = 



the function % being determined in each problem so as to avoid 

 aethereal compression. 



Across an abrupt transition, F, G-, H and the normal component 

 of (i, ri, w\) must be continuous, thus making up the four necessary 

 and sufficient interfacial conditions. The gradients of F, G, H are, 

 however, not continuous when there is magnetisation or dielectric 

 convection, on account of the effective interfacial current sheets 

 before mentioned. 



The exact value of the mechanical force (X, Y, Z) per unit 

 volume, comes out as 



Q , A , r> , n 



X (v~ 7 (w -y-)/3+A + B -f C-y 

 \ dt ! \ dt / dx dy dz 



where a = dHe dGtfc 4wA. 



* It is proposed to call a flow-vector which obeys this condition a stream, the 

 more general term^ow ovjlitx including cases like the variable stage of the flow of 

 heat in which the condition of absence of convergence is not satisfied. The two 

 main classes of physical vectors may be called fluxes and gradients, the latter name 

 including such entities as forces and being especially appropriate when the force 

 is the gradient of a potential. Lord Kelvin's term circuital flux has previously 

 been used to denote a stream vector ; but it is perhaps better to extend it to a 

 general vector which is directed along a system of complete circuits. 



f The (, v, w} of 13, however, included a part arising from convection of 

 electric polarisation. Notice that when this is transferred to the magnetism, as 

 here, we have u n' + dfldt + dfldt+pp: thus when there is no conduction and 

 p is therefore wholly convected so that Spjdt is null, the stream character of the 

 total current simply requires d(f+f'} l dx + d(g+g')ldy + d(h->rh')ldz == p. so that 

 the formulation is now easier and more natural. 



