370 Dr. J. Larmor. Complete Scheme of Electrodynamic 



In these formulae, with the exception of the one for ( ls v h w^ 

 above, (A, B, C) includes the quasi-magnetism arising from electric 

 convection, while (, r, w) is the total electric current that remains 

 after all magnetic effect of whatever type has been omitted. It is 

 to be noted that the final terms in X involve in strictness the 

 asthereal force, instead of the electric force as in 39. 



It follows from the formula for (P, Q, R) that 



^?_^9- _?^ / j,jL A 



dy dz dt \ dx dy dz 



hence Faraday's circuital relation holds good provided the velocity 

 (pj q, r) of the matter is uniform in direction and magnitude. 

 Again, since (F, Gr, H) is a stream vector, 



dc db _ 2-Bi _ / ,dG 

 dy dz \ dy 



where (, v, w) represents the total current of Maxwell, and (A, 

 B, C) the whole of the magnetism and the quasi- magnet ism of con- 

 vection : hence 



dy dz 



so that Ampere's circuital relation holds, with the above definition of 

 (a, /3, 7). under all circumstances. 



But in circumstances of electric convection these two circuital 

 relations would not usually by themselves form the basis of a com- 

 plete scheme of equations, as they do when the material medium is 

 at rest. 



To complete the scheme, the above dynamical equations must be 

 supplemented by the observational relations connecting the conduc- 

 tion current with the electric force, the electric polarisation Avith the 

 electric force, and the magnetism with the magnetic force. In the 

 simplest case of isotropy these relations are of types 



u' = ffP, f (K l)/47rC 2 P, A Kx + (rg'qh f ). 



It is to be observed that the physical constants which enter into the 

 expression of these relations will presumably be altered by motion 

 through the aether of the material system to which they belong : 

 but because there is nothing unilateral in the system, a reversal of 

 this motion should not change the constants, therefore their altera- 

 tion must depend on the square pf the ratio of the velocity of the 

 system to that of radiation, and would only enter in a second 

 approximation. 



The various problems relating to electric convection and optical 



