242 Lord Rayleigh on the Reflexion of Light 



Equations of a Dielectric Medium, of which the Magnetic 

 Permeability is Unity throughout. 



In Maxwell's notation the various components are repre- 

 sented as follows : — 



Electric Displacement /, g, h ; 



Current u, v, w ; 



Magnetic Force (or Induction) . . . . a, b, c ; 



Electromagnetic Momentum F, Gr, H ; 



Electromotive Force P, Q, R ; 



and the equations connecting them may be written 



df dq dh ,.,. 



u= i> v =di> w =dt> (1) 



dx dy dz ' ^ ' 



A _dc _db^ . __da__dc^ _db ___da .„. 



~ dy dz' dz dx' ~ dx dy' ' ^°' 



_dR_db h _^K_dR _db_dF 



a ~~ dy dz' °~dz dx' °~Tx fy' * (4) 



p ____^F__^ o-~^-^ P- dB - d ® (K\ 

 r ~ dt dx' H ~ dt dy' n -~^dt~~dz~- W 



In (1 ) it is assumed that the medium is a perfect insulator. 



Equations (4) and (5) may be replaced by 



da = dQ,__dR. db = dR__d? dc^dF^dQ 

 dt dz dy ' dt dx dz' dt dy ~dx ' * ^ 

 from which <P disappears. Thus 



, d 2 f . du d dc d db 

 dt 2 ~~ dt dydt dz dt 



^_d 2 F <PF _ d (d_Q,om\ 

 dy 2 dz* dxldy dz) 



Llidj ^_ LliV LIU LIZ J 



where as usual 



V 2 = d 2 /dx 2 + d*/dy* + d 2 /dz 2 . 



In (7) and the similar equations in g and h there is involved 

 no assumption as to the homogeneity or isotropy of the 



