and Electromagnetic Theory. 327 



forces modified by the translation (u v w). The index of 

 refraction will be denoted by //,, t. e. /r = KM, the product of 

 the electric and magnetic constants of the medium. The use 

 of the constant e to cover two cases which are held to be 

 distinct, will be pointed out after a short account of the 

 propagation of a plane wave. 

 Write 



3L = X f(lv + my + iiz — Q.t), a = a f(lx + my + nz--Q l t), ... 



with the same argument and function throughout ; then 



§ = -nx /',a„dg = zx /v... 



Thus (I.) is replaced by the algebraical equations 

 KnX=Y(n/3'-m<y / ), MOa=V(™Z'-ttY'). 

 From these follow 



2/X = 0, 11* = (22) 



corresponding to 



ax ax 



With the help of (IL), 



KnX = V(n/3-my) + eK{n(uZ-wX)-m(vX-uY)} 

 =Y(njS~my)-eKXJX 3 

 writing U for Hu, and quoting (22). Thus 



KX(X2 + eU)=V(n£-wy); 

 and Ma(n + eU) = V(mZ-nY) 



follows by similar work. Therefore 

 fJX (O + eU) 2 = V M (fl + eU) (n& - my) 



= V 2 {n(nX-lZ)-m(lY-mX)}=V 2 X 

 or + eU=+V//* (24) 



The two values correspond to waves travelling in the sensa 

 of the translation and opposite to it, both velocities measured 

 in the sense of the translation : the positive sign will be taken 

 for the standard c.ise. 



If we write x' = x + ut, ... the differential equations (I.) 

 become 



V Dt " dy' dz' ' VDt~~ dz' dy""' { } 

 where 



D d d d d 



Dt = dt+ u dJ' + v cV + w d2- 



} • (*3) 



