FKOr.tC.ITKKW or ELECTRIC U'AIES OVER THE E.lRTIl 223 



of s and / and ilu- .ippropri.Ki- soliiiions of ilio fimd.inuiit.il (•(|iialii>iis 

 (5) are 



A-' = .la.s.(/-^;.^). 



r= -.4 sin «(/-— V Mr = fi + a, 



A'" = ^l cos w (l-y-)' 



Y" = A sin /; ('-^'"-)' m/ = «i-". 



whirli rt-pri'si-nt two opposilcK- circularK' polari/ed components 

 traNclinj; with the different \elocities — and —. The plane of poiar- 

 ization is rotated through an angle of 2 tt in a distance given by 



The third case to be considered is that of propagation at right 

 angles to the magnetic field, say in the direction of x. For this case 

 equations (5) become: 



X = ^Y 



-„^>>'-("-f> 



n- 

 of which the solutions are 



A = — Fo f ^ 'I 

 «i 



.-(,-'^) , a' 



Z = Zo 



ll 1-^" 



The first of these is merely the (usually small) component of field 

 required to make the total current solenoidal, that is, to balance the 



