Gi ii)i:u ^^■AVE propagation thuoigii gyuomagxktic media, hi 11(11 



originally present //?* ' mode Avill be large; all others will at most be of the 

 order of the perturbation. Denoting perturbed quantities by the supeifix 

 + , we have for the distorted fields 



Elm = e '" ' ^"=1 PmnEtn , 

 J^ tm — C Zw 1=1 9mn" tn , 



where pmm and gmm are large compared AAith the other coefficients, ^ti 

 and the p's and g's are determined from equations (7a) and (7b). a„ in 

 these equations is identified with e""'*^'" ' p^r , hn ^^■ith e"-'^"' ' q^n ■ Since 

 all perturbation integrals involving Et and H^ , E^ vanish in the present 

 case, we obtain 



PnQmn PmPmn "T 



fit, - Ho)H'[mHtn dS -j f KH^*Htn clS 



and 



In the first of these equations, Htn , the perturbed magnetic field, con- 

 sists of QmrnHtm , plus an admixture of other modes with coefficients them- 

 selves of order m — Mo , «• Therefore, to first order, it suffices to write 



in the integrand, with the result: 



PnQmn PmPmn ■» mnQmrn j 



Pmn ^ Qmn > 



where 



IL = -^ [ ifi - H,)H„nHtn - JkHLHu] dS. 



An 



Elimination of p,„„ gives 



(/3^„ - ^m^)qmn = ^nltnqmn • 



The case n = m determines ^m': 



^t' = /3^(l - li,n,^J. (23) 



All other cases give, to first order, 



B 7"^ 



Ki-* "in 



