790 THE BELL SYSTEM TECHNICAL J(3URNAL, JULY 1952 



Multiplying (18) by [-a7\„)/e2 dv] dS, (19) by [a7\„o/ei du] dS, adding, 

 and integrating over the cross-section, we obtain 



-X(.)T .,(») + -^ = jco jj ^B. ^-^ - B. ^ dS . (22) 



In the first term the summation con\'ention should be ignored. Multiply- 

 ing (18) by [dT[,n]/ex du] dS, (19) by [dT[m]/e2 dv] dS, adding, and in- 

 tegrating we find 



dV[m] . ff I n dT[m] , „ dT[„,] 



Jc Bu -^ + B.. "-^ dS. (23) 



dz JJ \ e\ du 62 dv / 



Multiplying (21) by T[n,] dS and integrating, we have 



^[»] = -> f{B.T[„] dS. (24) 



Subjecting the right column of (17) to a similar treatment, we obtain 

 three additional equations. Summarizing, we have 



^ = j. ff (5„ ^ - B„ ^) dS + X(.)T^.(.) , (25) 



dz J J \ 62 dv 6i du J 



^ = -2. ff (Z). ^ + D. ^) dS, (26) 



dz J J \ 6i du 60 dv / 



^ = -j^ ff (b. ^ + 5. '^) dS, (27) 



dz J J \ 6i du 6-2 dv / 



'^^"' = Jo^ ff (-Du ^ + D. '-^^ dS + xt.]/-MH , (28) 



dz J J \ 6i dv Ci du 



Ff.] = -jo: fJBJ\,n^ dS, /(.) = -jo: \\D.T,m, dS. (29) 



In the last terms of equations (25) and (28) the summation convention 

 should be ignored. 



If the components of B and D are linear functions of the components 

 of H and E respectively, then with the aid of (15) and (16) they can be 

 expressed as linear functions of F(„) , V[n] , /(„) , I[n] , Vz,(„) , L,[n] - 

 Solving (29) for Fs,(„) and I,,[n] and making the appropriate substitu- 

 tions in (25), (26), (27), (28), we obtain the generalized telegraphist's 



