32(1 BELL SYSTEM TECHNICAL JOURNAL 



Similarly the boundary equations can be satisfied when H^, = pro- 

 vided n = but not when n 9^ 0. 



Although E; and Hz must co-exist in the dissipative case, one or 

 the other will predominate in the actual wave provided the conduc- 

 tivity is so high that 4ir(T2 » faW^^- a condition which is true of a good 

 conductor unless / ^ <x . That this is so or, in other words, that the 

 actual wave approximates either an E- or an //-wave will now be 

 shown from equation (40). Since it is assumed that the conductivity 

 is high or that 



47ra2 » eoco/c2 and Jh'^ » y\ (43) 



X = a\ — ^TTCitXiiixi and the asymptotic values of Knix) and Knix) are 

 valid. Equation (40) may then be written 



\Mi yJn{y) fJLia/\ yJn(y) ahi/ \y- a-hi^/ 



When ho = x , (44) reduces to 



Jn(y) = provided /„(>-) ^ (45) 



j^Xy) = provided Jn(y) 9^ 0. (46) 



and to 



Thus there are two possible solutions of (44). These are in the neigh- 

 borhood o{ y — r and of 3* = r', where r and r\ respectively, are roots 

 of Jniy) = and of Jn'{y) = 0, the equations characterizing the 

 E- and the Il-wave, respectively. We shall, therefore, refer to E- and 

 //-waves in the dissipative case with the understanding that the actual 

 wave approximates either one or the other type in a cylinder of suffi- 

 ciently high conductivity. 



As stated above, the propagation constant 7 may be determined by 

 solving equation (40). The procedure is straightforward but is com- 

 plicated by the necessity for approximations and does not easily admit 

 of physical interpretation. We may obtain the same attenuation for- 

 mulas by means of the quasi-synthetic method developed at the end 

 of Section II. 



The high-frequency attenuation of the symmetric E- and //-waves 

 is easily derived from equation (38). Here R, the resistance per unit 

 length of the cylinder for the E-wave at sufficiently high frequencies, 

 is given by 



R = yj^^ll^. (47) 



