HYPER-FREQUENCY TRANSMISSION 319 



and for the //-wave 



nn', rn/, • • • = 3.83, 7.02, • • • 

 rn',r,i', ••• = 1.84,5.33, •••. 



Hence, it is possible to transmit a fundamental /t-wave if the radius, 

 dielectric constant, permeability and frequency are so related that, 



fa^J^^2A05{c|2^^), (11) 



a fundamental //-wave provided, 



fa^[7fl ^ 3.83(c/27r), (12) 



the component En of the £-wave provided 



fa^|^^3.83(cJ2^^) (13) 



and the component II n of the //-wave provided 



/aV^^ 1.84(c/2x). (14) 



Thus from the standpoint of minimum physical constants and di- 

 mensions the component Hn of the //-wave is most advantageous. 

 The consideration of the attenuation characteristics below will show, 

 however, that this advantage is outweighed, since in practice the 

 attenuation will be the controlling factor. 



We shall now consider the characteristic impedance of the system. ^^ 

 While the derivation of the characteristic impedance is interesting and 

 valuable on its own merits, it also provides the basis for a quasi- 

 synthetic and approximate method of deriving the attenuation which 

 will be developed below. The results obtained here on the assumption 

 of a perfect conductor will be valid in the dissipative case of the 

 next section provided the conductivity is sufificiently high so that the 

 relation, 47ro- » eco/c^, obtains among the constants of the sheath. 



The characteristic impedance, K, is here defined as the transverse 

 Complex Poynting Vector, P, integrated over the cross section of the 

 system divided by the mean square current. Thus we have, in general. 



P =:l^jdSlE-H*:\, 



(15) 



= W + i2oi{T - U), 



'' See the discussion of the characteristic impedance in Section I of this paper. 

 Equation (15) below is in agreement with the definition there given. 



