TRANSMISSION PROPERTIES OF CLOGSTON TYPE CONDUCTORS 709 



where: ei = e(l + i^/O = Dielectric constant of insulation between 

 inner and outer conductors. 



At the present time no exact formulas for the internal components 

 of either L or C are available. The internal inductance, however, must 

 be nearly equal to that of a solid wire for the inner laminated conductor 

 and to that of a solid sheath for the outer laminated conductor, and 

 will be assumed so in this paper. 



It should be remembered that deep penetration of the currents will be 

 obtained when Clogston condition of constant speed of propagation over 

 the entire cross section of the cable is satisfied. The speed of propagation 

 over the laminated conductors is equal to iVLindn and in the main 

 dielectric between the two conductors equal to IVLexCex • Thus to obtain 

 the Clogston condition the following relation must hold: 



LinCin = Les^Cex • (27 ) 



By solving for the unknown quantity Cin and substituting the result 

 in (24), the impedance of Clogston I cable is found to be: 



z,= 



^in /Z/ex 



Led V Ce. 



1 + i^ i/^ ohms. (28) 



Formulas for Lin, Lex and Cex in units convenient for numerical evalu- 

 ation are given later in the section summarizing the formulas. 



2.3 Attenuation and Phase 



The attenuation of Clogston I cable neglecting leakance is obtained 

 from the following expression: 



The phase constant, at the frequencies considered, and where the 

 ac resistance of the conductors does not depart appreciably from the 

 dc value, is equal to: 



/3l = CO VLC = ^ /j/ (Lin + LeJ cJYCe. ' 



(30) 



which with (27) above reduces to: 



i8i = CO VL^iC;; . (31) 



