274 



BELL SYSTEM TECHNICAL JOURNAL 



distance from the conductors. Consequently, for a given area cir- 

 cumscribed by the shield, a reduction of attenuation can be secured 

 by changing the shape of the shield. 



The problem of determining the shape of shield which gives minimum 

 high-frequency attenuation presents extreme difficulty, and a rigorous 

 solution has not been obtained. However, it appears that a close 

 approach to the ideal shape can be obtained by a shield having the 

 cross-section shown in Fig. 14, which consists of two semi-circles 



joined by straight lines, the inner conductors being placed at the 

 centers of the semi-circles. For convenience this shape of shield will 

 be termed "oval." 



The optimum proportioning -" for a pair of conductors with such an 

 oval shield may be closely approximated by comparison with the 

 pair with circular shield and with the double coaxial circuit. In such 

 comparison the cross-sectional areas of the different circuits will be 

 assumed equal. 



Consideration will first be given to the case where the enclosed 

 conductors in Fig. 14 are of solid material. The conductivity of the 

 conductors will be assumed the same as that of the shield, it being 

 apparent that the same methods may be employed in the case of dif- 

 ferent conductivities. In arriving at the spacing ratio of the conduc- 

 tors for minimum attenuation, the condition for minimum capacitance 

 will be used as a stepping stone. The spacing ratio of the conductors 

 in Fig. 14 may be represented by ho/{co + h). Comparison with 

 Fig. 7 shows that the corresponding ratio for that figure is h/c, which, 



