1146 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



0.25 I , 1 ^ , ^ 1 , 1 1 1 0.75 



0.20 







3.0 



0.70 



0.65 ^ 



0.55 



0.5 



0.1 0,2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



(S, + S2)/b 



Fig. 15 — Relative proportions and relative attenuation constants of optimum 

 Clogston cables with different filling ratios and mo = m, «o = «■ 



mum values of these two ratios in the extreme Clogston 1 case, where 

 (si + So) « b, have already been given in equations (138) and (139) of 

 Section lY, while in a complete Clogston 2 with Si + So = h, the stacks 

 should be' divided at the radius 0.62766, where according to equation 

 (314) the current density is zero. For intermediate filling ratios, with 

 any fixed magnetic loading ratio mo/m, the optimum distribution of 

 laminated material can most easily be found numerically by calculating 

 Xi or (xiby for a number of different choices of the ratios a/b and 

 Si/(si + S2), and then locating the minimum by double interpolation. 



The results of applying this numerical procediu-e to Clogston cables 

 with various filling ratios and no magnetic loading are plotted in Fig. 

 15, the necessary values of xib having been found on the analog com- 

 puter and then refined by desk computation. Fig. 15(a) shows the op- 

 timum values of a/b and Si/(si + S2) as functions of the filling ratio 

 (si + S2)/b, while Fig. 15(b) shows the corresponding value of {xib/S.8S)', 



