CIRCULAR COILS OF RECTANGULAR 8FX7TION. 425 



It will be seen that in the application of this formuk the coefficient , neecl rarely 



xL It ^becomes important, however, when the mean radius is leas than the 



diagonal of the section and especially in this case when the section is square or 



1 1 < '.' M ly so. 



It is obvious that in a similar way to the above, series for A and R could be obtained 

 which, when substituted in the proposed formula would make it practically equivalent 

 to L, no matter to what order the integration, if performed, had been carried out 



5. In order to render convenient the practical application of the above formula to 

 termination of self-inductances the following tables* have been prepared. 



TABUS I. 



Table I. contains (l) values of ^>, that is of log,, for different values of the ratio 



r 



b/c or c/b (2) values of the ratio r/b + c for different values of b/c. It will be noticed 

 how nearly r the G.M.D. of a rectangle from itself is proportional to the sum of the 



* All the tables given in this paper have been calculated with the greatest care by the aid of a 

 " millionaire " calculating machine. Each separate series of numbers, not only the final series but every 

 intermediate series that had to be determined, was calculated at least twice, the end terms and one or two 

 intermediate terms of each series were carefully re-checked, and each series then examined by taking 

 successive differences. 



VOL. CCXIII. A. 3 I 



