531 Dr. A. Russell on the Effective Resistance 





ber30. 



bei 30. 



ber' 30. 



bei' 30. 



Mascart & Joubert ... 

 Formulae 



-4544X10^ 

 -4611x104 



11024x104 

 10995 X 104 



-10933x104 

 -10959x104 



4383X104 

 4330x104 





Hence the ordinary tables need revision. A more useful 

 set of tables, however, might be constructed of the functions 

 X, Y, Z, W, Y/X, Z/X, W/X, Z/Y, and W/Y. The ber 

 and bei functions never occur alone in any of the practical 

 formulae using these functions, with which the author is 

 acquainted. 



For instance, Heaviside * and Kelvin * have proved that 

 the ratio of the effective resistance of the inner core of 

 a concentric main with high frequency currents to its 

 resistance with direct currents can be written down almost 

 at once, when the ratio of W to Y is known. It was in 

 fact in order to find the value of this ratio that Kelvin had 

 a table of ber and bei functions computed. 



The values of W/Y given in Kelvin's paper and found 

 by (15) and also by direct computation are compared in 

 the following table : — 



X. 



Values given 1 Values computed 

 in Kelvin's paper. by (15). 



True Values. 



0-5 

 1-0 

 1-5 

 20 



4-0000 

 2-00014 

 1-3678 

 1-0805 



4-0013 

 20104 

 1-3678 

 1-0782 



4-0013 

 2-0104 

 1-3678 

 10782 



In Kelvin's table bei'l is given as 0*4:999, but its true 

 value is 0*4974. Making this correction and using Kelvin's 

 figures, we get 2*0104 for the value of W/Y when x is 1. 



Including the next term in the expansion of W/Y given 

 in (31), we find that 



°4^ • • (32) 



* 0-7071 + 1 + °^> 



. Y zx x 2 



The values of W/Y given in the first column of the 

 following table have been computed by this formula. 



* L, c. ante. 



