and Inductance of a Concentric Main. 



where 



p - <** 

 1 2(c*-h* > 



545 



!(c 2 -6 2 ) 



D 9 = 



2= » 9 - ^fic'-^ P^"'" 2 ^ 3 ^ 



aW(6 2 -a 2 ) c 

 + 2.4 2 . (c 2 -6 2 ) 2 g 6 



«W /. c\ 2 



7a 2 cW 



A U 7T« V a I to (y III *d -p. 4 



-CiCa + f-logm^m 4 , (99) 



and 

 m 2 ~ 



^ + D 1 (« + f-logmc)-^C 1 m 2 



f 7r 2 9 19c l "1 



+ \^6°i + ? C 2 + D 2 («+f - log me) + 2 2 .4*.6*.2 Dl j m 



. . . (100) 



Substituting these values in (89) and (90), and using the 

 approximate formulae for the functions, we get, after lengthy 

 algebraical operations, 





(101) 



where 



_ (7c , -y )(c»-y) w 



Pl ~ 192" ~ ' *~8(c , -P)' 



p» a " A/^/jM » and ? = 1 °g/:- 



4(c 2 -/^ 



It is interesting to notice that the coefficient of m 2 

 vanishes and that the numerical constants a and log?» have 

 cancelled out. This formula is in exact agreement with 

 that* given by Oliver Heaviside. It is not quite clear how 

 he obtains the formula, but he states that the work was 

 " very heavy." 



* 'Electrical Papers/ vol. ii. p. 192 (72), 

 Phil. Map. S. 6. Vol. 17. No. 100. April 1909. 2 P 



