﻿Self and Mutual Induction of Coaxial Coils. 591 



When ^>4, we obtain an accuracy of 1 in 10,000 if we 



use 



L=L 1 (i-?+|-g. > . . • • m 



in which a, /3, 7 are functions of ■?' and are tabulated below. 



Table V. 



r. 

 0-0 



«. 



,3. 



: 



>■ 



0-73238 



0-33333 



0-0953 



0-2 



073699 



0-33719 



0-0973 



04 



0-75574 



0-35579 



0-1071 



0'6 



0-78447 



0-39042 



0-1306 



0-8 



0-81718 



0-43906 



0-1701 



10 



0-84883 



0-50000 



0-2306 



The values of a, ft, 7 have been calculated from the 

 formulas 





'/y : 



.2 ( 



j^l)-2 ? ^,^)+^(^l)}, 



(49) 



with ~ = 4 in the expression for 7. Hence the tabulated 

 values of 7 are only correct for 3=4. However, for larger 

 values of 2?, the error in the final result is always less than 

 1 in 10,000. 



The above formulae fail when r=l, but in this case the 

 coil becomes a thin cylinder, the self-induction of which is 



t t /1 8 111 115 1 35 \ ,._ 



so 



that for r=l, 



8 ^ 1 1 5 



(U;- 



* Russell, Phil, Mag-, vol. xiii. p. 420 (1907) ; Elavelock, Phil Mas 

 vol. xv. p. 332 (1908). ' 



