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IX. On the Self-inductance of Circular Coil* of Rectangular Section, 

 Ity T. H. LYLE, M.A., Sc.D., F.K.S. 



Received February 27, Read March 13, 1913. 



As an approximate formula for the calculation of the self-inducfcince of a coil of 

 rectangular section, 



L = 47rn a jlog^-2} 



was first given by MAXWELL,* where a is the mean radius and > the geometric mean 

 distance of the section of the coil from itself, the current being supposed to be 

 uniformly distributed over the section. 



In the following paper it will be shown that the same formula will give the self- 

 inductance to any order of accuracy when in it are substituted for a and r the mean 

 radius and the G.M.D. respectively, each suitably modified by small quantities which 

 depend on a and on the section of the coil, provided, of course, that the series for L is 

 convergent. 



Tables will be given by means of which the modified values of a and r for any coil 

 of rectangular section can be found, and which, when substituted in the above formula, 

 will give L correct to the fourth order, uniform current density over the section being 

 assumed. 



1. For the purpose of this paper the mutual inductance of two coaxal circles can 

 best be obtained after WEiNSTElNt by substituting in MAXWELL'S exact elliptic 

 integral formula! 



M = Waft {(-*) F- fE 



I \ / " 



the series expressions for F and E in terms of the complementary modulus V. 

 Thus we obtain 



which is rapidly convergent when /', the ratio of the least to the greatest distance 

 between the circles, is small. 



* ' Elect, and Mag.,' vol. II., 706. 



t ' WiED. Ann.,' 21, p. 344, 1884. 



J ' Elect, and Mag.,' vol. II., 701. 



VOL. cexiir.-A 505. Pubiuhed -I*' J ""* 31 ' 101 *- 



