Coefficient of Mutual Induction of a Circle, fyc. 



247 



•J. W. S pen gel, " Das Urogenitalsysteni der Amphibien," 1 Arb. a.d. Zool.-zool. Inst. 



Wurzburg,' vol. 3, pp. 1—114, 1876. 

 H. Stannius, ' Handbuch der Anatomie der Wirbelthiere ' (2te Auflage), I. Buch. 



Die Fische, 1854. 



W. Turner, " On the Pori Abdominales of some Sharks," ' Journ. Anat. Phys./ 

 vol. 14, p. 101, 1879. 



M. Weber, " Die Abdominalporen der Salmoniden, nebst Bemerkungen iiber die 

 G-eschlechtsorgane der Fische," ' M'orph. Jahrb.,' vol. 12, pp. 366—406, 1886. 



<; On the Calculation of the Coefficient of Mutual Induction of 

 a Circle and a Coaxial Helix, and of the Electromagnetic 

 Force between a Helical Current and a Uniform Coaxial 

 Circular Cylindrical Current Sheet." By J. VlRlAMU Jones. 

 F.R.S. Received November 12, — Read December 9, 1897. 



(Abstract.) 



§ 1. Let M® be the coefficient of mutual induction of a circle and 

 a portion of a coaxial helix, beginning in the plane of the circle and 

 of helical angle ®. Then if M is the coefficient of mutual induction 

 of the circle, and any portion of the helix for which the extreme 

 points are determined by helical angles ®i and ® 2 , we have 



M = M© 2 — M @1 . 



It will therefore be sufficient to show how to calculate M for all 

 values of ©. 



Let the equations to the circle and coaxial helix be 



y — a cos 0~) \j — A cos 6' 



z = a sin V z — A sin 0' 



x = J x = 'pQ' 



Then it has been shown by the author* that M© may be expressed 

 by the following series which is convergent if x< A— -a 



M© = 



v ' v J 2.4.6 2m 2m + l\A + a) 



2 \/Aa _ 



where c — , x == p®, 



A + a 



cos 26d6 



2m+T 



o (1— c 2 sin 2 0)"~2~ 



* < Phil. Mag.,' January, 1889. 



