192 Prof. J V. Jones. Calculation of the Coefficient of 



" 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 Professor J. 

 VIRIAMU JONES, F.R.S. Received November 12, Read 

 December 9, 1897. 



1. In measuring electrical resistance by the method of Lorenz we 

 have to determine the coefficient of mutual induction of a helix of 

 wire and the circumference of a rotating circular disc placed coaxi- 

 ally with ifc, the mean planes of the helix and the disc being 

 coincident. In a paper presented to the Physical Society in 

 November, 1888, I gave a method of calculating this coefficient ; but 

 subsequent consideration of the problem in connection with the 

 Lorenz apparatus recently made for the McGill University, Montreal, 

 has led me both to a simplification of the method previously des- 

 cribed, and also to a more general solution. 



2. If M is the coefficient of mutual induction of any two curves 

 we have 



where r = the distance between two elements c7s, ds ; and e = the 

 an^le between these elements. Let the equations to the circle and 

 coaxial helix be 



y = a cos 0~] 



' z = a sin 6 



x = J 



and i/' = Acos 



z = A sin 9' 

 x' = pO' 

 dxdx' + dydy' + dvdz' 



- 



-r 



Jo 



Aacos(0-0'}cl0d0 f 



\/{A:*+O~ 2 AC* cos (0 0') -\-p~0'* 



If we change the variables, putting 



