1891.] Mr Macdonald, Self-induction of two Parallel Conductors. 259 



November 23, 1891. 

 Professor Lewis in the Chair. 



S. Skinner, M.A., Christ's College, was elected a Fellow of the 

 Society. 



The following Communications were made: 



(1) The Self-induction of Two Parallel Conductors. By H. 

 M. Macdonald, B.A., Clare College. 



(Abstract) 



In Article 685, Maxwell's Electricity arid Magnetism, Vol. II., 



b 2 

 the expression ^ (/a -f- //) + 2fi log — , is given for the self-in- 

 duction per unit length of two parallel infinite cylindrical con- 

 ductors, the radii of their sections being a, a', the distance between 

 their axes b, fi, // their magnetic permeabilities, and /n that of 

 the suiTounding medium. Lord Rayleigh remarked in the Phil. 

 Mag. 1886, that this expression only holds when //, = fx = /jl o . To 

 solve the general problem for steady currents it is necessary 

 to know the conditions satisfied by the components of vector 

 potential at the bounding surface of two media of different 

 magnetic permeabilities ; they are found to be 



iap im 7 



<-\ "i" / ^ / ^3 etc. 

 /u, on ja on 



Transforming the equations by the relation 

 x + ly = c tan \ (£ + trj), 



taking tj - a, w = — /3 as the bounding surfaces of the conductors, 

 we have 



d 2 II d"H 4>TTUC0 



d% z drf (cosh t] + cos gy ' ' ' 



d 2 H n d 2 H n n , .. 



d 2 H' d 2 H' ^TTLloy' 



0% drj (cosh 7] + cos I;) 2 ' 



when 7] = a, 



when i] = — /3, 



