288 Dr. S. P. Thompson on the Formulae of the 



it the general. But this does not stand examination ; the 

 work has to be done, whether we derive the special results 

 from the general, or conversely. 

 In the solid wire case 



P _ r Ji(f£) P 

 or «iJi( s i«i) 



Cr = a 2 i * + ^"P&P + i ™ 2 )0 2 - a l) 



H-ij^^/^ + i^W-^ 



Or, use the M and N functions of Part I., equations (42) . 

 For we have 



J (s 1 r) = (M + W)(s 1 ri>), 



where s^ri* takes the place of the y in those equations. M 

 contains the even and N the odd powers of (^> + w 2 /4tt^ 1 ^ 1 ). 

 We have also 



uv ' 27ra 1 J 1 (s 1 a 1 ) 7 



r o being T at r = ; and, since by the first of these 



r ai =Jo(si«i)r 



connects the boundary and axial current-densities, we see that 

 the ratio of their amplitudes in the S.H. case is 



(M 2 + N 2 )*, 



using the r — a x expressions, with m = 0. 



I hope to be able to conclude this paper in a third part. 



XXXIV. Further Notes on the Formulae of the Electromagnet 

 and the Equations of the Dynamo. By Professor Silvanus 

 P. Thompson, D.Sc, B.A.* 



1. The Lamont-Frolich Formula, 



B. 0. FROLICH has done me the honour of replying! 

 to a certain point in my former communication to the 

 Physical Society, " On the Law of the Electromagnet and the 

 Law of the Dynamo" J. In that communication I pointed 



* Communicated by the Physical Society : read June 26, 1886. 

 t Elektrotechnische Zeitschrift, vii. p. 163, May 1886. 

 % Phil. Mag. vol. xxi. p. 1, January 1886. 



D 



