164 



Mr MayaU, On Current Sheets, especially [Feb. 26, 



Suppose 



sm 



Oo = A,&P'J,r, (or) e±5^ md, 

 cos 



where J^ denotes a Bessel's function of the first kind and of order 

 m. We may then assume 



sm 



n, = A,e'P'K,n (qr) e^^' md, 

 cos 



sm 



•(14); 



n, = A^e^P'J,^ (qr) e±3^ mO 

 cos ; 



Km being the corresponding Bessel's function of the second kind, 



and equal to 



r°° dr 



Jm(qr)ljL^, 



a ' " m 



SO that K^ = J^ at the surface of the cylinder and vanishes when 

 r is infinitel}^ large. 



Then 4^7r^ = ft, - ft, 



sin 



= (^1 - A.) /,„, (qa) ^v^e-^i^ mO (15) 



sntia 



^ (^x - ^.) (- ^V ^^ ) J.. =-w (^. + ^o) j: ■ ■ -(16), 



)us at the surface 



AiK^ = A2,Jm (!')> 



hence substituting in (13) and denoting differentiation by dashes, 

 we have 



also since -y— is continuous at the surface 

 dr 



therefore 

 Ai A^ 



jO.! — wO.? 



T ' tr ' T ' — T^ ' 



" «?, -^i vn. ^ m. -^i- Tin. 



dr 



rO rfYt, 



yA^ — -n-a) ftt/m I 

 J a 



- ipaJJ \ J. 2 

 = (^^ + ^o) ^ . J: " by (16), 



dr 



47rV a^ '^^" 



y...(18), 



and therefore 



f dr 



and the constants are determined. 



ipaJ^Km I 



J a 



dr 



