4 ART. 15. — H. NAGAOKA : NOTE ON THE POTENTIAL 



But i> Jl?.o)= àjpUXp)) 



À dp 



Thus the potential of a circular disc is given by 



IJ=2' a/'Ä^ Joi^^x) JiXa) dX. (4) 







This expression was first obtained by H. Weber'^ in a somewhat 

 different manner. 



§ 4. Potential and lines of force of a nniform circular magnetic 

 shell. — The potential of a circular magnetic shell of unit strength is 

 evidently given by 



CO 



^= -^ = 2 - J e-'' Jlk x) J,{?. a) d k, (A) 







and for the function giving lines of force 



CD 



é= -x^^=27Taxfe-^-' J Ik x) JiX a) d X. (B) 



^x J 







The two expressions (A) and {B) can be greatly simplified by 

 using the addition theorem for JJß X) and Ji{R X). 



Differentiating (3) with respect to p and integrating between 

 the limits and t: of ^, 

 we obtain 



JlXx) J, {Xa)=^f-^^ (a-x cos 6) d 6. 







Similarly 



J,{Xx) J, {Xa)=^fjlXB) cos d dd. 







1) H. Weber, Crelle'e Journal, B(î. 75, p. 88. 



