162 Mr Mayall, On Current Sheets, especially [Feb. 26, 



and if when ^ = 0, fl^ =f{rOz), then at the time t 



SO that the effect on either side of the sheet is the same as if the 

 currents in it remained constant, while the sheet itself receded 



with a uniform velocity ^^ , as Maxwell shewed. 



(3) Next suppose the current sheet to be spherical, a being 

 again constant. Here 



ds'' = dr^+r^de^ + r''sm^edf, 



and equation (3) is now 



d . ^d^ 1 d'm 



"" \dd'''^''' dd '"sin6' • dfj^'J 



= -a^sin^^. |;(n + Oo) (8), 



in which a the radius of the sphere is substituted for r after differ- 

 entiation. 



Let no = A,e'P^Q'^Y^, 



and assume O, = J. , e'^* - F, , 



n, = A^e^p^(^-jY^, 



F„ being a spherical surface harmonic of order n. 



Then 4<7r^ .= H^ - II, (r = a) 



= (A^-A;)e^p^Y,^ (9), 



or on substituting in (8) 



o- ., .^(d.^dY^ 1 d^Y\ 



= — ipna sin 6 {A^ + ^o) F„, 



'''' "L ^^' ~ ^'^ *' ^'' + 1) ^« = - *>^« (^2 + ^o) ^«. 



i.e. (7i+l)^(A-^2)=*>«(-^2 + A) (10)- 



Again, since -^^ is continuous at the surface 

 ^ ' dr 



{n + l)A^ + nA^ = (11); 



