﻿202 Mr. G. H. Bryan on Electromagnetic Induction in 



sheet, we shall still have as for a plane sheet 



H 2 — fi 1 = 47r<£+ constant, .... (1) 



and by application of the second law to the small circuit 

 bounding the surface-element a dddz, we have at the sheet 



dt dr ~ dt dr~ GcXrdO rdd + dz 2 S 



1 f 1 d* d 2 \, n 

 -~4^cl?aW + d?S {U2 ~ ili) 



= ^c\d? + rahj {n *- ni) > 



(dtoA d( jn 2 \ 1 d d 



V-dFj- dtV^hl^Ucdr'dr^^^' ' ' W 



or 

 d 



dt 



Surface Conditions at a Spherical Sheet. 



6. In the case of a spherical sheet of small thickness, we 

 obtain in like manner 



d dD. x 

 dt dr 

 or 



d 

 dt 



" dt dr ~ 4>irCc\df* + r dr)^ h lh 



(-*)-a(^)-fiRs£^(*-^- W 



Extension to Curved Sheets of other Forms. 



7. When the sheet is of any form other than those above 

 considered, it is necessary to assume a certain law of variation 

 of the thickness in order to put the boundary conditions into 

 a form similar to those given above *. 



Let us use orthogonal coordinates a, /3, 7; let the line- 

 element be given by 



du> d& &f 

 h? + h? + V ' 



= ^ + 



and let the equation of the current sheet be 



7 = constant. 



Equation (1) still holds, and by applying Law II. to the 

 circuit enclosed on the sheet by the curves a, a + £«, (3 and 



* Compare Watson and Burbury, §426. 



