﻿THE 
  

   LONDON, 
  EDINBURGH, 
  and 
  DUBLIN 
  

  

  PHILOSOPHICAL 
  MAGAZINE 
  

  

  AND 
  

  

  JOURNAL 
  OP 
  SCIENCE, 
  

  

  

  [FIFTH 
  SERIES.] 
  

  

  MAY 
  1898. 
  \ 
  

  

  V 
  

  

  MA 
  

  

  XLII. 
  On 
  Electromagnetic 
  Induction 
  in 
  Plane, 
  Cpfinch-ical 
  , 
  

   and 
  Spherical 
  Current- 
  Sheets, 
  and 
  its 
  Representation 
  by 
  

   Moving 
  Trails 
  of 
  Images. 
  — 
  Parts 
  II. 
  & 
  III. 
  By 
  Gr. 
  H. 
  

   Bryan, 
  Sc.D. 
  9 
  F.B.S.* 
  

  

  Part 
  H. 
  Cylindrical 
  Sheets. 
  

  

  IN 
  the 
  Philosophical 
  Magazine 
  for 
  August 
  1894, 
  I 
  showed 
  

   how 
  to 
  obtain 
  in 
  a 
  simple 
  way 
  the 
  surface-conditions 
  

   satisfied 
  by 
  the 
  magnetic 
  potential 
  at 
  a 
  thin 
  sheet 
  of 
  metal 
  of 
  

   finite 
  conductivity 
  of 
  any 
  form, 
  in 
  which 
  currents 
  are 
  induced 
  

   by 
  the 
  motion 
  of 
  magnets 
  on 
  either 
  side 
  of 
  the 
  sheet. 
  

  

  In 
  the 
  case 
  of 
  a 
  cylindrical 
  sheet 
  of 
  small 
  thickness 
  c, 
  

   conductivity 
  C, 
  and 
  radius 
  a, 
  the 
  magnetic 
  potentials 
  X^ 
  and 
  

   Xl 
  2 
  inside 
  and 
  outside 
  the 
  sheet 
  were 
  found 
  to 
  be 
  connected 
  

   by 
  surface-conditions 
  (at 
  r 
  = 
  a) 
  which 
  may 
  be 
  written 
  

  

  d 
  / 
  rfQA 
  d( 
  tffiA 
  R 
  d 
  d 
  

  

  Tt{ 
  r 
  ^) 
  = 
  dt\ 
  r 
  ^)=2^ 
  r 
  dr^' 
  a 
  ^' 
  ' 
  ^ 
  

  

  involving 
  the 
  condition 
  d£lj/dr=d£l 
  2 
  /dr; 
  where 
  

  

  1 
  

  

  R= 
  

  

  2ttCc' 
  

  

  so 
  that 
  R 
  is 
  the 
  velocity 
  with 
  which 
  the 
  trails 
  of 
  images 
  in 
  a 
  

   plane 
  sheet 
  of 
  the 
  same 
  thickness 
  and 
  conductivity 
  would 
  

   move 
  away 
  from 
  the 
  sheet. 
  

  

  * 
  Communicated 
  by 
  the 
  Physical 
  Society 
  : 
  read 
  February 
  11, 
  1898. 
  

   Phil 
  Mag. 
  S. 
  5. 
  Vol. 
  45, 
  No. 
  276. 
  May 
  1898. 
  2D 
  

  

  