﻿Magnetic 
  Shells 
  equivalent 
  to 
  Circular 
  Coils. 
  327 
  

  

  pair 
  of 
  filaments 
  considered. 
  The 
  total 
  force 
  between 
  the 
  

   four 
  mutually 
  attracting 
  or 
  repelling 
  pairs 
  of 
  filaments 
  is 
  

  

  ■= 
  i^iTioC 
  2 
  X 
  sum 
  of 
  the 
  four 
  values 
  of 
  -, 
  — 
  . 
  

   * 
  ax 
  

  

  25. 
  As 
  an 
  example 
  I 
  give 
  the 
  leading 
  figures 
  in 
  the 
  

   calculation 
  of 
  the 
  constant 
  of 
  the 
  current-balance 
  used 
  by 
  

   Lord 
  Ray 
  lei 
  gh 
  and 
  Mrs. 
  Sidgwick. 
  

  

  Particulars 
  of 
  the 
  large 
  coils 
  : 
  — 
  

  

  tfjzzra/^ 
  24-81016 
  

   £ 
  1 
  = 
  l-5 
  ; 
  ^ 
  = 
  1-29. 
  

   Number 
  of 
  turns 
  on 
  each 
  = 
  ^ 
  = 
  225. 
  

   It 
  is 
  a 
  thick 
  double-shell 
  coil 
  and 
  its 
  equivalent 
  radius 
  r 
  x 
  

  

  being 
  ="i(l+^) 
  

   is 
  =24-81295. 
  

   Its 
  equivalent 
  breadth 
  2/3 
  is 
  given 
  by 
  

  

  ft- 
  12 
  ' 
  

  

  hence 
  

  

  /5 
  1 
  2 
  = 
  -0490 
  and 
  ft=-221. 
  

  

  The 
  distance 
  between 
  the 
  median 
  planes 
  of 
  the 
  two 
  large 
  

   coils 
  was 
  25 
  cms. 
  

  

  Particulars 
  of 
  the 
  suspended 
  coil 
  : 
  — 
  

  

  a 
  2 
  approximately 
  =10*25, 
  

  

  f 
  2 
  =l-3843, 
  77 
  2 
  = 
  -9690, 
  

  

  Number 
  of 
  turns 
  (>? 
  2 
  ) 
  — 
  242. 
  

  

  It 
  is 
  also 
  a 
  thick 
  double-shell 
  coil 
  whose 
  equivalent 
  radius 
  

   (V 
  2 
  ) 
  will 
  be 
  determined 
  by 
  Bosscha's 
  method 
  and 
  whose 
  

   equivalent 
  breadth 
  2/3 
  2 
  is 
  given 
  by 
  

  

  P*- 
  12 
  ' 
  

   hence 
  

  

  /3 
  2 
  2 
  = 
  -0814 
  and 
  /3 
  2 
  = 
  '285. 
  

  

  It 
  was 
  found 
  that 
  when 
  balance 
  was 
  obtained 
  in 
  Bosscha's 
  

   comparison 
  method 
  with 
  resistances 
  I^ 
  and 
  R 
  2 
  in 
  the 
  parallel 
  

   arms 
  containing 
  either 
  of 
  the 
  large 
  coils 
  and 
  the 
  small 
  coil 
  

  

  