﻿Magnetic 
  Shells 
  equivalent 
  to 
  Circular 
  Coils. 
  319 
  

  

  The 
  most 
  sensitive 
  position 
  in 
  which 
  to 
  place 
  the 
  small 
  coil 
  

   is 
  that 
  at 
  which 
  dH/dx 
  is 
  a 
  maximum, 
  that 
  is 
  when 
  the 
  small 
  

   coil 
  is 
  at 
  a 
  distance 
  from 
  the 
  needle 
  (and 
  the 
  plane 
  o£ 
  the 
  large 
  

   coil) 
  equal 
  to 
  one 
  half 
  of 
  its 
  equivalent 
  radius. 
  

  

  For 
  this 
  position, 
  equation 
  I. 
  becomes 
  

  

  so 
  that 
  

  

  111 
  n 
  2 
  8 
  

  

  B/.5^5 
  Ri 
  

   JV 
  8 
  IV 
  

  

  R 
  x 
  and 
  R 
  2 
  being 
  the 
  resistances 
  in 
  Bosscha's 
  comparison 
  

   method. 
  

  

  Hence 
  we 
  arrange 
  the 
  resistances 
  R/ 
  and 
  R 
  2 
  ' 
  so 
  that 
  

   their 
  ratio 
  is 
  5\/o/8 
  times 
  the 
  resistance 
  ratio 
  in 
  Bosscha's 
  

   method, 
  adjust 
  the 
  small 
  coil 
  accurately 
  first 
  on 
  the 
  east 
  and 
  

   then 
  on 
  the 
  west 
  o£ 
  the 
  large 
  coil 
  so 
  that 
  the 
  magnet 
  is 
  

   unaffected 
  ; 
  the 
  distance 
  between 
  these 
  two 
  positions 
  is 
  the 
  

   equivalent 
  radius 
  of 
  the 
  small 
  coil. 
  Four 
  determinations 
  of 
  

   r. 
  2 
  can 
  be 
  made 
  by 
  varying 
  the 
  relative 
  aspects 
  of 
  the 
  faces 
  of 
  

   the 
  two 
  coils, 
  and 
  increased 
  sensitiveness 
  can, 
  if 
  desired, 
  be 
  

   obtained 
  by 
  using 
  a 
  compensating 
  magnetic 
  system 
  to 
  partly 
  

   neutralize 
  the 
  earth's 
  field. 
  This 
  is, 
  however, 
  rarely 
  necessary 
  

   as 
  the 
  method 
  is 
  exceedingly 
  sensitive. 
  It 
  would 
  be 
  an 
  advan- 
  

   tage, 
  however, 
  when 
  extreme 
  accuracy 
  is 
  required, 
  as 
  one 
  

   could 
  then 
  work 
  with 
  smaller 
  currents, 
  and 
  so 
  minimize 
  the 
  

   variation 
  of 
  the 
  resistances 
  due 
  to 
  heating. 
  

  

  15. 
  Similar 
  treatment 
  can 
  obviously 
  be 
  applied 
  to 
  the 
  

   large 
  coil. 
  Thus 
  when 
  the 
  coplanar 
  resistance 
  ratio 
  is 
  now 
  

  

  13 
  // 
  8 
  1? 
  

  

  changed 
  to 
  R 
  1 
  // 
  /R2 
  // 
  so 
  that 
  —7-/ 
  = 
  — 
  ~r 
  ^ 
  anc 
  ^ 
  ^ 
  ne 
  large 
  

  

  J*2 
  5 
  v 
  5 
  1*2 
  

  

  coil 
  moved 
  to 
  equilibrium 
  positions 
  east 
  and 
  west 
  of 
  the 
  small 
  

   coil 
  and 
  the 
  needle, 
  the 
  distance 
  between 
  these 
  two 
  positions 
  

   of 
  the 
  large 
  coil 
  will 
  be 
  equal 
  to 
  its 
  equivalent 
  radius. 
  This 
  

   determination 
  can 
  then 
  be 
  used 
  to 
  check 
  the 
  one 
  made 
  by 
  

   moving 
  the 
  small 
  coil. 
  

  

  16. 
  Plate 
  VI. 
  shows 
  a 
  diagrammatic 
  section 
  of 
  the 
  apparatus 
  

   I 
  have 
  used 
  for 
  the 
  above 
  purpose. 
  

  

  A 
  is 
  a 
  strong 
  wooden 
  base 
  on 
  levelling-screws. 
  B 
  is 
  a 
  

   strong 
  flat 
  bar 
  which 
  can 
  slide 
  parallel 
  to 
  the 
  length 
  of 
  the 
  

   base, 
  and 
  can 
  be 
  clamped 
  in 
  any 
  position 
  to 
  a 
  slow-motion 
  

   screw 
  a 
  of 
  small 
  pitch 
  and 
  having 
  a, 
  small 
  range. 
  To 
  B 
  is 
  

   attached 
  an 
  upright 
  piece 
  C, 
  one 
  of 
  whose 
  faces 
  is 
  very 
  carefully 
  

   planed 
  and 
  set 
  perpendicular 
  to 
  the 
  upper 
  surface 
  of 
  B 
  and 
  to 
  

   the 
  line 
  of 
  motion 
  of 
  B. 
  To 
  C 
  the 
  larger 
  coil 
  is 
  to 
  be 
  attached 
  

  

  