﻿Magnetic 
  Shells 
  equivalent 
  to 
  Circular 
  Coils. 
  321 
  

  

  The 
  resistance 
  ratio 
  of 
  the 
  branches 
  will 
  now 
  require 
  slight 
  

   readjustment, 
  and 
  then 
  its 
  value 
  HJR2 
  is 
  determined 
  as 
  

   Lord 
  Rayleigh 
  * 
  and 
  Mrs. 
  Sidgwick 
  have 
  done 
  ; 
  by 
  means 
  of 
  a 
  

   specially 
  arranged 
  Wheatstone's 
  bridge. 
  The 
  resistances 
  in 
  

   the 
  branches 
  are 
  then 
  changed 
  to 
  R/ 
  and 
  R 
  2 
  ', 
  

  

  where 
  R/ 
  _ 
  5 
  */5 
  Ri 
  

  

  R? 
  ~ 
  ~8~ 
  R 
  2 
  ' 
  

  

  if 
  both 
  the 
  coils 
  are 
  single-shell 
  ones, 
  and 
  the 
  small 
  coil 
  moved 
  

   first 
  to 
  one 
  side 
  then 
  to 
  the 
  other 
  to 
  positions 
  in 
  which 
  with 
  

   currents 
  flowing 
  the 
  needle 
  is 
  not 
  affected. 
  The 
  distance 
  

   between 
  these 
  two 
  positions 
  is 
  the 
  equivalent 
  radius 
  of 
  the 
  

   small 
  coil. 
  

  

  The 
  small 
  coil 
  having 
  been 
  replaced 
  at 
  the 
  centre, 
  the 
  

   resistances 
  in 
  the 
  branches 
  are 
  again 
  changed 
  to 
  R/' 
  and 
  R 
  2 
  ", 
  

   where 
  

  

  R,"__ 
  8 
  R, 
  

  

  R 
  2 
  " 
  5V5V 
  

  

  •and 
  the 
  large 
  coil 
  is 
  now 
  moved, 
  first 
  to 
  one 
  side 
  and 
  then 
  to 
  

   the 
  other, 
  to 
  positions 
  of 
  equilibrium. 
  The 
  distance 
  between 
  

   these 
  two 
  positions 
  will 
  be 
  the 
  equivalent 
  radius 
  of 
  the 
  large 
  

   coil. 
  

  

  As 
  the 
  ratio 
  Ri/R 
  2 
  determined 
  in 
  the 
  first 
  part 
  of 
  this 
  

   process 
  gives 
  us 
  (see 
  § 
  13) 
  the 
  ratio 
  of 
  the 
  equivalent 
  radii 
  of 
  

   the 
  two 
  coils, 
  

  

  r 
  2 
  /i 
  2 
  R, 
  J 
  

  

  this 
  value 
  of 
  the 
  ratio 
  i\jr 
  2 
  can 
  be 
  used 
  as 
  a 
  check 
  on 
  the 
  ratio 
  

   of 
  the 
  values 
  of 
  r 
  x 
  and 
  r 
  2 
  determined 
  separately. 
  

  

  18. 
  If 
  both 
  coils 
  be 
  thick 
  double-shell 
  ones 
  the 
  second 
  

   resistance-ratio, 
  that 
  is 
  the 
  one 
  (R//R/) 
  used 
  in 
  measuring 
  r 
  2 
  , 
  

   must 
  be 
  adjusted 
  so 
  that 
  

  

  R/ 
  ~8V 
  2a 
  2 
  VR2 
  ; 
  

   and 
  the 
  third 
  resistance-ratio 
  R/'/R/', 
  i. 
  e. 
  the 
  one 
  used 
  in 
  

   measuring 
  7\, 
  must 
  be 
  adjusted 
  so 
  that 
  

  

  R/'___8/ 
  3_^ 
  2 
  \R, 
  

  

  R 
  2 
  //_ 
  5a/5V 
  2a 
  1 
  VR 
  2 
  ' 
  

  

  where 
  2ft 
  and 
  2ft 
  are 
  the 
  equivalent 
  breadths 
  of 
  the 
  two 
  coils 
  

   and 
  a, 
  and 
  a 
  2 
  their 
  approximate 
  mean 
  radii. 
  

  

  * 
  Phil. 
  Trans. 
  1884. 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  3. 
  No. 
  15. 
  March 
  1902. 
  Y 
  

  

  