﻿Magnetic 
  Shells 
  equivalent 
  to 
  Circular 
  Coils. 
  329* 
  

  

  the 
  length 
  of 
  the 
  needle 
  actually 
  used 
  by 
  Lord 
  Rayleigh 
  # 
  , 
  

   but 
  if 
  it 
  was 
  half 
  a 
  centimetre 
  long 
  or 
  4 
  mm. 
  between 
  its 
  

   poles 
  M 
  would 
  be 
  

  

  1*045154 
  instead 
  of 
  

  

  1-044595, 
  

  

  that 
  is 
  the 
  correction 
  would 
  be 
  54 
  in 
  100,000.. 
  For 
  other 
  

   lengths 
  the 
  correction 
  can 
  be 
  got 
  as 
  it 
  varies 
  as 
  the 
  square 
  o£ 
  

   the 
  distance 
  between 
  the 
  poles 
  of 
  the 
  needle. 
  Thus, 
  if 
  the 
  

   pole 
  distance 
  were 
  only 
  1 
  mm., 
  the 
  correction 
  would 
  be 
  more 
  

   than 
  3 
  parts 
  in 
  100,000, 
  and 
  if 
  it 
  were 
  3 
  mm. 
  (a 
  fairly 
  short 
  

   needle) 
  the 
  correction 
  would 
  be 
  3 
  parts 
  in 
  10,000, 
  which 
  

   would 
  affect 
  the 
  measurement 
  of 
  current 
  to 
  the 
  extent 
  of 
  

   lj 
  parts 
  in 
  10,000. 
  

  

  27. 
  In 
  the 
  case 
  of 
  a 
  standard 
  of 
  mutual 
  inductance 
  of 
  

   which 
  the 
  coils 
  are 
  very 
  approximately 
  single-shell 
  ones 
  

   whose 
  equivalent 
  radii 
  have 
  been 
  accurately 
  determined 
  by 
  

   the 
  electrical 
  method, 
  it 
  might 
  be 
  worth 
  while 
  taking 
  account 
  

   of 
  the 
  effect 
  of 
  change 
  of 
  temperature 
  on 
  the 
  value 
  of 
  M. 
  

  

  If 
  the 
  distance-piece 
  between 
  the 
  two 
  coils 
  be 
  of 
  the 
  same 
  

   material 
  as 
  that 
  on 
  which 
  the 
  coils 
  are 
  wound, 
  and 
  whose 
  

   coefficient 
  of 
  linear 
  expansion 
  a. 
  is 
  nearly 
  equal 
  to 
  that 
  of 
  the 
  

   copper 
  wire 
  in 
  the 
  coils, 
  then 
  at 
  once 
  

  

  M 
  t 
  = 
  M 
  (l+at), 
  

  

  seeing 
  that 
  M 
  is 
  a 
  homogeneous 
  function 
  of 
  r^ 
  r 
  2} 
  and 
  x 
  of 
  

   one 
  dimension. 
  

  

  For 
  a 
  current-balance 
  in 
  which 
  the 
  two 
  large 
  coils 
  are 
  

   wound 
  on 
  the 
  same 
  frame, 
  and 
  the 
  suspended 
  coil 
  wound 
  on 
  

   a 
  ring 
  of 
  the 
  same 
  material 
  whose 
  coefficient 
  of 
  expansion 
  

   is 
  nearly 
  equal 
  to 
  that 
  of 
  copper, 
  the 
  temperature-coefficient 
  

  

  of 
  its 
  constant 
  vanishes 
  seeing 
  that 
  -, 
  — 
  is 
  a 
  homogeneous 
  

  

  ax 
  

  

  function 
  of 
  r 
  x 
  r 
  2 
  , 
  and 
  x 
  of 
  no 
  dimensions. 
  

  

  * 
  In 
  the 
  discussion 
  on 
  the 
  paper, 
  when 
  read 
  before 
  the 
  Physical 
  

   Society, 
  Lord 
  Eayleigh 
  pointed 
  out 
  that 
  the 
  leugth 
  of 
  the 
  needle 
  was 
  

   one-tenth 
  of 
  an 
  inch, 
  and 
  the 
  error 
  due 
  to 
  the 
  neglect 
  of 
  the 
  length 
  was- 
  

   less 
  than 
  one 
  part 
  in 
  ten 
  thousand. 
  

  

  