﻿* 
  

  

  Horizontal 
  Intensity 
  of 
  the 
  Earth's 
  Magnetic 
  Field. 
  765 
  

  

  (4) 
  A 
  longitudinal 
  displacement 
  of 
  the 
  magnet 
  from 
  the 
  

   centre 
  of 
  the 
  tube. 
  

  

  The 
  field 
  at 
  any 
  point 
  along 
  the 
  axis 
  o£ 
  a 
  helix 
  can 
  be 
  

   shown 
  to 
  be 
  given 
  by 
  the 
  formula 
  

  

  H= 
  2 
  .»0[(l 
  + 
  ^f 
  + 
  (l 
  + 
  ^Pj 
  

  

  where 
  a 
  is 
  the 
  radius 
  of 
  the 
  helix, 
  and 
  I 
  and 
  i 
  x 
  are 
  the 
  

   distances 
  of 
  the 
  point 
  from 
  the 
  ends 
  of 
  the 
  helix. 
  

   At 
  the 
  centre 
  of 
  the 
  helix 
  used 
  this 
  reduces 
  to 
  

  

  ==«[{'HflT'] 
  

  

  = 
  4t™C 
  (-998592) 
  

  

  = 
  4irnC.(l- 
  -001408). 
  

  

  Suppose 
  the 
  magnet 
  to 
  be 
  displaced 
  3 
  cm. 
  from 
  its 
  central 
  

   position. 
  Then 
  

  

  H= 
  2 
  ,„c[{ 
  1+ 
  (^)-}-' 
  + 
  { 
  1+ 
  (5i')'}-] 
  

  

  =;4iroC(-998585). 
  

  

  Thus 
  a 
  displacement 
  of 
  3 
  cm. 
  causes 
  an 
  alteration 
  of 
  

   7 
  parts 
  in 
  10 
  6 
  . 
  As 
  the 
  magnet 
  can 
  easily 
  be 
  placed 
  in 
  its 
  

   correct 
  position 
  at 
  the 
  centre 
  of 
  the 
  helix 
  to 
  *5 
  cm., 
  we 
  see 
  

   that 
  any 
  error 
  likely 
  to 
  arise 
  from 
  a 
  displacement 
  of 
  the 
  

   magnet 
  from 
  its 
  central 
  position 
  is 
  altogether 
  negligible, 
  and 
  

   a 
  displacement 
  out 
  of 
  the 
  axis 
  must 
  give 
  still 
  less 
  variation. 
  

  

  (5) 
  A 
  residual 
  torsion 
  in 
  the 
  fibre. 
  

  

  At 
  first 
  sight 
  it 
  might 
  seem 
  that 
  a 
  slight 
  residual 
  torsion 
  

   in 
  the 
  fibre 
  would 
  be 
  of 
  no 
  effect 
  as 
  the 
  torsion 
  is 
  the 
  same 
  

   in 
  both 
  parts 
  of 
  the 
  experiment. 
  A 
  little 
  consideration 
  

   shows, 
  however, 
  that 
  this 
  is 
  not 
  the 
  case. 
  If 
  the 
  torsion 
  in 
  

   the 
  fibre 
  be 
  such 
  that 
  when 
  the 
  magnet 
  is 
  parallel 
  to 
  the 
  

   earth's 
  field 
  there 
  are 
  6 
  degrees 
  of 
  twist 
  in 
  the 
  fibre, 
  then 
  

   the 
  magnet 
  will 
  come 
  to 
  rest 
  making 
  an 
  angle 
  a 
  with 
  the 
  

   earth's 
  field, 
  where 
  

  

  21K 
  sin 
  a=n{0 
  -a) 
  (A) 
  

  

  n 
  being 
  the 
  force 
  produced 
  by 
  one 
  degree 
  of 
  torsion. 
  

  

  The 
  helix 
  is 
  placed 
  in 
  such 
  a 
  position 
  that 
  on 
  sending 
  a 
  

   current 
  through 
  it 
  no 
  alteration 
  in 
  the 
  zero 
  position 
  of 
  the 
  

  

  