﻿Horizontal 
  Intensity 
  of 
  the 
  Earth's 
  Magnetic 
  Field. 
  767 
  

  

  magnet. 
  It 
  is 
  difficult, 
  however, 
  to 
  get 
  rid 
  of 
  the 
  last 
  few 
  

   degrees 
  of 
  torsion, 
  and 
  it 
  was 
  thought 
  that 
  these 
  few 
  degrees 
  

   might 
  have 
  an 
  appreciable 
  influence. 
  The 
  magnitude 
  of 
  

   the 
  influence 
  was 
  determined 
  by 
  experiment. 
  360° 
  or 
  torsion 
  

   were 
  put 
  in 
  the 
  fibre 
  and 
  the 
  consequent 
  alteration 
  of 
  the 
  

   equilibrium 
  position 
  of 
  the 
  magnet 
  noted. 
  Upon 
  calculation 
  

   it 
  was 
  found 
  that 
  360° 
  of 
  torsion 
  rotated 
  the 
  magnet 
  through 
  

   an 
  angle 
  a 
  where 
  sin 
  «= 
  '00156. 
  

  

  There 
  would 
  certainly 
  be 
  not 
  more 
  than 
  20° 
  of 
  torsion 
  

   left 
  in 
  the 
  fibre, 
  and 
  we 
  get 
  the 
  maximum 
  angle 
  of 
  deflexion 
  

  

  owing 
  to 
  residual 
  torsion 
  to 
  be 
  sin 
  , 
  0QQ 
  approx. 
  or 
  

  

  cosine 
  « 
  = 
  -999999995 
  

  

  = 
  1-5x10-°. 
  

  

  By 
  neglecting 
  a 
  we 
  may 
  therefore 
  introduce 
  an 
  error 
  of 
  

   5 
  parts 
  in 
  10 
  9 
  , 
  which 
  is 
  altogether 
  negligible. 
  That 
  the 
  

   angle 
  was 
  inappreciable 
  was 
  shown 
  by 
  the 
  fact 
  that 
  on 
  

   reversing 
  the 
  magnet 
  the 
  zero 
  position 
  was 
  indistinguishable 
  

   from 
  the 
  zero 
  position 
  when 
  under 
  the 
  earth's 
  field 
  alone. 
  

   As 
  will 
  be 
  seen 
  from 
  the 
  above 
  the 
  anode 
  between 
  the 
  two 
  

   zero 
  positions 
  is 
  /3 
  where 
  

  

  2TL(0-*)a 
  

  

  Z(0-a)-H(0-2«)- 
  

  

  Putting 
  Z 
  = 
  2H 
  and 
  neglecting 
  a 
  2 
  , 
  we 
  get 
  /3 
  = 
  2«. 
  

  

  As 
  ft 
  could 
  not 
  be 
  measured 
  and 
  the 
  arrangement 
  was 
  

  

  such 
  that 
  an 
  angle 
  sin 
  ^^ 
  could 
  be 
  determined, 
  we 
  see 
  

  

  that 
  a 
  can 
  be 
  neglected. 
  

  

  (6) 
  Inaccurate 
  timing 
  of 
  the 
  period 
  of 
  oscillation. 
  

  

  The 
  timing 
  of 
  the 
  oscillations 
  is 
  the 
  chief 
  limitino- 
  factor 
  

   to 
  the 
  accuracy 
  with 
  which 
  the 
  determination 
  can 
  be 
  made. 
  

   Owing 
  to 
  the 
  shortness 
  of 
  the 
  silk 
  fibre, 
  the 
  magnet 
  system 
  

   tends 
  to 
  come 
  to 
  rest 
  comparatively 
  quickly. 
  Because 
  of 
  

   this 
  the 
  area 
  of 
  the 
  mirror 
  surface 
  must 
  be 
  as 
  small 
  as 
  

   possible 
  in 
  order 
  to 
  minimise 
  the 
  damping 
  effect, 
  and 
  the 
  

   magnet 
  must 
  be 
  as 
  strong 
  and 
  powerful 
  as 
  is 
  consistent 
  with 
  

   the 
  strength 
  of 
  the 
  finest 
  silk 
  fibre. 
  

  

  Taking 
  these 
  precautions, 
  the 
  system 
  can 
  be 
  made 
  to 
  

   oscillate 
  for 
  15 
  minutes, 
  which 
  permits 
  of 
  an 
  accuracy 
  of 
  

   1 
  in 
  10,000 
  being 
  made 
  in 
  the 
  determination 
  of 
  the 
  period 
  

   of 
  vibratiou. 
  

  

  A 
  silk 
  fibre 
  is 
  surprisingly 
  strong, 
  and 
  several 
  pieces 
  of 
  

  

  