﻿254 
  F. 
  H. 
  Bigelow 
  — 
  Variations 
  of 
  the 
  Magnetic 
  Needle. 
  

  

  would 
  be 
  required. 
  My 
  endeavor 
  was, 
  therefore, 
  to 
  simplify 
  

   the 
  fundamental 
  treatment 
  so 
  as 
  to 
  secure 
  not 
  only 
  a 
  sound 
  

   theory, 
  but 
  also 
  a 
  working 
  process 
  for 
  handling 
  the 
  observations. 
  

   To 
  do 
  this 
  two 
  distinct 
  sets 
  of 
  trial 
  computations 
  were 
  made, 
  

   first 
  by 
  the 
  theory 
  of 
  moments 
  about 
  the 
  rectangular 
  axes 
  

   whose 
  origin 
  was 
  in 
  the 
  spherical 
  surface 
  passing 
  through 
  the 
  

   north 
  end 
  of 
  the 
  needle, 
  concentric 
  with 
  the 
  surface 
  of 
  the 
  

   earth, 
  and 
  forming 
  equations 
  whose 
  solution 
  would 
  give 
  the 
  

   required 
  constants 
  of 
  the 
  phenomenon. 
  This 
  also 
  failed 
  to 
  be 
  

   sufficiently 
  simple 
  and 
  direct 
  to 
  show 
  the 
  action 
  in 
  its 
  general 
  

   relations. 
  The 
  second 
  attempt 
  was 
  an 
  empirical 
  one, 
  for 
  the 
  

   time 
  abandoning 
  theory, 
  and 
  building 
  up 
  from 
  the 
  simultane- 
  

   ous 
  observations 
  in 
  various 
  parts 
  of 
  the 
  earth 
  such 
  an 
  exhibi- 
  

   tion 
  of 
  facts 
  as 
  would 
  display 
  the 
  real 
  nature 
  of 
  the 
  laws 
  

   behind 
  them. 
  This 
  trial 
  has 
  been 
  successful 
  far 
  beyond 
  antici- 
  

   pation, 
  and 
  that 
  too 
  in 
  a 
  simple 
  and 
  practical 
  form. 
  The 
  

   theory 
  is 
  at 
  best 
  complicated, 
  as 
  it 
  depends 
  upon 
  the 
  laws 
  of 
  

   magnetic 
  induction 
  in 
  their 
  most 
  complex 
  conditions, 
  but 
  it 
  

   unifies 
  and 
  classifies 
  harmoniously 
  all 
  the 
  visible 
  motions 
  of 
  

   the 
  needle. 
  

  

  My 
  method 
  and 
  result 
  are, 
  briefly, 
  as 
  follows 
  : 
  The 
  month 
  

   of 
  June, 
  1883, 
  was 
  selected 
  because 
  of 
  the 
  material 
  collected 
  

   in 
  the 
  publications 
  of 
  the 
  International 
  Polar 
  Commission 
  

   applicable 
  simultaneously 
  over 
  a 
  large 
  area 
  of 
  the 
  earth, 
  also 
  

   because 
  the 
  north 
  polar 
  stations 
  were 
  at 
  that 
  time 
  exposed 
  to 
  

   sunlight 
  throughout 
  the 
  twenty-four 
  hours. 
  The 
  stations 
  

   used 
  were 
  : 
  Point 
  Barrow, 
  Fort 
  Pae, 
  Kiugua 
  Fjord, 
  Jan 
  

   May 
  en, 
  Bossekop, 
  Sodankyla, 
  Pawlowsk, 
  Wilhelm 
  shaven, 
  

   Yienna, 
  Tiflis, 
  Za-Ki-Wei, 
  Cape 
  Horn, 
  South 
  Georgien. 
  The 
  

   monthly 
  means 
  for 
  each 
  hour 
  local 
  time 
  of 
  the 
  horizontal 
  and 
  

   vertical 
  forces 
  and 
  the 
  declination 
  were 
  reduced 
  to 
  the 
  coordi- 
  

   nates, 
  x 
  positive 
  to 
  the 
  north 
  in 
  the 
  mean 
  magnetic 
  meridian 
  

   of 
  the 
  month, 
  y 
  positive 
  to 
  the 
  west, 
  z 
  positive 
  inwards 
  along 
  

   the 
  normal, 
  the 
  plane 
  xy 
  being 
  the 
  horizon 
  at 
  the 
  surface 
  of 
  

   the 
  earth 
  or 
  through 
  the 
  north 
  end 
  of 
  the 
  needle. 
  The 
  differ- 
  

   ences 
  between 
  the 
  mean 
  and 
  the 
  hourly 
  values, 
  namely 
  AH, 
  

   AD, 
  AZ, 
  were 
  plotted 
  on 
  paper, 
  smoothed 
  out, 
  the 
  resulting 
  

   values 
  dx, 
  dy, 
  dz, 
  combined 
  to 
  show 
  the 
  total 
  deflecting 
  force 
  

   at 
  the 
  station 
  with 
  its 
  magnetic 
  azimuth 
  and 
  altitude, 
  this 
  

   form 
  of 
  azimuth 
  being 
  finally 
  transformed 
  into 
  north 
  geo- 
  

   graphical 
  azimuth. 
  My 
  idea 
  was 
  that 
  the 
  needle 
  floating 
  

   freely 
  in 
  a 
  magnetic 
  line 
  indicated 
  simply 
  its 
  direction, 
  and 
  

   that 
  the 
  deflections 
  were 
  produced 
  by 
  a 
  component 
  coming 
  to 
  

   it 
  from 
  space, 
  the 
  motive 
  being 
  to 
  discover 
  the 
  condition 
  of 
  

   such 
  components 
  over 
  the 
  earth 
  at 
  the 
  same 
  time. 
  Next, 
  a 
  

   large 
  model 
  was 
  constructed 
  on 
  which 
  these 
  component 
  forces 
  

   were 
  represented 
  in 
  direction 
  and 
  magnitude. 
  By 
  assigning; 
  

  

  