﻿Relations 
  between 
  jEtlier, 
  Matter, 
  and 
  Electricity. 
  369 
  

   Then 
  (fig. 
  2), 
  

  

  v 
  = 
  2irr 
  sin 
  6 
  . 
  „= 
  ~^- 
  sin 
  V. 
  

  

  E 
  = 
  K-yr 
  sin6>.27rrsin(9. 
  

  

  _ 
  „ 
  27rr 
  sin 
  # 
  . 
  2irr 
  sin 
  # 
  27rKr 
  2 
  . 
  „ 
  

  

  C 
  = 
  K 
  7) 
  rTfi 
  — 
  = 
  ~~ 
  T" 
  sm 
  ° 
  d6 
  dr 
  - 
  

  

  rn 
  lirr 
  sin 
  C7 
  pi. 
  

  

  P 
  ' 
  rdddr 
  

  

  Whence 
  

  

  LC0= 
  ^-TiT 
  

  

  KpT 
  [" 
  (PlW 
  "" 
  C0 
  ^ 
  ) 
  ~S 
  (P2W 
  

   -P 
  1 
  (^)cos(9)p/| 
  + 
  x) 
  + 
  ...Vsin6>^^. 
  

  

  Integrating 
  this 
  from 
  = 
  to 
  6 
  = 
  ir 
  and 
  from 
  r 
  = 
  Q 
  to 
  

   r 
  = 
  A, 
  the 
  radius 
  of 
  the 
  earth, 
  we 
  have 
  

  

  8 
  tt 
  2 
  KA 
  5 
  . 
  ^ 
  

  

  If 
  F 
  w 
  = 
  the 
  vertical 
  component 
  and 
  ~F 
  h 
  the 
  horizontal 
  

   component 
  of 
  the 
  magnetic 
  intensity 
  at 
  a 
  point, 
  we 
  have 
  

  

  _, 
  d/ju 
  16 
  7r 
  2 
  K 
  KO 
  . 
  ■ 
  '; 
  

  

  F 
  -=-;m=T57T 
  AsmX 
  / 
  

  

  _, 
  d/i 
  1 
  dfi 
  8 
  w 
  2 
  K 
  .. 
  , 
  i' 
  

  

  Fv 
  dm 
  = 
  - 
  S 
  7^ 
  = 
  15 
  -pT 
  A 
  co 
  " 
  x 
  ) 
  

  

  (1) 
  

  

  when 
  R 
  = 
  A, 
  whence 
  

  

  ¥ 
  v 
  _16tt 
  2 
  K 
  

   sin 
  X 
  ~ 
  15 
  p 
  r 
  £ 
  

  

  A 
  2 
  = 
  2C 
  

  

  F* 
  8 
  7r 
  2 
  K 
  

  

  ^A* 
  = 
  C 
  

  

  (2) 
  

  

  (3) 
  

  

  cos 
  X 
  15 
  /oT 
  

  

  where 
  C 
  is 
  a 
  constant 
  defined 
  by 
  the 
  above 
  equation. 
  

   Also 
  

  

  K_ 
  15 
  TC 
  

  

  p 
  - 
  8 
  tt*A 
  2 
  

  

  The 
  present 
  investigation 
  requires 
  a 
  knowledge 
  of 
  only 
  

   the 
  order 
  of 
  magnitude 
  of 
  the 
  values 
  of 
  ~F 
  V 
  / 
  sin 
  \ 
  and 
  Fa/ 
  cos 
  A,. 
  

   To 
  determine 
  these 
  ten 
  observatories, 
  representing 
  all 
  sections 
  

   of 
  the 
  earth, 
  were 
  chosen 
  from 
  the 
  tables 
  given 
  by 
  Bigelow 
  

   in 
  Johnson's 
  Cyclopaedia, 
  vol. 
  v. 
  p. 
  469. 
  In 
  each 
  case 
  the 
  

   value 
  of 
  the 
  latitude 
  was 
  reduced 
  to 
  magnetic 
  co-ordinates, 
  

  

  