﻿OF 
  TERRESTRIAL 
  MAGNETISM 
  AT 
  SEVERAL 
  PLACES, 
  ETC. 
  451 
  

  

  The 
  horizontal 
  intensity 
  compared 
  with 
  that 
  at 
  Philadelphia 
  is, 
  from 
  

   A, 
  .92053, 
  and 
  from 
  C, 
  .93630. 
  The 
  relative 
  weights 
  to 
  be 
  attached 
  

   to 
  the 
  results 
  with 
  the 
  two 
  needles 
  are, 
  respectively, 
  1419 
  and 
  1113. 
  

  

  We 
  now 
  proceed 
  to 
  compare 
  the 
  horizontal 
  intensities, 
  deduced 
  from 
  

   both 
  series 
  of 
  observations, 
  to 
  obtain 
  the 
  mean. 
  

  

  As 
  the 
  methods 
  of 
  observation 
  in 
  the 
  two 
  series 
  are 
  liable 
  to 
  different 
  

   errors, 
  and 
  the 
  number 
  of 
  observations 
  are 
  different, 
  we 
  have 
  allowed 
  

   to 
  the 
  results 
  obtained 
  by 
  them, 
  weight 
  in 
  proportion 
  to 
  the 
  number 
  of 
  

   observations 
  directly, 
  and 
  the 
  square 
  of 
  the 
  mean 
  error 
  inversely. 
  

   The 
  mean 
  error 
  is 
  hardly 
  attained, 
  even 
  in 
  the 
  case 
  of 
  the 
  greatest 
  

   number 
  of 
  sets 
  of 
  observations 
  of 
  the 
  second 
  series; 
  but 
  an 
  approxi- 
  

   mation 
  to 
  it 
  will 
  afford 
  a 
  far 
  more 
  satisfactory 
  mode 
  of 
  deducing 
  the 
  

   mean 
  intensity 
  than 
  could 
  be 
  obtained 
  by 
  an 
  indiscriminate 
  mean 
  of 
  

   the 
  results. 
  

  

  The 
  numbers 
  found 
  for 
  the 
  weight 
  of 
  the 
  observations 
  with 
  each 
  

   needle 
  in 
  the 
  two 
  series, 
  have 
  been 
  of 
  course 
  used 
  instead 
  of 
  the 
  num- 
  

   ber 
  of 
  observations, 
  as 
  referred 
  to 
  in 
  the 
  preceding 
  paragraph. 
  And 
  a 
  

   mean 
  error 
  has 
  in 
  like 
  manner 
  been 
  deduced 
  from 
  the 
  combined 
  

   observations 
  with 
  each 
  needle 
  at 
  the 
  two 
  places. 
  Using 
  these 
  num- 
  

   bers, 
  we 
  have 
  obtained 
  the 
  following 
  for 
  the 
  relative 
  weights 
  of 
  the 
  

   observations 
  with 
  each 
  needle. 
  

  

  First 
  Series. 
  No. 
  1, 
  2728 
  Second 
  Series. 
  A, 
  29319 
  

  

  " 
  3, 
  476 
  " 
  G, 
  1136. 
  

  

  By 
  the 
  use 
  of 
  these 
  numbers, 
  and 
  of 
  the 
  horizontal 
  intensities 
  al- 
  

   ready 
  obtained, 
  we 
  have 
  for 
  the 
  mean, 
  h' 
  = 
  .92156. 
  

  

  The 
  superiority 
  of 
  the 
  method 
  in 
  the 
  rarefied 
  medium, 
  cannot 
  bet- 
  

   ter 
  be 
  shown 
  than 
  by 
  stating, 
  that 
  the 
  mean 
  error 
  with 
  needle 
  A, 
  sup- 
  

   posing 
  it 
  reached 
  in 
  the 
  observations, 
  was 
  .022 
  seconds 
  in 
  about 
  36^ 
  

   seconds, 
  while, 
  with 
  No. 
  1 
  in 
  the 
  first 
  series, 
  it 
  was 
  .129 
  seconds 
  in 
  

   about 
  46 
  seconds, 
  or 
  six 
  times 
  the 
  former. 
  

  

  The 
  probable 
  error* 
  in 
  the 
  time 
  of 
  ten 
  vibrations 
  of 
  Needle 
  A 
  is, 
  

   .0005 
  second. 
  

  

  * 
  Deduced 
  from 
  the 
  formula 
  P 
  = 
  85-^- 
  Young, 
  Phil. 
  Trans. 
  1819, 
  p. 
  77. 
  

   VOL. 
  V. 
  5 
  Q 
  

  

  