﻿OF 
  TERRESTRIAL 
  MAGNETISM 
  AT 
  SEVERAL 
  PLACES, 
  ETC. 
  449 
  

  

  The 
  horizontal 
  intensities 
  deduced 
  from 
  a 
  comparison 
  of 
  these 
  last 
  

   results 
  with 
  those 
  obtained 
  at 
  Philadelphia, 
  are, 
  from 
  No. 
  1, 
  .92977 
  ; 
  

   and 
  from 
  No. 
  3. 
  .90290, 
  the 
  horizontal 
  intensity 
  at 
  Philadelphia 
  being 
  

   assumed 
  as 
  unity. 
  The 
  relative 
  weights 
  of 
  the 
  observations 
  with 
  the 
  

   two 
  needles, 
  taking 
  the 
  whole 
  number 
  made 
  with 
  each 
  needle 
  as 
  be- 
  

   longing 
  to 
  one 
  set 
  of 
  observations, 
  will 
  be, 
  according 
  to 
  the 
  formula 
  of 
  

   Gauss,* 
  

  

  „ 
  ^ 
  T 
  4566x4510 
  

  

  For 
  No. 
  1, 
  2x 
  9Q76 
  = 
  4540; 
  

  

  . 
  , 
  , 
  XT 
  1100x1256 
  

   And 
  for 
  No. 
  3, 
  2 
  x 
  ^^ 
  = 
  1 
  174. 
  

  

  The 
  mean 
  horizontal 
  intensity 
  thus 
  deduced 
  is, 
  .92424. 
  An 
  arith- 
  

   metical 
  mean 
  of 
  the 
  two 
  intensities 
  would 
  have 
  given 
  .91633, 
  a 
  num- 
  

   ber 
  differing 
  sufficiently 
  from 
  that 
  just 
  found, 
  to 
  make 
  the 
  calculation 
  

   worth 
  pursuing, 
  notwithstanding 
  that 
  it 
  is 
  less 
  than 
  the 
  difference 
  of 
  the 
  

   intensities 
  determined 
  by 
  the 
  two 
  different 
  needles. 
  

  

  SECOND 
  SERIES. 
  

  

  These 
  observations 
  were 
  made 
  on 
  the 
  7th 
  and 
  8th 
  of 
  September 
  

   1835, 
  at 
  West 
  Point, 
  and 
  in 
  September 
  and 
  October 
  in 
  Philadelphia. 
  

   They 
  were 
  made 
  in 
  the 
  vacuum 
  apparatus, 
  and 
  although 
  the 
  number 
  

   of 
  observations 
  is 
  not 
  equal 
  to 
  that 
  of 
  the 
  first 
  series, 
  the 
  mean 
  error 
  is 
  

   so 
  much 
  diminished 
  by 
  the 
  superior 
  accuracy 
  of 
  the 
  results 
  in 
  the 
  

   rarefied 
  medium, 
  that 
  the 
  weight 
  of 
  the 
  observations 
  is 
  very 
  much 
  

   greater 
  than 
  that 
  of 
  the 
  more 
  numerous 
  ones 
  of 
  the 
  first 
  series. 
  

  

  The 
  following 
  tables, 
  Nos. 
  VIII. 
  and 
  IX., 
  are 
  arranged 
  nearly 
  as 
  the 
  

   preceding 
  ones, 
  and 
  require 
  no 
  specific 
  description. 
  

  

  The 
  table 
  for 
  Philadelphia 
  contains 
  observations 
  with 
  needle 
  No. 
  

   3 
  (B), 
  for 
  comparison 
  with 
  others 
  with 
  the 
  same 
  needle 
  at 
  different 
  

   places. 
  This 
  needle 
  was 
  not 
  oscillated 
  at 
  West 
  Point. 
  

  

  * 
  Baily 
  in 
  Trans. 
  Astr. 
  Soc. 
  Lond., 
  Vol. 
  II. 
  p. 
  19. 
  

  

  