﻿84 
  

  

  T. 
  0. 
  Mendenhall 
  — 
  Relation 
  of 
  

  

  ?=4Hz] 
  

  

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  p 
  

  

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  — 
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  1^ 
  

  

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  "I 
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  o 
  it 
  

  

  6 
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  6 
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  o» 
  

  

  o 
  

  

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   ■n 
  

  

  

  

  30 
  

  

  > 
  

   < 
  

  

  H 
  

  

  -< 
  

  

  And 
  it 
  will 
  be 
  seen 
  that 
  it 
  

   involves 
  the 
  relation 
  between 
  

   the 
  density 
  of 
  the 
  elevated 
  

   mass 
  and 
  the 
  mean 
  density 
  of 
  

   the 
  earth. 
  It 
  is 
  usual 
  to 
  as- 
  

   sume 
  this 
  relation 
  as 
  being 
  

   equal 
  to 
  one-half 
  ; 
  that 
  is, 
  to 
  

   assume 
  that 
  the 
  density 
  of 
  the 
  

   surface 
  material 
  is 
  one-half 
  

   that 
  of 
  the 
  mean 
  density 
  of 
  the 
  

   earth, 
  and 
  hence 
  that 
  it 
  is 
  

   about 
  2-75. 
  On 
  this 
  hypothe- 
  

   sis 
  the 
  excess 
  of 
  the 
  force 
  of 
  

   gravity 
  when 
  reduced 
  to* 
  the 
  

   sea 
  level 
  over 
  that 
  as 
  computed 
  

   for 
  the 
  theoretical 
  spheroid, 
  by 
  

   the 
  use 
  of 
  Helmert's 
  formula, 
  

   is 
  obtained, 
  and 
  the 
  difference 
  

   between 
  these 
  two 
  quantities 
  

   will 
  be 
  found 
  in 
  one 
  of 
  the 
  

   columns 
  of 
  the 
  table 
  given 
  

   above. 
  It 
  will 
  be 
  seen 
  that 
  

   nearly 
  all 
  of 
  these 
  differences 
  

   are 
  negative 
  ; 
  that 
  is 
  to 
  say, 
  

   that 
  the 
  gravity 
  as 
  actually 
  

   observed 
  at 
  the 
  various 
  points 
  

   across 
  the 
  Atlantic 
  is 
  less 
  than 
  

   it 
  should 
  be 
  in 
  acccordance 
  

   with 
  the 
  hypothesis 
  above 
  re- 
  

   ferred 
  to. 
  The 
  accompanying 
  

   diagram 
  shows 
  these 
  variations 
  

   in 
  a 
  very 
  much 
  simpler 
  way 
  

   than 
  they 
  can 
  be 
  exhibited 
  in 
  

   the 
  table, 
  and 
  by 
  plotting 
  side 
  

   by 
  side 
  the 
  elevations 
  of 
  the 
  

   several 
  points 
  and 
  the 
  differ- 
  

   ence 
  in 
  the 
  observed 
  and 
  com- 
  

   puted 
  force 
  of 
  gravity 
  referred 
  

   to, 
  the 
  relation 
  between 
  the 
  

   two 
  is 
  shown 
  in 
  a 
  very 
  strik- 
  

   ing 
  manner. 
  It 
  will 
  be 
  ob- 
  

   served 
  that 
  the 
  two 
  lines 
  rep- 
  

   resenting 
  these 
  quantities 
  run 
  

   side 
  by 
  side 
  very 
  closely, 
  indi- 
  

  

  