﻿42 
  JOURNAL 
  OF 
  THE 
  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  VOL. 
  12, 
  NO. 
  2 
  

  

  on 
  account 
  of 
  the 
  refinements 
  in 
  harmonic 
  analysis 
  already 
  referred 
  to. 
  

  

  In 
  table 
  3 
  X 
  is 
  the 
  west 
  longitude 
  of 
  the 
  meridian 
  along 
  which 
  the 
  

  

  major 
  axis 
  lies. 
  

  

  TABLE 
  3. 
  — 
  Direction 
  of 
  the 
  Major 
  Axis 
  of 
  the 
  Elwpse 
  of 
  Polar 
  Motion 
  (432.5 
  

  

  Day 
  Period) 
  

  

  The 
  first 
  three 
  lines 
  give 
  results 
  for 
  each 
  of 
  the 
  three 
  six-year 
  periods^^ 
  

   into 
  which 
  the 
  time 
  covered 
  by 
  the 
  observations 
  is 
  divided. 
  The 
  

   fourth 
  line 
  represents 
  a 
  series 
  cutting 
  across 
  two 
  other 
  series 
  and 
  serves 
  

   as 
  a 
  check. 
  Other 
  check 
  results, 
  not 
  given 
  here, 
  were 
  obtained 
  and 
  

   were 
  all 
  to 
  the 
  same 
  general 
  effect. 
  The 
  last 
  two 
  lines 
  are 
  mean 
  

   results 
  for 
  the 
  periods 
  specified. 
  A 
  mean 
  for 
  the 
  result 
  of 
  the 
  entire 
  

   discussion 
  might 
  be 
  taken, 
  somewhat 
  arbitrarily 
  perhaps, 
  as 
  90° 
  

   West. 
  Helmert^^ 
  has 
  determined 
  the 
  same 
  quantity 
  from 
  gravity 
  

   observations, 
  his 
  result 
  being 
  107 
  ° 
  West. 
  Since 
  gravity 
  can 
  at 
  present 
  

   be 
  observed 
  satisfactorily 
  only 
  on 
  land, 
  that 
  is, 
  on 
  one-fourth 
  only 
  of 
  

   the 
  Earth's 
  surface, 
  and 
  since 
  the 
  influence 
  on 
  gravity 
  of 
  local 
  topo- 
  

   graphic 
  and 
  geologic 
  conditions 
  is 
  considerable, 
  it 
  is 
  satisfactory 
  to 
  

   have 
  even 
  a 
  rough 
  agreement 
  of 
  the 
  results 
  from 
  the 
  two 
  methods. 
  

  

  The 
  amount 
  of 
  the 
  difference 
  between 
  the 
  principal 
  equatorial 
  

   moments, 
  A 
  and 
  B, 
  may 
  be 
  specified 
  by 
  giving 
  the 
  ratio 
  

  

  {B-A)^[C-y2{A+B)], 
  

   the 
  letter 
  C 
  denoting 
  the 
  moment 
  of 
  inertia 
  about 
  the 
  axis 
  of 
  rotation. 
  

   Helmert 
  finds 
  for 
  this 
  ratio 
  1/46. 
  The 
  same 
  ratio 
  may 
  be 
  deduced 
  

   from 
  the 
  eccentricity 
  of 
  the 
  ellipse 
  of 
  polar 
  motion 
  ; 
  the 
  results 
  of 
  this 
  

   investigation 
  point 
  to 
  a 
  value 
  of 
  the 
  same 
  order 
  of 
  magnitude 
  but 
  

   apparently 
  somewhat 
  larger, 
  perhaps 
  1/30 
  or 
  1/20, 
  ratios 
  which 
  would 
  

   follow 
  from 
  some 
  of 
  the 
  gravity 
  formulas 
  which 
  Helmert 
  derives 
  only 
  

   to 
  reject 
  in 
  favor 
  of 
  the 
  formula 
  leading 
  to 
  1/46. 
  From 
  the 
  ratio 
  

   (B—A^[C 
  — 
  }4{A-\-B)] 
  we 
  may 
  deduce 
  the 
  difference 
  between 
  the 
  

   greatest 
  equatorial 
  radius 
  of 
  the 
  Earth 
  and 
  the 
  least. 
  For 
  Helmert's 
  

   ratio 
  1/46 
  this 
  difference 
  is 
  230 
  meters; 
  for 
  larger 
  or 
  smaller 
  ratios 
  the 
  

   difference 
  between 
  the 
  equatorial 
  radii 
  varies 
  proportionally. 
  

  

  1^ 
  The 
  six-year 
  length 
  of 
  series 
  is 
  particularly 
  suitable 
  for 
  harmonic 
  analysis. 
  

   ^^ 
  F. 
  R. 
  Helmert. 
  Neue 
  Formeln 
  fiir 
  den 
  Verlauf 
  der 
  Schwerkraft 
  ini 
  Meeresniveau 
  

   beim 
  Festlande. 
  Sitz.-Ber. 
  kon. 
  preuss. 
  Akad. 
  Wiss. 
  1915: 
  676. 
  

  

  