﻿JAN. 
  19, 
  1922 
  LAMBERT: 
  LATITUDE 
  OF 
  UKIAH 
  41 
  

  

  for 
  terms 
  of 
  these 
  periods, 
  but 
  the 
  amplitudes 
  and 
  epochs 
  thus 
  found 
  

   differed 
  considerably 
  according 
  to 
  stations 
  used 
  and 
  the 
  period 
  of 
  time 
  

   covered 
  by 
  the 
  observations. 
  Probably 
  there 
  are 
  perceptible 
  terms 
  of 
  

   this 
  sort, 
  but 
  the 
  mathematical 
  expressions 
  for 
  them 
  are 
  still 
  quite 
  

   uncertain. 
  

  

  Expressions 
  in 
  harmonic 
  form 
  were 
  found 
  for 
  the 
  annual 
  portion 
  of 
  

   the 
  polar 
  motion 
  and 
  of 
  the 
  Kimura 
  term. 
  For 
  corresponding 
  periods 
  

   of 
  time 
  these 
  expressions 
  were 
  in 
  excellent 
  agreement 
  with 
  similar 
  

   expressions 
  deduced 
  by 
  the 
  International 
  Latitude 
  Service, 
  although 
  

   the 
  methods 
  of 
  deduction 
  were 
  quite 
  different. 
  

  

  Similar 
  expressions 
  in 
  harmonic 
  form 
  were 
  found 
  for 
  the 
  14-month 
  

   portion 
  of 
  the 
  motion 
  of 
  the 
  Pole. 
  In 
  deducing 
  these 
  terms 
  the 
  motion 
  

   of 
  the 
  pole 
  of 
  rotation 
  was 
  not 
  assumed 
  to 
  be 
  uniform 
  and 
  circular, 
  as 
  

   it 
  would 
  be 
  if 
  changes 
  in 
  position 
  of 
  the 
  pole 
  of 
  figure 
  were 
  strictly 
  

   periodic 
  and 
  if 
  the 
  two 
  principal 
  equatorial 
  moments 
  of 
  inertia 
  of 
  the 
  

   Earth 
  were 
  equal. 
  If, 
  however, 
  the 
  assumption 
  of 
  uniform 
  circular 
  

   motion 
  is 
  made 
  in 
  this 
  discussion, 
  as 
  it 
  is 
  in 
  the 
  work 
  of 
  the 
  Inter- 
  

   national 
  Latitude 
  Service, 
  the 
  expressions 
  for 
  the 
  14-month 
  motion 
  of 
  

   the 
  Pole 
  agree 
  well 
  with 
  the 
  corresponding 
  ones 
  deduced 
  by 
  the 
  Lati- 
  

   tude 
  Service, 
  in 
  spite 
  of 
  the 
  difference 
  in 
  methods. 
  Without 
  the 
  as- 
  

   sumption 
  of 
  circular 
  motion 
  the 
  observations 
  always 
  give 
  an 
  elliptical 
  

   14-month 
  path 
  for 
  the 
  Pole, 
  but 
  one 
  so 
  nearl}' 
  circular 
  that 
  the 
  exact 
  

   direction 
  of 
  its 
  major 
  axis 
  is 
  not 
  very 
  certain. 
  The 
  major 
  axis 
  should 
  

   coincide 
  in 
  direction 
  with 
  the 
  meridian 
  of 
  the 
  larger 
  principal 
  equatorial 
  

   moment 
  of 
  inertia^'' 
  if 
  there 
  is 
  any 
  perceptible 
  difference 
  in 
  the 
  principal 
  

   equatorial 
  moments, 
  and 
  it 
  is 
  for 
  this 
  reason 
  that 
  it 
  is 
  of 
  interest 
  to 
  

   determine 
  the 
  position 
  of 
  the 
  major 
  axis 
  of 
  the 
  ellipse 
  of 
  polar 
  motion. 
  

   Wanach 
  of 
  the 
  International 
  Service 
  speaks 
  discouragingly 
  of 
  the 
  

   results 
  obtained, 
  ^^ 
  but 
  in 
  the 
  present 
  investigation 
  the 
  results 
  for 
  

   different 
  six-year 
  periods 
  show 
  a 
  fair 
  degree 
  of 
  agreement, 
  perhaps 
  

  

  1^ 
  This 
  statement 
  is 
  subject 
  to 
  a 
  correction 
  for 
  the 
  effect 
  of 
  the 
  yielding 
  of 
  the 
  ocean 
  waters 
  

   to 
  the 
  forces 
  arising 
  from 
  a 
  change 
  in 
  position 
  of 
  the 
  Pole. 
  If 
  the 
  ocean 
  covered 
  the 
  Earth, 
  

   its 
  yielding 
  would 
  prolong 
  the 
  period 
  of 
  the 
  latitude 
  variation 
  as 
  compared 
  with 
  that 
  of 
  an 
  

   otherwise 
  similar 
  earth 
  without 
  an 
  ocean, 
  but 
  the 
  position 
  of 
  the 
  major 
  axis 
  of 
  the 
  ellipse 
  of 
  

   polar 
  motion 
  would 
  be 
  the 
  same 
  for 
  both 
  earths. 
  On 
  account 
  of 
  the 
  unsymmetrical 
  dis- 
  

   tribution 
  of 
  land 
  and 
  water 
  on 
  the 
  actual 
  Earth 
  the 
  position 
  of 
  the 
  axis 
  of 
  the 
  ellipse 
  of 
  polar 
  

   motion 
  is 
  affected, 
  but 
  the 
  amount 
  of 
  the 
  correction 
  appears 
  not 
  to 
  be 
  sufficient 
  to 
  change 
  the 
  

   general 
  character 
  of 
  the 
  observed 
  results. 
  The 
  subject 
  has 
  been 
  investigated 
  by 
  A. 
  Brill 
  

   in 
  his 
  doctor's 
  thesis 
  entitled 
  Uber 
  die 
  Elastizitdt 
  der 
  Erde 
  (Gottingen, 
  1908). 
  His 
  conclus- 
  

   ions 
  do 
  not 
  appear 
  to 
  be 
  in 
  a 
  form 
  immediately 
  applicable 
  to 
  the 
  problem 
  in 
  hand. 
  The 
  

   question 
  is 
  being 
  further 
  investigated. 
  

  

  1^ 
  ResuUate 
  des 
  InternaUonalen 
  Breitendienstes. 
  5: 
  220, 
  footnote. 
  

  

  