﻿30 
  JOURNAL 
  OP 
  THE 
  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  VOL. 
  12, 
  NO. 
  2 
  

  

  motion 
  of 
  the 
  Pole 
  other 
  than 
  the 
  mere 
  lengths 
  of 
  the 
  periods 
  concerned. 
  

   If 
  the 
  variation 
  of 
  latitude 
  conformed 
  to 
  the 
  simplifying 
  assumptions 
  

   that 
  we 
  often 
  make, 
  the 
  curve 
  would 
  be 
  a 
  simple 
  sine 
  curve 
  with 
  

   constant 
  amplitude 
  and 
  with 
  its 
  phase 
  changing 
  at 
  a 
  uniform 
  rate. 
  

   There 
  is, 
  however, 
  a 
  marked 
  increase 
  in 
  the 
  amplitude 
  although 
  the 
  

   phase 
  change 
  is 
  nearly 
  uniform. 
  The 
  ordinate 
  represents, 
  not 
  the 
  

   observed 
  latitude 
  itself, 
  but 
  the 
  difference, 
  A<^, 
  between 
  the 
  observed 
  

   latitude 
  and 
  an 
  arbitrary 
  but 
  fixed 
  initial 
  latitude. 
  The 
  initial 
  latitude 
  

   is 
  such 
  that 
  near 
  the 
  beginning 
  of 
  the 
  period 
  this 
  conventional 
  zero 
  

   line 
  of 
  A(j) 
  coincides 
  very 
  nearly 
  with 
  the 
  true 
  zero 
  line, 
  or 
  line 
  running 
  

   midway 
  between 
  the 
  points 
  of 
  maximum 
  and 
  minimum. 
  Towards 
  

   the 
  end 
  of 
  the 
  period 
  the 
  curve 
  has 
  shifted 
  so 
  much 
  that 
  most 
  of 
  it 
  

   lies 
  above 
  the 
  conventional 
  zero 
  line. 
  The 
  angle 
  between 
  the 
  true 
  zero 
  

   line 
  and 
  the 
  conventional 
  zero 
  line 
  represents 
  the 
  rate 
  of 
  increase 
  of 
  the 
  

   mean 
  latitude, 
  that 
  is, 
  of 
  the 
  latitude 
  freed 
  from 
  the 
  effects 
  of 
  all 
  known 
  

   periodic 
  terms. 
  This 
  slope 
  or 
  rate 
  Professor 
  Lawson 
  determined 
  by 
  a 
  

   graphic 
  adjustment 
  ; 
  he 
  drew 
  a 
  straight 
  line 
  passing 
  as 
  near 
  as 
  possible 
  

  

  Fig. 
  1. 
  The 
  latitude 
  of 
  Ukiah, 
  California, 
  from 
  Dyson's 
  curves, 
  with 
  lines 
  drawn 
  by 
  Lawson 
  

   to 
  show 
  the 
  progressive 
  increase 
  of 
  latitude. 
  

  

  to 
  the 
  maxima 
  of 
  the 
  curve 
  and 
  a 
  similar 
  line 
  for 
  the 
  minima, 
  and 
  then 
  

   drew 
  a 
  line 
  bisecting 
  the 
  angle 
  between 
  the 
  two 
  lines 
  just 
  found. 
  This 
  

   bisector 
  may 
  be 
  taken 
  as 
  representing 
  the 
  true 
  zero 
  line. 
  

  

  The 
  slope 
  of 
  this 
  true 
  zero 
  line 
  referred 
  to 
  the 
  conventional 
  one 
  is, 
  

   as 
  found 
  by 
  Professor 
  Lawson, 
  0'^0094 
  or 
  0.29 
  meter 
  a 
  year. 
  His 
  

   method 
  does 
  not 
  use 
  all 
  the 
  information 
  afforded 
  by 
  the 
  curve, 
  but 
  

   merely 
  the 
  maxima 
  and 
  minima; 
  the 
  lines 
  drawn 
  to 
  fit 
  these 
  are 
  

   necessarily 
  affected 
  by 
  personal 
  idiosyncrasies. 
  The 
  following 
  method 
  

   is 
  free 
  from 
  these 
  objections. 
  

  

  The 
  curve 
  supposedly 
  contains 
  only 
  the 
  effect 
  of 
  the 
  14-month 
  

   component 
  and 
  of 
  a 
  possible 
  progressive 
  shifting 
  of 
  the 
  zero 
  line. 
  

   The 
  former 
  effect 
  will 
  be 
  eliminated 
  from 
  the 
  mean 
  of 
  14 
  successive 
  

   calendar 
  months,^ 
  leaving 
  in 
  the 
  mean 
  only 
  the 
  progressive 
  shift 
  

  

  ^ 
  The 
  exact 
  period 
  is 
  432.5 
  days 
  rather 
  than 
  14 
  calendar 
  months 
  (426 
  days), 
  but 
  the 
  error 
  

   arising 
  from 
  the 
  substitution 
  of 
  one 
  period 
  for 
  the 
  other 
  is 
  negligible. 
  

  

  