﻿148 
  

  

  Sir 
  Oliver 
  Lodge 
  on 
  Astronomical 
  and 
  

  

  radius 
  vector 
  in 
  any 
  given 
  time. 
  This 
  is 
  a 
  curious 
  and 
  

   interesting 
  result, 
  since 
  it 
  is 
  independent 
  o£ 
  V 
  and 
  o£ 
  e 
  and 
  

   of 
  ot. 
  The 
  fact 
  may 
  require 
  attention 
  in 
  another 
  branch 
  of 
  

   physics 
  later 
  on 
  (see 
  concluding 
  remarks 
  in 
  Part 
  III.). 
  

  

  Over 
  the 
  main 
  factor, 
  -Ja 
  2 
  #, 
  we 
  have 
  no 
  control 
  ; 
  but 
  we 
  

   can 
  partly 
  determine 
  the 
  bracketed 
  factors 
  of 
  (2) 
  by 
  judi- 
  

   cious 
  selection 
  of 
  t-r 
  and 
  Jc 
  for 
  any 
  particular 
  planet 
  ; 
  though, 
  

   having 
  chosen 
  for 
  one, 
  the 
  others 
  all 
  follow. 
  

  

  The 
  observational 
  values 
  to 
  be 
  accommodated 
  by 
  theory 
  

   are 
  stated 
  by 
  Mr. 
  Harold 
  Jeffreys 
  in 
  the 
  ' 
  Monthly 
  Notices 
  ' 
  

   of 
  the 
  Royal 
  Astronomical 
  Society 
  for 
  December 
  1916, 
  

   whence 
  I 
  get 
  the 
  permissible 
  range 
  : 
  — 
  

  

  IT. 
  Unexplained 
  Secular 
  Variations 
  per 
  century, 
  as 
  observed. 
  

  

  

  edw. 
  

  

  edtsr. 
  

  

  Permissible 
  

   range. 
  

  

  de. 
  

  

  Permissible 
  

   range. 
  

  

  Mercury 
  

  

  Venus 
  

  

  848+0-43 
  

  

  -0-05+0-25 
  

  

  010±0'13 
  

  

  0-75±0-34 
  

  

  + 
  8-91 
  to 
  -f-8-05 
  

   -0-30 
  to 
  +0-20 
  

   +023 
  to 
  -0-03 
  

   +1-09 
  to 
  +0-41 
  

  

  -0-88+0-50 
  

   0-21+0-31 
  

  

  -1-38 
  to 
  -0-38 
  

   4-0-52 
  to 
  —0-10 
  

  

  Earth 
  

  

  0-02±0-10 
  +0-12 
  to 
  -0-08 
  

   0-29+0-27 
  -J-0-5A 
  to 
  -1-009 
  

  

  Mars 
  

  

  

  

  

  Hence 
  to 
  get 
  results 
  for 
  Mercury 
  and 
  Mars 
  from 
  the 
  

   above 
  equations, 
  such 
  as 
  will 
  correspond 
  in 
  sign 
  with 
  the 
  

   entries 
  in 
  the 
  above 
  table, 
  a 
  solar 
  drift 
  must 
  be 
  chosen 
  so 
  

   as 
  to 
  make 
  sin-sr 
  negative 
  for 
  both 
  planets, 
  with 
  cos 
  in- 
  

   negative 
  for 
  Mercury 
  and 
  positive 
  for 
  Mars. 
  This 
  suggests 
  

   an 
  obtuse 
  negative 
  angle 
  between 
  Mercury's 
  perihelion 
  and 
  

   the 
  solar 
  drift, 
  and 
  an 
  acute 
  negative 
  angle 
  for 
  that 
  of 
  Mars 
  ; 
  

   but 
  this 
  can 
  be 
  seen 
  to 
  be 
  impossible, 
  though 
  the 
  converse 
  

   would 
  be 
  easy. 
  A 
  troublesome 
  accommodation 
  difficulty 
  

   lies 
  in 
  the 
  fact 
  that 
  the 
  major 
  axes 
  of 
  these 
  two 
  planets 
  

   happen 
  to 
  cross 
  nearly 
  at 
  right-angles, 
  so 
  that 
  what 
  suits 
  

   one 
  is 
  hardly 
  likely 
  thoroughly 
  to 
  suit 
  the 
  other. 
  

  

  The 
  above 
  table 
  shows 
  moreover 
  that 
  both 
  the 
  observed 
  

   perturbations 
  for 
  Earth 
  and 
  Venus 
  are 
  small, 
  and 
  might 
  even 
  

   be 
  zero. 
  But 
  looking 
  at 
  the 
  equations 
  (3), 
  we 
  see 
  that 
  in 
  

   general 
  both 
  the 
  theoretical 
  perturbations 
  cannot 
  vanish 
  or 
  

   be 
  small 
  together 
  for 
  any 
  reasonable 
  value 
  of 
  Jc. 
  (There 
  is 
  

   no 
  sense 
  in 
  a 
  negative 
  value 
  for 
  Jc 
  such 
  as 
  —2/e.) 
  

  

  