﻿of 
  Matter 
  and 
  their 
  Astronomical 
  Consequences. 
  485 
  

  

  Turning 
  now 
  to 
  Walker's 
  astronomical 
  calculations, 
  it 
  may 
  

   be 
  pointed 
  out 
  that 
  his 
  detailed 
  calculations 
  deal 
  with 
  a 
  solar 
  

   system 
  at 
  rest 
  in 
  the 
  aether. 
  The 
  discussion 
  therefore 
  does 
  

   not 
  relate 
  to 
  Sir 
  Oliver 
  Lodge's 
  suggestion 
  as 
  to 
  the 
  effects 
  

   o£ 
  a 
  solar 
  motion, 
  nor 
  does 
  it 
  throw 
  light 
  on 
  the 
  point 
  sub- 
  

   sequently 
  brought 
  out 
  — 
  that 
  the 
  motion 
  of 
  the 
  solar 
  system 
  

   (if 
  any) 
  has 
  no 
  observable 
  effect 
  on 
  the 
  motions 
  o£ 
  Venus 
  

   and 
  the 
  Earth. 
  At 
  the 
  end 
  of 
  his 
  investigation 
  Walker 
  hints 
  

   that 
  a 
  satisfactory 
  theory 
  similar 
  to 
  Lodge's 
  might 
  be 
  con- 
  

   structed 
  by 
  using 
  the 
  more 
  general 
  type 
  of 
  Lagrangian 
  

   function. 
  He 
  has, 
  however, 
  already 
  three 
  unknown 
  con- 
  

   stants, 
  k 
  l9 
  k 
  2 
  , 
  & 
  3 
  ; 
  the 
  components 
  of 
  the 
  unknown 
  solar 
  

   motion 
  will 
  give 
  him 
  three 
  more; 
  with 
  six 
  constants 
  at 
  

   disposal, 
  he 
  can 
  scarcely 
  fail 
  to 
  secure 
  a 
  forced 
  agreement 
  

   of 
  the 
  perihelia 
  and 
  eccentricities 
  of 
  the 
  four 
  inner 
  planets, 
  

   and 
  it 
  is 
  difficult 
  to 
  find 
  any 
  observational 
  test 
  for 
  such 
  a 
  

   theory. 
  

  

  On 
  p. 
  337 
  it 
  is 
  stated 
  that 
  the 
  observed 
  motion 
  of 
  peri- 
  

   helion 
  of 
  Mercury 
  is 
  satisfied 
  by 
  supposing 
  that 
  the 
  attraction 
  

   depends 
  on 
  the 
  velocity 
  (j. 
  e. 
  relative 
  velocity) 
  according 
  to 
  

   the 
  law 
  

  

  and 
  that 
  Einstein 
  implicitly 
  introduces 
  this 
  comparatively 
  

   large 
  dependence 
  on 
  speed. 
  Einstein's 
  law 
  may 
  be 
  trans- 
  

   formed 
  in 
  a 
  great 
  many 
  ways 
  ; 
  but 
  1 
  do 
  not 
  think 
  any 
  

   possible 
  interpretation 
  of 
  it 
  reduces 
  to 
  this. 
  If 
  it 
  is 
  desired 
  

   to 
  put 
  the 
  new 
  wine 
  into 
  old 
  bottles, 
  I 
  think 
  we 
  must 
  say 
  

   that 
  the 
  theory 
  involves 
  different 
  effects 
  of 
  the 
  radial 
  and 
  

   transverse 
  components 
  of 
  velocity 
  in 
  modifying 
  gravitation, 
  or 
  

   to 
  quote 
  Walker's 
  earlier 
  remark 
  "the 
  modified 
  Lagrangian 
  

   function 
  depends 
  on 
  the 
  acceleration 
  as 
  well 
  as 
  on 
  the 
  speed 
  

   of 
  the 
  system 
  and 
  involves 
  also 
  the 
  relative 
  direction 
  of 
  these 
  "*. 
  

   The 
  point 
  is 
  perhaps 
  not 
  of 
  great 
  importance; 
  because 
  in 
  any 
  

   case 
  a 
  theory 
  which 
  deduces 
  the 
  exact 
  motion 
  of 
  Mercury 
  

   from 
  a 
  general 
  principle 
  stands 
  on 
  a 
  different 
  footing 
  from 
  

   theories 
  which 
  merely 
  use 
  the 
  motion 
  of 
  Mercury 
  to 
  obtain 
  

   an 
  empirical 
  determination 
  of 
  their 
  arbitrary 
  constants. 
  

  

  As 
  a 
  closely 
  connected 
  subject, 
  the 
  question 
  of 
  the 
  alleged 
  

   discordance 
  of 
  the 
  node 
  of 
  Venus 
  deserves 
  some 
  remarks. 
  

   Dr. 
  Jeffreys 
  (Nature, 
  April 
  11, 
  p. 
  103) 
  has 
  commented 
  on 
  

  

  * 
  "Walker's 
  method 
  of 
  taking 
  this 
  into 
  account 
  is 
  to 
  give 
  k 
  } 
  and 
  k 
  u 
  

   appropriate 
  values, 
  "but 
  in 
  calculating- 
  the 
  number 
  -% 
  he 
  has 
  used 
  the 
  

   quasi-stationary 
  values, 
  presumably 
  as 
  a 
  concession 
  to 
  relativists. 
  I 
  am 
  

   afraid 
  I 
  must 
  reject 
  the 
  concession, 
  and 
  insist 
  on 
  agreeing 
  with 
  his 
  true 
  

   opinion 
  on 
  this 
  point. 
  

  

  