﻿486 
  Electrical 
  Theories 
  of 
  Matter. 
  

  

  the 
  scant 
  attention 
  paid 
  to 
  this 
  as 
  compared 
  with 
  the 
  peri- 
  

   helion 
  of 
  Mercury. 
  It 
  may 
  be 
  well 
  to 
  explain 
  why 
  the 
  

   former 
  discordance 
  has 
  been 
  considered 
  unimportant. 
  The 
  

   residual 
  of 
  the 
  node 
  of 
  Venus 
  is 
  4J 
  times 
  its 
  probable 
  error 
  * 
  # 
  

   and 
  the 
  theoretical 
  chances 
  against 
  such 
  an 
  error 
  are 
  about 
  

   400 
  to 
  1. 
  But 
  it 
  must 
  not 
  be 
  f 
  or 
  gotten 
  that 
  this 
  element 
  lias 
  

   been 
  deliberately 
  selected 
  out 
  of 
  16 
  elements 
  as 
  showing 
  the 
  

   greatest 
  discordance. 
  To 
  apply 
  the 
  test 
  of 
  probable 
  error 
  we 
  

   must 
  select 
  fairly 
  and 
  not 
  pick 
  out 
  the 
  worst 
  cases. 
  Let 
  a 
  be 
  

   the 
  probability 
  of 
  an 
  error 
  less 
  than 
  as, 
  then 
  the 
  probability 
  

   that 
  all 
  sixteen 
  residuals 
  are 
  less 
  than 
  x 
  is 
  a 
  16 
  . 
  For 
  a 
  limit 
  

   of 
  4^ 
  times 
  the 
  probable 
  error 
  this 
  gives 
  a 
  probability 
  

   (*9976) 
  16 
  = 
  '962, 
  so 
  that 
  the 
  chance 
  of 
  the 
  largest 
  residual 
  

   being 
  as 
  much 
  as 
  4| 
  times 
  the 
  probable 
  error 
  is 
  "038, 
  or 
  

   about 
  1 
  in 
  26 
  — 
  an 
  adverse 
  probability, 
  but 
  not 
  very 
  emphatic. 
  

   To 
  put 
  the 
  matter 
  another 
  way, 
  we 
  find 
  (by 
  solving 
  a 
  l& 
  = 
  h) 
  

   that 
  the 
  largest 
  discordance 
  of 
  the 
  16 
  elements 
  should 
  just 
  

   exceed 
  3 
  times 
  the 
  probable 
  error. 
  We 
  may 
  therefore 
  ask, 
  

   What 
  is 
  the 
  probability 
  that 
  Newcomb 
  underestimated 
  his 
  

   errors 
  in 
  the 
  ratio 
  | 
  owing 
  to 
  unsuspected 
  sources 
  of 
  error? 
  

   The 
  evidence 
  for 
  a 
  genuine 
  discordance 
  seems 
  very 
  flimsy. 
  

   To 
  the 
  astronomer, 
  no 
  doubt, 
  it 
  is 
  an 
  indication 
  well 
  worth 
  

   looking 
  into: 
  but 
  it 
  would 
  be 
  extremely 
  rash 
  to 
  build 
  a 
  theory 
  

   on 
  so 
  slight 
  a 
  foundation. 
  

  

  The 
  present 
  state 
  of 
  the 
  problem 
  of 
  the 
  elements 
  of 
  the 
  

   four 
  inner 
  planets 
  appears 
  to 
  be 
  as 
  follows: 
  — 
  The 
  theory 
  

   given 
  in 
  Sir 
  Oliver 
  Lodge's 
  and 
  my 
  own 
  papers 
  leads 
  to 
  

   secular 
  perturbations 
  of 
  the 
  Earth 
  and 
  Venus, 
  which 
  ought 
  

   to 
  be 
  perceptible 
  to 
  observation 
  if 
  the 
  sun's 
  motion 
  is 
  greater 
  

   than 
  about 
  10 
  km. 
  per 
  sec. 
  Since 
  these 
  are 
  not 
  observed, 
  

   we 
  conclude 
  either 
  that 
  the 
  sun's 
  motion 
  happens 
  to 
  be 
  very 
  

   small, 
  or 
  that 
  there 
  must 
  be 
  compensating 
  terms 
  in 
  the 
  more 
  

   complete 
  theory. 
  Following 
  out 
  the 
  second 
  alternative, 
  there 
  

   are 
  again 
  two 
  possibilities. 
  Either 
  the 
  compensation 
  is 
  an 
  

   accident 
  due 
  to 
  the 
  particular 
  elements 
  of 
  the 
  orbits 
  and 
  their 
  

   relation 
  to 
  the 
  direction 
  of 
  the 
  sun's 
  motion, 
  or 
  it 
  is 
  a 
  general 
  

   compensation. 
  A 
  theory 
  can 
  no 
  doubt 
  be 
  constructed 
  which 
  

   gives 
  an 
  accidental 
  cancelling 
  for 
  Venus 
  and 
  the 
  Earth, 
  pro- 
  

   vided 
  it 
  contains 
  a 
  sufficient 
  number 
  of 
  disposable 
  constants 
  

   not 
  otherwise 
  determined 
  ; 
  but 
  such 
  a 
  theory 
  cannot 
  carry 
  

   much 
  conviction. 
  If 
  we 
  suppose 
  that 
  the 
  compensation 
  is 
  

   general, 
  then 
  we 
  are 
  adopting 
  effectively 
  a 
  relativity 
  theory 
  

   of 
  gravitation 
  — 
  that 
  uniform 
  motion 
  of 
  a 
  gravitating 
  system 
  

   produces 
  no 
  observable 
  effects. 
  This 
  involves 
  a 
  dependence 
  

  

  * 
  The 
  discordance 
  of 
  the 
  perihelion 
  of 
  Mercury 
  from 
  tl.e 
  Newtonian 
  

   theory 
  is 
  30 
  times 
  its 
  probable 
  error. 
  

  

  