﻿Gravitational 
  Bearings 
  of 
  Electrical 
  Theory 
  of 
  Matter. 
  149 
  

  

  Alternatives. 
  

  

  Now 
  let 
  us 
  consider 
  the 
  numerical 
  values 
  of 
  the 
  theoretical 
  

   perturbations 
  for 
  different 
  planets, 
  with 
  specially 
  selected 
  

   values 
  for 
  the 
  solar 
  drift. 
  TV 
  rite 
  them 
  

  

  } 
  • 
  00 
  

  

  ed'ur 
  = 
  \a?Q 
  . 
  h 
  . 
  (— 
  sin 
  -or 
  -f 
  \ke 
  cos 
  2ot 
  -f 
  e/k), 
  

   de 
  = 
  \o?Q 
  . 
  k 
  . 
  (cos 
  ot 
  + 
  \ke 
  sin 
  2 
  -or), 
  

  

  so 
  as 
  to 
  show 
  in 
  each 
  case 
  

  

  (1) 
  A 
  purely 
  planetary 
  factor 
  \o?Q, 
  concerning 
  which 
  

  

  we 
  have 
  no 
  choice 
  ; 
  

  

  (2) 
  A 
  numerical 
  factor 
  k, 
  depending 
  on 
  the 
  magnitude 
  

  

  of 
  assumed 
  solar 
  drift 
  and 
  varying 
  directly 
  as 
  ^r 
  

   for 
  different 
  planets 
  ; 
  

  

  (3) 
  A 
  trigonometrical 
  factor, 
  depending 
  mainly 
  on 
  the 
  

  

  direction 
  of 
  the 
  assumed 
  solar 
  drift. 
  

  

  For 
  moderate 
  values 
  of 
  k, 
  and 
  for 
  round 
  orbits, 
  the 
  first 
  

   term 
  of 
  each 
  direction 
  factor 
  (viz. 
  — 
  sin 
  ot 
  for 
  the 
  one, 
  cos 
  -or 
  

   for 
  the 
  other) 
  is 
  by 
  far 
  the 
  most 
  important. 
  

  

  Large 
  values 
  of 
  k 
  require 
  delicate 
  and 
  practically 
  im- 
  

   possible 
  adjustments, 
  so 
  that 
  if 
  for 
  any 
  planet 
  both 
  pertur- 
  

   bations 
  are 
  wanted 
  small 
  (as 
  they 
  are), 
  it 
  is 
  essential 
  to 
  keep 
  

   k 
  down 
  to 
  the 
  smallest 
  value 
  which 
  will 
  give 
  anything 
  like 
  

   the 
  desired 
  result 
  for 
  some 
  one 
  definite 
  planet. 
  

  

  Let 
  us 
  then 
  choose 
  k 
  or 
  Y/u 
  as 
  small 
  as 
  possible. 
  We 
  

   might 
  even 
  try 
  it 
  no 
  greater, 
  for 
  the 
  Earth, 
  than 
  suits 
  the 
  

  

  known 
  solar 
  motion 
  towards 
  "Vega 
  (viz. 
  19*5 
  ' 
  directed 
  

  

  G 
  v 
  sec. 
  

  

  towards 
  R.A. 
  18 
  h 
  2 
  m 
  or 
  longitude 
  270° 
  46', 
  and 
  declination 
  

  

  34° 
  or 
  latitude 
  57° 
  30'), 
  of 
  which 
  the 
  projected 
  component 
  

  

  will 
  be 
  about 
  half 
  of 
  two-thirds 
  of 
  the 
  earth's 
  orbital 
  speed, 
  

  

  or 
  ^-xl0" 
  4 
  6', 
  which 
  makes 
  k 
  for 
  the 
  earth 
  =^. 
  Then 
  for 
  

  

  the 
  other 
  planets 
  we 
  shall 
  have 
  k 
  varying 
  as 
  l/n 
  or 
  ^/r, 
  and 
  

  

  so 
  get 
  the 
  column 
  k 
  x 
  in 
  Table 
  III. 
  below. 
  

  

  But 
  the 
  resulting 
  value 
  of 
  k 
  for 
  Mercury, 
  viz. 
  "21, 
  is 
  far 
  

   too 
  small 
  to 
  explain 
  the 
  progress 
  of 
  Mercury's 
  perihelion 
  : 
  

   for 
  that 
  purpose 
  Mercury's 
  k 
  must 
  be 
  comparable 
  to 
  unity, 
  

   in 
  order 
  to 
  give 
  a 
  reasonable 
  factor 
  with 
  which 
  to 
  multiply 
  

   \ct?6: 
  but 
  what 
  its 
  necessary 
  value 
  is 
  will 
  depend 
  on 
  -cr, 
  

   i. 
  e. 
  on 
  the 
  direction 
  chosen 
  for 
  the 
  solar 
  drift 
  with 
  reference 
  

   to 
  the 
  planet's 
  major 
  axis. 
  Consider 
  then 
  what 
  is 
  the 
  best 
  

   direction 
  to 
  choose. 
  

  

  The 
  idea 
  on 
  which 
  we 
  started 
  (see 
  Phil. 
  Mag. 
  for 
  last 
  

  

  