﻿146 
  Sir 
  Oliver 
  Lodge 
  on 
  Astronomical 
  and 
  

  

  of 
  e. 
  These 
  equations, 
  for 
  convenience, 
  I 
  will 
  here 
  quote- 
  

   from 
  page 
  326, 
  vol. 
  xxxiv. 
  as 
  they 
  stand 
  : 
  — 
  

  

  ed*r= 
  a-j- 
  sm 
  ot 
  + 
  -£-* 
  e 
  + 
  -qt 
  e 
  cos 
  2«r, 
  

  

  de 
  = 
  —^-^-cos 
  7s 
  4- 
  -5-5-^sin 
  z-sr, 
  

  

  2r 
  8c 
  2 
  

  

  a) 
  

  

  where 
  V 
  is 
  the 
  component 
  of 
  true 
  solar 
  drift 
  projected 
  on 
  

  

  plane 
  of 
  orbit, 
  

   vr 
  is 
  longitude 
  of 
  planet's 
  perihelion 
  reckoned 
  from. 
  

  

  the 
  direction 
  of 
  V 
  as 
  zero, 
  

   u 
  is 
  that 
  constant 
  component 
  of 
  the 
  velocity 
  of 
  a 
  

  

  planet 
  which 
  is 
  normal 
  to 
  its 
  radius 
  vector, 
  

   6 
  is 
  the 
  angle 
  turned 
  through 
  by 
  radius 
  vector 
  per 
  

  

  century, 
  

  

  and 
  c 
  is 
  the 
  velocity 
  of 
  light. 
  

  

  I 
  proceed 
  to 
  apply 
  this 
  improvement 
  on 
  what 
  I 
  published 
  

   in 
  August, 
  so 
  as 
  to 
  ascertain 
  whether 
  or 
  not 
  the 
  theory 
  can 
  

   be 
  made 
  to 
  work. 
  

  

  Let 
  the 
  solar 
  drift 
  be 
  k 
  times 
  the 
  planet's 
  velocity 
  as- 
  

   specified, 
  say 
  Y 
  = 
  ku 
  ; 
  and 
  introduce 
  an 
  aberration 
  angte 
  

   oi 
  = 
  u 
  /c 
  ; 
  then 
  we 
  can 
  write 
  the 
  above 
  equations 
  thus 
  : 
  — 
  

  

  ed 
  t 
  a 
  = 
  iot 
  2 
  0( 
  — 
  k 
  sin 
  vr 
  + 
  £Pe 
  cos2-s7 
  + 
  <?), 
  1 
  . 
  . 
  

  

  de~\a?6{kQ,Qs^ 
  + 
  \Wes\nZTn). 
  J 
  

  

  The 
  common 
  factor 
  outside 
  the 
  brackets, 
  \a?0^ 
  is 
  inde- 
  

   pendent 
  of 
  solar 
  drift 
  and 
  cannot 
  be 
  evaded. 
  It 
  varies 
  as 
  

   the 
  reciprocal 
  of 
  the 
  5/3rd 
  power 
  of 
  the 
  periodic 
  time 
  for 
  

   different 
  planets, 
  or 
  as 
  the 
  — 
  2*5th 
  power 
  of 
  their 
  distances 
  ; 
  

   as 
  can 
  be 
  seen 
  thus 
  : 
  — 
  

  

  The 
  large 
  angle 
  is 
  27rn, 
  so 
  it 
  is 
  inversely 
  as 
  T 
  ; 
  a 
  is 
  

   proportional 
  to 
  u 
  , 
  which 
  is 
  practically 
  the 
  same 
  in 
  magni- 
  

   tude 
  as 
  the 
  average 
  orbital 
  velocity 
  ; 
  so 
  a 
  varies 
  inversely 
  

  

  as 
  y/r 
  or 
  as 
  T 
  by 
  Kepler's 
  third 
  law. 
  

  

  _5 
  5 
  —5. 
  

  

  Hence 
  \a?6 
  is 
  proportional 
  to 
  T 
  or 
  « 
  or 
  r 
  . 
  It 
  

   becomes 
  small, 
  therefore, 
  for 
  the 
  outer 
  planets. 
  It 
  is 
  also 
  

   plain 
  that 
  the 
  values 
  of 
  \o?Qy.k 
  for 
  different 
  planets 
  vary 
  

   inversely 
  as 
  the 
  square 
  of 
  their 
  distances 
  from 
  the 
  sun. 
  

  

  The 
  value 
  of 
  \o?6 
  for 
  the 
  Earth 
  is 
  IOOtt 
  x 
  10- 
  8 
  = 
  0"'648,. 
  

   and 
  from 
  this 
  it 
  can 
  be 
  reckoned 
  for 
  the 
  other 
  planets 
  by 
  

  

  