﻿150 
  Sir 
  Oliver 
  Lodge 
  on 
  Astronomical 
  and 
  

  

  August) 
  was 
  to 
  explain 
  simply 
  the 
  outstanding 
  perihelion 
  

   progression 
  of 
  Mercury, 
  43" 
  per 
  century 
  or 
  edvr 
  = 
  8"'6 
  ; 
  so 
  

   it 
  is 
  natural 
  to 
  select 
  values 
  of 
  k 
  and 
  ot 
  which 
  shall 
  give 
  an 
  

   approximation 
  to 
  this 
  value 
  in 
  the 
  case 
  of 
  Mercury 
  and 
  yet 
  

   keep 
  k 
  small 
  enough 
  not 
  to 
  spoil 
  agreement 
  for 
  the 
  other 
  

   planets. 
  The 
  most 
  favourable 
  possible 
  direction 
  is 
  90° 
  beyond 
  

   the 
  perihelion 
  longitude 
  of 
  Mercury, 
  which 
  is 
  75°. 
  For 
  this 
  

   drift 
  longitude 
  of 
  165° 
  will 
  make 
  -sr= 
  —90 
  and 
  sin 
  -57= 
  — 
  1. 
  

   The 
  drift-factor 
  for 
  edvr 
  then 
  attains 
  its 
  maximum,, 
  viz. 
  

  

  k 
  + 
  e(l-iP), 
  

  

  while 
  the 
  factor 
  for 
  de 
  is 
  zero. 
  In 
  that 
  case 
  the 
  value 
  of 
  k 
  

   for 
  Mercury 
  may 
  be 
  as 
  low 
  as 
  *9 
  ; 
  for, 
  since 
  e 
  = 
  '2, 
  this 
  will 
  

   give 
  a 
  factor, 
  1*1, 
  sufficient 
  to 
  convert 
  the 
  7" 
  belonging 
  to 
  

   \o?Q 
  for 
  Mercury 
  into 
  very 
  near 
  the 
  desired 
  8". 
  Corre- 
  

   sponding 
  values 
  of 
  k 
  for 
  other 
  planets 
  are 
  tabulated 
  in 
  the 
  

   column 
  k 
  2 
  below. 
  

  

  But 
  then 
  the 
  perihelion 
  longitude 
  for 
  Mars 
  happens 
  to 
  be 
  

   333°, 
  so 
  that 
  with 
  drift 
  longitude 
  165° 
  the 
  -sr 
  for 
  Mars 
  would 
  

   be 
  H- 
  168° 
  or 
  180—12° 
  ; 
  and 
  the 
  value 
  of 
  sin-sr 
  wall 
  be 
  small 
  

   and 
  positive, 
  and 
  of 
  cos 
  w 
  big 
  and 
  negative 
  — 
  an 
  arrange- 
  

   ment 
  which 
  does 
  not 
  suit 
  Mars 
  at 
  all 
  ; 
  hence 
  a 
  compromise 
  

   is 
  necessary. 
  

  

  If 
  we 
  choose 
  the 
  compromise 
  which 
  I 
  suggested 
  in 
  the 
  

   August 
  Phil. 
  Mag., 
  page 
  91, 
  viz. 
  294°, 
  or 
  rather 
  that 
  direc- 
  

   tion 
  reversed, 
  viz. 
  114°, 
  we 
  have 
  got 
  a 
  direction 
  equally 
  

   inclined 
  to 
  the 
  major 
  axes 
  of 
  Mercury 
  and 
  Mars, 
  and 
  also, 
  

   as 
  it 
  happens, 
  practically 
  equally 
  inclined 
  to 
  the 
  major 
  axes 
  

   of 
  Earth 
  and 
  Venus, 
  which 
  are 
  another 
  pair 
  that 
  may 
  be 
  

   considered 
  together. 
  The 
  angle 
  to- 
  for 
  Mercury 
  in 
  this 
  case 
  

   is 
  —39°, 
  and 
  for 
  Mars 
  is 
  180 
  + 
  39°; 
  so 
  in 
  both 
  cases 
  sin 
  -or 
  is 
  

   negative, 
  as 
  wanted, 
  though 
  the 
  less 
  said 
  about 
  cos 
  -57 
  the 
  

   better. 
  The 
  corresponding 
  values 
  of 
  k 
  for 
  all 
  the 
  planets, 
  

   including 
  that 
  needed 
  to 
  suit 
  Mercury's 
  perihelion 
  for 
  this 
  

   drift 
  direction 
  114°, 
  namely 
  1*5, 
  are 
  tabulated 
  below 
  

   as 
  ^ 
  3 
  . 
  

  

  The 
  table 
  shows 
  some 
  corresponding 
  values 
  of 
  k 
  and 
  «r 
  for 
  

   all 
  the 
  planets, 
  with 
  the 
  corresponding 
  assumed 
  longitude 
  

   for 
  solar 
  drift. 
  This 
  is 
  here 
  called 
  I 
  ; 
  and 
  it 
  must 
  be 
  

   remembered 
  that 
  this 
  solar 
  drift 
  direction, 
  and 
  not 
  the 
  first 
  

   point 
  of 
  Aries, 
  is 
  the 
  artificial 
  zero 
  from 
  which 
  to 
  reckon 
  «r. 
  

   The 
  <sr 
  are 
  got 
  by 
  subtracting 
  I 
  from 
  the 
  perihelion 
  longitude,, 
  

   as 
  cited. 
  The 
  k 
  vary 
  as 
  VV. 
  

  

  