﻿154 
  

  

  Sir 
  Oliver 
  Lodge 
  on 
  Astronomical 
  and 
  

  

  Perhaps 
  the 
  simplest 
  plan 
  of 
  calculating 
  perturbations 
  for 
  

   a 
  given 
  V, 
  is 
  to 
  reckon 
  \o?Q~k 
  for 
  one 
  planet, 
  say 
  the 
  Earth 
  ; 
  

   divide 
  this 
  by 
  relative 
  r 
  2 
  for 
  all 
  the 
  others 
  ; 
  and 
  then 
  

   multiply 
  the 
  numbers 
  so 
  obtained 
  by 
  the 
  respective 
  direc- 
  

   tion 
  factors 
  A 
  and 
  B 
  ; 
  which 
  consist 
  of 
  — 
  sin-sr 
  and 
  cos 
  txr 
  

   primarily, 
  corrected 
  by 
  addition 
  or 
  subtraction 
  of 
  small 
  

   functions 
  of 
  k 
  and 
  e 
  and 
  sin 
  2^ 
  and 
  cos 
  2«r. 
  Thus 
  a 
  first 
  

   approximation 
  is 
  

  

  '648£r 
  

  

  sin 
  w, 
  for 
  edvr, 
  

  

  and 
  

  

  •648£ 
  r 
  

  

  cos 
  -57, 
  for 
  de, 
  

  

  where 
  k 
  refers 
  to 
  the 
  Earth, 
  being 
  V/10" 
  4 
  c. 
  

  

  The 
  next 
  approximation 
  can 
  be 
  taken 
  from 
  equations 
  (3) 
  

   above, 
  viz. 
  the 
  factor 
  (1 
  + 
  JA« 
  sin 
  -bt) 
  for 
  both, 
  with 
  a 
  

   supplementary 
  term 
  for 
  one. 
  

  

  The 
  only 
  other 
  case 
  which 
  I 
  will 
  work 
  in 
  detail 
  is 
  the 
  case 
  

   when 
  a 
  direction 
  is 
  chosen 
  to 
  satisfy 
  both 
  ediz 
  and 
  de 
  for 
  

   Mercury. 
  We 
  can 
  then 
  see 
  what 
  happens 
  to 
  the 
  others. 
  

   This 
  is 
  the 
  case 
  which 
  we 
  previously 
  tabulated 
  as 
  & 
  4 
  and 
  

   ot^ 
  in 
  Table 
  III., 
  and 
  which 
  depends 
  on 
  the 
  solution 
  of 
  

   equations 
  (5). 
  

  

  V. 
  Calculated 
  Perturbations 
  for 
  the 
  Case 
  of 
  

  

  1 
  = 
  173° 
  and 
  V 
  = 
  l-7xl0" 
  4 
  

  

  

  "ST. 
  

  

  sin 
  -nr. 
  

  

  cos 
  -or. 
  

  

  *. 
  

  

  A. 
  

  

  B. 
  

  

  cdw. 
  

   +8-34 
  

  

  de. 
  

  

  Mercury... 
  

  

  180+82 
  

  

  -•990 
  

  

  -•139 
  

  

  1-056 
  

  

  1-14 
  

  

  -•124 
  

  

  -0-91 
  

  

  Venus 
  

  

  -44 
  

  

  -•695 
  

  

  + 
  •719 
  

  

  1-44 
  

  

  •70 
  

  

  •72 
  

  

  + 
  1-46 
  

  

  +1-52 
  

  

  Earth 
  

  

  -73 
  

  

  -•956 
  

  

  +•292 
  

  

  1-7 
  

  

  •96 
  

  

  •29 
  

  

  + 
  104 
  

  

  +0-32 
  

  

  Mars 
  

  

  180-20 
  

  

  +•342 
  

  

  -•940 
  

  

  2-1 
  

  

  -•26 
  

  

  -•97 
  

  

  -0-12 
  

  

  -0-46 
  

  

  On 
  the 
  whole 
  perhaps 
  these 
  perturbations 
  agree 
  rather 
  

   better 
  with 
  observation 
  than 
  do 
  those 
  in 
  Table 
  IV., 
  though 
  

   now 
  Mars 
  is 
  disappointing. 
  If 
  they 
  are 
  in 
  any 
  degree 
  

   tolerable, 
  one 
  may 
  note 
  that 
  the 
  drift, 
  of 
  magnitude 
  1'7 
  in 
  

   direction 
  173°, 
  thus 
  postulated, 
  ©an 
  be 
  considered 
  as 
  the 
  

  

  