﻿152 
  Sir 
  Oliver 
  Lodge 
  on 
  Astronomical 
  and 
  

  

  or, 
  since 
  £ 
  = 
  *206, 
  or 
  say 
  *2 
  for 
  correction 
  terms, 
  

  

  qt: 
  cos 
  2ot 
  — 
  k 
  sin 
  -st 
  = 
  1, 
  

  

  (5) 
  

  

  k 
  2 
  

  

  -^sin 
  2-G7 
  + 
  & 
  cos 
  -cr 
  = 
  — 
  -13. 
  

  

  A 
  solution 
  of 
  these 
  equations 
  * 
  is 
  very 
  nearly 
  

  

  OT 
  = 
  262°=-98°, 
  

   k 
  =1-056. 
  

  

  And 
  since 
  the 
  perihelion 
  position 
  for 
  Mercury 
  is 
  

  

  75° 
  = 
  -or 
  + 
  Z, 
  

  

  we 
  get 
  as 
  the 
  longitude 
  of 
  solar 
  drift 
  proper 
  to 
  account 
  for 
  

   both 
  perturbations 
  of 
  Mercury 
  

  

  Z=75°-262°=-187 
  =173 
  . 
  

  

  We 
  attend 
  to 
  this 
  case 
  further 
  in 
  Table 
  V. 
  below. 
  

  

  Numerical 
  calculation 
  for 
  special 
  cases. 
  

  

  In 
  taking 
  out 
  the 
  trigonometrical 
  functions 
  so 
  as 
  to 
  get 
  

   the 
  proper 
  factors 
  in 
  each 
  case 
  we 
  have 
  to 
  pay 
  particular 
  

  

  * 
  I 
  solved 
  these 
  by 
  successive 
  approximation, 
  the 
  upper 
  equation 
  

   mainly 
  determining 
  k, 
  while 
  the 
  lower 
  mainly 
  determines 
  -w 
  ; 
  general 
  

   consideration, 
  about 
  signs, 
  etc., 
  showing 
  that 
  -or 
  must 
  be 
  something 
  big 
  

   in 
  the 
  third 
  quadrant, 
  i. 
  e. 
  not 
  far 
  from 
  270° 
  ; 
  but 
  my 
  brother 
  has 
  now 
  

   solved 
  them 
  in 
  much 
  neater 
  fashion, 
  as 
  thus 
  : 
  — 
  

  

  t 
  r 
  2 
  cos20-2O.rsin0 
  = 
  2O, 
  | 
  

   x 
  2 
  sin 
  20+2O.r 
  cos 
  9= 
  —2*6, 
  f 
  

  

  „r 
  2 
  (cos 
  20+t 
  sin 
  20) 
  +20 
  u-(cos 
  0+z 
  sin 
  0) 
  = 
  20 
  - 
  2'6i, 
  

  

  {xe 
  ie 
  ) 
  2 
  +20i(xe 
  ie 
  )+(10i) 
  2 
  =-80-2-6i, 
  

  

  (xe 
  i6 
  +l0if 
  = 
  (a-\-ibf, 
  

  

  where 
  a 
  2 
  -b 
  2 
  =-80 
  and 
  ab 
  =-I'3. 
  

  

  .'. 
  xcos9 
  = 
  a, 
  xsm9 
  = 
  b 
  — 
  10, 
  and 
  x 
  2 
  = 
  a 
  2 
  -\-b 
  2 
  -\-100— 
  20b. 
  

  

  The 
  value 
  of 
  a 
  2 
  +b 
  2 
  is 
  80*04224 
  nearly, 
  and 
  

  

  a=+-1453252, 
  b= 
  +8-94545. 
  

  

  x 
  cos 
  = 
  + 
  -145325 
  ) 
  , 
  x 
  cos 
  9= 
  — 
  -145325, 
  

  

  or 
  

  

  x 
  sin 
  9= 
  -18-94545 
  f 
  U1 
  x 
  sin 
  0= 
  -1*05455 
  

  

  x 
  = 
  18-9460 
  I 
  or 
  x 
  = 
  1-0640, 
  

  

  = 
  270° 
  26£', 
  j 
  = 
  262° 
  9 
  '. 
  

  

  )\ 
  

  

  