﻿482 
  H. 
  A. 
  Newton 
  — 
  Capture 
  of 
  Comets 
  by 
  Planets. 
  

  

  available 
  for 
  comparison 
  with 
  the 
  earlier 
  determinations. 
  I 
  

   know 
  no 
  reason 
  to 
  suppose 
  that 
  the 
  determinations 
  of 
  latitude 
  

   already 
  made 
  at 
  the 
  other 
  stations 
  are 
  less 
  precise 
  than 
  that 
  at 
  

   Madison 
  and 
  a 
  rediscussion 
  of 
  this 
  determination 
  has 
  shown 
  

   that 
  by 
  the 
  aid 
  of 
  improved 
  star 
  places 
  the 
  latitude 
  referred 
  to 
  

   Auwers' 
  declination 
  system 
  is 
  determined 
  for 
  the 
  epoch 
  1873 
  

   with 
  a 
  probable 
  error 
  of 
  //# 
  05. 
  If 
  the 
  same 
  degree 
  of 
  pre- 
  

   cision 
  obtains 
  at 
  the 
  other 
  stations 
  a 
  new 
  set 
  of 
  determina- 
  

   tions 
  in 
  1892 
  would 
  furnish 
  for 
  a 
  single 
  pair 
  of 
  stations 
  a 
  

   value 
  of 
  the 
  annual 
  motion 
  of 
  the 
  pole 
  with 
  a 
  probable 
  error 
  

   of 
  only 
  0"-003. 
  

  

  But 
  little 
  difficulty 
  will 
  be 
  experienced 
  in 
  securing 
  new 
  de- 
  

   terminations 
  at 
  the 
  American 
  stations. 
  I 
  will 
  myself 
  become 
  

   responsible 
  for 
  the 
  observations 
  at 
  Madison, 
  and 
  it 
  is 
  probable 
  

   that 
  upon 
  a 
  proper 
  presentation 
  of 
  the 
  case 
  being 
  made 
  to 
  the 
  

   Superintendent 
  of 
  the 
  Coast 
  and 
  Geodetic 
  Survey 
  the 
  observa- 
  

   tions 
  at 
  Columbus 
  and 
  Macon 
  or 
  San 
  Diego 
  will 
  be 
  under- 
  

   taken 
  by 
  that 
  organization. 
  To 
  secure 
  the 
  reoccupation 
  of 
  the 
  

   Asiatic 
  stations, 
  however, 
  is 
  a 
  very 
  different 
  matter, 
  for 
  which 
  

   concerted 
  action 
  of 
  some 
  kind 
  will 
  probably 
  be 
  necessary, 
  and 
  

   it 
  is 
  with 
  a 
  view 
  to 
  securing 
  such 
  action 
  that 
  I 
  present 
  this 
  

   paper 
  to 
  the 
  Section 
  for 
  discussion. 
  

  

  Art. 
  LII. 
  — 
  On 
  the 
  Capture 
  of 
  Comets 
  by 
  Planets, 
  especially 
  

   their 
  Capture 
  by 
  Jupiter 
  ; 
  by 
  H. 
  A. 
  Newton. 
  

  

  [Continued 
  from 
  p. 
  199, 
  Sept., 
  1891.] 
  

  

  30. 
  If 
  there 
  are 
  assumed 
  to 
  be 
  n 
  comets 
  equably 
  distributed 
  

   in 
  each 
  unit 
  of 
  the 
  space 
  near 
  and 
  through 
  which 
  a 
  planet 
  is 
  

   moving, 
  and 
  if 
  these 
  comets 
  are 
  all 
  assumed 
  to 
  be 
  moving 
  in 
  

   parabolas 
  about 
  the 
  sun 
  with 
  the 
  velocity 
  v, 
  having 
  also 
  their 
  

   directions 
  of 
  motion 
  equably 
  distributed, 
  then 
  the 
  number 
  that 
  

   are 
  moving 
  from 
  quits 
  lying 
  within 
  an 
  element 
  dS 
  of 
  the 
  sur- 
  

   face 
  of 
  the 
  celestial 
  sphere 
  will 
  be 
  -r 
  — 
  Let 
  v 
  be 
  the 
  com- 
  

   mon 
  velocity 
  of 
  these 
  comets 
  relative 
  to 
  the 
  planet. 
  Then 
  

   suppose 
  that 
  a 
  spherical 
  surface 
  S' 
  is 
  described 
  with 
  a 
  radius 
  

   r' 
  about 
  the 
  planet 
  as 
  center 
  ; 
  r' 
  being 
  small 
  relative 
  to 
  the 
  

   sun's 
  distance, 
  yet 
  not 
  so 
  small 
  as 
  to 
  forbid 
  the 
  omission 
  of 
  

   the 
  planet's 
  perturbing 
  action 
  so 
  long 
  as 
  the 
  comet 
  is 
  without 
  

   the 
  surface 
  S 
  r 
  . 
  In 
  each 
  unit 
  of 
  time 
  out 
  of 
  these 
  comets 
  

   directed 
  from 
  the 
  element 
  dS 
  of 
  the 
  celestial 
  sphere 
  there 
  would 
  

  

  pass 
  nearer 
  than 
  r' 
  to 
  the 
  planet 
  n- 
  A 
  — 
  . 
  wr 
  ,% 
  v 
  = 
  \ 
  nv 
  r'* 
  dS 
  

  

  ■±7T 
  

  

  