﻿

  THE 
  

  

  AMERICAN 
  JOURNAL 
  OF 
  SCIENCE 
  

  

  [THIRD 
  SERIES.] 
  

  

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

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

  

  1. 
  Some 
  years 
  ago 
  I 
  obtained 
  and 
  published* 
  a 
  formula 
  ex- 
  

   pressing 
  in 
  simple 
  terms 
  the 
  total 
  result 
  of 
  the 
  action 
  of 
  a 
  

   planet 
  in 
  increasing 
  or 
  diminishing 
  the 
  velocity 
  of 
  a 
  comet 
  

   or 
  small 
  body 
  that 
  passes 
  near 
  the 
  planet. 
  This 
  formula 
  is 
  

   practically 
  a 
  modification 
  of 
  the 
  integral 
  of 
  energy, 
  the 
  smaller 
  

   terms 
  in 
  the 
  perturbing 
  function 
  being 
  omitted. 
  A 
  very 
  brief 
  

   and 
  partial 
  treatment 
  of 
  it 
  was 
  presented 
  to 
  the 
  British 
  Asso- 
  

   ciation 
  for 
  the 
  Advancement 
  of 
  Science 
  in 
  1879 
  at 
  its 
  Sheffield 
  

   meeting, 
  f 
  Within 
  the 
  last 
  two 
  or 
  three 
  years 
  several 
  astrono- 
  

   mers 
  have 
  made 
  special 
  study 
  of 
  the 
  manner 
  of 
  Jupiter's 
  action 
  

   in 
  changing 
  the 
  orbits 
  of 
  comets 
  that 
  pass 
  very 
  near 
  him. 
  M. 
  

   Tisserand 
  has 
  given 
  us 
  an 
  expression 
  connecting 
  the 
  major 
  axis, 
  

   inclination 
  and 
  parameter 
  of 
  the 
  orbit 
  described 
  before 
  coming 
  

   near 
  to 
  Jupiter 
  with 
  the 
  corresponding 
  elements 
  of 
  the 
  orbit 
  

   after 
  leaving 
  the 
  neighborhood 
  of 
  the 
  planet.;): 
  M. 
  Schulhof 
  

   has 
  applied 
  the 
  formula 
  of 
  M. 
  Tisserand 
  as 
  a 
  criterion 
  for 
  de- 
  

   termining 
  the 
  possible 
  identity 
  of 
  various 
  comets 
  whose 
  orbits 
  

   pass 
  near 
  to 
  Jupiter's 
  orbit.§ 
  Messrs. 
  Seeliger, 
  Callandreau 
  

   and 
  others 
  have 
  continued 
  these 
  investigations. 
  The 
  interest 
  

   thus 
  shown 
  in 
  the 
  problem 
  has 
  led 
  me 
  to 
  resume 
  the 
  study 
  of 
  

   the 
  subject, 
  and 
  to 
  work 
  out 
  the 
  results 
  of 
  the 
  formula 
  obtained 
  

   by 
  me 
  in 
  1878 
  more 
  fully 
  than 
  they 
  have 
  been 
  hitherto 
  devel- 
  

   oped. 
  

  

  * 
  This 
  Journal, 
  III, 
  vol. 
  xvi, 
  p. 
  175, 
  1878. 
  

   f 
  Report, 
  1879, 
  p. 
  274. 
  

  

  % 
  Sur 
  la 
  theorie 
  de 
  la 
  capture 
  des 
  cometes 
  periodiques, 
  Bull. 
  Astron., 
  Tome 
  vi, 
  

   juin 
  and 
  juillet, 
  1889. 
  

  

  § 
  Notes 
  sur 
  quelques 
  Cometes 
  a 
  courte 
  periode, 
  Astron. 
  Nachrichten, 
  No. 
  2964. 
  

   Am. 
  Jour. 
  Sci. 
  — 
  Third 
  Series, 
  Yol 
  XLII, 
  No. 
  249.— 
  September. 
  1891. 
  

   13 
  

  

  