﻿196 
  II. 
  A. 
  Newton 
  — 
  Capture 
  of 
  Comets 
  by 
  Planets. 
  

  

  tion 
  (13). 
  The 
  curves 
  that 
  in 
  each 
  figure 
  separate 
  the 
  shaded 
  

   area 
  from 
  the 
  non-shaded 
  area 
  are 
  the 
  ellipses 
  for 
  @=20, 
  and 
  

   @= 
  — 
  20 
  The 
  shading 
  is 
  introduced 
  in 
  order 
  to 
  compare 
  more 
  

   readily 
  the 
  corresponding 
  curves 
  in 
  the 
  figures. 
  

  

  25. 
  The 
  dotted 
  curve 
  in 
  the 
  several 
  figures 
  represents 
  those 
  

   values 
  of 
  d 
  and 
  h 
  for 
  which 
  the 
  total 
  change 
  of 
  direction 
  in 
  

   the 
  relative 
  orbit 
  is 
  10° 
  ; 
  that 
  is, 
  a=85°. 
  It 
  is 
  that 
  curve 
  

   whose 
  equation 
  is 
  A 
  tan 
  85° 
  = 
  B, 
  or 
  d 
  2 
  -\-h* 
  sin 
  2 
  6= 
  A 
  2 
  tan 
  2 
  85°. 
  

   It 
  is 
  therefore 
  an 
  ellipse 
  whose 
  center 
  is 
  the 
  origin 
  of 
  coordi- 
  

   nates, 
  and 
  it 
  is 
  similar 
  in 
  each 
  figure 
  to 
  the 
  isergonal 
  ellipses. 
  

  

  

  

  Fig 
  

  

  8 
  

  

  ; 
  a 
  

  

  = 
  

  

  40 
  c 
  

  

  

  

  

  

  H 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  V 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  S 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  N 
  

  

  

  

  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  J 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  - 
  - 
  - 
  _ 
  

  

  

  

  

  

  

  

  / 
  

  

  

  

  

  \ 
  

  

  

  

  

  A 
  

  

  

  

  

  h 
  

  

  

  

  

  / 
  

  

  

  

  

  / 
  

  

  

  

  y 
  

  

  

  

  

  

  

  

  

  

  yS 
  

  

  

  

  

  

  

  

  

  

  

  

  > 
  

  

  

  

  

  

  

  

  

  

  

  I 
  

  

  

  

  

  1 
  

  

  a 
  

  

  ^ 
  

  

  

  -- 
  

  

  \\ 
  

  

  .o 
  

  

  \ 
  

  

  

  

  \ 
  

  

  

  \ 
  

  

  N 
  

  

  Fig. 
  9; 
  w= 
  140. 
  

  

  ?0 
  

  

  26. 
  Hypotheses 
  about 
  the 
  parabolic 
  cometary 
  orbits. 
  — 
  It 
  will 
  

   be 
  convenient 
  to 
  make 
  two 
  assumptions 
  about 
  the 
  distribution 
  

   of 
  the 
  parabolic 
  comets, 
  and 
  the 
  distribution 
  of 
  the 
  goals 
  of 
  

   their 
  motions. 
  There 
  seems 
  to 
  be 
  no 
  very 
  well 
  marked 
  rela- 
  

   tion 
  between 
  the 
  ecliptic, 
  or 
  to 
  speak 
  more 
  strictly 
  the 
  invari- 
  

   able 
  plane 
  of 
  the 
  solar 
  system, 
  and 
  the 
  known 
  parabolic 
  comet- 
  

   ary 
  orbits. 
  The 
  following 
  two 
  assumptions 
  do 
  not 
  seem 
  likely 
  

   therefore 
  to 
  introduce 
  any 
  very 
  serious 
  error 
  into 
  our 
  reason- 
  

   ings. 
  

  

  