﻿H, 
  A. 
  Newton 
  — 
  Capture 
  of 
  Comets 
  by 
  Planets. 
  195 
  

  

  23. 
  Isergonal 
  ellipses 
  for 
  to 
  = 
  170°. 
  — 
  In 
  figure 
  3 
  are 
  drawn 
  

   the 
  three 
  ellipses 
  corresponding 
  to 
  the 
  values 
  of 
  @, 
  —5, 
  —20, 
  

   and 
  —50. 
  The 
  ellipses 
  above 
  ae 
  do 
  not 
  appear, 
  inasmuch 
  as 
  

   the 
  smallest 
  possible 
  elliptic 
  orbit 
  has 
  a 
  semi-axis 
  major 
  of 
  

   206-3 
  (Table 
  II), 
  and 
  a 
  period 
  of 
  about 
  3000 
  years. 
  The 
  radi- 
  

   cal 
  axis 
  ae 
  is 
  -08146 
  (or 
  over 
  8 
  divisions) 
  above 
  OE. 
  

  

  24. 
  Figures 
  4 
  and 
  5 
  are 
  like 
  diagrams 
  for 
  co=20 
  o 
  and 
  g>=160°. 
  

   With 
  altered 
  numbers 
  the 
  explanations 
  of 
  arts. 
  22 
  and 
  23 
  apply 
  

   with 
  slight 
  change 
  to 
  these 
  figures. 
  The 
  line 
  ae' 
  in 
  figs. 
  4 
  and 
  

   5 
  is 
  nearer 
  to 
  OE 
  than 
  is 
  the 
  same 
  line 
  in 
  figs. 
  2 
  and 
  3. 
  In 
  

  

  Fig. 
  7; 
  <y=150. 
  

  

  H 
  

  

  

  

  

  

  Fig 
  

  

  •6 
  

  

  : 
  

  

  d 
  — 
  

  

  30 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  S 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  s 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  \, 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  / 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  / 
  

  

  

  

  

  

  

  

  

  

  

  

  

  , 
  

  

  

  

  

  

  n 
  

  

  

  

  

  

  

  

  / 
  

  

  

  

  

  s 
  

  

  

  

  

  

  

  

  / 
  

  

  

  

  

  

  

  

  N 
  

  

  

  / 
  

  

  

  

  

  

  

  

  

  

  / 
  

  

  

  

  

  

  

  

  

  / 
  

  

  

  

  

  

  

  / 
  

  

  

  

  

  s 
  

  

  

  

  

  

  

  / 
  

  

  

  

  r" 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  1 
  

  

  

  

  

  

  

  

  

  

  

  

  

  n\ 
  

  

  

  V 
  

  

  CC; 
  

  

  

  

  ^\ 
  

  

  

  

  

  V\ 
  

  

  \S 
  

  

  H- 
  

  

  fig. 
  4 
  the 
  line 
  for 
  @= 
  —20 
  appears 
  below 
  ae, 
  while 
  above 
  ae 
  

   are 
  the 
  three 
  curves 
  for 
  +5, 
  +20, 
  and 
  +50, 
  respectively. 
  In 
  

   fig. 
  5 
  the 
  ellipse 
  for 
  @=50 
  is 
  wanting 
  since 
  the 
  minimum 
  

   ellipse 
  has 
  a 
  semi- 
  axis 
  major 
  52-36 
  (Table 
  II), 
  while 
  below 
  ae 
  

   the 
  three 
  curves 
  are 
  present. 
  

  

  In 
  figures 
  6 
  and 
  7 
  are 
  contrasted 
  in 
  like 
  manner 
  the 
  isergonal 
  

   curves 
  for 
  the 
  angles 
  a>=30, 
  and 
  &>=the 
  supplement 
  of 
  30°. 
  

   In 
  fig. 
  6 
  the 
  curve 
  @=— 
  5 
  is 
  wanting, 
  and 
  in 
  fig. 
  7 
  the 
  two 
  

   curves 
  @=5, 
  and 
  @=20 
  are 
  both 
  wanting. 
  

  

  In 
  like 
  manner 
  are 
  to 
  be 
  explained 
  the 
  figs. 
  8-18. 
  The 
  

   numbers 
  needed 
  for 
  drawing 
  the 
  figures 
  are 
  furnished 
  by 
  equa- 
  

  

  