﻿H. 
  A. 
  Newton 
  — 
  Capture 
  of 
  Comets 
  hy 
  Planets. 
  199 
  

  

  normal 
  between 
  ty 
  and 
  ty 
  + 
  dty, 
  have 
  perihelion 
  distances 
  

   between 
  q 
  arid 
  q+dq. 
  Hence 
  ]ST 
  may 
  also 
  represent 
  the 
  num- 
  

   ber 
  of 
  comets 
  that 
  in 
  the 
  given 
  period 
  of 
  time 
  pass 
  their 
  perihe- 
  

   lia, 
  and 
  whose 
  perihelion 
  distances 
  are 
  less 
  than 
  q. 
  Therefore 
  

  

  dJST 
  

  

  — 
  is 
  a 
  constant, 
  and 
  we 
  conclude 
  that 
  if 
  comets 
  be 
  grouped 
  

  

  according 
  to 
  their 
  perihelion 
  distances 
  the 
  number 
  of 
  comets 
  

   whose 
  perihelion 
  distances 
  are 
  less 
  than 
  ^is 
  proportional 
  to 
  q. 
  

  

  Fig. 
  16; 
  w=80°. 
  

  

  Fig. 
  17; 
  o>=90°, 
  

  

  Fig. 
  18; 
  <j=100. 
  

  

  r^ 
  

  

  

  

  

  

  s 
  

  

  \ 
  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  . 
  

  

  

  

  / 
  

  

  

  

  

  ) 
  

  

  / 
  

  

  

  

  

  

  

  -. 
  e 
  

  

  

  

  

  v\\ 
  

  

  

  29. 
  It 
  follows 
  as 
  a 
  corollary 
  to 
  art. 
  28 
  that 
  if 
  the 
  two 
  

   assumptions 
  of 
  art. 
  26 
  be 
  made 
  for. 
  the 
  spherical 
  surface 
  

   £j, 
  the 
  like 
  distributions 
  are 
  true 
  for 
  every 
  smaller 
  concentric 
  

   spherical 
  surface. 
  It 
  would 
  be 
  but 
  a 
  reasonable 
  extension 
  of 
  

   the 
  assumptions 
  to 
  make 
  them 
  apply 
  to 
  larger 
  spheres, 
  if 
  finite. 
  

  

  [To 
  be 
  continued.] 
  

  

  Am. 
  Jour. 
  Sol— 
  Third 
  Series, 
  Vol. 
  XLII, 
  No. 
  249. 
  — 
  September, 
  1891. 
  

   14 
  

  

  