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  Hubert 
  Anson 
  Newton. 
  

  

  In 
  regard 
  to 
  the 
  distribution 
  of 
  the 
  aphelia, 
  he 
  shows 
  that, 
  

   except 
  so 
  far 
  as 
  modified 
  by 
  the 
  perturbations 
  due 
  to 
  the 
  

   planets, 
  the 
  theory 
  of 
  internal 
  origin 
  would 
  require 
  all 
  the 
  

   aphelia 
  to 
  be 
  in 
  the 
  vicinity 
  of 
  the 
  ecliptic, 
  — 
  the 
  theory 
  of 
  exter- 
  

   nal 
  origin 
  would 
  make 
  all 
  directions 
  of 
  the 
  aphelia 
  equally 
  

   probable, 
  i. 
  e., 
  the 
  distribution 
  in 
  latitude 
  of 
  the 
  aphelia 
  should 
  

   be 
  that 
  in 
  which 
  the 
  frequency 
  is 
  as 
  the 
  cosine 
  of 
  the 
  latitude. 
  

   The 
  actual 
  distribution 
  comes 
  very 
  near 
  to 
  this, 
  but 
  as 
  the 
  

   effect 
  of 
  perturbations 
  would 
  tend 
  to 
  equalize 
  the 
  distribution 
  

   of 
  aphelia 
  in 
  all 
  directions, 
  Professor 
  Newton 
  does 
  not 
  regard 
  

   this 
  argument 
  as 
  entirely 
  decisive. 
  He 
  remarks, 
  however, 
  that 
  

   if 
  Kant's 
  hypothesis 
  be 
  true, 
  the 
  comets 
  must 
  have 
  been 
  

   revolving 
  in 
  their 
  orbits 
  a 
  very 
  long 
  time, 
  and 
  the 
  process 
  of 
  

   the 
  disintegration 
  of 
  comets 
  must 
  be 
  very 
  slow. 
  

  

  In 
  regard 
  to 
  the 
  distribution 
  of 
  the 
  orbits 
  in 
  inclination, 
  

   the 
  author 
  shows 
  that 
  the 
  theory 
  of 
  internal 
  origin 
  would 
  

   make 
  all 
  inclinations 
  equally 
  probable, 
  — 
  the 
  theory 
  of 
  external 
  

   origin 
  would 
  make 
  all 
  directions 
  of 
  the 
  normal 
  to 
  the 
  plane 
  of 
  

   the 
  orbit 
  equally 
  probable. 
  On 
  the 
  first 
  hypothesis, 
  therefore, 
  

   we 
  should 
  expect 
  a 
  uniform 
  distribution 
  in 
  inclination 
  ; 
  on 
  the 
  

   second, 
  a 
  frequency 
  proportioned 
  to 
  the 
  sine 
  of 
  the 
  inclination. 
  

   It 
  was 
  shown 
  by 
  a 
  diagram 
  in 
  which 
  the 
  actual 
  and 
  the 
  two 
  

   theoretical 
  distributions 
  are 
  represented 
  graphically, 
  that 
  the 
  

   actual 
  distribution 
  agrees 
  pretty 
  well 
  with 
  the 
  theory 
  of 
  exter- 
  

   nal 
  origin 
  and 
  not 
  at 
  all 
  with 
  that 
  of 
  internal 
  origin. 
  It 
  was 
  

   also 
  shown 
  that 
  the 
  curve 
  of 
  actual 
  distribution 
  cannot 
  be 
  made 
  

   to 
  agree 
  with 
  Kant's 
  hypothesis 
  by 
  any 
  simple 
  and 
  reasonable 
  

   allowances 
  for 
  perturbations. 
  On 
  the 
  other 
  hand, 
  if 
  we 
  assume 
  

   the 
  external 
  origin 
  of 
  comets, 
  and 
  ask 
  how 
  the 
  curve 
  of 
  sines 
  

   must 
  be 
  modified 
  in 
  order 
  to 
  take 
  account 
  of 
  perturbations, 
  it 
  

   is 
  shown 
  that 
  the 
  principal 
  effect 
  will 
  be 
  to 
  increase 
  somewhat 
  

   the 
  number 
  of 
  inclinations 
  between 
  90° 
  and 
  135° 
  at 
  the 
  

   expense 
  of 
  those 
  between 
  45° 
  and 
  90°. 
  It 
  is 
  apparent 
  

   at 
  once 
  from 
  the 
  diagram 
  that 
  such 
  a 
  change 
  would 
  make 
  a 
  

   very 
  good 
  agreement 
  between 
  the 
  actual 
  and 
  theoretical 
  curves, 
  

   the 
  only 
  important 
  difference 
  remaining 
  being 
  due 
  to 
  comets 
  

   of 
  short 
  periods, 
  which 
  mostly 
  have 
  small 
  inclinations 
  with 
  

   direct 
  motion. 
  These 
  should 
  not 
  weigh 
  very 
  much, 
  the 
  

   author 
  observes, 
  in 
  the 
  general 
  question 
  of 
  the 
  distribution 
  of 
  

   inclinations, 
  because 
  they 
  return 
  so 
  frequently 
  and 
  are 
  so 
  easily 
  

   detected 
  that 
  their 
  number 
  in 
  a 
  list 
  of 
  observed 
  comets 
  is 
  out 
  

   of 
  all 
  proportion 
  to 
  their 
  number 
  among 
  existing 
  comets. 
  But 
  

   this 
  grDup 
  of 
  comets 
  of 
  short 
  periods 
  can 
  easily 
  be 
  explained 
  

   on 
  the 
  theory 
  of 
  an 
  external 
  origin. 
  For 
  such 
  comets 
  must 
  

   have 
  lost 
  a 
  large 
  part 
  of 
  their 
  velocity 
  by 
  the 
  influence 
  of 
  a 
  

   planet. 
  This 
  is 
  only 
  likely 
  to 
  happen 
  when 
  a 
  comet 
  overtakes 
  

   the 
  planet 
  and 
  passes 
  in 
  front 
  of 
  it. 
  This 
  implies 
  that 
  its 
  orig- 
  

  

  