﻿Hubert 
  Anson 
  Newton. 
  363 
  

  

  showers 
  of 
  902 
  and 
  1833 
  by 
  28, 
  the 
  number 
  of 
  cycles 
  between 
  

   these 
  dates, 
  and 
  must 
  therefore 
  be 
  a 
  very 
  close 
  approximation. 
  

   For 
  if 
  these 
  showers 
  did 
  not 
  mark 
  the 
  precise 
  end 
  of 
  cycles, 
  

   the 
  resultant 
  error 
  would 
  be 
  divided 
  by 
  28. 
  Professor 
  Newton 
  

   showed 
  that 
  this 
  value 
  of 
  the 
  cycle 
  requires 
  that 
  the 
  number 
  of 
  

   revolutions 
  performed 
  by 
  the 
  meteoroids 
  in 
  one 
  year 
  should 
  be 
  

   either 
  2±g-^ 
  F 
  or 
  li-^g-g- 
  or 
  gg-Vo- 
  ^ 
  D 
  other 
  words, 
  the 
  

   periodic 
  time 
  of 
  the 
  meteoroids 
  must 
  be 
  either 
  180.0 
  or 
  185.4 
  

   or 
  354.6 
  or 
  376.6 
  days, 
  or 
  33.25 
  years. 
  Now 
  the 
  velocity 
  of 
  

   any 
  body 
  in 
  the 
  solar 
  system 
  has 
  a 
  simple 
  relation 
  to 
  its 
  peri- 
  

   odic 
  time 
  and 
  its 
  distance 
  from 
  the 
  sun. 
  Assuming, 
  therefore, 
  

   any 
  one 
  of 
  these 
  five 
  values 
  of 
  the 
  periodic 
  time, 
  we 
  have 
  the 
  

   velocities 
  of 
  the 
  Leonids 
  at 
  the 
  node 
  very 
  sharply 
  determined. 
  

   From 
  this 
  velocity, 
  with 
  the 
  position 
  of 
  the 
  apparent 
  radiant, 
  

   which 
  gives 
  the 
  direction 
  of 
  the 
  relative 
  motion, 
  and 
  with 
  the 
  

   knowledge 
  that 
  the 
  heliocentric 
  motion 
  is 
  retrograde, 
  we 
  may 
  

   easily 
  determine 
  the 
  orbit. 
  

  

  We 
  have, 
  therefore, 
  five 
  orbits 
  from 
  which 
  to 
  choose. 
  The 
  

   calculation 
  of 
  the 
  secular 
  motion 
  of 
  the 
  node 
  due 
  to 
  the 
  dis- 
  

   turbing 
  action 
  of 
  the 
  planets, 
  would 
  enable 
  us 
  to 
  decide 
  

   between 
  these 
  orbits. 
  

  

  Such 
  are 
  the 
  most 
  important 
  conclusions 
  which 
  Professor 
  

   Newton 
  derived 
  from 
  the 
  study 
  of 
  these 
  remarkable 
  showers, 
  

   interesting 
  not 
  only 
  from 
  the 
  magnificence 
  of 
  the 
  spectacle 
  

   occasionally 
  exhibited, 
  but 
  in 
  a 
  much 
  higher 
  degree 
  from 
  the 
  

   peculiarity 
  in 
  the 
  periodic 
  character 
  of 
  their 
  occurrence, 
  which 
  

   affords 
  the 
  means 
  of 
  the 
  determination 
  of 
  the 
  orbit 
  of 
  the 
  

   meteoroids 
  with 
  a 
  precision 
  which 
  would 
  at 
  first 
  sight 
  appear 
  

   impossible. 
  

  

  Professor 
  Newton 
  anticipated 
  a 
  notable 
  return 
  of 
  the 
  shower 
  

   in 
  1866, 
  with 
  some 
  precursors 
  in 
  the 
  years 
  immediately 
  preceding, 
  

   a 
  prediction 
  which 
  was 
  amply 
  verified. 
  In 
  the 
  mean 
  time 
  he 
  

   turned 
  his 
  attention 
  to 
  the 
  properties 
  which 
  belong 
  to 
  shooting 
  

   stars 
  in 
  general, 
  and 
  especially 
  to 
  those 
  average 
  values 
  which 
  

   relate 
  to 
  large 
  numbers 
  of 
  these 
  bodies 
  not 
  belonging 
  to 
  any 
  

   particular 
  swarm. 
  

  

  This 
  kind 
  of 
  investigation 
  Maxwell 
  has 
  called 
  statistical, 
  and 
  

   has 
  in 
  more 
  than 
  one 
  passage 
  signalized 
  its 
  difficulties. 
  The 
  

   writer 
  recollects 
  a 
  passage 
  of 
  Maxwell 
  which 
  was 
  pointed 
  out 
  to 
  

   him 
  by 
  Professor 
  Newton, 
  in 
  which 
  the 
  author 
  says 
  that 
  serious 
  

   errors 
  have 
  been 
  made 
  in 
  such 
  inquiries 
  by 
  men 
  whose 
  compe- 
  

   tency 
  in 
  other 
  branches 
  of 
  mathematics 
  was 
  unquestioned. 
  

   Doubtless 
  Professor 
  Newton 
  was 
  very 
  conscious 
  of 
  the 
  necessity 
  

   of 
  caution 
  in 
  these 
  inquiries, 
  as 
  is 
  indeed 
  abundantly 
  evident 
  from 
  

   the 
  manner 
  in 
  which 
  he 
  expressed 
  his 
  conclusions; 
  but 
  the 
  

   writer 
  is 
  not 
  aware 
  of 
  any 
  passage 
  in 
  which 
  he 
  has 
  afforded 
  an 
  

   illustration 
  of 
  Maxwell's 
  remark. 
  

  

  