﻿Celestial 
  Bodies 
  in 
  relation 
  to 
  Attraction 
  of 
  Gravitation, 
  525 
  

  

  velocity 
  *. 
  Nevertheless, 
  modern 
  scholasticism 
  has 
  not 
  yet 
  

   pronounced 
  decidedly 
  in 
  favour 
  of 
  the 
  law, 
  and 
  the 
  

   traditional 
  error 
  of 
  Descartes 
  and 
  Newton 
  still 
  survives 
  in 
  

   manuals 
  of 
  elementary 
  and 
  advanced 
  science, 
  under 
  the 
  

   name 
  of 
  momentum, 
  in 
  contradiction 
  of 
  Newton's 
  second 
  

   law 
  which 
  expressly 
  excludes 
  the 
  element 
  of 
  time 
  in 
  the 
  

   measure 
  of 
  the 
  quantity 
  of 
  motion 
  in 
  a 
  body. 
  

  

  5. 
  In 
  the 
  preface 
  to 
  his 
  ' 
  Principia 
  ' 
  Newton 
  set 
  forth 
  with 
  

   singular 
  lucidity 
  and 
  ingenuousness, 
  the 
  dependence 
  of 
  the 
  

   mathematical 
  principles 
  of 
  natural 
  philosophy 
  upon 
  experi- 
  

   mental 
  mechanics 
  in 
  their 
  application 
  to 
  the 
  motions 
  of 
  

   celestial 
  bodies. 
  It 
  will 
  therefore 
  be 
  obvious 
  that 
  the 
  

   question, 
  whether 
  the 
  quantity 
  of 
  motion 
  in 
  a 
  planetary 
  

   system 
  is 
  simply 
  as 
  the 
  velocity, 
  or 
  -as 
  the 
  square 
  of 
  the 
  

   velocity, 
  is 
  one 
  of 
  fundamental 
  importance. 
  So 
  far 
  as 
  I 
  

   know, 
  no 
  attempt 
  has 
  yet 
  been 
  made 
  to 
  deal 
  with 
  this 
  

   problem, 
  and 
  no 
  explication 
  of 
  astronomical 
  science 
  can 
  be 
  

   considered 
  complete 
  so 
  long 
  as 
  it 
  remains 
  unsolved. 
  

  

  6. 
  In 
  order 
  to 
  demonstrate 
  that 
  the 
  moving 
  force 
  by 
  which 
  

   the 
  moon 
  and 
  other 
  celestial 
  bodies 
  are 
  maintained 
  in 
  their 
  

   orbits 
  is 
  as 
  the 
  square 
  of 
  the 
  velocity, 
  it 
  is 
  postulated 
  as 
  

   general 
  knowledge 
  in 
  physical 
  astronomy 
  : 
  — 
  

  

  (a) 
  That 
  the 
  equatorial 
  circumference 
  of 
  the 
  earth 
  is 
  

   24,900 
  miles. 
  

  

  {U) 
  That 
  the 
  versed 
  sine 
  of 
  five 
  miles 
  (or 
  more 
  exactly, 
  

   I'936 
  miles) 
  of 
  the 
  earth's 
  circumference, 
  is 
  193 
  

   inches 
  = 
  16 
  feet 
  1 
  inch. 
  

  

  (c) 
  That 
  a 
  body 
  at 
  rest 
  near 
  the 
  earth's 
  surface 
  falls 
  

   perpendicularly 
  through 
  the 
  versed 
  sine 
  of 
  4*936 
  

   miles 
  of 
  arc 
  of 
  the 
  earth's 
  circumference 
  = 
  16 
  feet 
  

   1 
  inch 
  during 
  one 
  second 
  of 
  time. 
  

  

  {d) 
  That 
  as 
  versed 
  sines 
  are 
  as 
  the 
  squares 
  of 
  their 
  arcs, 
  

   and 
  the 
  accelerative 
  force 
  of 
  gravity 
  increases 
  in 
  the 
  

   same 
  proportion, 
  a 
  body 
  projected 
  horizontally 
  near 
  

   the 
  earth's 
  surface 
  with 
  a 
  velocity 
  4'936 
  miles 
  

   [2iJM2 
  feet) 
  per 
  second, 
  would 
  revolve 
  round 
  the 
  

   earth 
  continually 
  without 
  touching 
  it. 
  

  

  * 
  These 
  results 
  have 
  been 
  abundantly 
  confirmed 
  by 
  my 
  experiments 
  

   with 
  the 
  g}-roscope 
  described 
  in 
  the 
  lecture 
  referred 
  to, 
  wherein 
  it 
  was 
  

   shown 
  (1) 
  that 
  four 
  times 
  the 
  weight 
  falling 
  from 
  the 
  same 
  height 
  were 
  

   required 
  to 
  generate 
  a 
  double 
  velocity 
  of 
  the 
  revolving 
  disk 
  ; 
  (2) 
  that 
  one 
  

   unit 
  cf 
  weight 
  falling 
  throujrh 
  four 
  times 
  the 
  height 
  also 
  generates 
  a 
  

   double 
  velocity 
  of 
  the 
  disk 
  ; 
  (3) 
  that 
  the 
  moving 
  force 
  required 
  to 
  generate 
  

   a 
  double 
  velocity 
  of 
  the 
  disk 
  is 
  independent 
  of 
  the 
  time 
  of 
  its 
  application 
  

   and 
  is 
  as 
  the 
  square 
  of 
  the 
  velocity, 
  — 
  Manchester 
  Memoirs, 
  vol. 
  46, 
  1902. 
  

  

  