﻿526 
  Dr. 
  H. 
  Wilde 
  on 
  the 
  Moving 
  Force 
  of 
  Terrestrial 
  and 
  

  

  , 
  . 
  ^, 
  , 
  24900 
  miles 
  5044« 
  .107-. 
  1 
  .• 
  

   ie) 
  inat 
  -tttoT. 
  — 
  m^ 
  = 
  —ttt-- 
  =bi*0 
  7 
  minutes 
  = 
  the 
  time 
  

   4-936 
  miles 
  60^ 
  

  

  o£ 
  revolution 
  o£ 
  a 
  body 
  round 
  the 
  earth 
  with 
  an 
  

  

  angular 
  velocity 
  of 
  2^fi&2 
  feet 
  per 
  second 
  (d). 
  

  

  7. 
  The 
  mean 
  distance 
  of 
  the 
  moon 
  according 
  to 
  modern 
  

   astronomy, 
  is 
  60' 
  28 
  semi-diameters 
  o£ 
  the 
  earth, 
  and 
  the 
  

   time 
  of 
  its 
  revolution 
  in 
  respect 
  to 
  the 
  fixed 
  stars, 
  27 
  days, 
  

   7 
  hours, 
  43 
  minutes 
  = 
  39343 
  minutes. 
  Now 
  as 
  the 
  times 
  

   and 
  velocities 
  of 
  rotation 
  are 
  reciprocally 
  equivalents 
  of 
  each 
  

  

  39343m 
  

   other, 
  we 
  have 
  !. 
  = 
  468 
  as 
  the 
  ratio 
  of 
  the 
  orbital 
  

  

  times 
  or 
  velocities 
  of 
  a 
  body 
  revolving 
  round 
  the 
  circum- 
  

   ference 
  of 
  the 
  earth 
  and 
  the 
  moon''s 
  orbit 
  respectively. 
  

   Therefore 
  468 
  x 
  84-07 
  = 
  39344°^ 
  = 
  27 
  days, 
  7 
  hours, 
  44 
  

   minutes, 
  for 
  the 
  time 
  of 
  the 
  moon's 
  orbital 
  revolution. 
  

  

  8. 
  Again, 
  from 
  the 
  square 
  of 
  468, 
  as 
  a 
  velocity, 
  divided 
  by 
  

   the 
  moon's 
  distance 
  in 
  semi-diameters 
  of 
  the 
  earth 
  we 
  have 
  

  

  A 
  IX 
  G2 
  1 
  

  

  ■— 
  — 
  — 
  = 
  3634. 
  or 
  reciprocally 
  777^77 
  the 
  total 
  movincr 
  force 
  of 
  

   b0*28 
  ' 
  ^ 
  -^ 
  3634 
  ® 
  

  

  a 
  body 
  revolving 
  round 
  the 
  earth's 
  circumference 
  and 
  the 
  

  

  moon's 
  orbit 
  respectively, 
  the 
  numbers 
  being 
  the 
  same 
  as 
  

  

  those 
  deduced 
  from 
  the 
  law 
  of 
  attraction 
  of 
  gravitation 
  for 
  

  

  the 
  same 
  distance. 
  

  

  9. 
  As 
  the 
  radius 
  of 
  the 
  moon's 
  orbit 
  is 
  60*28 
  semi- 
  dia- 
  

   meters 
  of 
  the 
  earth, 
  we 
  have 
  with 
  the 
  earth's 
  radius 
  in 
  miles, 
  

   3964x2 
  x60-28x 
  3-1416 
  = 
  1501370 
  miles 
  for 
  the 
  circum- 
  

   ference 
  of 
  the 
  moon's 
  orbit. 
  Dividing 
  this 
  by 
  the 
  time 
  of 
  

  

  T 
  ,. 
  . 
  . 
  , 
  1 
  1501370 
  miles 
  00.1 
  /^a 
  

  

  revolution 
  m 
  minutes 
  we 
  nave 
  .^,^., 
  , 
  . 
  -^ 
  = 
  00 
  IbU 
  

  

  39o44 
  miles 
  

  

  miles 
  per 
  minute 
  =3358 
  feet 
  per 
  second 
  for 
  the 
  moon's 
  

  

  orbital 
  velocity. 
  

  

  10. 
  That 
  forces 
  of 
  any 
  kind 
  radiating 
  from 
  every 
  point 
  of 
  

   a 
  body 
  in 
  free 
  space 
  are 
  inversely 
  proportional 
  to 
  the 
  square 
  

   of 
  the 
  distance 
  is 
  a 
  proposition 
  requiring 
  but 
  little 
  demonstra- 
  

   tion 
  seeing 
  that 
  it 
  flows 
  directly 
  from 
  the 
  geometry 
  of 
  space. 
  

   It 
  will 
  be 
  sufficient 
  if 
  I 
  mention 
  in 
  this 
  connexion 
  the 
  intensity 
  

   of 
  light 
  which 
  increases 
  and 
  diminishes 
  in 
  this 
  same 
  ratio, 
  as 
  

   is 
  commonly 
  demonstrated 
  by 
  photometers. 
  Experimental 
  

   mechanics 
  were 
  not 
  sufficiently 
  advanced 
  in 
  Newton's 
  time 
  

   to 
  enable 
  him 
  to 
  determine 
  the 
  ratios 
  of 
  the 
  attractive 
  and 
  

   moving 
  forces 
  of 
  celestial 
  bodies, 
  as 
  there 
  was 
  apparently 
  no 
  

   physical 
  connexion 
  between 
  such 
  bodies, 
  and 
  it 
  was 
  chiefly 
  

   from 
  observation 
  and 
  his 
  geometry 
  that 
  the 
  law 
  of 
  attraction 
  

   of 
  gravitation 
  as 
  the 
  inverse 
  square 
  of 
  the 
  distance 
  was 
  

   established. 
  

  

  