﻿672 
  Prof. 
  S. 
  B. 
  McLaren 
  on 
  a 
  

  

  time 
  of 
  vibration 
  of 
  the 
  pendulum 
  is 
  increased 
  directly 
  as 
  p 
  a 
  . 
  

   Measured 
  by 
  the 
  number 
  of 
  vibrations 
  light 
  has 
  the 
  same 
  

   velocity 
  as 
  before. 
  

  

  § 
  10. 
  The 
  Limits 
  of 
  Mechanical 
  Theory. 
  

  

  The 
  quantity 
  p 
  a 
  of 
  last 
  section 
  is 
  assumed 
  to 
  be 
  real. 
  

   By 
  (86) 
  

  

  v-m-™- 
  

  

  Hence 
  J 
  is 
  not 
  precisely 
  the 
  Newtonian 
  potential, 
  or 
  near 
  

   attracting 
  matter 
  p 
  a 
  would 
  be 
  imaginary. 
  In 
  fact, 
  J 
  is 
  by 
  

   (40) 
  the 
  velocity-potential. 
  Suppose 
  the 
  aether 
  at 
  infinity 
  

   to 
  be 
  at 
  rest 
  and 
  of 
  density 
  p 
  . 
  Write 
  

  

  J=J 
  Q 
  -p 
  cH 
  (92) 
  

  

  — 
  ^-as 
  well 
  as 
  VJo 
  vanish 
  at 
  infinity, 
  and 
  the 
  equation 
  

  

  ( 
  v2 
  -^^+w 
  = 
  o 
  

  

  now 
  shows 
  that 
  J 
  is 
  the 
  Newtonian 
  potential. 
  

  

  Turn 
  to 
  (69), 
  the 
  only 
  other 
  result 
  in 
  which 
  J 
  is 
  involved. 
  

   It 
  is 
  

  

  ±(E*-W)-mJ 
  + 
  m 
  PQ 
  pt 
  + 
  V 
  m 
  - 
  V 
  a 
  = 
  0. 
  

  

  Now 
  suppose 
  

  

  V 
  m 
  =a— 
  mp 
  c 
  2 
  t, 
  (93) 
  

  

  and 
  then 
  

  

  i(B»-H»)+fiiJi=«-Fi 
  .... 
  (94) 
  

  

  (93) 
  implies 
  that 
  a 
  constant 
  force 
  along 
  the 
  time-axis 
  

   is" 
  applied 
  to 
  each 
  element 
  of 
  matter. 
  This 
  is 
  evidently 
  an 
  

   essential 
  feature 
  of 
  our 
  theory, 
  and 
  not 
  an 
  afterthought. 
  

   For 
  matter 
  was 
  to 
  form 
  a 
  constant 
  configuration 
  standing 
  

   against 
  the 
  stream 
  of 
  aether. 
  That 
  is 
  the 
  meaning 
  of 
  the 
  

   transformation 
  (B) 
  of 
  § 
  4. 
  Whether, 
  therefore, 
  matter 
  is 
  a 
  

   region 
  of 
  growth 
  or 
  decay, 
  a 
  constant 
  force 
  must 
  be 
  applied 
  

   so 
  that 
  it 
  may 
  not 
  be 
  carried 
  bodily 
  down 
  the 
  stream. 
  

  

  It 
  may 
  be 
  objected 
  that 
  if 
  the 
  aether 
  at 
  a 
  distance 
  is 
  at 
  

   rest 
  relative 
  to 
  one 
  three-dimensional 
  system, 
  it 
  is 
  in 
  motion 
  

   relative 
  to 
  any 
  other. 
  But 
  this 
  is 
  quite 
  harmless. 
  The 
  

   condition 
  (94) 
  is 
  invariant 
  according 
  to 
  the 
  principle 
  of 
  

  

  