﻿22 
  Prof. 
  L. 
  T. 
  More 
  on 
  Theories 
  

  

  which 
  in 
  (14) 
  refers 
  to 
  the 
  body, 
  and 
  in 
  the 
  following 
  

   equation 
  to 
  a 
  beam 
  of 
  radiation. 
  It 
  is 
  also 
  perplexing 
  to 
  

   understand 
  what 
  (7) 
  has 
  to 
  do 
  with 
  this 
  problem. 
  In 
  a 
  

   simple 
  discussion 
  of 
  the 
  momentum 
  of 
  a 
  moving 
  body 
  such 
  

   an 
  attribute 
  as 
  light 
  or 
  radiation 
  is 
  not 
  necessarily 
  involved, 
  

   nor 
  even 
  the 
  existence 
  of 
  an 
  absorbing 
  medium. 
  

  

  Granting 
  this 
  objection 
  is 
  not 
  valid, 
  we 
  arrive 
  by 
  simple 
  

   transformations 
  to 
  the 
  following 
  equation 
  

  

  where 
  Wq 
  is 
  the 
  mass 
  of 
  the 
  body 
  at 
  rest^ 
  m 
  its 
  mass 
  when 
  in 
  

   motion, 
  and 
  /3 
  the 
  ratio 
  v/V. 
  

  

  We 
  may 
  further 
  obtain 
  the 
  expression 
  for 
  the 
  kinetic 
  

   energy 
  acquired 
  by 
  a 
  moving 
  body 
  in 
  the 
  forms 
  

  

  E' 
  = 
  mV^{l-(l-^^)*}, 
  . 
  . 
  

  

  ■ 
  ■ 
  (16) 
  

  

  or 
  

  

  Il' 
  = 
  mY'{W 
  + 
  i^^+ 
  ... 
  }. 
  . 
  

  

  • 
  • 
  (17) 
  

  

  For 
  small 
  values 
  of 
  v 
  

  

  

  and 
  when 
  v 
  = 
  Y 
  

  

  

  E' 
  = 
  

  

  7nv* 
  

  

  The 
  writer 
  states 
  that 
  this 
  difference 
  for 
  the 
  energy 
  

   "instead 
  of 
  demolishing 
  our 
  theory 
  actually 
  furnishes 
  a 
  

   remarkably 
  satisfactory 
  argument 
  in 
  its 
  favour." 
  It 
  really 
  

   does 
  neither,, 
  for 
  the 
  ordinary 
  hydrodynamic 
  equation 
  for 
  

   energy, 
  given 
  later, 
  expresses 
  precisely 
  the 
  same 
  results 
  

   without 
  a 
  need 
  for 
  the 
  assumption 
  that 
  mass 
  varies 
  v\ith 
  

   velocity. 
  

  

  If 
  we 
  strip 
  the 
  problem 
  of 
  perplexing 
  details 
  and 
  then 
  

   compare 
  it 
  with 
  analogous 
  examples 
  taken 
  from 
  other 
  branches 
  

   of 
  physics, 
  the 
  earlier 
  ideas 
  of 
  inertia 
  should 
  be 
  easier 
  to 
  

   compare 
  with 
  those 
  of 
  the 
  present 
  time. 
  The 
  problem 
  may 
  

   be 
  put 
  in 
  the 
  following 
  form 
  : 
  — 
  in 
  all 
  cases 
  where 
  a 
  body 
  is 
  

   giving 
  or 
  receiving 
  energy 
  its 
  mass 
  is 
  a 
  variable. 
  This 
  inter- 
  

   change 
  of 
  energy 
  may 
  trike 
  place 
  between 
  two 
  bodies 
  or 
  

   between 
  a 
  body 
  and 
  a 
  fluid 
  in 
  which 
  it 
  is 
  immersed. 
  For 
  

   the 
  latter 
  the 
  fluid 
  must 
  be 
  of 
  such 
  a 
  nature 
  as 
  to 
  be 
  able 
  to 
  

   absorb 
  and 
  emit 
  energy, 
  and 
  so 
  be 
  endowed 
  with 
  what 
  

   Newton 
  called 
  ineriia. 
  It 
  is 
  evident 
  that 
  if 
  the 
  fluid 
  cannot 
  

   absorb 
  energy 
  there 
  can 
  be 
  no 
  loss 
  or 
  gain 
  of 
  energy 
  to 
  the 
  

   body, 
  and 
  consequently 
  no 
  cliange 
  in 
  its 
  mass. 
  

  

  Does 
  this 
  interchange 
  of 
  energy 
  require 
  a 
  real 
  change 
  in 
  

   the 
  mass 
  of 
  a 
  body, 
  or 
  does 
  it 
  produce 
  a 
  variation 
  in 
  other 
  

  

  