﻿522 
  Principle 
  of 
  Relativitjj 
  and 
  Non- 
  Newtonian 
  Mechanics. 
  

  

  which 
  the 
  energy 
  may 
  assume 
  and 
  we 
  are 
  thus 
  forced 
  to 
  the 
  

   important 
  conclusion 
  that 
  iclien 
  a 
  system 
  acquires 
  energy 
  in 
  

   any 
  form 
  it 
  acquires 
  mass 
  in 
  proportion, 
  the 
  ratio 
  of 
  the 
  energy 
  

   to 
  the 
  mass 
  being 
  equal 
  to 
  the 
  square 
  of 
  the 
  velocity 
  of 
  light. 
  

   We 
  might 
  go 
  further 
  and 
  assume 
  that 
  if 
  a 
  system 
  should 
  lose 
  

   all 
  its 
  energy 
  it 
  would 
  lose 
  all 
  its 
  mass. 
  If 
  we 
  admit 
  this 
  

   plausible 
  although 
  unproved 
  assumption, 
  then 
  we 
  may 
  regard 
  

   the 
  mass 
  of 
  every 
  body 
  as 
  a 
  measure 
  of 
  its 
  total 
  energy 
  

   according 
  to 
  the 
  equation, 
  

  

  ^>^ 
  = 
  ^2 
  (^) 
  

  

  For 
  a 
  body 
  at 
  rest 
  

  

  mt 
  

  

  Combining 
  this 
  equation 
  with 
  (3) 
  gives 
  

  

  E 
  _ 
  1 
  

  

  Eo 
  ~ 
  VI 
  -ye^* 
  

  

  We 
  thus 
  see 
  that 
  energy 
  changes 
  with 
  the 
  velocity 
  in 
  the- 
  

   same 
  way 
  that 
  mass 
  does, 
  and 
  that 
  the 
  so-called 
  kinetic 
  energy 
  

   is 
  a 
  " 
  second-order 
  effect 
  ^' 
  of 
  the 
  same 
  character 
  as 
  the 
  change 
  

   of 
  length 
  and 
  the 
  change 
  of 
  mass. 
  The 
  only 
  reason 
  that 
  this 
  

   effect 
  is 
  easily 
  measured, 
  and 
  has 
  become 
  a 
  familiar 
  concep- 
  

   tion 
  in 
  mechanics, 
  while 
  the 
  others 
  are 
  obtainable 
  only 
  by 
  the 
  

   most 
  precise 
  measurements^ 
  is 
  that 
  we 
  are 
  in 
  the 
  habit 
  of 
  

   measuring 
  quantities 
  of 
  energy 
  which 
  are 
  extremely 
  minute 
  

   in 
  comparison 
  with 
  the 
  total 
  energy 
  of 
  the 
  systems- 
  

   investigated. 
  

  

  Conclusion, 
  

  

  We 
  have 
  shown 
  how 
  observers 
  stationed 
  on 
  systems 
  in 
  

   motion 
  relative 
  to 
  one 
  another 
  have 
  been 
  able 
  to 
  preserve 
  

   their 
  fundamental 
  principles 
  of 
  mechanics 
  only 
  by 
  adopting 
  

   certain 
  novel 
  conclusions. 
  These 
  conclusions 
  are 
  self- 
  

   consistent 
  ; 
  in 
  the 
  one 
  case 
  where 
  they 
  have 
  been 
  tested 
  they 
  

   are 
  in 
  accord 
  with 
  experiment 
  ; 
  and 
  they 
  enable 
  us 
  to 
  save 
  

   all 
  the 
  fundamental 
  physical 
  concepts 
  which 
  have 
  been 
  found 
  

   useful 
  in 
  the 
  past. 
  We 
  have, 
  however, 
  considered 
  primarily 
  

   only 
  systems 
  which 
  are 
  initially 
  in 
  uniform 
  relative 
  motion. 
  

   Whether 
  our 
  conclusions 
  can 
  be 
  retained 
  when 
  we 
  consider 
  

   processes 
  in 
  which 
  the 
  relative 
  motion 
  is 
  being 
  established, 
  

   in 
  other 
  words, 
  processes 
  in 
  which 
  acceleration 
  takes 
  place, 
  

   it 
  is 
  not 
  our 
  present 
  purpose 
  to 
  determine. 
  

  

  The 
  ideas 
  here 
  presented 
  appear 
  somewhat 
  artificial 
  in 
  

   character, 
  and 
  we 
  cannot 
  but 
  suspect 
  that 
  this 
  is 
  due 
  to 
  the 
  

  

  