﻿Fundamental 
  Laws 
  of 
  Matter 
  and 
  Energy. 
  707 
  

  

  To 
  anyone 
  unfamiliar 
  with 
  the 
  prevailing 
  theories 
  of 
  light, 
  

   knowing 
  only 
  that 
  light 
  moves 
  with 
  a 
  certain 
  velocity 
  and 
  

   that 
  in 
  a 
  beam 
  of 
  light 
  momentum 
  and 
  energy 
  are 
  being- 
  

   carried 
  with 
  this 
  same 
  velocity, 
  the 
  natural 
  assumption 
  would 
  

   be 
  that 
  in 
  such 
  a 
  beam 
  something 
  jiossessing 
  mass 
  moves 
  with 
  

   the 
  velocity 
  of 
  light 
  and 
  therefore 
  has 
  momentum 
  and 
  energy. 
  

   Notwithstanding 
  its 
  apparent 
  divergence 
  from 
  the 
  commonly 
  

   accepted 
  light 
  theories, 
  I 
  propose 
  to 
  adopt 
  this 
  view 
  and 
  see 
  

   whither 
  it 
  leads. 
  

  

  Postulating 
  the 
  validity 
  of 
  the 
  fundamental 
  conservation 
  

   laws 
  mentioned 
  above, 
  we 
  shall 
  need 
  in 
  the 
  following 
  develop- 
  

   ment 
  only 
  this 
  one 
  cardinal 
  assumption, 
  that 
  a 
  beam 
  of 
  

   radiation 
  possesses 
  not 
  only 
  momentum 
  and 
  energy, 
  but 
  also 
  

   mass, 
  travelling 
  with 
  the 
  velocity 
  of 
  light, 
  and 
  that 
  a 
  body 
  

   absorbing 
  radiation 
  is 
  acquiring 
  this 
  mass 
  as 
  it 
  also 
  acquires 
  

   the 
  momentum 
  and 
  the 
  energy 
  of 
  the 
  radiation. 
  Therefore 
  a 
  

   body 
  which 
  absorbs 
  radiant 
  energy 
  increases 
  in 
  mass. 
  

  

  The 
  amount 
  of 
  this 
  increase 
  is 
  readily 
  found. 
  If 
  in 
  general 
  

   we 
  write 
  momentum 
  as 
  the 
  product 
  of 
  mass 
  and 
  velocity, 
  then 
  

   the 
  momentum 
  of 
  any 
  part 
  of 
  a 
  beam 
  of 
  radiation 
  having 
  the 
  

   mass 
  m 
  will 
  be 
  given 
  by 
  the 
  equation 
  : 
  

  

  M 
  = 
  mV 
  (5) 
  

  

  The 
  increase 
  dM. 
  in 
  the 
  momentum 
  of 
  the 
  body 
  absorbing 
  

   the 
  radiation 
  will 
  therefore 
  equal 
  the 
  increase 
  dm 
  in 
  its 
  mass, 
  

   multiplied 
  by 
  the 
  velocity 
  of 
  light, 
  

  

  dM 
  = 
  Ydm 
  (6) 
  

  

  Combining 
  this 
  equation 
  with 
  (3) 
  we 
  find 
  

  

  ^=^2, 
  (7) 
  

  

  or 
  if 
  we 
  write 
  V 
  = 
  3 
  X 
  10 
  10 
  centimetres 
  per 
  second, 
  

   dm 
  = 
  1-111 
  x!0- 
  21 
  dE. 
  

  

  Thus 
  a 
  body 
  receiving 
  or 
  emitting 
  radiant 
  energy 
  gains 
  or 
  

   loses 
  mass 
  in 
  proportion 
  and 
  by 
  the 
  amount 
  1*111 
  x 
  10 
  -21 
  

   grams 
  for 
  every 
  erg. 
  This 
  is 
  a 
  small 
  quantity, 
  indeed, 
  but 
  

   one 
  which 
  is 
  not 
  to 
  be 
  neglected. 
  

  

  Assuming 
  the 
  fundamental 
  conservation 
  law, 
  we 
  must 
  

   regard 
  mass 
  as 
  a 
  real 
  property 
  of 
  a 
  body 
  which 
  depends 
  

   upon 
  its 
  state, 
  and 
  not 
  upon 
  its 
  history. 
  Hence 
  it 
  is 
  obvious 
  

   that 
  if 
  in 
  any 
  other 
  way 
  than 
  by 
  radiation 
  the 
  body 
  gains 
  or 
  

   loses 
  energy 
  it 
  must 
  still 
  gain 
  or 
  lose 
  mass 
  in 
  just 
  the 
  above 
  

   proportion. 
  In 
  other 
  words, 
  any 
  change 
  in 
  a 
  body's 
  content 
  

   of 
  energy 
  is 
  accompanied 
  by 
  a 
  definite 
  change 
  in 
  its 
  mass, 
  

  

  3 
  A 
  2 
  

  

  