﻿706 
  Prof. 
  G. 
  N. 
  Lewis 
  : 
  A 
  Revision 
  of 
  the 
  

  

  namely, 
  the 
  law 
  of 
  conservation 
  of 
  energy, 
  the 
  law 
  of 
  con- 
  

   servation 
  of 
  mass, 
  and 
  the 
  law 
  of 
  conservation 
  of 
  momentum. 
  

   To 
  these 
  we 
  may 
  add, 
  if 
  we 
  will, 
  the 
  law 
  of 
  conservation 
  of 
  

   electricity. 
  

  

  The 
  Relation 
  of 
  Mass 
  to 
  Energy. 
  

  

  When 
  a 
  black 
  body 
  * 
  is 
  placed 
  in 
  a 
  beam 
  of 
  light 
  it 
  is 
  subject 
  

   to 
  a 
  pressure 
  or 
  force 
  which 
  tends 
  to 
  move 
  it 
  in 
  the 
  direction 
  

  

  in 
  which 
  the 
  light 
  is 
  moving. 
  If 
  —jp 
  denotes 
  the 
  time-rate 
  

  

  at 
  which 
  the 
  body 
  receives 
  energy, 
  / 
  the 
  force, 
  and 
  V 
  the 
  

   velocity 
  of 
  light, 
  we 
  have 
  in 
  rational 
  units 
  the 
  formula 
  

  

  f- 
  1 
  -™ 
  ... 
  (1) 
  

  

  This 
  important 
  equation, 
  which 
  was 
  obtained 
  by 
  Maxwell 
  

   as 
  a 
  consequence 
  of 
  his 
  electromagnetic 
  theory, 
  and 
  by 
  

   Boltzmann 
  through 
  the 
  direct 
  application 
  of 
  the 
  laws 
  of 
  

   thermodynamics, 
  has 
  recently 
  been 
  verified 
  with 
  remarkable 
  

   precision 
  in 
  the 
  beautiful 
  experiments 
  of 
  Nichols 
  and 
  Hull 
  f. 
  

  

  A 
  body 
  subjected 
  to 
  the 
  pressure 
  of 
  radiation 
  will 
  acquire 
  

   momentum, 
  and 
  if 
  we 
  are 
  to 
  accept 
  the 
  law 
  of 
  conservation 
  

   of 
  momentum, 
  we 
  must 
  conclude 
  that 
  some 
  other 
  system 
  

   is 
  losing 
  in 
  the 
  same 
  direction 
  an 
  equivalent 
  momentum. 
  

   We 
  are 
  thus 
  led 
  inevitably, 
  as 
  Poynting 
  has 
  shown^ 
  to 
  the 
  

   idea 
  that 
  the 
  beam 
  of 
  radiation 
  carries 
  not 
  only 
  energy 
  but 
  

   momentum 
  as 
  well. 
  

  

  The 
  body 
  subject 
  to 
  the 
  constant 
  force 
  of 
  radiation 
  /, 
  will 
  

   obviously 
  acquire 
  momentum 
  at 
  the 
  rate 
  

  

  #-/. 
  m 
  

  

  Combining 
  equations 
  (1) 
  and 
  (2) 
  gives 
  

  

  S=V 
  .- 
  (3) 
  

  

  The 
  ratio 
  of 
  the 
  acquired 
  energy 
  to 
  the 
  acquired 
  momentum 
  

   is 
  equal 
  to 
  the 
  velocity 
  of 
  light. 
  The 
  beam 
  of 
  radiation 
  must, 
  

   therefore, 
  possess 
  energy 
  and 
  momentum 
  in 
  the 
  same 
  ratio. 
  

   Hence 
  for 
  the 
  beam 
  itself, 
  or 
  any 
  part 
  of 
  it, 
  

  

  l= 
  v 
  w 
  

  

  * 
  In 
  place 
  of 
  a 
  black 
  body 
  we 
  might 
  consider 
  a 
  partially 
  reflecting 
  one. 
  

   The 
  equations 
  thus 
  obtained 
  are 
  more 
  complicated 
  but 
  lead 
  also 
  to 
  the 
  

   simple 
  equation 
  (7). 
  

  

  f 
  Phys. 
  Review, 
  xvii. 
  pp. 
  26 
  and 
  91 
  (1903). 
  

  

  