﻿712 
  

  

  Prof. 
  Gr. 
  N. 
  Lewis 
  : 
  A 
  Revision 
  of 
  the 
  

  

  light. 
  When 
  /3 
  is 
  zero, 
  m 
  = 
  m 
  . 
  m 
  represents 
  therefore 
  the 
  

   mass 
  of 
  the 
  body 
  at 
  rest. 
  

  

  If 
  we 
  substitute 
  in 
  this 
  equation 
  numerical 
  values 
  of 
  /3 
  we 
  

   find 
  that, 
  while 
  the 
  quotient 
  m/m 
  becomes 
  infinite 
  when 
  the 
  

   velocity 
  equals 
  the 
  velocity 
  of 
  light, 
  it 
  remains 
  almost 
  equal 
  to 
  

   unity 
  until 
  the 
  velocity 
  of 
  light 
  is 
  closely 
  approached. 
  Thus 
  a 
  

   ton 
  weight 
  given 
  the 
  velocity 
  of 
  the 
  fastest 
  cannon-ball 
  would, 
  

   according 
  to 
  this 
  equation, 
  gain 
  in 
  mass 
  by 
  less 
  than 
  one 
  

   millionth 
  of 
  a 
  gram. 
  It 
  is 
  obvious 
  that, 
  except 
  in 
  those 
  

   unusual 
  cases 
  in 
  which 
  we 
  deal 
  with 
  velocities 
  comparable 
  

   with 
  that 
  of 
  light, 
  our 
  non-Newtonian 
  equations 
  are 
  identical 
  

   with 
  those 
  of 
  ordinary 
  mechanics 
  far 
  within 
  the 
  limits 
  of 
  error 
  

   of 
  the 
  most 
  delicate 
  experiments. 
  

  

  Recently, 
  however, 
  it 
  has 
  been 
  possible 
  to 
  study, 
  in 
  the 
  

   negative 
  particles 
  emitted 
  by 
  radioactive 
  substances, 
  bodies 
  

   which 
  sometimes 
  move 
  with 
  a 
  velocity 
  only 
  a 
  little 
  less 
  than 
  

   that 
  of 
  light. 
  In 
  a 
  series 
  of 
  remarkably 
  skilful 
  experi- 
  

   ments 
  Kaufmann^" 
  was 
  able 
  to 
  measure 
  the 
  ratio 
  of 
  electric 
  

   charge 
  to 
  mass 
  (e/m) 
  for 
  negative 
  particles 
  moving 
  at 
  

   different 
  speeds. 
  Assuming 
  that 
  the 
  charge 
  is 
  constant, 
  

   the 
  fact 
  that 
  e/m 
  varies 
  with 
  the 
  speed 
  of 
  the 
  particle 
  must 
  be 
  

   attributed 
  to 
  a 
  variation 
  of 
  the 
  mass 
  with 
  the 
  speed. 
  On 
  this 
  

   assumption 
  it 
  is 
  possible 
  to 
  calculate 
  from 
  Kauf 
  mann's 
  experi- 
  

   ments 
  the 
  values 
  of 
  m/m 
  at 
  the 
  different 
  velocities. 
  

  

  The 
  mass 
  of 
  a 
  negative 
  particle 
  is 
  usually 
  spoken 
  of 
  as 
  

   electromagnetic 
  mass, 
  but 
  if 
  we 
  are 
  to 
  hold 
  to 
  our 
  definitions 
  

   we 
  must 
  recognize 
  only 
  one 
  kind 
  of 
  mass. 
  In 
  general 
  we 
  

   have 
  defined 
  the 
  mass 
  of 
  a 
  moving 
  body 
  as 
  the 
  quotient 
  of 
  

   the 
  time 
  during 
  which 
  it 
  will 
  be 
  brought 
  to 
  rest 
  by 
  unit 
  force, 
  

   divided 
  by 
  the 
  initial 
  velocity. 
  It 
  matters 
  not 
  what 
  the 
  

   supposed 
  origin 
  of 
  this 
  mass 
  may 
  be. 
  Equation 
  (15) 
  should 
  

   therefore 
  be 
  directly 
  applicable 
  to 
  the 
  experiments 
  of 
  

   Kaufmann. 
  In 
  the 
  following 
  table 
  are 
  given 
  the 
  values 
  of 
  

  

  m 
  

  

  m 
  ' 
  

  

  /3 
  (observed). 
  

  

  (3 
  (calculated). 
  

  

  1 
  

  

  

  

  

  

  1-34 
  

  

  ■73 
  

  

  •67 
  

  

  1-37 
  

  

  •75 
  

  

  •69 
  

  

  1-42 
  

  

  •78 
  

  

  •71 
  

  

  1-47 
  

  

  ■80 
  

  

  •73 
  

  

  1-54 
  

  

  •83 
  

  

  •76 
  

  

  1-65 
  

  

  •86 
  

  

  •80 
  

  

  1-73 
  

  

  •88 
  

  

  •82 
  

  

  2-05 
  

  

  •93 
  

  

  •88 
  

  

  2-14 
  

  

  •95 
  

  

  •89 
  

  

  2-42 
  

  

  •96 
  

  

  •91 
  

  

  * 
  Phys. 
  Zeit. 
  iv. 
  p. 
  54 
  (1902) 
  ; 
  Ann 
  Phys. 
  xix. 
  p. 
  487 
  (1906). 
  

  

  