﻿520 
  Messrs. 
  G. 
  N. 
  Lewis 
  and 
  R. 
  C. 
  Tolman 
  on 
  the 
  

  

  Vi-/S^ 
  

  

  than 
  it 
  would 
  be 
  i£ 
  the 
  

  

  is 
  smaller 
  by 
  the 
  ratio 
  

  

  system 
  were 
  at 
  rest. 
  And 
  we 
  conclude, 
  therefore, 
  that 
  the 
  

   unit 
  of 
  force 
  or 
  the 
  dyne 
  in 
  a 
  direction 
  transverse 
  to 
  the 
  line 
  

   of 
  motion 
  is 
  smaller 
  in 
  a 
  moving 
  system 
  than 
  in 
  one 
  at 
  rest 
  

   by 
  this 
  same 
  ratio. 
  

  

  In 
  order 
  now 
  to 
  obtain 
  a 
  value 
  for 
  the 
  force 
  in 
  a 
  longi- 
  

   tudinal 
  direction 
  in 
  the 
  moving 
  system, 
  let 
  us 
  consider 
  (fig. 
  3) 
  

   a 
  rigid 
  lever 
  ahc, 
  whose 
  arms 
  are 
  equal 
  and 
  perpendicular, 
  

   and 
  equal 
  forces 
  applied 
  at 
  a 
  and 
  c 
  in 
  directions 
  parallel 
  to 
  

   he 
  and 
  ha. 
  The 
  system 
  is 
  thus 
  in 
  equilibrium. 
  

  

  Fig. 
  3. 
  

  

  aL 
  

  

  jSTow 
  let 
  us 
  assume 
  that 
  the 
  whole 
  system 
  is 
  in 
  motion 
  with 
  

   velocity 
  v 
  in 
  the 
  direction 
  he. 
  Obviously, 
  merely 
  by 
  making 
  

   such 
  an 
  assumption 
  we 
  cannot 
  cause 
  the 
  lever 
  to 
  turn, 
  never- 
  

   theless 
  we 
  must 
  now 
  regard 
  the 
  length 
  he 
  as 
  shortened 
  in 
  

  

  the 
  ratio 
  

  

  \/l-yS^ 
  

  

  wdiiie 
  ah 
  has 
  the 
  same 
  length 
  as 
  at 
  rest. 
  

  

  We 
  must 
  therefore 
  conclude 
  that 
  to 
  maintain 
  equilibrium 
  the 
  

   force 
  at 
  a 
  must 
  be 
  less 
  than 
  the 
  force 
  at 
  c 
  in 
  the 
  same 
  ratio. 
  

   We 
  thus 
  see 
  that 
  in 
  a 
  moving 
  system 
  unit 
  force 
  in 
  the 
  longi- 
  

   tudinal 
  direction 
  is 
  smaller 
  than 
  unit 
  transverse 
  force 
  in 
  the 
  

  

  ratio 
  

  

  Vl-/3^ 
  

  

  and 
  therefore, 
  by 
  the 
  preceding 
  paragraph, 
  

  

  smaller 
  than 
  unit 
  force 
  at 
  rest 
  in 
  the 
  ratio 
  

  

  l-yS^ 
  

  

  It 
  

  

  IS 
  

  

  interesting 
  to 
  point 
  out, 
  as 
  Bumstead 
  * 
  has 
  already 
  done, 
  that 
  

   the 
  repulsion 
  between 
  two 
  like 
  electrons, 
  as 
  calculated 
  from 
  

  

  * 
  Bumstead, 
  loc, 
  cit. 
  . 
  

  

  