﻿710 
  Prof. 
  G. 
  N. 
  Lewis 
  : 
  A 
  Revision 
  of 
  the 
  

  

  the 
  axiom 
  which 
  we 
  have 
  abandoned 
  we 
  must 
  substitute 
  

   equation 
  (7). 
  

  

  Before 
  investigating 
  the 
  consequences 
  of 
  this 
  step 
  it 
  is 
  

   necessary 
  to 
  define 
  exactly 
  the 
  principal 
  mechanical 
  quantities 
  

   which 
  we 
  are 
  to 
  use. 
  

  

  Extension 
  in 
  space 
  (7) 
  and 
  time 
  (t) 
  will 
  be 
  measured 
  in 
  

   the 
  usual 
  way 
  and 
  the 
  centimetre 
  and 
  the 
  second 
  will 
  be 
  

   employed 
  as 
  units. 
  

  

  Force 
  (/) 
  will 
  be 
  given 
  its 
  usual 
  significance 
  and 
  the 
  unit, 
  

   the 
  dyne, 
  will 
  be 
  that 
  force 
  which, 
  acting 
  upon 
  the 
  Inter- 
  

   national 
  standard 
  kilogram, 
  when 
  the 
  latter 
  is 
  at 
  rest, 
  imparts 
  

  

  to 
  it 
  an 
  initial 
  acceleration 
  of 
  *001 
  — 
  \ 
  . 
  

  

  sec.- 
  

  

  The 
  momentum 
  (M) 
  of 
  a 
  moving 
  body 
  will 
  be 
  measured 
  

   by 
  the 
  time 
  in 
  which 
  it 
  is 
  brought 
  to 
  rest 
  under 
  the 
  influence 
  

   of 
  a 
  constant 
  opposing 
  force 
  of 
  one 
  dyne 
  acting 
  in 
  the 
  line 
  

   of 
  its 
  motion. 
  

  

  The 
  mass 
  (m) 
  of 
  a 
  moving 
  body 
  will 
  be 
  defined 
  as 
  the 
  

   momentum 
  divided 
  by 
  the 
  velocity 
  (u), 
  that 
  is, 
  

  

  m= 
  — 
  (lU) 
  

  

  v 
  

  

  The 
  limiting 
  ratio 
  of 
  the 
  momentum 
  of 
  a 
  body 
  to 
  its 
  velocity, 
  

   when 
  it 
  is 
  brought 
  to 
  rest, 
  will 
  be 
  called 
  its 
  mass 
  when 
  at 
  

   rest. 
  The 
  unit 
  of 
  mass 
  is 
  the 
  gram. 
  

  

  The 
  kinetic 
  energy 
  (E') 
  of 
  a 
  body 
  will 
  be 
  measured 
  by 
  the 
  

   distance 
  through 
  which 
  it 
  will 
  move 
  before 
  being 
  brought 
  to 
  

   rest 
  by 
  a 
  constant 
  opposing 
  force 
  of 
  one 
  dyne, 
  acting 
  in 
  the 
  

   line 
  of 
  the 
  body's 
  motion. 
  The 
  unit 
  of 
  energy 
  will 
  be 
  the 
  

   erg. 
  

  

  These 
  definitions, 
  although 
  somewhat 
  unusual 
  in 
  form, 
  are 
  

   perfectly 
  consistent 
  with 
  the 
  ordinary 
  definitions 
  of 
  Newtonian 
  

   mechanics. 
  But 
  they 
  have 
  been 
  so 
  chosen 
  as 
  to 
  be 
  consistent 
  

   also 
  with 
  equation 
  (7) 
  and 
  the 
  fundamental 
  conservation 
  

   laws. 
  Obviously 
  equation 
  (7) 
  itself 
  is 
  not 
  inconsistent 
  with 
  

   these 
  conservation 
  laws, 
  for 
  although 
  a 
  body 
  increases 
  in 
  

   mass 
  as 
  it 
  gains 
  kinetic 
  energy, 
  some 
  other 
  system 
  is 
  losing 
  

   the 
  same 
  mass 
  as 
  it 
  loses 
  the 
  same 
  energy. 
  

  

  In 
  accordance 
  with 
  the 
  above 
  definitions 
  we 
  may 
  write 
  

  

  dM=fdt, 
  (11) 
  

  

  cW=fdl. 
  . 
  ..... 
  . 
  . 
  (12) 
  

  

  Let 
  us 
  consider 
  a 
  body 
  originally 
  moving 
  with 
  a 
  velocity 
  v 
  

   subjected 
  for 
  the 
  time 
  dt 
  to 
  a 
  force 
  / 
  in 
  the 
  line 
  of 
  its 
  motion. 
  

  

  