﻿794 
  

  

  Sir 
  J. 
  J. 
  Thomson 
  on 
  

  

  he 
  

  

  momentum 
  of 
  a 
  corpuscle 
  about 
  an 
  axis 
  in 
  the 
  atom 
  to 
  be 
  an 
  

   absolute 
  constant 
  whose 
  value 
  did 
  not 
  depend 
  at 
  all 
  upon 
  the 
  

   nature 
  of 
  the 
  atom. 
  We 
  shall 
  not, 
  however, 
  at 
  this 
  stage 
  

   enter 
  into 
  any 
  consideration 
  as 
  to 
  the 
  origin 
  of 
  this 
  force 
  ; 
  

   we 
  shall 
  simply 
  postulate 
  its 
  existence. 
  

  

  If 
  a 
  corpuscle 
  at 
  P 
  were 
  inside 
  one 
  of 
  the 
  tubes 
  of 
  attrac- 
  

   tive 
  force 
  inside 
  the 
  atom, 
  it 
  could 
  be 
  removed 
  to 
  an 
  infinite 
  

   distance 
  (1) 
  by 
  moving 
  it 
  radially 
  outwards 
  and 
  keeping 
  it 
  

   inside 
  the 
  tube 
  of 
  attractive 
  force 
  the 
  whole 
  way. 
  If 
  the 
  

   attractive 
  force 
  on 
  unit 
  charge 
  at 
  a 
  distance 
  r 
  from 
  the 
  centre 
  

   is 
  A/r 
  2 
  , 
  the 
  work 
  required 
  to 
  move 
  the 
  corpuscle 
  in 
  this 
  way 
  

   from 
  r 
  to 
  an 
  infinite 
  distance 
  is 
  Ae/r 
  ; 
  the 
  corpuscle 
  could, 
  

   however, 
  be 
  moved 
  to 
  an 
  infinite 
  distance 
  in 
  another 
  way 
  

   (2) 
  by 
  moving 
  it 
  sideways 
  out 
  of 
  the 
  tube 
  at 
  P 
  and 
  then 
  

   moving 
  it 
  outside 
  the 
  tube 
  to 
  an 
  infinite 
  distance 
  — 
  the 
  latter 
  

   process 
  will 
  absorb 
  no 
  work, 
  as 
  the 
  attractive 
  force 
  vanishes 
  

   outside 
  the 
  tube. 
  By 
  the 
  Conservation 
  of 
  Energy 
  the 
  work 
  

   must 
  be 
  the 
  same 
  whether 
  we 
  adopt 
  process 
  (1) 
  or 
  (2), 
  hence 
  

   the 
  work 
  required 
  to 
  move 
  the 
  corpuscle 
  sideways 
  out 
  of 
  the 
  

   tabe 
  at 
  P 
  must 
  be 
  equal 
  to 
  Ae/r. 
  

  

  A 
  corpuscle 
  can 
  be 
  in 
  stable 
  equilibrium 
  when 
  in 
  a 
  region 
  

   where 
  it 
  is 
  acted 
  on 
  by 
  both 
  the 
  repulsive 
  and 
  the 
  attractive 
  

   forces. 
  Let 
  the 
  repulsive 
  force 
  on 
  unit, 
  charge 
  at 
  a 
  distance 
  

   r=C/r 
  s 
  , 
  the 
  attractive 
  A/r 
  2 
  , 
  then 
  there 
  will 
  be 
  equilibrium 
  

   at 
  a 
  distance 
  a 
  if 
  

  

  • 
  C 
  A 
  

  

  To 
  show 
  that 
  the 
  equilibrium 
  is 
  stable, 
  suppose 
  the 
  particle 
  

   is 
  displaced 
  radially 
  through 
  a 
  distance 
  x, 
  so 
  that 
  r 
  = 
  a-\-x 
  ; 
  

   then, 
  if 
  m 
  is 
  the 
  mass 
  of 
  a 
  corpuscle, 
  e 
  its 
  charge, 
  the 
  equation 
  

   of 
  motion 
  is 
  

  

  d 
  2 
  x 
  Ce 
  Ae 
  

  

  m 
  — 
  - 
  — 
  

  

  df 
  

  

  (a 
  + 
  xf 
  (a 
  + 
  xf 
  

   = 
  CW 
  1 
  _3.A_A,/ 
  1 
  _2, 
  ) 
  

   a 
  6 
  \ 
  a 
  J 
  a 
  2 
  \ 
  a 
  J 
  

  

  Cex 
  

  

  Thus 
  the 
  motion 
  is 
  stable, 
  and 
  if 
  T 
  is 
  the 
  time 
  of 
  vibration 
  

   2tt 
  = 
  /Ce 
  

   T 
  V 
  ma 
  v 
  

   The 
  work 
  done 
  by 
  the 
  repulsive 
  force 
  on 
  a 
  corpuscle 
  when 
  

   it 
  moves 
  from 
  r=a 
  to 
  r 
  = 
  infinity 
  is 
  ^— 
  g5 
  hence 
  we 
  see 
  that 
  

  

  