﻿of 
  Atoms 
  and 
  Molecules. 
  479 
  

  

  ring 
  of 
  n 
  electrons 
  rotating 
  round 
  a 
  nucleus 
  of 
  charge 
  Ne 
  

   we 
  have 
  (comp. 
  Part 
  L, 
  p. 
  20) 
  

  

  F 
  = 
  N 
  — 
  s 
  , 
  where 
  s 
  = 
  T 
  X 
  cosec 
  — 
  . 
  

  

  4, 
  = 
  i 
  » 
  

  

  The 
  values 
  for 
  s 
  n 
  from 
  ?i=l 
  to 
  w 
  = 
  16 
  are 
  given 
  in 
  the 
  table 
  

   on 
  p. 
  482. 
  

  

  For 
  systems 
  consisting 
  of 
  nuclei 
  and 
  electrons 
  in 
  which 
  

   the 
  first 
  are 
  at 
  rest 
  and 
  the 
  latter 
  move 
  in 
  circular 
  orbits 
  

   with 
  a 
  velocity 
  small 
  compared 
  with 
  the 
  velocity 
  of 
  light, 
  

   we 
  have 
  shown 
  (see 
  Part 
  L, 
  p. 
  24) 
  that 
  the 
  total 
  kinetic 
  

   energy 
  of 
  the 
  electrons 
  is 
  equal 
  to 
  the 
  total 
  amount 
  of 
  energy 
  

   emitted 
  during 
  the 
  formation 
  of 
  the 
  system 
  from 
  an 
  original 
  

   configuration 
  in 
  which 
  all 
  the 
  particles 
  are 
  at 
  rest 
  and 
  at 
  

   infinite 
  distances 
  from 
  each 
  other. 
  Denoting 
  this 
  amount 
  of 
  

   energy 
  by 
  W, 
  we 
  consequently 
  get 
  

  

  W=*£*=?^2F» 
  (3) 
  

  

  Putting 
  in 
  (1), 
  (2), 
  and 
  (3) 
  e 
  = 
  ^7 
  . 
  10" 
  10 
  , 
  ~ 
  = 
  5'31 
  . 
  10i*, 
  

   and 
  7i 
  = 
  6'5 
  . 
  10~ 
  27 
  we 
  get 
  

  

  e 
  

   m 
  

  

  a 
  = 
  0'55 
  . 
  IQ^F- 
  1 
  , 
  v='2'l 
  . 
  10 
  8 
  F, 
  a) 
  = 
  6*2 
  . 
  10 
  15 
  F 
  2 
  ") 
  

   and 
  [ 
  W 
  

  

  W 
  = 
  2-0 
  . 
  10- 
  n 
  lF 
  2 
  . 
  J 
  

  

  In 
  neglecting 
  the 
  magnetic 
  forces 
  due 
  to 
  the 
  motion 
  of 
  

   the 
  electrons 
  we 
  have 
  in 
  Part 
  I. 
  assumed 
  that 
  the 
  velocities 
  

   of 
  the 
  particles 
  _are 
  small 
  compared 
  with 
  the 
  velocity 
  of 
  light. 
  

   The 
  above 
  calculations 
  show 
  that 
  for 
  this 
  to 
  hold, 
  F 
  must 
  be 
  

   small 
  compared 
  with 
  1 
  50. 
  As 
  will 
  be 
  seen, 
  the 
  latter 
  con- 
  

   dition 
  will 
  be 
  satisfied 
  for 
  all 
  the 
  electrons 
  in 
  the 
  atoms 
  of 
  

   elements 
  of 
  low 
  atomic 
  weight 
  and 
  for 
  a 
  greater 
  part 
  of 
  the 
  

   electrons 
  contained 
  in 
  the 
  atoms 
  of 
  the 
  other 
  elements. 
  

  

  If 
  the 
  velocity 
  of 
  the 
  electrons 
  is 
  not 
  small 
  compared 
  with 
  

   the 
  velocity 
  of 
  light, 
  the 
  constancy 
  of 
  the 
  angular 
  momentum 
  

   no 
  longer 
  involves 
  a 
  constant 
  ratio 
  between 
  the 
  energy 
  and 
  

   the 
  frequency 
  of 
  revolution. 
  Without 
  introducing 
  new 
  

   assumptions, 
  we 
  cannot 
  therefore 
  in 
  this 
  case 
  determine 
  the 
  

   configuration 
  of 
  the 
  systems 
  on 
  the 
  basis 
  of 
  the 
  considera- 
  

   tions 
  in 
  Part 
  I. 
  Considerations 
  given 
  later 
  suggest, 
  how- 
  

   ever, 
  that 
  the 
  constancy 
  of 
  the 
  angular 
  momentum 
  is 
  the 
  

   principal 
  condition. 
  Applying 
  this 
  condition 
  for 
  velocities 
  

  

  2K2 
  

  

  