﻿of 
  Atoms 
  and 
  Molecules. 
  21 
  

  

  Denoting 
  the 
  kinetic 
  energy 
  of 
  an 
  electron 
  by 
  T 
  and 
  

   neglecting 
  the 
  electromagnetic 
  forces 
  due 
  to 
  the 
  motion 
  of 
  

   the 
  electrons 
  (see 
  Part 
  II.), 
  we 
  get, 
  putting 
  the 
  centrifugal 
  

   iorce 
  on 
  an 
  electron 
  equal 
  to 
  the 
  radial 
  force, 
  

  

  2T 
  e 
  IV 
  \ 
  

  

  or 
  

  

  From 
  this 
  we 
  get 
  for 
  the 
  frequency 
  of 
  revolution 
  

  

  27T 
  V 
  ma 
  6 
  

  

  The 
  total 
  amount 
  of 
  energy 
  W 
  necessary 
  transferred 
  to 
  the 
  

   system 
  in 
  order 
  to 
  remove 
  the 
  electrons 
  to 
  infinite 
  distances 
  

   apart 
  from 
  the 
  nucleus 
  and 
  from 
  each 
  other 
  is 
  

  

  W= 
  -P 
  - 
  nT 
  = 
  ~(E~ 
  esn) 
  = 
  nT, 
  

  

  equal 
  to 
  the 
  total 
  kinetic 
  energy 
  of 
  the 
  electrons. 
  

  

  We 
  see 
  that 
  the 
  only 
  difference 
  in 
  the 
  above 
  formula 
  and 
  

   those 
  holding 
  for 
  the 
  motion 
  of 
  a 
  single 
  electron 
  in 
  a 
  circular 
  

   orbit 
  round 
  a 
  nucleus 
  is 
  the 
  exchange 
  of 
  E 
  for 
  E 
  — 
  6S„. 
  It 
  is 
  

   also 
  immediately 
  seen 
  that 
  corresponding 
  to 
  the 
  motion 
  of 
  an 
  

   electron 
  in 
  an 
  elliptical 
  orbit 
  round 
  a 
  nucleus, 
  there 
  will 
  be 
  a 
  

   motion 
  of 
  the 
  n 
  electrons 
  in 
  which 
  each 
  rotates 
  in 
  an 
  ellip- 
  

   tical 
  orbit 
  with 
  the 
  nucleus 
  in 
  the 
  focus, 
  and 
  the 
  n 
  electrons 
  

   at 
  any 
  moment 
  are 
  situated 
  at 
  equal 
  angular 
  intervals 
  on 
  a 
  

   circle 
  with 
  the 
  nucleus 
  as 
  the 
  centre. 
  The 
  major 
  axis 
  and 
  

   frequency 
  of 
  the 
  orbit 
  of 
  the 
  single 
  electrons 
  will 
  for 
  this 
  

   motion 
  be 
  given 
  by 
  the 
  expressions 
  (1) 
  on 
  p. 
  3 
  if 
  we 
  

  

  w 
  

  

  replace 
  E 
  by 
  E— 
  es 
  n 
  and 
  W 
  by 
  — 
  . 
  Let 
  us 
  now 
  suppose 
  

  

  that 
  the 
  system 
  of 
  n 
  electrons 
  rotating 
  in 
  a 
  ring 
  round 
  a 
  

   nucleus 
  is 
  formed 
  in 
  a 
  way 
  analogous 
  to 
  the 
  one 
  assumed 
  for 
  

   a 
  single 
  electron 
  rotating 
  round 
  a 
  nucleus. 
  It 
  will 
  thus 
  be 
  

   assumed 
  that 
  the 
  electrons, 
  before 
  the 
  binding 
  by 
  the 
  nucleus, 
  

   were 
  at 
  a 
  great 
  distance 
  apart 
  from 
  the 
  latter 
  and 
  possessed 
  

   no 
  sensible 
  velocities, 
  and 
  also 
  that 
  during 
  the 
  binding 
  a 
  

   homogeneous 
  radiation 
  is 
  emitted. 
  As 
  in 
  the 
  case 
  of 
  a 
  single 
  

   electron, 
  we 
  have 
  here 
  that 
  the 
  total 
  amount 
  of 
  energy 
  emitted 
  

   during 
  the 
  formation 
  of 
  the 
  system 
  is 
  equal 
  to 
  the 
  final 
  kinetic 
  

   energy 
  of 
  tie 
  electrons. 
  If 
  we 
  now 
  suppose 
  that 
  during 
  the 
  

  

  