﻿of 
  Atoms 
  and 
  Molecules. 
  8G7 
  

  

  electron 
  rotating 
  in 
  a 
  circular 
  orbit 
  round 
  the 
  line 
  connecting 
  

   the 
  nuclei, 
  is 
  unstable 
  for 
  a 
  displacement 
  of 
  the 
  -electron 
  

   perpendicular 
  to 
  its 
  orbit, 
  since 
  in 
  the 
  configuration 
  of 
  

   equilibrium 
  G<0. 
  The 
  explanation 
  of 
  the 
  appearance 
  of 
  

   positively 
  charged 
  hydrogen 
  molecules 
  in 
  experiments 
  on 
  

   positive 
  rajs 
  may 
  therefore 
  at 
  first 
  sight 
  be 
  considered 
  as 
  a 
  

   serious 
  difficulty 
  for 
  the 
  present 
  theory. 
  A 
  possible 
  ex- 
  

   planation, 
  however, 
  might 
  be 
  sought 
  in 
  the 
  special 
  conditions 
  

   under 
  which 
  the 
  systems 
  are 
  observed. 
  We 
  are 
  probably 
  

   dealing 
  in 
  such 
  a 
  case 
  not 
  with 
  the 
  formation 
  of 
  a 
  stationary 
  

   system 
  by 
  a 
  regular 
  interaction 
  of 
  systems 
  containing 
  single 
  

   nuclei 
  (see 
  the 
  next 
  section), 
  but 
  rather 
  with 
  a 
  delay 
  in 
  the 
  

   breaking 
  up 
  of 
  a 
  configuration 
  brought 
  about 
  by 
  the 
  sudden 
  

   removal 
  of 
  one 
  of 
  the 
  electrons 
  by 
  impact 
  of 
  a 
  single 
  particle. 
  

   Another 
  stable 
  configuration 
  containing 
  a 
  few 
  electrons 
  is 
  

   one 
  consisting 
  of 
  a 
  ring 
  of 
  three 
  electrons 
  and 
  two 
  nuclei 
  uf 
  

   charges 
  e 
  and 
  2e. 
  A 
  numerical 
  calculation 
  gives 
  

  

  h 
  = 
  1-446, 
  - 
  2 
  = 
  0-137, 
  F 
  = 
  1-552, 
  

  

  a 
  a 
  

  

  where 
  a 
  is 
  the 
  radius 
  of 
  the 
  ring 
  and 
  b 
  x 
  and 
  b 
  2 
  the 
  distances 
  

   apart 
  of 
  the 
  nuclei 
  from 
  the 
  plane 
  of 
  the 
  ring. 
  By 
  help 
  of 
  

   (2) 
  and 
  (3) 
  we 
  further 
  get 
  

  

  a 
  = 
  0-644a 
  , 
  to 
  = 
  2-41o> 
  , 
  W 
  = 
  7;22W 
  , 
  

  

  where 
  co 
  is 
  the 
  frequency 
  of 
  revolution 
  and 
  W 
  the 
  total 
  

   energy 
  necessary 
  to 
  remove 
  the 
  particles 
  to 
  infinite 
  distances 
  

   from 
  each 
  other. 
  In 
  spite 
  of 
  the 
  fact 
  that 
  W 
  is 
  greater 
  than 
  

   the 
  sum 
  of 
  the 
  values 
  of 
  W 
  for 
  a 
  hydrogen 
  and 
  a 
  helium 
  

   atom 
  (W 
  + 
  6*13W 
  ; 
  comp. 
  Part 
  II. 
  p. 
  489), 
  the 
  configuration 
  

   in 
  question 
  cannot, 
  as 
  will 
  be 
  shown 
  in 
  the 
  next 
  section, 
  be 
  

   considered 
  to 
  represent 
  a 
  possible 
  molecule 
  of 
  hydrogen 
  and 
  

   helium. 
  

  

  The 
  vibration 
  of 
  the 
  system 
  corresponding 
  to 
  a 
  displace- 
  

   ment 
  of 
  the 
  nuclei 
  relative 
  to 
  each 
  other 
  shows 
  features 
  

   different 
  from 
  the 
  system 
  considered 
  above 
  of 
  two 
  nuclei 
  of 
  

   charge 
  e 
  and 
  two 
  electrons. 
  If, 
  for 
  example, 
  the 
  distance 
  

   between 
  the 
  nuclei 
  is 
  increased, 
  the 
  ring 
  of 
  electrons 
  will 
  

   approach 
  the 
  nucleus 
  of 
  charge 
  2e. 
  Consequently, 
  the 
  

   vibration 
  must 
  be 
  expected 
  to 
  be 
  connected 
  with 
  an 
  absorption 
  

   of 
  radiation. 
  

  

  § 
  4. 
  Formation 
  of 
  the 
  Systems. 
  

  

  As 
  mentioned 
  in 
  § 
  1, 
  we 
  cannot 
  assume 
  that 
  systems 
  con- 
  

   taining 
  more 
  than 
  one 
  nucleus 
  are 
  formed 
  by 
  successive 
  

   binding 
  of 
  electrons, 
  such 
  as 
  we 
  have 
  assumed 
  for 
  the 
  

  

  3N2 
  

  

  