﻿862 
  Dr. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  be 
  positive, 
  and 
  the 
  system 
  will 
  be 
  stable 
  for 
  the 
  displace- 
  

   ment. 
  Obviously 
  the 
  same 
  result 
  will 
  hold 
  in 
  the 
  case 
  o£ 
  

   the 
  distance 
  between 
  the 
  nuclei 
  diminishing. 
  It 
  may 
  be 
  

   noticed 
  that 
  in 
  the 
  above 
  considerations 
  we 
  have 
  not 
  made 
  

   use 
  of 
  any 
  new 
  assumption 
  on 
  the 
  dynamics 
  of 
  the 
  electrons, 
  

   but 
  have 
  only 
  used 
  the 
  principle 
  of 
  the 
  invariance 
  of 
  the 
  

   angular 
  momentum, 
  which 
  is 
  common 
  both 
  for 
  the 
  ordinary 
  

   mechanics 
  and 
  for 
  the 
  main 
  hypothesis 
  of 
  § 
  1. 
  

  

  For 
  a 
  system 
  consisting 
  of 
  a 
  ring 
  of 
  electrons 
  and 
  two 
  

   nuclei 
  of 
  unequal 
  charge, 
  the 
  investigation 
  of 
  the 
  stability 
  is 
  

   more 
  complicated. 
  As 
  before, 
  we 
  find 
  that 
  the 
  systems 
  are 
  

   always 
  stable 
  for 
  displacements 
  of 
  the 
  electrons 
  in 
  the 
  plane 
  

   of 
  the 
  ring 
  ; 
  also 
  an 
  expression 
  corresponding 
  to 
  (5) 
  will 
  hold 
  

   for 
  the 
  condition 
  of 
  stability 
  for 
  displacements 
  perpendicular 
  

   to 
  the 
  plane 
  of 
  the 
  ring. 
  This 
  condition, 
  however, 
  will 
  not 
  

   be 
  sufficient 
  to 
  secure 
  the 
  stability 
  of 
  the 
  system. 
  For 
  a 
  dis- 
  

   placement 
  of 
  the 
  electrons 
  perpendicular 
  to 
  the 
  plane 
  of 
  the 
  

   ring, 
  the 
  variation 
  of 
  the 
  radial 
  force 
  due 
  to 
  the 
  nuclei 
  will 
  

   be 
  of 
  the 
  same 
  order 
  of 
  magnitude 
  as 
  the 
  displacement 
  ; 
  

   therefore, 
  in 
  the 
  new 
  configuration 
  the 
  radial 
  force 
  will 
  not 
  

   be 
  in 
  equilibrium 
  with 
  the 
  centrifugal 
  force, 
  and, 
  if 
  the 
  

   radius 
  of 
  the 
  orbits 
  is 
  varied 
  until 
  the 
  radial 
  equilibrium 
  is 
  

   restored, 
  the 
  energy 
  of 
  the 
  system 
  will 
  decrease. 
  This 
  

   circumstance 
  must 
  be 
  taken 
  into 
  account 
  in 
  applying 
  the 
  

   condition 
  of 
  stability 
  of 
  § 
  1. 
  Similar 
  complications 
  arise 
  in. 
  

   the 
  calculation 
  of 
  stability 
  for 
  displacements 
  of 
  the 
  nuclei. 
  

   For 
  a 
  variation 
  of 
  the 
  distance 
  apart 
  of 
  the 
  nuclei 
  not 
  only 
  

   will 
  the 
  radius 
  of 
  the 
  ring 
  vary 
  but 
  also 
  the 
  ratio 
  in 
  which 
  

   the 
  plane 
  of 
  the 
  ring 
  divides 
  the 
  line 
  connecting 
  the 
  nuclei. 
  

   As 
  a 
  consequence, 
  the 
  full 
  discussion 
  of 
  the 
  general 
  case 
  is 
  

   rather 
  lengthy 
  ; 
  an 
  approximate 
  numerical 
  calculation, 
  

   however, 
  shows 
  that 
  the 
  systems, 
  as 
  in 
  the 
  former 
  case, 
  will 
  

   be 
  unstable 
  unless 
  the 
  charges 
  on 
  the 
  nuclei 
  are 
  small 
  and 
  the 
  

   ring 
  contains 
  very 
  few 
  electrons. 
  

  

  The 
  above 
  considerations 
  suggest 
  configurations 
  of 
  system 
  s 
  5 
  

   consisting 
  of 
  two 
  positive 
  nuclei 
  and 
  a 
  number 
  of 
  electrons, 
  

   which 
  are 
  consistent 
  with 
  the 
  arrangement 
  of 
  the 
  electrons 
  

   to 
  be 
  expected 
  in 
  molecules 
  of 
  chemical 
  combinations. 
  If 
  we 
  

   thus 
  consider 
  a 
  neutral 
  system 
  containing 
  two 
  nuclei 
  with 
  

   great 
  charges, 
  it 
  follows 
  that 
  in 
  a 
  stable 
  configuration 
  the 
  

   greater 
  part 
  of 
  the 
  electrons 
  must 
  be 
  arranged 
  around 
  each 
  

   nucleus 
  approximately 
  as 
  if 
  the 
  other 
  nucleus 
  were 
  absent 
  ; 
  

   and 
  that 
  only 
  a 
  few 
  of 
  the 
  outer 
  electrons 
  will 
  be 
  arranged 
  

   differently 
  rotating 
  in 
  a 
  ring 
  round 
  the 
  line 
  connecting 
  the 
  

   nuclei. 
  The 
  latter 
  ring, 
  which 
  keeps 
  the 
  system 
  together, 
  

   represents 
  the 
  chemical 
  " 
  bond." 
  

  

  