﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  73 
  

  

  any 
  displacement 
  in 
  the 
  plane 
  of: 
  the 
  paper. 
  Perpendicular 
  

   to 
  the 
  paper 
  it 
  has 
  been 
  shown 
  that 
  the 
  force 
  is 
  zero, 
  and 
  

   hence 
  the 
  atom 
  is 
  free 
  to 
  move 
  completely 
  around 
  the 
  small 
  

   circle 
  of 
  latitude 
  passing 
  through 
  the 
  points 
  of 
  intersection 
  

   of 
  the 
  two 
  dotted 
  curves 
  of 
  zero 
  force. 
  

  

  It 
  is 
  considered 
  that 
  two 
  atoms 
  coming 
  into 
  such 
  stable 
  

   positions 
  relative 
  to 
  each 
  other 
  as 
  at 
  A 
  and 
  A', 
  constitute 
  a 
  

   diatomic 
  molecule. 
  The 
  chart 
  clearly 
  shows 
  that 
  the 
  angles 
  

   at 
  the 
  equilibrium 
  positions 
  differ 
  according 
  to 
  the 
  particular 
  

   combination 
  of 
  atoms, 
  and 
  likewise 
  the 
  degree 
  of 
  stability 
  

   must 
  also 
  vary. 
  It 
  is 
  possible 
  to 
  measure 
  exactly 
  the 
  degree 
  

   of 
  stability, 
  and 
  to 
  say 
  which 
  combinations 
  are 
  the 
  most 
  likely 
  

   to 
  persist, 
  and 
  to 
  withstand 
  the 
  shocks 
  that 
  they 
  must 
  receive 
  

   in 
  order 
  to 
  exist 
  as 
  elements. 
  

  

  Some 
  consideration 
  has 
  been 
  given 
  to 
  the 
  equilibrium 
  

   positions 
  assumed 
  by 
  more 
  than 
  two 
  molecules, 
  and 
  the 
  figures 
  

   shown 
  in 
  fig. 
  13 
  have 
  been 
  calculated. 
  It 
  would 
  be 
  beyond 
  

   the 
  scope 
  of 
  this 
  paper 
  to 
  give 
  these 
  calculations 
  in 
  detail. 
  

  

  Internal 
  Moments. 
  

  

  There 
  is 
  another 
  condition 
  for 
  perfect 
  equilibrium 
  between 
  

   two 
  atoms 
  to 
  be 
  considered. 
  The 
  sum 
  of 
  the 
  moments 
  of 
  the 
  

   forces 
  which 
  the 
  revolving 
  electrons 
  in 
  one 
  atom 
  exert 
  upon 
  

   the 
  other 
  atom 
  should 
  be 
  zero. 
  To 
  examine 
  this 
  question 
  we 
  

   will 
  find 
  the 
  forces 
  which 
  one 
  electron 
  exerts 
  upon 
  another, 
  

   all 
  forces 
  being 
  resolved 
  along 
  the 
  tangent 
  line 
  to 
  the 
  orbit 
  

   of 
  the 
  first 
  atom 
  defined 
  by 
  the 
  unit 
  vector 
  

  

  T= 
  ^r 
  I=gj 
  _ 
  c 
  . 
  ( 
  . 
  2) 
  

  

  It 
  may 
  be 
  shown 
  from 
  equations 
  (1) 
  to 
  (4) 
  that 
  the 
  

   instantaneous 
  values 
  of 
  the 
  four 
  component 
  forces 
  resolved 
  

   along 
  this 
  unit 
  tangent 
  are 
  

  

  F 
  1 
  =~(C. 
  C 
  + 
  a'sm 
  7 
  )(S;-O0, 
  (53) 
  

  

  F,-_^^(C* 
  + 
  a'sin 
  7 
  )(S,--CO, 
  . 
  . 
  . 
  (54) 
  

  

  F 
  3 
  = 
  

  

  liee'aur 
  sin 
  y 
  

   fjuee' 
  

  

  •'aVsinyf^ 
  113,135,, 
  1 
  rKI 
  

  

  F 
  ^_^Vcos 
  7( 
  _ 
  fl{)+ 
  , 
  ( 
  , 
  /](U!/rl 
  ( 
  i 
  ( 
  (56) 
  

  

  