﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  75 
  

  

  atoms 
  are 
  once 
  in 
  this 
  fixed 
  position, 
  the 
  forces 
  keep 
  them 
  

   synchronized. 
  If 
  the 
  translational 
  position 
  is 
  other 
  than 
  

   that 
  of 
  equilibrium, 
  the 
  angles 
  tor 
  the 
  relative 
  phases 
  for 
  

   moment 
  equilibrium 
  differ. 
  For 
  example, 
  i 
  the 
  two 
  atoms 
  

   were 
  situated 
  in 
  positions 
  latitude 
  90° 
  and 
  distance 
  j3' 
  2 
  v 
  2 
  = 
  5, 
  

   the 
  phase 
  positions 
  for 
  stable 
  equilibrium 
  as 
  to 
  moments 
  

   would 
  be 
  7= 
  J 
  27r, 
  7 
  = 
  7r, 
  and 
  y=-^2ir. 
  

  

  Formation 
  of 
  Ions. 
  

  

  It 
  may 
  be 
  shown 
  that 
  a 
  perfectly 
  neutral 
  atom 
  — 
  that 
  is, 
  

   an 
  atom 
  the 
  sum 
  of 
  whose 
  positive 
  and 
  negative 
  charges 
  

   is 
  zero 
  — 
  will 
  attract 
  or 
  repel 
  a 
  charge, 
  say 
  an 
  electron, 
  

   or 
  a 
  positive 
  sphere 
  not 
  containing 
  an 
  electron, 
  according 
  to 
  

   the 
  relative 
  positions 
  of 
  the 
  atom 
  and 
  the 
  charge, 
  with 
  a 
  

   force 
  inversely 
  as 
  the 
  fourth 
  power 
  of 
  the 
  distance 
  when 
  the 
  

   distance 
  is 
  not 
  too 
  small. 
  The 
  force 
  becomes 
  inappreciable 
  

   beyond 
  molecular 
  range. 
  The 
  expressions 
  for 
  the 
  forces 
  are 
  

   derived 
  in 
  a 
  similar 
  manner 
  to 
  those 
  which 
  apply 
  to 
  atoms 
  in 
  

   (45) 
  and 
  (46), 
  

  

  F 
  along 
  =g§{32(l-l'5cos^>- 
  

  

  X)tr 
  6 
  + 
  ...}, 
  (6: 
  

  

  + 
  h 
  f 
  (-40 
  + 
  200 
  cos 
  2 
  X- 
  175 
  cos^ 
  

  

  r 
  perp 
  = 
  ££: 
  J^§{l6r- 
  + 
  |(-40 
  + 
  70cos^),-e 
  + 
  ...y 
  (6 
  2) 
  

  

  In 
  these 
  equations 
  e 
  is 
  to 
  be 
  taken 
  as 
  negative, 
  the 
  charge 
  

   of 
  one 
  electron, 
  and 
  e 
  positive 
  or 
  negative. 
  If 
  F 
  s 
  i 
  ong 
  is 
  

   positive 
  it 
  denotes 
  an 
  attraction, 
  and 
  if 
  F 
  perp< 
  is 
  positive 
  the 
  

   force 
  is 
  towards 
  the 
  axis 
  and 
  from 
  the 
  equator. 
  If 
  the 
  

   charge 
  is 
  positive 
  and 
  situated 
  on 
  the 
  equator, 
  where 
  cosX 
  = 
  l, 
  

   the 
  atom 
  attracts 
  the 
  charge 
  toward 
  itself. 
  The 
  perpendicular 
  

   component 
  forces 
  it 
  toward 
  the 
  equator. 
  If 
  the 
  positive 
  

   charge 
  is 
  on 
  the 
  axis 
  of 
  the 
  atom 
  the 
  charge 
  is 
  repelled 
  from 
  

   the 
  atom. 
  At 
  the 
  critical 
  angle 
  H6° 
  18' 
  the 
  force 
  changes 
  

   from 
  attraction 
  to 
  repulsion 
  for 
  large 
  distances. 
  

  

  7 
  lie 
  Force 
  at 
  Large 
  Distances. 
  

  

  When 
  the 
  distance 
  between 
  two 
  atoms 
  is 
  very 
  large 
  com- 
  

   pared 
  with 
  molecular 
  range, 
  as 
  in 
  gravitational 
  problems, 
  

   the 
  equations 
  for 
  the 
  force 
  become 
  much 
  simplified. 
  ( 
  Consider 
  

   the 
  action 
  of 
  one 
  revolving 
  electron 
  upon 
  another 
  situated 
  in 
  

   the 
  most 
  general 
  position, 
  their 
  axes 
  making 
  any 
  angle 
  with 
  

   each 
  other. 
  Equations 
  (.18) 
  and 
  (23) 
  give 
  the 
  instantaneous 
  

  

  