﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds, 
  47 
  

  

  these 
  equations 
  — 
  the 
  product, 
  (3v, 
  which 
  is 
  proportional 
  to 
  the 
  

   distance 
  between 
  the 
  atoms, 
  and 
  the 
  qmgle 
  of 
  latitude, 
  X, 
  each 
  

   of 
  which 
  is 
  thereby 
  determined. 
  It 
  is 
  shown 
  later 
  that 
  these 
  

   values 
  give 
  the 
  stable 
  position 
  of 
  the 
  two 
  atoms. 
  These 
  

   equations 
  for 
  the 
  zero 
  force 
  along 
  and 
  perpendicular 
  to 
  the 
  

   line 
  joining 
  the 
  centres 
  of 
  the 
  atoms 
  are 
  shown 
  graphically 
  for 
  

   several 
  different 
  combinations 
  of 
  atoms 
  in 
  fig. 
  8 
  (PI. 
  I.). 
  The 
  

   perpendicular 
  zero-force 
  curve 
  is 
  precisely 
  the 
  same, 
  to 
  this 
  

   degree 
  of 
  approximation, 
  for 
  each 
  combination 
  of 
  the 
  atoms, 
  

   the 
  equation 
  being 
  independent 
  of 
  h 
  ; 
  but 
  the 
  along-force 
  

   curve 
  differs 
  according 
  to 
  the 
  particular 
  atoms. 
  At 
  the 
  

   points 
  of 
  intersection 
  of 
  the 
  two 
  curves 
  the 
  force 
  is 
  zero 
  

   in 
  all 
  directions, 
  and 
  the^e 
  are 
  stable 
  equilibrium 
  positions 
  

   for 
  the 
  two 
  atoms. 
  All 
  the 
  along-force 
  curves 
  intersect 
  the 
  

   axis 
  at 
  a 
  common 
  distance 
  /3V 
  = 
  5, 
  and 
  the 
  perpendicular 
  

   curve 
  intersects 
  at 
  a 
  greater 
  distance, 
  /3 
  2 
  t 
  ,3 
  = 
  10. 
  The 
  direc- 
  

   tions 
  of 
  the 
  forces 
  are 
  shown 
  by 
  the 
  arrows 
  ; 
  for 
  all 
  points 
  

   above 
  or 
  without 
  the 
  along-curves 
  the 
  force 
  is 
  an 
  attraction 
  

   towards 
  O, 
  changing 
  direction 
  at 
  the 
  curve 
  of 
  zero 
  force 
  ; 
  

   and 
  for 
  points 
  within, 
  the 
  force 
  is 
  a 
  repulsion. 
  The 
  perpen- 
  

   dicular 
  force 
  has 
  a 
  direction 
  away 
  from 
  the 
  axis 
  for 
  all 
  points 
  

   within 
  the 
  critical 
  distance 
  /3 
  2 
  v' 
  2 
  =lQ, 
  and 
  toward 
  the 
  axis 
  for 
  

   all 
  points 
  without. 
  At 
  the 
  equator 
  the 
  perpendicular 
  force 
  

   is 
  zero, 
  but 
  for 
  any 
  small 
  displacement 
  it 
  is 
  away 
  from 
  the 
  

   equator. 
  It 
  is 
  evident 
  from 
  the 
  figure 
  that 
  the 
  forces 
  restore 
  

   the 
  atom 
  to 
  the 
  intersection 
  of 
  the 
  along 
  and 
  perpendicular 
  

   curves 
  for 
  any 
  small 
  displacement 
  from 
  this 
  position. 
  

  

  It 
  has 
  been 
  shown, 
  equation 
  (38), 
  that 
  the 
  force 
  upon 
  the 
  

   atom 
  alon<r 
  the 
  circle 
  of 
  latitude, 
  that 
  is^ 
  perpendicular 
  to 
  the 
  

   paper 
  in 
  the 
  figure, 
  is 
  zero. 
  The 
  atom 
  is, 
  therefore, 
  free 
  to 
  

   sir.nd 
  at 
  any 
  point 
  in 
  either 
  of 
  the 
  two 
  circles 
  of 
  revolution 
  

   generated 
  by 
  the 
  along 
  and 
  perpendicular 
  curves 
  about 
  the 
  

   axis. 
  The 
  distance 
  between 
  the 
  atoms 
  of 
  the 
  different 
  

   diatomic 
  molecules 
  is 
  represented 
  by 
  the 
  radius 
  vector 
  from 
  

   the 
  origin 
  to 
  some 
  point 
  upon 
  the 
  perpendicular 
  curve, 
  being- 
  

   greater 
  than 
  j3 
  2 
  u 
  2 
  = 
  7'015 
  and 
  less 
  than 
  /3V=10. 
  If 
  the 
  

   distance 
  between 
  the 
  atoms 
  in 
  the 
  diatomic 
  molecule 
  is 
  the 
  

   dimension 
  of 
  the 
  molecule, 
  then 
  it 
  appears 
  that 
  all 
  diatomic 
  

   molecules 
  have 
  about 
  the 
  same 
  dimensions, 
  even 
  though 
  the 
  

   atoms 
  of 
  which 
  they 
  are 
  composed 
  vary 
  greatly 
  in 
  size. 
  

  

  It 
  seems 
  that 
  there 
  is 
  yet 
  great 
  uncertainty 
  in 
  the 
  deter- 
  

   mination 
  of 
  the 
  relative 
  dimensions 
  of 
  the 
  atom, 
  the 
  molecule, 
  

   and 
  the 
  average 
  space 
  required 
  by 
  a 
  single 
  molecule 
  within 
  

   a 
  solid 
  or 
  liquid 
  substance. 
  The 
  latter 
  may 
  be 
  found 
  with 
  a 
  

   fair 
  degree 
  of 
  accuracy 
  in 
  the 
  case 
  of 
  a 
  few 
  substances 
  which 
  

   can 
  be 
  measured 
  in 
  both 
  the 
  gaseous 
  and 
  the 
  liquid 
  forms. 
  

  

  