﻿Jfolecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  49 
  

  

  Although 
  these 
  curves 
  in 
  terms 
  of 
  /3v 
  are 
  independent 
  of 
  the 
  

  

  speed 
  of 
  the 
  electrons, 
  the 
  distance, 
  v, 
  and 
  the 
  force 
  do 
  depend 
  

  

  upon 
  the 
  value 
  of 
  /3. 
  The 
  two 
  figures, 
  9 
  and 
  10, 
  represent 
  

  

  the 
  lines 
  of 
  equal 
  force 
  between 
  two 
  atoms. 
  In 
  making 
  such 
  

  

  figures 
  it 
  is 
  necessary 
  to 
  assume 
  a 
  definite 
  pair 
  of 
  atoms, 
  and 
  

  

  also 
  the 
  value 
  of 
  the 
  speed 
  of 
  the 
  electrons 
  ; 
  for 
  the 
  results 
  

  

  differ 
  for 
  different 
  atoms 
  and 
  the 
  speeds 
  of 
  their 
  electrons. 
  

  

  The 
  case 
  represented 
  is 
  that 
  of 
  two 
  similar 
  atoms 
  each 
  

  

  having 
  but 
  a 
  single 
  ring 
  of 
  three 
  electrons, 
  and 
  it 
  is 
  assumed 
  

  

  that 
  their 
  linear 
  velocity 
  is 
  1/316 
  that 
  of 
  light, 
  that 
  is, 
  

  

  ^ 
  = 
  •00316 
  and 
  /3 
  2 
  = 
  10 
  -5 
  . 
  The 
  dotted 
  curves 
  of 
  zero 
  force 
  

  

  are 
  alike 
  on 
  the 
  two 
  charts, 
  and 
  are 
  similar 
  to 
  the 
  /3u 
  curves 
  

  

  in 
  fig. 
  8 
  (PL 
  I.). 
  The 
  full 
  lines 
  are 
  lines 
  of 
  equal 
  force, 
  fig. 
  9 
  

  

  showing 
  the 
  force 
  along 
  the 
  radius 
  vector 
  joining 
  the 
  point 
  

  

  and 
  the 
  origin, 
  that 
  is, 
  "joining 
  the 
  two 
  atoms, 
  and 
  fig. 
  10 
  

  

  showing 
  the 
  force 
  upon 
  the 
  atom 
  perpendicular 
  to 
  this 
  radius, 
  

  

  in 
  the 
  meridian 
  plane. 
  The 
  rate 
  of 
  change 
  of 
  the 
  force 
  and 
  

  

  its 
  direction 
  at 
  each 
  point 
  are 
  shown. 
  In 
  passing 
  from 
  one 
  

  

  curve 
  to 
  the 
  adjacent 
  curve 
  the 
  force 
  changes 
  by 
  a 
  constant 
  

  

  3 
  e 
  2 
  

   amount, 
  — 
  , 
  — 
  , 
  x 
  10 
  16 
  dyne. 
  Upon 
  the 
  axis 
  the 
  force 
  is 
  an 
  

   lb 
  a 
  2 
  J 
  ' 
  

  

  attraction 
  which 
  increases 
  as 
  the 
  atoms 
  approach 
  from 
  an 
  

  

  infinite 
  distance 
  until 
  a 
  point 
  of 
  maximum 
  force 
  is 
  reached, 
  

  

  after 
  passing 
  which 
  the 
  force 
  decreases 
  to 
  zero 
  and 
  reverses 
  

  

  direction, 
  becoming 
  a 
  repulsion. 
  The 
  rate 
  of 
  change 
  is 
  then 
  

  

  very 
  rapid 
  with 
  decreasing 
  distance. 
  Some 
  curves 
  showing 
  

  

  the 
  variation 
  of 
  the 
  force 
  on 
  the 
  axis 
  and 
  on 
  the 
  equator 
  as 
  

  

  well 
  as 
  along 
  several 
  fixed 
  radii, 
  each 
  curve 
  being 
  designated 
  

  

  by 
  a 
  number 
  which 
  is 
  the 
  square 
  of 
  cosine 
  \, 
  are 
  given 
  in 
  

  

  fig. 
  11 
  for 
  the 
  forces 
  along 
  the 
  radius, 
  and 
  fig. 
  12 
  for 
  forces 
  

  

  perpendicular 
  to 
  the 
  radius. 
  The 
  force 
  is 
  a 
  repulsion 
  at 
  all 
  

  

  distances 
  on 
  the 
  equator. 
  It 
  should 
  be 
  stated, 
  however, 
  that 
  

  

  for 
  small 
  distances, 
  such 
  as 
  that 
  between 
  atoms 
  whose 
  positive 
  

  

  spheres 
  are 
  in 
  contact, 
  the 
  convergence 
  of 
  the 
  series 
  upon 
  

  

  which 
  these 
  formulae 
  depend 
  is 
  not 
  rapid, 
  and 
  they 
  must 
  not 
  

  

  be 
  employed 
  for 
  very 
  small 
  distances. 
  In 
  this 
  example 
  the 
  

  

  formulae 
  would 
  be 
  good 
  for 
  values 
  of 
  r 
  = 
  10 
  or 
  more. 
  In 
  

  

  figs. 
  9 
  and 
  10 
  the 
  scale 
  on 
  the 
  equatorial 
  line 
  gives 
  the 
  values 
  

  

  of 
  r. 
  

  

  More 
  than 
  two 
  Atoms 
  per 
  Molecule. 
  

  

  It 
  has 
  been 
  shown 
  that 
  there 
  are 
  at 
  least 
  two 
  stable 
  positions 
  

   in 
  which 
  three 
  atoms 
  may 
  come 
  to 
  equilibrium. 
  The 
  degree 
  

   of 
  stability 
  differs 
  in 
  each 
  case, 
  and 
  no 
  attempt 
  has 
  yet 
  been 
  

   made 
  to 
  measure 
  it, 
  and 
  to 
  predict 
  which 
  arrangement 
  would 
  

   be 
  the 
  more 
  likely 
  to 
  persist 
  and 
  withstand 
  the 
  shocks 
  received 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  151. 
  July 
  1913. 
  E 
  

  

  