﻿364 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  The 
  main 
  feature 
  of 
  (25) 
  being 
  verified, 
  we 
  shall 
  now 
  apply 
  

   it 
  to 
  investigate 
  the 
  remarkable 
  variation 
  of 
  u 
  with 
  tempera- 
  

   ture. 
  So 
  we 
  must 
  consider 
  f 
  more 
  closely. 
  The 
  first 
  

   business 
  is 
  to 
  find 
  the 
  number 
  of 
  HgO 
  molecules 
  kept 
  captive 
  

   by 
  an 
  electron, 
  or 
  rather 
  by 
  our 
  nucleolus. 
  We 
  have 
  already 
  

   seen 
  that 
  an 
  electron 
  in 
  air 
  increases 
  the 
  density 
  of 
  the 
  air 
  

   round 
  it. 
  In 
  the 
  same 
  way, 
  but 
  to 
  a 
  greater 
  extent, 
  it 
  

   increases 
  the 
  density 
  of 
  the 
  HgO 
  round 
  it, 
  because 
  HgO 
  has 
  

   an 
  exceptionally 
  large 
  electric 
  moment 
  es. 
  For 
  this 
  reason 
  

   an 
  electron 
  can 
  constrain 
  molecules 
  of 
  HgO 
  to 
  describe 
  orbits 
  

   of 
  finite 
  range 
  round 
  it. 
  In 
  the 
  sequel, 
  as 
  before, 
  let 
  suffix 
  1 
  

   refer 
  to 
  the 
  nucleolus, 
  3 
  to 
  the 
  gas 
  such 
  as 
  air 
  in 
  which 
  the 
  

   ion 
  is 
  moving, 
  and 
  2 
  to 
  HgO. 
  The 
  electric 
  moment 
  of 
  H2O 
  

   is 
  es2, 
  and 
  if 
  an 
  electron 
  e 
  is 
  at 
  distance 
  r 
  along 
  the 
  axis 
  from 
  

   the 
  centre 
  of 
  HgO, 
  their 
  mutual 
  potential 
  energy 
  is 
  e^sjr^. 
  

   Now 
  when 
  the 
  nucleolus 
  has 
  captured 
  one 
  or 
  two 
  H2O 
  

   molecules, 
  its 
  velocity 
  of 
  translation 
  may 
  be 
  neglected 
  in 
  

   comparison 
  with 
  that 
  of 
  the 
  air 
  molecules 
  and 
  of 
  the 
  free 
  HgO. 
  

   So 
  we 
  treat 
  the 
  electron 
  as 
  at 
  rest, 
  and 
  the 
  free 
  HgO 
  molecules 
  

   as 
  if 
  moving 
  with 
  velocity 
  v^ 
  past 
  it. 
  The 
  dynamical 
  con- 
  

   dition 
  that 
  a 
  molecule 
  of 
  H2O 
  with 
  velocity 
  v^ 
  at 
  distance 
  t 
  

   should 
  just 
  be 
  able 
  to 
  travel 
  to 
  infinity 
  is 
  m2t'2V2 
  = 
  ^^A^- 
  

   Within 
  this 
  radius 
  r 
  the 
  electron 
  gathers 
  a 
  number 
  of 
  HgO 
  

   molecules 
  whose 
  axes 
  all 
  tend 
  to 
  pass 
  through 
  it, 
  so 
  that 
  

   radially 
  these 
  molecules 
  will 
  attract 
  one 
  another, 
  while 
  each 
  

   will 
  repel 
  its 
  lateral 
  neighbours 
  which 
  are 
  at 
  the 
  same 
  

   distance 
  from 
  the 
  electron. 
  Thus 
  we 
  have 
  a 
  highly 
  charac- 
  

   teristic 
  field 
  of 
  force 
  in 
  our 
  cluster 
  of 
  H2O 
  molecules. 
  The 
  

   lateral 
  repulsions 
  will 
  nearly 
  equilibrate 
  one 
  another, 
  so 
  that 
  

   we 
  can 
  treat 
  all 
  the 
  H2O 
  molecules 
  as 
  revolving 
  round 
  the 
  

   centre 
  with 
  constant 
  average 
  linear 
  velocity 
  v^. 
  So 
  it 
  is 
  

   necessary 
  to 
  take 
  account 
  of 
  the 
  radial 
  cohesion. 
  The 
  

   cohesional 
  potential 
  energy 
  of 
  a 
  molecule 
  of 
  H2O 
  just 
  

   retained 
  on 
  the 
  outer 
  surface 
  of 
  radius 
  r 
  by 
  the 
  combined 
  

   effect 
  of 
  attraction 
  from 
  electron 
  and 
  of 
  cohesion 
  may 
  be 
  

   assumed 
  to 
  be 
  approximately 
  constant 
  and 
  be 
  written 
  in 
  

   kinetic 
  form 
  m.^x{3^l^. 
  Hence 
  to 
  determine 
  t 
  we 
  have 
  the 
  

   more 
  complete 
  equation 
  

  

  m2(^2'-^f^2')/2 
  = 
  eV^' 
  (26) 
  

  

  Now 
  that 
  we 
  have 
  taken 
  account 
  of 
  the 
  cohesional 
  energy, 
  

   we 
  can 
  make 
  a 
  correct 
  enough 
  average 
  case 
  by 
  treating 
  all 
  

   the 
  water 
  molecules 
  as 
  gathered 
  on 
  the 
  surface 
  of 
  this 
  sphere 
  

   of 
  radius 
  r 
  round 
  the 
  nucleolus 
  and 
  all 
  moving 
  with 
  the 
  

   average 
  velocity 
  of 
  the 
  ion. 
  We 
  shall 
  take 
  the 
  number 
  of 
  

   HgO 
  molecules 
  per 
  unit 
  surface 
  of 
  this 
  sphere 
  to 
  be 
  proper- 
  

  

  