﻿the 
  Ions 
  of 
  Gases. 
  343 
  

  

  I£ 
  cohesional 
  and 
  electric 
  force 
  were 
  neglected, 
  the 
  mole- 
  

   cules 
  of 
  gas 
  being 
  treated 
  as 
  forceless 
  spheres 
  of 
  radins 
  ag, 
  

   mass 
  ?n3, 
  and 
  number 
  per 
  cm.^ 
  Ng, 
  suffix 
  1 
  allotting 
  the 
  cor- 
  

   responding 
  quantities 
  to 
  the 
  ion, 
  the 
  expression 
  found 
  for 
  Fw 
  

   in 
  the 
  kinetic 
  theory 
  of 
  " 
  perfect 
  " 
  gases 
  is 
  

  

  Vu=i-^^{a, 
  + 
  a,n2^(v^ 
  + 
  vi)l?,\^^^u 
  . 
  . 
  (2) 
  

  

  The 
  immediate 
  problem 
  is 
  to 
  find 
  how 
  we 
  must 
  modify 
  

   this 
  expression 
  to 
  provide 
  for 
  the 
  greater 
  frequency 
  of 
  

   collisions 
  caused 
  by 
  electric 
  and 
  cohesional 
  force. 
  The 
  

   treatment 
  can 
  proceed 
  almost 
  exactly 
  on 
  the 
  lines 
  of 
  my 
  

   paper 
  on 
  the 
  Viscosity 
  of 
  Gases 
  and 
  Molecular 
  Force 
  

   (Phil. 
  Mag. 
  [5] 
  xxxvi. 
  1893, 
  p. 
  507). 
  Select 
  an 
  ion 
  and 
  a 
  

   molecule 
  which 
  are 
  initially 
  far 
  enough 
  apart 
  to 
  exert 
  

   negligible 
  force 
  on 
  one 
  another 
  and 
  are 
  each 
  destined 
  to 
  

   have 
  their 
  next 
  collision 
  with 
  one 
  another. 
  Let 
  Vi 
  and 
  r^ 
  be 
  

   their 
  distances 
  from 
  the 
  centre 
  of 
  mass 
  of 
  the 
  two, 
  so 
  that 
  

   m^ri 
  = 
  m^r-^ 
  and 
  let 
  Vi 
  + 
  r^ 
  their 
  distance 
  apart 
  be 
  denoted 
  

   by 
  r. 
  Let 
  the 
  cohesional 
  force 
  between 
  them 
  be 
  —d<p{r)/dr 
  

   and 
  the 
  electric 
  force 
  between 
  the 
  electron 
  of 
  the 
  ion 
  and 
  

   the 
  molecule 
  be 
  ~d'\lr(r)/dr, 
  then 
  using 
  z 
  for 
  1/r 
  v^e 
  have 
  

   for 
  the 
  motion 
  of 
  the 
  molecule 
  relative 
  to 
  the 
  centre 
  of 
  mass 
  

   the 
  usual 
  equation 
  

  

  d^ 
  

  

  in 
  which 
  7*3 
  is 
  twice 
  the 
  area 
  swept 
  out 
  by 
  r^ 
  as 
  it 
  describes 
  

   the 
  angle 
  6. 
  From 
  this 
  for 
  the 
  equation 
  of 
  relative 
  motion 
  

   we 
  get 
  

  

  dh 
  m,-\-m, 
  /d^jr) 
  ^i/r(r) 
  \ 
  ^ 
  

  

  de^^'^^ 
  m^m,h'z\ 
  dr 
  ^ 
  dr 
  ) 
  ^^ 
  ' 
  ' 
  V^^ 
  

  

  and 
  then 
  the 
  first 
  integral 
  of 
  this 
  gives 
  the 
  equation 
  of 
  

   energy 
  

  

  in 
  which 
  v 
  is 
  the 
  relative 
  velocity 
  when 
  ion 
  and 
  molecule 
  are 
  

   at 
  distance 
  r 
  apart, 
  and 
  V 
  is 
  the 
  relative 
  velocity 
  when 
  r 
  is 
  

   so 
  great 
  that 
  the 
  relative 
  orbit 
  nearly 
  coincides 
  with 
  its 
  

   asymptote. 
  Let 
  h 
  be 
  the 
  length 
  of 
  the 
  perpendicular 
  from 
  

   the 
  ion 
  on 
  the 
  asymptote 
  so 
  that 
  k 
  = 
  hY. 
  When 
  the 
  relative 
  

   orbit 
  is 
  such 
  that 
  there 
  is 
  no 
  collision, 
  we 
  can 
  determine 
  the 
  

  

  2 
  A2 
  

  

  