﻿362 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  and 
  H2 
  20. 
  If 
  with 
  COg 
  we 
  use 
  the 
  coefficient 
  509, 
  the 
  

   result 
  is 
  47. 
  If 
  in 
  (2a)2(l 
  + 
  CV288) 
  the 
  effective 
  diameter 
  

   of 
  Hg 
  were 
  increased 
  by 
  16 
  per 
  cent., 
  the 
  low 
  value 
  20 
  for 
  

   Hg 
  would 
  be 
  brought 
  up 
  to 
  50. 
  Such 
  uncertainties 
  must 
  be 
  

   cleared 
  up 
  by 
  new 
  experiments 
  and 
  by 
  fresh 
  interpretations 
  

   of 
  those 
  already 
  on 
  record, 
  which 
  have 
  been 
  worked 
  out 
  by 
  

   their 
  authors 
  on 
  the 
  basis 
  of 
  the 
  insufficient 
  Ni^ 
  formula. 
  

   The 
  foregoing 
  theory 
  of 
  A 
  may 
  be 
  summarised 
  by 
  its 
  results 
  

   in 
  the 
  following 
  way. 
  Let 
  I 
  be 
  the 
  mean 
  free 
  path 
  of 
  an 
  ion 
  

   in 
  the 
  gas, 
  being 
  •677/N37r(2a3)2(l 
  + 
  C7288) 
  which 
  for 
  

   nitrogen 
  (say, 
  air) 
  has 
  the 
  value 
  0*000004, 
  then 
  

  

  A 
  = 
  -0002484(^1 
  + 
  1^2) 
  ^-^'^^^^^/^^ 
  . 
  . 
  . 
  (24) 
  

  

  where 
  y2-2565 
  is 
  the 
  constant 
  length 
  0-000001754, 
  which 
  

   seems 
  to 
  be 
  a 
  fundamental 
  constant 
  in 
  the 
  physics 
  of 
  ions, 
  

   related 
  to 
  a 
  similar 
  one 
  in 
  the 
  statistics 
  of 
  molecules. 
  In 
  

   concluding 
  the 
  present 
  discussion 
  of 
  the 
  recombination 
  of 
  

   ions 
  it 
  may 
  be 
  helpful 
  to 
  notice 
  that 
  the 
  formula 
  (16) 
  of 
  

   Langevin 
  can 
  be 
  derived 
  from 
  our 
  method 
  of 
  laminse 
  in 
  the 
  

   following 
  way. 
  Suppose 
  the 
  ions 
  in 
  cubical 
  order 
  at 
  distance 
  

   R 
  apart. 
  In 
  a 
  laminar 
  distribution 
  we 
  get 
  density 
  ^/H^ 
  and 
  

   force 
  477^/11^ 
  between 
  the 
  laminae. 
  A 
  pair 
  of 
  oppositely 
  

   charged 
  ions 
  experiencing 
  this 
  force 
  would 
  acquire 
  relative 
  

   velocity 
  ^ire 
  {ui 
  + 
  u^jW 
  and 
  would 
  travel 
  R 
  in 
  time 
  

  

  RV47re 
  (2^1 
  + 
  ^2). 
  

  

  The 
  ions 
  begin 
  to 
  move 
  so 
  that 
  N 
  per 
  unit 
  volume 
  would 
  

   disappear 
  in 
  this 
  time. 
  In 
  the 
  actual 
  process 
  the 
  N 
  positive 
  

   and 
  the 
  N 
  negative 
  ions 
  do 
  not 
  suddenly 
  disappear 
  by 
  coming 
  

   together 
  simultaneously, 
  but 
  their 
  instantaneous 
  rate 
  dH^/dt 
  

   is 
  4:7re(ui 
  + 
  U2)^/W 
  and 
  since 
  NR^ 
  = 
  1, 
  this 
  is 
  (16) 
  with 
  e=l. 
  

   This 
  brings 
  out 
  the 
  assumption 
  involved 
  in 
  (15) 
  and 
  (16). 
  

  

  2. 
  The 
  Large 
  Ion 
  without 
  Liquid 
  or 
  Solid 
  Nucleus, 
  

  

  If 
  the 
  small 
  ion 
  investigated 
  in 
  the 
  previous 
  section 
  is 
  

   placed 
  in 
  a 
  gas 
  whose 
  molecules 
  it 
  attracts 
  so 
  strongly 
  that 
  it 
  

   carries 
  its 
  immediate 
  neighbours 
  with 
  it 
  as 
  satellites, 
  some 
  

   profound 
  changes 
  in 
  the 
  conditions 
  are 
  brought 
  about. 
  The 
  

   induced 
  viscosity 
  6 
  almost 
  disappears, 
  because 
  the 
  central 
  

   small 
  ion 
  has 
  but 
  little 
  relative 
  motion 
  to 
  its 
  immediate 
  

   neighbour 
  molecules 
  in 
  which 
  it 
  has 
  induced 
  electrization, 
  

   and 
  the 
  molecules 
  relative 
  to 
  which 
  it 
  is 
  moving 
  are 
  so 
  far 
  

   away 
  that 
  the 
  induced 
  electrization 
  in 
  them 
  is 
  small. 
  We 
  

   have 
  here 
  a 
  beautifully 
  simple 
  instance 
  of 
  the 
  way 
  in 
  which 
  

   a 
  rigidity 
  may 
  merge 
  into 
  a 
  viscosity. 
  It 
  is 
  probable 
  that 
  a 
  

  

  