﻿350 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  The 
  easiest 
  case 
  is 
  that 
  in 
  which 
  q 
  is 
  so 
  small 
  as 
  to 
  make 
  

   Kq~^^^ 
  negligible. 
  These 
  equations 
  then 
  take 
  the 
  same 
  form 
  

   as 
  (1) 
  with 
  F 
  replaced 
  by 
  ^ 
  + 
  F. 
  We 
  found 
  that 
  in 
  the 
  case 
  

   of 
  air 
  the 
  right-hand 
  side 
  of 
  (10) 
  must 
  be 
  made 
  8*6 
  times 
  as 
  

   large 
  as 
  it 
  is 
  to 
  give 
  the 
  facts 
  of 
  experiment. 
  Thus 
  for 
  air 
  

   then 
  we 
  have 
  d=7'6¥, 
  and 
  in 
  forming 
  the 
  theory 
  of 
  6 
  we 
  

   found 
  that 
  this 
  same 
  relation 
  must 
  hold 
  for 
  all 
  gases. 
  Thus 
  

   then 
  v\e 
  have 
  found 
  that 
  the 
  small 
  ion 
  in 
  gases 
  does 
  not 
  

   consist 
  of 
  a 
  cluster 
  of 
  molecules, 
  but 
  that 
  its 
  electric 
  charge 
  

   causes 
  it 
  to 
  experience 
  a 
  viscosity 
  of 
  electric 
  origin 
  and 
  also 
  

   to 
  behave 
  as 
  if 
  it 
  had 
  an 
  enlarged 
  radius. 
  Introducing 
  the 
  

   factor 
  S'6 
  into 
  the 
  right-hand 
  side 
  of 
  (10) 
  we 
  get 
  as 
  the 
  

   general 
  equation 
  for 
  the 
  mobility 
  of 
  a 
  small 
  ion 
  the 
  equation 
  

  

  ^ 
  -7- 
  = 
  30- 
  9N3a3^7??3r3 
  [1 
  + 
  2 
  {(/>(«! 
  + 
  as) 
  + 
  i/r(ai 
  + 
  ag) 
  j/mg^s^] 
  w 
  

  

  ^^ 
  l 
  = 
  7iT-i/2(l 
  + 
  C7T)/A'. 
  

  

  In 
  establishing 
  this 
  we 
  have 
  confirmed 
  the 
  theory 
  of 
  

   electrically 
  induced 
  viscosity 
  by 
  finding 
  that 
  it 
  is 
  the 
  chief 
  

   factor 
  in 
  determining 
  the 
  mobility 
  of 
  ions 
  in 
  gases. 
  We 
  

   have 
  also 
  found 
  that 
  the 
  potential 
  energy 
  of 
  ion 
  and 
  molecule 
  

   in 
  contact 
  in 
  gases 
  plays 
  the 
  same 
  part 
  as 
  the 
  mutual 
  potential 
  

   energy 
  of 
  molecules 
  in 
  contact 
  in 
  the 
  theory 
  of 
  the 
  ordinary 
  

   viscosity 
  of 
  gases. 
  Investigations 
  of 
  C 
  in 
  the 
  theory 
  of 
  

   gaseous 
  viscosity 
  and 
  of 
  C^ 
  in 
  (L2) 
  enable 
  us 
  to 
  study 
  the 
  

   potential 
  energy 
  of 
  molecules 
  under 
  ideally 
  simple 
  conditions. 
  

   To 
  find 
  C^ 
  directly 
  for 
  any 
  substance 
  experiments 
  like 
  those 
  

   of 
  Phillips 
  on 
  air 
  will 
  be 
  necessary. 
  But 
  from 
  the 
  known 
  

   values 
  of 
  u 
  for 
  different 
  substances 
  we 
  can 
  make 
  a 
  preli- 
  

   minary 
  indirect 
  determination 
  of 
  C^ 
  and 
  therefore 
  of 
  

  

  From 
  (12) 
  we 
  have, 
  when 
  f/E/^A' 
  — 
  volt/cm., 
  and 
  the 
  tempe- 
  

   rature 
  and 
  pressure 
  are 
  fixed, 
  

  

  umyV(l 
  + 
  C7T) 
  = 
  constant. 
  . 
  . 
  . 
  (13) 
  

  

  This 
  is 
  the 
  origin 
  of 
  a 
  roughly 
  approximate 
  law 
  announced 
  

  

  by 
  Lenard 
  that 
  um}^^ 
  is 
  constant 
  for 
  several 
  gases. 
  For 
  both 
  

  

  positive 
  and 
  negative 
  ion 
  in 
  air 
  at 
  15° 
  C. 
  we 
  have 
  seen 
  that 
  

  

  u{l 
  + 
  C'/T) 
  = 
  A'Ti/2 
  = 
  0-222 
  x 
  2SS^^^ 
  a 
  = 
  l'19 
  x 
  lO-^. 
  

  

  It 
  is 
  rather 
  more 
  convenient 
  at 
  present 
  to 
  use 
  B^^ 
  instead 
  of 
  

   a^, 
  B 
  being 
  the 
  limiting 
  volume 
  of 
  a 
  gramme-molecule, 
  and 
  

   to 
  use 
  the 
  ordinary 
  molecular 
  mass 
  M 
  instead 
  of 
  w, 
  namely 
  

   28*86 
  for 
  air. 
  The 
  relation 
  between 
  B 
  and 
  a 
  is 
  

   B 
  = 
  4xl0i9x22430(2a)3. 
  

  

  (12) 
  

  

  