﻿572 
  Prof, 
  J. 
  S. 
  Townsend 
  on 
  the 
  Conductivity 
  

  

  -ST 
  

  

  The 
  required 
  value 
  of 
  — 
  is 
  found 
  by 
  drawing 
  a 
  tangent 
  

   from 
  the 
  origin 
  to 
  the 
  curve. 
  The 
  values 
  of 
  — 
  • 
  for 
  which 
  

  

  a 
  is 
  a 
  maximum 
  are 
  thus 
  found 
  to 
  be 
  approximately 
  :— 
  - 
  

   350, 
  160, 
  380 
  for 
  air, 
  hydrogen, 
  and 
  carbonic 
  acid 
  

   respectively. 
  

  

  Stoletow 
  (loc. 
  cit.) 
  obtained 
  this 
  result 
  for 
  air 
  experi- 
  

   mentally. 
  He 
  found 
  that 
  when 
  the 
  force 
  was 
  constant 
  and 
  

   the 
  pressure 
  variable, 
  the 
  conductivity 
  reached 
  a 
  maximum 
  

   for 
  a 
  certain 
  critical 
  pressure. 
  He 
  also 
  found 
  that 
  this 
  

   pressure 
  was 
  proportional 
  to 
  the 
  force 
  and 
  independent 
  of 
  

   the 
  distance 
  between 
  the 
  plates. 
  When 
  the 
  force 
  is 
  expressed 
  

   in 
  volts 
  per 
  centimetre, 
  the 
  critical 
  pressure, 
  according 
  to 
  

   Stoletow's 
  experiments, 
  is 
  given 
  by 
  the 
  equation 
  : 
  

  

  _ 
  X 
  

  

  -^~380' 
  

  

  which 
  is 
  practically 
  the 
  same 
  result 
  that 
  I 
  obtained 
  by 
  

  

  X 
  

  

  drawing 
  a 
  tangent 
  to 
  the 
  curve. 
  The 
  exact 
  value 
  of 
  — 
  which 
  

  

  gives 
  the 
  critical 
  pressure 
  cannot 
  be 
  found 
  very 
  accurately 
  

   by 
  either 
  of 
  these 
  methods, 
  so 
  that 
  we 
  cannot 
  expect 
  the 
  two 
  

   numbers 
  to 
  agree 
  very 
  accurately. 
  

  

  We 
  can, 
  however, 
  fix 
  the 
  maximum 
  value 
  of 
  a. 
  with 
  greater 
  

   precision. 
  It 
  can 
  be 
  easily 
  seen 
  from 
  the 
  theory 
  that 
  the 
  

   maximum 
  value 
  of 
  a 
  for 
  a 
  given 
  force 
  X 
  is 
  got 
  from 
  the 
  

   slope 
  of 
  the 
  tangent 
  which 
  passes 
  through 
  the 
  origin. 
  

  

  The 
  coordinates 
  of 
  the 
  points 
  of 
  contact 
  of 
  the 
  tangents 
  to 
  

   the 
  curves 
  for 
  air, 
  hydrogen, 
  and 
  carbonic 
  acid 
  are 
  respectively 
  : 
  

  

  - 
  =5-2, 
  2-35, 
  6-1 
  

   P 
  

  

  ?=350, 
  160, 
  380. 
  

   P 
  

  

  Hence 
  when 
  X 
  is 
  given 
  and 
  the 
  pressure 
  altered 
  so 
  as 
  to 
  

   obtain 
  the 
  maximum 
  conductivity, 
  the 
  value 
  of 
  a 
  will 
  be 
  

  

  5-2 
  X 
  2-35 
  X 
  6-1 
  X 
  

  

  350 
  ' 
  160 
  ' 
  380 
  

  

  for 
  the 
  three 
  gases 
  respectively. 
  

  

  It 
  is 
  remarkable 
  that 
  these 
  three 
  numbers 
  are 
  nearly 
  equal. 
  

   7. 
  If 
  the 
  negative 
  ions 
  with 
  which 
  we 
  have 
  been 
  dealing 
  

  

  