﻿56S 
  Prof. 
  J. 
  S. 
  Townsend 
  on 
  the 
  Conductivity 
  

  

  shown 
  that 
  the 
  pressure 
  for 
  which 
  a 
  is 
  a 
  maximum 
  is 
  pro- 
  

   portional 
  to 
  X. 
  

  

  In 
  certain 
  cases 
  the 
  ratios 
  — 
  and 
  — 
  are 
  not 
  equal, 
  the 
  

  

  latter 
  being 
  much 
  the 
  larger 
  of 
  the 
  two. 
  This 
  effect 
  can 
  be 
  

   obtained 
  with 
  air 
  at 
  a 
  millimetre 
  pressure 
  when 
  the 
  maximum 
  

   potential-difference 
  between 
  the 
  plates 
  is 
  less 
  than 
  300 
  volts. 
  

   The 
  phenomenon 
  occurs 
  at 
  lower 
  voltages 
  in 
  hydrogen, 
  as 
  is 
  

   shown 
  by 
  the 
  experiments 
  given 
  in 
  Tables 
  X. 
  and 
  XL, 
  in 
  

   which 
  a 
  force 
  of 
  52'5 
  volts 
  per 
  millimetre 
  was 
  used. 
  With 
  

   this 
  force 
  the 
  conductivity 
  of 
  hydrogen 
  at 
  1*82 
  mms. 
  pressure 
  

   increases 
  by 
  the 
  factor 
  1*93 
  when 
  the 
  plates 
  are 
  separated 
  

   from 
  1 
  to 
  2 
  ' 
  or 
  from 
  2 
  to 
  3 
  millimetres 
  apart 
  ; 
  a 
  further 
  

   separation 
  of 
  the 
  plates 
  from 
  3 
  to 
  4 
  millimetres 
  increases 
  the 
  

   conductivity 
  by 
  the 
  factor 
  2*44. 
  This 
  process 
  continues 
  

   until 
  eventually 
  a 
  continuous 
  discharge 
  is 
  obtained 
  without 
  

   the 
  aid 
  of 
  the 
  ultra-violet 
  light. 
  With 
  the 
  same 
  force 
  (52*5 
  

   volts 
  per 
  millimetre) 
  a 
  similar 
  effect 
  is 
  produced 
  at 
  *82 
  milli- 
  

   metre, 
  the 
  ratios 
  — 
  and 
  — 
  a 
  being 
  2*14 
  and 
  2*81 
  respectively. 
  

  

  When 
  the 
  pressure 
  is 
  reduced 
  to 
  * 
  385 
  millimetre 
  or 
  increased 
  

   to 
  5*06 
  millimetres, 
  the 
  effect 
  disappears 
  for 
  distances 
  up 
  to 
  

   5 
  millimetres 
  between 
  the 
  plates. 
  I 
  hope 
  to 
  make 
  a 
  more 
  

   complete 
  examination 
  of 
  this 
  effect, 
  as 
  it 
  may 
  give 
  an 
  explana- 
  

   tion 
  of 
  some 
  of 
  the 
  complicated 
  phenomena 
  which 
  occur 
  in 
  

   the 
  vacuum-tube 
  discharge. 
  

  

  For 
  the 
  present 
  I 
  shall 
  confine 
  the 
  discussion 
  to 
  the 
  effects 
  

   produced 
  by 
  the 
  motion 
  of 
  the 
  negative 
  ions 
  through 
  the 
  gas. 
  

  

  5. 
  The 
  results 
  of 
  the 
  experiments 
  can 
  be 
  easily 
  represented 
  

   in 
  a 
  simple 
  form. 
  The 
  ratios 
  R 
  were 
  used 
  to 
  determine 
  the 
  

   values 
  of 
  u 
  corresponding 
  to 
  the 
  different 
  forces 
  and 
  pressures, 
  

   the 
  quantity 
  a 
  is 
  the 
  number 
  of 
  ions 
  which 
  a 
  negative 
  ion 
  pro- 
  

   duces 
  in 
  one 
  centimetre 
  of 
  the 
  gas 
  at 
  pressure 
  p 
  under 
  an 
  

   electric 
  force 
  X. 
  In 
  the 
  calculations 
  I 
  have 
  not 
  included 
  

  

  those 
  values 
  of 
  — 
  which 
  are 
  greater 
  than 
  — 
  by 
  an 
  amount 
  

   n 
  3 
  n 
  l 
  

  

  which 
  cannot 
  be 
  attributed 
  to 
  experimental 
  errors. 
  In 
  other 
  

   cases 
  the 
  mean 
  of 
  the 
  two 
  ratios 
  was 
  equated 
  to 
  e 
  aX 
  ' 
  2 
  in 
  order 
  

   to 
  determine 
  a, 
  *2 
  centimetre 
  being 
  the 
  increase 
  in 
  the 
  dis- 
  

   tance 
  between 
  the 
  plates. 
  

  

  As 
  I 
  have 
  already 
  pointed 
  out 
  (Phil. 
  Mag. 
  February 
  1901), 
  

   the 
  connexion 
  between 
  a, 
  X, 
  and 
  p 
  should 
  be 
  of 
  the 
  form 
  

  

  — 
  ). 
  The 
  simplest 
  method 
  of 
  testing 
  this 
  property 
  of 
  

  

  