﻿222 
  Mr. 
  P. 
  J. 
  Kirkby 
  on 
  the 
  Electrical 
  Conductivities 
  

  

  440 
  X 
  p, 
  we 
  may 
  suppose 
  05 
  to 
  be 
  the 
  mean 
  free 
  path 
  of 
  a 
  

   negative 
  ion, 
  and 
  that 
  whenever 
  its 
  free 
  path 
  constitutes 
  a 
  

   fall 
  through 
  more 
  than 
  22 
  volts, 
  the 
  molecular 
  impact 
  which 
  

   terminates 
  the 
  free 
  path 
  breaks 
  up 
  the 
  molecule 
  struck 
  into 
  

   two 
  other 
  ions. 
  This 
  is, 
  of 
  course, 
  only 
  a 
  statistical 
  inter- 
  

   pretation. 
  Some 
  collisions 
  which 
  terminate 
  a 
  greater 
  fall 
  

   than 
  one 
  of 
  22 
  volts 
  are 
  ineffective. 
  Others 
  which 
  terminate 
  

   a 
  lesser 
  fall 
  than 
  this 
  may 
  be 
  effective. 
  

  

  13. 
  When 
  X<440 
  the 
  above 
  equation 
  fails 
  to 
  represent 
  

   the 
  curve. 
  The 
  value 
  of 
  a 
  x 
  

  

  20 
  e-uo/Xx 
  

  

  is 
  then 
  too 
  small. 
  The 
  smallest 
  value 
  of 
  X 
  x 
  which 
  gives 
  an 
  

   appreciable 
  value 
  of 
  a 
  x 
  is 
  40. 
  The 
  curve 
  may 
  then 
  be 
  repre- 
  

   sented 
  for 
  a 
  small 
  range 
  of 
  Xj 
  by 
  

  

  220 
  

  

  a 
  1 
  = 
  20^"x- 
  1 
  (2) 
  

  

  Now 
  -£$ 
  cm. 
  is 
  about 
  the 
  true 
  free 
  path 
  of 
  a 
  negative 
  ion 
  

   in 
  a 
  pressure 
  of 
  1 
  mm., 
  so 
  that 
  this 
  equation 
  will 
  admit 
  of 
  a 
  

   similar 
  statistical 
  interpretation 
  to 
  that 
  given 
  to 
  the 
  equation 
  

  

  440 
  

  

  ai 
  = 
  20«"xl, 
  (1) 
  

  

  provided 
  the 
  field 
  of 
  force 
  is 
  constant 
  and 
  its 
  intensity 
  equal 
  

   to 
  40 
  p. 
  In 
  the 
  case 
  of 
  the 
  equation 
  (1) 
  just 
  written 
  the 
  

   only 
  condition 
  is 
  that 
  X 
  x 
  must 
  exceed 
  440 
  and 
  not 
  vary 
  too 
  

   rapidly. 
  

  

  14. 
  To 
  apply 
  these 
  results 
  it 
  is 
  to 
  be 
  remarked 
  that 
  in 
  the 
  

   theory 
  of 
  gases 
  only 
  100 
  e~ 
  3 
  , 
  i. 
  e. 
  only 
  about 
  5 
  paths 
  in 
  100, 
  

   exceed 
  three 
  times 
  the 
  mean 
  free 
  path 
  L. 
  Let 
  V 
  be 
  the 
  

   potential 
  of 
  the 
  aluminium 
  cylinder 
  when 
  the 
  current 
  shows 
  

   a 
  tendency 
  to 
  increase 
  along 
  with 
  the 
  force, 
  the 
  increase 
  

   being 
  slightly 
  less 
  than 
  5 
  per 
  cent. 
  

  

  Then 
  if 
  equation 
  (1) 
  held 
  for 
  all 
  values 
  of 
  X 
  x 
  we 
  should 
  

   have 
  

  

  t+3L 
  y 
  

  

  r 
  

  

  J 
  a 
  

  

  b 
  dr 
  = 
  22 
  volts, 
  

   r 
  lo£ 
  - 
  

  

  and 
  if 
  equation 
  (2) 
  held 
  universally 
  

  

  J 
  

  

  " 
  +SL 
  V 
  *= 
  11 
  volts. 
  

  

  r 
  log 
  - 
  

  

  