﻿218 
  Mr. 
  P. 
  J. 
  Kirkby 
  on 
  the 
  Electrical 
  Conductivities 
  

  

  to 
  errors 
  of 
  observation; 
  But 
  when 
  the 
  potential 
  was 
  lowered 
  

   to 
  — 
  74 
  the 
  negative 
  current 
  began 
  perceptibly 
  to 
  increase; 
  for 
  

   then 
  it 
  had 
  begun 
  to 
  exceed 
  the 
  positive 
  current 
  which 
  is 
  

   represented 
  too 
  highly 
  by 
  20. 
  Therefore 
  the 
  voltage 
  of 
  the 
  

   cylinder 
  beyond 
  which 
  the 
  negative 
  current 
  ceases 
  to 
  be 
  prac- 
  

   tically 
  C 
  lies 
  between 
  —37 
  and 
  —74. 
  And, 
  similarly, 
  it 
  

   may 
  be 
  seen 
  about 
  at 
  what 
  potential 
  of 
  the 
  cylinder 
  the 
  

   negative 
  current 
  begins 
  to 
  increase 
  for 
  the 
  other 
  pressures 
  of 
  

   the 
  tables. 
  

  

  7. 
  Unfortunately, 
  at 
  the 
  low 
  pressures 
  given 
  the 
  initial 
  

   ionization 
  was 
  so 
  small 
  that 
  it 
  would 
  have 
  been 
  useless 
  to 
  

   employ 
  a 
  voltage 
  numerically 
  lower 
  than 
  —37 
  with 
  the 
  view 
  

   of 
  finding 
  C 
  . 
  To 
  bring 
  C 
  within 
  the 
  range 
  of 
  accurate 
  

   observation 
  the 
  aluminium 
  cylinder 
  would 
  require 
  to 
  be 
  

   larger. 
  On 
  the 
  other 
  hand, 
  it 
  was 
  too 
  large 
  to 
  admit 
  of 
  an 
  

  

  evaluation 
  of 
  the 
  integral 
  I 
  r 
  dr 
  e.ia 
  in 
  the 
  expression 
  

  

  J 
  a 
  

  

  given 
  above 
  for 
  C, 
  though 
  this 
  would 
  be 
  possible 
  under 
  certain 
  

   more 
  restricted 
  circumstances, 
  by 
  using 
  the 
  approximate 
  form 
  

   for 
  a, 
  which 
  is 
  given 
  later. 
  

  

  8. 
  Professor 
  Townsend 
  gave 
  a/p 
  both 
  by 
  means 
  of 
  a 
  curve 
  

   determined 
  experimentally 
  and 
  by 
  means 
  of 
  a 
  series 
  of 
  the 
  

   form 
  

  

  

  

  the 
  coefficients 
  of 
  which 
  he 
  partly 
  determined 
  (Phil. 
  Mag. 
  Feb. 
  

   1901) 
  . 
  But 
  his 
  numbers 
  were 
  found 
  to 
  be 
  quite 
  inadequate 
  to 
  the 
  

   present 
  case 
  where 
  the 
  circumstances 
  are 
  different 
  from 
  his, 
  and 
  

   they 
  lead 
  to 
  a 
  series 
  which 
  scarcely 
  converges 
  at 
  all. 
  In 
  addition 
  

  

  this, 
  though, 
  since 
  Xoc 
  — 
  , 
  1 
  a 
  dr 
  can 
  be 
  immediately 
  found, 
  

  

  yet 
  the 
  next 
  step, 
  if 
  it 
  were 
  possible, 
  would 
  involve 
  great 
  

   labour. 
  Nevertheless 
  it 
  is 
  possible, 
  without 
  effecting 
  this 
  

   integration, 
  to 
  show 
  to 
  some 
  extent 
  that 
  the 
  figures 
  of 
  the 
  

   tables 
  are 
  in 
  agreement 
  with 
  Professor 
  Townsend's 
  results. 
  

  

  9. 
  The 
  force 
  between 
  the 
  cylinders 
  at 
  the 
  distance 
  r 
  from 
  

   their 
  common 
  axis 
  is 
  

  

  V| 
  

  

  ——b' 
  

  

  r 
  iotr 
  — 
  

   s 
  a 
  

  

  y 
  

  

  which,, 
  since 
  a 
  = 
  '0103 
  cm., 
  6 
  = 
  2*08 
  cm., 
  is 
  equal 
  to 
  „ 
  > 
  

  

  where 
  V 
  is 
  the 
  potential 
  of 
  the 
  outer 
  cylinder, 
  the 
  wire 
  being 
  

   approximately 
  at 
  zero. 
  The 
  strong 
  field 
  of 
  force 
  lies 
  close 
  

  

  to 
  

  

  