﻿358 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  ions 
  in 
  gases 
  under 
  different 
  pressures 
  has 
  been 
  subjected 
  to 
  

   some 
  criticism 
  in 
  the 
  Phil. 
  Mag. 
  (see 
  Gr. 
  W. 
  Walker, 
  viii. 
  

   1904, 
  p. 
  206, 
  Eobb, 
  x. 
  1905, 
  p. 
  237), 
  and 
  by 
  Langevin 
  

   {Journ. 
  de 
  Phys, 
  [4] 
  iv. 
  1905, 
  p. 
  322), 
  who 
  shows 
  that 
  on 
  

   the 
  basis 
  of 
  the 
  Ni''^ 
  formula 
  it 
  can 
  be 
  proved 
  that 
  in 
  the 
  

   experiments 
  at 
  a 
  pressure 
  of 
  one 
  atmo 
  diffusion 
  would 
  cause 
  

   one-tenth 
  o£ 
  the 
  effect 
  recorded 
  as 
  recombination 
  by 
  McClung, 
  

   ile 
  at 
  one-eighth 
  o£ 
  an 
  atmo 
  at 
  least 
  eight-tenths 
  o£ 
  the 
  

   recorded 
  effect 
  is 
  to 
  be 
  credited 
  to 
  diffusion. 
  Diffusion 
  must 
  

   also 
  have 
  produced 
  a 
  large 
  effect 
  in 
  the 
  large 
  apparent 
  varia- 
  

   tion 
  o£ 
  a 
  with 
  temperature 
  in 
  later 
  experiments 
  o£ 
  McClung's. 
  

   We 
  can 
  take 
  McClung's 
  experiments 
  at 
  1, 
  2, 
  and 
  3 
  atmos 
  to 
  

   be 
  complicated 
  with 
  not 
  more 
  than 
  10 
  per 
  cent, 
  of 
  diffusion 
  

   effect. 
  I 
  find 
  that 
  his 
  results 
  can 
  be 
  represented 
  as 
  well 
  by 
  

   the 
  Ni^/^ 
  formula 
  as 
  by 
  the 
  Ni^. 
  The 
  reason 
  for 
  this 
  fact 
  

   is 
  that 
  the 
  residual 
  experimental 
  error 
  in 
  these 
  difficult 
  

   measurements 
  is 
  such 
  that 
  when 
  Ni 
  is 
  graphed 
  as 
  ordinate 
  

   with 
  t 
  as 
  abscissa, 
  the 
  points 
  lie 
  on 
  an 
  area 
  which 
  is 
  traversed 
  

   just 
  as 
  well 
  by 
  the 
  curve 
  which 
  makes 
  Ni""^/^ 
  linear 
  in 
  t 
  as 
  

   that 
  which 
  makes 
  Ni~^ 
  linear 
  in 
  t. 
  Thus 
  I 
  think 
  I 
  have 
  

   shown 
  that 
  the 
  experimental 
  evidence 
  upon 
  which 
  J. 
  J. 
  

   Thomson 
  relies 
  for 
  verification 
  of 
  the 
  Ni^ 
  formula 
  (15) 
  is 
  on 
  

   the 
  whole 
  a 
  little 
  more 
  favourable 
  to 
  the 
  l^i^l^ 
  formula 
  (17). 
  

   But 
  (15) 
  fails 
  to 
  apply 
  to 
  the 
  experiments 
  of 
  Barus 
  given 
  

   previously 
  in 
  verification 
  of 
  (17), 
  which 
  is 
  therefore 
  the 
  

   better 
  approximation 
  to 
  the 
  truth. 
  In 
  this 
  connexion 
  it 
  

   would 
  be 
  important 
  to 
  make 
  a 
  full 
  review 
  of 
  Langevin's 
  

   own 
  experiments, 
  which, 
  on 
  account 
  of 
  wide 
  variations 
  of 
  

   the 
  conditions, 
  he 
  considers 
  to 
  verify 
  the 
  two 
  laws 
  that 
  ionic 
  

   velocity 
  is 
  proportional 
  to 
  strength 
  of 
  electric 
  field, 
  and 
  that 
  

   the 
  rate 
  of 
  recombination 
  of 
  the 
  two 
  sorts 
  of 
  ions 
  is 
  propor- 
  

   tional 
  to 
  the 
  product 
  of 
  their 
  numbers 
  per 
  c.c, 
  or 
  the 
  two 
  

   electrical 
  densities 
  which 
  he 
  denotes 
  by 
  p 
  and 
  n. 
  Thus 
  

   Langevin 
  holds 
  that 
  his 
  experiments 
  verify 
  the 
  l^i 
  formula. 
  

   The 
  theory 
  of 
  his 
  method 
  of 
  experimenting 
  is 
  rather 
  elaborate, 
  

   so 
  he 
  contents 
  himself 
  with 
  giving 
  only 
  final 
  results 
  and 
  

   samples 
  of 
  his 
  data 
  which 
  are 
  not 
  sufficient 
  to 
  allow 
  me 
  to 
  

   investigate 
  how 
  the 
  Nj^/^ 
  formula 
  would 
  apply 
  to 
  his 
  experi- 
  

   ments 
  directly. 
  But 
  the 
  theory 
  by 
  which 
  the 
  Ni^/^ 
  formula 
  

   is 
  established 
  receives 
  indirect 
  support 
  from 
  Langevin's 
  

   results, 
  if 
  we 
  work 
  it 
  out 
  in 
  greater 
  detail. 
  We 
  must 
  inves- 
  

   tigate 
  A 
  in 
  (17) 
  more 
  closely. 
  Imagine 
  the 
  two 
  sorts 
  of 
  

   ions 
  for 
  an 
  instant 
  uniformly 
  distributed, 
  alternately 
  at 
  the 
  

   corners 
  of 
  a 
  uniform 
  cubical 
  subdivision 
  of 
  the 
  volume 
  which 
  

   they 
  occupy. 
  On 
  account 
  of 
  its 
  thermal 
  velocity 
  each 
  ion 
  

   will 
  move 
  away 
  from 
  this 
  imaginary 
  position, 
  and 
  the 
  amount 
  

  

  