﻿366 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  mean 
  values 
  o£ 
  u 
  in 
  cm. 
  /sec. 
  for 
  d^jdx 
  = 
  volt/cm., 
  and 
  

   in 
  the 
  third 
  10^VT'^/*^(T-270) 
  which 
  by 
  (27) 
  is 
  to 
  be 
  

   constant. 
  

  

  Table 
  V. 
  

  

  Temp. 
  C 
  170° 
  110° 
  100° 
  70° 
  30° 
  16° 
  

  

  100?^ 
  39 
  17 
  16 
  10 
  3-7 
  1*7 
  

  

  317 
  276 
  300 
  308 
  317 
  292 
  

  

  This 
  theory 
  o£ 
  the 
  slower 
  ion 
  in 
  gases 
  leads 
  to 
  the 
  revela- 
  

   tion 
  o£ 
  an 
  error 
  in 
  the 
  ordinary 
  experimental 
  method 
  of 
  

   measuring 
  their 
  mobilities, 
  the 
  true 
  values 
  in 
  the 
  limit 
  being 
  

   only 
  half 
  of 
  those 
  assigned. 
  Let 
  AB 
  and 
  CD 
  be 
  two 
  

   electrodes 
  giving 
  an 
  electric 
  field 
  

   from 
  AB 
  to 
  CD 
  between 
  which 
  a 
  Fig. 
  3. 
  

  

  stream 
  of 
  ionized 
  gas 
  is 
  led 
  in 
  the 
  

   direction 
  of 
  the 
  arrow. 
  It 
  is 
  

   assumed 
  that, 
  when 
  all 
  the 
  ions 
  

   are 
  just 
  caught 
  as 
  the 
  stream 
  flows 
  

   uniforml}^ 
  a 
  positive 
  ion 
  entering 
  

   at 
  A 
  travels 
  along 
  AD, 
  and 
  a 
  

   negative 
  ion 
  entering 
  at 
  C 
  travels 
  along 
  CB. 
  But, 
  if 
  this 
  

   were 
  so, 
  the 
  positive 
  ion 
  after 
  it 
  had 
  crossed 
  the 
  intersection 
  

   of 
  AD 
  and 
  CB 
  would 
  have 
  no 
  neighbour 
  negative 
  ions, 
  and 
  

   would 
  be 
  free 
  from 
  the 
  viscous 
  resistance 
  J 
  of 
  electric 
  origin, 
  

   it 
  would 
  finish 
  its 
  path 
  more 
  swiftly 
  under 
  the 
  resistance 
  F 
  

   only. 
  The 
  paths 
  of 
  electrons 
  entering 
  at 
  A 
  and 
  C 
  are 
  AOD 
  

   and 
  COB. 
  If 
  Ua 
  is 
  the 
  mobility 
  along 
  AO 
  and 
  Ud 
  along 
  OD 
  

   at 
  right 
  angles 
  to 
  AB, 
  we 
  have 
  AC/K 
  = 
  AC/2wa 
  + 
  AC/2wd 
  or 
  

   2/u=l/ua-\-l/ud. 
  Thus 
  when 
  Ud 
  is 
  large^ 
  Ua 
  the 
  desired 
  

   mobility 
  is 
  only 
  half 
  of 
  u 
  which 
  is 
  usually 
  assigned 
  as 
  the 
  

   experimental 
  measure 
  of 
  w^. 
  Moreau's 
  values 
  of 
  u 
  quoted 
  in 
  

   this 
  paper 
  should 
  be 
  divided 
  by 
  2, 
  as 
  should 
  also 
  Langevin's 
  

   mobility 
  for 
  the 
  very 
  slow 
  ion 
  in 
  air, 
  namely 
  about 
  1/3000, 
  

   which 
  should 
  be 
  nearly 
  1/6000^ 
  and 
  a 
  similar 
  remark 
  applies 
  

   to 
  many 
  other 
  determinations 
  of 
  u. 
  Since, 
  so 
  far, 
  we 
  have 
  

   been 
  considering 
  only 
  relative 
  values 
  of 
  u 
  this 
  correction 
  is 
  

   not 
  needed 
  for 
  the 
  purposes 
  of 
  the 
  previous 
  part 
  of 
  this 
  

   section. 
  It 
  is 
  important 
  in 
  absolute 
  calculations 
  concerning 
  

   these 
  ions. 
  This 
  error 
  does 
  not 
  affect 
  the 
  velocities 
  of 
  

   the 
  small 
  ions 
  considered 
  in 
  section 
  1. 
  

  

  3. 
  The 
  Large 
  Ion 
  with 
  Liquid 
  or 
  Solid 
  Nucleus. 
  

  

  To 
  account 
  for 
  the 
  very 
  small 
  mobility 
  of 
  the 
  large 
  ion 
  of 
  

   Langevin 
  I 
  have 
  imagined 
  the 
  structure 
  already 
  described, 
  

  

  