﻿346 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  presence 
  o£ 
  impurity 
  there 
  may 
  be 
  a 
  tendency 
  for 
  one 
  or 
  

   both 
  sorts 
  of 
  electron 
  to 
  associate 
  specially 
  with 
  the 
  impurity. 
  

   But 
  in 
  spite 
  o£ 
  these 
  remaining 
  uncertainties 
  the 
  interpreta- 
  

   tion 
  of 
  the 
  experiments 
  by 
  (9) 
  proves 
  that 
  the 
  small 
  ion 
  in 
  

   air 
  does 
  not 
  attach 
  to 
  itself 
  satellite 
  molecules 
  whose 
  number 
  

   varies 
  with 
  temperature. 
  The 
  electric 
  force 
  of 
  the 
  ion 
  

   accounts 
  for 
  the 
  facts 
  just 
  as 
  cohesional 
  force 
  accounts 
  for 
  

   the 
  corresponding 
  facts 
  in 
  the 
  viscosity 
  of 
  gases. 
  I 
  may 
  

   mention 
  that 
  for 
  the 
  negative 
  ion 
  in 
  air 
  the 
  result 
  at 
  94° 
  

   can 
  be 
  expressed 
  as 
  well 
  as 
  all 
  the 
  others 
  by 
  changing 
  (9) 
  

   to 
  

  

  _ 
  AT^ 
  

   ''-1 
  + 
  C7(T-TJ 
  

   where 
  

  

  T, 
  = 
  70°, 
  A^ 
  = 
  0-1764, 
  0^ 
  = 
  150-5. 
  

  

  In 
  the 
  further 
  investigation 
  of 
  (8), 
  until 
  experiment 
  informs 
  

   us 
  definitely 
  as 
  to 
  the 
  atoms 
  or 
  radicals 
  which 
  form 
  the 
  ions, 
  

   we 
  shall 
  be 
  forced 
  to 
  make 
  assumptions. 
  For 
  the 
  diatomic 
  

   element 
  gases 
  we 
  can 
  write 
  m^^=2mi 
  if 
  the 
  ions 
  are 
  formed 
  

   of 
  their 
  atoms, 
  and 
  we 
  may 
  also 
  put 
  a^ 
  — 
  ^a^^ 
  although 
  we 
  

   must 
  be 
  on 
  the 
  watch 
  lest 
  the 
  atom 
  when 
  made 
  an 
  ion 
  may 
  

   undergo 
  change 
  of 
  volume. 
  Possibly 
  the 
  change 
  caused 
  by 
  

   the 
  positive 
  electron 
  is 
  different 
  from 
  that 
  caused 
  by 
  the 
  

   negative. 
  In 
  such 
  a 
  compound 
  gas 
  as 
  CO2 
  we 
  shall 
  assume 
  

   an 
  average 
  ion 
  of 
  mass 
  m^l2 
  and 
  of 
  volume 
  ^ira^jZ^ 
  and 
  shall 
  

   consider 
  the 
  average 
  of 
  the 
  nearly 
  equal 
  mobilities 
  of 
  the 
  

   positive 
  and 
  negative 
  ions. 
  Then 
  (8) 
  becomes 
  

  

  4- 
  =3-59N3«3'^^^3^3[l 
  + 
  2{(^(ai 
  + 
  a3) 
  A-^{a^-^ai)}lm^v^^-\u 
  , 
  (10) 
  

  

  (xiX 
  

  

  For 
  air 
  at 
  0° 
  C. 
  the 
  left 
  side 
  of 
  this 
  equation 
  has 
  the 
  value 
  

   10~i2 
  because 
  e 
  = 
  3xlO-io 
  and 
  6^/^^ 
  = 
  volt/cm. 
  = 
  1/300. 
  

   To 
  evaluate 
  the 
  right 
  side 
  we 
  put 
  ^3^13 
  = 
  0*001293, 
  and 
  

   ^37713^3^ 
  = 
  3py 
  in 
  the 
  usual 
  notation 
  of 
  the 
  gas 
  laws, 
  with 
  

   V 
  = 
  l, 
  and 
  p 
  = 
  1,014,000 
  dynes/cm.^, 
  and 
  2a3 
  = 
  2-38 
  x 
  10-« 
  

   (Phil. 
  Mag. 
  Feb. 
  1909, 
  p. 
  321), 
  while 
  

  

  [l 
  + 
  2{^(ai 
  + 
  a3)+^(«i 
  + 
  «3)}/w3^3']^=^^(l 
  + 
  C7T) 
  

  

  =A'T*=0-222x 
  273^ 
  = 
  3-67 
  

  

  for 
  both 
  the 
  positive 
  and 
  the 
  negative 
  small 
  ion 
  in 
  air 
  at 
  0° 
  C. 
  

   With 
  these 
  values 
  the 
  right 
  side 
  of 
  (10) 
  is 
  1*18 
  x 
  10"^^ 
  

   whereas 
  the 
  left 
  side 
  is 
  10 
  ~^^, 
  Here 
  we 
  meet, 
  even 
  in 
  a 
  

   more 
  pronounced 
  form, 
  the 
  discrepancy 
  which 
  has 
  led 
  

   previous 
  writers 
  to 
  suppose 
  the 
  small 
  ion 
  to 
  be 
  a 
  cluster 
  of 
  

   molecules, 
  for 
  which 
  2a3 
  would 
  be 
  large 
  enough 
  to 
  make 
  the 
  

  

  