﻿360 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  pressure 
  is 
  p^ 
  = 
  760 
  mm. 
  of 
  H^, 
  then 
  I 
  = 
  lopo/p-, 
  and 
  we 
  now 
  

   have 
  A 
  in 
  (17) 
  proportional 
  to 
  {ui 
  + 
  U2)e~''^^Po/p^ 
  

  

  .'. 
  log 
  A/(ui+ii2) 
  is 
  linear 
  in 
  1/p. 
  . 
  . 
  (22) 
  

  

  If 
  we 
  compare 
  (15) 
  and 
  (17), 
  and 
  suppose 
  them 
  applied 
  to 
  

   the 
  same 
  set 
  of 
  experiments 
  over 
  a 
  certain 
  range 
  of 
  values 
  of 
  

   Ni, 
  we 
  see 
  that 
  for 
  the 
  average 
  value 
  of 
  Ni 
  we 
  must 
  have 
  

   approximately 
  A 
  = 
  alSTi^/^. 
  But 
  in 
  Langevin's 
  experiments 
  

   Ni 
  was 
  the 
  number 
  of 
  ions 
  generated 
  bj 
  a 
  single 
  flash 
  from 
  

   a 
  Rontgen 
  bulb, 
  so 
  that 
  on 
  the 
  average 
  for 
  gas 
  at 
  different 
  

   pressures, 
  we 
  may 
  take 
  Ni 
  proportional 
  to 
  p. 
  Thus 
  then 
  A 
  

   is 
  proportional 
  to 
  ap^/^, 
  and 
  so 
  from 
  (16) 
  A/{ui 
  + 
  U2) 
  is 
  

   proportional 
  to 
  ep^^^, 
  and 
  so 
  from 
  (22) 
  log 
  ep^^^ 
  is 
  linear 
  in 
  

   1/p. 
  Thus 
  from 
  Langevin's 
  experiments 
  I 
  find 
  with 
  p 
  in 
  

   mm. 
  of 
  Hg 
  

  

  for 
  air 
  logio 
  epVs 
  = 
  1.35-745/p-) 
  

  

  forCOg 
  logio6;)V3=i.35_509/joJ' 
  • 
  * 
  ^ 
  ^ 
  

   which 
  furnish 
  the 
  following 
  comparison 
  with 
  experiment 
  : 
  — 
  

  

  Air. 
  

  

  p 
  

  

  152 
  

  

  375 
  

  

  760 
  

  

  1550 
  

  

  2320 
  

  

  3800 
  

  

  .€ 
  exper 
  

  

  -01 
  

  

  •06 
  

  

  •27 
  

  

  •62 
  

  

  •80 
  

  

  •90 
  

  

  y£ 
  calcul 
  

  

  -00005 
  

  

  •03 
  

   CO2. 
  

  

  •26 
  

  

  •64 
  

  

  •81 
  

  

  •91 
  

  

  

  

  

  *> 
  

  

  135 
  

  

  352 
  

   •13 
  

  

  550 
  

  

  •27 
  

  

  758 
  

   •51 
  

  

  1560 
  

   •95 
  

  

  '^SHO 
  

  

  ±' 
  

  

  e 
  exper 
  

  

  -01 
  

  

  •97 
  

  

  6 
  calcul 
  

  

  -0007 
  

  

  •11 
  

  

  •32 
  

  

  •50 
  

  

  •91 
  

  

  102 
  

  

  It 
  is 
  to 
  be 
  remembered 
  that 
  the 
  whole 
  theory 
  and 
  working 
  

   out 
  of 
  Langevin's 
  experiments 
  is 
  based 
  upon 
  (15) 
  and 
  (16) 
  

   with 
  the 
  condition 
  that 
  e 
  must 
  be 
  less 
  than 
  1. 
  In 
  these 
  

   circumstances 
  the 
  very 
  simple 
  law 
  e'^^, 
  which 
  has 
  been 
  

   worked 
  out 
  above 
  for 
  com.paring 
  departures 
  from 
  uniformity 
  

   of 
  distribution 
  favourable 
  to 
  recombination, 
  is 
  verified 
  as 
  well 
  

   as 
  possible. 
  

  

  From 
  the 
  values 
  found 
  for 
  a 
  in 
  (15) 
  for 
  various 
  gases 
  it 
  is 
  

   easy 
  to 
  obtain 
  A 
  in 
  (17). 
  For 
  instance, 
  Townsend 
  (Phil. 
  

   Trans, 
  cxciii. 
  1900, 
  p. 
  129), 
  by 
  an 
  electrical 
  method, 
  in 
  which 
  

   during 
  0'93 
  second 
  Ni 
  diminished 
  in 
  the 
  ratio 
  77 
  to 
  46 
  for 
  

   air, 
  found 
  a 
  = 
  3420^, 
  where 
  e 
  is 
  the 
  electron 
  charge 
  

   3 
  X 
  10-^^ 
  So 
  by 
  this 
  electrical 
  method 
  A 
  = 
  0-0000832. 
  

  

  