﻿Effects 
  at 
  the 
  Cathode 
  in 
  Vacuum 
  Tubes. 
  

  

  Table 
  II. 
  

   Gas 
  — 
  Oxygen. 
  

  

  419 
  

  

  Cathode. 
  

  

  Gas 
  pressure 
  

   in 
  mm. 
  

  

  -!• 
  

  

  iY. 
  

  

  «/£. 
  

  

  Cu 
  

  

  Pb 
  

  

  3-09 
  

   303 
  

   3'05 
  

   1-21 
  

   0-61 
  

   0-65 
  

   0-65 
  

  

  142 
  

   7-15 
  

   5-62 
  

   3-52 
  

   341 
  

   3-68 
  

   3*72 
  

  

  1-31 
  

  

  7-18 
  

   5-37 
  

   3-64 
  

   364 
  

   4-08 
  

   4-08 
  

  

  103 
  

   1-00 
  

   1-05 
  

   0-97 
  

   0-94 
  

   090 
  

   091 
  

  

  ! 
  Pb 
  

  

  | 
  Ni 
  

  

  1 
  Ni 
  

  

  Ag 
  

  

  Ae 
  

  

  

  Table 
  III. 
  

   Gas 
  — 
  Hydrogen. 
  

  

  Cathode. 
  ! 
  <>as 
  pressure 
  j 
  M 
  *9 
  

   in 
  mm. 
  dt 
  

  

  iY. 
  

  

  a/13. 
  

  

  Cu 
  3-16 
  

  

  Pb 
  363 
  

  

  Ni 
  2-48 
  

  

  Ni 
  2-48 
  

  

  |_Ni 
  1-92 
  

  

  Ag 
  ; 
  2-38 
  

  

  Ag 
  2-13 
  

  

  I 
  

  

  1-03 
  

   5-44 
  

  

  8-75 
  

   8-83 
  

   9 
  33 
  

   9-86 
  

   994 
  

  

  1-03 
  

   5-36 
  

   773 
  

  

  801 
  

  

  8-88 
  

   8-55 
  

   8-85 
  

  

  100 
  

   1-01 
  

   113 
  

   1-10 
  

   105 
  

   115 
  

   1-12 
  

  

  In 
  these 
  two 
  gases 
  the 
  value 
  o£ 
  a//3 
  is 
  approximately 
  1*0, 
  

   so 
  that 
  the 
  number 
  of 
  negative 
  carriers 
  taking 
  part 
  in 
  th® 
  

   discharge 
  is 
  relatively 
  small. 
  If 
  the 
  normal 
  cathode 
  fall 
  is 
  

   the 
  potential 
  through 
  which 
  a 
  positive 
  ion 
  must 
  fall 
  to 
  gain 
  

   energy 
  sufficient 
  to 
  ionize 
  the 
  cathode 
  metal*, 
  then 
  only 
  

   those 
  ions 
  which 
  pass 
  through 
  the 
  dark 
  space 
  without 
  a 
  

   collision 
  will 
  ionize. 
  This 
  is 
  a 
  very 
  small 
  fraction 
  of 
  the 
  

   total 
  number 
  bombarding 
  the 
  cathode, 
  as 
  can 
  be 
  seen 
  by 
  

   considering 
  a 
  special 
  case. 
  Consider 
  the 
  gas 
  hydrogen 
  at 
  a 
  

   pressure 
  of 
  1 
  mm., 
  with 
  a 
  cathode 
  fall 
  of 
  about 
  400 
  volts, 
  

   and 
  a 
  dark 
  space 
  3*7 
  mm. 
  in 
  length. 
  Now 
  the 
  mean 
  free 
  path 
  

   of 
  a 
  hydrogen 
  molecule 
  at 
  1 
  mm. 
  pressure 
  is 
  about 
  0*14 
  mm. 
  

   at 
  air 
  temperature. 
  So 
  that 
  in 
  order 
  to 
  strike 
  the 
  cathode 
  

   without 
  a 
  collision, 
  the 
  positive 
  ion 
  (if 
  it 
  is 
  moving 
  with 
  a 
  

   speed 
  o£ 
  the 
  same 
  order 
  as 
  the 
  mean 
  molecular 
  speed) 
  must 
  

   pass 
  through 
  a 
  distance 
  26 
  times 
  its 
  mean 
  free 
  path, 
  and 
  the 
  

   probability 
  of 
  its 
  performing 
  this 
  feat 
  is 
  extremely 
  small. 
  

   If 
  its 
  speed 
  is 
  great 
  compared 
  with 
  the 
  mean 
  molecular 
  

   speed, 
  its 
  mean 
  free 
  path 
  becomes 
  ^/2 
  X 
  0-14 
  mm., 
  or 
  0*2 
  mm 
  

   * 
  Stark, 
  Wiedemann's 
  Handbk. 
  d. 
  Phys. 
  Bd. 
  iv. 
  p. 
  516 
  

  

  