﻿416 
  Dr. 
  Hodgson 
  and 
  Mr. 
  Mainstone 
  on 
  Heating 
  

  

  § 
  5. 
  Absolute 
  measurement 
  of 
  the 
  heat 
  energy 
  given 
  

  

  to 
  the 
  cathode 
  with 
  normal 
  glow. 
  

  

  The 
  current 
  was 
  kept 
  constant 
  till 
  the 
  cathode 
  took 
  up 
  

  

  that 
  temperature 
  at 
  which 
  the 
  heat 
  lost 
  by 
  radiation, 
  &c, 
  

  

  was 
  equal 
  to 
  that 
  supplied 
  by 
  the 
  bombarding 
  positive 
  ions. 
  

  

  The 
  rate 
  of: 
  cooling 
  o£ 
  the 
  cathode 
  was 
  determined, 
  and 
  thus 
  

  

  M 
  . 
  — 
  could 
  be 
  obtained, 
  

   at 
  

  

  where 
  M 
  = 
  heat 
  capacity 
  of 
  cathode, 
  

  

  -tt 
  =rate 
  of 
  cooling 
  at 
  the 
  equilibrium 
  temperature 
  d. 
  

   az 
  

  

  The 
  quantities 
  involved 
  in 
  the 
  theoretical 
  calculation 
  of 
  

   the 
  heat 
  energy 
  given 
  to 
  the 
  cathode 
  are 
  i 
  the 
  current 
  and 
  

   V 
  the 
  mean 
  potential 
  through 
  which 
  the 
  bombarding 
  ions 
  

   fall. 
  

  

  If 
  n 
  positive 
  ions 
  strike 
  the 
  cathode 
  per 
  second, 
  then 
  neY 
  

   is 
  the 
  energy 
  communicated 
  per 
  second. 
  Now 
  if 
  the 
  current 
  

   is 
  carried 
  entirely 
  by 
  positive 
  ions 
  ne 
  = 
  i 
  and 
  the 
  energy 
  

   given 
  up 
  per 
  second 
  =iV. 
  

  

  The 
  two 
  quantities 
  M-^- 
  =a, 
  and 
  iV=/3 
  were 
  obtained 
  

  

  and 
  the 
  ratio 
  «//3 
  calculated, 
  assuming 
  V 
  to 
  be 
  the 
  normal 
  

   cathode 
  fall. 
  

  

  The 
  maximum 
  value 
  that 
  this 
  ratio 
  can 
  assume 
  is 
  l'O, 
  

   when 
  the 
  current 
  is 
  carried 
  by 
  positive 
  ions 
  only 
  (provided 
  

   that 
  no 
  internal 
  energy 
  of 
  the 
  molecule 
  is 
  evolved 
  as 
  heat 
  

   during 
  the 
  process 
  of 
  ionization). 
  Should 
  each 
  positive 
  ion 
  

   in 
  striking 
  the 
  cathode 
  ionize 
  and 
  produce 
  only 
  one 
  negative 
  

   carrier, 
  then 
  the 
  ratio 
  0*5 
  would 
  result. 
  If 
  more 
  than 
  one 
  

   negative 
  carrier 
  resulted 
  from 
  each 
  collision, 
  the 
  value 
  of 
  the 
  

   ratio 
  would 
  be 
  still 
  smaller. 
  

  

  Some 
  work 
  not 
  yet 
  published 
  has 
  shown 
  that 
  in 
  the 
  case 
  

   of 
  the 
  anode 
  the 
  energy 
  given 
  up 
  to 
  it 
  requires 
  the 
  negative 
  

   carriers 
  to 
  gain 
  energy 
  in 
  a 
  path 
  at 
  least 
  1 
  cm. 
  long 
  in 
  

   oxygen 
  at 
  a 
  pressure 
  of 
  2-4 
  mm. 
  In 
  this 
  distance 
  the 
  ion 
  

   collides 
  often, 
  and 
  in 
  order 
  that 
  its 
  energy 
  may 
  still 
  be 
  given 
  

   to 
  the 
  anode 
  it 
  is 
  necessary 
  that 
  on 
  collisions 
  complex 
  ions 
  

   be 
  formed. 
  A 
  neutral 
  gas 
  molecule 
  bombarding 
  the 
  anode 
  

   would 
  merely 
  recoil 
  and 
  give 
  up 
  no 
  energy. 
  

  

  In 
  the 
  case 
  of 
  the 
  cathode 
  the 
  same 
  thing 
  must 
  hold, 
  and 
  

   the 
  problem 
  that 
  presents 
  itself 
  is 
  the 
  question 
  as 
  to 
  the 
  length 
  

   of 
  path 
  through 
  which 
  the 
  positive 
  carriers 
  can 
  accumulate 
  

   energy. 
  This 
  is 
  settled 
  by 
  our 
  knowledge 
  of 
  the 
  discharge 
  

   in 
  vacuum-tubes. 
  The 
  negative 
  glow 
  is 
  the 
  source 
  of 
  most 
  

  

  