﻿Energy 
  of 
  Negative 
  Electrons 
  emitted 
  by 
  Hot 
  Bodies. 
  363 
  

  

  thin 
  platinum 
  foil 
  was 
  soldered 
  to 
  the 
  lower 
  side 
  of 
  the 
  upper 
  

   plate 
  so 
  as 
  to 
  avoid 
  any 
  effects 
  which 
  might 
  conceivably 
  be 
  

   due 
  to 
  anything 
  of 
  the 
  nature 
  of 
  contact 
  electromotive 
  

   force. 
  

  

  The 
  diameter 
  of 
  the 
  upper 
  plate 
  used 
  in 
  the 
  experiments 
  

   was 
  3*6 
  cms. 
  and 
  the 
  distance 
  between 
  the 
  two 
  plates 
  was 
  

   two 
  millimetres. 
  In 
  discussing 
  the 
  results 
  the 
  formulae 
  for 
  

   infinite 
  planes 
  will 
  be 
  used. 
  Strictly 
  speaking 
  we 
  ought 
  

   to 
  apply 
  formula 
  (8), 
  substituting 
  the 
  values 
  of 
  F(w 
  ) 
  and 
  

   F'(W) 
  in 
  (9). 
  When 
  this 
  is 
  done 
  an 
  integral 
  is 
  obtained 
  

   which 
  cannot 
  be 
  evaluated 
  in 
  finite 
  terms. 
  It 
  is, 
  however, 
  

   easy 
  to 
  show 
  from 
  expression 
  (8) 
  that 
  the 
  fractional 
  error 
  

   introduced 
  by 
  neglecting 
  the 
  finiteness 
  of 
  the 
  radius 
  p 
  of 
  

   the 
  upper 
  plate 
  will 
  be 
  comparable 
  with 
  a 
  quantity 
  lying 
  

  

  between 
  e 
  ' 
  Jx 
  °" 
  and 
  — 
  gT 
  — 
  i 
  e 
  ^ 
  > 
  depending 
  on 
  the 
  

  

  value 
  of 
  V. 
  A 
  preliminary 
  calculation 
  showed 
  that 
  with 
  

   the 
  dimensions 
  of 
  the 
  apparatus 
  chosen 
  this 
  error 
  would 
  

   always 
  be 
  smaller 
  than 
  the 
  expected 
  error 
  of 
  observation. 
  

   This 
  conclusion 
  was 
  subsequently 
  confirmed 
  by 
  experiments 
  

   in 
  which 
  the 
  current 
  to 
  the 
  upper 
  plate, 
  to 
  the 
  guard-ring, 
  

   and 
  to 
  the 
  two 
  together 
  were 
  measured 
  and 
  compared. 
  

   Under 
  all 
  conditions 
  the 
  current 
  to 
  the 
  guard-ring 
  was 
  small 
  

   compared 
  with 
  that 
  to 
  the 
  plate, 
  the 
  ratio 
  of 
  the 
  two 
  being- 
  

   smaller 
  than 
  the 
  probable 
  observational 
  error. 
  Since 
  the 
  

   guard-ring 
  was 
  constituted 
  so 
  as 
  to 
  intercept 
  all 
  the 
  ions 
  

   from 
  the 
  lower 
  plate 
  which 
  were 
  not 
  received 
  by 
  the 
  upper 
  

   plate, 
  it 
  is 
  clear 
  that 
  practically 
  all 
  the 
  ions 
  from 
  the 
  metal 
  

   strip 
  which 
  were 
  not 
  returned 
  to 
  the 
  lower 
  plate 
  by 
  the 
  field 
  

   reached 
  the 
  upper 
  plate. 
  

  

  The 
  fiducial 
  points 
  used 
  in 
  calibrating 
  the 
  temperature- 
  

   resistance 
  curve 
  were 
  the 
  temperature 
  of 
  the 
  room, 
  the 
  

   melting-point 
  of 
  potassium 
  sulphate 
  (1066° 
  C.) 
  and 
  the 
  

   melting-point 
  of 
  platinum 
  (18:20° 
  C.) 
  The 
  temperature 
  

   varied 
  perceptibly 
  along 
  the 
  strip 
  owing 
  chiefly 
  to 
  the 
  con- 
  

   duction 
  of 
  heat 
  from 
  the 
  ends. 
  In 
  standardizing 
  it, 
  there- 
  

   fore, 
  the 
  potassium 
  sulphate 
  was 
  placed 
  on 
  the 
  hottest 
  portion, 
  

   as 
  this, 
  owing 
  to 
  the 
  tremendous 
  rapidity 
  with 
  which 
  the 
  

   emission 
  of 
  ions 
  increases 
  with 
  the 
  temperature, 
  would 
  be 
  the 
  

   region 
  which 
  gave 
  rise 
  to 
  the 
  greater 
  proportion 
  of 
  the 
  total. 
  

   In 
  determining 
  the 
  resistance 
  at 
  the 
  melting-point 
  of 
  platinum, 
  

   that 
  at 
  which 
  the 
  strip 
  melted 
  was 
  observed. 
  This 
  would 
  

   obviously 
  give 
  the 
  temperature 
  of 
  the 
  hottest 
  portion. 
  When 
  

   the 
  three 
  temperatures 
  were 
  plotted 
  against 
  resistance 
  they 
  

   were 
  found 
  to 
  lie 
  as 
  nearly 
  as 
  possible 
  on 
  a 
  straight 
  line. 
  

  

  