﻿Energy 
  of 
  the 
  Ions 
  emitted 
  by 
  Hot 
  Bodies. 
  899 
  

  

  of 
  some 
  such 
  view. 
  In 
  order 
  to 
  avoid 
  effects 
  of 
  this 
  kind 
  a 
  

   very 
  low 
  potential-difference, 
  10"6 
  volts, 
  was 
  used 
  in 
  the 
  

   experiments 
  on 
  the 
  negative 
  ions. 
  This 
  is 
  a 
  long 
  way 
  below 
  

   the 
  potential 
  at 
  which 
  i 
  reaches 
  its 
  maximum 
  value. 
  It 
  was 
  

   not 
  considered 
  advisable 
  to 
  use 
  lower 
  potentials 
  than 
  this 
  on 
  

   account 
  of 
  the 
  assumption, 
  made 
  in 
  working 
  out 
  the 
  theory, 
  

   that 
  Ye 
  is 
  large 
  compared 
  with 
  Jj-mny. 
  The 
  ratio 
  Ve/?mw 
  2 
  

   with 
  V 
  = 
  10 
  6 
  volts 
  is 
  about 
  120." 
  

  

  Three 
  different 
  methods 
  of 
  applying 
  the 
  experimental 
  

   results 
  so 
  as 
  to 
  test 
  equations 
  (5) 
  to 
  (8) 
  have 
  been 
  made 
  use 
  

   of. 
  These 
  will 
  be 
  considered 
  separately, 
  and 
  under 
  each 
  

   method 
  we 
  shall 
  consider, 
  first 
  the 
  experiments 
  with 
  the 
  

   negative 
  ions, 
  and 
  afterwards 
  those 
  with 
  the 
  positive 
  ions. 
  

  

  § 
  4. 
  Method 
  I. 
  

  

  (a) 
  Negative 
  ions. 
  — 
  This 
  method 
  is 
  based 
  on 
  equation 
  (7), 
  

   which 
  may 
  be 
  written 
  in 
  either 
  of 
  the 
  forms 
  

  

  _ 
  Yne 
  n 
  _ 
  Yne 
  „ 
  

  

  i 
  = 
  i 
  Q 
  e 
  <iW;-2 
  x 
  ' 
  2 
  or 
  i=i 
  Q 
  x 
  10 
  ¥mo^ 
  x 
  ~ 
  (9) 
  

  

  It 
  consists 
  in 
  finding 
  by 
  trial 
  a 
  curve 
  of 
  the 
  form 
  i 
  — 
  ke~ 
  x 
  ^ 
  

   which 
  will 
  fit 
  the 
  experimental 
  numbers. 
  The 
  constant 
  A 
  is 
  

   readily 
  determined, 
  being 
  obviously 
  the 
  value 
  i 
  of 
  i 
  when 
  

   #=0 
  ; 
  it 
  is 
  the 
  height 
  of 
  the 
  maximum 
  ordinate 
  of 
  the 
  i.r, 
  

   curve 
  (see 
  fig. 
  1). 
  A 
  general 
  method 
  of 
  determining 
  J, 
  will 
  

   be 
  given 
  below. 
  The 
  following 
  table 
  gives 
  a 
  series 
  of 
  values 
  

   of 
  /, 
  expressed 
  as 
  a 
  ratio 
  of 
  electrometer 
  deflexions 
  in 
  the 
  

   manner 
  already 
  described, 
  for 
  different 
  values 
  of 
  x. 
  The 
  

   first 
  row 
  gives 
  the 
  value 
  of 
  ,r, 
  the 
  second 
  the 
  value 
  of 
  i 
  for 
  

   points 
  to 
  the 
  right 
  of 
  % 
  = 
  0, 
  and 
  the 
  third 
  the 
  value 
  of 
  i 
  for 
  

   points 
  to 
  the 
  left 
  of 
  ,?: 
  = 
  (). 
  This 
  is 
  necessary 
  as 
  the 
  values 
  

   are 
  not 
  quite 
  symmetrical 
  as 
  they 
  would 
  be 
  under 
  perfect 
  

   conditions. 
  The 
  fourth 
  row 
  gives 
  the 
  mean 
  of 
  the 
  two 
  

   experimental 
  values 
  of 
  ?', 
  and 
  the 
  last 
  contains 
  the 
  values 
  of 
  i 
  

   calculated 
  from 
  the 
  formula 
  £ 
  = 
  1*38 
  x 
  10~" 
  lx 
  ". 
  

  

  +tf(l=-0318cm.) 
  .... 
  

  

  0. 
  

  

  1. 
  

  

  2 
  # 
  

  

  o. 
  

  

  4. 
  

  

  5. 
  

  

  6. 
  

  

  7. 
  

  

  -{- 
  i 
  (arbitrary 
  units) 
  . 
  . 
  

  

  . 
  1-3.3 
  

  

  1-38 
  

  

  i-17 
  

  

  '75 
  

  

  •51 
  

  

  •34 
  

  

  •19 
  

  

  ■09 
  

  

  -/( 
  „ 
  „ 
  ) 
  ,- 
  

  

  . 
  1-33 
  

  

  1-25 
  

  

  1-09 
  

  

  ■85 
  

  

  •47 
  

  

  •30 
  

  

  •21 
  

  

  •13 
  

  

  mean 
  i 
  ( 
  „ 
  „ 
  ) 
  . 
  

  

  . 
  135 
  

  

  1-33 
  

  

  1 
  13 
  

  

  •80 
  

  

  •40 
  

  

  •32 
  

  

  •20 
  

  

  •11 
  

  

  i 
  calculated 
  

  

  . 
  1-33 
  

  

  1-31 
  

  

  110 
  

  

  ■83 
  

  

  •50 
  

  

  •34 
  

  

  •18 
  

  

  •09 
  

  

  The 
  agreement 
  between 
  the 
  theoretical 
  and 
  experimental 
  

   numbers 
  is 
  very 
  satisfactory. 
  This 
  is 
  also 
  shown 
  graphically 
  

   bv 
  fis:- 
  3, 
  in 
  which 
  the 
  smooth 
  curve 
  is 
  the 
  graph 
  of 
  

   y 
  ° 
  3 
  N 
  T 
  2 
  

  

  