﻿C50 
  Dr. 
  F. 
  C. 
  Brown 
  on 
  the 
  Kinetic 
  Energy 
  of 
  the 
  

  

  agitation 
  and 
  is 
  distributed 
  among 
  the 
  different 
  ions 
  in 
  

   accordance 
  with 
  Maxwell's 
  law, 
  then 
  the 
  current 
  carried 
  by 
  

   those 
  ions 
  escaping 
  from 
  a 
  hot 
  portion 
  of 
  an 
  infinite 
  plane 
  

   to 
  a 
  neighbouring 
  parallel 
  plane 
  can 
  be 
  expressed 
  by 
  the 
  

   formula 
  

  

  i 
  = 
  i^e 
  ^? 
  

  

  where 
  Y 
  is 
  the 
  difference 
  of 
  potential 
  between 
  the 
  

   planes^ 
  ne 
  is 
  the 
  quantity 
  of 
  electricity 
  carried 
  by 
  half 
  a 
  

   cubic 
  centimetre 
  of 
  hydrogen 
  in 
  electrolysis, 
  i 
  is 
  the 
  

   value 
  of 
  the 
  current 
  when 
  the 
  difference 
  of 
  potential 
  is 
  

   V, 
  2q 
  is 
  the 
  value 
  for 
  a 
  potential-difference 
  y 
  = 
  0, 
  ^ 
  is 
  

   the 
  absolute 
  temperature, 
  and 
  R 
  is 
  the 
  ordinary 
  gas 
  

   constant 
  in 
  the 
  equation 
  pv 
  = 
  B.6, 
  taken 
  for 
  a 
  unit 
  volume 
  

   of 
  gas 
  under 
  standard 
  conditions 
  of 
  pressure 
  and 
  

   temperature. 
  

  

  This 
  formula 
  was 
  tested 
  experimentally 
  for 
  the 
  negative 
  

   ions 
  from 
  platinum, 
  carbon, 
  and 
  sodium-potassium 
  alloy. 
  

   The 
  verification 
  was 
  quite 
  satisfactory 
  for 
  platinum, 
  but 
  it 
  

   was 
  not 
  so 
  for 
  carbon 
  or 
  the 
  alloy. 
  At 
  that 
  time 
  it 
  was 
  

   considered 
  that 
  the 
  failure 
  of 
  the 
  experimental 
  results 
  to 
  

   comply 
  with 
  the 
  theory 
  in 
  the 
  instances 
  mentioned, 
  was 
  due 
  

   to 
  the 
  disagreement 
  between 
  the 
  experimental 
  conditions 
  and 
  

   those 
  required 
  by 
  the 
  theory. 
  

  

  In 
  a 
  more 
  recent 
  paper 
  * 
  the 
  author 
  showed 
  that 
  the 
  above 
  

   formula 
  was 
  satisfactory 
  for 
  the 
  positive 
  ions 
  from 
  hot 
  

   platinum. 
  In 
  that 
  paper 
  the 
  hot 
  platinum 
  strip 
  described 
  

   was 
  constricted 
  slightly 
  in 
  the 
  middle, 
  so 
  that 
  only 
  a 
  small 
  

   portion 
  of 
  it 
  was 
  heated 
  by 
  the 
  electric 
  current. 
  It 
  was 
  

   estimated 
  that 
  no 
  portion 
  of 
  the 
  emitting 
  surface 
  differed 
  

   from 
  zero 
  potential 
  by 
  more 
  than 
  +0*04 
  volt. 
  Recently, 
  

   while 
  investigating 
  the 
  kinetic 
  energy 
  of 
  the 
  ions 
  from 
  

   tungsten 
  and 
  tantalum 
  filaments, 
  results 
  were 
  obtained 
  

   which 
  were 
  not 
  in 
  agreement 
  with 
  those 
  previously 
  ob- 
  

   tained 
  with 
  a 
  platinum 
  strip. 
  It 
  was 
  not 
  clear 
  if 
  the 
  

   disagreement 
  were 
  mainly 
  due 
  to 
  the 
  hot 
  body 
  not 
  having 
  a 
  

   plane 
  surface 
  or 
  to 
  the 
  fall 
  of 
  potential 
  over 
  the 
  conducting 
  

   surface. 
  It 
  will 
  be 
  seen 
  later 
  in 
  this 
  paper 
  that 
  the 
  errors 
  

   arising 
  from 
  a 
  small 
  fall 
  of 
  potential 
  over 
  the 
  strip 
  can 
  be 
  

   neglected 
  in 
  comparison 
  with 
  errors 
  arising 
  when 
  the 
  

   emitting 
  surface 
  is 
  not 
  a 
  plane, 
  and 
  parallel 
  to 
  the 
  receiving- 
  

   surface. 
  

  

  * 
  Phil. 
  Mag. 
  [6] 
  vol. 
  xvii. 
  p. 
  355 
  (1909). 
  

  

  