﻿354 
  Prof. 
  Richardson 
  and 
  Mr. 
  Brown 
  on 
  the 
  Kinetic 
  

  

  but 
  to 
  the 
  way 
  in 
  which 
  the 
  energy 
  is 
  distributed 
  among 
  the 
  

   different 
  electrons 
  as 
  well. 
  Although 
  a 
  knowledge 
  of 
  the 
  

   kinetic 
  energy 
  of 
  the 
  emitted 
  electrons 
  is 
  of 
  obvious 
  im- 
  

   portance, 
  no 
  attempt 
  appears 
  to 
  have 
  been 
  made 
  to 
  determine 
  

   it. 
  The 
  present 
  paper 
  embodies 
  the 
  results 
  of 
  an 
  investiga- 
  

   tion 
  of 
  the 
  portion 
  of 
  the 
  kinetic 
  energy 
  which 
  depends 
  upon 
  

   the 
  component 
  of 
  the 
  velocity 
  normal 
  to 
  the 
  emitting 
  surface. 
  

   What 
  is 
  determined 
  is 
  the 
  value 
  of 
  ^mu 
  2 
  , 
  where 
  m 
  is 
  the 
  

   mass 
  of 
  an 
  electron 
  and 
  u 
  is 
  its 
  component 
  of 
  velocity 
  per- 
  

   pendicular 
  to 
  the 
  surface 
  from 
  which 
  it 
  is 
  emitted. 
  Both 
  

   the 
  average 
  value 
  of 
  this 
  portion 
  of 
  the 
  energy 
  and 
  the 
  law 
  

   according 
  to 
  which 
  it 
  is 
  distributed 
  among 
  the 
  different 
  

   particles 
  given 
  off 
  are 
  examined. 
  The 
  method 
  employed 
  

   gives 
  no 
  information 
  about 
  the 
  part 
  of 
  the 
  energy 
  which 
  

   depends 
  on 
  the 
  component 
  of 
  velocity 
  parallel 
  to 
  the 
  surface 
  

   of 
  emission 
  : 
  the 
  sideways 
  energy 
  will 
  form 
  the 
  subject 
  of 
  

   another 
  communication 
  by 
  one 
  of 
  the 
  authors. 
  

  

  Theory 
  of 
  the 
  Method. 
  

  

  Stated 
  briefly 
  the 
  method 
  used 
  consisted 
  in 
  measuring 
  the 
  

   rate 
  at 
  which 
  an 
  insulated 
  plate 
  A 
  charged 
  up 
  when 
  a 
  portion 
  

   of 
  another 
  plate 
  B 
  parallel 
  to 
  A 
  consisted 
  of 
  metal 
  sufficiently 
  

   hot 
  to 
  emit 
  ions. 
  It 
  is 
  clear 
  that 
  as 
  the 
  metal 
  in 
  B 
  emits 
  

   negative 
  ions 
  the 
  plate 
  A 
  will 
  become 
  negatively 
  charged, 
  so 
  

   that 
  a 
  difference 
  of 
  potential 
  will 
  be 
  established 
  tending 
  to 
  

   stop 
  the 
  flow 
  of 
  electricity. 
  From 
  the 
  way 
  in 
  which 
  the 
  

   current 
  between 
  the 
  two 
  plates 
  varies 
  with 
  the 
  time 
  or 
  with 
  

   the 
  difference 
  of 
  potential 
  between 
  them 
  the 
  desired 
  infor- 
  

   mation 
  can 
  be 
  obtained. 
  

  

  Consider 
  two 
  parallel 
  planes 
  of 
  indefinite 
  extent 
  perpen- 
  

   dicular 
  to 
  the 
  axis 
  of 
  x. 
  The 
  lower 
  plane, 
  determined 
  by 
  

   # 
  = 
  0, 
  has 
  a 
  small 
  portion 
  of 
  its 
  central 
  region 
  heated 
  so 
  that 
  

   it 
  is 
  emitting 
  ions. 
  The 
  potential 
  of 
  this 
  plane 
  is 
  maintained 
  

   at 
  zero. 
  The 
  potential 
  of 
  the 
  upper 
  plane, 
  determined 
  by 
  

   x 
  = 
  x^ 
  has 
  the 
  value 
  V 
  at 
  the 
  instant 
  considered. 
  Consider 
  

   an 
  ion 
  whose 
  charge 
  is 
  e 
  and 
  mass 
  m 
  situated 
  at 
  a 
  point 
  

   between 
  the 
  planes 
  whose 
  coordinates 
  are 
  #, 
  y, 
  z. 
  Its 
  

   equation 
  of 
  motion 
  will 
  be 
  

  

  d 
  2 
  x 
  dY 
  d 
  2 
  y 
  d 
  2 
  z 
  

  

  >W=- 
  e 
  d*-> 
  m 
  oW 
  =m 
  o¥ 
  2 
  

  

  -z-r: 
  •> 
  m 
  ri= 
  m 
  ^2= 
  ' 
  • 
  • 
  C 
  1 
  ) 
  

  

  From 
  these 
  equations 
  it 
  follows 
  (see 
  Phil. 
  Trans. 
  A, 
  

   vol. 
  cci. 
  p. 
  499) 
  that 
  the 
  electron 
  will 
  only 
  arrive 
  at 
  the 
  

   upper 
  plate 
  provided 
  

  

  imi< 
  2 
  >Ye, 
  (2) 
  

  

  where 
  u 
  is 
  the 
  initial 
  velocity 
  perpendicular 
  to 
  the] 
  plate. 
  

  

  