﻿354 
  Prof. 
  J. 
  J. 
  Thomson 
  on 
  the 
  Fjfeet 
  of 
  a 
  

  

  metals, 
  and 
  comes 
  to 
  the 
  conclusion 
  that 
  the 
  theory 
  that 
  the 
  

   electric 
  current 
  is 
  carried 
  by 
  charged 
  particles 
  which 
  move 
  

   freely 
  through 
  the 
  metal 
  requires 
  the 
  resistance 
  to 
  be 
  dimi- 
  

   nished 
  by 
  a 
  transverse 
  magnetic 
  force 
  and 
  not 
  increased. 
  

  

  In 
  a 
  Report 
  presented 
  to 
  the 
  International 
  Congress 
  of 
  

   Physics 
  at 
  Paris, 
  1900, 
  I 
  had 
  previously 
  come 
  to 
  the 
  opposite 
  

   conclusion, 
  namely, 
  that 
  the 
  resistance 
  on 
  this 
  theory 
  ought 
  to 
  

   be 
  increased. 
  I 
  wish 
  in 
  this 
  letter 
  to 
  give 
  the 
  reasons 
  for 
  

   adhering 
  to 
  my 
  original 
  result. 
  Dr. 
  van 
  Everdingen's 
  results 
  

   are 
  based 
  on 
  the 
  assumption 
  that 
  the 
  corpuscles 
  which 
  carry 
  

   the 
  current 
  behave 
  like 
  a 
  perfect 
  gas 
  ; 
  that 
  the 
  collisions 
  which 
  

   the 
  corpuscles 
  make 
  with 
  the 
  molecules 
  through 
  which 
  they 
  move 
  

   are 
  similar 
  to 
  those 
  which 
  take 
  place 
  between 
  hard 
  elastic 
  bodies; 
  

   and 
  thirdly, 
  that 
  the 
  corpuscle 
  between 
  hvo 
  collisions 
  is 
  free 
  from 
  

   any 
  force 
  except 
  that 
  clue 
  to 
  the 
  external 
  field 
  producing 
  the 
  

   current. 
  

  

  The 
  second 
  and 
  third 
  of 
  these 
  assumptions 
  seem 
  to 
  me 
  

   extremely 
  unlikely 
  ; 
  but 
  before 
  discussing 
  them 
  I 
  will 
  explain 
  

   how 
  they 
  are 
  required 
  in 
  the 
  calculation 
  given 
  by 
  Dr. 
  van 
  

   Everdingen. 
  In 
  the 
  paper 
  alluded 
  to 
  1 
  showed 
  that 
  if 
  X 
  is 
  

   the 
  external 
  electric 
  force, 
  H 
  the 
  magnetic 
  force, 
  e 
  the 
  charge, 
  

   m 
  the 
  mass 
  of 
  a 
  corpuscle, 
  U 
  the 
  velocity 
  of 
  the 
  corpuscle 
  

   parallel 
  to 
  x 
  at 
  the 
  beginning 
  of 
  the 
  free 
  path, 
  t 
  the 
  free 
  time, 
  

   i. 
  e. 
  the 
  time 
  between 
  two 
  collisions, 
  then 
  the 
  mean 
  velocity 
  

   of 
  an 
  ion 
  parallel 
  to 
  the 
  axis 
  of 
  x 
  during 
  the 
  free 
  time 
  is 
  

  

  • 
  iSArp^u/,.;.^} 
  . 
  . 
  (1) 
  

  

  Z 
  m 
  \ 
  lz 
  nr 
  J 
  \ 
  b 
  nr 
  J 
  v 
  J 
  

  

  Thus 
  the 
  current 
  parallel 
  to 
  x 
  is 
  equal 
  to 
  

  

  2 
  \n 
  ( 
  1— 
  -r 
  — 
  -t 
  2 
  4 
  2wU 
  (1- 
  7 
  . 
  — 
  r 
  t*), 
  

  

  m 
  \ 
  lz 
  m 
  2 
  J 
  \ 
  b 
  nr 
  J 
  

  

  where 
  n 
  is 
  the 
  number 
  of 
  corpuscles 
  having 
  the 
  free 
  time 
  t. 
  

   The 
  effect 
  of 
  the 
  magnetic 
  field 
  is 
  represented 
  by 
  the 
  terms 
  

  

  ~3T 
  a\2*X* 
  8 
  — 
  -7 
  — 
  -InUt". 
  ... 
  (2) 
  

  

  Zi 
  m 
  b 
  m 
  2 
  v 
  J 
  

  

  The 
  first 
  of 
  these 
  represents 
  a 
  decrease 
  in 
  the 
  current, 
  and 
  

   therefore 
  an 
  increase 
  in 
  the 
  resistance 
  ; 
  it 
  is 
  only 
  the 
  second 
  

   term 
  that 
  we 
  need 
  consider. 
  Jn 
  the 
  paper 
  referred 
  to 
  1 
  took 
  

   zero 
  as 
  the 
  most 
  probable 
  value 
  of 
  this 
  term. 
  Dr. 
  van 
  

   Everdingen, 
  on 
  the 
  contrary, 
  makes 
  it 
  have 
  a 
  large 
  positive 
  

   value, 
  large 
  enough 
  to 
  swamp 
  the 
  negative 
  term 
  and 
  change 
  

  

  