﻿356 
  Effect 
  of 
  Magnetic 
  Field 
  on 
  Metallic 
  Resistance. 
  

  

  vanishes 
  ; 
  if 
  the 
  law 
  of 
  force 
  varies 
  less 
  rapidly 
  with 
  the 
  dis- 
  

   tance 
  than 
  the 
  inverse 
  fifth 
  power, 
  St 
  is 
  negative 
  and 
  the 
  second 
  

   and 
  first 
  terms 
  of 
  (2) 
  are 
  of 
  the 
  same 
  sign 
  : 
  thus 
  the 
  increase 
  in 
  

   resistance 
  is 
  greater 
  than 
  that 
  calculated 
  by 
  the 
  first 
  term 
  alone. 
  

   ] 
  have 
  calculated 
  that 
  it 
  is 
  not 
  until 
  the 
  force 
  varies 
  more 
  rapidly 
  

   than 
  the 
  inverse 
  ninth 
  power 
  of 
  the 
  distance 
  that 
  the 
  second 
  

   term 
  overpowers 
  the 
  first. 
  These 
  considerations 
  show 
  that 
  we 
  

   cannot 
  calculate 
  the 
  second 
  term 
  in 
  (2) 
  unless 
  we 
  know 
  the 
  law 
  

   of 
  force 
  ; 
  but 
  that 
  there 
  is 
  no 
  reason 
  why 
  it 
  should 
  reverse 
  the 
  

   effect 
  of 
  the 
  first 
  term 
  : 
  in 
  fact, 
  the 
  probability 
  is 
  the 
  other 
  

   way. 
  I 
  think, 
  however, 
  whatever 
  be 
  the 
  law 
  of 
  force, 
  the 
  

   second 
  term 
  will 
  be 
  small 
  compared 
  with 
  the 
  first: 
  for 
  take 
  

   the 
  most 
  favourable 
  case 
  for 
  the 
  second 
  term, 
  i. 
  e. 
  when 
  the 
  

   collision 
  is 
  between 
  hard 
  elastic 
  bodies 
  — 
  in 
  this 
  case 
  (3) 
  is 
  

   obtained 
  on 
  the 
  supposition 
  that 
  the 
  only 
  force 
  acting 
  on 
  the 
  

   system 
  during 
  its 
  free 
  path 
  is 
  that 
  due 
  to 
  the 
  external 
  electric 
  

   field. 
  Now 
  the 
  corpuscles 
  are 
  highly 
  charged 
  and 
  are 
  always 
  

   within 
  distances 
  of 
  less 
  than 
  10 
  -7 
  cm. 
  of 
  the 
  molecules 
  of 
  the 
  

   metal: 
  it 
  is 
  almost 
  certain, 
  therefore, 
  that 
  the 
  local 
  forces 
  

   exerted 
  on 
  the 
  corpuscle 
  by 
  the 
  surrounding 
  molecules 
  are 
  

   enormously 
  greater 
  than 
  those 
  exerted 
  by 
  the 
  external 
  electric 
  

   field, 
  and 
  that 
  at 
  the 
  end 
  of 
  its 
  free 
  path 
  the 
  corpuscle 
  rushes 
  

   into 
  or 
  past 
  the 
  molecule 
  with 
  which 
  it 
  is 
  colliding 
  with 
  a 
  

   velocity 
  very 
  large 
  compared 
  with 
  that 
  with 
  which 
  it 
  started. 
  

   Now 
  when 
  the 
  velocity 
  is 
  changing 
  during 
  the 
  free 
  path 
  it 
  

   is 
  easy 
  to 
  prove 
  that 
  St 
  ft 
  is 
  less 
  than 
  that 
  given 
  by 
  equation 
  

   (3) 
  in 
  the 
  proportion 
  of 
  the 
  initial 
  to 
  the 
  final 
  velocity 
  of 
  the 
  

   corpuscle. 
  As 
  this 
  proportion 
  is 
  small, 
  we 
  see 
  that 
  8t/t 
  will 
  be 
  

   very 
  small 
  compared 
  with 
  the 
  value 
  given 
  by 
  (3), 
  and 
  there- 
  

   fore 
  that 
  the 
  effect 
  of 
  the 
  second 
  term 
  is 
  very 
  small 
  compared 
  

   with 
  that 
  calculated 
  by 
  Dr. 
  E. 
  van 
  Everdingen. 
  

  

  The 
  conclusion 
  at 
  which 
  we 
  arrive 
  is 
  thus 
  that, 
  while 
  the 
  value 
  

   of 
  the 
  second 
  term 
  in 
  (3) 
  is 
  uncertain, 
  depending, 
  as 
  it 
  does, 
  

   upon 
  the 
  law 
  of 
  force 
  between 
  the 
  molecule 
  and 
  the 
  corpuscle, 
  

   this 
  uncertainty 
  is 
  not 
  important, 
  as 
  the 
  effect 
  of 
  it 
  is 
  small 
  

   compared 
  with 
  that 
  of 
  the 
  first 
  term 
  in 
  (3) 
  which 
  gives 
  an 
  

   increased 
  resistance 
  in 
  a 
  magnetic 
  field. 
  

  

  I 
  am, 
  Gentlemen, 
  

  

  Yours 
  very 
  truly, 
  

  

  J. 
  J. 
  Thomson. 
  

  

  