﻿Transverse 
  Magnetic 
  Fidel 
  on 
  Metallic 
  Resistance. 
  355 
  

  

  the 
  sign 
  of 
  this 
  effect. 
  The 
  way 
  in 
  which 
  this 
  result 
  is 
  

   arrived 
  at 
  is 
  substantially 
  as 
  follows. 
  If 
  we 
  consider 
  two 
  

   corpuscles, 
  one 
  projected 
  in 
  the 
  direction 
  of 
  the 
  current 
  and 
  

   the 
  other 
  with 
  equal 
  velocity 
  in 
  the 
  opposite 
  direction, 
  since 
  

   the 
  one 
  moving 
  along 
  the 
  current 
  has 
  its 
  velocity 
  increased 
  

   while 
  that 
  moving 
  against 
  the 
  current 
  has 
  its 
  velocity 
  di- 
  

   minished 
  by 
  the 
  external 
  electric 
  field 
  ; 
  thus 
  if 
  the 
  free 
  path 
  is 
  

   unaltered, 
  t 
  the 
  free 
  time 
  for 
  the 
  one 
  moving 
  against 
  the 
  

   current 
  and 
  for 
  wiiich 
  U 
  is 
  negative 
  will 
  be 
  greater 
  than 
  the 
  

   time 
  for 
  the 
  one 
  moving 
  down 
  stream 
  and 
  for 
  which 
  U 
  is 
  

   positive, 
  because 
  the 
  average 
  velocity 
  in 
  the 
  first 
  case 
  is 
  less 
  

   than 
  that 
  in 
  t;ie 
  second. 
  If 
  we 
  assume 
  that 
  the 
  free 
  path 
  

   does 
  not 
  depend 
  upon 
  the 
  velocity, 
  and 
  that 
  the 
  corpuscle 
  is 
  

   not 
  acted 
  on 
  by 
  any 
  forces 
  except 
  those 
  due 
  to 
  the 
  external 
  

   electric 
  field, 
  we 
  can 
  easily 
  show 
  that 
  if 
  28t 
  is 
  the 
  excess 
  of 
  

   the 
  free 
  time 
  for 
  the 
  ion 
  projected 
  against 
  the 
  current 
  over 
  

   that 
  for 
  the 
  ion 
  projected 
  along 
  it, 
  then 
  

  

  2& 
  * 
  X 
  m' 
  

  

  u 
  

  

  (3) 
  

  

  The 
  second 
  term 
  in 
  (2) 
  is 
  proportional 
  to 
  the 
  value 
  of 
  St, 
  

   and 
  with 
  the 
  value 
  of 
  $t 
  given 
  by 
  equation 
  (3) 
  is 
  greater 
  than 
  

   the 
  first, 
  indicating 
  that 
  the 
  resistance 
  is 
  diminished 
  by 
  the 
  

   magnetic 
  field. 
  Equation 
  (3) 
  depends, 
  however, 
  entirely 
  upon 
  

   the 
  assumption 
  that 
  the 
  mean 
  free 
  path 
  is 
  independ 
  -nt 
  of 
  the 
  

   velocity; 
  i. 
  e., 
  that 
  the 
  collision 
  between 
  a 
  corpuscle 
  and 
  a 
  

   molecule 
  is 
  analogous 
  to 
  that 
  between 
  two 
  hard 
  elastic 
  bodies 
  

   which 
  do 
  not 
  exert 
  any 
  force 
  upon 
  each 
  other 
  until 
  they 
  are 
  

   in 
  contact. 
  If 
  we 
  remember 
  that 
  the 
  corpuscles 
  are 
  highly 
  

   charged 
  with 
  electricity 
  and 
  always 
  within 
  very 
  short 
  distance 
  

   of 
  tiie 
  molecules, 
  it 
  seems 
  extremely 
  improbable 
  that 
  the 
  

   collision 
  can 
  be 
  of 
  the 
  type 
  of 
  that 
  between 
  hard 
  elastic 
  

   spheres. 
  It 
  would 
  seem 
  much 
  more 
  reasonable 
  to 
  adopt 
  a 
  view 
  

   of 
  the 
  collisions 
  analogous 
  to 
  that 
  used 
  by 
  Maxwell 
  when 
  he 
  

   investigated 
  the 
  properties 
  of 
  a 
  gas 
  in 
  which 
  the 
  force 
  between 
  

   the 
  molecules 
  varied 
  inversely 
  as 
  the 
  fifth 
  power 
  of 
  the 
  

   distance. 
  On 
  this 
  view 
  the 
  collision 
  consists 
  of 
  a 
  deflexion 
  of 
  

   the 
  path 
  of 
  the 
  corpuscle 
  due 
  to 
  the 
  force 
  exerted 
  on 
  it 
  by 
  a 
  

   molecule 
  near 
  to 
  which 
  it 
  passes. 
  If 
  we 
  take 
  this 
  view, 
  then 
  

   equation 
  (3) 
  no 
  longer 
  holds: 
  the 
  equation 
  which 
  replaces 
  it 
  

   depends 
  upon 
  the 
  law 
  of 
  force 
  between 
  the 
  corpuscle 
  and 
  the 
  

   molecule. 
  If, 
  for 
  example, 
  the 
  law 
  is 
  inversely 
  as 
  the 
  fifth 
  

   power 
  of 
  the 
  distance, 
  6t 
  = 
  and 
  the 
  second 
  term 
  in 
  (2) 
  

  

  