﻿474 
  Mr. 
  J. 
  S. 
  Townsend 
  on 
  Applications 
  of 
  

  

  We 
  have 
  

  

  du 
  v 
  dp 
  

  

  nm-j- 
  =n2Le 
  f 
  emu, 
  

  

  dt 
  dec 
  

  

  and 
  two 
  similar 
  equations 
  from 
  which 
  the 
  motion 
  of 
  the 
  gas 
  A 
  

   can 
  be 
  determined. 
  The 
  value 
  of 
  a, 
  as 
  given 
  by 
  Maxwell 
  

   (J. 
  C. 
  Maxwell, 
  " 
  Dynamical 
  Theory 
  of 
  Gases/' 
  Phil. 
  Mag. 
  

  

  1868, 
  vol. 
  xxxv.) 
  is 
  hA^ 
  — 
  = 
  hA 
  1 
  mp 
  2 
  . 
  In 
  this 
  case 
  p 
  2 
  isthe 
  

  

  density 
  of 
  B, 
  which 
  remains 
  constant, 
  so 
  that 
  a 
  is 
  also 
  

   constant. 
  

  

  Since 
  m 
  is 
  so 
  small 
  compared 
  with 
  the 
  other 
  quantities 
  we 
  

   may 
  omit 
  the 
  first 
  term, 
  and 
  we 
  obtain 
  

  

  Xe=- 
  C 
  ^ 
  + 
  aw 
  (1) 
  

  

  n 
  dx 
  

  

  dv 
  

   If 
  X 
  is 
  large, 
  so 
  that 
  j- 
  is 
  small 
  in 
  comparison 
  with 
  Xe, 
  

  

  we 
  have 
  the 
  velocity 
  u 
  proportional 
  to 
  X 
  ; 
  and 
  if 
  V 
  is 
  the 
  

   velocity 
  of 
  the 
  carrier 
  when 
  acted 
  on 
  by 
  a 
  force 
  of 
  1 
  volt 
  per 
  

   centimetre, 
  we 
  have 
  

  

  e 
  

  

  Hence 
  when 
  X, 
  Y, 
  and 
  Z 
  are 
  zero, 
  equation 
  (1) 
  reduces 
  to 
  

   I 
  dp 
  , 
  e 
  

  

  Let 
  N= 
  number 
  of 
  molecules 
  in 
  a 
  cubic 
  centimetre 
  of 
  gas 
  

   at 
  pressure 
  p 
  and 
  temperature 
  15° 
  C. 
  (being 
  the 
  temperature 
  

   at 
  which 
  we 
  suppose 
  the 
  conductivity 
  is 
  determined), 
  then 
  

  

  n 
  N 
  

  

  Hence 
  from 
  equation 
  (2) 
  

  

  3( 
  

  

  e 
  N 
  dx 
  

   similarly 
  

  

  - 
  pu 
  = 
  f£ 
  ; 
  (3) 
  

  

  p 
  e 
  N 
  dtp 
  P 
  e 
  N 
  dz 
  

  

  The 
  equation 
  of 
  continuity 
  is 
  

  

  dp 
  d 
  , 
  N 
  , 
  d 
  , 
  . 
  d 
  , 
  

  

  