﻿134 
  Mr. 
  John 
  S. 
  Townsend 
  on 
  Electrical 
  

  

  where 
  e 
  is 
  the 
  charge 
  on 
  the 
  carrier 
  and 
  k 
  is 
  a 
  constant 
  to 
  

   be 
  determined 
  experimentally. 
  Substituting 
  these 
  values 
  for 
  

   u, 
  v, 
  and 
  w 
  in 
  the 
  equation 
  of 
  continuity 
  we 
  obtain 
  

  

  - 
  -£ 
  — 
  <?v 
  2 
  <£ 
  = 
  0, 
  but 
  V 
  2( 
  / 
  > 
  = 
  —knpy 
  

  

  therefore 
  

  

  k 
  So 
  . 
  

  

  — 
  -£ 
  = 
  —\n7e. 
  

   p 
  ot 
  

  

  Integrating 
  we 
  obtain 
  

  

  p= 
  7lfe^ 
  (2) 
  

  

  * 
  k 
  

  

  where 
  p 
  is 
  the 
  initial 
  density, 
  which 
  is 
  uniform 
  throughout 
  

   the 
  space 
  considered. 
  

  

  Equation 
  (2) 
  shows 
  that 
  the 
  motion 
  takes 
  place 
  in 
  such 
  a 
  

   way 
  that 
  the 
  density 
  p 
  is 
  a 
  function 
  of 
  the 
  time 
  only, 
  and 
  

   does 
  not 
  vary 
  from 
  point 
  to 
  point 
  in 
  the 
  gas 
  ; 
  on 
  this 
  account 
  

   no 
  variation 
  in 
  the 
  pressure 
  of 
  the 
  charged 
  gas 
  takes 
  place, 
  

  

  and 
  the 
  terms 
  -f-. 
  -~-, 
  — 
  , 
  which 
  have 
  in 
  general 
  to 
  be 
  taken 
  

   da: 
  7 
  ay 
  dz 
  1 
  & 
  

  

  account 
  of 
  when 
  dealing 
  with 
  the 
  motion 
  of 
  gases, 
  can 
  be 
  

  

  omitted 
  in 
  equations 
  (1) 
  since 
  p 
  does 
  not 
  vary 
  from 
  point 
  to 
  

  

  point. 
  

  

  When 
  the 
  gas 
  is 
  in 
  a 
  closed 
  vessel 
  the 
  mutual 
  repulsion 
  of 
  

   the 
  carriers 
  of 
  the 
  electricity 
  drives 
  them 
  to 
  the 
  sides, 
  where 
  

   they 
  either 
  remain 
  so 
  close 
  to 
  the 
  walls 
  that 
  they 
  cannot 
  be 
  

   blown 
  out, 
  or 
  else 
  get 
  discharged 
  against 
  the 
  sides. 
  The 
  

   charged 
  gas 
  remaining 
  in 
  the. 
  vessel 
  has 
  a 
  uniform 
  density 
  given 
  

   by 
  equation 
  (2), 
  and 
  if 
  the 
  vessel 
  which 
  contains 
  it 
  is 
  an 
  in- 
  

   sulated 
  conductor 
  connected 
  to 
  a 
  pair 
  of 
  quadrants 
  of 
  an 
  

   electrometer 
  the 
  deflexion 
  on 
  the 
  electrometer-scale 
  will 
  be 
  

   proportional 
  to 
  p 
  when 
  the 
  charged 
  gas 
  is 
  blown 
  out 
  of 
  the 
  

   vessel. 
  

  

  10. 
  In 
  order 
  to 
  investigate 
  experimentally 
  the 
  rate 
  at 
  which 
  

   the 
  gas 
  loses 
  its 
  charge 
  to 
  the 
  sides 
  of 
  an 
  inductor, 
  or 
  in 
  other 
  

   words 
  to 
  find 
  how 
  the 
  density 
  p 
  will 
  vary 
  with 
  the 
  time, 
  a 
  

   metal 
  cylinder 
  C 
  (fig. 
  4), 
  30*2 
  centimetres 
  long 
  and 
  1*6 
  centi- 
  

   metres 
  in 
  diameter, 
  was 
  used. 
  The 
  two 
  ends 
  of 
  the 
  cylinder 
  

   fitted 
  into 
  paraffin 
  blocks, 
  P 
  x 
  and 
  P 
  2 
  , 
  into 
  which 
  were 
  also 
  

   fixed 
  the 
  glass 
  tubes 
  T 
  x 
  and 
  T 
  2 
  . 
  The 
  tube 
  T 
  lf 
  through 
  which 
  

   the 
  cylinder 
  was 
  filled, 
  had 
  several 
  layers 
  of 
  fine 
  copper 
  

   gauze 
  across 
  the 
  broad 
  end, 
  which 
  tended 
  to 
  distribute 
  the 
  

  

  