﻿Ions 
  in 
  Gases 
  under 
  Different 
  Pressures* 
  299 
  

  

  selected 
  for 
  the 
  determination 
  given 
  below. 
  A 
  considerable 
  

   number 
  of 
  absolute 
  determinations 
  at 
  other 
  pressures 
  have 
  

   been 
  made 
  as 
  well, 
  which 
  it 
  is 
  not 
  necessary 
  to 
  reproduce 
  

   here. 
  

  

  On 
  referring 
  to 
  equation 
  (7), 
  it 
  will 
  be 
  seen 
  that 
  it 
  is 
  

   necessary 
  to 
  make 
  an 
  absolute 
  determination 
  of 
  the 
  three 
  

   quantities 
  K, 
  Q, 
  and 
  N, 
  in 
  order 
  to 
  determine 
  a. 
  K 
  is 
  a 
  

   constant 
  depending 
  entirely 
  on 
  the 
  dimensions 
  and 
  position 
  

   of 
  the 
  apparatus. 
  Q 
  is 
  the 
  total 
  number 
  of 
  ions 
  produced 
  

   per 
  second 
  within 
  the 
  volume 
  of 
  the 
  cone 
  of 
  rays 
  included 
  

   between 
  the 
  two 
  extreme 
  electrodes, 
  and 
  is 
  proportional 
  to 
  

   the 
  deflexion 
  of 
  the 
  electrometer-needle 
  per 
  second. 
  N 
  is 
  

   the 
  total 
  number 
  of 
  ions 
  in 
  the 
  same 
  volume 
  at 
  the 
  instant 
  

   that 
  the 
  rays 
  cease, 
  and 
  is 
  proportional 
  to 
  the 
  steady 
  deflexion 
  

   of 
  the 
  electrometer-needle. 
  

  

  From 
  formula 
  (6) 
  

  

  K=ZA,(l 
  + 
  A) 
  2 
  , 
  

  

  where 
  the 
  quantities 
  I, 
  A 
  1? 
  and 
  d 
  represent 
  the 
  dimensions 
  as 
  

   described 
  in 
  fio-. 
  '6. 
  

  

  I 
  = 
  20 
  cms. 
  

  

  d 
  =25*07 
  cms. 
  

  

  A 
  ^ 
  XT 
  

  

  A 
  1= 
  =pXH, 
  

  

  where 
  H 
  = 
  area 
  of 
  the 
  orifice 
  in 
  the 
  lead 
  plate 
  through 
  which 
  

   the 
  rays 
  passed 
  before 
  entering 
  the 
  cylinder, 
  and 
  h 
  its 
  dis- 
  

   tance 
  from 
  the 
  source. 
  

  

  . 
  a 
  _25'07 
  2 
  

  

  ^-l—i 
  Q7rn2 
  x 
  ' 
  li 
  

  

  19-07 
  2 
  

   = 
  12*28 
  sq. 
  cms. 
  

  

  ••• 
  K 
  = 
  2 
  °x 
  i2 
  - 
  28 
  ( 
  i+ 
  5§iy 
  

  

  If 
  d 
  x 
  = 
  deflexion 
  of 
  the 
  electrometer 
  -needle 
  per 
  second 
  due 
  to 
  

   the 
  passage 
  of 
  the 
  ions 
  to 
  the 
  electrodes 
  ; 
  

   S 
  = 
  deflexion 
  due 
  to 
  a 
  standard 
  Clark 
  cell; 
  and 
  

   Ci 
  = 
  capacity 
  in 
  microfarads 
  of 
  electrometer, 
  connexions, 
  &c, 
  

  

  then 
  the 
  quantity 
  of 
  electricity 
  which 
  passes 
  between 
  the 
  

  

  electrodes 
  per 
  second 
  is 
  equal 
  to 
  

  

  ^ 
  X 
  — 
  ^ 
  — 
  X 
  ji* 
  X 
  3 
  x 
  10 
  9 
  electrostatic 
  units. 
  

  

  