﻿Properties 
  of 
  Newly 
  Prepared 
  Gases. 
  139 
  

  

  12 
  . 
  10 
  -7 
  . 
  Hence 
  the 
  carriers 
  are 
  large 
  compared 
  with 
  mole- 
  

   cular 
  dimensions. 
  

  

  The 
  velocities 
  obtained 
  for 
  the 
  curriers 
  in 
  the 
  conductivity 
  

   due 
  to 
  Rontgen 
  rays 
  are 
  far 
  greater 
  than 
  the 
  above. 
  Thus 
  

   for 
  oxygen 
  and 
  hydrogen 
  Mr. 
  Rutherford 
  obtains 
  velocities 
  

   of 
  5*2 
  and 
  1*4 
  centimetres 
  per 
  second 
  under 
  a 
  volt 
  per 
  

   centimetre 
  (Phil. 
  Mag. 
  Nov. 
  1897). 
  

  

  If 
  we 
  assume 
  that 
  the 
  charges 
  on 
  the 
  carriers 
  are 
  of 
  the 
  

   same 
  order 
  as 
  those 
  obtained 
  in 
  Section 
  7, 
  we 
  see 
  that 
  the 
  

   dimensions 
  of 
  the 
  carriers 
  are 
  smaller 
  than 
  those 
  with 
  which 
  

   we 
  are 
  here 
  dealing. 
  

  

  The 
  Discharging 
  Power 
  of 
  Tubes. 
  

  

  14. 
  It 
  has 
  been 
  shown 
  that 
  if 
  a 
  gas 
  with 
  a 
  uniform 
  charge 
  

   p 
  per 
  c. 
  c. 
  be 
  left 
  in 
  a 
  tube 
  for 
  a 
  time 
  t, 
  the 
  density 
  

   of 
  the 
  electrification 
  falls 
  to 
  a 
  uniform 
  value 
  p 
  } 
  given 
  by 
  

  

  the 
  equation 
  p= 
  =— 
  — 
  — 
  where 
  a 
  is 
  a 
  constant. 
  Now, 
  if 
  we 
  

   1 
  1 
  + 
  ap 
  t 
  

  

  suppose 
  that 
  the 
  velocity 
  of 
  a 
  gas 
  as 
  it 
  passes 
  along 
  a 
  tube 
  

  

  be 
  perfectly 
  uniform, 
  and 
  that 
  no 
  discharging 
  takes 
  place 
  

  

  due 
  to 
  accidental 
  circumstances, 
  the 
  values 
  of 
  t, 
  p, 
  and 
  p 
  

  

  would 
  be 
  connected 
  by 
  the 
  same 
  equation, 
  where 
  now 
  t 
  

  

  denotes 
  the 
  time 
  that 
  any 
  portion 
  of 
  the 
  gas 
  takes 
  to 
  traverse 
  

  

  the 
  tube, 
  p 
  and 
  p 
  being 
  the 
  densities 
  of 
  electrification 
  on 
  

  

  entering 
  and 
  escaping 
  from 
  the 
  tube. 
  When 
  the 
  gas 
  is 
  given 
  

  

  off 
  by 
  a 
  current 
  through 
  an 
  electrolyte, 
  the 
  volume 
  q 
  w 
  Inch 
  

  

  enters 
  the 
  tube 
  per 
  second 
  is 
  known 
  when 
  the 
  current 
  is 
  

  

  y 
  

   known; 
  so 
  that 
  t= 
  — 
  where 
  V 
  is 
  the 
  volume 
  of 
  the 
  tube, 
  

  

  and 
  the 
  above 
  equation 
  becomes 
  — 
  — 
  ^= 
  -^— 
  . 
  The 
  values 
  of 
  

  

  .P 
  . 
  9 
  

  

  p 
  and 
  p 
  are 
  easily 
  found 
  and 
  satisfy 
  this 
  equation 
  roughly, 
  

  

  so 
  that 
  a 
  can 
  be 
  determined 
  ; 
  its 
  value, 
  however, 
  is 
  greater 
  

  

  4*7r6 
  

   than 
  -y- 
  found 
  already. 
  This 
  is 
  due 
  to 
  accidental 
  discharg- 
  

   ing, 
  as 
  it 
  can 
  be 
  shown 
  that, 
  even 
  when 
  the 
  carrier 
  is 
  so 
  

   large 
  that 
  the 
  small 
  E.M.F. 
  driving 
  it 
  to 
  the 
  side 
  of 
  the 
  

   tube 
  could 
  have 
  no 
  appreciable 
  effect, 
  still 
  a 
  measurable 
  

   discharge 
  takes 
  place 
  (see 
  Section 
  21). 
  

  

  15. 
  If 
  the 
  gas 
  be 
  run 
  into 
  an 
  insulated 
  inductor 
  after 
  

  

  traversing 
  the 
  tube, 
  — 
  — 
  - 
  is 
  the 
  ratio 
  of 
  the 
  charge 
  gained 
  

  

  r 
  

  

  per 
  minute 
  by 
  the 
  tube 
  to 
  the 
  charge 
  gained 
  per 
  minute 
  by 
  

   the 
  inductor. 
  These 
  charges 
  can 
  be 
  easily 
  found 
  by 
  connecting 
  

   the 
  tube 
  and 
  inductor 
  alternately 
  to 
  the 
  insulated 
  quadrants 
  

  

  