﻿produced 
  in 
  Air 
  hy 
  the 
  Motion 
  of 
  Negative 
  Ions. 
  217 
  

  

  in 
  unit 
  volume 
  by 
  the 
  Rontgen 
  rays. 
  Let 
  C 
  r 
  be 
  the 
  steady 
  

   current 
  inwards 
  of 
  negative 
  ions 
  across 
  a 
  coaxial 
  cylinder 
  of 
  

   unit 
  length 
  and 
  of 
  radius 
  r. 
  

  

  Then 
  C 
  r 
  increases 
  as 
  r 
  diminishes. 
  Let 
  a 
  be 
  the 
  number 
  

   of 
  ions 
  generated 
  by 
  a 
  single 
  ion 
  in 
  moving 
  through 
  

   1 
  centimetre. 
  

  

  Then 
  

  

  — 
  dC 
  r 
  = 
  C 
  r 
  a 
  dr 
  + 
  2irr 
  dr 
  N 
  e. 
  

  

  e 
  being 
  the 
  charge 
  on 
  an 
  ion. 
  

   The 
  integral 
  of 
  this 
  equation 
  is 
  

  

  C 
  r 
  =27rlSr 
  o 
  el 
  pdp 
  

  

  ] 
  ? 
  r 
  «dr 
  

  

  since 
  C 
  6 
  = 
  0. 
  

  

  Therefore 
  the 
  quantity 
  of 
  negative 
  electricity 
  received 
  

   per 
  second 
  by 
  the 
  wire 
  is 
  

  

  f*P 
  \ 
  ado 
  

  

  C 
  = 
  27rN 
  ei 
  pdpe 
  da 
  . 
  

   If 
  a 
  = 
  we 
  have 
  

  

  Therefore 
  

  

  C 
  = 
  7rNe(//-a 
  2 
  ). 
  

  

  2C 
  f 
  » 
  

   > 
  2 
  -a 
  2 
  

  

  U 
  a 
  

  

  C 
  = 
  -I&- 
  (°rdrJ 
  a 
  

  

  6. 
  'C 
  may 
  be 
  approximately 
  determined 
  by 
  observation. 
  

   The 
  tables 
  show 
  that 
  for 
  small 
  forces 
  between 
  the 
  cylinders 
  

   the 
  positive 
  current 
  is 
  greater 
  than 
  the 
  corresponding 
  negative 
  

   current. 
  This 
  arises 
  from 
  the 
  secondary 
  radiation 
  which 
  

   originates 
  from 
  the 
  copper 
  wire. 
  Thus 
  it 
  has 
  been 
  shown 
  

   by 
  P. 
  Curie 
  and 
  G. 
  Sagnac 
  (Comptes 
  JRendus, 
  vol. 
  cxxx. 
  

   9th 
  April, 
  1900), 
  that 
  a 
  metal 
  like 
  copper 
  which 
  gives 
  out 
  a 
  

   large 
  secondary 
  radiation 
  loses 
  negative 
  electricity 
  under 
  the 
  

   action 
  of 
  the 
  Rontgen 
  r-iys. 
  In 
  the 
  present 
  case, 
  the 
  secondary 
  

   radiation 
  and 
  the 
  loss 
  of 
  negative 
  electricity 
  were 
  small 
  on 
  

   account 
  of 
  the 
  small 
  dimensions 
  of 
  the 
  wire. 
  Nevertheless, 
  it 
  

   was 
  sufficient 
  to 
  indicate 
  that 
  voltage 
  beyond 
  which 
  the 
  

   potential 
  of 
  the 
  aluminium 
  cylinder 
  cannot 
  be 
  lowered 
  without 
  

   causing 
  the 
  negative 
  current 
  sensibly 
  to 
  exceed 
  C 
  . 
  For 
  

   example, 
  to 
  consider 
  column 
  B, 
  it 
  is 
  clear 
  that 
  when 
  the 
  

   potential 
  of 
  the 
  cylinder 
  was 
  — 
  8*8, 
  —17*7, 
  — 
  37, 
  there 
  was 
  

   iro 
  detectable 
  increase 
  in 
  the 
  negative 
  current, 
  the 
  negative 
  

   being 
  so 
  far 
  less 
  than 
  the 
  corresponding 
  positive 
  current, 
  and 
  

   that 
  the 
  differences 
  in 
  both 
  currents 
  up 
  to 
  this 
  point 
  are 
  due 
  

  

  