﻿Active 
  Deposit 
  of 
  Actinium 
  in 
  Electric 
  Fields. 
  387 
  

  

  the 
  axis 
  when 
  the 
  sign 
  of 
  the 
  voltage 
  changes, 
  and 
  since 
  the 
  

   maximum 
  activity 
  is 
  found 
  on 
  the 
  cathode, 
  it 
  follows 
  that 
  

   none 
  of 
  the 
  deposit 
  atoms 
  carries 
  a 
  negative 
  charge, 
  and 
  that 
  

   only 
  neutral 
  and 
  positively 
  charged 
  atoms 
  exist 
  in 
  the 
  gas. 
  

  

  III. 
  

  

  Rutherford 
  * 
  has 
  shown 
  that 
  the 
  active 
  deposits 
  of 
  thorium 
  

   and 
  radium 
  have 
  approximately 
  the 
  same 
  mobility 
  in 
  an 
  

   electric 
  field 
  as 
  the 
  positive 
  ion. 
  Schmidt 
  f 
  has 
  shown 
  that 
  

   the 
  same 
  holds 
  in 
  the 
  case 
  of 
  radium 
  A. 
  Franck 
  J, 
  working 
  

   with 
  thorium 
  D, 
  showed 
  that 
  the 
  velocity 
  was 
  the 
  same 
  as 
  

   that 
  of 
  the 
  positive 
  ion 
  in 
  the 
  corresponding 
  gas. 
  It 
  there- 
  

   fore 
  appears 
  that 
  one 
  may 
  assume 
  that 
  recoil 
  atoms 
  of 
  all 
  

   radioactive 
  bodies 
  behave 
  like 
  positive 
  ions 
  in 
  the 
  same 
  gas. 
  

   Assuming 
  this 
  to 
  hold 
  for 
  actinium 
  A 
  and 
  B, 
  we 
  can 
  

   calculate 
  the 
  mean 
  time 
  of 
  passage 
  of 
  a 
  recoil 
  atom 
  out 
  of 
  

   the 
  gas 
  to 
  the 
  boundaries 
  of 
  the 
  vessel. 
  Consider 
  two 
  con- 
  

   centric 
  cylinders 
  radii 
  a 
  and 
  b. 
  The 
  electrostatic 
  force 
  R 
  at 
  

   any 
  point 
  distance 
  r 
  from 
  the 
  axis 
  is 
  given 
  by 
  

  

  R=V/(rlog^) 
  

  

  where 
  V 
  is 
  the 
  potential 
  difference 
  between 
  the 
  cylinders. 
  

   Let 
  /c 
  be 
  the 
  mobility 
  of 
  the 
  atom. 
  In 
  time 
  8t 
  the 
  distance 
  

   traversed 
  by 
  the 
  atom 
  is 
  

  

  whence 
  r 
  a 
  r 
  ^°g 
  

  

  %J 
  r 
  

  

  ~Y^ 
  dr 
  

  

  i 
  b 
  

  

  1 
  l 
  ° 
  g 
  a 
  

  

  2' 
  V/c 
  ^ 
  a) 
  ' 
  

  

  Consider 
  the 
  atoms 
  within 
  a 
  ring 
  of 
  radius 
  r 
  and 
  let 
  

   their 
  volume 
  density 
  be 
  p. 
  The 
  mean 
  time 
  of 
  passage 
  T 
  is 
  

   given 
  by 
  

  

  1 
  C 
  b 
  

  

  * 
  Rutherford. 
  Phil. 
  Mac-, 
  v. 
  p. 
  75 
  (1903). 
  

  

  t 
  Schmidt, 
  Phys. 
  Zeit. 
  ix. 
  p. 
  184 
  (1908). 
  

  

  % 
  Franck, 
  Verh. 
  D. 
  Phys. 
  Ges. 
  xi. 
  p. 
  397 
  (1909). 
  

  

  