﻿and 
  Active 
  Deposit 
  from 
  Thorium 
  and 
  Actinium. 
  295 
  

  

  the 
  length 
  o£ 
  the 
  free 
  path 
  along 
  each 
  radial 
  line 
  was 
  read 
  

   off 
  directly. 
  The 
  average 
  of 
  the 
  measurements 
  in 
  the 
  two 
  

   planes, 
  in 
  general, 
  gives 
  a 
  good 
  value 
  for 
  the 
  mean 
  free 
  path 
  

   of 
  an 
  a 
  particle 
  starting 
  from 
  the 
  given 
  point. 
  

  

  Table 
  II. 
  gives 
  the 
  results 
  of 
  the 
  measurements 
  for 
  the 
  

   mean 
  free 
  path 
  of 
  the 
  a 
  particle 
  of 
  thorium 
  emanation 
  in 
  the 
  

   larger 
  testing 
  vessel. 
  

  

  Table 
  II. 
  

  

  I. 
  

  

  II 
  a. 
  

  

  116. 
  

  

  II. 
  

  

  | 
  

   III. 
  

  

  0-5 
  

  

  5-5 
  

  

  55 
  

  

  55 
  

  

  2-75 
  

  

  T5 
  

  

  5-5 
  

  

  55 
  

  

  55 
  

  

  8-25 
  

  

  25 
  

  

  5-5 
  

  

  5-5 
  

  

  55 
  

  

  13-75 
  

  

  35 
  

  

  5-5 
  

  

  5-5 
  

  

  5-5 
  

  

  19-25 
  

  

  4-5 
  

  

  5'3 
  

  

  53 
  

  

  5-3 
  

  

  23-85 
  

  

  5-5 
  

  

  5-1 
  

  

  4-9 
  

  

  5-0 
  

  

  27-50 
  

  

  6-5 
  

  

  4-7 
  

  

  4-5 
  

  

  46 
  

  

  2990 
  

  

  7*5 
  

  

  41 
  

  

  39 
  

  

  4-0 
  

  

  30-00 
  

  

  8-5 
  

  

  33 
  

  

  3-0 
  

  

  32 
  

  

  27-20 
  

  

  1 
  405 
  

  

  

  

  

  182-5 
  

  

  !82'5 
  . 
  K 
  r 
  , 
  

  

  - 
  .,, 
  , 
  = 
  4 
  - 
  5 
  = 
  mean 
  free 
  path. 
  

   40-5 
  ^ 
  

  

  Column 
  I. 
  gives 
  the 
  distance 
  of 
  the 
  point 
  from 
  the 
  axis 
  of 
  

   the 
  cylinder. 
  Column 
  II. 
  is 
  the 
  mean 
  of 
  II 
  a. 
  and 
  II 
  b. 
  

   which 
  give 
  respectively 
  the 
  mean 
  free 
  paths 
  of 
  a. 
  particles 
  

   in 
  the 
  two 
  perpendicular 
  planes. 
  Since 
  the 
  emanation 
  is 
  

   uniformly 
  distributed 
  in 
  the 
  vessel, 
  the 
  number 
  of 
  atoms 
  of 
  

   the 
  emanation 
  at 
  a 
  given 
  distance 
  from 
  the 
  axis 
  of 
  the 
  

   cylinder 
  is 
  proportional 
  to 
  their 
  distance 
  from 
  the 
  axis. 
  

   Therefore 
  it 
  is 
  necessary 
  to 
  take 
  the 
  sum 
  of 
  the 
  product 
  of 
  

   columns 
  I. 
  and 
  II. 
  and 
  divide 
  by 
  the 
  sum 
  of 
  column 
  I. 
  in 
  

   order 
  to 
  get 
  the 
  mean 
  free 
  path 
  of 
  the 
  a 
  particles 
  for 
  the 
  

   entire 
  cylinder. 
  The 
  products 
  of 
  columns 
  I. 
  and 
  II. 
  is 
  given 
  

   in 
  column 
  III. 
  

  

  We 
  have 
  seen 
  that 
  the 
  sum 
  of 
  the 
  mean 
  free 
  paths 
  of 
  the 
  

   a. 
  particles 
  from 
  thorium 
  B 
  and 
  thorium 
  C 
  is 
  6'8 
  cms. 
  This 
  

   value 
  divided 
  by 
  45 
  cms. 
  gives 
  1*51, 
  which 
  should 
  be 
  the 
  

   ratio 
  of 
  the 
  ionization 
  due 
  to 
  the 
  active 
  deposit 
  to 
  that 
  due 
  

   to 
  the 
  emanation, 
  if 
  an 
  atom 
  of 
  each 
  substance 
  in 
  breaking 
  

   up 
  throws 
  out 
  one 
  a 
  particle, 
  and 
  if 
  the 
  number 
  of 
  ions 
  

   produced 
  per 
  cm. 
  by 
  an 
  a. 
  particle 
  is 
  the 
  same 
  for 
  each 
  cm. 
  

   of 
  its 
  path. 
  That 
  the 
  latter 
  assumption 
  is 
  not 
  strictly 
  true 
  

   has 
  been 
  shown 
  by 
  Bragg, 
  McClung, 
  Hahn, 
  as 
  well 
  as 
  by 
  

   the 
  writer. 
  This 
  introduces 
  only 
  a 
  small 
  correction, 
  however, 
  

   and 
  will 
  be 
  discussed 
  later. 
  Now 
  the 
  measured 
  ratio 
  of 
  the 
  

   activities 
  of 
  the 
  active 
  deposit 
  and 
  the 
  emanation 
  was 
  about 
  

  

  