﻿294 
  Dr. 
  H. 
  L. 
  Bronson 
  : 
  Relative 
  Activity 
  of 
  Emanation 
  

  

  deposit, 
  instead 
  of 
  being 
  greater, 
  was 
  less 
  than 
  one 
  half 
  that 
  

   due 
  to 
  the 
  emanation. 
  

  

  Before 
  attempting 
  any 
  explanation 
  of 
  the 
  above 
  results, 
  

   we 
  will 
  calculate 
  with 
  some 
  degree 
  of 
  accuracy 
  the 
  relative 
  

   activities 
  that 
  would 
  be 
  expected 
  from 
  the 
  emanation 
  and 
  its 
  

   active 
  deposit 
  under 
  the 
  conditions 
  of 
  the 
  above 
  experiment. 
  

   In 
  order 
  to 
  calculate 
  the 
  mean 
  free 
  paths 
  of 
  the 
  a 
  particles 
  

   from 
  the 
  different 
  substances, 
  certain 
  assumptions 
  were 
  made: 
  

   first, 
  that 
  the 
  cylinder 
  was 
  infinite 
  in 
  length, 
  that 
  is, 
  the 
  

   effect 
  of 
  the 
  ends 
  was 
  neglected 
  ; 
  second, 
  that 
  the 
  emanation 
  

   was 
  distributed 
  uniformly 
  throughout 
  the 
  cylinder 
  ; 
  third, 
  

   that 
  the 
  a 
  particles 
  were 
  shot 
  off 
  equally 
  in 
  every 
  direction, 
  

   and 
  therefore 
  that 
  only 
  one 
  half 
  of 
  those 
  from 
  the 
  active 
  

   deposit 
  produced 
  any 
  ions 
  in 
  the 
  air. 
  For 
  the 
  purpose 
  of 
  

   this 
  calculation, 
  the 
  first 
  assumption 
  should 
  be 
  approximately 
  

   true, 
  for 
  the 
  emanation 
  was 
  drawn 
  diagonally 
  across 
  the 
  

   testing 
  vessel, 
  entering 
  about 
  5 
  cms. 
  from 
  one 
  end 
  and 
  

   leaving 
  the 
  vessel 
  on 
  the 
  opposite 
  side 
  and 
  about 
  the 
  same 
  

   distance 
  from 
  the 
  other 
  end. 
  There 
  should, 
  therefore, 
  be 
  

   very 
  little 
  emanation 
  or 
  active 
  deposit 
  near 
  the 
  ends. 
  In 
  

   .any 
  case, 
  any 
  errors 
  introduced 
  into 
  the 
  calculations 
  by 
  this 
  

   assumption 
  would 
  affect 
  the 
  mean 
  free 
  paths 
  of 
  the 
  a 
  par- 
  

   ticles 
  from 
  the 
  emanation 
  and 
  active 
  deposit 
  by 
  nearly 
  the 
  

   same 
  amount, 
  and 
  would 
  therefore 
  have 
  very 
  little 
  effect 
  on 
  

   their 
  ratio. 
  It 
  is 
  difficult 
  to 
  estimate 
  the 
  accuracy 
  of 
  the 
  

   second 
  assumption, 
  but 
  the 
  air 
  current 
  was 
  so 
  rapid 
  at 
  the 
  

   entrance 
  to 
  the 
  vessel 
  that 
  the 
  emanation 
  snould 
  have 
  been 
  

   well 
  distributed. 
  The 
  third 
  assumption 
  is 
  commonly 
  made 
  

   in 
  all 
  radioactive 
  calculations. 
  

  

  On 
  these 
  assumptions 
  the 
  mean 
  free 
  path, 
  in 
  the 
  larger 
  

   testing 
  vessel, 
  of 
  the 
  u 
  particles 
  from 
  the 
  active 
  deposit 
  from 
  

   thorium 
  would 
  be 
  half 
  their 
  maximum 
  range, 
  since 
  one 
  half 
  

   the 
  a 
  particles 
  were 
  absorbed 
  by 
  the 
  metal 
  and 
  the 
  other 
  

   half 
  have 
  their 
  maximum 
  range 
  in 
  air. 
  This 
  gives 
  

  

  — 
  =6*8 
  cms. 
  as 
  the 
  sum 
  of 
  the 
  mean 
  free 
  paths 
  of 
  the 
  

  

  a 
  particles 
  from 
  thorium 
  B 
  and 
  thorium 
  C. 
  

  

  In 
  calculating 
  the 
  mean 
  free 
  path 
  of 
  the 
  a 
  particles 
  from 
  

   the 
  emanation, 
  it 
  was 
  found 
  easier 
  to 
  use 
  a 
  geometrical 
  than 
  

   an 
  analytical 
  method. 
  On 
  a 
  large 
  sheet 
  of 
  clear 
  mica 
  were 
  

   drawn 
  concentric 
  circles 
  from 
  1 
  to 
  9 
  cms. 
  in 
  radius 
  and 
  

   radial 
  lines 
  cutting 
  these 
  circles 
  every 
  10°. 
  In 
  order 
  to 
  find 
  

   the 
  mean 
  free 
  path 
  of 
  a. 
  particles 
  shot 
  out 
  from 
  a 
  given 
  

   point, 
  two 
  sections 
  of 
  the 
  cylinder 
  were 
  taken 
  through 
  this 
  

   point, 
  one 
  containing 
  the 
  axis 
  and 
  the 
  other 
  at 
  right 
  angles 
  

   to 
  it. 
  The 
  centre 
  of 
  the 
  concentric 
  circles 
  on 
  the 
  mica 
  was 
  

   then 
  placed 
  at 
  the 
  given 
  point 
  in 
  each 
  section 
  in 
  turn, 
  and 
  

  

  