﻿Amount 
  of 
  Radium 
  Emanation 
  in 
  the 
  Atmosphere, 
  623 
  

  

  pendent 
  of 
  the 
  total 
  strength 
  of 
  the 
  solution 
  employed, 
  

   ranging 
  from 
  1*57 
  x 
  10~ 
  7 
  to 
  10 
  -10 
  gram 
  of 
  radium. 
  

  

  Thus 
  the 
  emanation 
  from 
  1*56 
  m. 
  3 
  of 
  air 
  gave 
  an 
  electro- 
  

   scope 
  reading 
  of 
  0'125 
  division 
  a 
  minute, 
  and 
  that 
  from 
  

   1*57 
  X 
  10~ 
  9 
  grm. 
  of 
  radium 
  gave 
  0'98. 
  Hence 
  it 
  was 
  reasoned 
  

   that 
  one 
  cubic 
  metre 
  of 
  air 
  contained 
  the 
  emanation 
  which 
  

  

  ., 
  . 
  . 
  . 
  ri 
  . 
  .,, 
  0-125 
  1-57 
  xlO" 
  9 
  

  

  would 
  be 
  in 
  equilibrium 
  with 
  ^ 
  x 
  

  

  1-5G 
  0*98 
  

  

  or 
  

  

  127 
  x 
  10 
  ~ 
  12 
  gram 
  of 
  radium. 
  

  

  The 
  quantities 
  of 
  charcoal 
  employed 
  were 
  varied 
  and 
  

   experiments 
  were 
  made 
  at 
  intervals 
  during 
  several 
  weeks. 
  

   The 
  lowest 
  value 
  found 
  was 
  stated 
  to 
  be 
  24 
  x 
  10 
  ~ 
  12 
  , 
  and 
  the 
  

   highest 
  127 
  X 
  10 
  -12 
  , 
  with 
  a 
  probable 
  average 
  value 
  of 
  

   80 
  x 
  10- 
  13 
  gram. 
  

  

  There 
  is, 
  however, 
  a 
  somewhat 
  subtle 
  error 
  in 
  the 
  above 
  

   method 
  of 
  reasoning. 
  If 
  the 
  speed 
  of 
  the 
  air-current 
  through 
  

   the 
  tubes 
  is 
  varied, 
  the 
  percentage 
  amount 
  of 
  emanation 
  

   absorbed 
  by 
  the 
  charcoal 
  is 
  a 
  function 
  of 
  the 
  speed. 
  The 
  

   exact 
  relations 
  between 
  these 
  quantities 
  have 
  not, 
  however, 
  

   as 
  yet 
  been 
  determined 
  in 
  the 
  case 
  of 
  radium 
  emanation. 
  

   When 
  air 
  is 
  drawn 
  for 
  a 
  given 
  time 
  from 
  the 
  atmosphere 
  

   through 
  the 
  tubes, 
  it 
  is 
  clear 
  that, 
  on 
  varying 
  the 
  speed, 
  the 
  

   greater 
  the 
  amount 
  of 
  air, 
  the 
  greater 
  is 
  the 
  amount 
  of 
  

   emanation 
  passing 
  to 
  the 
  charcoal. 
  But 
  when 
  using 
  the 
  

   standard 
  solution 
  of 
  radium, 
  the 
  amount 
  of 
  emanation 
  passing 
  

   therefrom 
  to 
  the 
  charcoal 
  in 
  a 
  given 
  time 
  is 
  entirely 
  inde- 
  

   pendent 
  of 
  the 
  speed 
  of 
  the 
  air-current, 
  although 
  the 
  per- 
  

   centage 
  amount 
  absorbed 
  is 
  dependent 
  on 
  the 
  speed 
  in 
  both 
  

   cases. 
  It 
  will 
  be 
  seen 
  then 
  that 
  the 
  method 
  of 
  calculation 
  

   given 
  above 
  is 
  not 
  quite 
  correct, 
  and 
  it 
  should 
  be 
  replaced 
  

   by 
  the 
  following 
  : 
  — 
  

  

  I. 
  Let 
  1 
  grm. 
  of 
  radium 
  produce 
  m 
  grins, 
  of 
  emanation 
  per 
  

   second, 
  and 
  let 
  M 
  gms. 
  of 
  emanation 
  be 
  in 
  equilibrium 
  with 
  

   1 
  grm. 
  of 
  radium, 
  so 
  that 
  

  

  ° 
  /ICO 
  

  

  M=l 
  me-*dt 
  = 
  ™. 
  

   \ 
  X 
  

  

  II. 
  Let 
  the 
  amount 
  of 
  radium 
  in 
  the 
  standard 
  solution 
  be 
  

   B/, 
  and 
  suppose 
  that 
  initially 
  any 
  accumulation 
  of 
  emanation 
  

   has 
  been 
  removed 
  by 
  boiling 
  or 
  by 
  an 
  air- 
  current. 
  The 
  

   amount 
  of 
  emanation 
  given 
  off 
  is 
  m 
  W 
  grm. 
  per 
  second, 
  so 
  

   that 
  if 
  at 
  the 
  end 
  of 
  the 
  experiment, 
  after 
  absorption, 
  heating, 
  

   and 
  collection, 
  Y' 
  is 
  the 
  maximum 
  electroscope 
  reading, 
  in 
  

   divisions 
  per 
  minute, 
  due 
  to 
  the 
  emanation 
  from 
  the 
  solution, 
  

   we 
  have 
  

  

  Y' 
  = 
  \ 
  hmB! 
  e~ 
  kt 
  dt=kmW 
  ' 
  =— 
  i 
  — 
  . 
  . 
  . 
  (1) 
  

  

  '^ 
  A, 
  

  

  