﻿62± 
  Prof. 
  A. 
  IS. 
  Eve 
  on 
  the 
  Amount 
  of 
  Radium 
  

  

  Here 
  T 
  is 
  the 
  time 
  during 
  which 
  the 
  air-current 
  passes 
  

   through 
  the 
  charcoal, 
  and 
  h 
  is 
  a 
  constant 
  depending 
  on 
  the 
  

   electroscope 
  calibration 
  and 
  on 
  the 
  percentage 
  absorption 
  of 
  

   the 
  charcoal. 
  

  

  III. 
  In 
  the 
  case 
  of 
  air 
  drawn 
  from 
  outside 
  through 
  the 
  char- 
  

   coal, 
  let 
  X 
  equal 
  the 
  average 
  number 
  of 
  grams 
  of 
  emanation 
  

   present 
  in 
  one 
  cubic 
  metre 
  of 
  the 
  atmosphere 
  during 
  the 
  

   experiment, 
  and 
  let 
  v 
  be 
  the 
  volume, 
  in 
  cubic 
  metres, 
  of 
  air 
  

   passing 
  to 
  the 
  charcoal 
  every 
  second. 
  If 
  Y 
  is 
  the 
  maximum 
  

   reading 
  of 
  the 
  electroscope 
  in 
  divisions 
  per 
  minute, 
  after 
  

   collection, 
  heating, 
  and 
  introduction 
  in 
  the 
  electroscope, 
  we 
  

   find 
  

  

  Y= 
  ] 
  h>X.e-*dt 
  

  

  Jo 
  

  

  where 
  k 
  is 
  the 
  same 
  constant 
  as 
  before, 
  and 
  vT 
  = 
  Y 
  is 
  the 
  

   total 
  number 
  of 
  cubic 
  metres 
  of 
  air 
  passing 
  to 
  the 
  charcoal 
  

   in 
  time 
  T. 
  

  

  But 
  X 
  = 
  RM 
  = 
  R— 
  , 
  where 
  R 
  is 
  the 
  amount 
  of 
  pure 
  radium 
  

  

  A, 
  

  

  which 
  would 
  be 
  in 
  equilibrium 
  with 
  the 
  emanation 
  actually 
  

   present 
  in 
  each 
  cubic 
  metre 
  of 
  the 
  atmosphere 
  at 
  the 
  time 
  and 
  

   place 
  of 
  the 
  experiment. 
  

  

  So 
  that 
  Rm 
  l-g- 
  AT 
  

  

  Y 
  "^ 
  V 
  XT 
  X 
  ' 
  

   Comparing 
  (1) 
  and 
  (2) 
  

  

  Y'/Y=R'\T/RV, 
  

  

  and 
  finally 
  we 
  have 
  

  

  R=R'J 
  V 
  (3) 
  

  

  This 
  formula 
  will 
  first 
  be 
  applied 
  to 
  the 
  experiments 
  given 
  

   in 
  the 
  previously 
  published 
  paper 
  (Dec. 
  1907). 
  

  

  Case 
  1. 
  — 
  Eight 
  cubic 
  metres 
  of 
  air 
  were 
  passed 
  in 
  3*7 
  

   days 
  through 
  three 
  iron 
  tubes 
  in 
  parallel, 
  each 
  containing 
  

   220 
  grams 
  of 
  coconut 
  charcoal. 
  From 
  the 
  three 
  tubes 
  15 
  

   litres 
  of 
  gas 
  were 
  driven 
  off 
  by 
  heat, 
  collected 
  and 
  then 
  

   passed 
  very 
  slowly 
  through 
  three 
  small 
  glass 
  tubes 
  in 
  series, 
  

   each 
  containing 
  7 
  grams 
  of 
  charcoal. 
  In 
  turn 
  these 
  were 
  

   heated, 
  and 
  the 
  gases 
  driven 
  off 
  were 
  collected 
  over 
  water 
  

   and 
  inserted 
  in 
  the 
  electroscope. 
  

  

  