﻿594 
  Mr. 
  J. 
  Satterly 
  on 
  the 
  Amount 
  oj 
  

  

  Calculations. 
  

   The 
  factors 
  that 
  are 
  required 
  — 
  

  

  (1) 
  To 
  correct 
  for 
  the 
  decay 
  of 
  emanation 
  if 
  the 
  emanation 
  

   is 
  not 
  measured 
  till 
  some 
  time 
  after 
  it 
  is 
  absorbed; 
  

  

  (2) 
  To 
  correct 
  for 
  the 
  accumulation 
  of 
  emanation 
  in 
  the 
  

   charcoal 
  ; 
  

  

  (3) 
  To 
  calculate 
  the 
  amount 
  of 
  emanation 
  generated 
  in 
  a 
  

   given 
  time 
  by 
  the 
  solution 
  *; 
  

  

  are 
  all 
  obtained 
  from 
  the 
  decay 
  curve 
  of 
  radium 
  emanation, 
  

   and 
  its 
  inverse, 
  the 
  production 
  curve. 
  

  

  Taking 
  the 
  time 
  of 
  half 
  value 
  of 
  radium 
  emanation 
  to 
  be 
  

   3' 
  71 
  days, 
  we 
  have, 
  using 
  the 
  nomenclature 
  of 
  Rutherford, 
  

  

  T 
  = 
  3-71x 
  24x3600 
  seconds. 
  

  

  Now 
  if 
  A, 
  = 
  the 
  radioactive 
  constant 
  of 
  the 
  emanation, 
  

  

  \T=log 
  e 
  2 
  = 
  -693: 
  

  

  V. 
  \ 
  =2*16 
  xlO" 
  6 
  . 
  

  

  The 
  equation 
  of 
  the 
  ' 
  ; 
  decay 
  " 
  curve 
  of 
  radium 
  emanation 
  is 
  

  

  where 
  I 
  is 
  the 
  initial 
  amount 
  of 
  emanation 
  and 
  If 
  the 
  amount 
  

   in 
  existence 
  at 
  time 
  t. 
  

  

  If 
  a 
  radium 
  solution 
  is 
  completely 
  exhausted 
  of 
  its 
  ema- 
  

   nation 
  at 
  a 
  time 
  / 
  = 
  and 
  then 
  left 
  to 
  itself, 
  the 
  emanation 
  

   will 
  gradually 
  accumulate, 
  the 
  equation 
  of 
  the 
  " 
  production 
  " 
  

   curve 
  being 
  

  

  V=Io(l 
  

  

  '), 
  

  

  where 
  1/ 
  is 
  the 
  amount 
  in 
  existence 
  at 
  time 
  /, 
  and 
  I 
  the 
  

   amount 
  in 
  existence 
  after 
  an 
  infinite 
  time. 
  

  

  Taking 
  I 
  equal 
  to 
  50, 
  the 
  numbers 
  in 
  Table 
  I. 
  have 
  been 
  

   calculated. 
  They 
  give 
  the 
  corresponding 
  values 
  of 
  / 
  and 
  If, 
  

   t 
  and 
  1/, 
  t 
  in 
  the 
  tables 
  being 
  expressed 
  for 
  convenience' 
  sake 
  

   in 
  days. 
  

  

  Table 
  I. 
  

  

  t. 
  

  

  0. 
  

  

  1 
  

  

  ■2- 
  

  

  1. 
  

  

  2. 
  

  

  3. 
  

  

  28 
  

  

  4. 
  

   23 
  

  

  5. 
  

   19 
  

  

  6. 
  

   16 
  

  

  7. 
  

  

  00 
  . 
  

  

  It 
  

  

  50 
  

  

  45 
  

  

  41 
  

  

  34 
  

  

  13 
  

  

  

  

  If'. 
  .. 
  

  

  

  

  5 
  

  

  9 
  

  

  16 
  

  

  22 
  

  

  27 
  

  

  31 
  

  

  34 
  

  

  37 
  

  

  50 
  

  

  From 
  this 
  table 
  the 
  curves 
  AB, 
  CD 
  of 
  fig. 
  2 
  have 
  been 
  

  

  * 
  Eve 
  (Phil. 
  Mag. 
  Dec. 
  1907) 
  neglected 
  altogether 
  the 
  time 
  element 
  

   of 
  his 
  solution. 
  

  

  