﻿852 
  

  

  Mr. 
  F. 
  Soddy 
  on 
  the 
  

   Fior. 
  8. 
  

  

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  V. 
  Period 
  of 
  the 
  Direct 
  Parent 
  of 
  Radium. 
  

  

  As 
  detailed 
  in 
  the 
  last 
  communication 
  (III. 
  p. 
  635) 
  the 
  

   growth 
  o£ 
  radium 
  from 
  uranium 
  should 
  proceed 
  according 
  to 
  

   the 
  same 
  power 
  of 
  the 
  time 
  as 
  there 
  are 
  products 
  in 
  the 
  series 
  

   (counting 
  radium 
  itself) 
  between 
  the 
  two 
  elements, 
  provided 
  

   all 
  these 
  products 
  have 
  periods 
  long 
  compared 
  with 
  the 
  time 
  

   o£ 
  observation. 
  Rutherford, 
  assuming 
  only 
  one 
  intermediate 
  

   product 
  — 
  the 
  direct 
  parent 
  of 
  radium 
  — 
  to 
  exist, 
  first 
  showed 
  

   that 
  the 
  production 
  of 
  radium 
  should 
  proceed 
  according 
  to 
  

   the 
  formula 
  

  

  R 
  = 
  l/2X2\3Eo^2 
  or 
  l/2Xi\2Ut\ 
  

  

  where 
  R 
  represents 
  the 
  quantity 
  of 
  radium, 
  U 
  that 
  of 
  

   uranium, 
  Rq 
  the 
  quantity 
  of 
  radium 
  in 
  radioactive 
  equilibrium 
  

   with 
  the 
  uranium, 
  Xi, 
  A2, 
  X3 
  the 
  constants 
  of 
  uranium, 
  the 
  

   direct 
  parent 
  of 
  radium, 
  and 
  radium 
  respectively, 
  and 
  t 
  is 
  

   the 
  time. 
  This 
  may 
  be 
  written 
  

  

  where 
  R 
  represents 
  the 
  radium 
  formed 
  per 
  kilogram 
  of 
  

   uranium 
  and 
  Xg 
  and 
  t 
  are 
  expressed 
  in 
  years. 
  It 
  is 
  of 
  

   interest 
  to 
  calculate 
  the 
  value 
  of 
  Xg 
  from 
  this 
  equation, 
  

   although, 
  as 
  will 
  be 
  shown 
  later, 
  the 
  calculation 
  is 
  seriously 
  

   in 
  error 
  if 
  other 
  intermediate 
  bodies 
  of 
  period 
  comparable 
  

   with 
  the 
  time 
  of 
  observation 
  exist 
  in 
  the 
  series. 
  From 
  the 
  

  

  