﻿636 
  Mr. 
  F. 
  Soddy 
  on 
  the 
  Relation 
  

  

  Experiment 
  I. 
  

  

  R<5xl0- 
  n 
  , 
  *=2§ 
  years, 
  

   5 
  x 
  10- 
  11 
  > 
  JXs(l'2 
  x 
  10" 
  7 
  )(y 
  ) 
  2 
  , 
  

  

  x 
  2 
  <i-ixio- 
  4 
  . 
  

  

  Experiment 
  IT. 
  

  

  R<10- 
  n 
  , 
  * 
  = 
  1§ 
  years, 
  

  

  10- 
  n 
  >JX 
  2 
  (l-2xlO- 
  7 
  )(|) 
  2 
  , 
  

   X 
  2 
  < 
  6 
  x 
  10- 
  5 
  . 
  

  

  The 
  result 
  o£ 
  the 
  second 
  experiment 
  is 
  thus 
  the 
  best 
  at 
  the 
  

   present 
  time. 
  It 
  shows 
  conclusively 
  that, 
  i£ 
  only 
  one 
  inter- 
  

   mediate 
  parent 
  exists 
  between 
  uranium 
  X 
  and 
  radium, 
  its 
  

   period 
  of 
  average 
  life 
  must 
  be 
  far 
  greater 
  than 
  that 
  of 
  

   radium. 
  According 
  to 
  the 
  second 
  experiment 
  the 
  period 
  is 
  

   not 
  less 
  than 
  16,500 
  years. 
  This 
  is 
  six 
  times 
  that 
  o£ 
  radium, 
  

   so 
  that 
  the 
  quantity 
  in 
  minerals 
  should 
  be 
  at 
  least 
  six 
  times 
  

   greater 
  than 
  that 
  of 
  radium. 
  

  

  Other 
  considerations, 
  however, 
  indicate 
  that 
  there 
  may 
  be 
  

   two 
  or 
  more 
  intermediate 
  bodies 
  in 
  the 
  series. 
  For, 
  the 
  

   difference 
  between 
  the 
  atomic 
  weights 
  of 
  uranium 
  and 
  radium 
  

   is 
  12, 
  which 
  is 
  equal 
  to 
  the 
  mass 
  of 
  three 
  a 
  particles, 
  and 
  

   rayless 
  changes 
  are 
  certainly 
  to 
  be 
  expected 
  if 
  the 
  initial 
  decay 
  

   of 
  the 
  activity 
  of 
  UrX 
  is, 
  as 
  hitherto 
  supposed, 
  complete. 
  

  

  Rutherford's 
  method 
  of 
  calculation 
  appears 
  to 
  be 
  applicable 
  

   to 
  a 
  general 
  solution 
  for 
  the 
  initial 
  rate 
  of 
  production 
  of 
  

   radium, 
  however 
  many 
  intermediate 
  bodies 
  intervene, 
  pro- 
  

   vided 
  the 
  life 
  of 
  each 
  is 
  long 
  compared 
  with 
  the 
  time 
  of 
  

   observation. 
  The 
  method 
  of 
  calculation 
  in 
  reality 
  neglects 
  

   decrements 
  of 
  the 
  quantities 
  of 
  the 
  changing 
  substances, 
  and 
  

   considers 
  only 
  the 
  increments. 
  Any 
  member 
  of 
  the 
  changing 
  

   series 
  being 
  considered, 
  except 
  the 
  first, 
  it 
  experiences 
  an 
  

   increment 
  of 
  quantity 
  due 
  to 
  the 
  preceding 
  change, 
  and, 
  in- 
  

   cluding 
  the 
  first, 
  a 
  decrement 
  of 
  quantity 
  due 
  to 
  the 
  succeeding 
  

   change. 
  The 
  decrement 
  is 
  consistently 
  neglected 
  throughout, 
  

   as 
  by 
  hypothesis 
  in 
  the 
  initial 
  stage 
  of 
  the 
  change 
  it 
  is 
  insig- 
  

   nificant, 
  the 
  fraction 
  of 
  the 
  total 
  changing 
  being 
  always 
  

   small. 
  Changes 
  of 
  very 
  short 
  periods 
  compared 
  to 
  the 
  time 
  

   of 
  observation, 
  on 
  the 
  other 
  hand, 
  like 
  that 
  of 
  UrX, 
  may 
  be 
  

   omitted 
  altogether 
  without 
  serious 
  error. 
  

  

  If 
  the 
  radium 
  is 
  formed 
  after 
  n 
  changes, 
  so 
  that 
  the 
  change 
  

   of 
  the 
  radium 
  is 
  the 
  (n+ 
  l)th 
  change, 
  the 
  general 
  expression 
  is 
  

  

  R=(l/nI)X 
  1 
  X 
  s 
  ...XjJ*» 
  

  

  where 
  U 
  is 
  the 
  quantity 
  of 
  uranium. 
  If, 
  as 
  before, 
  a 
  kilogram 
  

  

  