﻿between 
  Uranium 
  and 
  Radium. 
  635 
  

  

  was 
  1-2 
  x 
  10- 
  11 
  gram. 
  In 
  the 
  last 
  test 
  on 
  August 
  8th, 
  1908, 
  

   586 
  days 
  from 
  the 
  start, 
  which 
  was 
  an 
  exceptionally 
  perfect 
  

   one, 
  the 
  amount 
  of 
  radium 
  was 
  found 
  to 
  be 
  only 
  0'7 
  x 
  10 
  — 
  ll 
  

   gram. 
  This 
  test 
  is 
  more 
  trustworthy 
  than 
  the 
  earlier 
  ones 
  

   and 
  is 
  in 
  accord 
  with 
  one 
  performed 
  on 
  June 
  10th, 
  1908. 
  

   For 
  these 
  extremely 
  minute 
  amounts 
  of 
  radium 
  the 
  figures 
  

   previously 
  were 
  rather 
  maximum 
  estimates 
  than 
  accurate 
  

   measurements; 
  but 
  with 
  the 
  slight 
  improvements 
  already 
  

   referred 
  to 
  smaller 
  quantities 
  of 
  radium 
  can 
  be 
  more 
  accu- 
  

   rately 
  determined 
  than 
  formerly. 
  

  

  The 
  increase 
  in 
  this 
  experiment, 
  if 
  any, 
  is 
  certainly 
  less 
  

   than 
  5 
  x 
  10~ 
  12 
  gram. 
  The 
  amount 
  of 
  radium 
  formed 
  per 
  

   kilogram 
  of 
  uranium 
  is 
  certainly 
  not 
  above 
  10 
  -11 
  gram 
  in 
  the 
  

   first 
  586 
  days, 
  or 
  1|- 
  years. 
  

  

  From 
  these 
  data 
  the 
  period 
  of 
  average 
  life, 
  or 
  its 
  reciprocal 
  

   the 
  radio-active 
  constant, 
  of 
  the 
  intermediate 
  parent 
  of 
  radium, 
  

   may 
  be 
  calculated, 
  at 
  least 
  so 
  far 
  as 
  to 
  indicate 
  a 
  minimum 
  

   value 
  for 
  the 
  average 
  life, 
  as 
  shown 
  by 
  Rutherford 
  {Jalir, 
  

   Radioaldivitcit, 
  1908, 
  v. 
  p. 
  164). 
  The 
  calculation 
  is 
  here 
  

   reproduced. 
  Let 
  P 
  refer 
  to 
  the 
  quantity 
  of 
  uranium 
  under 
  

   observation, 
  and 
  Q 
  , 
  Ro, 
  to 
  the 
  quantities 
  of 
  the 
  parent 
  of 
  

   radium, 
  and 
  of 
  radium, 
  respectively 
  in 
  equilibrium 
  with 
  P 
  . 
  

   Xj, 
  X 
  2 
  , 
  and 
  X 
  3 
  denote 
  the 
  respective 
  radioactive 
  constants, 
  or 
  

   fractions 
  changing 
  per 
  year, 
  of 
  uranium, 
  the 
  parent 
  of 
  radium, 
  

   and 
  of 
  radium. 
  Then 
  

  

  X]F 
  o 
  = 
  X 
  2 
  Qo 
  = 
  X3±io* 
  

  

  The 
  intermediate 
  body 
  UrX 
  is 
  neglected 
  in 
  the 
  calculation, 
  

   being 
  of 
  too 
  short 
  period 
  to 
  affect 
  the 
  result, 
  and 
  the 
  assump- 
  

   tion 
  is 
  made 
  that 
  the 
  time, 
  t 
  in 
  years, 
  is 
  short 
  compared 
  with 
  

   the 
  period 
  of 
  average 
  life 
  of 
  the 
  intermediate 
  parent, 
  while 
  

   the 
  latter 
  is 
  short 
  compared 
  with 
  that 
  of 
  the 
  primary 
  parent, 
  

   uranium. 
  

  

  The 
  amount 
  of 
  uranium 
  changing, 
  and 
  the 
  amount 
  of 
  the 
  

   parent 
  formed, 
  in 
  the 
  time 
  of 
  the 
  experiment 
  is 
  XiPo^. 
  The 
  

   amount 
  of 
  radium 
  formed 
  in 
  short 
  time 
  dt 
  is 
  X 
  2 
  (X 
  1 
  P 
  £)f7£. 
  If 
  

   R 
  is 
  the 
  amount 
  of 
  radium 
  formed 
  in 
  the 
  time 
  of 
  the 
  

   experiment, 
  

  

  R 
  = 
  ( 
  X 
  2 
  (XxPoO 
  dt 
  = 
  iXiXsPo* 
  2 
  = 
  |X 
  2 
  X 
  3 
  R 
  £ 
  2 
  . 
  

   Jo 
  

  

  From 
  this 
  X 
  2 
  may 
  at 
  once 
  be 
  deduced 
  from 
  the 
  data 
  given. 
  

   If 
  R 
  is 
  made 
  to 
  represent 
  the 
  amount 
  of 
  radium 
  formed 
  per 
  

   kilogram 
  of 
  uranium 
  in 
  time 
  t, 
  the 
  numerical 
  value 
  of 
  XiP 
  or 
  

   X 
  3 
  Ro 
  is 
  3-5 
  x 
  10~ 
  4 
  x 
  3-4 
  x 
  10~ 
  4 
  = 
  1-2 
  x 
  10~ 
  7 
  . 
  

  

  