﻿Helium 
  from 
  the 
  Primary 
  Radio- 
  Elements. 
  515 
  

  

  Throughout 
  the 
  most 
  recent 
  value 
  for 
  the 
  latter, 
  3*48 
  X 
  10 
  -4 
  

   (year) 
  -1 
  , 
  given 
  by 
  Boltwood 
  (Am. 
  Journ. 
  Sci., 
  June 
  1908, 
  

   p. 
  493), 
  will 
  be 
  taken. 
  Multiplying 
  it 
  by 
  the 
  most 
  recent 
  

   value 
  (3*4 
  X 
  JO 
  -7 
  ) 
  for 
  the 
  ratio 
  of 
  radium 
  to 
  uranium 
  in 
  

   minerals 
  (Boltwood, 
  loc. 
  cit. 
  April 
  1908, 
  p. 
  297), 
  gives 
  

   l'2xl0- 
  10 
  (year) 
  -1 
  , 
  which 
  may 
  be 
  taken 
  as 
  the 
  present 
  

   theoretical 
  value 
  for 
  the 
  rate 
  of 
  disintegration 
  of 
  uranium 
  

   according 
  to 
  these 
  data, 
  and 
  will 
  be 
  referred 
  to 
  as 
  the 
  " 
  direct 
  

   value." 
  For 
  thorium 
  we 
  have 
  yet 
  no 
  such 
  direct 
  method, 
  

   and 
  the 
  difficulties 
  commence. 
  

  

  It 
  is 
  necessary, 
  before 
  any 
  further 
  progress 
  can 
  be 
  made 
  

   with 
  the 
  calculation, 
  to 
  introduce 
  the 
  assumption 
  that 
  the 
  

   a-particle 
  is 
  an 
  atom 
  of 
  helium, 
  and 
  to 
  first 
  deduce, 
  from 
  

   the 
  rate 
  of 
  disintegration 
  of 
  uranium, 
  the 
  rate 
  of 
  production 
  

   of 
  helium, 
  on 
  the 
  assumption 
  that 
  one 
  atom 
  of 
  uranium 
  gives 
  

   rise 
  to 
  some 
  definite 
  number 
  (N) 
  of 
  atoms 
  of 
  helium. 
  As 
  

   the 
  a-radiation 
  of 
  uranium 
  is 
  apparently 
  homogeneous, 
  and 
  

   produced 
  in 
  the 
  apparently 
  single 
  change 
  of 
  uranium 
  into 
  

   uranium 
  X, 
  it 
  is 
  reasonable 
  to 
  assume 
  at 
  first 
  that 
  one 
  atom 
  

   of 
  helium 
  is 
  produced 
  from 
  one 
  atom 
  of 
  uranium, 
  and 
  

   therefore 
  that 
  the 
  helium 
  is 
  one-sixtieth 
  of 
  the 
  weight 
  of 
  

   uranium 
  disintegrating. 
  This 
  gives 
  2 
  x 
  10~ 
  12 
  (year) 
  -1 
  for 
  

   the 
  rate 
  of 
  production 
  of 
  helium 
  from 
  uranium. 
  

  

  To 
  find 
  from 
  this 
  the 
  rate 
  of 
  production 
  of 
  helium 
  from 
  

   thorium 
  it 
  suffices, 
  on 
  the 
  assumptions 
  made, 
  to 
  compare 
  the 
  

   relative 
  a-radiation 
  of 
  uranium 
  and 
  thorium 
  and 
  the 
  average 
  

   velocities 
  of 
  the 
  a-particle 
  of 
  uranium 
  and 
  thorium 
  re- 
  

   spectively. 
  For 
  present 
  purposes 
  perhaps 
  a 
  sufficient 
  

   approximation 
  is 
  reached 
  if 
  we 
  regard 
  the 
  relatively 
  greater 
  

   average 
  velocity 
  of 
  the 
  thorium 
  a-particle 
  as 
  just 
  com- 
  

   pensating 
  for 
  the 
  relatively 
  higher 
  specific 
  a-activity 
  of 
  

   thorium. 
  This 
  gives 
  the 
  same 
  rate 
  of 
  production 
  of 
  helium 
  

   for 
  both 
  uranium 
  and 
  thorium, 
  viz. 
  2 
  x 
  10 
  -12 
  (year)"" 
  3 
  . 
  

  

  The 
  unfortunate 
  feature 
  about 
  this 
  calculation 
  is 
  that 
  it 
  

   may 
  not 
  be 
  allowable 
  to 
  calculate 
  the 
  ratio 
  of 
  the 
  rate 
  of 
  

   disintegration 
  of 
  radium 
  to 
  that 
  of 
  uranium, 
  from 
  the 
  ratio 
  of 
  

   their 
  respective 
  quantities 
  in 
  minerals, 
  because 
  it 
  is 
  uncertain 
  

   that 
  the 
  disintegration 
  theory 
  in 
  its 
  simplest 
  form 
  applies. 
  

   Rutherford 
  has 
  suggested 
  tentatively, 
  in 
  order 
  to 
  bring 
  

   actinium 
  into 
  the 
  scheme 
  of 
  radioactive 
  changes 
  in 
  pitch- 
  

   blende, 
  that 
  actinium 
  may 
  be 
  a 
  product 
  of 
  disintegration 
  of 
  

   uranium 
  produced 
  simultaneously 
  with 
  the 
  radium 
  series, 
  

   and 
  not 
  in 
  the 
  direct 
  line 
  between 
  uranium 
  and 
  radium. 
  

   If 
  this 
  is 
  true, 
  in 
  equilibrium 
  the 
  number 
  of 
  atoms 
  of 
  radium 
  

   formed 
  are 
  but 
  a 
  fraction 
  of 
  the 
  atoms 
  of 
  uranium 
  dis- 
  

   integrating, 
  and 
  the 
  rate 
  of 
  disintegration 
  of 
  uranium 
  must 
  

  

  2M2 
  

  

  