180     Prof.  McCoy  on  tlie  Relation  betiveen  Radioactivity 
The  theoretical  value  of    -  for  an  infinitely  thin  film  may  be 
a  J  -  J 
readily  found  by  plotting  the  values  of  this  ratio  for  thin  films 
of  various  weights  and  finding,  by  a  small  graphical  extra- 
polation,   the  zero  value.       This  value  may    be    designated 
asp). 
Therefore  h  =  2j(~)  • 
I  \a  /u 
The  values  of  ki  as  found  by  this  second  method  agreed  well, 
in  the  case  of  pure  uranium  compounds,  with  those  as  deter- 
mined by  the  first  method. 
The  Radioactivity  of  Uranium  Ores. 
Having  found  satisfactory  methods  of  determining  accu- 
rately the  total  radioactivity  of  pure  uranium  compounds, 
these  methods  have  now  been  applied  to  the  further  study  of 
uranium  ores.  The  theory  that  radium  is  a  disintegration 
product  of  uranium  demands  that  all  uranium  compounds 
sufficiently  old  should  contain  radium  in  amounts  directly 
proportional  to  their  uranium  content.  It  should  therefore 
be  found  that  the  total  radioactivity  of  any  uranium  ore 
should  be  directly  proportional  to  its  percentage  of  uranium. 
This  was,  in  fact,  found  to  be  approximately  true  for  twelve 
ores  from  widely  different  localities  *.  The  average  deviation 
from  the  mean  value  of  the  ratio  of  activity  to  percentage  of 
uranium  was  7*1  per  cent.  The  determinations  of  the  activity, 
in  the  above  cases,  were  made  upon  equal  weights  of  ore 
without  due  allowance  being  made  for  difference  of  absorption. 
The  method  of  determining  total  activity,  which  depends 
upon  a  determination  of  the  absorption  coefficient  of  the 
substance,  can  be  applied  only  to  those  substances  for  which 
the  absorption  coefficient  is  a  true  constant.  This  condition 
will  obviously  be  fulfilled  only  by  substances  the  radiations  of 
which  are  homogeneous.  If  we  disregard  the  beta  rays,  the 
ionizing  effect  of  which  is  negligible,  the  radiation  of  every 
pure  uranium  compound  is  homogeneous.  For  every  such 
compound  the  absorption  coefficient  is  a  constant.  Uranium 
ores  all  contain  radium  andits  numerous  active  transformation 
products.  The  alpha  rays  of  these  bodies  have  quite 
different  penetrating  powers.  It  was  actually  found,  as 
anticipated,  that  the  absorption  coefficient  of  ores  wras  not 
constant,  but  varied  with  the  thickness  of  the  film.     While 
*  McCoy,  Ber.  d.  chem.  Ges.  xxxvii.  p.  2654  (1905). 
