The  a.  Particles  of  Uranium  and  Thorium.  755 
screen  to  the  range  of  the  particle  :  so  that  if  experiment  is 
made  the  one  can  be  found  in  terms  of  the  other.  The 
stopping  power  o£  the  screen  may  be  made  the  subject  of  a 
direct  measurement,  and  so  the  range  of  the  a  particle  can  be 
determined.  I  find  it  better,  however,  to  compare  the  range 
of  the  uranium  or  thorium  a.  particle  with  that  of  radium, 
working  the  experiment  by  a  substitution  method  :  for  the 
range  in  the  case  of  radium  is  known  with  some  accuracy, 
and  the  method  itself  is  accurate  enough  when  employed  in 
comparing  ranges,  but  a  little  uncertain  in  its  application  to 
direct  determinations,  as  will  be  explained  later. 
Experiments  of  this  kind  have  already  been  made  by 
several  observers,  notably  by  Professor  Rutherford  and 
Miss  Brooks  (Phil.  Mag.  July  1900).  But  at  the  time 
when  they  were  made  it  was  believed  that  the  "  a  rays  "  were 
absorbed  according  to  an  exponential  law:  it  was  not  known 
that  each  a  particle  possessed  a  definite  range  or  penetrating 
power.  Consequently  the  results  were  not  in  all  cases 
expressed  in  such  a  way  as  to  render  them  available  for  the 
calculation  of  the  range.  I  have  therefore  found  it  con- 
venient to  repeat  them. 
In  the  following  theoretical  treatment  of  the  question  three 
cases  are  considered  : — 
(a)  When  the  layer  of  radioactive  material  is  so  thick  that 
the  a  rays  from  the  bottom  of  it  are  unable  to  reach 
the  air  above  :  such  a  thickness  is  of  the  order 
•002  cm. 
(b)  When  the  layer  is  extremely  thin. 
(c)  When  the  layer  is  thicker  than  in  (b)  but  not  so  thick 
as  in  (a). 
The  first  and  second  are  really  special  cases  of  the  third. 
Uranium  and  thorium  are  conveniently  treated  under  case 
(a);  radium  under  (c)  ;  and  the  induced  activities  under  (b). 
Case  (a)  :  Thick  layer  of  radioactive  material  over  which  a 
sheet  of  absorbing  material  is  laid. — Let  the  surface  of  the 
radioactive  material  be  of  unit  area  :  the  full  range  of  the  a. 
particle  in  air  be  11,  and  the  range  lost  by  passing  normally 
through  the  absorbing  sheet  be  I). 
Let  the  stopping  power  of  the  radioactive  material  per 
radioactive  atom  be  s.  This  means  that  if  an  a  particle  passes, 
parallel  to  the  axis,  along  a  cylinder  containing  only  as  much 
matter  as  goes  with  one  radioactive  atom  of  the  radioactive 
material,  the  loss  of  range  is,  on  the  average  of  a  great 
number  of  such  passages,  s  times  the  loss  when  an  average  air 
molecule  is  substituted  for  the  other  matter.  The  length  of 
the  cylinder  is,  of  course,  immaterial. 
