a  Particles  of  Uranium  and  Thorium.  767 
material.  By  its  aid  we  may  find  the  relative  numbers  of 
a  particles  emitted  by  uranium  and  thorium,  when  the 
ionization  currents  due  to  known  areas  of  the  layers  have 
been  measured.  Since  the  ranges  are  so  nearly  alike,  it  is 
sufficient  to  use  the  simpler  formula 
n0 
8s 
.R 
If  now  the  suffixes  U  and  T  refer  to  uranium  and  thorium, 
we  have 
Iu_    NuRfjST 
and  therefore 
1T       NtJ^x^u 
rs  t       TtHu^t 
Each  time  that  a  thorium  experiment  was  completed,  a 
comparison  was  made  of  the  currents  It  and  Iu-  In  the 
first  case  IT/Iu  was  found  to  be  '234,  in  the  second  *234. 
(Ru/Rt)2,  as  may  be  seen  from  the  results  given  above,  can 
be  taken  as  equal  to  (456/476j2  =  *916. 
Also  ST  _  V232  +  2y/i6  __  23-2 
assuming  the   square-root  law  (Bragg  and  Kleeman,  PhiL 
Mag.  Sept.  1905)  to  hold  for  uranium  and  thorium. 
Hence  finally 
^  =  -234x-916x§H 
JNu  2o'2 
=  •190. 
This  result  may  be  a  little  too  small,  since  the  range  of  the 
a  particle  of  thorium  may  be  slightly  overestimated.  The 
square  of  the  range  enters  into  the  formula  of  comparison  ; 
but  on  the  other  hand,  any  a  rays  of  long  range  which  have 
not  been  removed  from  the  thorium  would  make  It  too  large. 
On  the  whole,  therefore,  the  actual  value  cannot  be  far  from 
*20;  i.  e.  the  uranium  atoms  break  down  very  nearly  five 
times  as  fast  as  the  thorium. 
I  have  preferred  to  make  the  method  one  of  comparison  of 
ranges  rather  than  of  absolute  determination.  For  there  are 
two  or  three  difficulties  in  using  it  for  the  latter  purpose,     In 
