a  Particles  of  Uranium  and  Thorium.  759 
sufficient  accuracy,   though  the  actual  value  of  the  range  of 
the  a  particle  from  these  substances  is  nearly  3*5. 
The  curve  is  plotted  from  the  following  figures:  — 
D/B...  I   -067  I   -110  I  '167  I  '250  I  '333  I  '443  I  '568  I  '667  I  -833  I 
ill I   -773  I  '657  I  -532  |  "378  |  '262  |  -148  |  "069  |  -030  |  '010  | 
Case  {!>).  Very  thin  layer  of  radioactive  material. — Let^  D 
he  the  air  equivalent  of  the  layer  of  radioactive  material, 
i.  e.  the  loss  of  range  which  an  a  particle  would  experience 
in  crossing  the  layer  normally. 
The  limits  of  6  are  now  0X  +  02,  where 
Dsec0!  +  r  =  R  and  (D  +  D')  secd2  +  r=R. 
Hence  the  total  number  of  particles  whose  ranges  lie 
between  r  and  r  +  Br  is 
N*.f(D  +  D')'_^lSr 
4s   I  (R-r)2       (R-r)2  J 
NnoDD'      8r         _.electin2  WK 
nej 
2s       (R-r)*       * 
Hence  the  ionization  (i) 
=  ^*-lv^d-Vddr 
2s  Jo  (R-r)2 
(R-r)' 
Nfa0D'r    /i5 — r-is       n         D      ^„\/R(\/R+d  +  \/R  +  d-D)  1 
and  when  D  =  0,  the  ionization  (I) 
=      2s     {VR  +  d-Vd}. 
If  we  had  here  neglected  the  variation  of  ionization  with 
velocity  and  supposed  the  ionization  caused  in  traversing  a 
distance  r  to  be  proportional  to  r,  we  should  have  found  that 
More  difference  is  made  in  this  case  by  neglecting  the 
variation  of  ionization  with  velocity.  Curve  B  is  plotted 
from  the  more  accurate  formula  for  the  values  R=  7,  d=l'3'3. 
The  curve  is  plotted  from  the  following  figures : — 
D/R...  I    -061    I    -124   I    -250   ]    -357    I    '500    I    -690    I    -833   I 
i/l |    -807        G72       -467       '335    |    -193       -077        023   | 
