760  Prof.  W.  H.  Bragg  on  the 
Case  (c).  Layer  of  moderate  thickness. — Let  the  air  equi- 
valent of  the  radioactive  layer  be  D'. 
This  case  must  be  considered  in  two  parts  : — 
(a)  When  r  is  such  that  D  +  D;  +  r<R:  the  limits   of  6 
being  then  cos-1-^ and  cos-1^ ,  and  those  of  r,  0  and 
It  —  r  ±1  —  r 
R— D-D'. 
(b)  When  r  is   such  that  D  +  D'  +  r    R,  the   limits  of  0 
being  then  0  and  cos-1^ ,  and  those  of  r,  0  and  cos-1 
—  r  1\  —  r 
Hence 
m<n 
~^s 
,  NZ«orE-D-i>'  r  (D  +  D')2-D2  J  ,    . ,- 
and 
4.9Z 
i^-=*(R  +  ^-D)"-f(R  +  ^-D-D')§-2DV^-Dv/li  +  ^-D 
_  D/2+2DD'  lotr  ^R(  VK  +  rf+  VR  +  ^-D-PQ 
v/R  +  d       &         VD  +  D'(  VRT^+  V<0 
Curve  C  shows  the  result  of  plotting  this  formula  for  the 
case  when  R  =  35,  D/  =  ,5,  and  d  —  VZZ. 
The  curve  is  plotted  from  the  following  figures  : — 
D/R...  I    -057    I    '143   I    -200    I    -257    I    "380   I    -500    I    -714    I 
z/I J    -833    I    '642    I    -539    |    -449    |    -288    |    '174    |    -044   | 
Pakt  II. 
The  apparatus  employed  was  of  the  usual  form,  and  very 
similar  to  that  described  by  Rutherford  ('  Radioactivity,' 
1905,  p.  98).  As  shown  in  fig.  2,  the  material  was  laid  on 
the  high-potential  plate  B,  at  such  a  distance  from  the  upper 
plate  A  that  no  a  particle  could  reach  it.  Thus  every  a  par- 
ticle ran  to  its  extreme  range ;  and,  fco  make  more  certain  of 
catching  all  the  ions^  the  upper  plate  was  extended  down- 
wards at  the  sides. 
