produced  by  Rotitgen  Rays  in  Different  Metals.       311 
The  secondary  rays  from  such  metals  as  lead  and  zinc 
consist  o£  two  well-defined  groups,  one  of  which  is  completely 
absorbed  in  less  than  10  mm.  o£  air,  the  other  being  much 
more  penetrating.  Let  us  consider  first  the  less  penetrating- 
rays.  It  is  stated  in  the  introductoiy  portion  of  this  paper 
that  these  rays  must  form  a  large  fraction  of  all  the  secondary 
rays  generated :  this  statement  appears  at  first  sight  to  be 
in  contradiction  with  the  experimental  result  obtained  by 
H.  !S.  Allen  *,  who  found  that  the  ionization  produced  by 
these  easily  absorbed  secondary  rays  from  brass  is  1/1900  of 
that  which  would  be  produced  by  complete  absorption  of  the 
primary  rays  in  the  gas.  A  little  consideration,  however, 
shows  that,  with  rays  so  easily  absorbed,  a  large  number 
must  be  generated  in  the  metal  to  permit  even  so  small  a 
fraction  to  escape. 
Let  the  intensity  of  the  primary  rays  which  have  pene- 
trated at  a  distance  x  into  the  metal  be 
The  absorption  in  an  element  of  thickness  dx  will  be 
Wdx,  and  we  may  assume  that  this  is  proportional  to  the 
intensity  of  the  secondary  rays  (of  the  more  absorbable  type) 
generated  in  this  element,  say 
L  dx  =  ^X1  lt  dx. 
The  question  is  as  to  the  value  of  the  fraction  a  necessary 
to  produce  the  observed  secondary  rays  outside  the  metal. 
Let  us  assume  that  half  of  the  secondary  rays  so  generated 
are  propagated  straight  back  to  the  surface :  this  will  give 
us  an  over-estimate  of  the  rays  which  escape  with  a  given 
value  of  a,  or  an  under-estimate  of  a.  necessary  to  account  for 
the  observed  secondary  rays.  The  effect,  at  the  surface,  of  the 
secondary  rays  generated  in  the  element  dx  will  be  then 
^J2dxe~^x, 
and  the  total  intensity  of  the  secondary  rays  at  the  surface  of 
the  metal  will  be 
=  ~  i 
2  ,  >0  M 
The  value  of  the  coefficient  o£  absorption,  in  air.  o£  the 
*  Phil.  Mag-,  iii.  p.  126  (1902). 
