Radiation  from  Ordinary  Materials.  213 
found  that  px  (corresponding  to  jlv)  was   given   more  accu- 
rately by  the  formula 
p'v=Iy(l-e-^)        (7') 
than  by  Bragg's  formula. 
Hence  for  the  unscreened  curve  we  shall  have  to  add  to  (8) 
the  terms 
y=pf{l-e-Xx)+v'abx (9) 
This  curve  is  of  the  same  form  as  (8),  and  is  similarly 
related  to  p'  and  t/,  as  regards  its  straight  portion. 
§  9.  From  what  has  been  said  it  should  be  obvious  how  to 
deduce,  by  working  backwards,  the  quantities  p, p',  v,  v\  a,  \ 
from  the  experimental  curves.  The  matter  is  slightly  com- 
plicated by  the  fact  that  the  screens  used  were  only  so  thick 
as  to  cut  off  two-thirds  of  the  external  radiation  ;  the  weight 
of  lead  required  to  cut  off  all  the  radiation  from  a  box  of  the 
size  used  was  almost  prohibitive.  Accordingly,  observations 
were  treated  in  the  following  manner. 
The  values  of  /j,  were  first  ascertained  (see  §  10),  and  fix 
subtracted  from  the  readings  recorded  before  they  were 
plotted  in  the  diagrams  from  which  figs.  2-12  are  copied. 
Smoothed  curves  were  then  drawn  through  the  experimental 
points.  In  most  cases,  there  was  no  doubt  as  to  where  the 
curve  should  lie,  but  when  the  points  were  irregularly  dis- 
tributed it  was  feared  that  the  drawing  of  the  curve  might 
be  influenced  by  knowledge  derived  from  the  former  series 
of  experiments.  In  these  cases  the  help  of  an  unprejudiced 
friend  was  invoked ;  in  all  cases  two  independent  workers 
drew  substantially  the  same  curve. 
The  "  screened  curve  "  (A)  was  now  subtracted  from  the 
"  unscreened '"  (B).  The  resulting  curve  (C)  gives  the  effects 
of  (4),  (5),  and  (6),  and  has  the  equation 
y=p'(l-e-^)+v'abx! (10) 
From  the  intercept  and  the  inclination  of  the  straight 
portion  we  can  find  j/  and  v  at  once.  Subtracting  v'  x  from 
each  point  of  the  curve  (C)  we  get  the  curve  (D),  which 
should  represent  the  effects  of  the  easily  absorbable  secondary 
radiation,  and  have  the  equation 
</=y>,=p'(i-<'-'u)- 
This  is  compared  with  curves  drawn  from  calculation  of 
the  formulae  (7)  and  (7')  for  different  values  of  a  and  X. 
As  stated  above,  it  always  agreed  best  with  (7')  ;  the  value 
which   gave  best  agreement  between  experiment  and  ealeu- 
