212  Mr.  N.  B.  Campbell  on  the 
For  the  whole  slabs  we  have 
a 
+  4*Ifi §^(a- pl+ pllogg)dl  .    .      (6) 
P 
for  when  the  depth  I  is  so  great  that  none  of  the  rays  from 
the  element  strike  the  opposite  slab,  we  must  return  to  the 
previous  case. 
.*.  2nv— —x\ s —   +.i'  loo-  -     ;   but  »=Ift-s— D 
7  p        I      2  cea_\'  l        °  2p 
p*=p  — 
t(l_hog*)l     .     (7) 
«\4  2       °rt/_ 
When  #  =  «  this  becomes  p  ;  for  #>a  the  formula  breaks 
down  owing  to  certain  assumptions  made  implicitly  above. 
From  the  nature  of  the  physical  problem  it  is  easy  to  see 
that  for  x  >a  px  =p. 
Hence,  summing  up  the  three  sources  of  ionization,  the 
curve  representing  the  relation  between  the  ionization  (y) 
and  the  distance  of  the  sliding  side  from  the  end  [x)  is 
y 
=^[}-^-ll^'a)''Vahj^^'    '     '     (8> 
This  curve  near  the  origin  is  concave  to  the  axis  of  x,  but 
after  the  point  x—a  becomes  identical  with  the  straight  line 
y=p  +  vabx  +  p,x.  Thus  p  is  the  intercept  of  the  straight 
line  on  the  axis  of  y,  and  tan  0  =  vab  -f  p,,  where  6  is  the 
inclination  of  the  straight  line  to  the  axis  of  x. 
§  8.  If  the  screens  are  removed  we  shall  have  to  add  the 
effects  of  (4),  the  external  penetrating  radiation  (5),  the 
penetrating  secondary  radiation  excited  by  it,  and  (6)  the 
easily  absorbable  radiation  excited  by  it.  (4)  and  (5)  will 
give  terms  proportional  to  the  volume  ;  let  their  sum  be 
v'abx ;  (6)  will  give  a  relation  between  ionization  and  volume 
analogous  to  that  given  by  (1).  It  does  not  follow,  however, 
that  the  absorption  of  the  secondary  rays  will  follow  Bragg's 
law,  for  analogy  leads  us  to  expect  that  the  easily  absorbable 
secondary  rays  will  be  negatively  charged,  slow-moving, 
cathode  rays,  which  are  absorbed  according  to  an  exponential 
law.     In  fact,  we  may  anticipate  and  say  that  it  was  actually 
