Radiation  from  Ordinary  Materials.  209 
(2)  will  give  an  ionization  proportional  to  the  volume, 
say  vabx. 
(3)  will  give  an  ionization  proportional  to  the  area  of  the 
wire  gauze  exposed,  say  fix. 
The  ionization  due  to  (1)  is  more  complicated.  In  the 
former  paper  it  was  calculated  on  the  assumption  that  the 
rays  were  absorbed  according  to  an  exponential  law ;  but 
lately  our  conception  of  the  absorption  of  a.  rays  has  been 
completely  altered  by  the  important  paper  of  Prof.  Bragg*. 
The  calculation  must  now  be  based  on  the  theory  propounded 
therein,  which  is  fortunately  amenable  to  mathematical 
treatment. 
§  7.  According  to  this  theory  an  a,  particle  travels  a  dis- 
tance a  in  air  producing  approximately  the  same  number  of 
ions  per  unit  length  at  all  points  of  its  path  ;  when  the 
distance  a  is  reached  it  produces  no  more  ions  and  may  be 
said  to  be  totally  absorbed.  If  it  traverses  a  thickness  t  of 
some  other  substance  than  air,  its  path  in  air  will  be  curtailed 
by  pt,  where  p  is  the  density  of  the  substance  referred  to 
air  =  l. 
Let  A  be  the  number  of  ions  produced  by  the  rays  from 
unit  mass  of  the  material  when  those  rays  are  wholly 
absorbed  in  air.  Then  dA  will  be  the  number  of  ions 
produced  by  the  rays  from  unit  volume,  where  d  is  the 
density  of  the  substance  referred  to  water  =  1.  It  is  con- 
venient to  introduce  a  quantity  T0  such  that  I0do  is  the 
number  of  ions  produced  in  unit  volume  of  the  surrounding- 
air  at  unit  distance  by  the  rays  from  an  element  of  volume 
do  of  the  material,  so  that  the  ionization  in  an  element  of 
volume  dv  at  a  distance   r  from   the   radiating  element  is 
— — g —  •     I0  *s  connected  with  A  by  the  following  equation  : — 
("2k  Ca  C  *r  T  fin 
d<f>  \    dr  \     dO.^f-.  r2 sin 6  =  dA  .  do,      .     (1) 
i,0  Jo         Jo  r 
.'.     4-77- I0a  do  —  dA.  .  do, 
Now  consider  an  element  at  0  of  volume  d$  .  dl  in  an 
infinite  slab  of  the  material  distant  /  from  the  plane  surface 
*  Phil.  Mag.  December  1904. 
Phil.  Mag.  S.  6.  Vol.  11.  No.  (52.  Feb.  1906.  P 
