Number  of  Corpuscles  in  an  Atom.  781 
Thus  U,  the  number  o£  corpuscles  crossing  unit  area  in 
unit  time,  varies  as  e~Kx,  where 
4ttN^(M1+M2)1      (aV2    MXM 
x=  ::     ,:*  o2iiog 
V4       MXM22       &    e*    Mi  +  M2 
-')• 
X  is  the  coefficient  of  absorption.     If  M1  =  M2,  i.  e.  i£  the 
corpuscles  are  quite  free  to  move  in  the  atom, 
„       Sir^e*         ZlM2aV2      ,\ 
If  Mx  is  infinite,  i.  e.  if  the  corpuscles  are  held  fixed  by  the 
forces  between  them,  we  have 
_4ttNV         (\  M2aV2        \ 
-  v4m22  logA2  ~?      lr 
the  value  used  in  Method  3. 
We  can  get  an  approximate  value  of  X  very  simply  by  the 
following  method.  Consider  a  stream  of  corpuscles  moving 
horizontally  ;  the  forward  motion  of  any  particle  will  be 
stopped  by  a  collision  in  which  its  direction  of  motion  is 
turned  through  an  angle  equal  to   or  greater  than  a  right 
7T  .  1 
angle  ;  i.  e.  if  6  is  equal  to  or  greater  than  j  or  sin20>  ^> 
sin2  6  will  be  greater  than  1/2  if 
«*/M1+M,y 
<  V4V  MiM2  / 
The  number  of  collisions  made  by  a  corpuscle  for  which 
b  is  not  greater  than  this  value,  as  the  corpuscle  moves  over 
a  distance  A#,  is 
TrN^/M^MoV 
V4   I  MXM2  /  *x' 
Hence,  if  U  is  the  number  of  corpuscles  crossing  unit  area 
in  unit  time,  we  have,  if  we  neglect  the  effect  of  collisions 
which  do  not  result  in  a  total  stoppage  of  the  particle, 
dx  "      U  '    V4l  M,M2  )  ' 
or,  if  X  is  the  coefficient  of  absorption, 
IW/Mx  +  MA2 
X-    V1  V  M.Mo  /  " 
