Q28  Prof.  W.  H.  Bragg  on  the  Ionization 
break  ought  to  appear,  and  the  photographic 
result  is  quite  in  accordance  with  the  theory 
that  the  particles  lose  speed  as  they  pass 
through  matter. 
In  order  that  this  may  be  clear,  it  is 
necessary  first  to  consider  the  order  of  the 
deflexions  o£  the  a  rays  in  the  magnetic  field, 
on  the  various  theories  that  have  been  proposed. 
Suppose  that  an  a  particle  is  projected  from 
0  in  the  direction  ON  with  velocity  v0,  and 
that  the  action  of  a  field  H  causes  it  to  describe 
the  curved  path  OA. 
In  the  first  place,  let  the  velocity  be  constant 
throughout,  and  the  path  be  therefore  circular 
as  M.  Becquerel  supposes.  Then,  since  the 
curvature  is  small,  AN=a2/2/>,  where  ON  =  a, 
and  p  is  the  radius  of  curvature. 
of 
AN  = 
Re 
a" 
mvn  '  2 
In  the  second  place  let  the  velocity  diminish  as  the 
distance  from  0  increases  :  and  let  us  take  the  extreme  case, 
where  the  velocity  vanishes  at  a  distance  a  from  0.  Let 
the  path  in  this  case  be  OA'.  It  does  not  make  very  much 
difference  what  law  of  diminution  of  velocity  we  adopt  :  let 
us  suppose,  as  my  experimental  results  seem  to  indicate,  that 
the  particle  spends  its  energy  at  a  rate  which  is  inversely 
proportional  to  the  square  of  its  speed.     In  this  case, 
dv2       , 
•     ds 
—  2 
s  being  measured  from  0,  and  therefore, 
vAcc  (a  —  s), 
so  that 
Thus 
a  —  s 
a 
«•  4 
mvQf        s\* 
P-KeV-J' 
and  we  obtain  easily  that,  if  p  =  ds/dyjr, 
t  =  ^{1_(1_if}li 
3     L        V        a/     J   mv0 
