Various  Gases  by  the  a.  Particles  of  Radium.  ()29 
Now,  provided  that  j  -\jr  ds  is  small,  this  quantity  is  very 
nearly  equal  to  A'N,  the  total  deflexion  of  the  ray. 
But  this  integral 
"—  1 1  -  (l  ~  -Y/4  V  ds     — 
i 
~  mv0  '    7    ' 
and  this   quantity  is   very  small,   since   it  is    only  slightly 
greater  than  AN. 
Finally  then  we  have  that 
A'N/AN  =  8/7. 
It  is  easily  found  that  if  we  had  supposed  the  particle  to 
spend  its  energy  uniformly  along  its  path,  we  should  have 
obtained  the  result  A'N/AN  =  4/3. 
It  will  thus  be  clear  that,  on  any  reasonable  hypothesis  as 
to  the  particular  law  of  diminution  of  velocity,  the  actual 
path  of  the  particle  differs  very  little  from  a  circle.  In  the 
extreme  case  which  I  have  considered,  the  small  deviation 
therefrom  at  the  end  of  the  path  is  small  compared  with  the 
widths  of  the  images  in  M.  BecquerePs  photograph.  If  the 
particle  ceases  to  ionize  whilst  its  velocity  is  still  great,  as 
has  been  shown  by  Prof.  Rutherford,  the  variation  is 
still  less. 
Let  us  now  consider  the  circumstances  of  M.  Becquerel's 
experiment. 
As  a  first  approximation,  suppose  the  widths  of  the 
groove  containing  the  radium  salt  and  of  the  slit  to  be 
negligible. 
If  no  magnetic  field  is  acting,  all  the  ol  particles  move  in 
the  vertical  line  ON.  The  range  of  the  particles  from  Ra  C 
is  very  nearly  7*0  cm.;  from  which  it  follows  that  the  number 
which  pass  any  given  point  P  is  proportional  to  the  defect  of 
OP  from  7'0  cm.,  or,  in  other  words,  that  the  number  n  which 
end  their  flight  on  any  unit  of  length  of  ON  is  a  constant. 
The  other  three  groups  of  particles  have,  as  their  furthest  dis- 
tances of  penetration,  4*8,  4*2,  and  3"5  cm.  respectively.  Thus 
between  4' 8  and  4' 2,  2n  particles  end  their  flight  on  each  unit 
of  length,  between  4'2  and  3'5  the  number  is  3n,  and  from 
that  point  up  to  the  radium  4n.  The  radium  salt  is  supposed 
deep  enough  to  supply  all  these,  i.  e.  its  depth  is  taken  to  be 
at  least  *001  cm.      Suppose  now  a  powerful  magnetic  field  to 
