4G8     Prof.  "\V.  H.  Brao-o-  and  Mr.  R.  D.  Kleeman  on  the 
CO 
bilitv  lias  been  already  sug-o-ested  by  Rutherford  (''Radio- 
activity/  p.  33).  An  electron,  which  has  just  been  ejected 
from  an  atom  by  a  passing  a.  particle,  does  not  go  far  before 
encountering  a  neighbouring  atom.  The  encounter,  perhaps, 
results  in  a  temporary  attachment,  for  we  know  that  ion- 
clusters  are  formed  in  this  way.  In  any  case,  it  is  probable 
that  the  electron  loses  much  of  its  velocity  of  projection .  Now, 
it  is  still  under  the  attraction  of  the  atom  from  which  it  has 
come.  Supposing  this  atom  to  have  only  lost  one  electron, 
the  strength  of  the  electric  force  which  it  exerts  at  the 
distance  of  the  mean  free  path  is  equal  to 
e/r2  =  3  x  10-10/10-10  =  3  E.S.U., 
or  000  volts  per  cm.  This  is  large  compared  with  the  usual 
impressed  electric  forces  of  experiment.  It  is  by  no  means 
improbable,  therefore,  that  the  electron  may  finally  slip  back 
into  its  old  place.  Such  a  possibility  is  not  considered  in  the 
equations  as  usually  formed.  For  all  writers  begin  their 
arguments  by  the  statement : — "  Let  p  be  the  number  of 
positive  ions  in  a  cubic  centimetre,  and  n  the  number  of 
negative/''  In  doing  so  they  tacitly  assume  that  the  relations 
of  any  one  ion  to  all  others  of  opposite  sign  are  of  the  same 
character.  But  if  a  pair  of  newly-formed  ions  ran  a  special 
chance  of  recombination  until  they  got  away  from  each  other, 
then  the  relations  of  either  of  these  two  to  the  other  would 
be  quite  different  to  its  relation  to  all  other  ions. 
Let  us,  then,  for  the  moment  suppose  that  there  is  a  special 
form  of  recombination,  which  we  may  call  "initial/''  as  distin- 
guished from  general  recombination,  and  let  us  consider  the 
nature  of  its  effects,  in  order  that  we  may  find  means  of 
testing  the  correctness  of  the  supposition. 
Now,  it  is  clear  that  the  effects  of  initial  recombination  do 
not  depend  upon  the  shape  of  the  ionization  chamber,  and 
this  at  once  differentiates  them  from  those  of  general 
recombination.  For  the  special  or  initial  recombination 
concerns  only  the  ion  and  its  parent  atom.  But  general 
recombination  depends  on  the  chance  of  an  ion  meeting 
others  of  the  opposite  sign,  which  chance  depends  on  the 
number  in  a  c.cm.,  and  this,  again,  on  the  shape  of  the  chamber. 
If,  for  example,  a  particles  cross  a  chamber  3  mm.  wide,  and 
a  sufficient  potential  gradient  is  applied,  most  of  the  ions  will 
be  carried  to  the  electrodes.  If  the  width  of  the  chamber  is 
increased  to  6  mm.  the  magnitude  of  the  stream  of  ions  is 
doubled,  each  positive  meets  twice  as  many  negatives  as 
before,  and  therefore  the  chance  that  any  one  ion  enters  into 
recombination  is  twice  as  great.  Suppose  the  saturation 
current  for  a  3  mm.  chamber  were  100,  using  any  arbitrary 
