Recombination  of  Ions  in  Air  and  other  Gases.         469 
system  of  units,  and  the  actual  current  for  a  moderate 
potential  were  90,  then  for  the  6  mm.  chamber,  under  an 
equal  potential  gradient,  the  current  would  be  160,  not  180; 
the  saturation  current  being  200.  This  is  recognized  in  tlie 
usual  formulae.     For  example,  Langevin  finds  that — 
?=H1+f) 
where  Q0  is  the  saturation  current  per  sq.cm.  of  electrode, 
and  Q  is  the  current  when  such  a  potential  is  applied  that  a 
is  the  density  thereby  caused  to  exist  on  each  sq.cm.  of  the 
electrode.  "\Vhen  Q  and  Q0  are  both  small  compared  to  <r,  it 
follows  that : — 
eQ  __  eQ0  _  e2Qo2 
a  a  2a2 
,      Qn-Q.    =€Qo 
Qo  '2a-  • 
Thus,  the  relative  lack  of  saturation,  viz.  (Q0  —  Q)/Qo,  is 
proportional  to  Q0,  which  itself  depends  on  the  depth  of  the 
chamber.     Other  formulas  show  the  same  dependence. 
But  experiment  shows  that  when  the  density  of  the  ions  is 
small  the  depth  of  the  ionization  chamber  has  very  little  effect 
on  the  degree  of  saturation.  This  may  be  illustrated  by  the 
following  experiments  : — 
Five  mmg.  of  radium  bromide  were  so  placed  that  the  a 
rays  passed  upwards  through  an  aperture  in  a  lead  plate  and 
crossed  the  gauze  of  the  ionization  chamber.    The  rays  formed 
o( 
a  cone  whose  vertical  angle  was  about  20°,  The  apparatus 
used  was  the  same  as  that  of  the  previous  experiment 
described,  but  the  currents  were  so  strong  that  a  capacity  of 
1070  cms.  had  to  be  put  in  parallel  with  the  electrometer. 
Determinations  were  then  made  of  the  strengths  ot  the 
current  at  various  potentials: — (l)When  the  ionization 
chamber  was  3  mm.  wide;  (2)  when  6  mm.  wide  ;  and  (o) 
when  9  mm.  wide.  The  values  obtained  were  then  reduced 
so  that  the  saturation  current  in  each  case  was  set  at  the 
same  value.  Comparison  then  showed  that  the  curves  were 
almost  identical  except  at  low  potentials,  and  this  was  in 
agreement  with  the  hypothesis  now  put  forward.  For  at  all 
but  low  potentials  an2  was  so  small  as  to  be  negligible.  When 
the  potential  was  very  low,  one  or  two  volts  per  centimetre, 
then  the  ions  moved  so  slowly  that  n  was  larger,  and  an2  was 
not  negligible,  and  under  those  circumstances  the  curve 
showed  a  difference  of  the  right  kind.  That  is  to  say,  the 
9  mm.  curve  was  further  from  being  saturated  than  the  others. 
The  currents  were  specially  made   not   too  weak   in   order  to 
