310       .Dr.  Gandry  on  the  Asymmetrical  Action  of  an 
In  this  way,  Kruger  obtains  the  formula  for  the  polarization : 
p  =  -^—.  log,  (  1  +  k 7—  :,sm  mi  J, 
where  i0sinm£  is  the  alternating  current, 
q  the  area  of  the  electrode, 
e  the  electric  charge  on  a  gramme-ion, 
and       cQ  the  concentration  of  the  Hg  ions  in  the  neighbourhood 
of  the  large  electrode. 
The  asymmetry  of  the  logarithm  gives  rise,  once  more,  to 
a  mean  E.M.F.,  corresponding  to  a  direct  current  : 
i__  M    J-i'k*  l  i  +  1  k*1  4-3'+      1 
l~     &».w  12K  ■?T+i-K-2I-T72+— ■■/' 
where  K=         ^  °    , ---.,. 
eq  .  6,r  .  k{c\r 
The  series  is  convergent,  because  K<  1. 
If  the  alternating  current  is  so  weak  that  the  asymmetry 
just  appears,  we  can  neglect  K4,  K6,  &c,  and 
1  R0  /        1         \2  .  Mm 
~  =  ~^T-Tv  {-■*     -/-:,=  const.    .     .     .       10 
The    direct  current   is,    in    this    case,    independent    of  the 
frequency. 
Disturbing  Effect  clue  to  the  Asymmetry  of  the 
Current  itself. 
When  the  electrolyte  was  dilute  sulphuric  acid,  it  was  clear 
from  the  experiments  that  a  disturbing  effect  of  a  totally 
different  nature  was  present,  and  that  this  masked  that  pre- 
viously described.  This  effect  showed  itself,  unlike  the  other, 
in  a  permanent  increase  of  the  concentration  in  the  neigh- 
bourhood of  the  electrode.  There  was  always  an  after-effect. 
When  the  alternating  current  ceased  to  flow,  the  galvano- 
meter sloidy  went  back  to  zero. 
*I  attribute  this  disturbing  effect  to  the  following  cause. 
Only  a  limited  number  of  Hg  ions  are  at  hand  to  carry  the 
current  from  electrolyte  to  electrode.  If  the  number  imme- 
diately surrounding  the  electrode  does  not  suffice,  it  is  only 
by  the  slow  process  of  diffusion  that  the  defect  may  be 
made  up.  The  result  is  that  part  of  the  pulse  of  the  current 
is  carried  by  hydrogen  ions.  Before  the  return  pulse  of  the 
current  from  electrode  to  electrolyte,  some  of  the  hydrogen 
