Passage  of  Electricity  through  Liquids.  519 
n  A. 
(14) 
M 
—  is  then  the  number  of  partial  molecules  which  pass  to  the 
M' 
cathode,  —  the  number  of  partial  molecules  which  pass  to  the 
anode  in  the  unit  of  time.  Each  of  these  particles  is  the  bearer 
of  a  quantity  of  electricity  e  or  e';  and  therefore  through  the  sec- 
tion of  the  thread  of  liquid  there  pass  in  the  unit  of  time  the 
quantities  of  electricity 
M         .p 
a  X 
a!  X 
(15) 
According  to  the  sign  of  €  or  e'  they  may  be  positive  or  negative, 
and  have  in  general  different  magnitudes. 
In  electrical  currents  in  metals  it  is  assumed,  on  the  contrary, 
that  the  same  quantity  of  positive  electricity  flows  in  one  direc- 
tion through  a  definite  section,  as  of  negative  electricity  in  the 
opposite  direction*.  That, notwithstanding  this,  no  difference  can 
be  perceived f  between  the  action  of  the  same  electrical  current 
whether  it  flows  through  an  electrolyte  or  a  metal,  is  in  com- 
plete accordance  with  other  phenomena — for  instance,  the  dis- 
charge of  the  Leyden  jar,  where  no  difference  is  observed,  whether 
the  quantity  -\-e  flows  in  one  or  —  e  in  the  other  direction 
through  the  conductor.  If  i  be  the  intensity  of  the  current,  in 
a  metallic  conductor,  this  means  that  through  a  section  of  the 
metal  the  quantity  -f-i  of  positive  electricity  flows  in  one,  and 
—  i  in  the  other  direction  in  the  unit  of  time.  The  whole 
quantity  of  positive  and  negative  electricity  which  traverses  the 
same  section  in  the  unit  of  time  is  therefore  2i.  Hence  the  en- 
tire quantity  of  electricity  carried  in  the  unit  of  time  through 
the  section  of  the  thread  of  liquid  is  =  2i,  and  we  have 
M       M'  v 
2i=-e+^re'  =  i{  (Ce«  +  CV»),    .     .     .     (16a) 
a  a  A. 
where  the  signs  of  e  and  e7  need  not  be  taken  into  account. 
If  from  equations  (13)  and  (14)  the  values  of  M,  M',  and  a, 
*  Kirchhoff,  Pogg.  Ann.  vol.  lxxviii.  p.  509. 
t  Kohlrausch,  Pogg.  Ann.  vol.  xcvii.  (1856)  p.  559. 
