Passage  of  Electricity  through  Liquids.  521 
m       -• 
i-5-s^w*-^). (17> 
2rQr  =2r|  ,r  =  J  S^C^-C'^X 
2,QV=2,  ^=^2^(0^-0'^)^ 
U  -  A. 
(18) 
2rQr=2J,    2rQ'r=-2J, (19) 
where  the  %r  are  to  be  extended  to  all  the  r  various  chemical 
compounds  which  are  simultaneously  decomposed  in  the  liquid. 
These  equations  hold  even  if  a  complete  molecule  of  a  chemical 
compound  is  not  decomposed  by  the  electrical  current.  If  we 
designate  by  p  the  corresponding  value  of  r  for  a  complete  mo- 
lecule, we  have,  since  both  partial  molecules  must  move  with  the 
same  velocity,  according  to  equation  (7), 
<te-<V,5 (so) 
or  the  two  magnitudes  ep  and  e'p  must  have  the  same  sign. 
From  equations  (20),  (14),  and  (17)  we  get  then 
a    '    a'         an       a' 
p  p         p  p 
As,  moreover,  in  every  volume  of  the  whole  liquid  there  must  be 
equal  quantities  of  positive  and  negative  electricity, 
2r?r(er  +  er)=0, (21) 
where  the  sum  is  to  be  extended  to  all  the  r  substances  or  salts 
present  in  the  liquid,  to  those  even  whose  total  molecules  are  not 
decomposed. 
If  the  intensity  of  the  current  in  the  column  of  liquid  is  the 
same  as  in  the  metallic  part  of  the  conduction,  as  experiment 
shows  (compare  §  69),  then 
i= J (22) 
When  the  same  current  is  sent  through  several  liquids  adjacent 
to  one  another  so  that  it  traverses  one  liquid  after  the  other,  no 
free  molecules  appear  at  the  boundary  of  the  various  electrolytes, 
provided  the  partial  molecules  liberated  at  the  cathode  of  one 
liquid  can  again  form  a  chemical  compound  with  those  liberated 
at  the  anode  of  the  adjacent  liquid. 
From  this  follows  Faraday's  celebrated  electrolytic  law*,  that 
the  number  of  equivalents  (partial  molecules)  liberated  at  the 
electrodes  in  the  unit  of  time  is  a  measure  for  the  quantity  of 
*  Faraday,  Experimental  Researches,  §  377,  pp.  504  &  505,  783  et  seqq. 
