(10) 
374  M.  G.  Quincke  on  Electrolysis,  and  the 
poorer  by  (l  +  -  JM  parts  by  weight  of  neutral  salt.  If,  there- 
fore, fi  or  fjJ  be  the  parts  by  which  the  liquid  at  the  cathode  or 
the  anode  has  become  richer  in  the  unit  of  time,  then 
—  (1+?)M'> 
If  M  and  M'  are  both  negative,  equations  (9)  and  (10)  still 
hold;  only  then  m  and  fju  are  negative,  m!  and  p!  positive;  that 
is,  m!  is  the  quantity  of  partial  molecules  separated  at  the  cathode, 
m  that  at  the  anode ;  at  the  cathode  the  concentration  of  the 
liquid  has  become  smaller*  but  greater  at  the  anode. 
Equations  (9)  and  (10)  hold  moreover  for  the  case  (and  this,  by 
the  way,  is  the  most  frequent  one)  that  the  two  partial  molecules 
are  moved  to  different  sides  by  the  electrical  current,  and  that 
M  and  M;  have  thus  opposite  signs.  If  M'  is  negative,  /a  is  so 
also ;  that  is,  the  liquid  undergoes  a  smaller  degree  of  concen- 
tration both  at  the  positive  and  the  negative  electrode,  apart 
from  the  quantity  of  liberated  or  decomposed  partial  molecules. 
From  equations  (9)  and  (10)  the  following  results  ensue.  If 
M  and  M'  have  opposite  signs,  then 
M<m,     M'<m', (11«) 
and  the  concentration  of  the  liquid  decreases.  If  M  and  M' 
have  the  same  sign,  then 
m<M,     m!<W, (lib) 
and  the  concentration  of  the  liquid  increases  at  one  electrode  and 
decreases  at  the  other.  The  increase  takes  place  at  that  elec- 
trode towards  which  the  greater  equivalent-number  of  partial 
molecules  is  driven  by  the  current. 
Both  equations  (9)  may  also  be  written  thus, 
a!m=      a'M-«M', 
W=-a'M  +  «M'; 
or,  taking  equation  (7)  into  consideration, 
T  5t~t} <12> 
m  —  —qct(v—v');J 
that  is,  the  quantities  of  the  ions  liberated  are  proportional  to  the 
relative  mean  velocity  with  which  the  partial  molecules  move  past 
each  other  in  the  liquid. 
By  the  adjacent  geometric  construction  an  idea  of  the  whole 
process  may  be  obtained. 
Let  the  line  F0G0  represent  the  equivalent-number  of  sodium- 
molecules  of  the  thread  of  liquid,  and  P0  Q0  the  equivalent-num- 
