372  M.  G.  Quincke  on  Electrolysis,  and  the 
If  the  resistance  W,  as  is  frequently  the  case,  is  very  small  com- 
pared with  the  resistance  of  the  electrolyzed  column  of  liquid,  the 
expression  (5)  passes  into 
K=^(Be-BV) .     (6) 
The  force  which  tends  to  separate  the  partial  molecules  {the  ions) 
increases  with  the  electromotive  force  of  the  battery  used,  is  in- 
versely proportional  to  the  length  of  the  thread  of  liquid  to  be  elec- 
trolyzed, but  independent  of  its  section  and  conductivity. 
If  the  resistance  of  the  elements  and  the  metallic  conduction 
cannot  be  neglected  in  comparison  with  the  resistance  of  the 
electrolyzed  thread  of  liquid,  the  force  K  is  still  smaller  than  is 
given  by  expression  (6). 
The  force  depends  here  very  much  on  e  and  e'.  In  the  case 
of  solid  bodies,  where  the  partial  molecules  are  hardly  or  not 
at  all  mobile,  and  the  constants  B  B'  have  the  value  0,  we  have 
also  K=0,  and  there  is  no  electrochemical  decomposition  of  the 
total  molecule. 
§54. 
Since  each  chlorine-  and  each  sodium-molecule  moves  with  a 
certain  velocity,  the  relative  velocity  of  these  partial  molecules 
will  be  retarded  by  the  attracting  forces  which  chlorine  and 
sodium  exert  upon  each  other.  On  the  other  hand,  the  attrac- 
tion towards  the  adjacent  sodium- or  chlorine-particle  of  the  next 
or  preceding  complete  molecule  will  again  increase  this  velocity 
to  the  same  extent.  It  may  hence  be  assumed  that  when  the 
electrolyte  is  generally  decomposed,  and  conducts  electricity 
electrolytically,  the  particles  will  move  past  each  other  with  a 
mean  constant  relative  velocity. 
If  in  the  unit  of  volume  of  liquid  there  are  a  parts  by  weight 
of  sodium  and  a!  parts  by  weight  of  chlorine,  a  and  af  are  to  each 
other  in  the  ratio  of  their  chemical  equivalents.  If  M  is  the 
entire  quantity  of  the  one  ion  (sodium),  and  M'  that  of  the  other 
(chlorine),  which  are  carried  along  in  the  direction  of  the  positive 
x  by  the  unit  of  length  of  the  thread  of  liquid,  we  have 
dV 
M  =  quv=:  —  Ce  .  got . 
M=qct>v'=-C'e'.qal.~; 
dV 
or,  placing  for  -7—  its  value  from  equation  (3), 
M  =za  —> 
M'=tV  ~£ 
A.    ■J 
(7) 
(8) 
