Passage  of  Electricity  through  Liquids.  371 
the  moving  mass  and  on  the  friction  against  the  surrounding 
liquid,  also  depends  on  the  greater  or  less  difficulty  with  which 
the  electrical  mass  e  is  detached  from  the  material  constituent- 
molecule. 
The  force  with  which  the  constituent-molecules  (in  this  case 
chlorine  and  sodium)  are  separated  can  be  supposed  proportional 
to  the  relative  mean  velocity  of  the  two  molecules,  and  for  a  given 
distance  is 
K=A{v-v')  =  -~{B6-B'e')>  .     ...     (2) 
where  A  and  B  are  constants. 
If  q  is  the  section,  \  the  conductivity  of  the  entire  liquid,  i 
the  intensity  of  the  current,  then* 
f  =  -f       (3) 
ax  Kq 
and 
K=4*=^;       (4) 
q  A. 
that  is,  the  force  which  tends  to  separate  the  partial  molecules 
or  the  so-called  ions  of  the  same  electrolyte  is  greater  the  greater 
the  density  of  the  current,  if  by  density  we  understand,  as  usual, 
the  quotient  of  the  current-intensity  and  the  section. 
Hence  substances  which  for  definite  currents  are  insulators 
would  become  conductors  if  the  density  of  the  current  -  were 
suitably  increased,  and  would  undergo  decomposition.  The 
latter  would  occur  provided  the  force  K  were  greater  than  the 
attraction  which  the  two  partial  molecules  exert  upon  each  other 
in  consequence  of  chemical  action. 
§53. 
Let  us  assume  that  the  electrical  current  i  in  the  linear  con- 
ductor (the  thread  of  liquid  under  electrolysis)  arises  from  a 
Grove's  battery  of  n  cells.  Let  G  be  the  electromotive  force  of 
one  element,  I  the  length  of  the  thread  of  liquid  traversed  by 
the  current,  "W  the  resistance  of  the  metallic  conduction  and  of 
the  elements ;  then  by  Ohm's  law, 
TlG 
Xq 
and  this  value  inserted  in  equation  (4)  gives 
K-W^B*-BV> <5> 
*  Pogg.  Ann.  vol.  cxiii.  p.  586,  §  46;  and  Kirchhoff,  Pogg.  Ann. 
vol.  lxxv.  p.  191. 
2B2 
