6  Prof.  W.Weber  on  Electricity  in  relation  to 
the  latter  becomes 
r  \  ee'      cc  J 
ee'  ~-i-J 
(       0e  +  e'    ee'\ 
r  [r  —  2 r 
V  ee'      cc  J 
Hence  it  appears  that,  in  the  case  of  permanent  relative  rest,  the 
(e  _i_  g'    ee!\ 
r  —  2  — r- '       I  is  common  to  numerator  and  denomi- 
ee      cc  J 
nator.     The  value  of  the  quotient,  which  is  thus  independent  of 
ee' 
this  factor,  namely  — ,  consequently  gives  the  expression  for  the 
force,  in  the  case  of  permanent  relative  rest,  in  complete  agree- 
ment with  the  fundamental  laws  of  electrostatics,  according  to 
which  this  force  has  a  positive  value  for  particles  of  the  same 
kind  at  all  distances. 
3.  The  Law  of  Electrical  Potential. 
In  the  previous  section  the  law  of  electrical  force  is  shown  to 
be,  in  two  respects,  of  a  very  complicated  character,  namely  : — in 
the  first  place,  in  that  the  repulsive  force  between  two  electrical 
particles  is  dependent  on  things  that  do  not  appertain  either  to 
the  nature  of  the  particles  which  exert  the  force  upon  each  other, 
or  to  their  relative  positions  in  space,  or  their  existing  relative 
motion,  but  depends  upon  other  bodies;  and  secondly,  in  that 
repulsion  may  be  exerted  upon  each  other  at  certain  distances 
by  the  same  particles,  and  attraction  at  other  distances. 
Compared  with  this  complicated  law  of  electrical  force,  the  law 
of  electrical  potential  is  very  simple. 
The  value  of  the  potential  V  of  two  electrical  particles  e  and  e\ 
in  fact,  as  I  pointed  out  as  long  ago  as  the  year  1848  in  Pog- 
gendorfFs  Annalen  (vol.  lxxiii.  p.  229),  is  determined  by  the 
following  law, 
V—  ee'  (  ]■     drq      ,^ 
r  \cc    dt2        / 
dr 
Observing  that  both  r  and  -j,  nave  different  values  at  different 
times  for  both  the  particles  e  and  e',  and  that  consequently  both 
dr 
are  functions  of  the  time,  it  follows  that  -r  may  also  be  regarded 
at 
as  a  function  of  r,  which  may  be  denoted  by  fr.     We  thus  obtain 
^=tG;W2-1) 
