8  Prof.  W.  Weber  on  Electricity  in  relation  to 
final  arrangements  and  movements  of  the  particles,  and  is  inde- 
pendent of  the  way  by  which  the  transition  has  been  effected, 
and  also  independent  of  states  of  motion  which  may  have  existed 
during  the  transition. 
4.  Fundamental  Electrical  Laws. 
The  law  of  electrical  potential  certainly  appears  to  stand,  in 
view  of  its  simplicity,  in  a  much  closer  relation  to  the  true  fun- 
damental laws  of  electricity  than  the  far  more  complex  law  of 
electrical  force ;  but  the  expression  of  the  former  law  may  still 
be  resolved  into  two  simpler  laws,  which  may  be  stated  in  the 
following  manner : — 
First  Law. — If  two  particles  e  and  e'  are  at  relative  rest  or 
possess  the  same  relative  motion  at  two  different  distances  r  and 
p,  the  quantities  of  work  V  and  U  which  are  expended  in  sepa- 
rating the  particles,  while  mutually  acting  on  each  other,  from 
these  distances  to  an  infinite  distance,  are  to  each  other  inversely 
as  these  two  distances,  that  is, 
Y:V=p:r (1) 
Second  Law. — The  work  U,  which  is  expended  in  separating 
the  particles  e  and  e'  while  subject  to  the  force  exerted  by  them 
on  each  other  from  a  given  distance  p  (  =  —  J  proportional  to 
the  quantity  ee'  to  an  infinite  distance,  makes  together  with  the 
vis  viva  x,  which  belonged  to  the  particles  in  consequence  of 
their  relative  motion  at  the  distance  p,  a  constant  sum,  namely  a ; 
that  is, 
V  +  w=a (2) 
For  from  equation  (1)  it  follows  that 
P 
and  hence,  by  equation  (2), 
«• 
or,  since  p= — > 
r      a 
ee' 
r  \        a/ 
But  the  relative  vis  viva  x  is  proportional  to  the  square  of  the 
dr 
relative  velocity  -j-,  so  that  we  may  substitute  for  a  a  new  con- 
