16  Prof.  W.  Weber  on  Electricity  in  relation  to 
is  accomplished  if  we  assign  to  it  the  value  2- .  — ,  a 
distance  which  is  given  by  the  particles  e,  e1,  by  their  masses  e,  e', 
and  by  the  known  electrical  constant  c. 
If  we  now  put  the  smaller  distance  equal  to  the  value  of  p,  we 
get,  in  virtue  of  the  equations 
r  \cc       r 
p—r^^p—r    ee1 /uu        \ 
p        ~~    p        r  \cc       J' 
the  required  value  of  the  potential  energy,  namely 
r  Tr         ee1  /uu      _  \      1     ee     ,  x 
_~V= 1 1 1=  -——j  (cc—uu). 
p  P\CC  /       2  6  +  6M  ' 
In  accordance  with  the  distinction  which  is  here  drawn  between 
the  potential  and  the  potential  energy  of  two  electrical  particles 
and  with  the  corresponding  determination  of  their  relation  to  each 
other,  an  analogous  distinction  may  also  be  made  between  the 
vis  viva  and  the  kinetic  energy  of  two  particles.  For  there  is  no 
necessity  that  the  kinetic  energy  of  two  particles  should  be  taken 
as  being  equal  to  the  total  vis  viva  of  the  two  particles ;  all  that 
is  generally  essential  is  a  definite  determination  of  the  relation 
subsisting  between  the  kinetic  energy  of  two  particles  and  the  total 
vis  viva  belonging  to  them  both. 
Now  the  total  vis  viva  possessed  by  the  two  particles  was  re- 
presented in  the  note  to  section  4  as  the  sum  of  two  parts,  of 
1     e  e       dr 
which  the  first  part,  namely  ~ -,  •  -j-^,  was  called  the  rela- 
£  e  -f-  e     dt 
tive  vis  viva.  The  second  part  was  that  which  the  two  particles 
possessed  in  virtue  of  their  revolution  about  each  other  in  space, 
and  in  virtue  of  the  motion  of  their  centre  of  gravity  in  space. 
If  now,  in  order  to  establish  the  conception  of  the  energy  of 
two  particles,  we  take  it  as  our  starting-point  that  the  prin- 
ciple of  the  conservation  of  energy  of  two  particles  must  be  based 
upon  the  essential  characters  of  the  two  particles,  and  in  fact 
upon  what  is  essential  to  them  when  regarded  as  constituting  a 
detached  system,  it  is  obvious  that  for  this  purpose  the  concep- 
tion of  the  energy  of  two  particles  must  be  made  to  depend  only 
on  the  relations  presented  by  the  system  of  the  two  particles  as 
such,  quite  irrespectively  of  the  relations  in  which  these  parti- 
cles may  stand  to  all  other  bodies  in  space. 
Applying  this  fundamental  principle  to  the  kinetic  energy  of 
two  particles  in  the  same  way  as  it  has  just  been  done  in  respect 
of  the  potential  energy,  we  see  that  the  kinetic  energy  must  be 
taken  as  dependent  upon  the  first  part  of  the  total  vis  viva  be- 
