18  Prof.  W.Weber  on  Electricity  in  relation  to 
7.  Application  to  other  Bodies. 
If  we  distinguish,  in  accordance  with  the  last  section,  between 
the  potential  and  the  potential  energy  of  two  particles — that  is  to 
say,  if  we  define 
Potential  as  the  amount  of  work  which,  in  consequence  of  the 
mutual  action  of  the  two  particles,  is  done   during   the 
transference  of  the  particles  from  an  infinite  distance  to  the 
dr 
actual  distance  r  with  the  existing  relative  velocity  -g-j; 
and 
Potential  energy  as  that  amount  of  work,  taken  negatively, 
which,  in  consequence  of  the  mutual  action  of  the  two  par- 
ticles, is  done  during  the  transference  of  the  particles  from 
the  greater  distance  r=  ao  to  the  smaller  distance  r=p  deter- 
mined by  the  particles  e,  e1,  their  masses  e,  e',  and  by  the 
dr 
constant  c,  with  the  existing  relative  velocity  -j-> 
the  latter  (that  is  to  say,  the  potential  energy  in  the  sense  that 
has  been  indicated)  may  be  resolved  into  two  parts,  one  of  them 
equal  and  opposite  to  the  potential,  and  therefore  identical  with 
the  magnitude  which  has  hitherto  been  alone  called  potential 
energy,  but  which,  regarded  henceforward  as  only  a  part  of  the 
potential  energy,  we  may  call  the  free  potential  energy,  the  re- 
mainder is  the  second  part,  which  may  be  called  the  latent  poten- 
tial energy. 
Hence  the  principle  of  the  conservation  of  energy  may  be 
enunciated  in  the  first  place  in  the  earlier  wider  sense  as  follows: — 
For  a  detached  system  of  two  particles  the  sum  of  the  kinetic 
energy  and  of  the  free  potential  energy  is  always  the  same. 
For  so  long  as  no  kinetic  energy  is  either  lost  or  communicated 
from  without,  every  change  in  the  free  potential  energy  will  be 
compensated  by  an  equal  and  opposite  change  in  the  kinetic 
energy. 
But  the  principle  of  the  conservation  of  energy  may  also  be 
enunciated,  secondly,  in  the  narrower  sense  as  follows  (potential 
energy  and  kinetic  energy  being  understood  in  the  sense  that 
has  just  been  defined)  : — 
The  relative  kinetic  energy  of  two  particles,  and  the  total  poten- 
tial energy  which  they  possess  along  with  this  kinetic  energy, 
together  give  always  the  same  sum. 
Upon  this  the  following  remarks  may  be  made  : — 
(1)  One  particle  regarded  by  itself  can  only  possess  kinetic 
energy. 
(2)  Two  particles  likewise  possess  in  the  first  place  kinetic 
energy,  which  is  the  sum  of  those  which  they  possess  when  con- 
sidered separately. 
