10  Prof.  W.  Weber  on  Electricity  in  relation  to 
We  thus  obtain 
r  \       cc    dt2J 
Here  V  denotes  the  work  expended  in  separating  the  two  par- 
ticles from  the  distance  r  to  an  infinite  distance.  If  V  is  to  de- 
note the  work  done  in  bringing  the  particles  from  an  infinite  dis- 
tance to  the  distance  r,  as  it  is  usually  understood  to  do,  so  that 
dV 
positive  values  of  -7—  may  indicate  repulsion,  we  obtain 
V~"  r\cc    df      1J> 
that  is  to  say,  the  law  of  electrical  potential. 
5.  Principle  of  the  Conservation  of  Energy  for  Two  Particles 
which  form  a  detached  system. 
The  two  fundamental  laws  laid  down  in  the  foregoing  section, 
which  may  be  called 
The  Law  of  the  dependence  of  the  Potential  on  the  distance 
for  a  constant  relative  motion,  and 
The  Law  of  the  dependence  of  the  Potential  on  the  relative 
motion  for  a  constant  distance, 
require  to  be  further  discussed  in  relation  to  their  bearing  upon 
the  principle  of  the  Conservation  of  Energy. 
In  accordance  with  the  principle  of  the  conservation  of  energy, 
three  forms  of  energy  are  to  be  distinguished  from  each  other — 
namely,  energy  of  motion  (kinetic  energy), potential  energy,  and 
energy  of  heat  (thermal  energy). 
The  energy  of  motion  is  that  part  of  the  energy  which  depends 
upon  the  existing  movements ;  and  a  special  determination  is 
given  of  the  way  in  which  it  depends  upon  movement — namely, 
partly  upon  the  magnitude  of  the  moving  mass,  and  partly  upon 
the  velocity  with  which  this  mass  moves. 
The  same  determination  also  appies  to  thermal  energy,  if  this 
is  regarded,  in  accordance  with  the  mechanical  theory  of  heat, 
the  two  particles  j  while  the  first  two  parts  taken  together,  namely 
1  eg'    /, 
2  e+e'  V 
dt*  +  dt2/' 
represent  the  total  internal  vis  viva,  or  the  total  internal  kinetic  energy  of 
the  system;  and  the  third  part,  namely  -  '^"^  *  '  +(e+€')yy  >  repre- 
sents the  external  vis  viva,  or  the  external  kinetic  energy  of  the  system  (thsit 
is,  the  vis  viva  of  the  centre  of  gravity  of  the  two  particles). 
