the  Principle  of  the  Conservation  of  Energy. 
17 
longing  to  the  two  particles — that  is  to  say,  upon  their  relative 
vis  viva — and  not  upon  the  second  part  of  the  total  vis  viva,  or 
that  which  the  two  particles  possess  in  virtue  of  their  revolution 
about  one  another  in  space  or  of  the  motion  of  their  centre  of 
gravity  in  space ;  for  this  latter  part  depends  upon  relations 
which  the  two  particles  do  not  of  themselves  directly  present. 
For  the  two  particles  taken  by  themselves  do  not  directly  pre- 
sent any  relation  to  space  except  their  distance  apart,  from 
which  no  knowledge  can  be  had  of  their  rotation  or  of  the 
motion  of  their  centre  of  gravity  in  space. 
Consequently,  in  what  follows,  by  the  kinetic  energy  of  two 
particles  is  to  be  understood,  not  the  total  vis  viva  possessed  by 
the  two  particles,  but  only  their  relative  vis  viva. 
But  it  is  easy  to  see  that,  in  accordance  with  this,  while  a 
system  of  two  electrical  particles  e,  ef  receives  from  without  an 
amount  of  kinetic  energy  =a,  it  really  undergoes  an  alteration 
of  its  potential  energy  = — a;  so  that  the  whole  energy  of  the 
system  must  always  retain  the  same  value  not  only  when  the 
two  particles  constitute  a  detached  system,  but  also  when  they 
do  not  do  so.  For  if  we  represent  the  kinetic  energy  communi- 
cated from  without  by 
1    ee* 
a  = 
2  e+e' 
w, 
while  the  kinetic  energy  of  the  particles  before  the  communica- 
tion of  this  portion  w  as 
_1    ee7 
"26  +  e''* 
the  kinetic  energy  existing  after  the  communication  is 
1  _£?! 
2e  +  e,""w      2  e  +  e' 
Consequently  the  potential  energy  before  the  communication  is 
1    ee* 
1        ^      /  _L        A 
pV-2e  +  e' 
{cc-v0u0), 
whereas  the  potential  energy  after  the  communication  is 
V  =  —  ;  {CC  —  UU)  =  £ ; — ,  [CC  —  U0UQ)  — 
p 
2  e 
■  w; 
so  that,  in  consequence  of  the  communication  from  without  of 
kinetic  energy  equal  to  +o,  a  change  of  potential  energy  has  oc- 
curred which  is  represented  by 
1  66* 
—  -  ;  w=-  —a. 
2  e  +  e7 
Phil.  Mag.  S.  4.  Vol.  43.  No.  283.  Jan.  1872.  C 
