the  Principle  of  the  Conservation  of  Energy.  13 
We  have,  for  the  potential  of  such  a  system  of  two  electrical 
particles, 
V—  ee'  fuu     "l\ 
"~   r  \cc        J' 
and,  for  the  internal  kinetic  energy  of  the  system, 
2  e  +  e  v  '      pec  v  ' 
dr 
if  w=  —  denotes  the  relative  velocity  of  the  two  particles,  and  a 
the  difference  of  their  velocities  in  space  at  right  angles  to  r. 
But,  for  such  a  detached  system,  when  we  put  r=r0  and  «  =  «0 
for  «=0,  it  is  easy  to  obtain 
«—  r°  „ 
r—p  \ra  r       °  v 
and  consequently  the  sum 
NV      V~r0  +  p       cc    *  r0  +2e4-e''^o- 
This  sum  likewise  retains  the  same  value  so  long  as  the  values 
of  7*0  and  u0  remain  unchanged — that  is,  so  long  as  the  system  of 
two  particles  undergoes  neither  loss  nor  gain  of  energy  from 
without  f.  The  same  principle  holds  good  in  relation  to  the  external 
kinetic  energy  of  a  detached  system  of  two  electrical  particles 
and  to  that  of  two  ponderable  particles. 
*  See  Section  11. 
t  In  Professor  Tait's  very  instructive  work,  '  A  Sketch  of  Thermodyna- 
mics '  (Edinburgh,  18(18),  the  following  passage  occurs  at  page /6,  in  refer- 
ence to  the  investigations  of  Riemann  and  Lorenz  which  appeared  in  Pog- 
gendorff's  Annalen  for  186/ [Phil.  Mag.  S.  4. vol.  xxxiv.pp.368  and  287]  : — 
"  But  the  investigations  of  these  authors  are  entirely  based  on  Weber's  inad- 
missible theory  of  the  forces  exerted  on  each  other  by  moving  electric  particles, 
for  which  the  conservation  of  energy  is  not  true,  while  Maxwell's  result  is 
in  perfect  consistence  with  that  great  principle."  This  assertion  of  Pro- 
fessor Tait's  seems  to  be  in  contradiction  with  the  above.  At  page  56  of 
the  same  work  Mr.  Tait  mentions  that  Helmholtz  has  based  the  doctrine 
of  energy  on  Newton's  principle  and  on  the  following  postulate  : — "  Matter 
consists  of  ultimate  particles  which  exert  upon  each  other  forces  whose 
directions  are  those  of  the  lines  joining  each  pair  of  particles,  and  whose 
magnitudes  depend  solely  on  the  distances  between  the  particles."  The 
contradiction  between  the  fundamental  law  of  electricity  and  this  postulate 
is  evident ;  but  the  contradiction  between  it  and  the  principle  of  the  conser- 
vation of  energy  is  by  no  means  evident, — a  distinction  which  Professor 
Tait  seems  to  have  overlooked. 
