the  Principle  of  the  Conservation  of  Energy.  141 
If  we  here  put,  to  consider  a  special  case, 
(that  is  to  say,  the  case  in  which,  for  a  —  0,  the  two  particles  re- 
main, according  to  section  16,  at  the  same  distance  during  their 
rotation),  we  obtain 
d(.        ^\r\    dr*\  %(r—rQ),9         x      6ar, 
which  becomes  =0,  first,  when  w  =  0  and  consequently  ?'  =  ?'0, 
a  =  oi0,  and  cost>=  —1,  and,  secondly,  when 
_        3ar(r0  +  r  cos  v) 
a  case  which  occurs  for  small  values  of  a,  if  cos  v  =  -f  1  and  so 
6a?'l 
r  =  r0— — j-  approximately. 
ao 
Hence  it  follows  that,  just  as,  according  to  section  16,  one  of 
two  dissimilar  electrical  particles,  for  which  p  =  —  2r0  -^-2,  could 
move  round  the  other  in  a  circular  orbit  when  not  acted  on  by 
segregating  force,  so  also  when  two  dissimilar  electrical  particles, 
for  which  p=  —  2?*0  (-^-^  +  Gr0J,  are  acted  on  by  a  segregating 
force  [  =  a),  one  of  them  can  revolve  about  the  other  in  a  closed 
orbit,  though  the  orbit  is  not  circular.  The  distance  between 
the  particles  varies,  in  fact,  according  as  the  moving  particle  lies 
before  or  behind  the  central  particle  considered  relatively  to  the 
direction  of  the  segregating  force,  being  in  the  latter  case  =r0, 
and  in  the  former  case  =r0— 6-^- a. 
aoao 
Such  an  eccentrical  position  of  the  one  particle  in  the  plane 
of  the  orbit  described  (under  the  influence  of  a  segregating 
force)  by  the  other  particle  about  this  one,  may  be  compared  to 
the  separation  of  electric  fluids  at  rest  under  the  influence  of  a 
similar  segregating  force ;  but  the  remarkable  difference  presents 
itself  that  the  separation  takes  place  in  opposite  directions  in 
the  two  cases. 
It  follows  from  this,  that  in  all  conductors  that  have  been 
charged  in  the  usual  way  under  the  influence  of  a  force  of 
electrical  segregation,  the  electricity  cannot  be  contained  only  in 
the  state  of  aggregation  corresponding  to  Ampere's  molecular 
currents,  since  in  that  case  the  resulting  segregation  would  take 
