118  Lord  Ravleioh  on  Electrical  Vibrations 
& 
them  is  that  the  positive  is  eons-trained  to  remain  undis- 
placed, while  the  negative  is  free  to  move.  In  equilibrium 
the  negative  distributes  itself  with  uniformity  throughout 
the  sphere  occupied  by  the  positive,  so  that  the  total  density 
is  everywhere  zero.  There  is  then  no  force  at  any  point ; 
but  if  the  negative  be  displaced,  a  force  is  usually  called  into 
existence.  We  may  denote  the  density  of  the  negative  at 
any  time  and  place  by  p,  that  of  the  positive  and  of  the 
negative,  when  in  equilibrium,  being  p0.  The  repulsion 
between  two  elements  of  negative  prtY,  p'dY'  at  distance  r  is 
denoted  by 
j.r-2.pdY.p'dY' (1). 
The  negative  fluid  is  supposed  to  move  without  circulation, 
so  that  a  velocity-potential  (<£)  exists;  and  the  lirst  question 
which  presents  itself,  is  as  to  whether  there  is  "  condensation/'' 
If  this  be  denoted  by  s,  the  equation  of  continuity  is,  as 
usual  *, 
|+V>=0 (2). 
Again,  since  there  is  no  outstanding  pressure  to  be  taken 
into  account,  the  dynamical  equation  assumes  the  form 
3=* p>. 
where  R  is  the  potential  of  the  attractive  and  repulsive  forces. 
Eliminating  <f>,  we  get 
S  =  -^ ("); 
In  equilibrium  R  is  zero,  and  the  actual  value  depends 
upon  the  displacements,  which  are  supposed  to  be  small.  By 
Poisson's  formula 
V2R  =  47T7/30S (5), 
so  that 
5+**W  =  ° (6). 
This  applies  to  the  interior  of  the  sphere  ;  and  it  appears 
that  any  departure  from  a  uniform  distribution  brings  into 
play  forces  giving  stability,  and  further  that  the  times  of 
oscillation  are  the  same   whatever  be  the   character  of  the 
*  ' Theory  of  Sound.'  S  244. 
