126  Prof.  W.  Weber  on  Electricity  in  relation  to 
other),  there  would  be  always  a  certain  velocity  of  rotation  «0 
for  which  the  attracting  force  required  by  the  rotation  should  be 
equal  to  the  attracting  force  resulting  from  the  reciprocal  action 
of  the  two  particles,  so  that  the  two  particles  rotating  about 
each  other  would  remain,  for  this  velocity  of  rotation,  at  the 
same  distance  rQ.  This,  however,  is  not  the  case,  since  the 
attracting  force  resulting  from  the  reciprocal  action  of  the  two 
particles  depends  not  only  upon  the  distance  r0,  but  also  upon 
the  velocity  of  rotation  a0,  and  increases  with  the  latter  in  such 
a  manner  that  it  always  remains  greater  than  the  attracting  force 
required  by  the  rotation,  so  that  with  any  such  rotation  there  is 
always  involved  a  mutual  approach  of  the  two  particles. 
It  follows  indeed  easily  that,  in  the  case  of  two  similar  par- 
ticles e  and  ef,  when  p  has  a.  positive  value  and  r=r0,  and  con- 
du 
sequently  m=0,  there  is  no  value  of  a0  for  which  —  =0,  as  must 
be  the  case  if  the  two  particles  are  to  remain  at  an  invariable 
distance  r0.  For  when  r=r0,  it  results  from  the  equation  at 
the  end  of  section  1 1  that 
dY  =     ee'    (\  i  o"o*oy 
dr       r0{r0—p)\        "  cc  )3 
and  from  this  it  further  follows,  since 
du  __  ex.*  _  f\      1 WV  __  p  cc    dY 
dt        r  ~~  \€       ev  dr  "~  2  ee}     dr ' 
that 
du 
di 
du 
whence   ,—  can  be  equal  to  nothing  only  when 
1  P 
a°a°=-2^ 
which  for  a  positive  value  of  p  (that  is,  when  e  and  e'  are  of  the 
same  kind)  is  impossible. 
It  follows  further  that,  in  the  case  of  two  similar  particles,  if 
r=r0)  -j-  is  either  positive  or  negative,  according  as  r0>  p  or  r0<:p. 
Consequently  the  two  particles  separate  always  to  a  greater  and 
greater  distance  from  each  other  when  r=r0>p,  and  approach 
always  nearer  to  each  other  when  r=r0<p,  whatever  value  a0 
may  have. 
14.  On  the  Time  of  Oscillation  of  an  Electrical  Atomic  Pair. 
Two  similar  electrical  particles  at  a  distance  r0<p  from  each 
other  (at  which  their  relative  velocity  =0)  do  not  remain  at  this 
2  r0-p\r0  cc  J 
