136  Prof.  W.  Weber  on  Electricity  in  relation  to 
dent  that  the  electrical  particle  -f  e,  spoken  of  above,  must  of  its  elf, 
without,  electromotive  force,  continue  indefinitely  its  rotatory 
motion  about  the  particle  — e,  and  therefore  must  correspond 
entirely  with  the  molecular  currents  assumed  by  Ampere  in  this 
respect  also. 
VVe  accordingly  obtain  in  this  way,  as  a  deduction  from  the 
laws  of  the  molecular  state  of  aggregation  of  two  dissimilar  elec- 
trical particles,  developed  in  the  preceding  section,  a  simple  con- 
struction for  the  molecular  currents  assumed  by  Ampere  without 
proof  that  their  existence  was  possible. 
18.  Movements  of  two  dissimilar  particles  in  Space  under 
the  Action  of  an  Electrical  Segregating  Force  (Scheidungskraft). 
liir  +  v  denotes  the  angle  which  the  direction  of  the  electrical 
segregating  force  makes  with  r,  and  a  denotes  the  magnitude  of 
the  relative  acceleration  of  the  two  particles  depending  upon  the 
segregating  force,  — fl.cosv  and  a.sinv  are  the  components  of 
a, — the  former  expressing  the  part  of  the  relative  acceleration 
du 
-j-  which  is  dependent  on  the  segregating  force,  and  the  latter 
da 
the  part  of  —  which  depends  on  the  same  force,  where  a  is  the 
difference  of  the  velocities  of  the  two  particles  in  a  direction  per- 
pendicular to  r.  It  is  presupposed  that  the  direction  of  the  se- 
gregating force  lies  in  the  plane  in  which  the  two  particles  rotate 
about  each  other. 
If  now  the  first  component,  namely  —  a  .  cos  v,  as  the  part  of 
■j-  which   depends  upon    the   segregating  force,  and  also    — > 
as  the  part  of  -j  which  depends  upon  the  velocity  u,  be  deducted 
"*  .       du 
from  the  total  acceleration  t=-    the  difference 
dt 
rdu  clol\ 
-r-  +  a  .  cos  v J 
jit  r  J 
c 
denotes  the  part  of  the  relative  acceleration  which  results  from 
the  force  which  the  two  particles  e  and  e1  exert  upon  each  other, 
namely 
\6+ef)  dr~2  ee1'  dr' 
and  hence  the  following  equation  is  obtained : — 
du  act      p  cc      dV 
dt         '  r  ~~  2  ee1     dr 
If  we  deduct  the  last  component,  namely  a  .  sin  v,  as  the  part 
