cc 
120  Prof.  W.  Weber  on  Electricity  in  relation  to 
mutual  action,  we  have,  according  to  the  fundamental  laws  of 
Section  4,  by  putting 
/l       1W         _  1     ee'      dr*         _1    ee' 
p-Z\€+e')cJ'     X-2e  +  erdt*'     a~2e  +  6' 
and  also  giving  a  negative  sign  to  U  and  V,  so  as  to  denote 
thereby  the  potentials, 
\e       e/cc 
TT      1    ee'       dr*  _  1     ee' 
"v  +  2l+?"dF2~27T7'cc; 
and  therefore 
r  \e      e/cc  r  \cc    at*        / 
If  there  is  no  motion  of  rotation  of  the  particles  about  each 
1    dV 
other  in  space,  -  •  -j-  is  the  acceleration  of  the  particle  e  in  the 
1   dV  . 
direction  of  r,  and  -,•  -7-  is  the  acceleration  of  the  particle  e'  iu 
the  opposite  direction.     Hence  the  relative  acceleration  of  the 
two  particles  becomes 
ddr  _  /l      1\  dV 
dP  ~  \e  +  e7  dr  ' 
and  from  this,  by  integrating  between  the  limits  r=r0  and  r=r 
dr 
(r0  denoting  the  value  of  r  for  the  moment  when  — =w  =  0), 
(1      1\  ee' 
-  +  -» )  — >  we  obtain 
6         €V  CC 
dr*  r~rn    P 
—  —uu— "•  -^  .  cc. 
at*  r—p    r0 
—  has  always  a  positive  or  negative  value  differing  from  no- 
r0 
(1      1  \  ee' 
-  +  -j J  —  has  a  given  finite  although  very  small 
value,  which  is  positive  or  negative  according  as  eer  is  positive 
r 
or  negative ;  and  r0=  — — —  has  also  a  positive  or  nega- 
r+—  •  — ^ 
cc      p 
tive  value  differing  from  nothing,  since  the  initial  values  of  r 
and  uu,  by  which  r0  is  to  be  determined,  must  be  considered  as 
positive  measurable  quantities  to  be  determined  by  experiment. 
