124  Prof.  W.  Weber  on  Electricity  in  relation  to 
If  we  deduct  this  part  —  from  the  total  acceleration  -y-.  the 
r         r  at 
difference  [-=- J  expresses  that  part  of  the  relative  acce- 
leration of  the  two  particles  which  results  from  the  forces 
exerted  by  them   upon  each   other.      According   to  section  9 
this  latter  part  was  =  (  -  +  —  J  -7-  ;  and  hence  we  obtain  the  fol- 
lowing equation, 
dt       r  ~~\e        e'  /  dr 
Multiplying  this  equation  by  udt=dr,  we  get 
,  dr      ,1      1\   dV. 
udu—ucx. —  =[  — h  -7  ]•  -=-  dr : 
r       \e       e  /     dr 
and  hence,  by  integrating  from  the  instant  at  which  u  —  0,  the 
value  of  r  corresponding  to  this  instant  beiug  denoted  by  r0, 
g  +  l)(V_Vc)=i««-£^, 
in  which  V=  —  ( 1  )   and  V0= ,  but  where,  in  order 
r  \cc        /  t*q 
to  perform  the  last  integration,  act  must  be  represented  as  a 
function  of  r. 
Now  r .  atdt  is  the  element  of  surface  described  by  the  line  con- 
necting the  two  repelling  or  attracting  particles  while  they  move 
about  each  other  for  the  element  of  time  dt;  and  for  equal  ele- 
ments of  time  dt  this  superficial  element  retains  always  the  same 
value,  whence  radt  =  rQetQdt.     Introducing  the  resulting  value 
1 
«*=Wo*o-  — 
in  the  last  member  of  the  above  equation,  and  carrying  out  the 
integration,  we  obtain  the  following  equation, 
uu       ctQctQ    r0r0—rr 
cc         cc  rr 
\  e      e  y  cc  \  rrQ        r    cc  / 
(.1       1  \  eel 
-  +  —  I—  —pt  the  equation  of  motion 
uu  =  r-rQfp       r  +  r0    cc0a0\ 
cc       r—p  \rn  r         cc  J 
