140  Prof.  W.  Weber  on  Electricity  in  relation  to 
or 
a 
de^—^sinvdvj (19) 
from  (18)  and  (19), 
n 
dUr)       a    o   •         dv  ,om 
_l_z  _.  _  r3  sin  v        . (20) 
dr         n  dr 
and  from  (17)  and  (19), 
£->+'*<>«..* (2D 
If  we  now  substitute  the  values  of    ^       and  —   given  by  (20) 
and  (21)  in  the  following  equation  resulting  from  (11)  and  (15), 
namely 
«2  sin  v2 
m  ^  .  /i^V.  (-04, ^^o _ -,_2flC0. A(22) 
r— p     \  dr    /     \   r0        rA  r  r  J 
we  obtain,  by  again  patting  for  n  its  value  a0r0,  the  following 
equation  between  r  and  v,  namely 
*\r\    dr^_r— r0  /  p       r  +  r0_a$\ 
rV  '  dv2      r—p\r0  +     r        C*J 
By  differentiating  this  equation,  after  multiplying  it  by  r(r—p), 
we  obtain 
d_ 
dr 
(fe-^-£)-5+^@+(-<+5) 
2  (^ V  +  ^r2  C0S  V)  • 
*  From  the  above  equation,  since  -u  may  be  substituted  for  — ,  we 
«  dv 
obtain 
Ao _ °/C.+  -ZU>  .  _M_  I  ,^+-1^  cos  vdr), 
et°r*      cc       r—p  \r0  r         c2 )       [r  —  p)cl\  rJ  J 
which,  when  the  segregating  force  a  vanishes,  and  therefore,  according  to 
section  11,  etr=ecQrQi  passes  over  into  the  equation 
™  =  r~r°  (P.  +  r+ro  .  f^!)_ 
cc       r—p  V0  r        c2/ 
that  is  to  say,  into  the  same  equation  that  was  arrived  at  already  for  this 
case  in  section  11. 
