Dielectric  Strength  of  Air.  245 
From  1  to  15  millimetres  V  is  given  roughly  by  the  equation 
V=30  +  12d. 
It  will  be  seen  that  the  diameter  of  the  corona  for  a 
pressure  o£  18  kilovolts  is  0*025  cm.  Thus  if  the  diameter 
of  the  wire  is  less  than  0*025  cm.,  in  a  dark  room  it  will  be 
seen  surrounded  with  a  corona  when  the  pressure  between  it 
and  the  earth  is  greater  than  18  kilovolts.  Approaching  an 
earthed  conductor  to  the  wire  will  increase  the  luminous 
effects.  E.  Jona  found  that  the  diameter  of  the  corona  was 
1*5  cm.  whether  the  wire  were  0*01  or  1*4  cm.  in  diameter, 
when  the  pressure  was  196  kilovolts. 
6.  The  Stress  in  the  Dielectric  round  Two  Particles  having 
equal  and  opposite  charges  of  Electricity. 
Let  there  be  a  charge  +  q  of  electricity  at  P  (fig.  1)  and 
a  charge  ~q  at  N.  The  potential  v  at  a  point  distant  1\  and 
r2  from  P  and  N  respectively  is  given  by 
v  =  q/r1  —  q/r2 (a) 
The  locus  of  the  points,  the  bipolar  coordinates  of  which 
satisfy  the  equation  (a)  for  a  given  value  of  v,  will  give  the 
surface  on  which  the  potential  is  v.  Hence  these  surfaces 
(fig.  1)  can  be  easily  constructed.  We  see  that  the  equi- 
potential   surfaces  near    P  and  N    are   practically    spheres. 
Kar.l 
Equipotential  surfaces  round  two  points  having  equal  and  opposite 
charges. 
Hence  the  equipotential  lines  shown  in   the  figure  are  ap- 
proximately the  same  as  those  of  two  spheres  at  a  considerable 
distance  apart. 
