214 
Mr.  A.  Russell  on  the 
cylinders  be  separated 
point  P  in  the  air  at 
cylinders  is  given  by* 
by  air,  the 
a   distance 
dY 
electric 
r  from 
intensity  R  at  a 
the  axis   of  the 
R=-~  = 
dr        r  log  [0/a] 
where  V  is  the  P.D.  between  the  cylinders.  R  has  obviously 
its  maximum  value  Rm  when  r  =  a.     We  also  have 
if  V  and  b  remain  constant.  Hence,  if  a  be  less  than  b/e, 
where  e  is  the  base  of  Neperian  logarithms,  RTO  will  diminish 
as  a  increases.  In  this  case  a  corona  will  be  formed.  When 
the  radius  of  the  corona  is  nearly  equal  to  b/e  a  disruptive 
discharge  will  ensue. 
If  the  radius  of  the  inner  cylinder  be  greater  than  b/e,  a 
disruptive  discharge  ensues  whenever  the  intensity  at  the 
surface  of  the  inner  cylinder  equals  Rmax..  This  was  verified 
roughly  by  Gaugainf- 
The  same  formulae  apply  when  the  dielectric  coefficient  of 
the  insulating  material  between  the  conductors  is  not  unity. 
We  see,  therefore,  that  the  "  factor  of  safety  "  of  concentric 
mains  is  not  necessarily  increased  by  diminishing  the  radius 
of  the  inner  conductor.  This  result  is  of  considerable  prac- 
tical importance. 
5.  The  Corona  round  a  Cylinder. 
The  luminous  effects  produced  when  a  cylinder  is  main- 
tained at  a  very  high  alternating  potential  from  earth  have 
been  investigated  experimentally  by  E.  JonaJ.  He  found 
that  a  cylindrical  wire  supported  by  high-tension  insulators 
becomes  luminous  when  the  voltage  between  it  and  surround- 
ing objects  attains  a  definite  value,  which  depends  mainly  on 
the  diameter  of  the  cylinder.  The  corona  in  this  case  is 
practically  a  concentric  cylinder,  the  diameter  d  of  which 
varies  with  the  voltage  V.  In  the  following  table  V  is  in 
kilovolts  and  d  is  in  millimetres. 
Table  I, — E.  Jona's  experiments  on  the  diameter  of  the 
corona  round  a  thin  wire  at  various  voltages. 
V... 
d... 
123 
18-2 
28 
42 
57 
81 
106 
127 
152 
185 
125 
196 
150 
0-12!    0-25 
050 
1-00 
2  00 
4-00 
G00 
7-00 
10-0 
*  Russell,  '  Alternating  Currents/  vol.  i.  p.  95. 
t  Annates  de  Chimie  et  ae  Physique,  viii.  p.  75  (1866). 
X  E.  Jona,  Elettricista,   Rome,  xiii.  pp.   113-115,   April  15,   1904 
Science  Abstracts,  vol.  vii.  B,  p.  605. 
