Dielectric  Strength  of  Air.  261 
12.    The  Disruptive  Discharge  between  Two  Parallel 
Cylinders. 
It  is  well  known  in  practice  that  when  we  have  two  parallel 
wires  with  a  high  P.D.  between  them,  then  in  certain  cases 
coronse  envelope  the  wires.  When  they  are  close  together, 
however,  this  effect  is  not  produced,  a  disruptive  discharge 
occurring  directly  the  P.D.  attains  a  certain  value.  It  is 
important  therefore  to  know  what  distance  apart  the  wires 
must  be  in  order  that  coronaB  can  be  formed. 
If  we  assume  that  sec  0  =  d/2a,  we  find  that 
P    -  V  tan  0 
m~  d(l-,Cos  ey  log  (tan  0 +;sec  0) ' 
Let  d  be  constant  and  let  a  vary,  then,  solving' the  equation 
<mm/d6=0i  we  find  that 
log  tan  (tt/4  +  0/2)  =   .   JT  °       ,. 
sm-  6— cos  6 
When  6  is  nearly  70°  this  equation  is  satisfied,  and  in  this 
case  d  =  5*85 a  nearly. 
Hence  making  the  assumption  that  the  coronse  are  cylin- 
drical in  shape,  we  see  that  Hm  diminishes  as  a  increases 
when  d  is  greater  than  5*85  a.  In  practice,  therefore,  we 
should  not  expect  coronae  to  be  formed  when  the  wires  were 
at  a  less  distance  apart  than  about  three  times  their  diameter. 
13.    The  Application  of  the  Formulce  to  Experimental  Results. 
I.  With  Direct  Pressures. 
(i.)    Lord  Kelvin's  tests  with  large  electrodes. 
Lord  Kelvin  *  was  the  first  to  make  accurate  tests  on  the 
disruptive  voltages  between  electrodes  in  air.  He  found  that 
the  apparent  dielectric  strength  of  a  thin  stratum  of  air  was 
much  greater  than  that  of  a  thick  one.  The  apparent 
dielectric  strength  in  our  notation  being  Vf/%,  we  have 
V//^=Rmax.  +  0-8//^ 
where  V  is  in  kilovolts,  and  P  .,  the  dielectric  strength  of 
air,  is  a  constant.  In  Kelvin's  experiments/' was  practically 
equal  to  unity  at  all  distances,  and  thus  V/x  increases  rapidly 
as  x  diminishes. 
From  his  experimental  resultsf  Lord  Kelvin  concludes 
that  a  battery  of  5510  Danieli  cells  could  produce  a  spark 
between  two  slightly   convex   electrodes  when  the  minimum 
*  Proc.  Roy.  Soc.  1860,  or  <  Reprint/  p.  24. 
t  Proc.  Roy.  Soc.  April  ll>,  1860,  p.  259. 
