Dielectric  Strength- of-  Air. 
257 
For  values  of  xja  greater  than  1*5  the  values  of /given  in 
the  last  column  are  correct  to  four  decimal  figures.  We 
have  shown  above  by  direct  calculation  that  the  value  of  / 
when  xja  is  0*5  is  1*1726.  The  KirohhofT-Schuster  formula 
makes  it  1*1724.  This  formula  is  therefore  very  accurate  for 
values  of  xja  less  than  0*5,  and  these  are  the  values  which 
it  is  so  laborious  to  find  by  direct  computation  from  (15). 
In  the  following  table  for  the  values  of  f1  the  first  column 
is  taken  from  Table  III.  The  next  column  is  calculated  by 
the  equation 
/./■'    z  +  ia   kk'K2 
A  =  Va'~2a-'     tt    ' 
and  the  last  column  for  fx  is  got  by  the  equation 
/i=/+A. 
Table  I V.— Values  of  A. 
xja. 
/from  Table  III. 
A. 
| 
A. 
0 
1-000 
o-ooooo 
1-000 
o-i 
1-034 
o-ooooi 
1-034 
0-2 
10676 
0-0008 
1-068 
0-3 
1-102 
0-004 
1-106 
0-4 
1-137 
0-013 
1-150 
0-5 
1-173 
0026 
1-199 
0-6 
1-208 
0045 
1-253 
0-7 
1-245 
0-068 
1-313 
0-8 
1-283 
0-095 
1-378 
0-9 
1-321 
0-125 
1-446 
1-0 
1-359 
0-158 
1-517 
i 
The  values  of  fi  given  in  this  table  are  in  exact  agreement 
with  the  numbers  given  by  Professor  Schuster  *. 
9.  The  Disruptive  Discharge  between  Tivo  Spherical  Electrodes. 
The  formulae  and  tables  given  above  enable  us  to  find  the 
maximum  value  RTO  of  the  intensity  of  the  electric  field 
round  two  spherical  electrodes  provided  that  the  electrodes 
are  not  enveloped  by  coronse;  that  is,  provided  that  none  of  the 
air  surrounding  them  is  broken  down.  If  no  coronas  are 
formed  before  the  disruptive  discharge  ensues,  then  we  can 
calculate  RWi  at  this  instant,  and  so  find  Rmax.  the  dielectric 
strength  of  the  air.     As  in  the  case  of  a  concentric  main  oi 
*  Phil  Mag-,  vol.  xxix.  p.  192, 
Phil.  Mag.  S.  6.  Vol.  11.  No.  62.  Feb.  1906.  8 
