240  Mr.  A.  Russell  on  the 
value  at  the  boundary  o£  the  metal,  and  so  there  is  equi- 
librium, a  corona  being  formed. 
The  explanation  o£  the  varying  numbers  obtained  when 
large  electrodes  are  used  and  the  disruptive  voltages  con- 
sidered are  small,  is  more  difficult.  When  the  minimum 
distance  x  between  the  electrodes  is  less  than  3/jl,  the  sparking 
potentials  are  practically  independent  o£  the  nature  of  the 
gas  between  the  electrodes  *.  Since  the  material  of  which 
the  electrodes  is  made  exerts  an  important  influence  on  the 
sparking  potential  Y,  at  these  small  distances,  it  is  highly 
probable  that  the  carriers  of  the  discharge  come  from  the 
metal  and  not  from  the  gas.  For  a  certain  distance  greater 
than  3/x,  G.  M.  Hobbs  finds  in  some  cases  that  V  remains 
constant  and  equal  to  the  minimum  spark-potential  which  in 
air  is  about  o50  volts  t.  For  slightly  greater  distances  Y 
increases  uniformly  with  x. 
Jt  is  obvious,  therefore,  that  when  the  electrodes  are  very 
close  tooether,  we  cannot  assume  that  we  have  a  homogeneous 
medium  bounded  by  rigid  equipotential  surfaces.  Hence,  as 
the  equipotential  surfaces  are  unknown,  we  cannot  apply  the 
ordinary  electrostatic  equations.  For  these  reasons  we  have 
in  the  following  paper  only  considered  experimental  results 
obtained  for  values  of  x  greater  than  one  millimetre.  If  we 
had  only  considered  distances  greater  than  half  a  centimetre 
(one  filth  of  an  inch),  it  would  have  been  unnecessarv  to 
make  any  assumptions  about  the  actions  that  take  place  at 
the  end  of  the  tube  subjected  to  the  maximum  electric  stres.-. 
as  the  maximum  values  of  the  electric  intensity,  at  the 
instant  of  discharge,  are  found  to  be  in  satisfactory  agree- 
ment. In  order,  however,  to  include  in  our  formulae  the 
sparking  potentials  for  values  of  x  lying  between  O'l  and 
0-5  cm.,  we  have  found  that  it  is  necessary  to  make  the 
following  assumption.  At  the  moment  of  the  disruptive 
discharge,  the  pressure  on  the  ends  of  the  Faraday  tube 
subjected  to  the  maximum  stress  is  Y  —  e,  where  e  represents 
what  we  shall  call  the  lost  volts.  When  the  electrodes  are 
surrounded  with  coronee  an  assumption  of  this  nature  must 
be  made  J,  but  in  this  case  e  will  be  a  function  of  Y  and  x. 
In  the  cases  we  consider  we  assume  that  e  is  constant  and 
equal  to  0*8  of  a  kilovolt.      Making   this   assumption  and, 
*  G.  M.  Hobbs,  "The  Relation  between  P.D.  and  Spark-length  for 
Small  Values  of  the  latter."    Phil.  Mag.  [6]  x.  p.  617  (Dec.  1905)". 
f  The  Hon.  Ft.  J.  Strutt,  "  On  the  Least  Potential-Difference  required 
to  produce  Discharge  through  Various  Gases. ;'  Phil.  Trans,  vol.  198.  A. 
p.  877  (1899-1900). 
%  H.  J.  Rvan,  "The  Conductivity  of  the  Atmosphere  at  High 
Voltages."     Trans.  Am.  Inst.  El.  Eng.  Vol.  xxiii.  p.  101  (1904). 
