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  LXXII. 
  Alternatina- 
  Current 
  Spai^k 
  Potentials 
  and 
  their 
  Rela- 
  

   tion 
  to 
  the 
  Radius 
  of 
  the 
  Curvature 
  of 
  the 
  Electrodes. 
  By 
  

   Joseph 
  de 
  Kowalskt, 
  Fh.I)., 
  Professor 
  of 
  Experimental 
  

   Physics 
  at 
  the 
  University 
  of 
  Finhourg^ 
  Switzerland^ 
  and 
  

   ULEI.CH 
  J. 
  Rappel, 
  Ph.D', 
  Assistant 
  in 
  Physics 
  at 
  said 
  

   University* 
  . 
  

  

  [Plate 
  XIX.] 
  

  

  Introduction. 
  

  

  r|^HE 
  phenomena 
  of 
  the 
  disruptive 
  discharge, 
  and 
  the 
  

   X 
  measurement 
  of 
  the 
  respective 
  spark 
  potentials, 
  have 
  

   lono; 
  occupied 
  the 
  attention 
  of 
  physicists. 
  In 
  an 
  excellent 
  

   work 
  by 
  J. 
  J. 
  Thomson 
  f, 
  we 
  find 
  an 
  extensive 
  enumeration 
  

   of 
  the 
  principal 
  works 
  on 
  this 
  subject. 
  A 
  series 
  of 
  accurate 
  

   measurements 
  have 
  been 
  made 
  by 
  Lord 
  Kelvin, 
  Paschen, 
  

   Bailie, 
  Heydweiller, 
  Orgler, 
  de 
  Kowalski, 
  Voigt, 
  Algermissen, 
  

   and 
  C. 
  Mueller, 
  all 
  with 
  direct 
  current. 
  The 
  measurements 
  

   carried 
  out 
  up 
  to 
  the 
  present 
  time 
  with 
  alternating 
  current 
  

   were 
  more 
  or 
  less 
  of 
  a 
  technical 
  character, 
  with 
  the 
  possible 
  

   exception 
  of 
  SteinmetzJ. 
  But 
  with 
  our 
  present 
  improved 
  

   methods 
  these 
  can 
  to-day 
  be 
  carried 
  out 
  more 
  accurately, 
  and 
  

   this 
  has 
  furnished 
  the 
  motive 
  for 
  the 
  following 
  work. 
  AVe 
  

   have 
  endeavoured 
  to 
  find 
  a 
  method 
  of 
  the 
  greatest 
  accuracy. 
  

   It 
  seemed 
  to 
  us 
  that 
  a 
  method 
  should 
  give 
  results 
  of 
  a 
  higher 
  

   degree 
  of 
  accuracy 
  than 
  those 
  carried 
  out 
  up 
  to 
  the 
  present 
  

   (1 
  per 
  cent, 
  to 
  2 
  per 
  cent.), 
  in 
  order 
  to 
  justify 
  theoretical 
  

   deductions. 
  

  

  In 
  the 
  first 
  part 
  of 
  the 
  work, 
  the 
  methods 
  applied 
  for 
  

   obtaining 
  this 
  accuracy 
  are 
  set 
  forth, 
  with 
  the 
  results 
  of 
  the 
  

   direct 
  measurements. 
  In 
  the 
  second 
  part, 
  these 
  figures 
  are 
  

   utilized 
  in 
  examining 
  more 
  closely 
  the 
  theory 
  of 
  the 
  relation 
  

   of 
  spark 
  potentials 
  to 
  the 
  radius 
  of 
  curvature 
  of 
  the 
  electrode, 
  

   as 
  expounded 
  by 
  the 
  leading 
  physicists. 
  

  

  * 
  Communicated 
  by 
  the 
  Authors. 
  Paper 
  presented 
  on 
  the 
  3rd 
  of 
  

   May 
  at 
  the 
  Imperial 
  Academy 
  of 
  Sciencs, 
  at 
  Cracow. 
  

  

  t" 
  J. 
  J. 
  Thomson, 
  * 
  Conduction 
  of 
  Electricity 
  through 
  Gases/ 
  p. 
  366 
  

   (1906). 
  

  

  t 
  C. 
  Steinmetz, 
  Trans, 
  of 
  Amer. 
  Iiidt. 
  of 
  Elec. 
  Eng-. 
  vol. 
  xy. 
  p. 
  281 
  

   (1898). 
  

  

  3 
  A2 
  

  

  