﻿Distribution 
  of 
  Energy 
  in 
  the 
  Spectra 
  of 
  Gases. 
  811 
  

  

  second. 
  This 
  latter 
  number 
  is, 
  unfortunately, 
  not 
  fixed 
  and 
  

   definite. 
  

  

  The 
  appearance 
  of 
  the 
  image 
  in 
  the 
  rotating 
  mirror 
  is 
  

   shown 
  in 
  fig. 
  6 
  (PI. 
  XIII.) 
  for 
  three 
  cases. 
  

  

  In 
  the 
  first 
  there 
  was 
  no 
  condenser 
  in 
  parallel 
  with 
  the 
  

   discharge-tube, 
  and 
  we 
  have 
  the 
  sine-curve 
  characteristic 
  of 
  

   the 
  alternator. 
  The 
  second 
  case 
  is 
  that 
  of 
  a 
  condensed 
  dis- 
  

   charge 
  at 
  higher 
  pressure, 
  but 
  without 
  a 
  spark-gap 
  in 
  series 
  

   with 
  the 
  tube. 
  It 
  is 
  to 
  be 
  noticed 
  that 
  the 
  current, 
  during 
  

   the 
  early 
  part 
  of 
  each 
  cycle, 
  is 
  running 
  into 
  the 
  condenser 
  

   and 
  not 
  through 
  the 
  discharge-tube. 
  

  

  When 
  a 
  certain 
  potential 
  is 
  reached 
  the 
  condenser 
  empties 
  

   itself 
  through 
  the 
  discharge-tube 
  and 
  gives 
  rise 
  to 
  a 
  very 
  

   high 
  peak 
  in 
  the 
  curve. 
  The 
  finite 
  width 
  of 
  this 
  part 
  of 
  the 
  

   curve 
  results 
  only 
  from 
  the 
  finite 
  width 
  of 
  the 
  glow 
  on 
  the 
  

   electrodes 
  in 
  the 
  measuring-tube, 
  and 
  does 
  not 
  mean 
  that 
  

   the 
  condenser 
  current 
  lasts 
  for 
  a 
  time 
  comparable 
  with 
  the 
  

   alternating 
  current. 
  The 
  condenser 
  discharges 
  itself 
  but 
  

   once 
  in 
  each 
  cycle, 
  and 
  the 
  rest 
  of 
  the 
  curve 
  is 
  therefore 
  

   similar 
  to 
  the 
  curve 
  obtained 
  in 
  the 
  absence 
  of 
  a 
  condenser. 
  

   Another 
  point 
  to 
  be 
  noticed 
  is 
  that 
  only 
  during 
  the 
  instant 
  

   when 
  the 
  condenser 
  is 
  discharging 
  itself 
  is 
  the 
  space 
  between 
  

   the 
  electrodes 
  of 
  the 
  measuring 
  tube 
  luminous. 
  

  

  The 
  third 
  figure 
  shows 
  the 
  appearance 
  in 
  the 
  rotating 
  

   mirror 
  when 
  a 
  spark-gap 
  is 
  introduced 
  in 
  series 
  with 
  the 
  

   two 
  tubes. 
  

  

  Fig. 
  7 
  (PL 
  XIII.) 
  is 
  a 
  diagram 
  of 
  the 
  arrangement 
  in 
  this 
  case. 
  

  

  The 
  current 
  is 
  now 
  only 
  able 
  to 
  pass 
  when 
  the 
  potential 
  

   difference 
  between 
  the 
  spark-balls 
  S 
  exceeds 
  a 
  certain 
  

   value. 
  

  

  The 
  course 
  of 
  a 
  cycle 
  is 
  probably 
  something 
  as 
  follows 
  : 
  — 
  

  

  The 
  potential 
  difference 
  between 
  the 
  ends 
  of 
  the 
  trans- 
  

   former, 
  and 
  therefore 
  between 
  the 
  plates 
  of 
  the 
  condenser, 
  

   rises 
  uniformly 
  at 
  the 
  beginning 
  of 
  the 
  cycle, 
  and 
  when 
  a 
  

   certain 
  potential 
  difference 
  exists 
  the 
  spark-gap 
  S 
  is 
  broken 
  

   down 
  and 
  a 
  large 
  current 
  flows 
  through 
  the 
  tubes, 
  being 
  

   indicated 
  in 
  the 
  mirror 
  by 
  a 
  peak 
  in 
  the 
  image. 
  

  

  Now, 
  the 
  potential 
  difference 
  between 
  the 
  plates 
  of 
  the 
  

   condenser 
  is 
  given 
  by 
  

  

  E-R.z, 
  

   where 
  E 
  = 
  voltage 
  of 
  transformer 
  [i.e. 
  -^— 
  ) 
  at 
  the 
  particular 
  

  

  instant, 
  R= 
  resistance 
  of 
  transformer 
  (secondary 
  coil), 
  and 
  

   i 
  = 
  current 
  passing. 
  

  

  Hence, 
  as 
  soon 
  as 
  "/"" 
  increases 
  to 
  a 
  large 
  value, 
  the 
  

  

  