﻿Ionization 
  and 
  Wireless 
  Telegraphy 
  . 
  571 
  

  

  or, 
  plotting 
  the 
  relation 
  as 
  a 
  graph, 
  we 
  have 
  the 
  parabola 
  

  

  y 
  = 
  x{a—x) 
  (7 
  a) 
  

  

  shown 
  in 
  fig. 
  2. 
  

  

  Fig. 
  2. 
  — 
  Variation 
  of 
  Frequency 
  with 
  Leakance. 
  

  

  Y 
  

  

  i. 
  e. 
  

  

  Thus 
  y 
  has 
  the 
  maximum 
  value 
  a 
  2 
  / 
  4 
  for 
  a=a/2, 
  

  

  3 
  2 
  has 
  the 
  maximum 
  value 
  R. 
  2 
  /4L 
  2 
  ~> 
  

   forN/S 
  = 
  R/L 
  J 
  

  

  > 
  2 
  — 
  

  

  (3) 
  

  

  (N.B. 
  — 
  This 
  is 
  analogous 
  to 
  the 
  relation 
  K/S 
  = 
  R/L 
  for 
  

   Oliver 
  Heaviside's 
  distortionless 
  telephone 
  circuit.) 
  

  

  Again, 
  

  

  or 
  

  

  y 
  = 
  for 
  cc 
  = 
  a 
  ; 
  

   q=g 
  for 
  N/2S 
  = 
  R/L. 
  

  

  .... 
  (9) 
  

  

  For 
  values 
  of 
  the 
  leakance 
  exceeding 
  this, 
  q 
  is 
  less 
  than 
  q 
  

   and 
  decreases 
  continuously 
  with 
  increase 
  of 
  N, 
  as 
  shown 
  in 
  

   the 
  graph. 
  

  

  Initial 
  Experiments. 
  — 
  In 
  the 
  primary 
  circuit 
  of 
  a 
  Fleming 
  

   cymometer 
  a 
  spark-gap 
  of 
  3 
  mm. 
  was 
  used, 
  and 
  the 
  usual 
  

   rectangle 
  of 
  wire 
  had 
  a 
  second 
  turn 
  added, 
  an 
  air-condenser 
  

   being 
  used 
  for 
  the 
  capacity. 
  The 
  latter 
  consisted 
  of 
  two 
  

   polished 
  tin 
  plates, 
  30*4 
  cm. 
  in 
  diameter 
  and 
  placed 
  1 
  cm. 
  

   apart. 
  Parallel 
  to 
  the 
  above 
  circuit 
  and 
  at 
  a 
  clear 
  distance 
  

   of 
  35 
  cm. 
  was 
  the 
  responding 
  circuit 
  of 
  the 
  Fleming 
  cymo- 
  

   meter 
  (see 
  fig. 
  3, 
  p. 
  572). 
  The 
  long 
  helix 
  serving 
  as 
  a 
  self- 
  

   inductance 
  was 
  disconnected 
  and 
  replaced 
  by 
  a 
  straight 
  wire 
  

   (0*5 
  cm. 
  diameter) 
  of 
  equal 
  length. 
  With 
  the 
  apparatus 
  in 
  

   this 
  more 
  sensitive 
  form 
  a 
  good 
  neon 
  tube 
  was 
  used 
  as 
  

   detector. 
  The 
  air 
  between 
  the 
  plates 
  of 
  the 
  condenser 
  was 
  

  

  