﻿64 
  L. 
  Dc 
  For 
  est 
  — 
  Reflection 
  of 
  Hertzian 
  Waves 
  

  

  Letting 
  7it 
  = 
  — 
  , 
  

  

  3 
  (l 
  +^S>)c^-<^' 
  g 
  

   n(<^~<^')sin^= 
  ^--^_ 
  cos-', 
  where 
  <^'=^><^(5) 
  

  

  We 
  find 
  that 
  the 
  angle 
  of 
  phase 
  difference 
  may 
  be 
  considered 
  

   as 
  in 
  the 
  second 
  quadrant, 
  the 
  cosines 
  having 
  negative 
  signs. 
  

   So 
  here 
  if 
  we 
  write 
  the 
  cosine 
  of 
  eq. 
  (4) 
  = 
  — 
  cos. 
  of 
  (5), 
  and 
  at 
  

   same 
  time 
  make 
  tlie 
  coefiicient 
  of 
  reflection 
  h 
  of 
  (4) 
  equal 
  — 
  h 
  

   of 
  (5), 
  we 
  can 
  solve 
  between 
  the 
  two 
  equations. 
  

   Hence 
  

  

  Where 
  K 
  = 
  

  

  __ 
  -2L?;S^nK 
  __ 
  . 
  2KyX 
  

   tan 
  6^ 
  _ 
  Y-JU^^^^^Kf 
  " 
  K'J^^^ 
  

  

  (6) 
  

  

  l4-5 
  + 
  '^SJ.v 
  

  

  7 
  

  

  From 
  (6) 
  we 
  get^ 
  

  

  S 
  

  

  _ 
  s 
  / 
  cosa, 
  + 
  i 
  \ 
  

  

  From 
  this 
  equation 
  the 
  capacity 
  of 
  the 
  terminal 
  arrange- 
  

   ment 
  can 
  be 
  calculated 
  from 
  the 
  observed 
  values 
  of 
  Sj 
  and 
  the 
  

   wave 
  length 
  \ 
  used. 
  

  

  For 
  X 
  large 
  compared 
  to 
  7 
  (as 
  was 
  the 
  case 
  for 
  the 
  wave- 
  

   lengths 
  used) 
  K 
  is 
  nearly 
  unity 
  for 
  ^ 
  = 
  1, 
  and 
  for 
  h 
  as 
  small 
  as 
  

  

  17 
  

   0*7, 
  K=— 
  only. 
  K 
  is 
  taken 
  as 
  unity 
  throughout. 
  

  

  The 
  value 
  of 
  S 
  = 
  — 
  calculated 
  for 
  the 
  parallel 
  wires 
  is 
  '067 
  

  

  Ju 
  

  

  C. 
  G. 
  S. 
  units. 
  For 
  these 
  wires 
  and 
  frequencies 
  any 
  correc- 
  

   tion 
  terms 
  for 
  S 
  or 
  L, 
  as 
  by 
  Rayleigh's 
  or 
  Heaviside's 
  formulae, 
  

   are 
  absolutely 
  negligible, 
  although 
  the 
  resistances 
  for 
  these 
  

   oscillations 
  are 
  not 
  at 
  all 
  the 
  same 
  as 
  for 
  steady 
  currents. 
  

  

  Formula 
  (7) 
  was 
  applied 
  to 
  the 
  determination 
  of 
  end 
  capaci- 
  

   ties 
  for 
  the 
  wire 
  ends 
  bare, 
  and 
  again 
  carrying 
  two 
  brass 
  balls, 
  

   and 
  under 
  varying 
  conditions, 
  for 
  wave-lengths 
  ranging 
  from 
  

   60 
  to 
  170 
  centimeters. 
  

  

  The 
  indicator 
  tube 
  was 
  placed 
  across 
  the 
  wires, 
  generally 
  in 
  

   the 
  second 
  loop 
  from 
  the 
  ends, 
  sometimes 
  in 
  the 
  last 
  (one- 
  

   quarter 
  wave-length). 
  In 
  the 
  latter 
  position 
  8^^°" 
  were 
  allowed 
  

   for 
  its 
  presence. 
  No 
  bridge 
  could 
  be 
  placed 
  between 
  the 
  tube 
  

   and 
  the 
  ends 
  in 
  either 
  case, 
  because 
  it 
  was 
  found 
  that 
  the 
  oscil- 
  

   lation 
  of 
  any 
  '' 
  system 
  " 
  between 
  two 
  successive 
  bridges, 
  was 
  

   not 
  perceptibly 
  affected 
  by 
  the 
  resonance 
  or 
  non-resonance 
  of 
  

  

  