﻿on 
  Electric 
  Waves 
  in 
  Short 
  Wire 
  Systems. 
  593 
  

  

  Calling 
  that 
  part 
  o£ 
  the 
  wire 
  system 
  near 
  the 
  condenser 
  

   the 
  primary, 
  and 
  the 
  part 
  remote 
  the 
  secondary 
  circuit, 
  in 
  

   the 
  case 
  shown 
  in 
  fig. 
  3 
  the 
  corrected 
  length 
  of 
  the 
  primary 
  

   circuit 
  is 
  25*92 
  m., 
  that 
  of 
  the 
  secondary 
  being 
  5*18 
  m. 
  

   The 
  ratio 
  of 
  the 
  lengths 
  of 
  the 
  primary 
  and 
  secondary 
  circuits 
  

   being 
  5/1, 
  it 
  is 
  necessary 
  for 
  complete 
  resonance 
  between 
  

   them 
  that 
  there 
  should 
  be 
  five 
  nodes 
  in 
  the 
  primary 
  circuit, 
  

   or 
  any 
  odd 
  multiple 
  of 
  this 
  number. 
  As 
  the 
  condenser-plates 
  

   are 
  separated 
  the 
  amplitude 
  of 
  the 
  vibration 
  in 
  the 
  secondary 
  

   circuit, 
  as 
  shown 
  by 
  the 
  deflexions, 
  increases 
  as 
  the 
  period 
  of 
  

   the 
  condenser 
  oscillation 
  approaches 
  more 
  nearly 
  that 
  of 
  the 
  

   free 
  period 
  of 
  some 
  mode 
  of 
  vibration 
  of 
  the 
  primary 
  circuit. 
  

   From 
  the 
  figure, 
  it 
  appears 
  that 
  there 
  is 
  complete 
  resonance 
  

   between 
  the 
  condenser 
  and 
  primary 
  circuits 
  when 
  the 
  con- 
  

   denser-plates 
  are 
  separated 
  by 
  1'33 
  cms. 
  At 
  this 
  point 
  the 
  

   calculated 
  wave-length 
  in 
  air 
  of 
  the 
  condenser 
  radiation 
  is 
  

   11*0 
  in., 
  while 
  if 
  it 
  is 
  considered 
  that 
  the 
  length 
  of 
  the 
  pri- 
  

  

  5 
  

   mary 
  circuit 
  is 
  ~-, 
  X 
  comes 
  out 
  10*4 
  m. 
  The 
  calculated 
  

  

  values 
  may 
  therefore 
  be 
  considered 
  about 
  5 
  per 
  cent, 
  too 
  

   high. 
  

  

  As 
  the 
  condenser-plates 
  are 
  further 
  separated 
  the 
  deflexion 
  

   rapidly 
  decreases. 
  A 
  secoud 
  maximum 
  occurs 
  when 
  the 
  

   wave-length 
  of 
  the 
  condenser 
  radiation 
  is 
  equal 
  to 
  2/7 
  of 
  the 
  

   length 
  of 
  the 
  primary 
  circuit 
  ; 
  a 
  condition 
  which 
  could 
  not 
  be 
  

   quite 
  reached 
  with 
  the 
  present 
  apparatus. 
  The 
  second 
  maxi- 
  

   mum 
  is 
  shown 
  in 
  the 
  figure 
  by 
  the 
  dotted 
  line. 
  It 
  is 
  less 
  

   than 
  the 
  first 
  one, 
  for 
  although 
  at 
  this 
  point 
  there 
  is 
  complete 
  

   resonance 
  between 
  the 
  condenser 
  and 
  primary 
  circuits, 
  the 
  

   conditions 
  are 
  not 
  right 
  for 
  complete 
  resonance 
  between 
  

   the 
  primary 
  and 
  secondary 
  circuits, 
  there 
  being 
  7 
  nodes 
  in 
  the 
  

   primary 
  circuit, 
  the 
  ratio 
  of 
  the 
  lengths 
  of 
  the 
  two 
  circuits 
  

   being 
  as 
  before 
  5/1. 
  

  

  In 
  general, 
  when 
  the 
  bridge 
  is 
  in 
  a 
  fixed 
  position 
  the 
  

   amplitude 
  of 
  the 
  vibration 
  in 
  the 
  secondary 
  circuit 
  will 
  de- 
  

   pend 
  on 
  that 
  in 
  the 
  primary 
  circuit. 
  Let 
  the 
  ratio 
  of 
  the 
  

   lengths 
  of 
  the 
  tw 
  T 
  o 
  circuits 
  be 
  m/n, 
  m 
  and 
  n 
  being 
  small 
  odd 
  

   numbers. 
  If 
  P 
  is 
  the 
  length 
  of 
  the 
  primary 
  circuit 
  and 
  X 
  

   the 
  wave-length 
  of 
  the 
  condenser 
  radiation, 
  the 
  amplitude 
  of 
  

   the 
  vibration 
  in 
  the 
  primary 
  circuit 
  will 
  be 
  a 
  maximum 
  when 
  

  

  where 
  h 
  is 
  an 
  integer. 
  So 
  the 
  amplitude 
  of 
  the 
  vibration 
  in 
  

   the 
  secondary 
  circuit 
  (directly 
  measured 
  by 
  the 
  detector 
  de- 
  

   flexions) 
  will 
  be 
  a 
  maximum 
  as 
  the 
  condenser 
  capacity 
  is 
  

  

  