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  713 
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  LXXIII. 
  Musical 
  Arc 
  Oscillation 
  in 
  Coupled 
  Circuits. 
  By 
  

   E. 
  Taylor 
  Jones, 
  D.Sc, 
  Professor 
  of 
  Physics 
  in 
  the 
  

   University 
  College 
  of 
  North 
  Wales, 
  and 
  Morris 
  Owen, 
  

   B.Sc, 
  Isaac 
  Roberts 
  Student 
  of 
  the 
  University 
  College 
  of 
  

   North 
  Wales, 
  Bangor 
  "^^ 
  

  

  [Plate 
  XX.] 
  

  

  IN 
  a 
  recent 
  communication 
  t 
  one 
  of 
  us 
  has 
  shown 
  that 
  if 
  

   the 
  primary 
  of 
  a 
  pair 
  of 
  coupled 
  circuits^ 
  in 
  series 
  with 
  

   a 
  condenser, 
  forms 
  the 
  shunt 
  to 
  a 
  Duddell 
  musical 
  arc 
  ; 
  and 
  

   if 
  the 
  secondary 
  coil 
  is 
  connected 
  to 
  another 
  condenser, 
  

   either 
  of 
  two 
  notes 
  may 
  under 
  certain 
  circumstances 
  be 
  heard. 
  

   It 
  was 
  also 
  shown 
  that 
  the 
  frequencies 
  of 
  the 
  electrical 
  oscil- 
  

   lations 
  in 
  the 
  circuits 
  corresponding 
  to 
  the 
  two 
  notes 
  are 
  

   generally 
  much 
  lower 
  than 
  those 
  calculated 
  for 
  the 
  circuits 
  

   from 
  the 
  inductances 
  of 
  the 
  coils 
  and 
  the 
  capacities 
  of 
  the 
  

   condensers, 
  the 
  resistances 
  being 
  neglected. 
  

  

  In 
  the 
  present 
  paper 
  the 
  influence 
  of 
  the 
  resistances 
  of 
  the 
  

   circuits 
  is 
  considered. 
  It 
  is 
  shown 
  that 
  the 
  difference 
  between 
  

   the 
  observed 
  and 
  and 
  calculated 
  frequencies 
  cannot 
  be 
  mainly 
  

   attributed 
  to 
  the 
  resistances,, 
  and 
  a 
  different 
  explanation 
  is 
  

   suggested. 
  

  

  One 
  of 
  the 
  chief 
  difficulties 
  attending 
  experiments 
  on 
  this 
  

   subject 
  is 
  that 
  of 
  obtaining 
  really 
  simultaneous 
  values 
  of 
  

   the 
  two 
  frequencies. 
  It 
  is 
  of 
  little 
  use 
  to 
  sound 
  the 
  two 
  

   notes 
  one 
  after 
  the 
  other 
  and 
  determine 
  their 
  frequencies. 
  

   The 
  conditions 
  in 
  the 
  arc 
  can 
  change 
  so 
  rapidly 
  that 
  the 
  

   constants 
  of 
  the 
  circuits 
  cannot 
  be 
  regarded 
  as 
  identical 
  on 
  

   two 
  occasions, 
  even 
  if 
  separated 
  by 
  only 
  a 
  short 
  interval 
  of 
  

   time. 
  

  

  A 
  number 
  of 
  cases 
  are 
  considered 
  in 
  the 
  present 
  paper 
  in 
  

   which 
  the 
  two 
  oscillations 
  were 
  recorded 
  simultaneously. 
  

   Tlie 
  method 
  consists 
  usually 
  in 
  arranging 
  matters 
  so 
  that 
  one 
  

   oscillation 
  corresponds 
  to 
  the 
  octave 
  or 
  a 
  higher 
  harmonic 
  of 
  

   the 
  other. 
  Some 
  cases 
  are 
  also 
  considered 
  in 
  which, 
  in 
  

   addition 
  to 
  the 
  two 
  ordinary 
  arc 
  notes, 
  a 
  third 
  note 
  is 
  pro- 
  

   duced 
  ; 
  and 
  the 
  view 
  is 
  put 
  forward 
  that 
  this 
  is 
  a 
  difference-tone 
  

   of 
  the 
  other 
  two, 
  arising, 
  however, 
  from 
  an 
  electrical 
  oscil- 
  

   lation 
  of 
  the 
  same 
  frequency 
  in 
  the 
  circuits. 
  

  

  The 
  oscillations 
  were 
  studied 
  by 
  means 
  of 
  the 
  short-period 
  

   electrometer, 
  or 
  electrostatic 
  oscillograph, 
  described 
  by 
  one 
  

  

  * 
  Communicated 
  by 
  the 
  Authors. 
  

  

  t 
  E. 
  T. 
  Jones, 
  PhiL 
  Mag. 
  p. 
  42, 
  January 
  1909. 
  This 
  paper 
  will 
  be 
  

   referred 
  to 
  as 
  " 
  /. 
  c." 
  

  

  PhiL 
  Mag. 
  S. 
  6. 
  Vol. 
  18. 
  No. 
  107. 
  Nov. 
  1909. 
  3 
  B 
  

  

  