﻿Musical 
  Arc 
  Oscillation 
  in 
  Coupled 
  Circuits 
  » 
  111 
  

  

  oscillations 
  are 
  easily 
  stopped 
  by 
  " 
  brushing 
  '' 
  or 
  sparking 
  at 
  

   the 
  terminals 
  of 
  the 
  secondary 
  circuit. 
  

  

  Further, 
  in 
  arriving 
  at 
  the 
  above 
  calculated 
  values 
  the 
  

   resistances 
  of 
  the 
  circuits 
  are 
  not 
  taken 
  into 
  account. 
  These 
  

   considerations 
  are 
  probably 
  sufficient 
  to 
  account 
  for 
  the 
  small 
  

   difference 
  between 
  the 
  observed 
  and 
  calculated 
  values 
  of 
  the 
  

   frequency, 
  while 
  the 
  close 
  agreement 
  between 
  these 
  values 
  

   gives 
  support 
  to 
  the 
  views 
  that 
  during 
  these 
  oscillations 
  the 
  

   arc 
  may 
  be 
  regarded 
  as 
  having 
  a 
  constant 
  self-inductance, 
  

   and 
  that 
  when 
  the 
  two 
  frequencies 
  of 
  the 
  system 
  are 
  nearly 
  

   an 
  octave 
  apart, 
  and 
  when 
  the 
  lower 
  note 
  is 
  sounding, 
  the 
  

   octave 
  of 
  this 
  note 
  produces 
  forced 
  oscillations 
  of 
  great 
  

   amplitude 
  in 
  the 
  system. 
  

  

  Case 
  II. 
  — 
  This 
  case 
  is 
  similar 
  to 
  the 
  last. 
  • 
  The 
  coils 
  were 
  

   the 
  same, 
  and 
  the 
  capacities 
  were 
  Ci 
  = 
  11*63, 
  C2 
  = 
  *00U3911 
  

   microfarad. 
  The 
  lower 
  note 
  only* 
  was 
  heard, 
  and 
  at 
  a 
  

   certain 
  length 
  of 
  the 
  arc 
  the 
  octave 
  resonance 
  occurs. 
  Several 
  

   photographs 
  were 
  taken 
  of 
  the 
  curve 
  of 
  secondary 
  potential, 
  

   but 
  in 
  none 
  of 
  them 
  was 
  the 
  amplitude 
  quite 
  at 
  its 
  maximum. 
  

   Two 
  curves 
  showing 
  the 
  intensified 
  octave 
  were 
  measured, 
  

   the 
  observed 
  frequencies 
  being 
  490 
  and 
  546. 
  

  

  Assuming 
  as 
  before 
  that 
  n^ 
  = 
  2ni 
  the 
  values 
  of 
  Lj 
  deduced 
  

   from 
  (2) 
  are 
  -0019362 
  . 
  10^ 
  and 
  '0080879 
  . 
  10^ 
  cm., 
  the 
  former 
  

   of 
  which 
  is 
  inadmissible. 
  Taking, 
  therefore 
  L^ 
  = 
  '0080879 
  . 
  10^ 
  

   (2) 
  gives 
  fbr?Zi 
  the 
  value 
  510" 
  5, 
  which 
  does 
  not 
  differ 
  greatly 
  

   from 
  either 
  of 
  the 
  observed 
  values. 
  

  

  Case 
  III. 
  — 
  Another 
  example 
  of 
  the 
  same 
  kind 
  is 
  given 
  by 
  

   Ci 
  = 
  16'98,C2 
  = 
  '0004771 
  microfarad. 
  Several 
  photographs 
  

   were 
  taken 
  showing 
  the 
  intensified 
  octave, 
  and 
  the 
  curve 
  

   having 
  the 
  greatest 
  amplitude 
  was 
  found 
  to 
  have 
  a 
  frequency 
  

   of 
  452-9. 
  

  

  With 
  ??2 
  = 
  2?ii, 
  equation 
  (2) 
  gives 
  Li 
  = 
  -006471 
  . 
  10^ 
  and 
  

   7?i 
  = 
  469-9. 
  

  

  The 
  difference 
  between 
  the 
  observed 
  and 
  calculated 
  values 
  

   is 
  here 
  again 
  probably 
  within 
  the 
  limits 
  of 
  error 
  explained 
  

   under 
  Case 
  I. 
  

  

  Case 
  IV. 
  — 
  This 
  case 
  differs 
  in 
  one 
  respect 
  from 
  the 
  otliers. 
  

   The 
  capacities 
  were 
  Oi= 
  14-62, 
  Cg 
  = 
  '0002898 
  microfarad. 
  

   If 
  the 
  condition 
  Qi^ 
  = 
  2ni 
  is 
  inserted 
  in 
  (2). 
  the 
  two 
  values 
  of 
  

   Li 
  obtained 
  are 
  less 
  than 
  the 
  self-inductance 
  of 
  the 
  primary 
  

   coil, 
  and 
  are 
  therefore 
  inadmissible. 
  For 
  all 
  possible 
  values 
  

   of 
  Li 
  n2 
  is 
  greater 
  than 
  2ni. 
  

  

  The 
  question 
  therefore 
  arises 
  whether 
  the 
  octave 
  relation 
  

   may 
  not 
  be 
  satisfied 
  by 
  the 
  two 
  frequencies 
  if 
  the 
  resistances 
  

   of 
  the 
  circuits 
  are 
  taken 
  into 
  account. 
  A 
  few 
  trials 
  showed 
  

   f 
  * 
  Cf. 
  I. 
  c. 
  p. 
  41. 
  

  

  