﻿Musical 
  Ai'c 
  Oscillation 
  in 
  Coupled 
  Circuits. 
  719 
  

  

  The 
  curve 
  of 
  secondary 
  potential 
  is 
  shown 
  in 
  Plate 
  XX. 
  

   fig. 
  2. 
  The 
  frequency 
  determined 
  from 
  the 
  photograph 
  is 
  

   285-2. 
  

  

  If 
  we 
  assume 
  7i2 
  = 
  4:ni 
  in 
  equation 
  (2), 
  we 
  find) 
  

  

  Li== 
  -016289 
  . 
  10^ 
  cm., 
  hence 
  ?Zi 
  = 
  285-4. 
  

  

  Case 
  YII. 
  — 
  Using 
  a 
  still 
  larger 
  capacity 
  in 
  the 
  primary 
  

   circuit, 
  Ci 
  = 
  21"32 
  microfarad, 
  and 
  the 
  same 
  secondary 
  con- 
  

   denser, 
  a 
  photograph 
  was 
  obtained 
  showing 
  a 
  prominent 
  fifth 
  

   harmonic. 
  This 
  is 
  shown 
  in 
  Plate 
  XX. 
  fig. 
  3. 
  The 
  observed 
  

   frequency 
  is 
  224*5. 
  

  

  With 
  ?i2 
  = 
  5% 
  equation 
  (2) 
  gives 
  Lj 
  = 
  '023088 
  . 
  10^ 
  cm. 
  

   Hence 
  7^1 
  = 
  226*7. 
  

  

  Case 
  VIII. 
  — 
  With 
  the 
  same 
  capacities 
  as 
  in 
  Case 
  YII. 
  

   and 
  a 
  slightly 
  longer 
  arc, 
  a 
  still 
  deeper 
  note, 
  about 
  a 
  minor 
  

   third 
  below 
  the 
  last, 
  can 
  be 
  recognized 
  as 
  producing 
  resonance. 
  

   We 
  did 
  not 
  succeed 
  in 
  obtaining 
  a 
  photograph 
  of 
  the 
  curve 
  

   for 
  this 
  case. 
  If^ 
  however, 
  the 
  relation 
  ?^2 
  = 
  6;^l 
  is 
  inserted 
  in 
  

   equation 
  (2), 
  we 
  find 
  Li 
  = 
  '03361 
  . 
  10^ 
  cm., 
  giving 
  «i 
  = 
  188, 
  

   which 
  is 
  very 
  nearlv 
  a 
  minor 
  third 
  below 
  the 
  note 
  of 
  

   Case 
  VIL 
  

  

  (3) 
  ^* 
  Difference 
  Tones 
  " 
  produced 
  in 
  Coupled 
  Circuits 
  

   by 
  the 
  Musical 
  Arc. 
  

  

  Case 
  IX. 
  — 
  It 
  was 
  pointed 
  out 
  in 
  the 
  previous 
  paper 
  * 
  

   that 
  if 
  a 
  certain 
  relation 
  exists 
  between 
  the 
  primary 
  and 
  

   secondary 
  capacities 
  the 
  two 
  notes 
  of 
  the 
  arc 
  are 
  equallv 
  

   stable. 
  This 
  is 
  the 
  case 
  with 
  Ci 
  = 
  16-98, 
  C2 
  = 
  -001098 
  micro- 
  

   farad, 
  and 
  the 
  two 
  notes 
  are 
  separated 
  by 
  an 
  interval 
  of 
  about 
  

   a 
  fifth. 
  If, 
  with 
  these 
  two 
  condensers, 
  the 
  lower 
  note 
  is 
  

   sounding 
  and 
  the 
  arc-length 
  is 
  gradually 
  diminished 
  (the 
  

   pitch 
  gradually 
  rising), 
  at 
  a 
  certain 
  stage 
  the 
  note 
  suddenly 
  

   drops 
  by 
  an 
  octave. 
  This 
  deep 
  note 
  is 
  fairly 
  rich 
  in 
  quality, 
  

   and 
  it 
  differs 
  from 
  the 
  ordinary 
  arc 
  notes 
  in- 
  that 
  it 
  is 
  perfectly 
  

   definite 
  in 
  pitch. 
  Any 
  alteration 
  in 
  the 
  arc-length 
  made 
  

   when 
  the 
  deep 
  note 
  is 
  sounding 
  either 
  causes 
  the 
  sound 
  to 
  

   stop 
  altogether, 
  or 
  changes 
  it 
  into 
  one 
  of 
  the 
  two 
  primary 
  

   notes. 
  The 
  deep 
  note 
  was 
  not 
  very 
  staWe 
  in 
  this 
  case, 
  and 
  

   several 
  exposures 
  had 
  to 
  be 
  made 
  before 
  a 
  photograph 
  was 
  

   obtained 
  showing 
  the 
  curve 
  of 
  secondary 
  potential 
  while 
  this 
  

   note 
  was 
  sounding. 
  The 
  photograph 
  is 
  shown 
  in 
  Plate 
  XX. 
  

   fig. 
  4. 
  The 
  photograph 
  in 
  fig. 
  5 
  happened 
  to 
  be 
  taken 
  just 
  

   as 
  the 
  note 
  was 
  changing 
  from 
  the 
  Jower 
  primary 
  into 
  the 
  

   deep 
  note 
  an 
  octave 
  below, 
  and 
  covers 
  the 
  whole 
  period 
  of 
  

  

  * 
  Z. 
  c. 
  p. 
  41. 
  

  

  