﻿720 
  Prof. 
  E. 
  Taylor 
  Jones 
  and 
  Mr. 
  Morris 
  Owen 
  on 
  

  

  this 
  change. 
  The 
  photograDhs 
  show 
  that 
  the 
  deep 
  note 
  corre- 
  

   sponds 
  to 
  an 
  electrical 
  oscillation 
  o£ 
  the 
  same 
  frequency 
  in 
  

   the 
  circuits, 
  and 
  is 
  not 
  merely 
  produced 
  in 
  the 
  air, 
  or 
  in 
  the 
  

   ear, 
  as 
  is 
  sometimes 
  the 
  case 
  wlien 
  the 
  difference-tone 
  of 
  two 
  

   musical 
  notes 
  sounding 
  simultaneously 
  is 
  heard. 
  

  

  The 
  deep 
  note 
  appears 
  to 
  be 
  the 
  difference-tone 
  of 
  the 
  two 
  

   primary 
  notes, 
  and 
  is 
  due 
  to 
  an 
  electrical 
  oscillation 
  in 
  the 
  

   system 
  which 
  is 
  only 
  produced 
  when 
  the 
  two 
  primaries 
  are 
  

   equally 
  stable 
  and 
  (in 
  the 
  present 
  case) 
  when 
  the 
  ratio 
  of 
  

   their 
  frequencies 
  is 
  exactly 
  3/2. 
  

  

  3 
  . 
  . 
  

  

  If 
  we 
  assume 
  7?2= 
  j.ni 
  in 
  equation 
  (2) 
  we 
  obtain 
  the 
  two 
  

  

  values 
  -004633 
  . 
  10^ 
  and 
  '007586 
  . 
  10^ 
  for 
  L,. 
  Taking 
  the 
  

   smaller 
  value 
  (since 
  the 
  arc 
  was 
  very 
  short 
  when 
  the 
  differ- 
  

   ence-tone 
  was 
  sounding), 
  and 
  substituting 
  in 
  (2) 
  we 
  find 
  

   7^l=484:•73, 
  ^2= 
  727-09. 
  Hence 
  922-^11 
  = 
  242-36. 
  

  

  The 
  frequency 
  of 
  the 
  difference-tone 
  measured 
  from 
  the 
  

   photograph 
  was 
  237*5. 
  The 
  observed 
  frequency 
  of 
  the 
  deep 
  

   note 
  therefore 
  agrees 
  closely 
  with 
  the 
  difference 
  of 
  tha 
  

   frequencies 
  of 
  the 
  two 
  primes 
  calculated 
  on 
  the 
  assumption 
  

   that 
  the 
  interval 
  between 
  them 
  is 
  a 
  perfect 
  fifth. 
  

  

  Case 
  X.-^Ci 
  = 
  14-62, 
  C3 
  = 
  -0008722 
  microfarad. 
  In 
  this 
  

  

  case 
  also 
  the 
  two 
  primary 
  notes 
  are 
  equally 
  stable, 
  and 
  the 
  

  

  deep 
  note, 
  an 
  octave 
  below 
  the 
  lower 
  primary, 
  is 
  produced 
  at 
  

  

  a 
  certain 
  arc-length. 
  

  

  3 
  

   Assuming 
  as 
  before 
  n2 
  = 
  ^ 
  ^i 
  in 
  (2), 
  the 
  values 
  '004734 
  . 
  10^ 
  

  

  and 
  -006540 
  . 
  10^ 
  cm. 
  are 
  obtained 
  for 
  Lj. 
  Taking 
  the 
  

   former 
  value 
  as 
  being 
  more 
  appropriate 
  for 
  a 
  short 
  arc 
  and 
  

   inserting 
  it 
  in 
  (2), 
  we 
  find 
  % 
  = 
  529-7, 
  713 
  = 
  794*5. 
  Hence 
  

   ^2-% 
  = 
  264*8. 
  

  

  This 
  agrees 
  closely 
  with 
  the 
  frequency 
  of 
  the 
  deep 
  note 
  

   determined 
  from 
  the 
  photograph, 
  w^hich 
  was 
  263*8. 
  

  

  Case 
  XL— 
  Ci 
  = 
  5'64, 
  C2 
  = 
  -0002886 
  microfarad. 
  In 
  this 
  

   case 
  the 
  difference-tone 
  was 
  exceptionally 
  stable 
  and 
  powerful, 
  

   quite 
  as 
  loud, 
  in 
  fact, 
  as 
  either 
  of 
  the 
  tw^o 
  primary 
  notes, 
  and 
  

   more 
  easily 
  produced 
  and 
  maintained 
  than 
  in 
  the 
  two 
  previous 
  

   cases. 
  The 
  lower 
  primary 
  note 
  was 
  often 
  heard 
  simultaneously 
  

   with 
  the 
  difference-tone, 
  but 
  we 
  are 
  not 
  sure 
  that 
  the 
  upper 
  

   primary 
  could 
  be 
  distinguished 
  when 
  the 
  latter 
  was 
  sounding. 
  

   The 
  length 
  of 
  the 
  arc 
  when 
  the 
  difference-tone 
  was 
  sounding- 
  

   was 
  about 
  0'75 
  mm., 
  the 
  current 
  in 
  the 
  arc 
  generally 
  about 
  

   2*5 
  amperes. 
  Several 
  photopraphs 
  were 
  taken 
  with 
  the 
  

   difference-tone 
  sounding. 
  These 
  (as 
  well 
  as 
  those 
  of 
  Case 
  X.) 
  

   are 
  very 
  similar 
  in 
  character 
  to 
  the 
  curve 
  shown 
  in 
  Plate 
  XX. 
  

   fig. 
  4, 
  and 
  are 
  not 
  reproduced 
  here. 
  

  

  