﻿Musical 
  Arc 
  Oscillation 
  in 
  Coupled 
  Circuits. 
  721 
  

  

  The 
  frequency 
  of 
  the 
  difference-tone 
  determined 
  from 
  the 
  

   photographs 
  was 
  438*6. 
  

  

  With 
  regard 
  to 
  the 
  calculated 
  frequency 
  the 
  assumption 
  

  

  7i2= 
  -^Hi 
  in 
  equation 
  (2) 
  leads 
  to 
  no 
  real 
  values 
  of 
  Li 
  in 
  this- 
  

  

  case. 
  The 
  resistances 
  must 
  therefore 
  be 
  taken 
  into 
  account. 
  

   After 
  a 
  number 
  of 
  trials 
  Table 
  II. 
  was 
  drawn 
  up 
  showing 
  the 
  

   values 
  of 
  the 
  two 
  frequencies, 
  calculated 
  from 
  equations 
  (1), 
  

   for 
  various 
  values 
  of 
  the 
  resistance,, 
  Ei, 
  of 
  the 
  primary 
  

   circuit, 
  the 
  self-inductance 
  of 
  the 
  primary 
  circuit 
  being- 
  

   taken 
  as 
  -0049 
  . 
  10^ 
  cm. 
  

  

  Table 
  II. 
  

  

  ohms. 
  

  

  ohms. 
  

  

  ''"' 
  

  

  : 
  

  

  

  

  869-2 
  i 
  

  

  5 
  

  

  14000 
  

  

  873-4 
  1 
  

  

  8 
  

  

  !J 
  

  

  880- 
  1 
  

  

  10 
  

  

  5' 
  

  

  888-7 
  1 
  

  

  20 
  

  

  >J 
  

  

  969-8 
  

  

  n. 
  

  

  1328-3 
  

   1325-7 
  

   1322-5 
  

   1311-9 
  

  

  1-528 
  

   1-517 
  

   1-503 
  

   1-476 
  

  

  1238-1 
  I 
  1-277 
  

  

  459-1 
  

   452-3 
  

   442-4 
  

   423-2 
  

  

  268-3 
  

  

  It 
  is 
  clear, 
  therefore, 
  that 
  if 
  the 
  primary 
  circuit 
  has 
  a 
  

   resistance 
  of 
  slightly 
  over 
  8 
  ohms 
  (z.^. 
  if 
  the 
  resistance 
  of 
  the 
  

   arc 
  is 
  about 
  7 
  ohms), 
  and 
  a 
  self 
  -inductance 
  of 
  the 
  above 
  value, 
  

   the 
  ratio 
  of 
  the 
  two 
  frequencies 
  will 
  be 
  exactly 
  3/2, 
  and 
  their 
  

   difference 
  will 
  agree 
  closely 
  with 
  the 
  observed 
  frequency 
  of 
  

   the 
  deep 
  note. 
  

  

  From 
  the 
  measurements 
  given 
  by 
  Duddell* 
  it 
  appears 
  

   that 
  7 
  ohms 
  is 
  not 
  an 
  impossible 
  value 
  for 
  the 
  resistance 
  of' 
  

   the 
  arc 
  under 
  the 
  circumstances 
  of 
  this 
  experiment. 
  

  

  (4) 
  Conclusions. 
  

  

  From 
  the 
  above 
  results 
  it 
  may 
  be 
  concluded 
  : 
  — 
  

   (1) 
  That 
  the 
  great 
  differences 
  between 
  the 
  observed 
  fre- 
  

   quencies 
  of 
  the 
  electrical 
  oscillations 
  in 
  coupled 
  circuits 
  

   produced 
  bj 
  the 
  musical 
  arc 
  and 
  the 
  values 
  calculated 
  

   from 
  the 
  inductances 
  of 
  the 
  coils 
  and 
  the 
  capacities 
  of 
  

   the 
  condensers, 
  cannot 
  be 
  accounted 
  for 
  merely 
  by 
  

   allowing 
  for 
  the 
  resistances 
  of 
  the 
  circuits. 
  

  

  * 
  \V. 
  Duddelb 
  Pliil. 
  Trans, 
  vol.ccili. 
  (A) 
  pp. 
  323, 
  326 
  (1904). 
  

  

  