﻿Musical 
  Arc 
  Oscillation 
  in 
  Coupled 
  Circuits. 
  715 
  

  

  primary 
  circuit. 
  In 
  these 
  calculations 
  the 
  following 
  formulae, 
  

   given 
  by 
  Drude 
  *, 
  were 
  employed 
  : 
  — 
  

  

  2/3(T2-T'0= 
  -(^i-^2)(Ti^-T2^), 
  

   (T2-T'2)2^8)S2(T2+T'2) 
  = 
  (Ti2-T/)2 
  

   - 
  2(Ti2 
  + 
  T/)(^i 
  - 
  e,f 
  + 
  4M2C1C2, 
  

  

  (1) 
  

  

  where 
  

  

  ^1= 
  2^1^17 
  

   1 
  

  

  27r7ii' 
  

  

  T 
  = 
  

  

  1 
  

  

  :LiCi, 
  

   :L2C2, 
  

  

  27r«2 
  

  

  and 
  y8 
  is 
  a 
  constant 
  which 
  vanishes 
  when 
  the 
  resistances'^ 
  of 
  

   the 
  circuits 
  are 
  neglected. 
  

  

  The 
  elimination 
  of 
  T 
  and 
  T^ 
  between 
  these 
  equations 
  leads 
  

   to 
  a 
  cubic 
  for 
  B^. 
  In 
  each 
  of 
  the 
  cases 
  examined 
  the 
  cubic 
  

   had 
  only 
  one 
  positive 
  root 
  (giving 
  real 
  values 
  for 
  /8), 
  and 
  /6^ 
  

   being 
  thus 
  determined 
  the 
  above 
  equations 
  allow 
  T 
  and 
  ,T', 
  

   and 
  hence 
  the 
  frequencies 
  % 
  and 
  n^, 
  to 
  be 
  calculated. 
  

  

  Table 
  I. 
  contains 
  the 
  values 
  of 
  /3^, 
  Wi, 
  and 
  ^2, 
  calculated 
  in 
  

   this 
  way 
  for 
  various 
  values 
  of 
  Ri, 
  the 
  other 
  constants 
  having 
  

   the 
  values 
  given 
  above, 
  and 
  L^ 
  being 
  taken 
  as 
  the 
  self- 
  

   inductance 
  of 
  the 
  primary 
  coiL 
  

  

  Table 
  I. 
  

  

  El 
  in 
  ohms. 
  (P 
  . 
  W. 
  

  

  n^. 
  

  

  1 
  

  

  1 
  : 
  

  

  0005 
  

  

  721-8 
  

  

  1309 
  

  

  3 
  

  

  •002112 
  

  

  725-1 
  

  

  1300-5 
  

  

  5 
  1 
  

  

  0066H9 
  

  

  729 
  

  

  1296-7 
  

  

  ! 
  10 
  i 
  

  

  02964 
  

  

  747-5 
  

  

  1285-4 
  

  

  15 
  ! 
  

  

  071804 
  

  

  781-8 
  

  

  1264-9 
  

  

  32-995 
  

  

  472159 
  

  

  1187-8 
  

  

  1187-8 
  

  

  1 
  38 
  

  

  665507 
  

  

  1643-6 
  

  

  1178-1 
  

  

  40 
  \ 
  

  

  750912 
  

  

  2113-5 
  

  

  1173-6 
  

  

  41 
  

  

  795478 
  

  

  2596-6 
  

  

  1172-2 
  

  

  50 
  1 
  

  

  250994 
  

  

  Imaginary 
  

  

  1163-2 
  

  

  * 
  Drude, 
  Ann. 
  der 
  Fhysik, 
  xiii. 
  p. 
  534 
  (1904), 
  

  

  3B2 
  

  

  