﻿716 
  Prof. 
  E. 
  Taylor 
  Jones 
  and 
  Mr. 
  Morris 
  Owen 
  on 
  

  

  From 
  the 
  last 
  two 
  columns 
  it 
  will 
  be 
  seen 
  thai 
  as 
  the 
  value 
  

   o£ 
  Ri 
  is 
  increased 
  the 
  frequency 
  of 
  the 
  slower 
  oscillation 
  

   increases^ 
  and 
  that 
  the 
  ratio 
  of 
  the 
  two 
  frequencies 
  at 
  first 
  

   deviates 
  more 
  and 
  more 
  from 
  the 
  octave 
  relation. 
  

  

  It 
  is 
  clear, 
  therefore, 
  that 
  the 
  observed 
  frequency 
  613 
  of 
  

   the 
  musical 
  arc 
  note 
  and 
  the 
  intensification 
  of 
  the 
  octave 
  

   of 
  this 
  note 
  cannot 
  be 
  accounted 
  for 
  by 
  merely 
  assuming 
  that 
  

   the 
  arc 
  has 
  any 
  constant 
  resistance 
  during 
  the 
  oscillations 
  

   and 
  including 
  this 
  in 
  our 
  calculations. 
  

  

  It 
  seems 
  desirable 
  to 
  examine 
  next 
  the 
  hypothesis 
  that 
  the 
  

   arc 
  behaves 
  as 
  if 
  it 
  had 
  self-inductance. 
  This 
  supposition 
  is 
  

   not 
  a 
  new 
  one. 
  It 
  has 
  been 
  employed 
  * 
  to 
  account 
  for 
  the 
  

   well-known 
  fact 
  that 
  the 
  alternate-current 
  arc 
  has 
  a 
  power- 
  

   factor 
  different 
  from 
  unity. 
  It 
  has 
  also 
  been 
  pointed 
  out 
  by 
  

   M. 
  La 
  Rosa 
  f 
  that 
  oscillations 
  may 
  be 
  produced 
  by 
  the 
  musical 
  

   arc 
  even 
  when 
  the 
  shunt 
  circuit 
  connected 
  to 
  it 
  has 
  no 
  natural 
  

   period 
  of 
  oscillation. 
  Very 
  intense 
  high 
  notes 
  may 
  in 
  fact 
  

   be 
  produced 
  by 
  connecting 
  the 
  carbons 
  to 
  a 
  paraffin-paper 
  

   condenser 
  by 
  well-twisted 
  insulated 
  wires, 
  no 
  coil 
  being 
  

   included 
  in 
  the 
  circuit. 
  

  

  Assuming, 
  therefore, 
  that 
  the 
  arc 
  has 
  self-inductance 
  which 
  

   is 
  to 
  be 
  added 
  to 
  that 
  of 
  the 
  circuit 
  connected 
  to 
  it, 
  the 
  

   problem 
  in 
  the 
  present 
  case 
  is 
  to 
  find 
  what 
  value 
  of 
  Li 
  will 
  

   make 
  the 
  frequency 
  of 
  one 
  oscillation 
  of 
  the 
  system 
  twice 
  

   that 
  of 
  the 
  other. 
  Neglecting 
  the 
  resistances 
  of 
  the 
  circuits, 
  

   the 
  frequencies 
  of 
  the 
  system 
  are 
  given 
  by 
  Oberbeck's 
  

   formula 
  

  

  ^'^'''^= 
  '^_w_ 
  [Mh 
  "*" 
  l;c2 
  -V 
  i 
  (la 
  '"" 
  ^y 
  "^ 
  lTlTca 
  i 
  J 
  

  

  L1L2 
  

  

  Substituting 
  the 
  above 
  values 
  of 
  L2, 
  Ci, 
  C2, 
  M, 
  and 
  putting 
  

   ?^.■, 
  = 
  2/^l, 
  we 
  have 
  a 
  quadratic 
  equation 
  for 
  L^, 
  the 
  roots 
  of 
  

   which 
  are 
  '00381 
  1.10^ 
  and 
  '0066795.109. 
  The 
  former 
  

   value 
  is 
  less 
  than 
  the 
  self-inductance 
  of 
  the 
  primary 
  coil 
  

   ('004619 
  . 
  109), 
  and 
  is 
  therefore 
  discarded. 
  Takings 
  therefore, 
  

   Li 
  = 
  '0066795. 
  10^ 
  cm., 
  and 
  substituting 
  in 
  (2) 
  we 
  find 
  for 
  

   the 
  frequencies 
  of 
  the 
  system 
  617 
  and 
  1234. 
  

  

  It 
  was 
  pointed 
  out 
  in 
  the 
  previous 
  paper 
  that 
  at 
  the 
  time 
  

   when 
  the 
  photograph 
  was 
  taken, 
  the 
  amplitude 
  of 
  the 
  wave 
  

   was 
  not 
  quite 
  at 
  its 
  maximum; 
  so 
  that 
  the 
  frequency 
  corre- 
  

   sponding 
  to 
  the 
  exact 
  octave 
  relation 
  is 
  slightly 
  different 
  

   from 
  the 
  measured 
  value 
  613. 
  It 
  is 
  in 
  fact 
  very 
  difficult 
  to 
  

   obtain 
  a 
  photograph 
  during 
  strong 
  resonance, 
  since 
  the 
  

  

  * 
  Cf. 
  Ayrton 
  and 
  Sumpner, 
  Proc. 
  Roy. 
  Soc. 
  vol. 
  xlix. 
  p. 
  424 
  (1891). 
  

   t 
  Science 
  Abstracts, 
  p. 
  697 
  (1907). 
  

  

  