﻿718 
  Prof. 
  E. 
  Taylor 
  Jones 
  and 
  Mr. 
  Morris 
  Owen 
  on 
  

  

  that 
  this 
  was 
  the 
  case. 
  I£ 
  Lj 
  is 
  taken 
  as 
  *006 
  . 
  10^ 
  cm., 
  

   equation 
  (2) 
  gives 
  72i 
  = 
  528*7, 
  ^2=1205-4. 
  With 
  R2 
  = 
  14000 
  

   ohms, 
  Ri=:15 
  ohms 
  [i. 
  e. 
  nearly 
  14 
  ohms 
  being 
  assumed 
  for 
  

   the 
  arc), 
  equations 
  (1) 
  give 
  wi 
  = 
  572, 
  M2'=1194: 
  while 
  

   Ilj 
  = 
  25 
  ohms 
  makes 
  n2 
  less 
  than 
  ^n^. 
  

  

  The 
  observed 
  frequency 
  in 
  this 
  case 
  was 
  573 
  ; 
  and 
  it 
  is 
  

   clear 
  that 
  this 
  condition 
  and 
  the 
  octave 
  relation 
  are 
  satisfied 
  

   by 
  assuming 
  Lj 
  to 
  be 
  slightly 
  greater 
  than 
  '006 
  . 
  10^, 
  and 
  Ri 
  

   rather 
  greater 
  than 
  15 
  ohms. 
  

  

  The 
  length 
  of 
  the 
  arc 
  during 
  the 
  octave 
  resonance 
  was 
  

   about 
  1*5 
  mm., 
  the 
  current 
  in 
  the 
  arc 
  about 
  1*7 
  ampere. 
  

   From 
  the 
  results 
  given 
  by 
  Duddell 
  * 
  it 
  seems 
  probable 
  that 
  

   an 
  arc 
  of 
  this 
  length 
  conveying 
  so 
  small 
  a 
  current 
  might 
  

   have 
  a 
  resistance 
  of 
  over 
  14 
  ohms. 
  

  

  The 
  photographs 
  for 
  Cases 
  II.-IV. 
  are 
  similar 
  in 
  character 
  

   to 
  that 
  given 
  in 
  the 
  previous 
  paper 
  for 
  Case 
  I., 
  and 
  are 
  not 
  

   reproduced 
  here. 
  

  

  (2) 
  Resonance 
  of 
  Higlier 
  Harmonics* 
  

  

  Case 
  V. 
  — 
  With 
  a 
  large 
  capacity 
  in 
  the 
  primary 
  circuit 
  

   and 
  a 
  small 
  secondary 
  capacity, 
  other 
  notes, 
  lower 
  than 
  

   that 
  which 
  gives 
  the 
  octave 
  resonance, 
  become 
  prominent, 
  

   and 
  are 
  accompanied 
  by 
  high 
  potentials 
  at 
  the 
  terminals 
  of 
  

   the 
  secondary 
  condenser. 
  These 
  appear 
  to 
  be 
  due 
  to 
  reso- 
  

   nance 
  of 
  the 
  third 
  and 
  higher 
  harmonics 
  of 
  the 
  arc 
  note. 
  

  

  Thus 
  with 
  Ci= 
  14*62, 
  03= 
  -0002898 
  microfarad 
  (as 
  in 
  

   Case 
  IV.), 
  if 
  the 
  arc-length 
  is 
  made 
  slightly 
  greater 
  than 
  

   the 
  value 
  which 
  gives 
  the 
  octave 
  resonance, 
  the 
  note 
  falls 
  

   gradually 
  in 
  pitch, 
  but 
  becomes 
  fairly 
  stable 
  and 
  prominent 
  

   when 
  about 
  a 
  fifth 
  below 
  the 
  value 
  given 
  in 
  Case 
  IV. 
  The 
  

   photograph 
  showing 
  the 
  curve 
  of 
  secondary 
  potential 
  for 
  

   this 
  ease 
  is 
  given 
  in 
  Plate 
  XX. 
  fig. 
  1. 
  The 
  curve 
  appears 
  

   to 
  consist 
  chiefly 
  of 
  a 
  prominent 
  third 
  harmonic 
  superposed 
  

   upon 
  the 
  fundamental. 
  The 
  frequency 
  of 
  the 
  latter, 
  deter- 
  

   mined 
  by 
  comparison 
  with 
  the 
  curve 
  given 
  by 
  a 
  768 
  tuning- 
  

   fork 
  photographed 
  simultaneously, 
  was 
  found 
  to 
  be 
  359*4. 
  

  

  If 
  we 
  insert 
  the 
  relation 
  ?22 
  = 
  3% 
  in 
  equation 
  (2), 
  we 
  find 
  

   Li 
  = 
  *011589 
  .10^ 
  cm., 
  and 
  hence, 
  by 
  (2), 
  72i 
  = 
  385. 
  The 
  

   difference 
  between 
  the 
  observed 
  and 
  calculated 
  values 
  is 
  

   within 
  the 
  limits 
  that 
  may 
  be 
  expected 
  from 
  the 
  considerations 
  

   explained 
  above. 
  

  

  Case 
  VI.— 
  With 
  Ci=19*03, 
  C2 
  = 
  *00029 
  microfarad, 
  reso- 
  

   nance 
  of 
  the 
  fourth 
  harmonic 
  of 
  the 
  arc 
  note 
  may 
  be 
  obtained. 
  

  

  * 
  Duddell, 
  Phil. 
  Trans, 
  vol, 
  cciii. 
  (A) 
  pp. 
  323^ 
  326 
  (1904). 
  

  

  