﻿Sharpness 
  of 
  Resonance 
  under 
  Sustained 
  Forcing. 
  143 
  

  

  and 
  0/4 
  respectively, 
  thus 
  giving 
  frequencies 
  as 
  one 
  to 
  two 
  

   (each 
  being 
  millions 
  per 
  second). 
  But 
  no 
  appreciable 
  change 
  

   in 
  the 
  sharpness 
  of 
  resonance 
  was 
  observable 
  by 
  the 
  method 
  

   then 
  in 
  use, 
  viz., 
  the 
  neon 
  tube. 
  

  

  It 
  is 
  thus 
  evident, 
  both 
  on 
  theoretical 
  and 
  experimental 
  

   grounds, 
  that 
  a 
  more 
  extended 
  examination 
  is 
  needed 
  for 
  the 
  

   investigation 
  of 
  electrical 
  forced 
  vibrations 
  and 
  their 
  responses 
  

   under 
  various 
  conditions. 
  This 
  is 
  accordingly 
  reserved 
  for 
  

   another 
  occasion. 
  

  

  Summary. 
  

  

  AVe 
  may 
  now 
  briefly 
  summarize 
  as 
  follows: 
  — 
  

  

  1. 
  In 
  the 
  case 
  of 
  vibrations 
  executed 
  under 
  sustained 
  

   harmonic 
  forcing, 
  it 
  has 
  been 
  shown 
  theoretically 
  and 
  

   experimentally 
  that 
  the 
  sharpness 
  of 
  response 
  (as 
  here 
  

   quantitatively 
  defined, 
  see 
  equations 
  (19) 
  to 
  (21)) 
  varies 
  

   directly 
  as 
  the 
  frequency 
  of 
  the 
  vibrations 
  it 
  is 
  sought 
  to 
  

   elicit, 
  provided 
  the 
  damping 
  coefficient 
  remains 
  constant. 
  

  

  2. 
  These 
  relations 
  are 
  held 
  to 
  apply 
  to 
  any 
  forced 
  vibra- 
  

   tions 
  fulfilling 
  the 
  above 
  conditions, 
  whether 
  mechanical, 
  

   acoustical, 
  or 
  electrical. 
  

  

  3. 
  This 
  principle 
  affords 
  a 
  valuable 
  clue 
  to 
  the 
  best 
  arrange- 
  

   ment 
  of 
  certain 
  experiments 
  on 
  forced 
  vibrations 
  whether 
  of 
  

   a 
  merely 
  qualitative 
  nature 
  to 
  illustrate 
  lectures, 
  or 
  of 
  a 
  strictly 
  

   quantitative 
  character 
  for 
  laboratory 
  determinations. 
  

  

  4. 
  In 
  the 
  case 
  of 
  brass 
  instruments 
  the 
  variation 
  of 
  the 
  

   range 
  of 
  resonance 
  with 
  pitch 
  is 
  specially 
  noticeable. 
  It 
  

   serves 
  to 
  elucidate 
  the 
  apparently 
  anomalous 
  production 
  on 
  

   certain 
  instruments 
  of 
  a 
  low 
  note 
  (written 
  as 
  " 
  F 
  '') 
  by 
  its 
  

   inclusion 
  in 
  the 
  upward 
  spread 
  resonance 
  of 
  the 
  fundamental 
  

   (called 
  the 
  pedal 
  and 
  written 
  as 
  C). 
  The 
  range 
  of 
  resonance 
  

   at 
  this 
  low* 
  pitch 
  really 
  embraces 
  these 
  two 
  notes 
  (a 
  major 
  

   fourth 
  apart) 
  and 
  everything 
  that 
  lies 
  between 
  them. 
  

  

  Various 
  other 
  points 
  in 
  the 
  theory 
  and 
  practice 
  of 
  brass 
  

   instruments 
  are 
  also 
  rendered 
  clearer 
  by 
  the 
  theory 
  here 
  

   advanced. 
  

  

  5. 
  The 
  strongly-damped 
  electrical 
  oscillations 
  usually 
  dealt 
  

   with 
  on 
  Dr. 
  Fleming's 
  cymometer 
  lie 
  outside 
  the 
  scope 
  of 
  

   the 
  simple 
  theory 
  here 
  developed 
  for 
  the 
  responses 
  under 
  

   sustained 
  forcing. 
  The 
  simple 
  theory 
  may, 
  however, 
  be 
  

   expected 
  to 
  apply 
  to 
  any 
  cases 
  where 
  the 
  forcing 
  is 
  due 
  

   (i.) 
  to 
  commercial 
  alternations 
  of 
  sine 
  form, 
  or 
  (ii.) 
  to 
  the 
  

   sustained 
  electric 
  waves 
  of 
  the 
  Poulsen 
  or 
  other 
  such 
  system 
  

   of 
  wireless 
  telegraphy. 
  

  

  University 
  College, 
  Nottingham, 
  

   March 
  22, 
  1913. 
  

  

  