﻿Sharpness 
  of 
  Resonance 
  under 
  Sustained 
  Forcing. 
  129 
  

  

  The 
  table 
  shows 
  that 
  the 
  junior 
  experimenters 
  pushed 
  the 
  

   forcing 
  to 
  a 
  greater 
  extreme 
  and 
  so 
  had 
  larger 
  mistunings 
  

   throughout 
  than 
  ruled 
  in 
  the 
  writer's 
  experiment. 
  At 
  this 
  

   stage 
  no 
  attempt 
  was 
  made 
  to 
  evaluate 
  the 
  diminution 
  of 
  

   response, 
  but 
  the 
  intention 
  was 
  to 
  keep 
  it 
  constant 
  for 
  any 
  

   one 
  set 
  of 
  experiments 
  with 
  the 
  four 
  forks. 
  It 
  is 
  seen 
  that 
  

   the 
  range 
  of 
  resonance 
  appears 
  to 
  increase 
  with 
  period 
  even 
  

   more 
  than 
  theory 
  predicts 
  on 
  the 
  assumption 
  of 
  a 
  constant 
  

   value 
  of 
  the 
  damping 
  coefficient 
  (&/2) 
  for 
  the 
  various 
  

   periods. 
  

  

  It 
  may 
  be 
  noted 
  that 
  the 
  mistiming 
  in 
  these 
  experiments 
  

   was 
  effected 
  by 
  sharpening 
  or 
  flattening 
  the 
  natural 
  frequency 
  

   of 
  the 
  responding 
  vibrator 
  and 
  not 
  that 
  of 
  the 
  impressed 
  

   force. 
  This 
  plan 
  was 
  obviously 
  much 
  easier 
  to 
  carry 
  out 
  

   and 
  may 
  be 
  accounted 
  equally 
  effective. 
  

  

  Meldes 
  Experiment 
  with 
  Constant 
  Number 
  of 
  Segments. 
  — 
  

   It 
  seemed 
  desirable 
  next 
  to 
  test 
  the 
  responses 
  of 
  a 
  length 
  of 
  

   silk 
  thread 
  to 
  the 
  same 
  forks, 
  keeping 
  the 
  number 
  of 
  seg- 
  

   ments 
  constant 
  and 
  varying 
  the 
  tension 
  to 
  tune 
  it 
  to 
  the 
  

   various 
  forks. 
  For 
  if, 
  while 
  the 
  damping 
  coefficient 
  remains 
  

   unaltered, 
  the 
  frequency 
  is 
  by 
  any 
  means 
  changed 
  in 
  a 
  given 
  

   ratio, 
  then 
  the 
  range 
  of 
  resonance 
  may 
  be 
  expected 
  

   theoretically 
  to 
  change 
  in 
  the 
  inverse 
  ratio. 
  And 
  this 
  

   result 
  should 
  be 
  quite 
  unaffected 
  by 
  the 
  particular 
  means 
  

   used 
  to 
  effect 
  the 
  change 
  of 
  frequency. 
  Hence 
  this 
  different 
  

   mode 
  of 
  changing 
  the 
  frequency 
  afforded 
  a 
  crucial 
  test 
  of 
  

   the 
  theory. 
  

  

  With 
  the 
  forks 
  and 
  loads 
  available, 
  a 
  vibration 
  in 
  three 
  

   segments 
  was 
  found 
  convenient 
  and 
  was 
  adopted. 
  This 
  

   series 
  of 
  experiments 
  was 
  made 
  rather 
  more 
  quantitative. 
  

   Thus 
  it 
  was 
  endeavoured 
  to 
  keep 
  the 
  bowing 
  of 
  the 
  fork 
  

   the 
  same 
  throughout 
  and 
  to 
  adjust 
  the 
  lengths 
  in 
  use 
  until 
  

   the 
  amplitude 
  of 
  the 
  responding 
  vibration 
  was 
  reduced 
  to 
  

   one-half 
  its 
  maximum 
  value 
  for 
  best 
  tuning. 
  That 
  corre- 
  

   sponds 
  to 
  about 
  a 
  quarter 
  value 
  of 
  the 
  kinetic 
  energy 
  (or 
  

   D 
  = 
  v3), 
  and 
  so 
  admits 
  of 
  an 
  estimate 
  of 
  the 
  value 
  of 
  the 
  

   sharpness 
  of 
  resonance 
  H. 
  The 
  results 
  are 
  shown 
  in 
  

   Table 
  III. 
  (p. 
  130). 
  It 
  will 
  be 
  seen 
  that 
  they 
  are 
  nearly 
  in 
  

   accord 
  with 
  a 
  constant 
  value 
  of 
  &=58. 
  That 
  would 
  mean 
  that 
  

   the 
  energy 
  of 
  the 
  natural 
  vibrations 
  of 
  the 
  silk 
  thread 
  would 
  

   fall 
  to 
  \\et\\ 
  of 
  its 
  value 
  in 
  l/58th 
  of 
  a 
  second, 
  which 
  seems 
  

   quite 
  probable. 
  In 
  this 
  experiment 
  the 
  scholars 
  0. 
  Hayes 
  

   and 
  A. 
  Warren 
  assisted. 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  Xo. 
  151. 
  July 
  1913. 
  K 
  

  

  