﻿Range 
  and 
  Sharpness 
  of 
  Resonance 
  under 
  Forcing. 
  Ill 
  

  

  The 
  flax 
  along 
  the 
  channel 
  may 
  be 
  found 
  by 
  expressing 
  y 
  

   as 
  a 
  power 
  series 
  in 
  x 
  and 
  integrating 
  

  

  j 
  \ 
  10 
  die 
  dy, 
  

  

  or 
  by 
  an 
  approximate 
  numerical 
  evaluation 
  in 
  any 
  special 
  

   case. 
  This 
  has 
  not 
  yet 
  been 
  done, 
  and 
  the 
  purposes 
  o£ 
  this 
  

   paper 
  are 
  more 
  to 
  indicate 
  what 
  has 
  already 
  been 
  done, 
  and 
  

   to 
  point 
  out 
  what 
  appear 
  to 
  be 
  the 
  most 
  promising 
  methods 
  

   for 
  future 
  advancement, 
  than 
  to 
  attempt 
  any 
  complete 
  solution 
  

   of 
  the 
  problem. 
  

  

  It 
  appears 
  that 
  the 
  steady 
  flow 
  along 
  a 
  valley 
  may 
  be 
  

   completely 
  solved 
  by 
  the 
  procedure 
  indicated 
  above, 
  so 
  long- 
  

   as 
  the 
  stream-lines 
  are 
  all 
  parallel 
  ; 
  the 
  next 
  question 
  re- 
  

   quiring 
  attention 
  refers 
  to 
  the 
  case 
  where 
  the 
  stream-lines 
  

   are 
  not 
  parallel, 
  but 
  the 
  stream 
  becomes 
  deeper 
  or 
  shallower 
  

   as 
  it 
  proceeds. 
  This 
  may 
  be 
  due 
  to 
  ablation 
  or 
  alteration 
  of 
  

   slope. 
  But 
  the 
  mathematical 
  difficulties 
  are 
  very 
  great. 
  

  

  IV. 
  Range 
  and 
  Sharpness 
  of 
  Resonance 
  under 
  Sustained 
  

   Forcing 
  and 
  tlieir 
  Variations 
  ivith 
  Fitch. 
  By 
  Edwin 
  H. 
  

   Barton, 
  F).Sc, 
  F.R.S.F., 
  Professor 
  of 
  Experimental 
  

   Physics, 
  University 
  College, 
  Nottingham 
  *. 
  

  

  Contents. 
  

  

  Page 
  

   Introduction 
  Ill 
  

  

  Mathematical 
  Theory. 
  

  

  Equations 
  for 
  Forced 
  Vibrations 
  113 
  

  

  Response 
  under 
  Damped 
  and 
  Sustained 
  Forcing 
  .... 
  114 
  

  

  "Resonance, 
  its 
  Range 
  and 
  Sharpness 
  117 
  

  

  Graphs 
  for 
  Range 
  and 
  Sharpness 
  of 
  Resonance 
  119 
  

  

  Range 
  of 
  Resonance 
  nearly 
  proportional 
  to 
  Decrement. 
  120 
  

  

  Helniholcz's 
  Theory 
  for 
  the 
  Ear 
  122 
  

  

  Bjerknes 
  on 
  Electric 
  Resonance 
  123 
  

  

  Zenneck 
  on 
  Sharpness 
  of 
  Resonance 
  124 
  

  

  Raman 
  on 
  Maintenance 
  of 
  Oscillations 
  124 
  

  

  Illustrative 
  Experiments. 
  

  

  The 
  Double 
  Pendulum 
  125 
  

  

  Melde's 
  Experiment, 
  with 
  constant 
  tension 
  127 
  

  

  Do. 
  do. 
  with 
  constant 
  number 
  of 
  segments. 
  129 
  

  

  Helmholtz's 
  Experiment 
  , 
  130 
  

  

  Adjustable 
  Resonator 
  and 
  Forks 
  132 
  

  

  Braflfl 
  Instruments 
  133 
  

  

  Possible 
  Electrical 
  Examples 
  141 
  

  

  Summary 
  143 
  

  

  I~XCTN 
  DAMENTAL 
  in 
  the 
  theory 
  of 
  resonance 
  is 
  the 
  result 
  

   that 
  the 
  response 
  is 
  fuller 
  when 
  the 
  tuning 
  between 
  force 
  

   and 
  responding 
  system 
  is 
  closer. 
  Further, 
  it 
  is 
  well 
  known 
  

   * 
  Communicated 
  by 
  the 
  Author. 
  

  

  