﻿C. 
  K. 
  Wead 
  — 
  Intensity 
  of 
  Sound. 
  31 
  

  

  of 
  tone, 
  the 
  boards 
  will 
  be 
  found 
  to 
  be 
  too 
  widely 
  opened 
  

   when 
  the 
  left 
  hand 
  plays 
  the 
  melody 
  on 
  the 
  great 
  key-board 
  

   and 
  the 
  right 
  on 
  the 
  swell, 
  the 
  stops 
  remaining 
  unchanged. 
  

   Another 
  points 
  out 
  that 
  if, 
  with 
  a 
  single 
  stop 
  or 
  combination 
  

   of 
  stops, 
  one 
  runs 
  over 
  the 
  key-board 
  ascending 
  the 
  effect 
  is 
  of 
  

   a 
  crescendo. 
  This 
  would 
  indicate 
  that 
  the 
  organ-builder 
  in- 
  

   tentionally 
  makes 
  the 
  higher 
  pipes 
  louder 
  instead 
  of 
  keeping 
  

   them 
  of 
  equal 
  loudness 
  as 
  assumed 
  previously, 
  and 
  also 
  shows 
  

   that 
  the 
  ear 
  is 
  more 
  sensitive 
  to 
  high 
  notes 
  than 
  to 
  low 
  ones 
  

   under 
  the 
  conditions 
  in 
  which 
  music 
  is 
  heard, 
  whatever 
  the 
  

   case 
  may 
  be 
  with 
  foghorns 
  heard 
  at 
  sea 
  and 
  reported 
  by 
  Allard. 
  

  

  Some 
  time 
  after 
  the 
  preceding 
  experiments 
  had 
  been 
  dis- 
  

   cussed 
  and 
  reported 
  on 
  Mr. 
  F. 
  H. 
  Hastings 
  kindly 
  furnished 
  

   the 
  writer 
  with 
  a 
  copy 
  of 
  Topfer's 
  great 
  w 
  T 
  ork,* 
  and 
  a 
  sum- 
  

   mary 
  of 
  his 
  views 
  may 
  fitly 
  be 
  connected 
  with 
  this 
  paper. 
  

   Through 
  many 
  hundred 
  pages 
  the 
  author 
  discusses 
  the 
  theory 
  

   of 
  organ 
  pipes 
  and 
  gives 
  formulae 
  for 
  their 
  dimensions, 
  and 
  for 
  

   the 
  quantity 
  of 
  wind 
  they 
  require. 
  He 
  determined 
  this 
  last 
  

   experimentally 
  by 
  the 
  method 
  already 
  described, 
  using 
  a 
  bel- 
  

   lows 
  of 
  63 
  cubic 
  feet 
  capacity 
  ; 
  9 
  min, 
  57 
  sec. 
  were 
  required 
  

   for 
  this 
  volume 
  of 
  air 
  to 
  leak 
  out 
  under 
  a 
  pressure 
  of 
  3*2 
  

   Weimar 
  inches 
  of 
  water 
  (= 
  7o 
  ,mm 
  ), 
  (II, 
  95). 
  The 
  experiments 
  

   must 
  have 
  been 
  very 
  tedious 
  with 
  so 
  large 
  a 
  bellows 
  ; 
  they 
  are 
  

   open 
  to 
  the 
  criticism 
  that 
  the 
  leakage 
  is 
  greater 
  than 
  the 
  wind 
  

   consumption 
  of 
  any 
  pipe, 
  except 
  a 
  few 
  of 
  the 
  largest 
  ones 
  ; 
  so 
  

   errors 
  of 
  observation 
  make 
  large 
  errors 
  in 
  the 
  final 
  result, 
  as 
  

   previously 
  pointed 
  out. 
  

  

  The 
  author's 
  theory 
  on 
  the 
  subject 
  is 
  curious. 
  He 
  says 
  (II, 
  

   65) 
  pipes 
  of 
  equal 
  length 
  consume 
  volumes 
  of 
  wind 
  propor- 
  

   tioned 
  to 
  the 
  squares 
  of 
  their 
  diameter, 
  and 
  those 
  of 
  the 
  same 
  

   diameter 
  quantities 
  inversely 
  proportional 
  to 
  the 
  square 
  root 
  

   of 
  their 
  length, 
  [or 
  directly 
  proportional 
  to 
  the 
  square 
  root 
  of 
  

   the 
  vibration 
  frequency]. 
  

  

  Therefore 
  Q=K-- 
  

  

  V 
  L 
  

  

  QyTj 
  -^D 
  2 
  = 
  K' 
  = 
  coefficient 
  which 
  measures 
  "intensity 
  of 
  vibra- 
  

   tion." 
  

  

  Q^/L 
  -f- 
  area 
  of 
  mouth 
  = 
  K" 
  = 
  coefficient 
  which 
  measures 
  " 
  sharp- 
  

   ness 
  of 
  tone." 
  

  

  Q 
  is 
  expressed 
  in 
  Weimar 
  cu. 
  in. 
  per 
  sec. 
  

  

  K' 
  is 
  found 
  to 
  range 
  from 
  68 
  to 
  110, 
  average 
  85 
  : 
  

  

  K" 
  from 
  394 
  to 
  536, 
  average 
  450. 
  

  

  * 
  J. 
  G. 
  Topfer: 
  Lehrbuch 
  der 
  Orgelbaukunst. 
  Weimar, 
  1855. 
  About 
  1,800 
  

   pages 
  and 
  130 
  plates 
  folio. 
  Mr. 
  Hastings 
  calls 
  it 
  "by 
  far 
  the 
  most 
  complete 
  

   book 
  on 
  organ 
  building."' 
  

  

  