﻿C. 
  K. 
  Wead 
  — 
  Intensity 
  of 
  Sound. 
  33 
  

  

  Again, 
  it 
  is 
  found 
  he 
  tells 
  us 
  (p. 
  153-4) 
  that 
  in 
  practice 
  the 
  

   quantities 
  of 
  wind 
  used 
  are 
  nearly 
  as 
  1:2 
  for 
  the 
  8ve, 
  some- 
  

   times 
  less, 
  and 
  fortifies 
  himself 
  by 
  a 
  quotation 
  from 
  Chladni 
  

   (Akustik, 
  p. 
  233) 
  : 
  that 
  if 
  two 
  tones 
  of 
  different 
  pitch 
  are 
  to 
  

   have 
  equal 
  effect 
  the 
  forces 
  which 
  each 
  vibration 
  exerts 
  must 
  

   be 
  inversely 
  as 
  its 
  vibration-frequency 
  ; 
  but 
  this 
  force 
  is 
  pro- 
  

   portional 
  to 
  the 
  mass 
  of 
  air 
  used 
  ; 
  therefore 
  Q 
  varies 
  inversely 
  

   as 
  n. 
  

  

  By 
  the 
  proceeding 
  formula 
  

  

  Q 
  = 
  K'D'L-i 
  J 
  q 
  = 
  K'd'f^ 
  

   If 
  the 
  pipes 
  are 
  an 
  8ve 
  apart 
  L 
  = 
  21 
  and 
  Q 
  = 
  2q 
  : 
  

  

  Then 
  

  

  

  Q 
  

  

  q 
  d* 
  f 
  L 
  cF 
  

  

  .-. 
  D 
  2 
  = 
  dWs 
  = 
  2-83^ 
  2 
  ; 
  D 
  = 
  d 
  Z/l 
  = 
  d 
  X 
  '2 
  T 
  

  

  This 
  proof 
  is 
  clearly 
  very 
  unsatisfactory; 
  but 
  the 
  "scale" 
  

   thus 
  determined, 
  and 
  published 
  by 
  Topfer 
  in 
  1332, 
  has 
  been 
  

   largely 
  used 
  by 
  organ 
  builders. 
  By 
  it 
  pipes 
  4 
  8ves, 
  48 
  semi- 
  

   tones 
  apart, 
  have 
  diameters 
  in 
  the 
  ratio 
  of 
  1:8, 
  or 
  pipes 
  16 
  

   semitones 
  apart, 
  a 
  major 
  10th, 
  are 
  in 
  the 
  ratio 
  of 
  1:2. 
  

  

  Another 
  scale 
  may 
  be 
  had 
  by 
  letting 
  the 
  16th 
  pipe 
  (15 
  semi- 
  

   tones) 
  have 
  the 
  double 
  diameter; 
  the 
  ratio 
  for 
  the 
  8ve 
  is 
  then 
  

   1 
  : 
  3, 
  or 
  more 
  accurately 
  1 
  : 
  ^/16 
  = 
  1 
  : 
  3*032. 
  But 
  the 
  bass 
  

   pipes 
  have 
  too 
  little 
  wind. 
  

  

  If, 
  on 
  the 
  other 
  hand, 
  the 
  18th 
  pipe 
  (17 
  semitones) 
  have 
  the 
  

  

  12 
  

  

  double 
  (or 
  half) 
  diameter, 
  the 
  ratio 
  is 
  1:4 
  17 
  or 
  1:2*661; 
  the 
  

   higher 
  pipes 
  are 
  relatively 
  " 
  sharper." 
  This 
  defect 
  may 
  be 
  

   corrected 
  by 
  cutting 
  their 
  mouths 
  lower, 
  and 
  conversely 
  for 
  

   the 
  low 
  pipes, 
  remembering 
  that 
  for 
  " 
  gleiehe 
  Klangstarke 
  " 
  

   the 
  quantity 
  of 
  wind 
  and 
  therefore 
  the 
  area 
  of 
  mouth 
  must 
  be 
  

   in 
  the 
  ratio 
  of 
  1 
  : 
  v/8 
  for 
  the 
  8ve 
  (p. 
  244). 
  If, 
  in 
  the 
  last 
  case, 
  

   the 
  ratio 
  of 
  height 
  of 
  mouth 
  to 
  breadth 
  be 
  for 
  c' 
  - 
  25, 
  it 
  will 
  be 
  

   for 
  c 
  6 
  0*23, 
  for 
  C 
  2 
  0*41. 
  

  

  Another 
  scale 
  might 
  be 
  formed 
  doubling 
  the 
  diameter 
  at 
  the 
  

   19th 
  pipe 
  ; 
  the 
  same 
  correction 
  is 
  to 
  be 
  made 
  but 
  its 
  execution 
  

   is 
  doubtful. 
  A 
  uniform 
  quality 
  is 
  the 
  first 
  condition 
  in 
  a 
  stop 
  

   (p. 
  295). 
  

  

  fcyThe 
  author 
  then 
  goes 
  on 
  to 
  apply 
  his 
  theories 
  to 
  the 
  laying 
  

   down 
  of 
  several 
  " 
  normal 
  scales 
  ;" 
  these 
  all 
  have 
  121 
  pipes, 
  60 
  

   each 
  way 
  from 
  No. 
  61 
  assumed 
  27'" 
  (53 
  mm 
  ) 
  diameter. 
  In 
  these 
  

   tables 
  we 
  iind, 
  for 
  example, 
  with 
  the 
  ratio 
  of 
  sections 
  : 
  

  

  1 
  : 
  V8 
  = 
  1 
  : 
  2*83, 
  diam. 
  No. 
  1, 
  363*2"' 
  ; 
  No. 
  61, 
  27'" 
  ; 
  No. 
  121, 
  2'" 
  

   1 
  : 
  8/3 
  = 
  1:2*67 
  311*8 
  27 
  2*3 
  

  

  1 
  : 
  5/2 
  = 
  1:2-5 
  272*1 
  27 
  2*7 
  

  

  Am. 
  Jour. 
  Sci.— 
  Third 
  Series, 
  Vol. 
  XLII, 
  Eo. 
  247.— 
  July, 
  1891. 
  

   3 
  

  

  