﻿C. 
  K. 
  Wead 
  — 
  Intensity 
  of 
  Sound. 
  27 
  

  

  in 
  a 
  following 
  column. 
  To 
  obtain 
  V" 
  in 
  cols. 
  10 
  and 
  11, 
  table 
  

   I, 
  the 
  ratio 
  was 
  assumed 
  as 
  VX 
  

  

  Observations 
  of 
  the 
  same 
  quantity 
  on 
  different 
  days 
  agree 
  to 
  

   within 
  a 
  few 
  per 
  cent 
  (e. 
  g. 
  key 
  C 
  with 
  9 
  stops, 
  *0662, 
  '0667, 
  

   •0681) 
  but 
  since 
  they 
  differ 
  more 
  than 
  the 
  probable 
  error 
  of 
  a 
  

   single 
  day's 
  observations 
  the 
  results 
  in 
  the 
  different 
  tables 
  

   should 
  not 
  be 
  combined 
  if 
  accurate 
  relative 
  values 
  are 
  desired, 
  

   nor 
  should 
  results 
  in 
  the 
  same 
  table 
  be 
  combined 
  unless 
  they 
  

   are 
  based 
  on 
  the 
  same 
  value 
  of 
  L. 
  The 
  data 
  for 
  table 
  I 
  were 
  

   obtained 
  in 
  April 
  and 
  May, 
  1883, 
  and 
  are 
  not 
  quite 
  as 
  accurate 
  

   as 
  the 
  data 
  obtained 
  in 
  July, 
  1884, 
  for 
  the 
  later 
  tables. 
  

  

  Conclusions. 
  — 
  The 
  results 
  of 
  experiments 
  with 
  different 
  

   stops 
  are 
  shown 
  in 
  table 
  I 
  It 
  is 
  very 
  clear 
  from 
  them 
  that 
  no 
  

   exact 
  or 
  important 
  conclusions 
  can 
  be 
  drawn 
  from 
  the 
  loudness 
  

   of 
  the 
  sound 
  as 
  to 
  the 
  relative 
  quantity 
  of 
  wind 
  required 
  to 
  

   blow 
  pipes 
  of 
  different 
  construction 
  : 
  thus, 
  the 
  soft 
  Dulciana 
  

   takes 
  more 
  than 
  half 
  as 
  much 
  wind 
  as 
  the 
  comparatively 
  loud 
  

   Open 
  Diapason 
  (102-7-188). 
  Again, 
  the 
  Trumpet 
  stop 
  in 
  this 
  

   organ 
  is 
  voiced 
  very 
  loud, 
  yet 
  its 
  pipes 
  require 
  absolutely 
  less 
  

   energy 
  than 
  any 
  others 
  that 
  sound 
  the 
  same 
  note 
  : 
  this 
  is 
  a 
  con- 
  

   clusive 
  proof 
  that 
  a 
  reed-pipe 
  has 
  a 
  much 
  higher 
  efficiency 
  as 
  a 
  

   wave-producing 
  mechanism 
  than 
  a 
  flue 
  jjipe. 
  

  

  The 
  results 
  on 
  different 
  pipes 
  of 
  the 
  same 
  stop 
  or 
  of 
  the 
  

   same 
  combination 
  of 
  stops 
  are 
  shown 
  in 
  all 
  the 
  tables 
  ; 
  in 
  table 
  

   I 
  for 
  the 
  eight 
  notes 
  of 
  an 
  octave 
  taken 
  together 
  in 
  various 
  

   parts 
  of 
  the 
  scale, 
  a 
  single 
  stop 
  being 
  drawn 
  ; 
  in 
  table 
  II 
  for 
  

   each 
  of 
  the 
  twenty-five 
  notes 
  in 
  a 
  range 
  of 
  two 
  octaves, 
  nine 
  

   stops 
  being 
  drawn 
  ; 
  in 
  table 
  III 
  for 
  various 
  combinations 
  of 
  

   stops. 
  Some 
  of 
  the 
  conclusions 
  from 
  these 
  are 
  very 
  clear, 
  and 
  

   some 
  curious. 
  We 
  must 
  assume 
  with 
  Mr. 
  Bosanquet 
  that 
  a 
  

   set 
  of 
  pipes 
  gives 
  us 
  a 
  series 
  of 
  sounds 
  of 
  the 
  same 
  quality 
  and 
  

   of 
  nearly 
  the 
  same 
  loudness 
  as 
  judged 
  by 
  the 
  ear 
  of 
  an 
  expert, 
  

   and 
  also 
  assume 
  that 
  all 
  pipes 
  of 
  the 
  same 
  stop 
  are 
  equally 
  

   efficient 
  sound-producers. 
  Now 
  if 
  we 
  recall 
  Topfer's 
  law, 
  that 
  

   the 
  consumption 
  of 
  wind 
  varies 
  inversely 
  as 
  the 
  length 
  of 
  the 
  

   pipe, 
  we 
  should 
  expect 
  to 
  find 
  for 
  the 
  octave 
  approximately 
  

   the 
  ratio 
  *500, 
  or 
  a 
  little 
  less, 
  since 
  the 
  higher 
  pipes 
  are 
  rela- 
  

   tively 
  larger 
  than 
  the 
  lower 
  ones 
  and 
  so 
  must 
  be 
  relatively 
  

   shorter. 
  But 
  not 
  a 
  single 
  ratio 
  can 
  be 
  found 
  in 
  the 
  tables 
  to 
  

   confirm 
  this 
  view 
  ; 
  everywhere 
  the 
  ratio 
  is 
  considerably 
  greater 
  

   than 
  *5. 
  The 
  tables 
  give 
  the 
  values 
  in 
  a 
  dozen 
  cases 
  (not 
  in- 
  

   cluding 
  the 
  Trumpet 
  stop) 
  and 
  from 
  table 
  II 
  a 
  dozen 
  more 
  

   values 
  can 
  readily 
  be 
  found. 
  

  

  To 
  some 
  of 
  the 
  observations 
  it 
  seemed 
  worth 
  while 
  to 
  apply 
  

   the 
  method 
  of 
  least 
  squares 
  as 
  already 
  said 
  ; 
  the 
  several 
  ratios 
  

   found 
  for 
  the 
  octave 
  are 
  given 
  in 
  table 
  IY. 
  

  

  