﻿26 
  

  

  C. 
  K. 
  Wead 
  — 
  Intensity 
  of 
  Sound. 
  

  

  The 
  numbers 
  in 
  the 
  column 
  ratio 
  (except 
  in 
  table 
  LV) 
  are 
  

   found 
  by 
  dividing 
  the 
  number 
  against 
  which 
  they 
  are 
  placed 
  

   by 
  the 
  preceding 
  one 
  ; 
  if 
  Topfer's 
  law 
  were 
  true 
  these 
  ratios 
  

   would 
  be 
  for 
  the 
  octave 
  everywhere 
  *500. 
  

  

  Table 
  III. 
  — 
  Miscellaneous. 
  

  

  1. 
  

  

  2. 
  

  

  3. 
  

  

  4. 
  

  

  5. 
  

  

  6. 
  

  

  7. 
  

  

  Stops 
  drawn. 
  

  

  Key. 
  

  

  t. 
  

  

  1-*-*. 
  

  

  y. 
  

  

  Ratio. 
  

  

  Energy. 
  

  

  

  

  

  

  c 
  c. 
  

  

  

  ergs. 
  sec. 
  

  

  

  

  sec. 
  

  

  

  3-4xl0 
  5 
  x 
  

  

  

  10 
  6 
  x 
  

  

  1 
  6' 
  Bourdon 
  

  

  L 
  

  

  69-44 
  

  

  0144 
  

  

  

  

  

  

  C 
  

  

  22 
  66 
  

  

  •0441 
  

  

  •0297 
  

  

  

  

  74 
  

  

  

  D 
  

  

  28-59 
  

  

  •0350 
  

  

  •0206 
  

  

  

  

  52 
  

  

  

  E 
  

  

  33-22 
  

  

  .0301 
  

  

  •0157 
  

  

  

  

  39 
  

  

  

  F 
  

  

  33-50 
  

  

  •0299 
  

  

  •0155 
  

  

  

  39 
  

  

  

  C 
  

  

  3559 
  

  

  •0281 
  

  

  •0137 
  

  

  

  

  34 
  

  

  

  A 
  

  

  38-04 
  

  

  •0263 
  

  

  •0119 
  

  

  

  30 
  

  

  

  B 
  

  

  39-58 
  

  

  0253 
  

  

  •0109 
  

  

  

  

  27 
  

  

  

  C 
  

  

  32-37 
  

  

  •0309 
  

  

  •0165 
  

  

  

  

  41 
  

  

  

  C-c 
  

  

  6-375 
  

  

  •1569 
  

  

  •1425 
  

  

  

  

  356 
  

  

  8 
  / 
  Open 
  Diapason, 
  ) 
  

   Melodia, 
  Dulciana 
  \ 
  

  

  L 
  

  

  69-62 
  

  

  •0144 
  

  

  

  

  

  C 
  

  

  18-21 
  

  

  •0549 
  

  

  0405 
  

  

  .... 
  

  

  101 
  

  

  

  c 
  

  

  26-62 
  

  

  •0376 
  

  

  •0232 
  

  

  •572 
  

  

  58 
  

  

  

  c' 
  

  

  35-25 
  

  

  •0284 
  

  

  •0140 
  

  

  •603 
  

  

  35 
  

  

  

  c" 
  

  

  43-69 
  

  

  •0229 
  

  

  •0085 
  

  

  •608 
  

  

  21 
  

  

  9 
  stops 
  

  

  L 
  

  

  70-6 
  

  

  •0142 
  

  

  

  

  

  

  C 
  

  

  12-37 
  

  

  •0808 
  

  

  •0667 
  

  

  

  167" 
  

  

  

  c 
  

  

  17-96 
  

  

  0557 
  

  

  •0415 
  

  

  •632 
  

  

  104 
  

  

  

  c' 
  

  

  2600 
  

  

  •0385 
  

  

  0243 
  

  

  •586 
  

  

  61 
  

  

  

  <f' 
  

  

  34-25 
  

  

  •0292 
  

  

  •0150 
  

  

  •619 
  

  

  38 
  

  

  

  c'" 
  

  

  44 
  62 
  

  

  •0224 
  

  

  •0083 
  

  

  •550 
  

  

  21 
  

  

  9 
  stops 
  

  

  L 
  

  

  80-62 
  

  

  0124 
  

  

  

  For 
  17 
  th. 
  

  

  

  

  C 
  

  

  12 
  42 
  

  

  •0805 
  

  

  •0681 
  

  

  

  170 
  

  

  

  e 
  

  

  23-25 
  

  

  •0430 
  

  

  •0306 
  

  

  •449 
  

  

  77 
  

  

  

  g'# 
  

  

  37-46 
  

  

  •0267 
  

  

  •0143 
  

  

  •467 
  

  

  36 
  

  

  

  c'" 
  

  

  47-92 
  

  

  •0209 
  

  

  •0085 
  

  

  •592 
  

  

  21 
  

  

  In 
  several 
  cases 
  the 
  results 
  have 
  been 
  discussed 
  mathemat- 
  

   ically 
  and 
  thus 
  a 
  computed 
  value 
  of 
  V 
  is 
  found 
  (T. 
  I, 
  col. 
  8 
  ; 
  

   T. 
  II, 
  col. 
  5) 
  : 
  in 
  these 
  cases 
  an 
  exponential 
  formula 
  was 
  as- 
  

   sumed 
  similar 
  to 
  that 
  for 
  the 
  vibration-frequency 
  of 
  the 
  tones 
  

   in 
  a 
  tempered 
  scale, 
  and 
  the 
  logarithmic 
  formulae 
  derived 
  from 
  

   it 
  were 
  combined 
  by 
  the 
  method 
  of 
  least 
  squares 
  ; 
  thus 
  

   yr 
  n 
  = 
  V 
  

   log 
  y 
  + 
  n 
  log 
  r 
  — 
  log 
  V= 
  

   Whence 
  (n 
  + 
  l) 
  log 
  y 
  + 
  ^(n) 
  log 
  r 
  — 
  -^(log 
  V) 
  = 
  

   2(n) 
  log?/ 
  4- 
  2(n*) 
  log 
  r 
  — 
  ^(?*log 
  V)= 
  

   The 
  values 
  of 
  r 
  thus 
  found 
  are 
  collected 
  in 
  table 
  IV. 
  The 
  

   difference 
  between 
  the 
  computed 
  and 
  observed 
  values 
  of 
  Vis 
  

   divided 
  by 
  the 
  former 
  and 
  the 
  quotient, 
  as 
  a 
  per 
  cent, 
  is 
  placed 
  

  

  