﻿Lord 
  Rayleigh 
  : 
  Acoustical 
  Isotes. 
  237 
  

  

  I 
  have 
  recently 
  made 
  a 
  few 
  observations 
  on 
  the 
  vibrations 
  

   of 
  loaded 
  wires 
  in 
  illustration 
  o£ 
  these 
  formula?. 
  A 
  simple 
  

   case 
  is 
  afforded 
  by 
  (2). 
  A 
  lump 
  of 
  wax 
  is 
  attached 
  at 
  the 
  

   centre 
  of 
  a 
  stretched 
  wire, 
  so 
  that 
  sin 
  2 
  (r7rb/l) 
  = 
  when 
  r 
  is 
  

   even, 
  and 
  when 
  r 
  is 
  odd 
  takes 
  the 
  value 
  unity, 
  independently 
  

   of 
  the 
  particular 
  value 
  of 
  r. 
  It 
  is 
  easily 
  verified 
  on 
  trial 
  

   that 
  the 
  partial 
  tones 
  of 
  even 
  order 
  are 
  undisturbed, 
  and 
  that 
  

   those 
  of 
  odd 
  order, 
  though 
  displaced, 
  still 
  constitute 
  a 
  

   harmonic 
  series. 
  The 
  observation 
  is 
  best 
  made 
  with 
  the 
  aid 
  

   of 
  resonators 
  by 
  comparison 
  with 
  the 
  partial 
  tones 
  of 
  a 
  note 
  

   on 
  the 
  harmonium. 
  The 
  load 
  may 
  conveniently 
  be 
  chosen 
  

   so 
  as 
  to 
  depress 
  the 
  pitch 
  by 
  one 
  or 
  more 
  complete 
  semitones. 
  

   If 
  also 
  the 
  tension 
  (due 
  to 
  a 
  weight) 
  be 
  suitably 
  adjusted, 
  

   both 
  series 
  of 
  partial 
  tones 
  may 
  be 
  brought 
  into 
  tune 
  with 
  

   the 
  harmonium, 
  either 
  exactly, 
  or 
  (what 
  is 
  better 
  in 
  practice) 
  

   approximately. 
  

  

  A 
  more 
  elaborate 
  experiment 
  was 
  next 
  attempted 
  in 
  illus- 
  

   tration 
  of 
  the 
  result 
  expressed 
  in 
  (9;. 
  But 
  some 
  modification 
  

   is 
  necessary, 
  inasmuch 
  as 
  in 
  practice 
  we 
  are 
  limited 
  to 
  

   2>ositive 
  loads. 
  But 
  a 
  uniform 
  loading 
  has 
  little 
  significance 
  

   from 
  our 
  present 
  point 
  of 
  view, 
  lowering 
  all 
  the 
  partial 
  tones 
  

   by 
  the 
  same 
  musical 
  interval 
  and 
  being 
  capable 
  of 
  compen- 
  

   sation 
  by 
  varying 
  the 
  tension 
  (T^. 
  It 
  suffices 
  therefore 
  to 
  

   take 
  $p/p 
  proportional 
  to 
  1 
  — 
  cos 
  (27T^/Z); 
  and 
  the 
  experi- 
  

   ment 
  consists 
  in 
  verifying 
  that 
  the 
  first 
  partial 
  is 
  depressed 
  

   relatively 
  to 
  all 
  the 
  other 
  tones, 
  and 
  that 
  these 
  latter 
  retain 
  

   their 
  harmonic 
  relations. 
  

  

  The 
  length 
  of 
  the 
  wire 
  was 
  adjusted 
  to 
  720 
  mm., 
  and 
  loads 
  

   proportional 
  to 
  1 
  — 
  cos 
  (27rx/l) 
  were 
  attached 
  at 
  intervals 
  of 
  

   30 
  mm., 
  beginning 
  at 
  a? 
  = 
  and 
  corresponding 
  to 
  angles 
  0°, 
  

   15°, 
  30°, 
  &c. 
  The 
  unit 
  load 
  (about 
  J 
  gm. 
  of 
  wax) 
  was 
  at 
  

   the 
  points 
  distant 
  from 
  the 
  ends 
  by 
  one 
  quarter 
  of 
  the 
  length 
  

   (90°, 
  270°), 
  and 
  the 
  maximum 
  load 
  (2) 
  was 
  at 
  the 
  centre 
  

   (180°). 
  At 
  the 
  ends 
  (0°, 
  360°) 
  the 
  loads 
  were 
  zero. 
  By 
  

   varying 
  the 
  tension 
  the 
  whole 
  was 
  tuned 
  conveniently 
  to 
  suit 
  

   the 
  harmonium. 
  

  

  The 
  results 
  agreed 
  fairly 
  well 
  with 
  theoretical 
  anticipations. 
  

   The 
  second 
  and 
  third 
  partials 
  retained 
  very 
  accurately 
  their 
  

   harmonic 
  relation 
  (fifth). 
  The 
  fourth 
  and 
  fifth 
  partials 
  were 
  

   too 
  sharp 
  relatively 
  to 
  the 
  second 
  and 
  third 
  by 
  nearly 
  half 
  a 
  

   semitone. 
  The 
  depression 
  of 
  the 
  first 
  partial 
  relatively 
  to 
  

   the 
  second 
  and 
  third 
  was 
  3 
  semitones 
  or 
  a 
  minor 
  third. 
  

  

  These 
  estimations 
  of 
  pitch 
  were 
  made 
  separately 
  by 
  Mr. 
  

   Enock 
  and 
  myself, 
  and 
  in 
  the 
  case 
  of 
  the 
  higher 
  partials 
  

   demanded 
  some 
  care. 
  Useful 
  indications 
  are 
  afforded 
  by 
  but 
  

   partially 
  depressing 
  the 
  key 
  of 
  the 
  harmonium 
  note, 
  whereby 
  

  

  