﻿On 
  Flutings 
  in 
  a 
  Sound- 
  Wave. 
  471 
  

  

  Before 
  closing 
  it 
  should 
  be 
  stated 
  that 
  the 
  present 
  research 
  

   has 
  been 
  greatly 
  facilitated 
  by 
  funds 
  awarded 
  by 
  the 
  Govern- 
  

   ment 
  Grant 
  Committee 
  of 
  the 
  Royal 
  Society. 
  This 
  oppor- 
  

   tunity 
  is 
  taken 
  to 
  thank 
  Professor 
  Schuster 
  for 
  so 
  kindly 
  

   placing 
  the 
  ample 
  resources 
  of 
  his 
  laboratory 
  at 
  my 
  disposal 
  ; 
  

   my 
  thanks 
  are 
  also 
  due 
  to 
  the 
  Committee 
  of 
  the 
  Davy-Faraday 
  

   Research 
  Laboratory 
  for 
  the 
  loan 
  of 
  certain 
  parts 
  of 
  the 
  

   apparatus. 
  Lastly, 
  it 
  is 
  only 
  just 
  to 
  state 
  that 
  the 
  satisfactory 
  

   results 
  obtained 
  with 
  the 
  apparatus 
  described 
  are 
  attributed 
  

   to 
  the 
  care 
  and 
  skilled 
  workmanship 
  of 
  Mr. 
  Charles 
  W. 
  Cook. 
  

  

  LTV. 
  On 
  Flutings 
  in 
  a 
  Sound- 
  Wave 
  and 
  the 
  Forces 
  due 
  

   to 
  a 
  Flux 
  of 
  a 
  Viscous 
  Fluid 
  around 
  Spheres. 
  By 
  S. 
  R. 
  

   Cook, 
  M.S., 
  A.M., 
  Former 
  Fellow 
  in 
  Physics, 
  University 
  

   of 
  Nebraska 
  ; 
  Professor 
  of 
  Physics 
  in 
  Washburn 
  Coll 
  eye, 
  

   Kansas 
  *. 
  

  

  A 
  COUSTIC 
  attractions 
  and. 
  repulsions 
  have 
  been 
  carefully 
  

   jTjL 
  studied 
  and 
  much 
  of 
  the 
  accompanying 
  phenomena 
  

   explained 
  by 
  Messrs. 
  Guyot 
  f, 
  Schellbach 
  %, 
  Guthrie 
  §, 
  and 
  

   Lord 
  Kelvin 
  ||. 
  Attractions 
  and 
  repulsions 
  with 
  the 
  sound- 
  

   wave 
  have 
  been 
  more 
  recently 
  discussed 
  by 
  Walter 
  

   Koenig 
  %. 
  

  

  In 
  his 
  discussion 
  Koenig 
  makes 
  use 
  of 
  the 
  hydrodynamical 
  

   equations 
  for 
  a 
  perfect 
  fluid, 
  and 
  from 
  them 
  deduces 
  formulae 
  

   which 
  represent 
  forces 
  brought 
  into 
  action 
  by 
  the 
  flux 
  of 
  a 
  

   fluid 
  around 
  spheres. 
  He 
  finds 
  that 
  the 
  flux 
  of 
  a 
  perfect 
  

   fluid 
  around 
  spheres 
  produces 
  a 
  force 
  of 
  repulsion 
  parallel, 
  

   and 
  attraction 
  perpendicular 
  to 
  the 
  stream-lines 
  ; 
  also 
  a 
  

   movement 
  of 
  rotation 
  tending 
  to 
  move 
  an 
  ellipsoid 
  or 
  disk 
  

   into 
  a 
  plane 
  transverse 
  to 
  the 
  stream-lines. 
  These 
  forces 
  are 
  

   considered 
  by 
  Koenig 
  sufficient 
  to 
  explain 
  the 
  formation 
  

   of 
  laminae 
  and 
  flutings 
  in 
  the 
  sound-wave. 
  

  

  Although 
  Koenig's 
  explanation 
  has 
  been 
  generally 
  ac- 
  

   cepted 
  **, 
  yet 
  it 
  seemed 
  to 
  the 
  writer 
  that 
  frictional 
  forces 
  

   must 
  be 
  present, 
  and 
  that 
  opposite 
  forces 
  were 
  necessary 
  

   to 
  maintain 
  the 
  particles 
  forming 
  the 
  laminae 
  in 
  their 
  respec- 
  

   tive 
  positions. 
  

  

  The 
  purpose 
  of 
  this 
  paper 
  was 
  to 
  make 
  a 
  careful 
  study 
  

  

  * 
  Read 
  before 
  the 
  Denver 
  Meeting 
  of 
  the 
  American 
  Association 
  for 
  the 
  

   Advancement 
  of 
  Science. 
  Communicated 
  by 
  Prof. 
  J). 
  JB. 
  Brace. 
  

   f 
  Ifvesse 
  Scientifique, 
  1861, 
  t. 
  iii. 
  p. 
  130. 
  

   X 
  Pogg. 
  Ann. 
  vol. 
  cxxxix. 
  st. 
  4, 
  p. 
  670. 
  

   § 
  Phil. 
  Mag. 
  [4] 
  xli. 
  1871, 
  p. 
  405. 
  

   ]| 
  Phil. 
  Mag. 
  [4] 
  xli. 
  1871, 
  p. 
  423. 
  

  

  «[ 
  Wied. 
  Ann. 
  t. 
  xlii. 
  pp. 
  353, 
  549 
  ; 
  t. 
  xliii. 
  p. 
  43 
  (1891). 
  

   ** 
  Lord 
  Rayleigh, 
  Theory 
  of 
  Sound, 
  vol. 
  ii. 
  p. 
  46. 
  

  

  