﻿Flutings 
  in 
  a 
  Sound- 
  Wave. 
  473 
  

  

  particle 
  is 
  in 
  the 
  form 
  of 
  an 
  ellipsoid 
  or 
  disk, 
  Koenig 
  finds 
  

   a 
  moment 
  M 
  tending 
  to 
  diminish 
  the 
  angle 
  6, 
  

  

  M 
  = 
  4pB 
  2 
  3 
  W 
  2 
  sin2<9, 
  (3) 
  

  

  where 
  R 
  2 
  is 
  the 
  radius 
  of 
  the 
  disk. 
  

  

  When 
  8— 
  - 
  , 
  n 
  being 
  an 
  integer, 
  

  

  x 
  3*^TO 
  

  

  When 
  d=smr 
  

  

  V 
  

  

  r 
  4 
  W 
  

  

  This 
  gives 
  repulsion 
  parallel 
  and 
  attraction 
  perpendicular 
  

   to 
  the 
  stream-lines. 
  

  

  In 
  the 
  equations, 
  the 
  factors 
  susceptible 
  to 
  variation 
  are 
  the 
  

   density 
  of 
  the 
  medium 
  p, 
  the 
  size 
  and 
  shape 
  of 
  the 
  particles 
  

   used 
  for 
  fluting 
  material, 
  R, 
  R 
  x 
  , 
  and 
  R 
  2 
  > 
  an( 
  l 
  tne 
  stream 
  

   velocity 
  W 
  . 
  

  

  I 
  shall 
  first 
  allow 
  p 
  and 
  W 
  to 
  remain 
  constant 
  and 
  vary 
  

   the 
  fluting 
  material. 
  

  

  1. 
  A 
  study 
  of 
  various 
  fluting 
  materials 
  with 
  air 
  as 
  a 
  

  

  medium. 
  — 
  The 
  ordinary 
  form 
  of 
  the 
  Kundt 
  sound-apparatus 
  

  

  was 
  used 
  ; 
  the 
  medium 
  being 
  maintained 
  at 
  normal 
  pressure. 
  

  

  Flutings 
  were 
  obtained 
  with 
  the 
  following 
  materials 
  : 
  — 
  

   © 
  © 
  

  

  magnesium 
  carbonate, 
  lycopodium, 
  amorphous 
  silica, 
  cork 
  

   dust, 
  magnesium, 
  anthracene, 
  ammonium 
  chloride 
  (as 
  

   fumes), 
  sand, 
  aluminium, 
  brass 
  and 
  iron 
  filings, 
  timothy 
  blue 
  

   grass, 
  red 
  top, 
  and 
  petunia 
  seed. 
  

  

  After 
  a 
  careful 
  microscopical 
  examination 
  of 
  these 
  materials, 
  

   it 
  was 
  noticed 
  that 
  as 
  the 
  radii 
  of 
  the 
  particles 
  or 
  disks 
  

   increased, 
  the 
  mass 
  of 
  the 
  particles 
  remaining 
  the 
  same, 
  the 
  

   more 
  readily 
  flutings 
  formed 
  ; 
  that 
  the 
  more 
  nearly 
  spherical 
  

   the 
  particles 
  were 
  the 
  more 
  easily 
  they 
  swept 
  into 
  the 
  nodes 
  ; 
  

   and 
  that 
  the 
  greater 
  the 
  radii 
  of 
  the 
  particles 
  the 
  farther 
  

   apart 
  the 
  laminae. 
  

  

  2. 
  A 
  study 
  of 
  various 
  fluting 
  material 
  wiili 
  carbon 
  dioxide 
  

   and 
  chlorine 
  as 
  media. 
  — 
  With 
  carbon 
  dioxide 
  as 
  medium 
  

   flutings 
  were 
  obtained 
  in 
  all 
  the 
  substances 
  used 
  with 
  air, 
  and 
  

   in 
  addition 
  flutings 
  were 
  obtained 
  in 
  filings 
  of 
  coin 
  silver. 
  

   It 
  was 
  noted 
  that 
  flutings 
  were 
  obtained 
  more 
  easily 
  in 
  carbon 
  

   dioxide 
  than 
  in 
  air. 
  This 
  was 
  clearly 
  shown 
  by 
  the 
  fact 
  that 
  

   flutings 
  with 
  coin 
  silver 
  could 
  not 
  be 
  obtained 
  in 
  air. 
  With 
  

   chlorine 
  as 
  medium, 
  in 
  addition 
  to 
  the 
  above-mentioned 
  

   substances, 
  flutings 
  were 
  obtained 
  with 
  platinum 
  filings. 
  It 
  

   is 
  to 
  be 
  noted 
  that 
  in 
  the 
  last 
  two 
  experiments 
  the 
  density 
  p 
  

  

  