﻿472 
  Prof. 
  S. 
  E. 
  Cook 
  on 
  

  

  of 
  the 
  formation 
  of 
  laminae 
  by 
  different 
  fluting 
  materials, 
  with 
  

   different 
  media 
  under 
  varying 
  conditions, 
  for 
  the 
  purpose 
  of 
  

   making 
  manifest 
  other 
  forces 
  than 
  those 
  of 
  a 
  perfect 
  fluid, 
  

   and 
  also 
  to 
  experimentally 
  verify 
  the 
  presence 
  of 
  the 
  forces 
  

   theoretically 
  deduced 
  from 
  hydrodynamical 
  equations 
  for 
  

   a 
  perfect 
  fluid. 
  

  

  The 
  apparatus 
  were 
  modified 
  forms 
  of 
  the 
  Kundt 
  sound- 
  

   apparatus. 
  The 
  vibrating 
  brass 
  bar 
  was 
  277*7 
  cm. 
  in 
  length, 
  

   with 
  a 
  frequency 
  of 
  1287*5 
  per 
  second 
  and 
  an 
  amplitude 
  

   of 
  vibration, 
  with 
  ordinary 
  bowing, 
  of 
  0'2 
  mm. 
  ; 
  the 
  bar 
  

   being 
  clamped 
  for 
  its 
  first 
  overtone. 
  

  

  In 
  the 
  stationary 
  sound-wave, 
  as 
  that 
  of 
  the 
  organ-pipe 
  or 
  

   Kundt 
  tube, 
  are 
  to 
  be 
  found 
  two 
  distinct 
  phenomena 
  : 
  — 
  1st, 
  

   The 
  separation 
  of 
  the 
  tube 
  into 
  nodes 
  and 
  antinodes; 
  2nd, 
  the 
  

   formation 
  in 
  the 
  antinodes 
  or 
  ventral 
  segments 
  of 
  flutings 
  

   and 
  laminae. 
  Two 
  theories 
  have 
  been 
  advanced 
  to 
  explain 
  

   the 
  formation 
  of 
  these 
  laminae 
  : 
  — 
  1st, 
  They 
  are 
  the 
  nodes 
  

   of 
  very 
  high 
  overtones 
  produced 
  in 
  the 
  vibrating 
  system 
  ; 
  

   2nd, 
  they 
  are 
  produced 
  by 
  forces 
  originated 
  by 
  the 
  flux 
  

   of 
  the 
  medium. 
  

  

  I. 
  As 
  Nodes 
  of 
  High 
  Overtones. 
  

  

  The 
  rapid 
  motion 
  of 
  the 
  particles 
  in 
  the 
  laminae, 
  the 
  move- 
  

   ments 
  of 
  these 
  laminae, 
  the 
  breaking 
  up 
  of 
  old 
  and 
  the 
  

   forming 
  of 
  new 
  laminae, 
  make 
  it 
  highly 
  improbable 
  that 
  they 
  

   are 
  produced 
  by 
  overtones. 
  However, 
  in 
  order 
  that 
  this 
  

   might 
  be 
  more 
  firmly 
  established, 
  a 
  tone 
  was 
  produced 
  by 
  a 
  

   siren 
  in 
  front 
  of 
  a 
  tube 
  closed 
  at 
  one 
  end 
  by 
  a 
  moving 
  piston. 
  

   With 
  the 
  proper 
  adjustment 
  of 
  the 
  vibrating 
  air-column, 
  

   laminae 
  of 
  magnesium 
  carbonate 
  could 
  easily 
  be 
  produced. 
  

  

  II. 
  Lamince 
  due 
  to 
  Bydrodynamical 
  Forces. 
  

  

  Koenig's 
  solution 
  of 
  the 
  hydrodynamical 
  equations 
  for 
  a 
  

   perfect 
  fluid 
  seem 
  to 
  give 
  a 
  more 
  rational 
  explanation 
  of 
  the 
  

   problem. 
  The 
  formulae 
  obtained 
  by 
  Koenig 
  for 
  the 
  forces 
  

   between 
  two 
  spheres, 
  whose 
  radii 
  are 
  R 
  and 
  Kj 
  and 
  whose 
  

   distance 
  apart 
  is 
  r 
  , 
  were 
  

  

  X= 
  — 
  ^Jl 
  J 
  L 
  -sin 
  0(1 
  — 
  5cos 
  z 
  0), 
  . 
  . 
  (1) 
  

  

  z= 
  _ 
  iTrpRsy 
  Wo 
  2 
  cos 
  e 
  (3 
  _ 
  5 
  cog2 
  e) 
  . 
  ^ 
  m 
  (2) 
  

  

  W 
  being 
  the 
  velocity 
  of 
  the 
  stream, 
  p 
  the 
  density 
  of 
  the 
  

   medium, 
  and 
  the 
  angle 
  which 
  the 
  line 
  of 
  centres 
  of 
  

   the 
  spheres 
  makes 
  with 
  the 
  direction 
  of 
  the 
  stream. 
  If 
  the 
  

  

  