﻿Flutings 
  in 
  a 
  Sound- 
  Wave. 
  

  

  475 
  

  

  •0000318, 
  the 
  ratio 
  of 
  the 
  density 
  of 
  hydrogen 
  to 
  air 
  being 
  

   5*85, 
  that 
  of 
  air 
  to 
  hydrogen 
  '17. 
  

  

  In 
  these 
  experiments, 
  since 
  R, 
  R 
  l5 
  R 
  2 
  , 
  r 
  o, 
  an 
  d 
  W 
  have 
  been 
  

   made 
  constant 
  for 
  the 
  two 
  gases, 
  if 
  X 
  1? 
  Z 
  l5 
  and 
  M 
  x 
  are 
  the 
  

   forces 
  of 
  minimum 
  disturbance 
  in 
  air 
  ; 
  X 
  2 
  , 
  Z 
  2 
  , 
  M 
  2 
  for 
  the 
  

   carbon 
  dioxide, 
  then 
  v 
  r/ 
  ' 
  r 
  

  

  ±y—h 
  -^k-Pi 
  . 
  (c\ 
  

  

  where 
  p 
  l 
  and 
  p 
  2 
  are 
  the 
  densities 
  of 
  air 
  and 
  carbon 
  dioxide 
  

   respectively. 
  And 
  since 
  at 
  minimum 
  disturbance 
  X 
  l5 
  Z 
  1? 
  Mj 
  

   must 
  be 
  equal 
  respectively 
  to 
  X 
  2 
  , 
  Z 
  2 
  , 
  M 
  2 
  , 
  then, 
  if 
  there 
  are 
  no 
  

   forces 
  other 
  than 
  the 
  forces 
  of 
  a 
  perfect 
  fluid, 
  the 
  ratio 
  p\\p 
  2 
  

   should 
  be 
  unity 
  ; 
  and 
  since 
  this 
  is 
  not 
  the 
  case, 
  the 
  supposition 
  

   is 
  that 
  there 
  are 
  other 
  forces 
  which 
  do 
  not 
  vary 
  directly 
  

   as 
  the 
  density, 
  and 
  since 
  the 
  internal 
  friction 
  of 
  fluids, 
  within 
  

   the 
  limits 
  of 
  these 
  experiments, 
  is 
  independent 
  of 
  the 
  density,, 
  

   it 
  is 
  not 
  improbable 
  that 
  these 
  forces 
  partake 
  of 
  the 
  nature 
  of 
  

   frictional 
  forces. 
  

  

  For 
  any 
  gas 
  the 
  coefficient 
  of 
  internal 
  friction 
  R 
  — 
  kpc\* 
  

   and 
  for 
  any 
  other 
  gas 
  of 
  equal 
  density 
  R 
  1 
  = 
  A 
  , 
  pc 
  1 
  X 
  1 
  . 
  

  

  Taking 
  the 
  ratios 
  Tl 
  _ 
  a^ 
  

  

  Hl 
  " 
  ClV 
  '*'*'/. 
  '. 
  

   Hence, 
  if 
  there 
  are 
  forces 
  other 
  than 
  the 
  perfect 
  fluid 
  forces 
  

  

  proportional 
  to 
  the 
  coefficient 
  of 
  internal 
  friction, 
  they 
  must 
  

  

  also 
  be 
  proportional 
  to 
  the 
  product 
  of 
  the 
  velocity 
  and 
  the 
  

  

  mean 
  free 
  path. 
  This 
  led 
  to 
  the 
  study 
  of 
  the 
  influence 
  of 
  

  

  the 
  density 
  on 
  flutings 
  and 
  the 
  ratio 
  of 
  the 
  mean 
  free 
  path 
  

  

  to 
  the 
  distance 
  apart 
  of 
  the 
  laminae. 
  

  

  4. 
  Ratio 
  of 
  the 
  mean 
  free 
  path 
  of 
  the 
  molecule 
  to 
  the 
  distance 
  

  

  apart 
  of 
  the 
  lamince. 
  — 
  A 
  Kundt 
  tube 
  was 
  so 
  arranged 
  that 
  the 
  

  

  pressure 
  could 
  ' 
  be 
  reduced 
  to 
  any 
  desired 
  amount 
  and 
  

  

  accurately 
  determined. 
  The 
  following 
  table 
  obtains 
  for 
  

  

  amorphous 
  silica 
  and 
  air. 
  

  

  Table 
  II. 
  

  

  Density. 
  

  

  Molecular 
  

   Velocity 
  C. 
  

  

  Mean 
  free 
  

   path 
  = 
  X. 
  

  

  Distance 
  apart 
  

   of 
  flutings 
  — 
  d. 
  

  

  d/\. 
  

  

  •000180 
  

  

  502 
  

  

  6114X10- 
  8 
  

  

  •72 
  

  

  118000 
  

  

  •000228 
  

  

  506 
  

  

  4748 
  xl0~ 
  8 
  

  

  •50 
  

  

  105000 
  

  

  •0003G0 
  

  

  504 
  

  

  3077 
  Xl0~ 
  8 
  

  

  •32 
  

  

  104000 
  

  

  •000695 
  

  

  502 
  

  

  1557 
  Xl0~ 
  8 
  

  

  •23 
  

  

  146000 
  \ 
  

  

  •001152 
  

  

  501 
  

  

  iKOxlO 
  -3 
  

  

  •15 
  

  

  159000 
  

  

  * 
  Boltzmanu, 
  Gas 
  Theorie, 
  t. 
  i. 
  p. 
  81. 
  

  

  