﻿964 
  

  

  Prof. 
  A. 
  H. 
  Gibson 
  on 
  the 
  Motion 
  of 
  

  

  been 
  used 
  to 
  calculate 
  the 
  wave-length 
  I. 
  The 
  following 
  

   are 
  the 
  results 
  of 
  the 
  calculations. 
  

  

  Diam. 
  of 
  ~) 
  

   tube 
  (cm.). 
  ) 
  

  

  1-680. 
  

  

  2'695. 
  

  

  5*09 
  

  

  Length 
  of 
  bubble 
  

   L 
  cm. 
  

  

  1*5 
  

  

  2-0 
  

  

  4-0 
  

  

  6-0 
  

  

  8-0 
  

  

  2-5 
  

  

  4-0 
  

  

  6-0 
  8-0 
  

  

  io-o 
  

  

  4-0 
  

  

  6-0 
  

  

  8-0 
  

  

  io-o 
  

  

  

  1 
  

   •705 
  '738 
  

  

  •799 
  

  

  •832 
  

  

  •850 
  

  

  •667 
  

  

  •720 
  

  

  •762 
  

  

  •790 
  

  

  •808 
  

  

  •677 
  

  

  •717 
  

  

  •747 
  

  

  •767 
  

  

  A 
  

  

  

  ,51'0 
  ,57-2 
  

  

  75-0 
  

  

  89-9 
  

  

  100-2 
  

  

  70-4 
  

  

  83-6 
  

  

  98-6 
  

  

  111-2 
  

  

  122-0 
  

  

  92-5 
  

  

  1057 
  

  

  118-0 
  

  

  128-2 
  

  

  

  h 
  cm 
  

  

  •135 
  -119 
  

  

  •0895 
  

  

  •0689 
  

  

  •0655 
  

  

  •248 
  

  

  •205 
  

  

  •171 
  

  

  •149 
  

  

  •136 
  

  

  •450 
  

  

  •390 
  

  

  •345 
  

  

  •315 
  

  

  1 
  cm. 
  (calculated) 
  

   h 
  

  

  •175 
  -139 
  

  

  •77 
  -8fi 
  

  

  •0810 
  

  

  •0564 
  

  

  •0453 
  

  

  •092 
  

  

  •0651 
  

  

  •0470 
  

  

  •0370 
  

  

  •0306 
  

  

  •0533 
  

  

  •0408 
  

  

  •0327 
  

  

  •0277 
  

   11-4 
  

  

  1-11 
  

  

  1-22 
  

  

  1-44 
  

  

  2-70 
  

  

  3-15 
  

  

  3-64 
  

  

  4-02 
  

  

  4-45 
  

  

  8-45 
  

  

  9-55 
  

  

  10-6 
  

  

  I 
  

  

  

  

  In 
  fig. 
  4 
  these 
  relationships 
  between 
  the 
  lengths 
  of 
  bubble 
  

   and 
  of 
  ripple 
  are 
  shown 
  by 
  the 
  full-line 
  curves, 
  and 
  against 
  

   these 
  are 
  plotted 
  the 
  measured 
  values 
  of 
  the 
  wave-lengths. 
  

  

  4 
  

  

  •rye 
  

  

  

  

  

  

  

  

  

  Fig. 
  

  

  4. 
  

  

  

  

  

  

  

  

  

  

  

  

  

  I 
  

  

  

  

  _J 
  1 
  

  

  

  

  ! 
  

  

  

  

  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  \ 
  

  

  

  

  \. 
  

  

  

  

  •ISO 
  

  

  

  I 
  

  

  

  V 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  *v 
  

  

  

  

  

  \ 
  

  

  -/z& 
  

  

  

  

  \ 
  

  

  

  

  , 
  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  + 
  

  

  x 
  

  

  

  

  

  

  

  

  

  \ 
  

  

  \ 
  

  

  

  •loo 
  

  

  

  

  \ 
  

  

  

  

  

  S 
  

  

  

  \ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  

  

  

  

  \ 
  

  

  

  \ 
  

  

  

  

  

  

  v 
  

  

  

  

  V 
  

  

  

  ■oys 
  

  

  

  

  \ 
  

  

  < 
  

  

  >\ 
  

  

  

  \ 
  

  

  

  

  

  \ 
  

  

  

  > 
  

  

  

  s. 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  V. 
  

  

  

  \ 
  

  

  

  *\ 
  

  

  

  

  

  

  

  

  

  

  

  

  ^^> 
  

  

  \ 
  

  

  

  " 
  v 
  v^ 
  i 
  

  

  

  

  

  

  

  

  

  

  ^* 
  

  

  

  \+ 
  

  

  

  oso 
  

  

  J 
  

  

  

  

  

  i^- 
  

  

  

  

  

  w 
  

  

  

  

  

  

  "^L_ 
  

  

  

  

  -— 
  i 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  i 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  ' 
  — 
  —H 
  

  

  

  

  

  1 
  | 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  | 
  

  

  

  - 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  ! 
  

  

  

  -tj 
  

  

  1 
  i 
  1 
  

  

  4- 
  S- 
  6 
  7 
  

  

  From 
  these 
  it 
  appears 
  that 
  the 
  agreement 
  between 
  measured 
  

   and 
  calculated 
  values 
  is 
  very 
  close 
  for 
  all 
  the 
  tubes 
  so 
  long- 
  

   as 
  the 
  length 
  of 
  bubble 
  exceeds 
  the 
  bore 
  of 
  the 
  tube. 
  For 
  

   shorter 
  bubbles 
  the 
  measured 
  values 
  are, 
  as 
  would 
  be 
  ex- 
  

   pected, 
  greater 
  than 
  those 
  calculated 
  from 
  these 
  equations. 
  

  

  

  