﻿Long 
  Air-Bubbles 
  in 
  a 
  Vertical 
  Tube. 
  953 
  

  

  and 
  the 
  mean 
  diameter, 
  although 
  increasing 
  with 
  length, 
  

   not 
  altering 
  greatly. 
  

  

  The 
  body 
  of 
  the 
  bubble, 
  although 
  for 
  convenience 
  termed 
  

   cylindrical, 
  is 
  not 
  actually 
  of 
  the 
  same 
  diameter 
  throughout, 
  

   but 
  gradually 
  increases 
  to 
  a 
  maximum 
  at 
  its 
  lower 
  extremity. 
  

  

  If 
  the 
  bore 
  of 
  the 
  tube 
  exceeds 
  about 
  1 
  cm., 
  such 
  a 
  bubble 
  

   shows 
  a 
  beautiful 
  series 
  of 
  well-defined 
  waves 
  or 
  ripples 
  

   around 
  the 
  lower 
  portion 
  of 
  its 
  barrel 
  (PI. 
  XX. 
  figs. 
  2 
  

   &"3). 
  These 
  are 
  stationary 
  relative 
  to 
  the 
  surface 
  of 
  the 
  

   bubble, 
  and, 
  when 
  the 
  length 
  of 
  the 
  latter 
  does 
  not 
  exceed 
  

   the 
  bore 
  of 
  the 
  tube, 
  are 
  of 
  comparatively 
  large 
  amplitude 
  

   and 
  length 
  and 
  extend 
  over 
  the 
  whole 
  length 
  of 
  the 
  bubble. 
  

   As 
  the 
  length 
  increases, 
  the 
  wave-length 
  and 
  amplitude 
  and 
  

   the 
  extent 
  of 
  surface 
  covered 
  by 
  the 
  ripples 
  diminish 
  rapidly, 
  

   while 
  with 
  a 
  given 
  length 
  of 
  bubble 
  the 
  wave-length 
  

   diminishes 
  with 
  an 
  increase 
  in 
  the 
  bore 
  of 
  the 
  tube. 
  Thus 
  

   with 
  a 
  bubble 
  5 
  cm. 
  long 
  experiment 
  shows 
  that 
  the 
  wave- 
  

   length 
  approximates 
  to 
  '075 
  cm. 
  in 
  a 
  tube 
  of 
  1*25 
  cm. 
  bore; 
  

   to 
  '05 
  cm. 
  with 
  a 
  bore 
  of 
  2'5 
  cm.; 
  and 
  to 
  '045 
  cm. 
  with 
  a 
  

   bore 
  of 
  5 
  cm. 
  

  

  If 
  the 
  bore 
  is 
  less 
  than 
  about 
  1 
  cm. 
  the 
  ripple 
  formation 
  

   is 
  somewhat 
  peculiar. 
  Immediately 
  ahead 
  of 
  the 
  stern 
  of 
  the 
  

   bubble 
  a 
  ripple 
  consisting 
  of 
  a 
  single 
  depression 
  of 
  compa- 
  

   ratively 
  large 
  amplitude 
  and 
  length 
  (PL 
  XX. 
  fig. 
  1) 
  is 
  formed, 
  

   and 
  for 
  lengths 
  greater 
  than 
  about 
  two 
  diameters 
  even 
  this 
  

   is 
  not 
  fully 
  developed. 
  Where 
  the 
  bubble 
  passes 
  any 
  slight 
  

   roughness 
  in 
  the 
  interior 
  surface 
  of 
  the 
  tube, 
  however, 
  a 
  

   series 
  of 
  true 
  ripples 
  of 
  very 
  much 
  smaller 
  pitch 
  make 
  their 
  

   appearance. 
  

  

  2. 
  Experimental 
  Data. 
  — 
  With 
  a 
  view 
  of 
  examining 
  these 
  

   phenomena 
  in 
  the 
  case 
  of 
  air-bubbles 
  in 
  motion 
  through 
  

   water, 
  and 
  of 
  comparing 
  experimental 
  results 
  with 
  those 
  

   deduced 
  from 
  calculations, 
  the 
  experiments 
  to 
  be 
  described 
  

   have 
  been 
  carried 
  out 
  on 
  a 
  series 
  of 
  glass 
  tubes 
  with 
  diameters 
  

   ranging 
  from 
  '420 
  cm. 
  to 
  7' 
  78 
  cm. 
  Each 
  tube 
  was 
  mounted 
  

   vertically 
  ; 
  an 
  air-bubble 
  was 
  introduced 
  by 
  means 
  of 
  a 
  

   rubber 
  bulb 
  at 
  its 
  lower 
  end 
  ; 
  and, 
  when 
  the 
  motion 
  had 
  

   become 
  steady, 
  the 
  time 
  taken 
  to 
  traverse 
  a 
  known 
  dis- 
  

   tance 
  was 
  measured 
  by 
  chronograph. 
  In 
  the 
  case 
  of 
  four 
  

   tubes, 
  of 
  diameters 
  - 
  788, 
  1'680, 
  2*695, 
  and 
  5'09 
  cmm., 
  instan- 
  

   taneous 
  photographs 
  having 
  an 
  exposure 
  of 
  1/1000 
  second 
  

   were 
  taken 
  of 
  bubbles 
  of 
  various 
  lengths 
  up 
  to 
  about 
  8 
  cm. 
  

   Figs. 
  1-3 
  are 
  typical 
  of 
  these. 
  The 
  resulting 
  negatives 
  were 
  

   then 
  projected 
  on 
  to 
  a 
  screen, 
  and 
  the 
  wave-lengths 
  were 
  

   measured 
  from 
  the 
  magnified 
  image 
  thus 
  obtained. 
  

  

  The 
  temperature 
  of 
  the 
  water 
  during 
  the 
  experiments 
  

   Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  156. 
  Dec. 
  1913. 
  3 
  T 
  

  

  