﻿952 
  Prof. 
  A. 
  H. 
  Gibson 
  on 
  the 
  Motion 
  of 
  

  

  However, 
  our 
  result 
  can 
  only 
  be 
  taken 
  as 
  preliminary. 
  

   The 
  calculated 
  value, 
  as 
  will 
  be 
  seen 
  from 
  equation 
  (2), 
  

   depends 
  on 
  the 
  square 
  of 
  \, 
  and 
  this 
  constant 
  is 
  only 
  known 
  

   to 
  within 
  a 
  few 
  per 
  cent. 
  We 
  hope 
  to 
  make 
  experiments 
  to 
  

   determine 
  X 
  more 
  exactly 
  and 
  also 
  to 
  make 
  a 
  fuller 
  investiga- 
  

   tion 
  of 
  the 
  effusion 
  rate. 
  

  

  We 
  are 
  greatly 
  indebted 
  to 
  Dr. 
  N. 
  Bohr 
  for 
  drawing 
  our 
  

   attention 
  to 
  this 
  method 
  of 
  determining 
  molecular 
  weights, 
  

   and 
  to 
  Prof. 
  E. 
  Rutherford 
  for 
  his 
  kind 
  interest 
  in 
  the 
  

   experiments. 
  

  

  LXXXIV. 
  On 
  the 
  Motion 
  of 
  Long 
  Air-bubbles 
  in 
  a 
  Vertical 
  

   Tube. 
  By 
  Prof. 
  A. 
  H. 
  Gibson, 
  D.Sc, 
  University 
  College, 
  

   Dundee*. 
  

  

  [Plate 
  XX.] 
  

  

  1. 
  Introduction. 
  

  

  2. 
  Experimental 
  data. 
  

  

  3. 
  Velocity 
  of 
  long 
  bubbles. 
  

  

  4. 
  Ripple 
  formation 
  on 
  surface 
  of 
  a 
  long 
  bubble. 
  

  

  5. 
  Limiting 
  length 
  for 
  stability 
  of 
  motion. 
  

  

  1. 
  npnE 
  motion 
  of 
  an 
  air-bubble 
  rising, 
  under 
  gravity, 
  

   JL 
  through 
  the 
  liquid 
  in 
  a 
  vertical 
  tube 
  depends 
  largely 
  

   on 
  its 
  dimensions, 
  both 
  absolute 
  and 
  relative 
  to 
  that 
  of 
  the 
  

   tube. 
  

  

  If 
  the 
  bubble 
  is 
  very 
  small 
  its 
  form 
  is 
  approximately 
  

   spherical 
  and 
  its 
  motion 
  steady. 
  As 
  the 
  size 
  is 
  increased 
  the 
  

   shape 
  changes, 
  becoming 
  more 
  and 
  more 
  contracted 
  in 
  a 
  

   vertical 
  direction, 
  while 
  the 
  curvature 
  of 
  the 
  lower 
  surface 
  

   becomes 
  much 
  less 
  than 
  that 
  of 
  the 
  upper 
  surface. 
  When 
  in 
  

   a 
  tube 
  of 
  moderate 
  dimensions, 
  these 
  changes 
  become 
  accen- 
  

   tuated. 
  The 
  motion 
  of 
  such 
  a 
  bubble, 
  of 
  diameter 
  between 
  

   one-fourth 
  and 
  two-thirds 
  that 
  of 
  the 
  tube, 
  is 
  very 
  irregular. 
  

   Not 
  only 
  does 
  it 
  zigzag 
  across 
  the 
  tube 
  from 
  side 
  to 
  side, 
  but 
  

   its 
  motion 
  is 
  accompanied 
  by 
  violent 
  oscillations 
  about 
  a 
  

   horizontal 
  axis 
  which 
  show, 
  in 
  a 
  striking 
  manner, 
  the 
  periodic 
  

   variation 
  of 
  the 
  magnitude 
  and 
  distribution 
  of 
  the 
  pressure 
  

   on 
  its 
  lower 
  face 
  due 
  to 
  eddy 
  formations 
  in 
  its 
  rear. 
  As 
  the 
  

   size 
  is 
  further 
  increased 
  the 
  irregularities 
  are 
  diminished, 
  

   until 
  when 
  the 
  diameter 
  is 
  about 
  *75 
  times 
  that 
  of 
  the 
  tube 
  

   the 
  bubble 
  begins 
  to 
  adopt 
  a 
  more 
  or 
  less 
  cylindrical 
  form 
  

   with 
  an 
  ogival 
  head 
  and 
  flat 
  stern, 
  and 
  the 
  motion 
  becomes 
  

   steady. 
  Any 
  further 
  increase 
  in 
  the 
  volume 
  is 
  mainly 
  effec- 
  

   tive 
  in 
  increasing 
  the 
  length 
  of 
  the 
  cylindrical 
  portion 
  of 
  

   the 
  body, 
  the 
  form 
  of 
  the 
  head 
  remaining 
  sensibly 
  unchanged, 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  