﻿958 
  Prof. 
  A. 
  H. 
  Gibson 
  on 
  the 
  Motion 
  of 
  

  

  Series 
  B. 
  

  

  No 
  

  

  1. 
  

  

  2. 
  

  

  3. 
  

  

  4. 
  

  

  5. 
  

  

  6. 
  

  

  7. 
  

  

  8. 
  

  

  9. 
  

  

  10. 
  

  

  Vel. 
  cm. 
  sec. 
  ... 
  

  

  43-1 
  

  

  •0546 
  

  

  54-5 
  

  

  677 
  

  

  77-8 
  

  

  87-2 
  

  

  106-1 
  

  

  125-8 
  

  

  149-0 
  

  

  197 
  

  

  56-7 
  

  

  

  •052 
  

  

  0546 
  

  

  •057 
  

  

  •0488 
  

  

  •054 
  

  

  •048 
  

  

  •0540 
  

   •037 
  

  

  •0546 
  

   •028 
  

   •029 
  

  

  •069 
  

   •021 
  

   022 
  

  

  •132 
  

   •155 
  

  

  

  , 
  f 
  measured 
  

  

  •175 
  

  

  •150 
  

  

  •109 
  

  

  •086 
  

  

  •070 
  

  

  cm 
  - 
  \ 
  calculated 
  

  

  •180 
  

  

  •155 
  

  

  •112 
  

  

  •086 
  

  

  070 
  

  

  •047 
  

  

  •038 
  

  

  h 
  

  

  •303 
  

  

  •348 
  

  

  •50 
  

  

  •66 
  

  

  •69 
  

  

  1-12 
  

  

  1-45 
  

  

  1-88 
  

  

  330 
  

  

  •852 
  

  

  I 
  

  

  From 
  these 
  results 
  it 
  appears 
  that 
  for 
  such 
  depths 
  of 
  water 
  

   which, 
  as 
  will 
  appear, 
  are 
  less 
  than 
  those 
  obtaining 
  in 
  the 
  

   walls 
  of 
  the 
  bubbles 
  formed 
  in 
  all 
  the 
  tubes 
  of 
  diameter 
  

   exceeding 
  "78 
  cm., 
  the 
  modifying 
  effect 
  of 
  viscosity 
  is 
  very 
  

   small, 
  nor 
  is 
  this 
  appreciably 
  more 
  effective 
  as 
  a 
  disturbing 
  

   factor 
  at 
  the 
  smallest 
  depth 
  ('02 
  cm.) 
  than 
  in 
  those 
  (*05 
  to 
  

   *06 
  cm.) 
  more 
  than 
  twice 
  as 
  great. 
  The 
  mean 
  difference 
  

   between 
  calculated 
  and 
  observed 
  results 
  is 
  about 
  1'5 
  per 
  cent., 
  

   the 
  measured 
  lengths 
  being 
  in 
  general 
  less 
  than 
  those 
  calcu- 
  

   lated. 
  Where 
  the 
  ratio 
  of 
  h-r-l 
  is 
  greater 
  than 
  '5 
  the 
  agree- 
  

   ment 
  is 
  even 
  closer, 
  and 
  as 
  in 
  the 
  case 
  of 
  the 
  bubbles 
  this 
  

   ratio 
  is 
  in 
  general, 
  as 
  will 
  appear, 
  greater 
  than 
  this 
  the 
  

   simple 
  formula 
  (4) 
  , 
  modified 
  where 
  necessary 
  as 
  in 
  (5), 
  will 
  

   be 
  adopted 
  in 
  all 
  calculations. 
  

  

  Before 
  these 
  formulae 
  can 
  be 
  applied 
  to 
  determine 
  the 
  

   wave-length 
  for 
  any 
  particular 
  bubble 
  it 
  is 
  necessary, 
  how- 
  

   ever, 
  to 
  determine 
  the 
  radius 
  r 
  and 
  the 
  velocity 
  v 
  of 
  the 
  

   surrounding 
  fluid, 
  at 
  the 
  point 
  of 
  wave-formation. 
  

  

  These 
  may 
  be 
  deduced 
  with 
  a 
  fair 
  degree 
  of 
  approximation 
  

   from 
  general 
  hydrodynamical 
  considerations, 
  as 
  follows. 
  

  

  If 
  suffixes 
  (1) 
  and 
  (2) 
  refer 
  to 
  points 
  immediately 
  ahead 
  

   and 
  astern 
  of 
  the 
  bubble 
  whose 
  overall 
  length 
  is 
  L 
  cm., 
  the 
  

   equation 
  of 
  energy 
  for 
  flow 
  past 
  the 
  bubble 
  becomes 
  

  

  Loss 
  accompanying 
  change 
  of- 
  

   kinetic 
  energy 
  of 
  flow 
  past 
  

   maximum 
  section 
  of 
  bubble 
  \> 
  +!H 
  2 
  , 
  (6) 
  

   into 
  pressure 
  energy 
  in 
  rear 
  

   I 
  of 
  bubble. 
  

  

  -ST 
  

  

  + 
  L 
  = 
  

  

  P2 
  

  

  where 
  iHg 
  is 
  the 
  resistance 
  to 
  flow 
  through 
  the 
  annular 
  space 
  

   between 
  bubble 
  and 
  tube-wall. 
  Except 
  where 
  the 
  bubble 
  is 
  

   very 
  long 
  (at 
  least 
  18 
  diameters) 
  the 
  clear 
  glassy 
  appearance 
  

  

  