﻿Lona 
  Air-Bubbles 
  in 
  a 
  Vertical 
  Tube. 
  

  

  957 
  

  

  While 
  there 
  is 
  ample 
  evidence 
  as 
  to 
  the 
  validity 
  of 
  

   formulae 
  (4) 
  and 
  (5) 
  in 
  fairly 
  deep 
  water, 
  where 
  viscosity 
  has 
  

   little 
  apparent 
  effect 
  in 
  modifying 
  wave-length 
  and 
  velocity, 
  

   it 
  is 
  not 
  obvious 
  that 
  this 
  will 
  be 
  true 
  of 
  the 
  case 
  in 
  question, 
  

   where 
  the 
  depth 
  of 
  water 
  on 
  which 
  the 
  ripples 
  are 
  formed 
  is 
  

   extremely 
  small, 
  and 
  where, 
  in 
  consequence, 
  the 
  effect 
  of 
  

   viscosity 
  and 
  of 
  the 
  solid 
  boundaries 
  might 
  be 
  expected 
  to 
  be 
  

   more 
  pronounced. 
  

  

  With 
  a 
  view 
  of 
  investigating 
  this 
  point 
  the 
  following 
  series 
  

   of 
  experiments 
  was 
  carried 
  out. 
  In 
  these 
  a 
  steady 
  stream 
  

   of 
  water 
  from 
  a 
  vertical 
  nozzle 
  was 
  allowed 
  to 
  impinge 
  on 
  

   the 
  centre 
  of 
  a 
  circular 
  horizontal 
  glass 
  plate 
  20 
  cm. 
  in 
  

   diameter, 
  flow 
  taking 
  place 
  radially 
  outwards 
  in 
  all 
  direc- 
  

   tions. 
  The 
  discharge 
  was 
  caught 
  and 
  weighed. 
  The 
  depth 
  of 
  

   the 
  sheet 
  of 
  water 
  was 
  measured 
  at 
  a 
  series 
  of 
  radii 
  by 
  means 
  

   of 
  a 
  spherometer 
  with 
  a 
  needle-point 
  which 
  was 
  gradually 
  

   lowered 
  to 
  make 
  contact 
  with 
  the 
  fluid 
  surface. 
  Ripples 
  

   were 
  then 
  formed 
  at 
  these 
  same 
  radii 
  by 
  means 
  of 
  a 
  needle- 
  

   point, 
  and 
  their 
  length 
  was 
  measured 
  by 
  microscope. 
  The 
  

   estimated 
  depth 
  of 
  water 
  is 
  probably 
  correct 
  to 
  within 
  about 
  

   '015 
  mm., 
  and 
  the 
  estimated 
  wave-length 
  within 
  about*025 
  mm. 
  

  

  In 
  this 
  case 
  both 
  gravity 
  and 
  surface-tension 
  are 
  operative, 
  

   and 
  in 
  deep 
  water 
  formula 
  (4) 
  becomes 
  

  

  „ 
  2 
  _ 
  2 
  ^ 
  T 
  gi 
  

  

  Iffl 
  

  

  ZlT 
  

  

  (4<) 
  

  

  while 
  if 
  the 
  depth 
  is 
  moderate 
  compared 
  with 
  the 
  wave 
  

   length 
  (5) 
  becomes 
  

  

  I 
  (_ 
  TaTI 
  LIT 
  J 
  

  

  2tt1i 
  

   I 
  

  

  • 
  (5') 
  

  

  is 
  nearly 
  

  

  For 
  values 
  of 
  h-r-l 
  greater 
  than 
  one 
  half, 
  tank 
  

  

  equal 
  to 
  unity, 
  and 
  the 
  two 
  formulae 
  become 
  sensibly 
  identical* 
  

   Formula 
  (5') 
  has 
  been 
  used 
  to 
  calculate 
  wave-lengths, 
  h 
  

   being 
  taken 
  as 
  the 
  depth 
  of 
  the 
  undisturbed 
  water, 
  with 
  the 
  

   following 
  results. 
  

  

  Series 
  A. 
  

  

  No 
  1. 
  

  

  2. 
  3. 
  

  

  Mean 
  vel. 
  cm. 
  per 
  sec 
  53'7 
  

  

  62-2 
  74-0 
  

  

  h 
  cm 
  ... 
  -090S 
  

  

  •0198 
  

  

  •0183 
  

  

  

  

  I 
  

   cm. 
  

  

  ' 
  measured 
  '120 
  

  

  •095 
  

  

  •073 
  

  

  calculated 
  -122 
  

  

  •096 
  

  

  •076 
  

  

  i 
  ™ 
  

  

  •195 
  -244 
  

  

  