﻿962 
  Prof. 
  A. 
  H. 
  Gibson 
  on 
  the 
  Motion 
  of 
  

  

  loss 
  is, 
  in 
  general, 
  a 
  small 
  fraction 
  of 
  the 
  total 
  loss, 
  any 
  pro- 
  

   portional 
  error 
  which 
  it 
  may 
  involve 
  in 
  the 
  final 
  results 
  will 
  

   be 
  extremely 
  small. 
  In 
  the 
  tube 
  of 
  diameter 
  1'68 
  cm. 
  an 
  

   error 
  of 
  50 
  per 
  cent, 
  in 
  the 
  value 
  of 
  K 
  only 
  involves 
  an 
  error 
  

   of 
  the 
  order 
  of 
  2 
  per 
  cent, 
  in 
  the 
  calculated 
  wave-lengths, 
  

   while 
  for 
  larger 
  tubes 
  the 
  error 
  is 
  even 
  less 
  than 
  this. 
  

  

  As 
  regards 
  the 
  term 
  — 
  - 
  — 
  2 
  , 
  in 
  the 
  general 
  equation 
  of 
  

  

  energy 
  (6), 
  we 
  have 
  

  

  in 
  -ex 
  \r 
  2 
  

  

  ,') 
  <») 
  

  

  where 
  r\ 
  and 
  r 
  2 
  are 
  the 
  radii 
  of 
  curvature 
  of 
  the 
  two 
  ends 
  of 
  

   the 
  bubble. 
  Experiment 
  shows 
  that 
  r 
  2 
  is 
  large 
  compared 
  

   with 
  r 
  l5 
  so 
  that 
  this 
  term, 
  which 
  is 
  always 
  small, 
  may 
  be 
  

  

  2T 
  

  

  written 
  as 
  sensibly 
  equal 
  to 
  ^^ 
  . 
  

  

  Making 
  these 
  substitutions, 
  equation 
  (6) 
  finally 
  becomes 
  

  

  ;- 
  +KL 
  (A^T>- 
  L 
  ( 
  i 
  -^) 
  =o 
  ' 
  • 
  (i5) 
  

  

  ov, 
  since 
  v 
  = 
  V 
  — 
  A 
  — 
  — 
  / 
  

  

  A—a 
  '■ 
  

  

  V» 
  + 
  ^v-^ 
  ? 
  (l-" 
  f 
  U 
  . 
  (16) 
  

   a 
  a 
  12 
  \ 
  otKL/ 
  v 
  y 
  

  

  2T 
  

  

  Writing 
  1— 
  = 
  a, 
  and 
  solving, 
  this 
  gives 
  

  

  2(V 
  2 
  - 
  9 
  ah) 
  ±V 
  I 
  2(V 
  2 
  -guL) 
  ) 
  + 
  V 
  2 
  -^aL" 
  

  

  .... 
  (17) 
  

   Since 
  Tr 
  „,. 
  114-0 
  

  

  v=o4 
  ' 
  6 
  -^TMl2 
  cm 
  ' 
  sec 
  ' 
  

  

  ^"aSSoT' 
  • 
  ' 
  ' 
  ' 
  ' 
  W 
  

  

  where 
  A 
  is 
  in 
  (cm.) 
  2 
  , 
  a' 
  may 
  then 
  be 
  obtained 
  in 
  terms 
  of 
  A. 
  

   The 
  value 
  of 
  v 
  is 
  then 
  given 
  by 
  the 
  relationship 
  

  

  A 
  — 
  a" 
  

  

  