﻿C. 
  Barus 
  — 
  Motion 
  of 
  a 
  Submerged 
  Index 
  Thread, 
  etc. 
  139 
  

  

  Art. 
  XIV. 
  — 
  The 
  Motion 
  of 
  a 
  Submerged 
  Index 
  Thread 
  of 
  

   Mercury 
  in 
  the 
  lapse 
  of 
  Time 
  y 
  by 
  0. 
  Barus. 
  

  

  1. 
  If 
  a 
  short 
  thread 
  of 
  mercury 
  M 
  is 
  used 
  under 
  water 
  as 
  

   an 
  index 
  in 
  the 
  vertical 
  stem 
  of 
  a 
  bulb 
  B, 
  it 
  is 
  a 
  common 
  

   observation 
  to 
  find 
  that 
  the 
  mercury 
  will 
  gradually 
  creep 
  down- 
  

   ward 
  into 
  the 
  bulb. 
  Thus 
  to 
  take 
  the 
  case 
  of 
  an 
  old 
  Oersted 
  

   piezometer 
  bulb 
  (capacity 
  35 
  cm3 
  ) 
  surmounted 
  by 
  a 
  stem 
  0*l 
  cm 
  in 
  

   diameter 
  internally 
  and 
  exposed 
  to 
  variations 
  of 
  atmospheric 
  

   temperature, 
  the 
  positions 
  of 
  the 
  mercury 
  meniscus 
  were 
  (neg- 
  

   lecting 
  intermediate 
  observations) 
  

  

  Top 
  

  

  meniscus 
  

  

  1896, 
  Feb. 
  

  

  Temp. 
  17° 
  C. 
  

  

  9 
  10 
  h 
  

  

  10 
  10 
  h 
  

  

  11 
  15 
  h 
  

  

  12 
  12 
  h 
  

  

  1'2< 
  

  

  Bottom 
  

  

  meniscus 
  

  

  3'8 
  C 
  

  

  1.4° 
  

   15° 
  

   19° 
  

   17° 
  

  

  3-1 
  

   2-5 
  

   2-1 
  

   2-9 
  

  

  5-7 
  

   5-1 
  

   4-7 
  

   5*5 
  

  

  Since 
  the 
  thread 
  returns 
  to 
  the 
  same 
  tem- 
  

   perature 
  on 
  the 
  12th 
  as 
  on 
  the 
  8th 
  of 
  Feb- 
  

   ruary, 
  1896, 
  the 
  motion 
  of 
  the 
  thread 
  down- 
  

   ward 
  during 
  the 
  intervening 
  4 
  days 
  and 
  3 
  

   hours 
  (say 
  100 
  hours) 
  was 
  l'7 
  cm 
  . 
  

  

  From 
  this 
  it 
  apparently 
  follows 
  that 
  there 
  

   must 
  be 
  leakage 
  of 
  liquid 
  around 
  the 
  mer- 
  

   cury 
  and 
  that 
  a 
  thin 
  cylindrical 
  shell 
  of 
  

   liquid 
  may 
  be 
  sought 
  for, 
  between 
  the 
  

   thread 
  of 
  mercury 
  and 
  the 
  inner 
  wall 
  of 
  the 
  

   glass 
  stem. 
  The 
  viscosity 
  of 
  mercury 
  being 
  

   larger 
  than 
  that 
  of 
  water, 
  this 
  motion 
  will 
  

   persist 
  in 
  the 
  main 
  by 
  shearing 
  the 
  shell 
  of 
  

   water 
  in 
  question. 
  Under 
  these 
  circum- 
  

   stances 
  (accepted 
  as 
  a 
  first 
  hypothesis) 
  the 
  

   condition 
  of 
  motion 
  may 
  be 
  computed. 
  

  

  Let 
  r 
  be 
  the 
  radius 
  of 
  the 
  tube, 
  8r 
  the 
  

   thickness 
  of 
  the 
  shell 
  of 
  water 
  subjected 
  to 
  

   a 
  cylindrical 
  shear. 
  Let 
  I 
  be 
  the 
  length 
  of 
  the 
  thread 
  of 
  mer- 
  

   cury, 
  t 
  the 
  time 
  in 
  which 
  the 
  thread 
  creeps 
  down 
  the 
  length 
  

   hi. 
  Then 
  the 
  tangential 
  stress 
  shearing 
  the 
  film 
  is 
  per 
  unit 
  of 
  

   area 
  irrH 
  13*6 
  g/2irrl 
  — 
  6700 
  r 
  nearly, 
  when 
  g 
  is 
  the 
  accelera- 
  

   tion 
  of 
  gravity. 
  On 
  the 
  other 
  hand, 
  the 
  rate 
  at 
  which 
  the 
  

   shear 
  is 
  increased 
  is 
  in 
  the 
  same 
  c.g.s. 
  units 
  8l/tSr. 
  Therefore 
  if 
  

   r) 
  be 
  the 
  viscosity 
  of 
  water 
  at 
  20° 
  (about 
  -01 
  say), 
  

  

  8r 
  = 
  v 
  8^/6700 
  tr 
  = 
  -0000015 
  M/tr, 
  nearly. 
  

  

  In 
  the 
  above 
  piezometer 
  8/ 
  = 
  r7 
  cm 
  , 
  r 
  = 
  -05 
  cm 
  , 
  t 
  = 
  36X10 
  4 
  sec. 
  

   Hence 
  Sr 
  = 
  Llxl0" 
  10cm 
  . 
  If, 
  therefore, 
  the 
  film 
  were 
  uniform, 
  

  

  