﻿C. 
  Barns 
  — 
  Diffusion 
  of 
  Air 
  through 
  Water. 
  399 
  

  

  ture 
  in 
  v 
  is, 
  at 
  20° 
  and 
  one 
  atmosphere, 
  about 
  3*6°. 
  Even 
  if 
  

   the 
  diver 
  falls 
  quietly 
  to 
  the 
  bottom 
  of 
  the 
  vessel 
  of 
  about 
  a 
  

   foot 
  in 
  height, 
  the 
  temperature-increment 
  is 
  adiabatically 
  *23°. 
  

   Good 
  measurement, 
  on 
  the 
  other 
  hand, 
  requires 
  that 
  the 
  tem- 
  

   perature 
  of 
  v 
  should 
  be 
  known 
  to 
  at 
  least 
  '1° 
  C. 
  R 
  is 
  so 
  

   placed 
  that 
  the 
  diver 
  permanently 
  floats 
  at 
  the 
  top 
  and 
  remains 
  

   permanently 
  sunk 
  at 
  the 
  bottom 
  of 
  A. 
  Very 
  slight 
  suction 
  

   and 
  pressure 
  alternating 
  now 
  suffice 
  to 
  find 
  the 
  level 
  of 
  unstable 
  

   equilibrium. 
  After 
  some 
  practice 
  this 
  adjustment 
  may 
  be 
  

   made 
  within 
  a 
  millimeter. 
  A 
  steel 
  ring 
  sliding 
  on 
  A 
  (kept 
  in 
  

   vertical 
  position) 
  will 
  indicate 
  this 
  position, 
  so 
  that 
  the 
  head, 
  A, 
  

   may 
  afterwards 
  be 
  read 
  off 
  at 
  pleasure 
  by 
  the 
  cathetometer 
  or 
  

   directly. 
  Immediately 
  after 
  finding 
  the 
  level 
  in 
  question 
  it 
  is 
  

   best 
  to 
  sink 
  the 
  thermometer 
  into 
  the 
  region 
  to 
  get 
  its 
  tem- 
  

   perature. 
  

  

  The 
  conditions 
  of 
  floatation 
  here 
  involved 
  follow 
  roughly 
  

   from 
  hydrostatics 
  and 
  Boyle's 
  law, 
  viz 
  : 
  

  

  where 
  ^T 
  is 
  the 
  height 
  of 
  the 
  barometer 
  at 
  0° 
  C, 
  p 
  m 
  the 
  normal 
  

   density 
  of 
  mercury, 
  p 
  lc 
  that 
  of 
  the 
  head 
  of 
  water, 
  h. 
  Further- 
  

   more 
  R 
  is 
  the 
  gas 
  constant, 
  m 
  the 
  mass 
  and 
  r 
  the 
  absolute 
  

   temperature 
  of 
  the 
  gas 
  in 
  v, 
  M 
  the 
  mass 
  and 
  p 
  g 
  the 
  density 
  of 
  

   the 
  walls 
  of 
  the 
  diver. 
  The 
  temperature 
  in 
  h 
  is 
  taken 
  as 
  the 
  

   same 
  as 
  that 
  of 
  the 
  water 
  in 
  A. 
  Equation 
  (1) 
  is 
  for 
  dry 
  gases 
  ; 
  

   for 
  wet 
  gases 
  ])' 
  Jp 
  lc 
  g 
  is 
  to 
  be 
  added, 
  if 
  p' 
  is 
  the 
  vapor 
  pressure 
  

   of 
  water. 
  

  

  It 
  will 
  be 
  at 
  once 
  seen 
  that 
  there 
  are 
  grave 
  objections 
  against 
  

   making 
  the 
  float 
  of 
  glass 
  : 
  in 
  such 
  a 
  case 
  the 
  temperature, 
  t, 
  

   cannot 
  be 
  accurately 
  found, 
  and 
  this 
  is 
  the 
  critically 
  important 
  

   datum. 
  A 
  metal 
  vessel 
  is 
  therefore 
  preferable, 
  in 
  which 
  case 
  

   moreover 
  the 
  value 
  p 
  w 
  /p 
  g 
  will 
  be 
  small 
  enough 
  to 
  make 
  the 
  

   coefficient 
  of 
  r 
  in 
  an 
  empirical 
  equation 
  constant. 
  Unfortu- 
  

   nately 
  the 
  level 
  of 
  the 
  inclosed 
  liquid 
  is 
  not 
  at 
  once 
  given. 
  

   The 
  temperature 
  discrepancy 
  also 
  requires 
  the 
  exclusion 
  of 
  

   bulky 
  non-conducting 
  air 
  masses 
  in 
  v. 
  Other 
  conditions 
  of 
  

   sensitiveness 
  are 
  obvious. 
  

  

  If 
  air 
  diffuses 
  out 
  of 
  the 
  apparatus, 
  m/M 
  will 
  decrease 
  ; 
  in 
  

   other 
  words, 
  the 
  coefficient 
  of 
  temperature, 
  t, 
  in 
  the 
  empiric 
  

   equation 
  

  

  h 
  + 
  H^= 
  A+£(t-20), 
  (2) 
  

  

  Pw 
  

  

  modeled 
  after 
  (1), 
  i. 
  e., 
  B 
  will 
  decrease. 
  A 
  is 
  a 
  constant 
  and 
  

   observations 
  are 
  taken 
  near 
  20° 
  C. 
  Xow 
  B 
  can 
  be 
  found 
  with 
  

   ease 
  from 
  an 
  even 
  number 
  of 
  measurements 
  by 
  differences, 
  

  

  