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  XXX. 
  Some 
  Problems 
  of 
  Evaporation. 
  By 
  Harold 
  

   Jeffreys, 
  M.A., 
  D.Sc, 
  'Fellow 
  of 
  St. 
  John's 
  College, 
  

   Cambridge*. 
  

  

  THE 
  problem 
  of 
  evaporation 
  is 
  practically 
  one 
  of 
  gaseous 
  

   diffusion 
  : 
  that 
  is 
  to 
  say, 
  if 
  V 
  denote 
  the 
  fraction 
  of 
  

   the 
  density 
  o£ 
  the 
  air 
  at 
  any 
  point 
  that 
  is 
  due 
  to 
  water 
  

   vapour, 
  Y 
  will 
  vary 
  from 
  time 
  to 
  time 
  and 
  place 
  to 
  place 
  

   according 
  to 
  the 
  equation 
  

  

  where 
  k 
  is 
  the 
  effective 
  coefficient 
  of 
  diffusion, 
  / 
  the 
  time, 
  

   and 
  djdt 
  denotes 
  the 
  total 
  differential 
  following 
  a 
  particle 
  of 
  

   the 
  fluid. 
  In 
  general 
  V, 
  as 
  above 
  defined, 
  will 
  be 
  referred 
  

   to 
  as 
  the 
  concentration. 
  

  

  Then 
  if 
  u, 
  v, 
  w 
  be 
  the 
  components 
  of 
  velocity 
  and 
  V 
  be 
  

   supposed 
  expressed 
  as 
  a 
  function 
  of 
  #, 
  ?/, 
  z, 
  and 
  t, 
  

  

  dV 
  dV 
  dV 
  dV 
  sv 
  ... 
  

  

  -dt=-W+ 
  u 
  ^ 
  +v 
  Ty 
  +W 
  *i-- 
  • 
  ■ 
  (2) 
  

  

  The 
  boundary 
  conditions 
  are 
  that 
  the 
  air 
  in 
  contact 
  with 
  

   a 
  liquid 
  surface 
  is 
  saturated, 
  so 
  that 
  V 
  is 
  there 
  equal 
  to 
  the 
  

   concentration 
  in 
  saturated 
  air 
  at 
  the 
  temperature 
  of 
  the 
  

   liquid, 
  and 
  that 
  at 
  a 
  great' 
  distance 
  from 
  any 
  liquid 
  V 
  tends 
  

   to 
  a 
  finite 
  value. 
  

  

  The 
  equation 
  (1) 
  is 
  identical 
  in 
  form 
  with 
  those 
  that 
  

   determine 
  the 
  transference 
  of 
  heat 
  and 
  momentum 
  ; 
  and 
  

   when 
  the 
  transference 
  is 
  due 
  entirely 
  to 
  turbulence 
  the 
  

   quantity 
  k 
  has 
  the 
  same 
  value 
  in 
  all 
  three 
  cases 
  f. 
  In 
  contact 
  

   with 
  a 
  solid 
  or 
  liquid 
  surface, 
  on 
  the 
  other 
  hand, 
  the 
  velocity 
  

   of 
  the 
  medium 
  is 
  zero, 
  and 
  h 
  diminishes 
  to 
  the 
  value 
  it 
  has 
  

   when 
  there 
  is 
  no 
  turbulence 
  : 
  that 
  is 
  to 
  say, 
  in 
  the 
  evaporation 
  

   problem 
  k 
  is 
  equal 
  to 
  the 
  coefficient 
  of 
  diffusion 
  of 
  the 
  

   vapour 
  ; 
  in 
  the 
  thermal 
  problem 
  it 
  is 
  the 
  thermometric 
  con- 
  

   ductivity 
  of 
  air 
  ; 
  and 
  in 
  the 
  equations 
  of 
  motion 
  it 
  is 
  the 
  

   kinematic 
  viscosity 
  of 
  air. 
  These 
  three 
  quantities 
  are 
  of 
  

   the 
  same 
  order 
  of 
  magnitude, 
  but 
  are 
  not 
  equal. 
  When 
  the 
  

   air 
  is 
  at 
  rest 
  k 
  is 
  a 
  constant 
  in 
  all 
  cases 
  and 
  the 
  problem 
  is 
  

   simply 
  that 
  of 
  solving 
  the 
  equation 
  

  

  S 
  = 
  *V'V, 
  (3) 
  

  

  where 
  V 
  2 
  denotes 
  the 
  Laplacian 
  operator. 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  f 
  G. 
  I. 
  Taylor, 
  "Eddy 
  Motion 
  in 
  the 
  Atmosphere," 
  Phil. 
  Trans. 
  

   215 
  A. 
  (1915). 
  

  

  