﻿Problems 
  of 
  Evaporation, 
  279 
  

  

  smaller. 
  Thus 
  u, 
  being 
  the 
  velocity 
  within 
  the 
  region 
  to 
  

   which 
  the 
  diffusion 
  from 
  a 
  stoma 
  extends, 
  is 
  much 
  less 
  than 
  

   the 
  velocity 
  oatside. 
  Similarly 
  k 
  is 
  the 
  true 
  coefficient 
  of 
  

   diffusion, 
  about 
  0*24 
  cm. 
  2 
  /sec. 
  The 
  thickness 
  of 
  the 
  layer 
  of 
  

   shearing 
  being 
  40/ 
  U, 
  it 
  fellows 
  that 
  u 
  is 
  of 
  order 
  U 
  2 
  a/40. 
  

   Thus 
  the 
  quantity 
  just 
  obtained 
  is 
  of 
  order 
  100 
  n 
  2 
  ~V 
  (Jcla)i 
  /U 
  , 
  

   which 
  is 
  about 
  100 
  V 
  . 
  It 
  follows 
  by 
  argument 
  similar 
  to 
  

   that 
  used 
  in 
  the 
  case 
  of 
  no 
  wind 
  that 
  the 
  earlier 
  stomata 
  

   saturate 
  the 
  air 
  before 
  the 
  later 
  ones 
  are 
  reached. 
  Thus 
  the 
  

   total 
  evaporation 
  is 
  not 
  very 
  different 
  from 
  that 
  in 
  the 
  case 
  

   where 
  the 
  whole 
  surface 
  of 
  the 
  leaf 
  is 
  wet 
  *, 
  and 
  is 
  therefore 
  

   proportional 
  to 
  I 
  1 
  ' 
  5 
  , 
  where 
  I 
  is 
  now 
  proportional 
  to 
  the 
  linear 
  

   dimensions 
  of 
  the 
  leaf. 
  

  

  This 
  approximation 
  will 
  break 
  down 
  if 
  n 
  2 
  aismuch 
  smaller,. 
  

   for 
  then 
  the 
  residual 
  saturation 
  from 
  the 
  earlier 
  stomata 
  may 
  

   be 
  small 
  compared 
  with 
  V 
  , 
  and 
  the 
  rate 
  of 
  evaporation 
  will 
  

   then 
  be 
  the 
  same 
  as 
  that 
  obtained 
  by 
  summing 
  the 
  results 
  

   for 
  the 
  individual 
  stomata, 
  each 
  being 
  supposed 
  isolated 
  ; 
  

   this 
  sum 
  is 
  27r?i 
  2 
  kpcY 
  A. 
  A 
  similar 
  result 
  may 
  be 
  obtained 
  

   if 
  u/k 
  is 
  much 
  greater. 
  It 
  must 
  always 
  be 
  noted, 
  however, 
  

   that 
  this 
  formula 
  can 
  be 
  applied 
  only 
  when 
  the 
  result 
  it 
  gives 
  

   is 
  less 
  than 
  the 
  rate 
  of 
  evaporation 
  from 
  a 
  wet 
  leaf 
  with 
  the 
  

   wind 
  blowing 
  over 
  it 
  ; 
  otherwise 
  we 
  should 
  again 
  have 
  the 
  

   absurdity 
  of 
  the 
  evaporation 
  from 
  a 
  part 
  being 
  greater 
  than 
  

   that 
  from 
  the 
  whole. 
  

  

  The 
  best 
  method 
  of 
  determining 
  whether 
  it 
  is 
  better 
  to 
  

   employ 
  the 
  sum 
  of 
  the 
  possible 
  evaporations 
  from 
  the 
  

   individual 
  stomata, 
  or 
  to 
  regard 
  the 
  whole 
  surface 
  of 
  the 
  leaf 
  

   as 
  wet, 
  is 
  probably 
  to 
  calculate 
  the 
  rate 
  of 
  evaporation 
  on 
  

   both 
  bases 
  and 
  take 
  the 
  smaller 
  of 
  the 
  two 
  results 
  as 
  

   supplying 
  the 
  correct 
  upper 
  limit 
  to 
  the 
  amount 
  of 
  respiration 
  

   the 
  leaf 
  can 
  perform. 
  Similar 
  remarks 
  wall 
  apply 
  to 
  the 
  

   possible 
  absorption 
  of 
  substances 
  from 
  the 
  air. 
  

  

  It 
  may 
  be 
  remarked 
  that 
  when 
  the 
  number 
  of 
  stomata 
  is 
  

   so 
  large 
  as 
  to 
  make 
  the 
  problem 
  reduce 
  to 
  that 
  of 
  a 
  w 
  r 
  et 
  leaf,, 
  

   the 
  total 
  evaporation 
  is 
  not 
  a 
  function 
  of 
  the 
  number 
  of 
  

   stomata, 
  but 
  that 
  from 
  any 
  single 
  stoma 
  is 
  inversely 
  pro- 
  

   portional 
  to 
  the 
  number. 
  Thus 
  increasing 
  the 
  number 
  

   diminishes 
  the 
  w 
  y 
  ork 
  thrown 
  on 
  any 
  individual, 
  which 
  may 
  

   be 
  of 
  some 
  physiological 
  importance. 
  

  

  The 
  above 
  investigation 
  concerns 
  only 
  the 
  purely 
  physical 
  

  

  * 
  O. 
  Renner, 
  Flora, 
  vol. 
  100. 
  pp. 
  451-547 
  (1910), 
  states 
  on 
  p. 
  485 
  

   that 
  the 
  evaporation 
  from 
  a 
  leaf 
  is 
  the 
  same 
  as 
  that 
  from 
  a 
  water 
  

   surface 
  

  

  