﻿432 
  On 
  Transpiration 
  from 
  Leaf- 
  Stomata. 
  

  

  can 
  be 
  well 
  determined 
  ; 
  the 
  wet-leaf 
  limit 
  is 
  then 
  found 
  to 
  

   be 
  the 
  smaller 
  and 
  therefore 
  gives 
  the 
  more 
  useful 
  criterion. 
  

   When 
  the 
  air 
  is 
  in 
  motion 
  the 
  question 
  is 
  much 
  more 
  difficult, 
  

   for 
  while 
  the 
  evaporation 
  from 
  isolated 
  stomata 
  remains 
  prac- 
  

   tically 
  constant 
  with 
  ordinary 
  wind 
  velocities, 
  that 
  from 
  a 
  

   wet 
  leaf 
  increases 
  rapidly 
  with 
  the 
  velocity 
  and 
  may 
  come 
  

   to 
  exceed 
  the 
  isolated-stomata 
  limit. 
  In 
  most 
  particular 
  

   cases 
  it 
  is 
  probably 
  best 
  to 
  find 
  the 
  wet-leaf 
  limit 
  by 
  direct 
  

   experiment, 
  for 
  its 
  theoretical 
  value 
  depends 
  on 
  the 
  wind 
  

   velocity 
  and 
  the 
  amount 
  of 
  turbulence, 
  which 
  are 
  more 
  

   difficult 
  to 
  determine. 
  The 
  isolated-stomata 
  limit 
  can 
  be 
  

   calculated 
  without 
  difficulty 
  from 
  the 
  formula 
  I 
  gave. 
  

  

  I 
  stated 
  in 
  my 
  paper 
  that 
  to 
  decide 
  which 
  limit 
  was 
  the 
  

   more 
  important 
  in 
  a 
  wind 
  depended 
  on 
  the 
  particular 
  circum- 
  

   stances 
  considered. 
  When 
  a 
  wind 
  is 
  blowing 
  over 
  a 
  fixed 
  flat 
  

   surface 
  the 
  air 
  behaves 
  differently 
  in 
  two 
  regions. 
  In 
  contact 
  

   with 
  the 
  surface 
  the 
  velocity 
  is 
  zero, 
  and 
  within 
  a 
  certain 
  

   small 
  distance, 
  estimated 
  by 
  Major 
  Taylor 
  as 
  40/ 
  U 
  centimetres, 
  

   where 
  U 
  is 
  the 
  velocity 
  at 
  a 
  great 
  distance 
  measured 
  in 
  centi- 
  

   metres 
  per 
  second, 
  the 
  motion 
  is 
  purely 
  laminar. 
  The 
  

   velocity 
  at 
  the 
  edge 
  of 
  this 
  layer 
  is 
  a 
  considerable 
  fraction 
  

   of 
  U, 
  say 
  ^U 
  or 
  JU. 
  Within 
  this 
  layer 
  heat 
  is 
  communicated 
  

   by 
  heat-conduction, 
  momentum 
  by 
  ordinary 
  viscosity, 
  and 
  

   gaseous 
  constituents 
  by 
  ordinary 
  diffusion. 
  Outside 
  of 
  it 
  

   the 
  motion 
  ceases 
  to 
  be 
  laminar 
  and 
  becomes 
  turbulent. 
  

   The 
  turbulence 
  causes 
  masses 
  of 
  air 
  to 
  be 
  transported 
  bodily 
  

   for 
  considerable 
  distances 
  in 
  all 
  directions, 
  and 
  their 
  mixture 
  

   with 
  surrounding 
  air 
  causes 
  a 
  great 
  increase 
  in 
  the 
  ease 
  of 
  

   transference 
  of 
  heat, 
  momentum, 
  and 
  gases. 
  The 
  effect 
  of 
  

   this 
  is 
  to 
  add 
  to 
  the 
  coefficients 
  of 
  kinematic 
  viscosity, 
  

   thermometric 
  conductivity, 
  and 
  diffusion 
  the 
  same 
  quantity, 
  

   called 
  the 
  eddy 
  conductivity, 
  which 
  is 
  much 
  greater 
  than 
  any 
  

   of 
  their 
  values 
  in 
  non-turbulent 
  motion. 
  Now 
  the 
  problem 
  

   of 
  evaporation 
  consists 
  of 
  two 
  parts: 
  first, 
  the 
  diffusion 
  across 
  

   the 
  layer 
  of 
  laminar 
  motion, 
  and 
  second, 
  through 
  the 
  tur- 
  

   bulent 
  region. 
  Sir 
  Joseph 
  Larmor 
  neglects 
  the 
  resistance 
  

   to 
  diffusion 
  in 
  this 
  region, 
  thus 
  practically 
  taking 
  the 
  eddy 
  

   conductivity 
  as 
  infinite, 
  which 
  appears 
  to 
  be 
  justifiable 
  in 
  the 
  

   case 
  he 
  considers. 
  In 
  the 
  notation 
  I 
  used 
  previously 
  the 
  

   rate 
  of 
  evaporation 
  on 
  the 
  isolated-stomata 
  hypothesis 
  is 
  

   2irn 
  2 
  kpcY 
  A, 
  and 
  for 
  a 
  circular 
  leaf 
  of 
  radius 
  I 
  and 
  circular 
  

   stomata 
  of 
  radius 
  a 
  this 
  becomes 
  4zTrn 
  2 
  kpal 
  2 
  Y 
  . 
  The 
  wet-leaf 
  

   hypothesis 
  gives 
  3'95/3V 
  (KU7 
  3 
  )2, 
  where 
  K 
  is 
  the 
  eddy 
  con- 
  

   ductivity. 
  The 
  ratio 
  of 
  these 
  is 
  practically 
  -.„,..', 
  . 
  With 
  

   n 
  2 
  =33000/cm. 
  2 
  , 
  a 
  = 
  5x 
  10- 
  4 
  cm., 
  1=5 
  cm., 
  &=0'24 
  cm-Vsec, 
  

  

  