﻿Problems 
  of 
  Evaporation. 
  277 
  

  

  would 
  be 
  2'irkcYo 
  *, 
  where 
  c 
  is 
  the 
  electrostatic 
  capacity 
  o£ 
  a 
  

   disk 
  of 
  the 
  dimension 
  of 
  the 
  stoma, 
  and 
  from 
  all 
  the 
  stomata 
  

   on 
  a 
  leaf 
  of 
  area 
  A 
  it 
  would 
  be 
  2Trk?i 
  2 
  cY 
  A, 
  if 
  they 
  did 
  not 
  

   inHuence 
  one 
  another. 
  On 
  the 
  other 
  hand, 
  the 
  evaporation 
  

   in 
  unit 
  time 
  from 
  the 
  whole 
  surface 
  of 
  a 
  leaf 
  when 
  completely 
  

   wet 
  is 
  47r&CV 
  . 
  The 
  ratio 
  of 
  these 
  two 
  rates 
  is 
  of 
  order 
  

   n 
  2 
  aA/2l, 
  or 
  practically 
  n 
  2 
  al. 
  Now, 
  taking 
  I 
  to 
  be 
  3 
  cm., 
  

   and 
  a 
  = 
  0*00053 
  cm., 
  it 
  follows 
  that 
  n 
  2 
  al 
  is 
  unity 
  if 
  n 
  2 
  is 
  as 
  

   large 
  as 
  600. 
  Hence, 
  if 
  there 
  are 
  more 
  than 
  600 
  stomata 
  

   per 
  square 
  centimetre, 
  the 
  rate 
  of 
  evaporation 
  from 
  them 
  

   will 
  be 
  greater 
  than 
  that 
  from 
  the 
  whole 
  surface 
  of 
  a 
  wet 
  

   leaf, 
  which 
  is 
  absurd- 
  If 
  follows 
  that 
  evaporation 
  must 
  be 
  

   enormously 
  restricted 
  by 
  the 
  presence 
  of 
  other 
  stomata. 
  

   Brown 
  and 
  Escombe 
  have 
  stated 
  that 
  " 
  the 
  interference 
  of 
  

   the 
  density 
  shells 
  of 
  small 
  holes 
  set 
  at 
  10 
  diameters 
  or 
  more 
  

   apart 
  is 
  small, 
  each 
  hole 
  beyond 
  this 
  limit 
  acting 
  almost 
  

   independently 
  according 
  to 
  the 
  diameter 
  law.' 
  5 
  The 
  above 
  

   result 
  shows 
  that 
  this 
  is 
  erroneous 
  | 
  ; 
  in 
  fact, 
  the 
  authors 
  

   themselves 
  imply 
  its 
  error 
  in 
  the 
  diagram 
  they 
  give 
  of 
  the 
  

   lines 
  of 
  flow 
  through 
  a 
  multiperforate 
  septum, 
  when 
  they 
  

   make 
  them 
  become 
  approximately 
  parallel 
  at 
  a 
  short 
  distance 
  

   from 
  the 
  septum. 
  

  

  Again, 
  taking 
  n 
  2 
  = 
  33000/cm. 
  2 
  and 
  Z 
  = 
  3 
  cm., 
  we 
  see 
  that 
  

   n 
  2 
  al 
  is 
  greater 
  than 
  unity 
  unless 
  a 
  is 
  less 
  than 
  10 
  ~ 
  5 
  cm. 
  

   Hence 
  we 
  shall 
  still 
  have 
  the 
  result 
  that 
  the 
  evaporation 
  is 
  

   practically 
  independent 
  of 
  the 
  opening 
  of 
  the 
  stomata 
  as 
  long 
  

   as 
  a 
  exceeds 
  this 
  limit 
  ; 
  in 
  other 
  words, 
  until 
  the 
  stomata 
  

   contract 
  to 
  ^ 
  of 
  their 
  original 
  diameter, 
  the 
  rate 
  of 
  

   evaporation 
  will 
  be 
  practically 
  independent 
  of 
  the 
  diameter 
  \ 
  ; 
  

   when 
  they 
  have 
  closed 
  still 
  further 
  it 
  will 
  decrease, 
  and 
  will 
  

   finally 
  vanish 
  when 
  they 
  are 
  quite 
  closed. 
  This 
  appears 
  to 
  

   contain 
  the 
  answer 
  to 
  Sir 
  F. 
  Darwin's 
  criticism 
  § 
  of 
  some 
  

   results 
  of 
  Lloyd 
  ||. 
  Lloyd 
  has 
  stated 
  that 
  the 
  regulatory 
  

   function 
  of 
  stomata 
  is 
  almost 
  nil, 
  which 
  Sir 
  F. 
  Darwin 
  

  

  * 
  We 
  must 
  have 
  2 
  instead 
  of 
  4, 
  as 
  evaporation 
  can 
  only 
  take 
  place 
  

   from 
  one 
  side 
  of 
  the 
  stoma. 
  

  

  t 
  In 
  Brown 
  and 
  Esconibe's 
  experiments 
  with 
  multiperforate 
  septa 
  

   the 
  radius 
  a 
  was 
  0*019 
  cm., 
  n 
  2 
  was 
  100 
  to 
  2*77, 
  and 
  I 
  about 
  2 
  cm., 
  

   making 
  n 
  2 
  al 
  equal 
  to 
  about 
  4 
  at 
  the 
  most, 
  and 
  in 
  most 
  cases 
  much 
  

   smaller. 
  The 
  results 
  are 
  therefore 
  irrelevant 
  to 
  the 
  case 
  of 
  a 
  leaf. 
  

  

  % 
  Brown 
  and 
  Escombe, 
  Phil. 
  Trans. 
  193 
  B. 
  p. 
  278 
  (1900), 
  say 
  that 
  

   stomata 
  can 
  close 
  to 
  y$ 
  of 
  their 
  diameter 
  without 
  affecting 
  assimilation. 
  

  

  § 
  " 
  The 
  Eelation 
  between 
  Transpiration 
  and 
  Stomatal 
  Aperture," 
  

   Phil. 
  Trans. 
  207 
  B. 
  p. 
  413 
  (1915-16). 
  

  

  II 
  F. 
  E. 
  Lloyd, 
  " 
  The 
  Physiology 
  of 
  Stomata/' 
  Carnegie 
  Institution, 
  

   1908. 
  

  

  