﻿276 
  Dr. 
  H. 
  Jeffreys 
  on 
  some 
  

  

  whether 
  carbon 
  dioxide 
  can 
  by 
  simple 
  diffusion 
  enter 
  these 
  

  

  holes 
  as 
  fast 
  as 
  is 
  indicated 
  by 
  the 
  observed 
  rate 
  of 
  carbon 
  

  

  assimilation. 
  I£ 
  the 
  rate 
  of 
  absorption 
  were 
  proportional 
  to 
  

  

  the 
  area 
  of 
  the 
  holes 
  it 
  could 
  not 
  be 
  great 
  enough, 
  but 
  if 
  

  

  each 
  hole 
  absorbed 
  at 
  a 
  rate 
  proportional 
  to 
  its 
  radius 
  (this 
  

  

  being 
  the 
  correct 
  law 
  for 
  an 
  isolated 
  hole 
  as 
  small 
  as 
  a 
  stoma) 
  

  

  the 
  total 
  absorption 
  would 
  be 
  much 
  greater 
  than 
  is 
  required. 
  

  

  Some 
  points 
  in 
  the 
  theory 
  still 
  require 
  examination 
  ; 
  it 
  is 
  

  

  not 
  obvious 
  that 
  the 
  surrounding 
  stomata 
  will 
  not 
  interfere 
  

  

  with 
  the 
  action 
  of 
  any 
  individual 
  to 
  an 
  important 
  extent, 
  

  

  and 
  a 
  wind 
  blowing 
  over 
  the 
  surface, 
  though 
  unimportant 
  

  

  for 
  a 
  single 
  stoma, 
  may 
  be 
  important 
  when 
  there 
  are 
  thousands 
  

  

  of 
  them 
  spread 
  over 
  a 
  considerable 
  area. 
  The 
  problem 
  is 
  

  

  mathematically 
  the 
  same 
  as 
  that 
  of 
  evaporation 
  from 
  the 
  

  

  stomata, 
  by 
  which 
  it 
  will 
  be 
  replaced. 
  

  

  First, 
  consider 
  the 
  leaf 
  to 
  be 
  in 
  a 
  steady 
  state 
  and 
  

   wind 
  absent. 
  Let 
  the 
  radius 
  of 
  a 
  stoma 
  be 
  a, 
  and 
  the 
  

   number 
  per 
  unit 
  area 
  n 
  2 
  . 
  Then 
  the 
  average 
  distance 
  between 
  

   stomata 
  is 
  of 
  order 
  1/rc, 
  and 
  is 
  large 
  compared 
  with 
  a. 
  The 
  

   value 
  of 
  V 
  over 
  the 
  surface 
  of 
  any 
  stoma 
  is 
  V 
  . 
  Then 
  at 
  a 
  

   distance 
  r 
  from 
  an 
  isolated 
  stoma 
  V 
  is 
  of 
  order 
  V 
  a/r. 
  Now, 
  

   if 
  the 
  stomata 
  acted 
  independently 
  of 
  one 
  another, 
  consider 
  

   some 
  particular 
  stoma. 
  By 
  itself 
  it 
  would 
  make 
  V=V 
  

   over 
  it 
  ; 
  the 
  others 
  will 
  together 
  add 
  to 
  this 
  an 
  amount 
  

  

  2—^-, 
  which 
  is 
  not 
  very 
  different 
  from 
  I 
  I 
  — 
  — 
  n 
  2 
  dS, 
  taken 
  

  

  over 
  the 
  whole 
  surface 
  of 
  the 
  leaf. 
  This 
  is 
  of 
  order 
  27rY 
  an 
  2 
  l, 
  

   where 
  I 
  is 
  of 
  the 
  order 
  of 
  the 
  dimensions 
  of 
  the 
  leaf. 
  Now 
  

   Jorgensen 
  and 
  Stiles 
  give* 
  for 
  a 
  typical 
  case 
  2a 
  = 
  0"00107 
  

   cm.'; 
  n 
  2 
  = 
  33,000/cm. 
  2 
  Thus 
  the 
  addition 
  to 
  Y 
  by 
  the 
  

   neighbouring 
  stomata 
  would 
  be 
  of 
  the 
  order 
  of 
  300 
  V 
  for 
  a 
  

   leaf 
  of 
  radius 
  3 
  cm. 
  This 
  is 
  of 
  course 
  impossible, 
  for 
  V 
  

   cannot 
  be 
  greater 
  than 
  V 
  . 
  The 
  meaning 
  of 
  the 
  result 
  is 
  

   that 
  the 
  surroundings 
  are 
  enough 
  to 
  cause 
  the 
  air 
  at 
  any 
  

   point 
  to 
  be 
  practically 
  saturated, 
  and 
  only 
  a 
  small 
  portion 
  of 
  

   the 
  vapour-pressure 
  over 
  any 
  stoma 
  is 
  maintained 
  by 
  that 
  

   stoma 
  itself. 
  The 
  total 
  evaporation 
  from 
  the 
  surface 
  of 
  a 
  

   leaf 
  is 
  therefore 
  the 
  same 
  as 
  would 
  take 
  place 
  if 
  V 
  were 
  

   equal 
  to 
  V 
  over 
  the 
  whole 
  surface, 
  and 
  its 
  amount 
  is 
  there- 
  

   fore 
  47r&OV 
  , 
  where 
  C 
  is 
  the 
  electrostatic 
  capacity 
  of 
  the 
  

   whole 
  surface 
  of 
  the 
  leaf. 
  

  

  Looking 
  at 
  the 
  matter 
  in 
  another 
  way, 
  the 
  rate 
  of 
  evapor- 
  

   ation 
  from 
  a 
  single 
  stoma 
  uninfluenced 
  by 
  its 
  surroundings 
  

  

  * 
  ' 
  Carbon 
  Assimilation/ 
  p. 
  63. 
  

  

  