﻿On 
  Transpiration 
  through 
  Leaf- 
  Stomata. 
  351 
  

  

  aperture 
  is 
  isolated 
  from 
  the 
  others 
  and 
  the 
  transpiration 
  occurs 
  

   within 
  its 
  own 
  cylindrical 
  tube 
  of 
  diffusion 
  ; 
  this 
  will 
  not 
  

   sensibly 
  affect 
  the 
  course 
  of 
  the 
  phenomena. 
  The 
  electric 
  

   idea 
  of 
  conductance 
  of 
  the 
  diffusion-current 
  along 
  this 
  path 
  

   is 
  now 
  the 
  appropriate 
  aid 
  to 
  discussion. 
  We 
  can 
  imagine 
  

   the 
  tube 
  prolonged 
  on 
  the 
  other 
  side 
  beyond 
  the 
  stoma, 
  and 
  

   thus 
  consider 
  the 
  parallel 
  case 
  of 
  electric 
  flow 
  along 
  a 
  con- 
  

   ductor 
  having 
  a 
  sharp 
  local 
  constriction 
  representing 
  the 
  

   stoma, 
  whose 
  area 
  is 
  much 
  smaller 
  than 
  the 
  cross-section 
  of 
  

   the 
  conductor. 
  The 
  resistance 
  of 
  the 
  whole 
  tube 
  is 
  propor- 
  

   tional 
  to 
  its 
  length, 
  provided 
  the 
  latter 
  is 
  increased 
  by 
  a 
  

   constant 
  correction 
  in 
  order 
  to 
  include 
  the 
  extra 
  resistance 
  

   arising 
  at 
  the 
  constriction 
  *. 
  The 
  methods 
  by 
  which 
  this 
  

   correction 
  may 
  be 
  practically 
  estimated 
  were 
  developed 
  by 
  

   Lord 
  Rayleigh 
  in 
  1870 
  : 
  cf. 
  'Theory 
  of 
  Sound,' 
  ii. 
  ch. 
  xvi. 
  

   The 
  current 
  being 
  the 
  same 
  all 
  along 
  the 
  tube, 
  the 
  resistance 
  

   in 
  any 
  segment 
  of 
  it 
  is 
  proportional 
  to 
  the 
  fall 
  of 
  head 
  (of 
  

   potential, 
  or 
  of 
  density 
  of 
  diffusing 
  substance) 
  between 
  its 
  

   ends. 
  When 
  the 
  constriction 
  by 
  a 
  transverse 
  barrier 
  is, 
  as 
  

   here, 
  to 
  less 
  than 
  one-fifth 
  of 
  the 
  radius 
  of 
  the 
  tube, 
  it 
  will 
  

   not 
  be 
  far 
  wrong 
  to 
  estimate 
  the 
  tall 
  of 
  head 
  across 
  the 
  con- 
  

   striction 
  as 
  if 
  the 
  enclosing 
  tube 
  were 
  absent. 
  This 
  procedure 
  

   leads, 
  on 
  the 
  same 
  lines 
  as 
  in 
  Brown 
  and 
  Escombe 
  quoted 
  by 
  

   Dr. 
  Jeffreys 
  (p. 
  275), 
  for 
  a 
  circular 
  constriction 
  of 
  radius 
  a, 
  

   to 
  a 
  correction 
  to 
  the 
  length 
  of 
  each 
  half 
  I 
  of 
  the 
  doubled 
  

   tube, 
  of 
  amount 
  equal 
  to 
  the 
  area 
  of 
  the 
  section 
  of 
  the 
  tube 
  

   divided 
  by 
  4 
  a. 
  

  

  Now 
  Dr. 
  Jeffreys 
  considers 
  that 
  under 
  natural 
  conditions 
  a 
  

   layer 
  of 
  air, 
  as 
  much 
  as 
  1 
  mm. 
  thick 
  before 
  the 
  disturbed 
  motion 
  

   beyond 
  is 
  reached 
  around 
  the 
  leaf, 
  may 
  be 
  regarded 
  as 
  still. 
  

   For 
  the 
  dimensions 
  of 
  stomata 
  quoted 
  by 
  him, 
  a 
  would 
  be 
  

   \ 
  . 
  10~ 
  3 
  cm. 
  and 
  the 
  area 
  of 
  section 
  3 
  . 
  10" 
  5 
  cm. 
  2 
  , 
  while 
  I 
  would 
  

   be 
  taken 
  as 
  1 
  mm. 
  The 
  correction 
  to 
  I 
  would 
  then 
  be 
  ]- 
  mm. 
  

   As 
  this 
  is 
  a 
  small 
  fraction 
  of 
  I 
  the 
  main 
  resistance 
  to 
  tran- 
  

   spiration 
  would 
  arise 
  in 
  getting 
  across 
  this 
  highly 
  saturated 
  

   layer 
  of 
  air, 
  as 
  much 
  as 
  1 
  mm. 
  thick 
  around 
  the 
  leaf. 
  The 
  

   stomata 
  would 
  transpire 
  into 
  it, 
  and 
  the 
  vapour 
  would 
  not 
  

   get 
  awa}' 
  as 
  rapidly 
  as 
  it 
  could 
  be 
  supplied 
  ; 
  the 
  case 
  is 
  

   analogous 
  in 
  a 
  lesser 
  degree 
  to 
  a 
  leaf 
  enclosed 
  in 
  a 
  bottle 
  

   with 
  narrow, 
  open 
  neck, 
  in 
  which 
  the 
  air 
  would 
  soon 
  become 
  

   nearly 
  saturated 
  with 
  vapour 
  and 
  the 
  transpiration 
  would 
  be 
  

  

  * 
  For 
  the 
  problem 
  in 
  two 
  dimensions 
  of 
  space 
  the 
  exact 
  solution 
  is 
  

   known, 
  and 
  a 
  diagram 
  of 
  flow 
  is 
  given 
  by 
  Prof. 
  Lamb, 
  'Hydrodynamics/ 
  

   § 
  306. 
  In 
  that 
  case 
  the 
  correction 
  to 
  be 
  added 
  to 
  the 
  half 
  length 
  I 
  (infra) 
  

   in 
  order 
  to 
  obtain 
  the 
  effective 
  half 
  length, 
  when 
  the 
  resistance 
  of 
  the 
  

   constrictions 
  is 
  included, 
  proves 
  to 
  be 
  — 
  log 
  c 
  sin 
  \ 
  irk, 
  where 
  h 
  is 
  the 
  ratio 
  of 
  

   the 
  area 
  of 
  the 
  straight 
  stomatal 
  strips 
  to 
  the 
  whole 
  area. 
  But 
  this 
  result 
  

   is 
  hardly 
  applicable 
  even 
  to 
  illustrate 
  the 
  actual 
  problem 
  of 
  local 
  stomata. 
  

  

  