﻿278 
  Dr. 
  H. 
  Jeffreys 
  on 
  some 
  

  

  regards 
  as 
  inconsistent 
  with 
  his 
  further 
  results 
  that 
  " 
  com- 
  

   plete 
  closure 
  reduces 
  transpiration 
  to 
  or 
  nearly 
  to 
  

  

  cuticular 
  rate," 
  and 
  " 
  when 
  the 
  stomata 
  are 
  open 
  to 
  their 
  

   utmost 
  limit 
  the 
  highest 
  rate 
  of 
  transpiration 
  is 
  the 
  maximum 
  

   of" 
  which 
  the 
  leaf 
  is 
  capable." 
  A 
  more 
  satisfactory 
  statement 
  

   would 
  be 
  that 
  until 
  the 
  stomatal 
  aperture 
  is 
  reduced 
  to 
  a 
  

   certain 
  very 
  small 
  value 
  the 
  possible 
  rate 
  of 
  transpiration 
  is 
  

   practically 
  independent 
  of 
  the 
  aperture, 
  and 
  nearly 
  all 
  of 
  the 
  

   reduction 
  to 
  zero 
  when 
  the 
  stoma 
  closes 
  takes 
  place 
  in 
  the 
  

   last 
  2 
  per 
  cent, 
  of 
  the 
  reduction 
  of 
  aperture. 
  

  

  Next, 
  consider 
  the 
  effect 
  of 
  wind. 
  Suppose 
  for 
  simplicity 
  

   that 
  the 
  stomata 
  are 
  arranged 
  in 
  straight 
  rows, 
  the 
  distance 
  

   between 
  consecutive 
  rows 
  and 
  between 
  consecutive 
  stomata 
  

   on 
  the 
  same 
  row 
  being 
  b. 
  Then 
  b=\/n. 
  Consider 
  a 
  square 
  

   column 
  of 
  air 
  of 
  side 
  b. 
  To 
  pass 
  over 
  a 
  stoma 
  it 
  would 
  take 
  

   a 
  time 
  b/u, 
  and 
  if 
  it 
  were 
  unsaturated 
  at 
  the 
  commencement 
  

   it 
  would 
  therefore 
  acquire 
  a 
  weight 
  of 
  vapour 
  27rkpcY 
  b/u, 
  

   if 
  there 
  were 
  no 
  mutual 
  influence 
  between 
  stomata. 
  Now 
  

   suppose 
  the 
  air 
  to 
  have 
  moved 
  forward 
  a 
  distance 
  x, 
  in 
  time 
  

   ocju. 
  Then 
  the 
  vapour 
  in 
  it 
  will 
  have 
  spread 
  out 
  by 
  diffusion 
  

   through 
  a 
  radius 
  comparable 
  with 
  2(kx/u)*; 
  and 
  if 
  xjb 
  is 
  

   great 
  diffusion 
  parallel 
  to 
  the 
  surface 
  of 
  the 
  leaf 
  and 
  across 
  

   the 
  wind 
  will 
  have 
  practically 
  ceased, 
  and 
  thus 
  the 
  vapour 
  

   will 
  occupy 
  half 
  a 
  flat 
  cylinder 
  of 
  radius 
  2(kx/u)i 
  and 
  

   thickness 
  b, 
  its 
  centre 
  being 
  of 
  course 
  at 
  the 
  point 
  x. 
  Thus 
  

   the 
  concentration 
  in 
  it 
  will 
  be 
  of 
  order 
  cY^x. 
  Further, 
  the 
  

   number 
  of 
  stomata 
  much 
  affected 
  will 
  be 
  of 
  order 
  

  

  4ri 
  2 
  b(kx\u)% 
  = 
  4:n 
  (Jcx/u)i. 
  

  

  Similarly, 
  the 
  number 
  of 
  stomata 
  whose 
  influence 
  at 
  this 
  

   time 
  will 
  have 
  affected 
  the 
  column 
  of 
  air 
  when 
  it 
  has 
  

   travelled 
  a 
  distance 
  between 
  x—^b 
  and 
  x 
  + 
  \b 
  is 
  4n(kx/u)* 
  r 
  

   and 
  therefore 
  the 
  total 
  concentration 
  produced 
  by 
  them 
  is 
  

   4.ncY 
  (k/ux)i. 
  This 
  is 
  then 
  the 
  concentration 
  acquired 
  by 
  a 
  

   mass 
  of 
  air 
  on 
  account 
  of 
  what 
  happened 
  between 
  times 
  

   (x±^b)/u 
  previously, 
  and 
  the 
  total 
  produced 
  by 
  all 
  times 
  is 
  

   to 
  be 
  found 
  by 
  summing 
  the 
  series 
  for 
  all 
  such 
  intervals. 
  

   Put 
  x/b 
  = 
  r. 
  The 
  total 
  is 
  then 
  4,ncY 
  (k/ub)i%r~i,the 
  summa- 
  

   tion 
  being 
  from 
  r=l 
  to 
  r=l/b, 
  where 
  I 
  is 
  the 
  distance 
  of 
  the 
  

   mass 
  from 
  the 
  stoma 
  nearest 
  the 
  margin. 
  When 
  I 
  is 
  great 
  

   this 
  is 
  of 
  the 
  order 
  o£ 
  8n 
  2 
  cY 
  (kl/u) 
  i. 
  Now 
  b 
  is 
  about 
  0*05 
  mm 
  ., 
  

   and 
  thus 
  is 
  usually 
  small 
  compared 
  with 
  the 
  thickness 
  of 
  the 
  

   layer 
  of 
  rapid 
  shearing 
  *. 
  A 
  fortiori 
  a, 
  and 
  hence 
  c, 
  are 
  

  

  * 
  See 
  p. 
  271. 
  

  

  