﻿274 
  Dr. 
  H. 
  Jeffreys 
  on 
  some 
  

  

  It 
  has 
  been 
  assumed 
  in 
  this 
  treatment 
  that 
  the 
  linear 
  

   dimensions 
  are 
  so 
  large 
  that 
  ^— 
  g- 
  and 
  ^— 
  g 
  are 
  negligible 
  in 
  

   comparison 
  with 
  ^-f. 
  

  

  Now 
  the 
  value 
  of 
  Y 
  in 
  (6) 
  makes 
  the 
  first 
  two 
  quantities 
  

   of 
  order 
  Y 
  /a 
  2 
  and 
  the 
  last 
  of 
  order 
  \ 
  7 
  /h?a. 
  The 
  condition 
  

   required 
  for 
  the 
  method 
  to 
  be 
  justifiable 
  is 
  therefore 
  that 
  a 
  

   shall 
  be 
  large 
  compared 
  with 
  h 
  2 
  ; 
  in 
  other 
  words, 
  ua/k 
  shall 
  

   be 
  large. 
  

  

  It 
  has 
  also 
  been 
  assumed 
  that 
  k/u 
  is 
  constant. 
  This 
  

   requires 
  that 
  the 
  distance 
  out 
  to 
  which 
  the 
  disturbance 
  

   extends 
  shall 
  be 
  sufficiently 
  small 
  for 
  the 
  change 
  in 
  kju 
  from 
  

   its 
  value 
  just 
  outside 
  a 
  thin 
  surface-layer 
  to 
  be 
  small 
  compared 
  

   with 
  the 
  whole. 
  This 
  distance 
  is 
  of 
  order 
  2ha%. 
  Thus 
  

  

  2a?dh/dz 
  must 
  be 
  small. 
  Now 
  j 
  -y- 
  is 
  probably 
  of 
  the 
  same 
  

  

  order 
  as 
  --7-. 
  But 
  kp 
  1 
  — 
  when 
  ~ 
  = 
  is 
  about 
  *003pw 
  2 
  , 
  for 
  

   udz 
  r 
  dz 
  r 
  

  

  each 
  quantity 
  is 
  equal 
  to 
  the 
  skin 
  friction 
  per 
  unit 
  area. 
  

   Thus 
  -006(ua/k)* 
  must 
  be 
  small. 
  This 
  method 
  is 
  therefore 
  

   correct 
  provided 
  ua/k 
  lies 
  between, 
  say, 
  4 
  and 
  10 
  4 
  . 
  

  

  Consider 
  first 
  an 
  'outdoor 
  case, 
  with 
  w 
  = 
  400 
  cm./sec, 
  

   £=1000 
  cm. 
  2 
  /sec. 
  Then 
  a 
  must 
  be 
  between 
  10 
  cms. 
  and 
  

   250 
  metres. 
  In 
  a 
  room 
  with 
  little 
  draught, 
  we 
  may 
  have 
  

   u 
  = 
  4: 
  cm./sec, 
  k 
  = 
  l 
  cm. 
  2 
  /sec, 
  and 
  a 
  must 
  be 
  between 
  1 
  cm. 
  

   and 
  25 
  metres. 
  

  

  When 
  ua/k 
  is 
  much 
  less 
  than 
  unity, 
  the 
  velocity 
  of 
  the 
  

   wind 
  may 
  be 
  neglected 
  and 
  the 
  problem 
  becomes 
  one 
  of 
  

   steady 
  diffusion 
  ; 
  the 
  rate 
  of 
  evaporation 
  is 
  then 
  proportional 
  

   to 
  the 
  linear 
  dimensions. 
  When 
  ua/k 
  is 
  large 
  compared 
  with 
  

   10 
  4 
  , 
  the 
  effect 
  will 
  extend 
  upwards 
  for 
  such 
  a 
  distance 
  that 
  

   in 
  most 
  of 
  the 
  volume 
  concerned 
  u 
  and 
  k 
  will 
  be 
  nearly 
  

   constant 
  and 
  equal 
  to 
  their 
  values 
  at 
  a 
  considerable 
  height. 
  

   The 
  air 
  up 
  to 
  such 
  a 
  height 
  will 
  be 
  practically 
  saturated, 
  

   and 
  vapour 
  will 
  diffuse 
  from 
  the 
  upper 
  surface 
  of 
  the 
  

   saturated 
  air 
  precisely 
  as 
  before 
  ; 
  the 
  law 
  that 
  the 
  rate 
  of 
  

   evaporation 
  is 
  proportional 
  to 
  a 
  1 
  ' 
  5 
  will 
  therefore 
  still 
  hold, 
  

   with 
  different 
  values 
  of 
  u 
  and 
  k. 
  

  

  The 
  result 
  that 
  for 
  bodies 
  of 
  medium 
  dimensions 
  the 
  rate 
  

   of 
  evaporation 
  is 
  practically 
  proportional 
  to 
  a 
  1 
  " 
  5 
  has 
  been 
  

   discovered 
  experimentally 
  by 
  Thomas 
  and 
  Ferguson*, 
  who 
  

   also 
  point 
  out 
  that 
  this 
  gives 
  a 
  fair 
  representation 
  of 
  Renner's 
  t 
  

  

  * 
  N. 
  Thomas 
  and 
  A. 
  Ferguson, 
  Phil. 
  Mag. 
  xxxiv. 
  pp. 
  308-321 
  (1917). 
  

   t 
  O. 
  Kenner, 
  Flora, 
  100. 
  p. 
  474 
  (1910). 
  

  

  