﻿272 
  Dr. 
  H. 
  Jeffreys 
  on 
  some 
  

  

  is 
  also 
  satisfied 
  by 
  the 
  potential 
  in 
  electrostatic 
  problems 
  ;*it 
  

   follows 
  that, 
  provided 
  the 
  initial 
  change 
  is 
  not 
  too 
  abrupt 
  

   and 
  the 
  dimensions 
  are 
  not 
  too 
  great, 
  the 
  value 
  of 
  V 
  at 
  any 
  

   point 
  is 
  the 
  same 
  as 
  the 
  electric 
  potential 
  at 
  that 
  point 
  when 
  

   the 
  wetted 
  surface 
  is 
  regarded 
  as 
  a 
  conductor 
  charged 
  to 
  

   potential 
  V 
  , 
  where 
  V 
  is 
  the 
  concentration 
  at 
  the 
  edge 
  of 
  

   the 
  layer 
  of 
  shearing 
  when 
  the 
  air 
  is 
  moving, 
  and 
  the 
  

   saturation 
  concentration 
  at 
  the 
  boundary 
  when 
  it 
  is 
  at 
  rest. 
  

   The 
  charge 
  needed 
  for 
  this 
  is 
  CV 
  . 
  where 
  C 
  is 
  the 
  electro- 
  

   static 
  capacity 
  of 
  the 
  conductor. 
  Now 
  the 
  rate 
  of 
  trans- 
  

   ference 
  outwards 
  from 
  the 
  boundary 
  is 
  

  

  -jJ^giS, 
  

  

  where 
  ~dv 
  denotes 
  the 
  element 
  of 
  the 
  outward 
  normal, 
  p 
  is 
  

   the 
  density 
  of 
  air, 
  and 
  the 
  integral 
  is 
  taken 
  over 
  . 
  the 
  

   boundary. 
  

  

  But 
  in 
  the 
  electrostatic 
  problem, 
  if 
  a 
  denotes 
  the 
  density 
  

   of 
  the 
  electric 
  charge 
  on 
  the 
  surface, 
  

  

  9V 
  A 
  

  

  and 
  hence] 
  

  

  - 
  rf|^^S 
  = 
  47r(To-^S 
  = 
  47rCV 
  . 
  

  

  Hence 
  the 
  rate 
  of 
  transference 
  outwards 
  is 
  

  

  47rfyCV 
  (4) 
  

  

  This 
  determines 
  the 
  rate 
  of 
  evaporation, 
  which 
  is 
  shown, 
  

   other 
  things 
  being 
  equal, 
  to 
  be 
  proportional 
  to 
  the 
  linear 
  

   dimensions, 
  since 
  the 
  electrostatic 
  capacity 
  varies 
  in 
  this 
  

   way 
  for 
  bodies 
  of 
  the 
  same 
  shape. 
  

  

  The 
  above 
  is 
  practically 
  Stefan's 
  * 
  solution, 
  w 
  r 
  hich 
  has 
  

   been 
  experimentally 
  proved 
  to 
  be 
  correct 
  subject 
  to 
  the 
  

   conditions 
  stated 
  ]. 
  When 
  the 
  velocity 
  is 
  large 
  enough 
  to 
  

   need 
  to 
  be 
  taken 
  into 
  account, 
  a 
  general 
  solution 
  is 
  no 
  longer 
  

   possible, 
  but 
  for 
  a 
  large 
  wetted 
  surface 
  the 
  curvature 
  may 
  

   be 
  neglected, 
  and 
  the 
  problem 
  reduces 
  to 
  that 
  of 
  a 
  wind 
  

   blowing 
  over 
  a 
  flat 
  surface. 
  This 
  is 
  treated 
  in 
  the 
  next 
  

   section. 
  

  

  * 
  Wien. 
  Akad. 
  Ber. 
  lxxxiii. 
  Abteil 
  2, 
  p. 
  613 
  (1881). 
  

  

  t 
  H. 
  T. 
  Brown 
  & 
  F. 
  Escombe, 
  Phil. 
  Trans. 
  193 
  B. 
  pp. 
  223-291. 
  

  

  