﻿6 
  Lord 
  Rayleigh 
  on 
  the 
  

  

  With 
  the 
  above 
  value 
  of 
  k 
  y 
  viz. 
  2*2, 
  

  

  H=1-27A 
  1} 
  (19) 
  

  

  fixing 
  the 
  place 
  of 
  maximum 
  pressure- 
  

   Again, 
  from 
  (16) 
  with 
  the 
  same 
  value 
  of 
  k, 
  

  

  £_a 
  = 
  0-4231c, 
  (20) 
  

  

  which 
  gives 
  the 
  distance 
  of 
  the 
  centre 
  of 
  pressure 
  from 
  the 
  

   trailing 
  edge. 
  

  

  And, 
  again 
  with 
  the 
  same 
  value 
  of 
  &, 
  by 
  (17) 
  

  

  F/P 
  = 
  4-707 
  tl 
  /c 
  (21) 
  

  

  Since 
  hi 
  may 
  be 
  very 
  small, 
  it 
  would 
  seem 
  that 
  F 
  may 
  be 
  

   reduced 
  to 
  insignificance. 
  

  

  In 
  (18) 
  .... 
  (21) 
  the 
  choice 
  of 
  k 
  has 
  been 
  such 
  as 
  to 
  make 
  

   P 
  a 
  maximum. 
  An 
  alternative 
  would 
  be 
  to 
  make 
  F/P 
  a 
  

   minimum. 
  But 
  it 
  does 
  not 
  appear 
  that 
  this 
  would 
  make 
  

   much 
  practical 
  difference. 
  In 
  Michell's 
  bearings 
  it 
  is 
  the 
  

   position 
  of 
  the 
  centre 
  of 
  pressure 
  which 
  determines 
  the 
  value 
  

   of 
  k 
  by 
  (16). 
  If 
  we 
  use 
  (20), 
  k 
  will 
  be- 
  2*2, 
  or 
  thereabouts, 
  

   as 
  above. 
  

  

  When 
  in 
  (16) 
  k 
  is 
  very 
  large, 
  the 
  right-hand 
  member 
  tends 
  

   to 
  zero, 
  as 
  also 
  does 
  a/c, 
  so 
  that 
  x 
  — 
  a 
  tends 
  to 
  vanish, 
  c 
  being 
  

   given. 
  As 
  might 
  be 
  expected, 
  the 
  centre 
  of 
  pressure 
  is 
  then 
  

   close 
  to 
  the 
  trailing 
  edge. 
  On 
  the 
  other 
  hand, 
  when 
  k 
  exceeds 
  

   unity 
  but 
  little, 
  the 
  right-hand 
  member 
  of 
  (16) 
  assumes 
  an 
  

   indeterminate 
  form. 
  When 
  we 
  evaluate 
  it, 
  we 
  find 
  

  

  For 
  all 
  values 
  of 
  k 
  (> 
  1) 
  the 
  centre 
  of 
  pressure 
  lies 
  nearer 
  

   the 
  narrower 
  end 
  of 
  the 
  layer 
  of 
  fluid. 
  

  

  The 
  above 
  calculations 
  suppose 
  that 
  the 
  second 
  surface 
  is 
  

   plane. 
  The 
  question 
  suggests 
  itself 
  whether 
  any 
  advantage 
  

   would 
  arise 
  from 
  another 
  choice 
  of 
  form. 
  The 
  integrations 
  

   are 
  scarcely 
  more 
  complicated 
  if 
  we 
  take 
  

  

  h 
  — 
  mx 
  n 
  . 
  ...... 
  (22) 
  

  

  We 
  denote, 
  as 
  before, 
  the 
  ratio 
  of: 
  the 
  extreme 
  thicknesses 
  

   (/ia/Aj) 
  by 
  k, 
  and 
  c 
  still 
  denotes 
  b 
  — 
  a. 
  For 
  the 
  total 
  pressure 
  

   we 
  get 
  from 
  (15) 
  

  

  _P 
  c 
  2 
  ( 
  3n-l 
  (&- 
  2 
  +^-l)(&- 
  3+2 
  /"--l) 
  

  

  6>U" 
  (^ 
  TC 
  -l) 
  2 
  /i 
  1 
  2 
  l(2n-l)(3^-2) 
  &-3+i/« 
  

  

  from 
  which 
  we 
  may 
  fall 
  back 
  on 
  (15) 
  by 
  making 
  n 
  = 
  l. 
  

  

  