﻿926 
  Mr. 
  A. 
  Ferguson 
  on 
  the 
  Forces 
  acting 
  on 
  a 
  

  

  negligible 
  compared 
  with 
  the 
  curvature 
  in 
  the 
  plane 
  of 
  the 
  

   paper, 
  gives 
  

  

  d 
  2 
  = 
  4a 
  2 
  , 
  . 
  . 
  . 
  ■ 
  (i.) 
  

  

  and 
  hence, 
  if 
  P 
  be 
  the 
  pull 
  required 
  to 
  detach 
  the 
  plate, 
  and 
  

   A 
  its 
  area, 
  

  

  T 
  = 
  Agpd 
  — 
  2Agpa 
  (ii.) 
  

  

  T 
  

   where, 
  as 
  usual, 
  a 
  2 
  = 
  — 
  . 
  

  

  gp 
  

  

  More 
  exactly, 
  if 
  we 
  consider 
  a 
  point 
  P 
  on 
  the 
  upper 
  part 
  

   of 
  the 
  meniscus, 
  we 
  have 
  for 
  the 
  differential 
  equation 
  to 
  the 
  

   surface 
  at 
  P, 
  

  

  V+- 
  

  

  1 
  t^2 
  

  

  % 
  + 
  ^r> 
  <*"•) 
  

  

  Substituting 
  for 
  B^ 
  and 
  E 
  2 
  their 
  values, 
  transferring 
  the 
  

   origin 
  to 
  0', 
  and 
  dividing 
  throughout 
  by 
  r, 
  we 
  obtain, 
  as 
  

   previously 
  explained 
  *, 
  

  

  _^ 
  dj> 
  ,dj> 
  «V 
  (1 
  2) 
  = 
  «y 
  {1 
  +f)i 
  _ 
  (1+ 
  2 
  i 
  . 
  (iv>) 
  

  

  r 
  ax 
  ax 
  r 
  ' 
  r 
  J 
  ^ 
  K 
  L 
  ' 
  

  

  dp 
  . 
  

   remembering 
  that, 
  at 
  points 
  such 
  as 
  P, 
  ,- 
  is 
  negative. 
  

  

  When 
  r 
  is 
  infinite, 
  this 
  becomes 
  

  

  «vJ 
  = 
  -.'/(i+i' 
  2 
  )% 
  (v 
  - 
  } 
  

  

  giving 
  on 
  integration, 
  

  

  2a 
  2 
  

  

  y 
  2 
  =v+ 
  7(T+7J 
  ( 
  vi 
  -) 
  

  

  From 
  y 
  = 
  h, 
  downwards, 
  the 
  problem 
  is 
  exactly 
  that 
  of 
  a 
  

   liquid 
  of 
  zero 
  contact-angle 
  in 
  external 
  contact 
  with 
  a 
  

   cylinder 
  of 
  radius 
  r. 
  Hence 
  f 
  

  

  V-2^-3--- 
  — 
  . 
  . 
  . 
  ( 
  V1 
  .a) 
  

  

  and 
  

  

  7 
  il 
  2 
  (r=00) 
  = 
  2a 
  2 
  . 
  

  

  * 
  X. 
  c. 
  p. 
  839. 
  

  

  t 
  £. 
  c. 
  p. 
  841. 
  Put 
  ;=0, 
  and 
  7i 
  2 
  ~2a 
  2 
  in 
  the 
  small 
  terms 
  of 
  

   equation 
  (xi.). 
  

  

  