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  XVII. 
  On 
  the 
  Lubricating 
  and 
  other 
  Properties 
  of 
  Thin 
  Oily 
  

   Films. 
  By 
  Lord 
  Rayleigh, 
  O.M., 
  F.R.S* 
  

  

  I^HE 
  experiments 
  about 
  to 
  be 
  described 
  were 
  undertaken 
  

   to 
  examine 
  more 
  particularly 
  a 
  fact 
  well 
  known 
  in 
  most 
  

   households. 
  A 
  cup 
  of 
  tea, 
  standing 
  in 
  a 
  dry 
  saucer, 
  is 
  apt 
  

   to 
  slip 
  about 
  in 
  an 
  awkward 
  manner, 
  for 
  which 
  a 
  remedy 
  is 
  

   found 
  in 
  the 
  introduction 
  of 
  a 
  few 
  drops 
  of 
  water, 
  or 
  tea, 
  

   wetting 
  the 
  parts 
  in 
  contact. 
  The 
  explanation 
  is 
  not 
  obvious, 
  

   and 
  I 
  remember 
  discussing 
  the 
  question 
  with 
  Kelvin 
  many 
  

   years 
  ago, 
  with 
  but 
  little 
  progress. 
  

  

  It 
  is 
  true 
  that 
  a 
  drop 
  of 
  liquid 
  between 
  two 
  curved 
  sur- 
  

   faces 
  draws 
  them 
  together 
  and 
  so 
  may 
  increase 
  the 
  friction. 
  

   If 
  d 
  be 
  the 
  distance 
  between 
  the 
  plates 
  at 
  the 
  edge 
  of 
  the 
  

   film, 
  T 
  the 
  capillary 
  tension, 
  and 
  a 
  the 
  angle 
  of 
  contact, 
  the 
  

   whole 
  force 
  is 
  f 
  - 
  

  

  2ATcosa 
  .„„ 
  . 
  

  

  j 
  4-BTsma, 
  

  

  a 
  

  

  A 
  being 
  the 
  area 
  of 
  the 
  film 
  between 
  the 
  plates 
  and 
  B 
  its 
  

   circumference. 
  If 
  the 
  fluid 
  wets 
  the 
  plate, 
  a 
  = 
  and 
  we 
  

   have 
  simply 
  2AT/d. 
  For 
  example, 
  if 
  d=6 
  X 
  10~ 
  5 
  cm., 
  equal 
  

   to 
  a 
  wave-length 
  of 
  ordinary 
  light, 
  and 
  T 
  (as 
  for 
  water) 
  be 
  

   74 
  dynes 
  per 
  cm., 
  the 
  force 
  per 
  sq. 
  cm. 
  is 
  25 
  x 
  10 
  5 
  dynes, 
  a 
  

   suction 
  of 
  2i 
  atmospheres. 
  For 
  the 
  present 
  purpose 
  we 
  

   may 
  express 
  d 
  in 
  terms 
  of 
  the 
  radius 
  of 
  curvature 
  (p) 
  of 
  one 
  

   of 
  the 
  surfaces, 
  the 
  other 
  being 
  supposed 
  flat, 
  and 
  the 
  dis- 
  

   tance 
  (,z) 
  from 
  the 
  centre 
  to 
  the 
  edge 
  of 
  the 
  film. 
  In 
  two 
  

   dimensions 
  d 
  = 
  x 
  2 
  /2p, 
  and 
  A 
  (per 
  unit 
  of 
  length 
  in 
  the 
  third 
  

   dimension) 
  =2#, 
  so 
  that 
  the 
  force 
  per 
  unit 
  of 
  length 
  is 
  

   8/oT/#, 
  inversely 
  as 
  x. 
  On 
  the 
  other 
  hand, 
  in 
  the 
  more 
  

   important 
  case 
  of 
  symmetry 
  round 
  the 
  common 
  normal 
  

   A 
  = 
  7r# 
  2 
  , 
  and 
  the 
  whole 
  force 
  is 
  47rpT, 
  independent 
  of 
  #, 
  but 
  

   increasing 
  with 
  the 
  radius 
  of 
  curvature. 
  For 
  example, 
  if 
  

   T 
  = 
  74 
  dynes 
  per 
  cm., 
  and 
  /> 
  = 
  100 
  cm., 
  the 
  force 
  is 
  925 
  

   dynes, 
  or 
  the 
  weight 
  of 
  about 
  1 
  gram. 
  The 
  radius 
  of 
  cur- 
  

   vature 
  (p) 
  might 
  of 
  course 
  be 
  much 
  greater. 
  There 
  are 
  

   circumstances 
  where 
  this 
  force 
  is 
  of 
  importance 
  ; 
  but, 
  as 
  we 
  

   shall 
  see 
  presently, 
  it 
  does 
  not 
  avail 
  to 
  explain 
  the 
  effects 
  

   now 
  under 
  consideration. 
  

  

  My 
  first 
  experiments 
  were 
  very 
  simple 
  ones, 
  with 
  a 
  slab 
  of 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  See 
  for 
  example 
  Maxwell 
  on 
  Capillarity. 
  Collected 
  Papers, 
  vol. 
  ii. 
  

   p. 
  571. 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  206. 
  Feb. 
  1918. 
  N 
  

  

  