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  925 
  ] 
  

  

  LXXX. 
  On 
  the 
  Forces 
  acting 
  on 
  a 
  Solid 
  Sphere 
  in 
  contact 
  with 
  

   a 
  Liquid 
  Surface. 
  By 
  Allan 
  Ferguson, 
  B.Sc.{Lond.), 
  

   Assistant-Lecturer 
  in 
  Physics 
  in 
  the 
  University 
  College 
  of 
  

   JS'orth 
  Wales, 
  Bangor 
  *. 
  

  

  THE 
  study 
  of 
  the 
  problem 
  from 
  which 
  this 
  paper 
  takes 
  

   its 
  title 
  originated 
  in 
  an 
  attempt 
  made 
  by 
  the 
  writer 
  to 
  

   apply 
  the 
  methods 
  of 
  approximation 
  described 
  in 
  previous 
  

   papers 
  f 
  to 
  the 
  problem 
  of 
  the 
  force 
  required 
  to 
  detach 
  a 
  

   circular 
  disk 
  from 
  the 
  surface 
  of 
  a 
  liquid. 
  Approximate 
  

   solutions 
  to 
  this 
  latter 
  analytical 
  problem 
  have 
  been 
  given 
  by 
  

   Laplace 
  + 
  and 
  Poisson§, 
  whilst, 
  as 
  an 
  experimental 
  method 
  

   for 
  the 
  evaluation 
  of 
  surface 
  tensions, 
  it 
  has 
  been 
  much 
  

   favoured 
  by 
  earlier 
  experimenters 
  ||. 
  

  

  As 
  considerable 
  historic 
  interest 
  attaches 
  to 
  the 
  problem, 
  a 
  

   brief 
  resume 
  of 
  the 
  results 
  obtained 
  by 
  the 
  above 
  methods 
  of 
  

   approximation 
  will 
  first 
  be 
  given, 
  more 
  especially 
  as 
  they 
  

   differ 
  in 
  some 
  respects 
  from 
  those 
  obtained 
  by 
  other 
  analysts, 
  

   and 
  as 
  some 
  of 
  the 
  formulae 
  developed 
  will 
  be 
  used 
  in 
  the 
  

   problem 
  of 
  the 
  sphere. 
  

  

  Fig. 
  1. 
  

  

  ^! 
  

  

  O 
  

  

  Let 
  AB 
  be 
  the 
  trace 
  of 
  the 
  circular 
  disk, 
  raised 
  to 
  a 
  height 
  

   d 
  above 
  the 
  general 
  level 
  of 
  the 
  liquid 
  surface. 
  The 
  

   elementary 
  theory 
  % 
  which 
  assumes 
  the 
  curvature 
  of 
  the 
  

   liquid 
  surface 
  perpendicular 
  to 
  the 
  plane 
  of 
  the 
  paper 
  

  

  * 
  Communicated 
  by 
  Prof. 
  E. 
  Taylor 
  Jones. 
  

  

  + 
  Phil. 
  Mag-. 
  Dec. 
  1912, 
  and 
  April 
  1913. 
  (The 
  former 
  paper 
  will 
  be 
  

   cited 
  hereinafter 
  as 
  7. 
  c). 
  

  

  } 
  Mec. 
  Celeste, 
  tome 
  x. 
  Supp. 
  pp. 
  48 
  seqq. 
  

  

  § 
  ' 
  Nouvelle 
  Theorie 
  de 
  Taction 
  capillaire,' 
  pp. 
  226 
  seqq. 
  

  

  |i 
  Gay-Lussac 
  (quoted 
  by 
  Laplace, 
  op. 
  cit. 
  p. 
  54) 
  ; 
  Buys-Ballot, 
  Pogg. 
  

   Ann. 
  p/191 
  (1847) 
  ; 
  Merian, 
  Pogg. 
  Ann. 
  p. 
  485 
  (1848/; 
  Hagen, 
  Pogg. 
  

   Ann. 
  p. 
  464 
  (1849), 
  &c. 
  

  

  51 
  See, 
  e. 
  g., 
  Poynting 
  & 
  Thomson, 
  ' 
  Properties 
  of 
  Matter/ 
  p. 
  161. 
  

  

  