﻿Solid 
  Sphere 
  in 
  contact 
  with 
  a 
  Liquid 
  Surface. 
  931 
  

   we 
  have, 
  substituting 
  for 
  r 
  in 
  (xvi.) 
  and 
  reducing, 
  

  

  In 
  equation 
  (xiv.) 
  the 
  first 
  term 
  is 
  by 
  far 
  the 
  largest 
  ; 
  in 
  

   the 
  remaining 
  small 
  terms 
  the 
  approximate 
  value 
  d 
  = 
  2a 
  

   may 
  be 
  substituted. 
  Making 
  these 
  substitutions, 
  we 
  easily 
  

   obtain 
  

  

  The 
  last 
  term 
  is 
  usually 
  negligible, 
  giving 
  

  

  m 
  = 
  4.7rpa 
  2 
  < 
  H 
  ^— 
  — 
  77 
  f, 
  « 
  ■ 
  (xviii.) 
  

  

  a 
  simple 
  equation 
  from 
  which 
  to 
  calculate 
  a 
  2 
  when 
  m 
  and 
  R, 
  

   are 
  known. 
  It 
  is 
  best 
  solved 
  by 
  successive 
  approximations. 
  

  

  In 
  order 
  to 
  apply 
  equation 
  (xviii.) 
  to 
  determine 
  surface 
  

   tensions, 
  a 
  large 
  hollow 
  sphere 
  of 
  glass 
  was 
  taken 
  and 
  its 
  

   external 
  radius 
  measured 
  by 
  means 
  of 
  a 
  spherometer. 
  No 
  

   appreciable 
  variation 
  in 
  the 
  radius 
  could 
  be 
  detected 
  over 
  the 
  

   portion 
  which 
  was 
  subsequently 
  in 
  contact 
  with 
  the 
  liquid 
  

   under 
  examination. 
  The 
  sphere, 
  after 
  having 
  been 
  cleansed 
  

   by 
  alternate 
  washings 
  with 
  caustic 
  soda 
  solution 
  and 
  distilled 
  

   water, 
  was 
  dried 
  and 
  fastened 
  by 
  a 
  thread 
  about 
  20 
  cm. 
  

   in 
  length 
  to 
  the 
  underside 
  of 
  the 
  pan 
  of 
  a 
  balance 
  standing 
  

   on 
  a 
  high 
  shelf, 
  the 
  thread 
  passing 
  through 
  holes 
  in 
  the 
  base- 
  

   board 
  of 
  the 
  balance 
  and 
  the 
  shelf. 
  On 
  a 
  lower 
  shelf, 
  

   underneath 
  the 
  sphere, 
  stood 
  a 
  small 
  table 
  whose 
  height 
  

   could 
  be 
  adjusted 
  by 
  means 
  of 
  a 
  screw, 
  which 
  table 
  carried 
  

   a 
  carefully 
  cleaned 
  porcelain 
  basin 
  containing 
  the 
  liquid 
  

   under 
  examination. 
  

  

  The 
  sphere 
  having 
  been 
  first 
  counterpoised, 
  the 
  balance 
  

   was 
  left 
  perfectly 
  free 
  and 
  the 
  height 
  of 
  the 
  table 
  adjusted 
  

   until 
  the 
  liquid 
  just 
  touched 
  the 
  vertex 
  of 
  the 
  sphere. 
  This 
  

   point 
  was 
  sharply 
  defined 
  by 
  the 
  sudden 
  swing 
  of 
  the 
  balance- 
  

   pointer 
  as 
  the 
  sphere 
  touched 
  the 
  liquid 
  and 
  was 
  pulled 
  down. 
  

   (In 
  order 
  to 
  obtain 
  consistent 
  results, 
  great 
  care 
  must 
  be 
  taken 
  

   that 
  the 
  balance 
  is 
  quite 
  at 
  rest 
  and 
  the 
  pointer 
  exactly 
  over 
  

   the 
  zero 
  at 
  the 
  instant 
  when 
  the 
  sphere 
  and 
  liquid 
  make 
  

   contact.) 
  Weights 
  were 
  then 
  added 
  till 
  the 
  pointer 
  was 
  

   brought 
  back 
  to 
  the 
  zero, 
  the 
  mass 
  of 
  these 
  weights 
  being 
  

   the 
  m 
  of 
  equation 
  (xviii.). 
  

  

  