﻿268 
  A. 
  M. 
  Mayer— 
  On 
  the 
  Flotation 
  of 
  

  

  We 
  now 
  come 
  to 
  the 
  consideration 
  of 
  the 
  upward 
  hydro- 
  

   static 
  pressure 
  on 
  a 
  ring 
  at 
  the 
  moment 
  the 
  weight 
  on 
  the 
  ring 
  

   is 
  sufficient 
  to 
  cause 
  it 
  to 
  break 
  through 
  the 
  water-surface. 
  

   Fig. 
  5 
  shows 
  a 
  vertical 
  section 
  of 
  a 
  straight 
  wire 
  and 
  of 
  the 
  

   contour- 
  of 
  the 
  depressed 
  water-surfaces 
  at 
  or 
  near 
  the 
  moment 
  

   when 
  the 
  ring 
  breaks 
  through 
  the 
  water, 
  and 
  fig. 
  9 
  shows 
  the 
  

   section 
  of 
  the 
  wire 
  of 
  a 
  ring 
  and 
  the 
  contours 
  of 
  the 
  depressed 
  

   water-surfaces. 
  I 
  say 
  at 
  or 
  near 
  the 
  moment 
  when 
  the 
  ring 
  

   breaks 
  through 
  the 
  water 
  because, 
  though 
  I 
  have 
  made 
  scores 
  

   of 
  observations 
  on 
  the 
  upper 
  surface 
  of 
  the 
  ring 
  between 
  the 
  

   two 
  opposed 
  sheets 
  of 
  depressed 
  water, 
  with 
  a 
  microscope 
  pro- 
  

   vided 
  with 
  a 
  micrometer 
  eye- 
  piece, 
  I 
  have 
  not 
  been 
  able 
  to 
  

   decide 
  whether 
  the 
  surfaces 
  of 
  fig. 
  5 
  and 
  fig. 
  9 
  break 
  near 
  the 
  

   ring 
  when 
  the 
  surfaces 
  have 
  approached 
  to 
  T 
  V 
  mm 
  , 
  as 
  shown 
  in 
  

   the 
  figures, 
  or 
  whether 
  these 
  surfaces, 
  as 
  shown 
  in 
  fig. 
  10, 
  come 
  

   suddenly 
  in 
  contact 
  the 
  instant 
  before 
  the 
  ring 
  

   Fig. 
  10. 
  sinks. 
  On 
  some 
  days 
  I 
  would 
  rise 
  from 
  the 
  

   microscope 
  confident 
  that 
  the 
  surfaces 
  gave 
  way 
  

   before 
  they 
  came 
  in 
  contact 
  ; 
  on 
  other 
  days 
  I 
  

   would 
  be 
  equally 
  decided 
  that 
  they 
  really 
  met 
  

   just 
  as 
  the 
  ring 
  went 
  through 
  the 
  surface 
  of 
  the 
  

   water. 
  I 
  am 
  of 
  the 
  opinion 
  that 
  the 
  latter 
  con- 
  

   dition 
  is 
  more 
  likely 
  to 
  be 
  true. 
  

  

  Evidently 
  the 
  upward 
  hydrostatic 
  pressure 
  on 
  

   the 
  ring 
  will 
  differ 
  in 
  the 
  two 
  cases. 
  Suppos- 
  

   ing 
  that 
  fig. 
  5 
  and 
  fig. 
  9 
  give 
  the 
  real 
  conditions 
  

   at 
  the 
  moment 
  of 
  rupture 
  of 
  the 
  water-film, 
  

   then 
  the 
  upward 
  hydrostatic 
  pressure 
  per 
  centimeter 
  on 
  the 
  

   ring 
  equals 
  the 
  volume 
  of 
  one 
  centimeter 
  in 
  length 
  of 
  the 
  

   shaded 
  portion 
  of 
  the 
  section 
  of 
  the 
  wire 
  (see 
  fig. 
  5), 
  multi- 
  

   plied 
  by 
  *9989, 
  the 
  density 
  of 
  water 
  at 
  16°. 
  To 
  this 
  is 
  added 
  

   the 
  upward 
  hydrostatic 
  pressure 
  or 
  the 
  area 
  of 
  T 
  V 
  mm 
  ^J 
  l 
  cm 
  on 
  

   the 
  bottom 
  of 
  the 
  wire. 
  This 
  equals 
  •01x*503x 
  , 
  9989, 
  making 
  

   •01186 
  for 
  the 
  total 
  upward 
  pressure. 
  But 
  if 
  the 
  two 
  opposed 
  

   surfaces 
  meet 
  at 
  the 
  instant 
  the 
  ring 
  sinks, 
  as 
  shown 
  in 
  fig. 
  10, 
  

   we 
  have 
  for 
  the 
  upward 
  hydrostatic 
  pressure 
  on 
  one 
  centime- 
  

   ter 
  of 
  the 
  ring, 
  # 
  00T85 
  CC 
  , 
  the 
  volume 
  of 
  one 
  centimeter 
  of 
  the 
  

   wire, 
  X 
  -9989, 
  the 
  density 
  of 
  water 
  at 
  16° 
  ; 
  this 
  equals 
  -00784 
  

  

  Determination 
  of 
  the 
  surface 
  tension 
  of 
  toater 
  from 
  the 
  experi- 
  

   ments 
  on 
  the 
  rings. 
  

  

  Let 
  W 
  = 
  the 
  weight 
  required 
  to 
  make 
  the 
  ring 
  break 
  

   through 
  the 
  depressed 
  water-surface 
  ; 
  P 
  = 
  the 
  upward 
  hydro- 
  

   static 
  pressure 
  on 
  the 
  ring 
  at 
  the 
  instant 
  it 
  breaks 
  through 
  the 
  

   water 
  ; 
  and 
  T 
  = 
  the 
  vertical 
  resultant 
  of 
  the 
  surface 
  tension 
  

  

  

  