﻿Disks 
  and 
  Rings 
  of 
  Metal. 
  257 
  

  

  seriously 
  the 
  interesting 
  phenomena 
  presented 
  in 
  the 
  flotation 
  

   of 
  metals. 
  He 
  is 
  the 
  first 
  to 
  make 
  quantitative 
  experiments. 
  

   I 
  have 
  not 
  been 
  able 
  to 
  consult 
  the 
  volume 
  in 
  which 
  his 
  re- 
  

   search 
  appeared 
  and 
  all 
  I 
  have 
  of 
  his 
  work 
  is 
  the 
  abstract 
  of 
  it 
  

   given 
  bv 
  Daguin 
  in 
  his 
  Traite 
  de 
  Physique, 
  1878, 
  vol. 
  1, 
  p. 
  

   277. 
  

  

  Leboucher 
  floated 
  on 
  water 
  thin 
  plates 
  of 
  various 
  substances 
  

   and 
  then 
  loaded 
  these 
  gradually 
  till 
  they 
  broke 
  through 
  the 
  

   surface 
  of 
  the 
  water. 
  He 
  then 
  computes, 
  <?, 
  the 
  thickness 
  a 
  

   plate 
  must 
  have 
  so 
  that 
  it 
  will 
  just 
  not 
  float. 
  Knowing 
  TF, 
  the 
  

   total 
  weight 
  required 
  to 
  make 
  the 
  plate 
  sink 
  ; 
  d, 
  the 
  density 
  of 
  

   the 
  substance, 
  and 
  s, 
  the 
  area 
  of 
  the 
  plate, 
  we 
  have 
  W=s 
  e 
  d. 
  

   The 
  value 
  of 
  e 
  found 
  for 
  slate, 
  mica, 
  and 
  brass 
  is 
  respectively 
  

  

  1.5mm 
  -jmm^ 
  and 
  . 
  5 
  mm 
  # 
  

  

  To 
  ascertain 
  the 
  upward 
  hydrostatic 
  pressure 
  on 
  the 
  plate 
  he 
  

   measured 
  the 
  depth, 
  h, 
  of 
  the 
  bottom 
  of 
  the 
  loaded 
  plate 
  below 
  

   the 
  general 
  level 
  of 
  the 
  water 
  by 
  means 
  of 
  a 
  spherometer, 
  the 
  

   screw 
  of 
  which 
  was 
  brought 
  in 
  contact 
  with 
  the 
  surface 
  of 
  the 
  

   water 
  and 
  then 
  with 
  the 
  surface 
  of 
  the 
  plate. 
  The 
  spher- 
  

   ometer 
  rested 
  on 
  a 
  horizontal 
  annulus 
  of 
  glass 
  placed 
  on 
  the 
  

   rim 
  of 
  the 
  vessel 
  holding 
  the 
  water. 
  Adding 
  e 
  to 
  the 
  depth 
  

   measured 
  we 
  have 
  A, 
  and 
  the 
  upward 
  pressure 
  on 
  the 
  plate 
  

   =s 
  h 
  X 
  density 
  of 
  water. 
  

  

  Leboucher 
  does 
  not 
  arrive 
  at 
  an 
  equation 
  of 
  the 
  forces 
  act- 
  

   ing 
  on 
  the 
  floating 
  plate, 
  but 
  states 
  that 
  the 
  upward 
  hydrostatic 
  

   pressure 
  on 
  the 
  plate 
  is 
  a 
  little 
  less 
  than 
  the 
  weight 
  of 
  the 
  

   plate 
  ; 
  the 
  difference 
  is 
  generally 
  yL- 
  to 
  4- 
  of 
  the 
  weight 
  of 
  the 
  

   latter; 
  which 
  he 
  explains 
  by 
  the 
  supposed 
  existence 
  of 
  a 
  capil- 
  

   lary 
  tension 
  on 
  the 
  lower 
  edge 
  of 
  the 
  plate 
  which 
  is 
  always 
  

   slightly 
  rounded. 
  This 
  tension 
  acts 
  with 
  the 
  upward 
  hydro- 
  

   static 
  pressure 
  irixbalancing 
  the 
  weight 
  of 
  the 
  plate. 
  I 
  shall 
  

   recur 
  to 
  this 
  opinion 
  of 
  M. 
  Leboucher. 
  

  

  Equation 
  of 
  the 
  forces 
  acting 
  in 
  the 
  flotation 
  of 
  a 
  disk 
  of 
  metal. 
  

  

  Three 
  forces 
  are 
  acting 
  on 
  a 
  floating 
  disk 
  of 
  metal 
  (1) 
  W 
  = 
  

   the 
  weight 
  of 
  the 
  disk 
  ; 
  (2) 
  P 
  = 
  the 
  upward 
  hydrostatic 
  pres- 
  

   sure 
  on 
  the 
  bottom 
  of 
  the 
  disk; 
  (3j 
  T= 
  the 
  vertical 
  resultant 
  

   of 
  the 
  surface 
  tension 
  of 
  the 
  water 
  along 
  the 
  circumference 
  of 
  

   the 
  upper 
  edge 
  of 
  the 
  disk. 
  The 
  relation 
  of 
  these 
  forces 
  is 
  

   given 
  by 
  the 
  simple 
  formula 
  

  

  W 
  = 
  P+T 
  

  

  We 
  can 
  measure 
  W 
  and 
  P, 
  and 
  T=W— 
  P. 
  Let 
  circ 
  = 
  the 
  

  

  T 
  

  

  circumference 
  of 
  the 
  disk, 
  then 
  A 
  = 
  - 
  — 
  i-cos. 
  angle 
  of 
  vertical 
  

  

  circ 
  " 
  

  

  with 
  the 
  depressed 
  water 
  surface 
  at 
  upper 
  edge 
  of 
  disk 
  ; 
  A 
  

  

  