﻿Disks 
  and 
  Rings 
  of 
  Metal. 
  263 
  

  

  The 
  values 
  of 
  A 
  given 
  by 
  the 
  experiments 
  on 
  the 
  three 
  disks 
  

   are 
  -0767, 
  -0821, 
  -0787. 
  The 
  mean 
  value 
  is 
  -0791. 
  The 
  mean 
  

   value 
  of 
  28 
  determinations 
  of 
  A 
  is 
  -0772. 
  The 
  value 
  of 
  A 
  

   found 
  from 
  the 
  experiments 
  on 
  the 
  disks 
  is 
  so 
  close 
  to 
  this 
  

   value 
  (only 
  2 
  T 
  \ 
  per 
  cent 
  higher), 
  that 
  the 
  formula 
  W=P+T 
  

   seems 
  to 
  be 
  the 
  correct 
  expression 
  for 
  the 
  equation 
  of 
  the 
  forces 
  

   concerned 
  in 
  the 
  notation 
  of 
  a 
  disk. 
  However, 
  I 
  do 
  not 
  think 
  

   that 
  experiments 
  on 
  floating 
  disks 
  are 
  of 
  value 
  in 
  determining 
  

   A, 
  for 
  the 
  determination 
  of 
  the 
  value 
  of 
  A, 
  and 
  consequently 
  

   of 
  P, 
  is 
  too 
  uncertain. 
  The 
  maximum 
  value 
  of 
  A 
  obtained 
  

   from 
  the 
  experiments 
  on 
  the 
  disks 
  is 
  7 
  per 
  cent 
  higher 
  than 
  

   the 
  minimum 
  and 
  even 
  this 
  degree 
  of 
  concordance 
  I 
  regard 
  as 
  

   accidental. 
  

  

  It 
  is 
  seen 
  that 
  I 
  do 
  not 
  agree 
  with 
  M. 
  Leboucher 
  in 
  locating 
  

   the 
  upward 
  action 
  of 
  the 
  surface 
  tension 
  of 
  the 
  water 
  along 
  

   the 
  lower 
  edge 
  of 
  the 
  disk, 
  where 
  M. 
  Leboucher 
  evidently 
  

   regards 
  the 
  water 
  as 
  having 
  a 
  free 
  surface 
  ; 
  which 
  it 
  has 
  not, 
  

   as 
  I 
  shall 
  subsequently 
  show. 
  I 
  locate 
  it 
  on 
  the 
  free 
  curved 
  

   surface 
  of 
  the 
  water 
  above 
  the 
  upper 
  edge 
  of 
  the 
  disk. 
  

  

  If 
  this 
  upward 
  pressure 
  on 
  the 
  disk 
  should 
  be 
  produced 
  as 
  M. 
  

   Leboucher 
  supposes, 
  then 
  this 
  pressure 
  will 
  be 
  nearly 
  indepen- 
  

   dent 
  of 
  the 
  radius 
  of 
  curvature 
  of 
  the 
  lower 
  edge 
  of 
  the 
  disk, 
  

   for 
  the 
  area 
  of 
  this 
  curved 
  surface 
  will 
  vary 
  as 
  its 
  radius 
  while 
  

   the 
  capillary 
  pressure 
  will 
  vary 
  inversely 
  as 
  its 
  radius. 
  The 
  

  

  capillary 
  pressure 
  P 
  = 
  A 
  (^-f^) 
  ; 
  where 
  K 
  is 
  the 
  radius 
  of 
  

  

  the 
  curved 
  edge, 
  which 
  we 
  suppose 
  variable, 
  while 
  W 
  remains 
  

   constant, 
  varying 
  very 
  little 
  from 
  the 
  radius 
  of 
  the 
  disk 
  ; 
  but 
  

  

  ^ 
  is 
  so 
  very 
  small 
  compared 
  with 
  ^ 
  that 
  the 
  value 
  of 
  P 
  varies 
  

  

  but 
  little 
  with 
  various 
  values 
  of 
  P.* 
  

  

  On 
  the 
  equation 
  of 
  the 
  forces 
  acting 
  on 
  a 
  floating 
  ring 
  of 
  metal, 
  

   and 
  on 
  measures 
  of 
  surf 
  ace 
  tension 
  obtained 
  from 
  experiments 
  

   on 
  floating 
  rings 
  made 
  of 
  various 
  metals. 
  

  

  The 
  floating 
  ring 
  presents 
  more 
  complicated, 
  but 
  more 
  inter- 
  

   esting 
  phenomena, 
  than 
  those 
  given 
  by 
  a 
  floating 
  disk. 
  In 
  the 
  

   floating 
  disk 
  we 
  have 
  W 
  and 
  P 
  quantities 
  about 
  ten 
  times 
  

   larger 
  than 
  T, 
  and 
  T 
  is 
  the 
  vertical 
  resultant 
  of 
  the 
  tension 
  

   acting 
  along 
  only 
  one 
  circumference 
  ; 
  whereas 
  in 
  the 
  case 
  of 
  

   the 
  floating 
  ring 
  P 
  is 
  a 
  small 
  fraction, 
  only 
  T 
  ^ 
  or 
  ^ 
  T 
  , 
  of 
  W, 
  

   and 
  W 
  is 
  nearly 
  equal 
  to 
  the 
  vertical 
  resultant 
  of 
  the 
  surface- 
  

  

  * 
  A 
  drawing 
  of 
  the 
  edge 
  of 
  disk 
  No. 
  3 
  with 
  a 
  microscope 
  and 
  camera 
  lucida 
  

   gave 
  ^ 
  mm 
  for 
  the 
  radius 
  of 
  curvature 
  of 
  the 
  edge 
  This 
  makes 
  - 
  =200, 
  while 
  — 
  

   is 
  only 
  0-36. 
  

  

  