﻿Disks 
  and 
  Rings 
  of 
  Metal. 
  267 
  

  

  reflected 
  edge 
  of 
  the 
  scale 
  becomes 
  straight 
  and 
  parallel 
  to 
  the 
  

   edge 
  of 
  the 
  scale 
  itself, 
  we 
  determine 
  the 
  extent 
  of 
  the 
  de- 
  

   pressed 
  water-surface 
  on 
  either 
  side 
  of 
  the 
  vertical 
  passing 
  

   through 
  the 
  axis 
  of 
  the 
  wire. 
  This 
  depression 
  of 
  the 
  surface 
  

   was 
  found 
  to 
  extend 
  to 
  15 
  mm 
  on 
  either 
  side 
  of 
  the 
  wire, 
  when 
  

   the 
  latter 
  was 
  so 
  deep 
  that 
  it 
  was 
  just 
  on 
  the 
  point 
  of 
  breaking 
  

   through 
  the 
  surface. 
  I 
  measured 
  the 
  area 
  of 
  the 
  vertical 
  sec- 
  

   tion 
  of 
  this 
  depression 
  below 
  the 
  horizontal 
  surface 
  of 
  the 
  

   water 
  and 
  found 
  it 
  to 
  be 
  about 
  25 
  times 
  the 
  area 
  of 
  the 
  cross- 
  

   section 
  of 
  the 
  wire. 
  

  

  The 
  weight 
  on 
  one 
  centimeter 
  of 
  a 
  ring, 
  formed 
  of 
  wire 
  l 
  mm 
  

   in 
  diameter, 
  when 
  on 
  the 
  point 
  of 
  sinking, 
  is 
  *1696 
  gram, 
  and 
  

   the 
  volume 
  of 
  one 
  centimeter 
  in 
  length 
  of 
  the 
  depression 
  in 
  

   the 
  water, 
  including 
  the 
  volume 
  of 
  the 
  wire, 
  if 
  supposed 
  to 
  be 
  

   formed 
  of 
  water, 
  will 
  weigh 
  '2 
  grams, 
  or 
  20 
  per 
  cent 
  more 
  

   than 
  the 
  weight 
  on 
  one 
  centimeter 
  of 
  the 
  wire. 
  

  

  Evidently 
  the 
  two 
  opposite 
  surfaces 
  of 
  the 
  depression 
  in 
  the 
  

   water 
  made 
  by 
  the 
  ring 
  cannot 
  be 
  similar, 
  as 
  is 
  the 
  case 
  in 
  

   fig. 
  5, 
  showing 
  the 
  contour 
  of 
  the 
  surfaces 
  on 
  either 
  side 
  of 
  the 
  

   straight 
  wire, 
  for 
  the 
  curvatures 
  of 
  the 
  water-surfaces 
  in 
  the 
  

   horizontal 
  and 
  vertical 
  planes 
  on 
  the 
  outer 
  circumference 
  of 
  

   the 
  ring 
  are 
  opposed 
  to 
  one 
  another, 
  while 
  these 
  curvatures 
  on 
  

   the 
  inner 
  circumference 
  of 
  the 
  ring 
  have 
  the 
  same 
  sign. 
  It 
  

  

  follows 
  that 
  P=A 
  (77 
  — 
  -ar) 
  gives 
  the 
  molecular 
  pressure 
  of 
  

  

  the 
  outer 
  and 
  lower 
  border 
  of 
  the 
  surface 
  of 
  the 
  depression, 
  

  

  and 
  P=A( 
  — 
  + 
  — 
  - 
  , 
  the 
  pressure 
  of 
  the 
  lower 
  border 
  of 
  the 
  

  

  inner 
  surface. 
  Assuming 
  these 
  pressures 
  equal 
  to 
  the 
  hydro- 
  

   static 
  pressure, 
  the 
  -radius 
  of 
  curvature 
  on 
  the 
  vertical 
  plane 
  of 
  

   the 
  inner 
  surface 
  will 
  be 
  to 
  the 
  radius 
  of 
  curvature 
  in 
  the 
  ver- 
  

   tical 
  plane 
  of 
  the 
  outer 
  surface 
  as 
  1 
  : 
  1*162, 
  as 
  is 
  shown 
  in 
  fig. 
  9. 
  

  

  Rings 
  of 
  wire 
  l 
  mm 
  in 
  diameter 
  were 
  made 
  of 
  

   iron, 
  tinned 
  iron, 
  copper, 
  brass 
  and 
  of 
  german 
  

   silver. 
  The 
  average 
  diameter 
  of 
  the 
  axes 
  of 
  these 
  

   rings 
  is 
  5*35 
  cm 
  . 
  The 
  weight 
  on 
  a 
  centimeter 
  of 
  

   the 
  circumference 
  of 
  the 
  axis 
  of 
  a 
  ring 
  required 
  

   to 
  make 
  the 
  ring 
  sink, 
  averaged, 
  for 
  the 
  Hve 
  

   rings, 
  -1696 
  gram. 
  

  

  Experiments 
  on 
  rings 
  from 
  3 
  to 
  7*5 
  centimeters 
  

   in 
  diameter 
  showed 
  that, 
  within 
  these 
  limits, 
  the 
  

   weight 
  per 
  centimeter 
  of 
  circumference 
  required 
  

   to 
  sink 
  the 
  ring 
  is 
  constant, 
  and 
  therefore 
  inde- 
  

   pendent 
  of 
  the 
  length 
  of 
  the 
  circumference 
  of 
  the 
  

   ring. 
  The 
  difference 
  between 
  the 
  weight 
  per 
  centimeter 
  re- 
  

   quired 
  to 
  sink 
  the 
  ring 
  of 
  3 
  cm 
  and 
  the 
  ring 
  of 
  7'5 
  cm 
  , 
  as 
  given 
  

   by 
  the 
  experiments, 
  amounted 
  to 
  only 
  -J- 
  of 
  one 
  per 
  cent. 
  

  

  