﻿of 
  various 
  Substances 
  on 
  Solidification. 
  219 
  

  

  Now 
  the 
  effective 
  repellent 
  surfaces 
  are 
  here 
  those 
  of 
  the 
  lower 
  circles 
  

   of 
  the 
  respective 
  disks, 
  and 
  these 
  surfaces 
  are 
  to 
  each 
  other 
  in 
  the 
  ratio 
  

   of 
  1 
  (the 
  larger) 
  to 
  J. 
  "Whatever 
  be 
  the 
  nature, 
  therefore, 
  of 
  the 
  repel- 
  

   lent 
  force, 
  it 
  seems 
  to 
  be 
  proportionate 
  to 
  some 
  function 
  of 
  the 
  effective 
  

   surface 
  as 
  already 
  denned, 
  and 
  not 
  to 
  the 
  immersed 
  volume 
  of 
  the 
  solid 
  

   cast 
  iron 
  which 
  floats 
  upon 
  a 
  liquid 
  less 
  dense 
  than 
  itself. 
  

  

  In 
  all 
  these 
  experiments 
  the 
  mass 
  of 
  the 
  molten 
  cast 
  iron 
  was 
  large 
  in 
  

   proportion 
  to 
  the 
  pieces 
  placed 
  upon 
  it, 
  and 
  the 
  surface 
  was 
  kept 
  by 
  care- 
  

   ful 
  skimming 
  almost 
  perfectly 
  free 
  from 
  scoriae 
  or 
  oxide. 
  A 
  good 
  deal 
  

   of 
  difficulty 
  exists 
  in 
  observing 
  the 
  phenomena 
  in 
  such 
  experiments 
  as 
  

   these, 
  owing 
  to 
  the 
  glare 
  and 
  heat 
  of 
  the 
  molten 
  metal. 
  "Whatever 
  light 
  

   these 
  five 
  experiments 
  may 
  throw 
  upon 
  the 
  nature 
  of 
  the 
  force 
  which 
  

   produces 
  flotation, 
  the 
  subject 
  must 
  as 
  yet 
  be 
  viewed 
  as 
  very 
  incomplete. 
  

   There 
  are 
  some 
  facts 
  of 
  which 
  no 
  complete 
  explanation 
  can 
  be 
  offered 
  

   without 
  further 
  experimental 
  study 
  ; 
  such 
  as, 
  for 
  example, 
  that 
  a 
  piece 
  of 
  

   cold 
  cast 
  iron 
  which 
  floats 
  on 
  liquid 
  iron 
  of 
  its 
  own 
  quality 
  if 
  forcibly 
  

   thrust 
  to 
  the 
  bottom 
  and 
  rapidly 
  and 
  at 
  once 
  released, 
  rises 
  again 
  rapidly 
  

   to 
  the 
  surface 
  with 
  all 
  the 
  appearance 
  of 
  a 
  buoyant 
  body, 
  which 
  it 
  cer- 
  

   tainly 
  cannot 
  be. 
  

  

  From 
  what 
  precedes, 
  however, 
  we 
  may 
  summarize 
  as 
  follows 
  : 
  — 
  

  

  If 
  F 
  be 
  the 
  force 
  which 
  keep 
  the 
  solid 
  iron 
  floating, 
  B 
  the 
  buoyancy 
  

   + 
  of 
  the 
  solid 
  piece, 
  and 
  E 
  the 
  repellent 
  force, 
  then, 
  in 
  the 
  case 
  of 
  a 
  

   piece 
  floating 
  upon 
  molten 
  iron 
  of 
  its 
  own 
  quality, 
  B 
  is 
  always 
  negative, 
  

   and 
  F=E— 
  B, 
  the 
  value 
  of 
  E 
  for 
  any 
  given 
  case 
  depending 
  upon 
  the 
  

   effective 
  surface 
  of 
  the 
  solid, 
  and 
  that 
  of 
  B 
  upon 
  its 
  volume, 
  both 
  being 
  

   modified 
  by 
  the 
  initial 
  difference 
  in 
  temperature 
  between 
  the 
  solid 
  and 
  

   liquid 
  metals. 
  In 
  the 
  case 
  of 
  the 
  solid 
  being 
  placed 
  on 
  liquid 
  cast 
  iron 
  

   differing 
  in 
  quality 
  from 
  it, 
  B 
  may 
  be 
  either 
  positive 
  or 
  negative, 
  and 
  E 
  

   still 
  dependent 
  upon 
  the 
  conditions 
  already 
  stated. 
  Hence 
  in 
  any 
  such 
  

   case 
  we 
  may 
  have 
  

  

  F=K— 
  B 
  or 
  = 
  E 
  + 
  B. 
  

  

  These 
  conditions 
  kept 
  in 
  view 
  may 
  clear 
  up 
  many 
  phenomena 
  at 
  first 
  

   apparently 
  anomalous. 
  

  

  [However 
  feeble 
  may 
  be 
  the 
  ascending 
  currents, 
  above 
  referred 
  to, 
  

   upon 
  the 
  floating 
  disks 
  in 
  experiment 
  5, 
  their 
  effect 
  must 
  be 
  viewed 
  as 
  

   proportionate 
  to 
  the 
  lower 
  surfaces, 
  and 
  therefore 
  proportionate 
  to 
  

   the 
  repellent 
  force, 
  and 
  as 
  possibly 
  adding, 
  though 
  slightly, 
  to 
  its 
  

   effect.] 
  

  

  The 
  following 
  experiments 
  were 
  made 
  at 
  the 
  Eoyal 
  Arsenal, 
  Woolwich, 
  

   with 
  a 
  view 
  to 
  ascertain 
  whether 
  any 
  sensible 
  expansive 
  force 
  could 
  be 
  

   recognized 
  as 
  due 
  to 
  the 
  enlargement 
  in 
  volume 
  by 
  consolidation 
  of 
  a 
  

   spherical 
  mass 
  of 
  cast 
  iron 
  : 
  — 
  Two 
  spherical 
  bomb-shells, 
  each 
  of 
  about 
  

   10" 
  in 
  diameter 
  and 
  l"-5 
  in 
  thickness, 
  whose 
  external 
  orthogonal 
  dia- 
  

  

  