﻿216 
  

  

  Mr. 
  R. 
  Mallet 
  on 
  the 
  alleged 
  Expansion 
  

  

  duces 
  this 
  curio 
  us 
  phenomenon 
  and 
  often 
  in 
  direct 
  opposition 
  to 
  gravity, 
  

   is 
  a 
  different 
  and 
  a 
  much 
  more 
  delicate 
  and 
  difficult 
  inquiry, 
  which 
  he 
  

   must 
  leave 
  to 
  physicists 
  to 
  fully 
  investigate. 
  The 
  following 
  experiment 
  s, 
  

   however, 
  may 
  be 
  placed 
  on 
  record 
  as 
  tending 
  to 
  afford 
  some 
  little 
  dawn 
  

   of 
  light 
  upon 
  the 
  subject. 
  

  

  The 
  following 
  experiments 
  were 
  made 
  with 
  pieces 
  of 
  iron 
  cast 
  from 
  

   cast 
  iron 
  of 
  the 
  same 
  quality 
  as 
  that 
  which 
  filled 
  the 
  experimental 
  cone, 
  

   placed 
  upon 
  or 
  immersed 
  in 
  molten 
  cast 
  iron 
  of 
  like 
  quality 
  with 
  them- 
  

   selves, 
  so 
  far 
  as 
  such 
  can 
  be 
  secured 
  by 
  " 
  tapping 
  " 
  at 
  nearly 
  the 
  same 
  

   time 
  from 
  the 
  same 
  cupola 
  charged 
  with 
  the 
  same 
  materials. 
  

  

  Before 
  proceeding 
  to 
  describe 
  these, 
  it 
  will 
  be 
  necessary 
  to 
  deduce 
  from 
  

   the 
  cone 
  experiment 
  a 
  mean 
  coefficient 
  of 
  total 
  cubic 
  dilatation 
  for 
  the 
  

   whole 
  range 
  between 
  60° 
  and 
  2400° 
  Fahr. 
  for 
  the 
  grey 
  cast 
  iron 
  em- 
  

   ployed 
  in 
  these 
  experiments. 
  The 
  total 
  dilatation 
  was, 
  as 
  we 
  have 
  seen, 
  

   such 
  as 
  reduced 
  the 
  specific 
  gravity 
  of 
  the 
  cast 
  iron 
  when 
  cold 
  ( 
  = 
  7'17) 
  to 
  

   6-65 
  when 
  in 
  fusion. 
  The 
  cubic 
  dilatation 
  was 
  therefore 
  in 
  the 
  inverse 
  

   ratio 
  of 
  these 
  numbers, 
  or 
  as 
  1000 
  : 
  1078 
  ; 
  and 
  dividing 
  this 
  increase 
  in 
  

   volume 
  by 
  2340° 
  Fahr., 
  the 
  total 
  range 
  of 
  temperature, 
  we 
  obtain 
  for 
  

   the 
  mean 
  coefficient 
  of 
  cubic 
  dilatation 
  of 
  this 
  grey 
  cast 
  iron 
  for 
  1° 
  Fahr. 
  

   = 
  0-0000333, 
  or 
  approximately 
  for 
  its 
  mean 
  coefficient 
  of 
  linear 
  dilata- 
  

   tion 
  ™2^L 
  3 
  = 
  0-0000111. 
  These 
  coefficients 
  are 
  nearly 
  double 
  those 
  ob- 
  

   tained 
  by 
  Roy 
  and 
  by 
  Lavoisier 
  for 
  a 
  range 
  of 
  temperature 
  of 
  180° 
  Fahr., 
  

   viz. 
  between 
  32° 
  and 
  212°, 
  which 
  is 
  quite 
  what 
  we 
  should 
  expect, 
  as 
  the 
  

   coefficient 
  of 
  dilatation 
  in 
  all 
  bodies 
  increases 
  with 
  the 
  temperature. 
  

  

  We 
  have 
  seen 
  from 
  what 
  precedes 
  that 
  two 
  forces 
  at 
  least 
  are 
  concerned 
  

   in 
  the 
  phenomenon 
  of 
  cold 
  cast 
  iron 
  floating 
  upon 
  the 
  same 
  when 
  liquid, 
  

   viz. 
  : 
  — 
  

  

  A. 
  Buoyancy 
  or 
  its 
  opposite, 
  dependent 
  upon 
  the 
  relation 
  between 
  the 
  

   actual 
  specific 
  gravity 
  of 
  the 
  cold 
  metal 
  and 
  that 
  of 
  the 
  liquid 
  metal 
  upon 
  

   which 
  it 
  is 
  placed, 
  and 
  whose 
  absolute 
  power 
  for 
  any 
  given 
  difference 
  of 
  

   specific 
  gravity 
  depends 
  upon 
  the 
  volume 
  only 
  of 
  the 
  floating 
  mass. 
  

  

  3. 
  A 
  repulsive 
  force 
  of 
  some 
  kind 
  tending 
  to 
  repel 
  the 
  surfaces 
  in 
  contact 
  

   of 
  the 
  hot 
  and 
  cold 
  metals. 
  "Whatever 
  be 
  the 
  form 
  of 
  the 
  floating 
  solid, 
  

   this 
  repulsive 
  force 
  can 
  only 
  be 
  effective 
  m 
  producing 
  flotation 
  upon 
  

   such 
  surfaces 
  of 
  the 
  floating 
  solid 
  as 
  are 
  parallel 
  to 
  the 
  surface 
  of 
  the 
  

   liquid 
  metal, 
  or 
  at 
  least 
  so 
  circumstanced 
  that 
  repulsions 
  upon 
  one 
  sur- 
  

   face, 
  or 
  part 
  of 
  a 
  surface, 
  are 
  not 
  equilibrated 
  and 
  nullified 
  by 
  repulsions 
  

   upon 
  others 
  in 
  the 
  opposite 
  direction. 
  Thus 
  if 
  a 
  parallelopiped 
  float 
  with 
  

   one 
  of 
  v 
  its 
  surfaces 
  parallel 
  to 
  that 
  of 
  the 
  liquid 
  metal, 
  the 
  repulsions 
  

   upon 
  its 
  immersed 
  vertical 
  sides, 
  taken 
  two 
  and 
  two 
  respectively, 
  are 
  in 
  

   opposite 
  directions, 
  and 
  therefore 
  nullified, 
  and 
  the 
  bottom 
  or 
  horizontal 
  

   surface 
  is 
  alone 
  effective 
  in 
  producing 
  flotation. 
  So 
  also 
  if 
  a 
  cylinder 
  

   float 
  with 
  its 
  axis 
  horizontal, 
  the 
  ends 
  are 
  ineffective, 
  as 
  is 
  also 
  all 
  that 
  

   portion 
  of 
  the 
  cyliudric 
  surface 
  immersed 
  which 
  is 
  above 
  the 
  level 
  of 
  

   the 
  horizontal 
  diameter 
  of 
  the 
  cylinder. 
  

  

  