﻿Thevmil 
  Expansion 
  of 
  Porcelain. 
  639 
  

  

  (within 
  the 
  same 
  specified 
  limits) 
  whose 
  mean 
  is 
  t, 
  is 
  ex- 
  

   pressed 
  by 
  

  

  « 
  = 
  a 
  + 
  2^ 
  = 
  10- 
  9 
  (7566 
  + 
  44-580- 
  

  

  The 
  value 
  obtained 
  by 
  Bedford 
  for 
  the 
  linear 
  expansion 
  for 
  

   the 
  interval 
  0° 
  to 
  600° 
  was 
  as 
  follows 
  : 
  — 
  

  

  L 
  f 
  =L 
  [l 
  + 
  (3425* 
  + 
  l-07* 
  2 
  ) 
  10~ 
  9 
  ], 
  

  

  and 
  a 
  =a 
  + 
  26*= 
  (3425 
  + 
  2*140 
  10~ 
  9 
  - 
  

  

  Beyond 
  600° 
  the 
  formula 
  does 
  not 
  accurately 
  reproduce 
  

   the 
  observations, 
  which 
  were 
  carried 
  out 
  as 
  far 
  as 
  830°. 
  

   For 
  the 
  cubical 
  expansion 
  Bedford 
  gives 
  : 
  

  

  V*=V 
  [1+ 
  (10275 
  < 
  + 
  3-24^)10- 
  9 
  ], 
  

  

  and 
  a 
  =a 
  + 
  2bt 
  = 
  (L0275 
  + 
  &4:St)10- 
  9 
  . 
  

  

  The 
  result 
  obtained 
  by 
  Chappuis 
  for 
  the 
  linear 
  expansion 
  

   between 
  0° 
  and 
  83° 
  was 
  the 
  following 
  : 
  — 
  

  

  L, 
  = 
  L 
  [1 
  + 
  (2824-1^ 
  + 
  6-17^) 
  10- 
  9 
  ], 
  

  

  * 
  =a 
  + 
  2^= 
  (2824-1 
  + 
  12-34010- 
  9 
  . 
  

  

  And 
  for 
  the 
  cubical 
  expansion 
  : 
  

  

  V,=V 
  [l+(8472-4* 
  + 
  18-53* 
  2 
  )10- 
  9 
  ] 
  J 
  

  

  a 
  =a 
  + 
  2fo=(8472-4 
  + 
  37'06010- 
  9 
  . 
  

  

  The 
  considerable 
  difference 
  thus 
  presented 
  between 
  the 
  

   results 
  of 
  Bedford 
  and 
  Chappuis 
  is 
  most 
  striking 
  with 
  regard 
  

   to 
  the 
  increment 
  of 
  the 
  coefficient, 
  the 
  constant 
  b 
  in 
  the 
  linear 
  

   expansion 
  being 
  six 
  times 
  greater 
  according 
  to 
  Chappuis 
  than 
  

   according 
  to 
  Bedford. 
  The 
  constant 
  a 
  is 
  at 
  the 
  same 
  time 
  

   reduced. 
  

  

  The 
  results 
  now 
  presented 
  by 
  the 
  author 
  agree 
  tolerably 
  

   well 
  with 
  those 
  of 
  Chappuis, 
  but 
  emphasize 
  this 
  difference, 
  

   the 
  constant 
  b 
  being 
  seven 
  times 
  larger 
  than 
  according 
  to 
  

   Bedford, 
  and 
  the 
  constant 
  a 
  slightly 
  smaller 
  than 
  according 
  

   to 
  Chappuis. 
  

  

  In 
  the 
  following 
  table 
  are 
  set 
  forth 
  the 
  actual 
  coefficients 
  of 
  

   linear 
  expansion 
  at 
  particular 
  temperatures, 
  for 
  every 
  10° 
  up 
  

   to 
  the 
  limit 
  of 
  the 
  determinations, 
  deduced 
  from 
  the 
  obser- 
  

   vations 
  of 
  the 
  author 
  and 
  of 
  Chappuis 
  respectively. 
  The 
  

   actual 
  lengths 
  when 
  L 
  =l 
  are 
  also 
  graphically 
  expressed 
  by 
  

   the 
  two 
  curves 
  in 
  fig. 
  2 
  (the 
  dotted 
  one 
  representing 
  the 
  results 
  

   of 
  Chappuis), 
  for 
  which 
  degrees 
  of 
  temperature 
  are 
  taken 
  as 
  

   abscissae 
  and 
  the 
  lengths 
  as 
  ordinates. 
  

  

  2U2 
  

  

  