﻿638 
  Mr. 
  A. 
  E. 
  Tutton 
  on 
  the 
  

  

  It 
  will 
  be 
  sufficient 
  here 
  merely 
  to 
  state 
  the 
  formulae, 
  which 
  

   are 
  as 
  follows: 
  — 
  

  

  & 
  = 
  (fr 
  + 
  M 
  (Lfr-L,,) 
  _ 
  (t 
  1 
  + 
  t 
  2 
  )(L 
  t 
  -'Lt 
  1 
  ) 
  

  

  (t2-h)(h-t 
  2 
  ) 
  {h-h)[t 
  d 
  -t 
  2 
  ) 
  ' 
  

  

  a,— 
  ^ 
  — 
  L^ 
  __ 
  L/ 
  q 
  — 
  -L 
  fl 
  

  

  9 
  ~ 
  (*« 
  - 
  h) 
  to 
  - 
  1 
  2 
  ) 
  ~ 
  (t 
  2 
  - 
  h) 
  (/» 
  - 
  y 
  ' 
  

  

  Lo— 
  L/i— 
  ^i 
  — 
  <M 
  2 
  > 
  

   a 
  = 
  r 
  , 
  b 
  = 
  -. 
  

  

  The 
  results 
  for 
  the 
  three 
  pieces 
  of 
  porcelain 
  tube 
  are 
  com- 
  

   pared 
  in 
  the 
  following 
  table, 
  and 
  the 
  final 
  mean 
  result 
  for 
  

   the 
  linear 
  expansion 
  of 
  Bayeux 
  porcelain 
  is 
  given 
  at 
  the 
  foot. 
  

  

  Specimen 
  1 
  O000 
  002 
  534 
  0*000 
  000 
  008 
  08 
  

  

  „ 
  2 
  2521 
  709 
  

  

  3 
  2510 
  713 
  

  

  Final 
  mean 
  values 
  : 
  a 
  = 
  0'000 
  002 
  522, 
  6 
  = 
  0'000 
  000 
  007 
  43. 
  

  

  This 
  investigation, 
  therefore, 
  affords 
  as 
  the 
  mean 
  coefficient 
  

   of 
  linear 
  expansion, 
  a 
  + 
  bt, 
  of 
  Bayeux 
  porcelain, 
  between 
  

   0° 
  and 
  f, 
  within 
  the 
  limits 
  of 
  0° 
  and 
  120°, 
  the 
  value 
  

  

  10- 
  9 
  (2522 
  + 
  7-43*). 
  

   That 
  is, 
  

  

  L, 
  = 
  L 
  [l 
  + 
  10- 
  9 
  (2522£ 
  + 
  7-43* 
  2 
  )]. 
  

  

  The 
  true 
  coefficient, 
  a, 
  of 
  linear 
  expansion 
  at 
  t°, 
  or 
  the 
  mean 
  

   coefficient 
  between 
  any 
  two 
  temperatures 
  (within 
  the 
  limits 
  

   of 
  0° 
  and 
  120°) 
  whose 
  mean 
  is 
  t, 
  is 
  as 
  follows 
  : 
  — 
  

  

  a 
  = 
  a 
  + 
  2bt=0-000 
  002 
  522 
  + 
  0-000 
  000 
  014 
  86t 
  ; 
  

  

  or 
  10- 
  9 
  (2522 
  + 
  14-860- 
  

  

  The 
  mean 
  coefficient 
  of 
  the 
  cubical 
  expansion 
  between 
  

   0° 
  and 
  t°, 
  for 
  the 
  same 
  limits 
  of 
  0° 
  and 
  120°, 
  derived 
  from 
  this 
  

   investigation, 
  is 
  : 
  

  

  a 
  + 
  6* 
  = 
  0-000 
  007 
  566 
  + 
  0*000 
  000 
  022 
  29*; 
  

  

  or 
  10- 
  9 
  (7566 
  + 
  22-290- 
  

  

  That 
  is 
  

  

  V,=V 
  [l 
  + 
  10- 
  9 
  (7566/ 
  + 
  22-29* 
  2 
  )]. 
  

  

  The 
  actual 
  coefficient 
  of 
  cubical 
  expansion, 
  «, 
  at 
  any 
  tem- 
  

   perature 
  t, 
  within 
  the 
  limits 
  0° 
  to 
  120°, 
  and 
  also 
  the 
  mean 
  

   coefficient 
  of 
  cubical 
  expansion 
  between 
  any 
  two 
  temperatures 
  

  

  