﻿Thermal 
  Expansion 
  of 
  Porcelain. 
  635 
  

  

  / 
  2 
  is 
  the 
  observed 
  number 
  of 
  bands 
  for 
  the 
  first 
  interval, 
  

   and 
  f 
  s 
  for 
  the 
  second. 
  

  

  The 
  small 
  correction 
  which 
  follows 
  is 
  that 
  which 
  has 
  to 
  be 
  

   applied 
  for 
  the 
  alteration 
  of 
  the 
  refractive 
  index 
  of 
  air 
  due 
  to 
  

   change 
  of 
  temperature 
  and 
  pressure. 
  It 
  is 
  fully 
  discussed 
  

   on 
  p. 
  349 
  o£ 
  the 
  memoir 
  (loc. 
  cit.) 
  on 
  the 
  dilatometer. 
  The 
  

   formula 
  is 
  

  

  where 
  /represents 
  the 
  observed 
  and/ 
  7 
  the 
  corrected 
  number 
  

   of 
  bands, 
  a 
  the 
  coefficient 
  of 
  expansion 
  of 
  air, 
  and 
  n 
  the 
  

   refractive 
  index 
  of 
  air 
  for 
  the 
  wave-length 
  X 
  of 
  the 
  light 
  

   employed. 
  f 
  2 
  ' 
  and// 
  are 
  consequently 
  the 
  corrected 
  numbers 
  

   of 
  bands 
  for 
  the 
  two 
  intervals. 
  

  

  Then 
  follows 
  the 
  actual 
  amount 
  of 
  diminution 
  of 
  thickness 
  

   of 
  the 
  air-layer, 
  as 
  given 
  by 
  the 
  product 
  /'A/2, 
  where 
  A/2 
  is 
  

   0-0003281 
  mm. 
  

  

  The 
  expansion 
  of 
  the 
  platinum-iridium 
  screws 
  and 
  of 
  the 
  

   aluminium 
  compensator 
  are 
  next 
  given, 
  calculated 
  from 
  the 
  

   formulae 
  (vide 
  Phil. 
  Trans. 
  A, 
  vol. 
  cxci. 
  pp. 
  353 
  & 
  356 
  ; 
  for 
  

   determinations 
  of 
  these 
  coefficients): 
  — 
  

  

  For 
  the 
  screws, 
  / 
  puW 
  8600 
  + 
  4-56 
  ^ 
  2 
  )] 
  fe-*i), 
  

   „ 
  aluminium, 
  ? 
  a 
  flQ- 
  8 
  ('2204 
  + 
  2-12^^^1 
  {t 
  2 
  -h), 
  

  

  for 
  the 
  first 
  interval, 
  and 
  substituting 
  u 
  for 
  U 
  for 
  the 
  second 
  

   interval. 
  

  

  The 
  slight 
  excess 
  of 
  expansion 
  on 
  the 
  part 
  of 
  the 
  aluminium 
  

   over 
  that 
  of 
  the 
  screws, 
  acts 
  like 
  the 
  expanding 
  porcelain 
  in 
  

   diminishing 
  the 
  thickness 
  of 
  the 
  air-layer, 
  and 
  has 
  therefore 
  

   to 
  be 
  deducted 
  from 
  the 
  total 
  observed 
  diminution; 
  the 
  

   resulting 
  differences 
  represent 
  the 
  amounts 
  of 
  expansion 
  of 
  

   the 
  porcelain 
  for 
  the 
  two 
  intervals. 
  Then 
  follow 
  the 
  calcu- 
  

   lations 
  of 
  the 
  two 
  constants 
  a 
  and 
  b 
  of 
  the 
  coefficient 
  of 
  

   expansion 
  of 
  porcelain. 
  For 
  the 
  discussion 
  of 
  the 
  formula} 
  

   employed, 
  and 
  the 
  mode 
  of 
  deriving 
  them, 
  the 
  memoir 
  

   on 
  the 
  dilatometer 
  should 
  be 
  consulted 
  (loc. 
  cit. 
  p. 
  352). 
  

  

  