﻿522 
  Mr. 
  W.Williams 
  on 
  the 
  Temperature 
  Variation 
  oj 
  

  

  Thus 
  y 
  =i(/3 
  / 
  -8'), 
  v 
  =.-ib'(l3'-~8'), 
  &c, 
  and 
  in 
  the 
  

   approximate 
  temperature-factor 
  — 
  — 
  1 
  + 
  at 
  + 
  bt 
  2 
  , 
  which 
  holds 
  

  

  between 
  0° 
  and 
  100°, 
  a 
  = 
  e 
  + 
  i(fi-&) 
  and 
  b 
  = 
  ie(ff 
  — 
  8'). 
  

  

  This 
  result, 
  however, 
  cannot 
  at 
  present 
  be 
  subjected 
  to 
  any 
  

   reliable 
  and 
  decisive 
  test. 
  For 
  the 
  accurate 
  investigation 
  of 
  

   the 
  temperature-variation 
  of 
  a 
  over 
  wide 
  ranges 
  of 
  tem- 
  

   perature 
  has 
  not 
  been 
  made 
  for 
  pure 
  metals, 
  while, 
  though 
  

   various 
  observers 
  have 
  investigated 
  the 
  temperature-variations 
  

   of 
  s, 
  there 
  is 
  a 
  considerable 
  want 
  of 
  accordance 
  between 
  the 
  

   results 
  obtained. 
  The 
  accurate 
  determination 
  of 
  both 
  thermal 
  

   expansibility 
  and 
  specific 
  heat 
  are 
  matters 
  of 
  very 
  great 
  

   difficulty, 
  trifling 
  differences 
  in 
  the 
  values 
  of 
  either 
  quantity 
  

   producing 
  very 
  serious 
  differences 
  in 
  the 
  values 
  of 
  the 
  tem- 
  

   perature-variations 
  deduced 
  from 
  them. 
  Thus, 
  according 
  to 
  

   Naccari, 
  the 
  specific 
  heat 
  of 
  copper 
  at 
  100° 
  C. 
  is 
  '09422, 
  and 
  

   •09634 
  at 
  200° 
  0. 
  Assuming 
  the 
  latter 
  value 
  to 
  be 
  only 
  

   i 
  per 
  cent, 
  too 
  high, 
  the 
  value 
  at 
  200° 
  C. 
  would 
  be 
  '09586. 
  

   In 
  the 
  former 
  case 
  the 
  temperature-variation 
  is 
  '0000212, 
  in 
  

   the 
  latter 
  '000016 
  ; 
  so 
  that 
  a 
  difference 
  of 
  only 
  J 
  per 
  cent, 
  

   per 
  100° 
  in 
  the 
  value 
  of 
  s 
  produces 
  a 
  difference 
  of 
  30 
  per 
  

   cent, 
  in 
  the 
  value 
  of 
  the 
  temperature-variation. 
  Now, 
  apart 
  

   altogether 
  from 
  experimental 
  difficulties, 
  which 
  are 
  certainly 
  

   very 
  considerable, 
  differences 
  greater 
  than 
  this 
  can 
  arise 
  in 
  

   the 
  values 
  of 
  s 
  at 
  the 
  same 
  temperature 
  of 
  different 
  specimens 
  

   of 
  the 
  same 
  metal 
  from 
  differences 
  in 
  mechanical 
  qualities 
  

   alone. 
  Unless, 
  therefore, 
  the 
  values 
  of 
  <r, 
  a, 
  and 
  s 
  are 
  

   accurately 
  determined 
  for 
  the 
  same 
  specimen 
  and 
  over 
  a 
  

   considerable 
  range 
  of 
  temperature, 
  we 
  cannot 
  expect 
  a 
  close 
  

   and 
  definite 
  relation 
  to 
  exist 
  between 
  their 
  temperature 
  - 
  

   variations. 
  Hence, 
  as 
  the 
  experimental 
  information 
  has 
  to 
  

   be 
  collected 
  from 
  different 
  observers 
  for 
  different 
  specimens, 
  

   probably 
  in 
  different 
  mechanical 
  conditions, 
  we 
  must 
  be 
  

   satisfied 
  if 
  the 
  relation 
  y 
  = 
  ±(/3 
  / 
  — 
  8 
  r 
  ) 
  yields 
  values 
  of 
  the 
  proper 
  

   order 
  of 
  magnitude, 
  differing 
  from 
  those 
  obtained 
  experi- 
  

   mentally 
  by 
  no 
  more 
  than 
  those 
  values 
  for 
  the 
  same 
  metals 
  

   according 
  to 
  different 
  observers 
  differ 
  from 
  one 
  another. 
  

  

  In 
  spite, 
  however, 
  of 
  the 
  imperfections 
  of 
  the 
  experimental 
  

   data 
  available 
  to 
  test 
  the 
  matter, 
  enough 
  appears 
  to 
  be 
  known 
  

   to 
  shoAV 
  that 
  (j)(6), 
  for 
  many 
  of 
  the 
  metals, 
  is 
  mainly 
  deter- 
  

   mined 
  by 
  /3 
  and 
  8, 
  that 
  the 
  probable 
  form 
  of 
  the 
  function 
  is 
  

  

  ~- 
  , 
  and 
  that 
  7= 
  l-(/3' 
  — 
  S'), 
  as 
  the 
  following 
  results 
  will 
  

  

  show. 
  

  

  In 
  selecting 
  experimental 
  data 
  respecting 
  j3 
  and 
  8, 
  the 
  

   results 
  of 
  Fizeau 
  bv 
  the 
  interferometer 
  method 
  have 
  been 
  

  

  