﻿-526 
  Mr. 
  W. 
  Williams 
  on 
  the 
  Temperature 
  Variation 
  of 
  

  

  denoted 
  by 
  F, 
  those 
  given 
  by 
  Benoit 
  denoted 
  by 
  B, 
  and 
  

   those 
  given 
  by 
  Vicentini 
  and 
  Omodei 
  denoted 
  by 
  V, 
  have 
  

   also 
  been 
  inserted. 
  The 
  values 
  calculated 
  from 
  Fleming 
  and 
  

   Dewar's 
  observations 
  have 
  been 
  obtained 
  by 
  applying 
  to 
  

  

  them 
  the 
  approximate 
  relation 
  — 
  =(l 
  + 
  et)(l+yt) 
  between 
  

   0° 
  and 
  100°. 
  °"° 
  

  

  T 
  denotes 
  the 
  values 
  obtained 
  from 
  thermal 
  data, 
  8 
  and 
  /3, 
  

   while 
  E, 
  in 
  the 
  case 
  of 
  copper, 
  denotes 
  the 
  values 
  given 
  by 
  

   Elmore. 
  

  

  In 
  the 
  case 
  of 
  the 
  metals 
  tabulated 
  above, 
  it 
  will 
  be 
  found 
  

   that 
  not 
  only 
  is 
  7 
  approximately 
  i(/3' 
  — 
  8') 
  and 
  a 
  approxi- 
  

   mately 
  e 
  + 
  ^((3' 
  — 
  8'), 
  but 
  that 
  7 
  is 
  also 
  approximately 
  J/3 
  or 
  

   J/3', 
  and 
  a 
  approximately 
  e 
  + 
  J/3, 
  or 
  e-f 
  J/3', 
  as 
  the 
  table 
  

   opposite 
  (p. 
  527) 
  will 
  show. 
  

  

  In 
  the 
  table 
  the 
  column 
  headed 
  7 
  contains 
  the 
  values 
  

  

  calculated 
  for 
  that 
  constant 
  from 
  Fleming 
  and 
  Dewar's 
  

  

  observations 
  ; 
  the 
  first 
  column 
  headed 
  Diff. 
  indicates 
  the 
  

  

  07 
  . 
  -. 
  

  

  percentage 
  difference 
  of 
  -~ 
  from 
  its 
  mean 
  value 
  1*046, 
  while 
  

  

  the 
  second 
  is 
  the 
  percentage 
  difference 
  of 
  -£ 
  from 
  its 
  mean 
  

   value 
  -896. 
  * 
  

  

  From 
  the 
  table 
  it 
  will 
  be 
  seen 
  that 
  the 
  order 
  in 
  which 
  the 
  

   metals 
  stand 
  as 
  regards 
  the 
  values 
  of 
  7 
  is, 
  with 
  the 
  exception 
  

   of 
  aluminium, 
  the 
  same 
  as 
  that 
  as 
  regards 
  the 
  values 
  of 
  J/3 
  

  

  and 
  J/3' 
  ; 
  that 
  the 
  ratios 
  -± 
  and 
  -2 
  are 
  approximately 
  con- 
  

   stant 
  ; 
  and 
  that 
  the 
  values 
  deduced 
  for 
  a 
  from 
  7, 
  namely 
  

   € 
  + 
  7, 
  are 
  practically 
  the 
  same 
  as 
  those 
  deduced 
  from 
  /3 
  and 
  

   J3', 
  namely 
  e+J/3, 
  and 
  e 
  + 
  J/3'. 
  

  

  Hence, 
  since 
  for 
  these 
  metals 
  7 
  is 
  approximately 
  i(/3' 
  — 
  £')• 
  

   and 
  also 
  approximately 
  J/3 
  or 
  J/3', 
  it 
  follows 
  that 
  8' 
  must 
  be 
  

   approximately 
  J/3', 
  and 
  8 
  approximately 
  J/3. 
  That 
  is, 
  that 
  

   the 
  temperature- 
  variation 
  of 
  the 
  specific 
  heat 
  must 
  depend 
  

   upon 
  that 
  of 
  the 
  thermal 
  expansibility, 
  or, 
  more 
  correctly 
  

   perhaps, 
  that 
  tlie 
  temperature-variation 
  of 
  the 
  specific 
  heat 
  and 
  

   that 
  of 
  the 
  thermal 
  expansibility 
  must 
  depend 
  upon 
  the 
  tern- 
  

   perature-variation 
  of 
  the 
  same 
  physical 
  property 
  of 
  the 
  metal. 
  

   This 
  result, 
  again, 
  on 
  account 
  of 
  uncertainties 
  respecting 
  the 
  

   experimental 
  data 
  bearing 
  upon 
  it, 
  cannot 
  be 
  accepted 
  without 
  

   considerable 
  doubt 
  and 
  hesitation. 
  I 
  have 
  only 
  ventured 
  to 
  

   put 
  it 
  forward 
  because 
  it 
  appears 
  to 
  have 
  enough 
  probability 
  

   in 
  its 
  favour, 
  and 
  to 
  be 
  sufficiently 
  interesting 
  and 
  suggestive 
  

   to 
  deserve 
  a 
  fuller 
  consideration, 
  and 
  to 
  have 
  a 
  special 
  in- 
  

   vestigation 
  into 
  the 
  experimental 
  facts 
  bearing 
  upon 
  it 
  made 
  

   by 
  competent 
  observers. 
  

  

  