﻿1875.] 
  

  

  On 
  Dulong 
  and 
  Petit' 
  's 
  Law 
  of 
  Cooling. 
  

  

  465 
  

  

  VI. 
  u 
  Note 
  on 
  Dulong 
  and 
  Petit's 
  Law 
  of 
  Cooling/' 
  By 
  

   Donald 
  Macfarlane. 
  Communicated 
  by 
  Prof. 
  Sir 
  W. 
  

   Thomson, 
  F.R.S. 
  Received 
  June 
  10, 
  1875. 
  

  

  The 
  ' 
  Journal 
  de 
  Physique 
  ' 
  for 
  December 
  1873 
  contains 
  a 
  friendly 
  

   notice 
  by 
  Professor 
  A. 
  Cornu 
  of 
  experiments 
  made 
  to 
  determine 
  sur- 
  

   face-conductivity 
  for 
  heat 
  (or, 
  as 
  we 
  may 
  call 
  it, 
  " 
  thermal 
  emissivity") 
  

   in 
  absolute 
  measure, 
  an 
  account 
  of 
  which 
  was 
  communicated 
  to 
  the 
  Eoyal 
  

   Society, 
  and 
  read 
  January 
  1872 
  (see 
  Proceedings, 
  vol. 
  xx. 
  p. 
  90). 
  On 
  the 
  

   results 
  there 
  given 
  M. 
  Cornu 
  remarks 
  : 
  — 
  

  

  " 
  Ces 
  nombres 
  verifient 
  la 
  conclusion 
  de 
  Dulong 
  et 
  Petit, 
  a 
  savoir 
  

   que 
  les 
  vitesses 
  de 
  refroidissement 
  ne 
  dependent 
  dei'etat 
  des 
  surfaces 
  que 
  

   par 
  une 
  constante 
  de 
  proportionality. 
  

  

  " 
  L'acceleration 
  negative 
  du 
  rapport 
  des 
  pouvoirs 
  emissifs 
  n'infirme 
  pas 
  

   sensiblement 
  cette 
  conclusion 
  ; 
  elle 
  est 
  si 
  faible 
  qu'elle 
  peut 
  etre 
  attribute 
  

   a 
  une 
  petite 
  erreur 
  reguliere 
  dans 
  revaluation 
  des 
  differences 
  de 
  tempera- 
  

   ture 
  ; 
  en 
  effet, 
  l'auteur 
  ne 
  parait 
  tenir 
  aucun 
  compte 
  d'une 
  cause 
  delicate 
  

   d'erreur 
  qui 
  avait 
  preoccupe 
  Dulong 
  et 
  Petit, 
  a 
  savoir 
  la 
  resistance 
  inegale 
  

   a 
  la 
  transmission 
  de 
  la 
  chaleur 
  dans 
  les 
  deux 
  cas. 
  II 
  est 
  evident 
  que, 
  dans 
  

   le 
  refroidissement 
  le 
  plus 
  rapide, 
  la 
  temperature 
  est 
  distribue'e 
  moins 
  

   uniformement 
  que 
  dans 
  le 
  cas 
  d'un 
  refroidissement 
  lent 
  ; 
  l'aiguille 
  ther- 
  

   moelectrique 
  indique 
  done 
  moins 
  bien 
  la 
  temperature 
  moyeime 
  de 
  la 
  masse 
  

   que 
  les 
  boules 
  de 
  mercure 
  des 
  physiciens 
  francais." 
  

  

  On 
  this 
  it 
  is 
  to 
  be 
  remarked 
  that 
  a 
  rigorous 
  proportionality 
  in 
  the 
  rates 
  

   of 
  cooling 
  of 
  different 
  surfaces 
  is 
  in 
  itself 
  not 
  probable 
  ; 
  and 
  my 
  experi- 
  

   ments 
  in 
  fact 
  disprove 
  it, 
  so 
  far 
  as 
  it 
  is 
  not 
  at 
  all 
  likely 
  that 
  the 
  errors 
  of 
  

   observation 
  could 
  be 
  so 
  great 
  or 
  so 
  consistently 
  regular 
  in 
  the 
  same 
  direc- 
  

   tion 
  as 
  the 
  truth 
  of 
  the 
  supposed 
  law 
  would 
  require. 
  

  

  As 
  to 
  the 
  variation 
  of 
  temperature 
  from 
  centre 
  to 
  surface 
  occasioned 
  

   by 
  the 
  rapid 
  cooling 
  of 
  the 
  ball, 
  this 
  was 
  certainly 
  not 
  overlooked 
  in 
  

   planning 
  the 
  experiments. 
  Sir 
  William 
  Thomson 
  considered 
  the 
  matter 
  

   carefully, 
  and 
  selected 
  copper, 
  on 
  account 
  of 
  its 
  high 
  conductivity, 
  esti- 
  

   mating 
  that 
  in 
  a 
  copper 
  ball 
  of 
  the 
  dimensions 
  used 
  (diameter 
  4 
  centi- 
  

   metres) 
  the 
  temperature 
  must 
  be 
  sensibly 
  uniform 
  throughout. 
  A 
  very 
  

   simple 
  calculation 
  (made 
  in 
  consequence 
  of 
  M. 
  Cornu's 
  criticism, 
  and 
  

   appended 
  below) 
  from 
  Pouriers 
  celebrated 
  formula 
  for 
  the 
  cooling 
  of 
  a 
  

   homogeneous 
  solid 
  globe 
  shows, 
  in 
  fact, 
  that, 
  in 
  the 
  case 
  of 
  a 
  copper 
  globe 
  

   of 
  2 
  centimetres 
  radius, 
  the 
  centre 
  is 
  warmer 
  than 
  the 
  surface 
  by 
  only 
  

   about 
  -^jVo" 
  °^ 
  the 
  excess 
  of 
  its 
  temperature 
  above 
  that 
  of 
  the 
  surrounding 
  

   medium. 
  There 
  would 
  be 
  a 
  much 
  greater 
  difference 
  of 
  temperature 
  

   between 
  surface 
  and 
  centre 
  in 
  a 
  globe 
  of 
  mercury 
  of 
  the 
  same 
  dimensions, 
  

   because 
  mercury 
  is 
  a 
  much 
  worse 
  conductor 
  of 
  heat 
  than 
  copper, 
  and 
  

   because 
  a 
  much 
  greater 
  difference 
  of 
  temperatures 
  than 
  that 
  which 
  there 
  

   is 
  in 
  the 
  copper 
  would 
  be 
  required 
  to 
  produce 
  any 
  considerable 
  convection 
  

   of 
  heat 
  by 
  currents 
  in 
  the 
  liquid. 
  Moreover 
  the 
  glass 
  envelope 
  con- 
  

  

  2o2 
  

  

  