THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



DECEMBER 1889. 



LII. On the Law of Cooling, and its bearing on certain Equa- 

 tions in the Analytical Theory of Heat. By Charles 

 H. Lees, M.Sc, Berkeley Fellow of Owens College, Man- 

 chester*. 



ALTHOUGH it is a well-known fact that the temperature 

 of a heated body allowed to cool in air does not follow 

 " Newton's Law," it has been usual to assume that law to hold 

 in cases in which the loss of heat of a body through contact of 

 its surface with air had to be taken into account. In calori- 

 metry the error thus introduced is probably small ; but it 

 becomes of much greater importance in those methods of 

 determining thermal conductivity in which the ratio of the 

 outer to the inner conductivity of the body is a quantity 

 determined experimentally, and this ratio used in conjunction 

 with a value of the outer conductivity f (supposed to follow 

 Newton's law) to determine the inner conductivity. 



The method to which I specially refer is that of Briot, 

 Despretz, &c, in which a bar of the substance whose conduc- 

 tivity is required is placed in a horizontal position in air, and 

 heated at one end. The equation of motion of heat in the 

 bar is then, assuming the isothermal surfaces to be planes, 



ot ox\ o^ q 



* Communicated by the Author. 



f The " Conductibilite exterieure " of Fourier, or the surface emissivity 

 of Thomson, art. " Heat," Encyc. Brit. p. 577. 



X Fourier, Theorie Analytique de la Chaleur. Thomson, ' Collected 

 Papers/ toI. ii. p. 42, or Encyc. Brit, art. " Heat," p. 579. 



Phil. Mag. S. 5. Yol. 28. No. 175. Dec. 1889. 2 K 



