Law of Cooling. 57 



On the Law of Cooling, and its bearing on the Theory 

 of the Motion of Heat in Bars. By Charles H. Lees, 

 M.Sc, Berkeley Fellow of Owens College. Com- 

 municated by Arthur Schuster, Ph.D., F.R.S. 



{Received October 29th, 1889.) 



During the summer of last year I carried out at Stras- 

 burg some experiments on thermal conductivity which 

 involved the "steady periodic" state of motion of heat in 



o 



a bar, a method first used by Angstrom. It consists in 

 periodically heating and cooling one end of a bar, and after 

 sufficient time has elapsed to make the temperature at any 

 point of the bar aperiodic function of the time only, determin- 

 ing by observation this function at several points of the bar. 

 Observations at two points furnish in a very neat manner 

 both the inner and outer * conductivity of the bar. Unfor- 

 tunately, however, I found that the variation of temperature 

 along the bar I used, could not be represented by the 

 expression deduced by Angstrom from Fourier's equation 

 to the motion of heat in a bar. It was in the endeavour to 

 find the cause of this discrepancy that the following work 

 was undertaken on my return to Manchester. 



Fourier's equation for the motion of heat in a bar is : — 



Zv c 2 v p 

 C Pk =k W~q- hV - (I) 



*By inner conductivity is meant the conductivity of the material of the 

 bar, and by outer conductivity the amount of heat lost from i sq. cm. of surface 

 of the bar when that surface is at a temp. i° C. higher than the surrounding gas. 

 For details of the theory see Angstrom, Phil. Mag. (4) 25, p. 130 (1863), orTait, 

 Proc. R.S.E. 8, p. 55 (1873). 



