430 Mr. C. H. Lees on the Law of Cooling, and its bearing 



where v = excess of temperature at a point x of bar above 

 temperature of air, which is supposed constant ; c = specific 

 heat, p = density, k = inner conductivity, h = outer conduc- 

 tivity, at temperature-excess v ; p = perimeter of section of 

 bar ; q = area of section of bar. 



Assuming, with Fourier, that c, p, k, h are constant, we 

 have for the " steady state " the equation 



"d 2 v _ ph 

 ^^ qk ' 

 the solution of which is 



— a y 2* ju v.o v ** 



v = Ae^ qk +B 



where A and B are constants of integration. By determining 

 the temperature at different points of a bar thns heated, the 



value of \/^~f can be found. Briot and Despretz determined 



the temperature by means of thermometers placed in holes in 

 the bars. This would, on account of the different conduc- 

 tivities of the bars and the glass and mercury of the thermo- 

 meters, make the isothermal surfaces deviate considerably 

 from planes. The results, however, of both experimenters show 



evidence of an increase of a /PI with temperature, especially 



V qk 



where the bars are of the poorer conducting metals, and 



the effects of the holes therefore less. This is also the case 



with the results of Wiedemann and Franz, who determined 



the temperature by means of a therm ojunction brought into 



contact with the surface of the bar at different points. 



From the experiments which follow it will be seen that h 

 increases about 50 per cent, as the temperature varies from 

 30° C. to 80° C, while k and c for a metal are not found to vary 

 more than about 5 per cent, in the same interval. The most 

 important source of error in the assumptions of Fourier is, 

 then, that introduced by the variation of h, and it is towards 

 a more accurate determination of this variation that the 

 following experiments have been conducted*. 



A bar of infinite length originally heated to a uniform 

 temperature would_, if allowed to cool in air, continue to satisfy 



the condition ^-- =0, and it will be assumed that for the bars 



used in these experiments this is still the case. Since the 



* The experiments were carried out in t|ie Owens College Physical 

 Laboratory. 



