PEIRCE AND WILLSON. THERMAL CONDUCTIVITIES. 31 



and the temperature is 46°.48. 



If tlie radii of the slabs and the metal sheet had been infinite, the 

 temperature in these media would have been given by the expressions 

 Mz, M(fx c + 1 — fi), and M(z -\- ^\ (fi — 1)), respectively, where 

 31= 100/(1.98 + .02 /x). In all practical cases the temperatures of 

 points on the rim of the disk increase gradually from the cold face to the 

 warm face, and it would be easy to show that those portions of the 

 isothermal surfaces which we have used in computing the results of our 

 observations are sensibly plane. 



The characteristic differential equation which gives the relation between 

 tlie temperature, the space co-ordinates, and the time in a body in which 

 there is an unsteady flow of heat, involves the specific heat of the body, 

 which is itself a function of tlie temperatui-e. Without attempting just 

 here to investigate the nearness of the approximation obtained in any 

 given case by assuming the specific heat to be constant, we will give for 

 future reference some numerical results obtained by using several differ- 

 ent values of z, t, and c in the solution of Problem 3. 



An infinite homogeneous lamina of thickness I is originally at the 

 temperature c Vq throughout. From a given time, < = 0, one face is 

 kept at the constant temperature Fq, and the other face at the tempera- 

 ture 0°. The ratio of the conductivity of the slab to its specific beat is to 

 ^be denoted by the constant d^, the ratio of /^ to a^ n"^ by T, and the 

 distance of any point in the lamina from the face which is kept at the 

 temperature Vq, by z. 



The numbers in Table VITI. show the rate of flow across the cold face 

 of the lamina in fractional parts of the final rate for different values of 

 c and t, while the numbers in Table IX. give the rate of flow across 

 different planes parallel to the lamina faces at different times, for the 

 special case c = I. 



