PEIRCE AND WILLSON. 



THERMAL CONDUCTIVITIES. 



25 



and from this expression, with the help of the numbers in the body of 

 Table IV., many special problems can be solved with very little labor. 

 The expression 



A (1 _ 2 7; - 2 ?;_,) + 2 B Ti._,+ 2di.T^+ (0, - 5) (l - ^) 



gives the final temperatures in a homogeneous disk of radius a and 

 height I, one face {z =. 0) of which is kept at the uniform temperature 

 ^0, the other face (s = /) at the uniform temperature 0i, and the rim at 



constant temperatures given by the law A -\- (0(i — B) il — ,) . From 



this we may see, that, with a very rude approximation to a uniform 

 gradient in the temperatures of the edge of a disk of relatively large 

 thickness, the final temj^eratures on the axis are sensibly the same as for 

 an infinite disk of the same thickness. 



100 



Figure 1. 



