358 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



The last factor of this expression has its maximum value at the 

 middle point of the axis where z = ^c. 



Figure 1. The ordinates of the curve show the temperatures, for dif- 

 ferent values of a, of a point Q in the centre of the axis (OS) of a square slab 

 (a X a X c) of given thickness c, when one face (a X a) is kept at the tem- 

 perature 100° while the other face and the edges are kept at 0°. The hori- 

 zontal unit is c, and it appears that when a = 5 c, the temperature (49.9° +) 

 of Q differs only slightly from the temperature (50°) which it would have if 

 a were infinite. The shaded area above indicates the section of the slab for 

 different values of a. 



The value of W for the centre of the axis of the slab is given for 

 several different values of a in Table I. When the ratio of a to c is 

 large, the double series which defines W converges very slowly. Thus 

 to obtain the last number in the table more than one hundred and fifty 

 terms of the series were needed. 



Figure 1 represents the numbers of Table I. graphically. 



It is interesting to compare these results with similar ones for cir- 

 cular disks which Professor R W. Willson and I obtained 2 several 

 years ago. 



3 These Proceedings, 1898, 34, 1. 



