MARGINAL TEMPERATURE KEPT CONSTANT 

 Table I. 



391 



Pm =u/Uo 



'' ' = yj 

















.1125 



.1 



88 



.2227 



.2 



88 



.3286 



.3 



88 



.4284 



.4 



88 



.5205 



.5 



88 



.6039 



.6 



87 



.6778 



.7 



87 



.7421 



.8 



86 



.7969 



.9 



85 



.8427 



1.0 



83 



.8802 



1.1 



80 



.9103 



1.2 



78 



.9340 



1.3 



75 



.9661 



1.4 



70 



.9763 



1.5 



67 



.9838 



1.6 



64 



.9891 



1.7 



55 



.9928 



1.8 



49 



.9953 



1.9 



45 



1.0000 



00 



00 



Case of the Contact Zone 



When we come to consider the case that the sheet is supposed to have 

 a heated contact zone, we have again as important the conditions close 

 to the margin and those at the center, and in each case we can find rela- 

 tively simple expressions for the grain, though the intermediate grain 

 does not depend on them so simply. 



First we can see that a formula which we found in the Isle Royal 

 report will enable us readily to construct the curves of decreasing tem- 

 perature, which are shown in plates 55 and 56, in the former when the 

 contact zone supposed heated is narrow, and in the latter when it is as 

 wide as to the distance to the center of the dike. 



If -y represents the temperature at a time t of a point at a distance of z 

 from the center of the sheet, the thickness of the sheet being 2iu with a 

 contact zone of breadth y on either side, so that the whole zone affected 

 or c is equal to 22(; -f- 2y, then — 



(2) 



a 



u 4- u 



w + z 



where ^^ , is the temperature which would exist at the same time t after 



w -\- z 



