464 W. P. White — Melting Point Determination. 



If, therefore, the specific heat S increases n times, becoming 

 ftS, the rate, — , will evidently diminish n times. The time 



Cit 



lag (equation (6) ) will increase n times. The temperature dis- 

 tribution can be found by substituting from (7) in (5). The 

 result is : 



A0]dQ dQ 1 



^T COnSt = W 6K < R -^ < 8) 



In this expression the specific heat does not appear at all. The 

 equilibrium temperature distribution, therefore, is not altered 

 by a change in the specific heat. Among these results of a 

 change in specific heat the increase of the time lag is of most 

 immediate interest. Occurring under constant heat supply to 

 the whole charge, it involves a retardation in the supply to the 

 center, and one which is proportional to the square of the 

 radius. The formulae thus express in a roughly quantitative 

 way the otherwise obvious fact that as the melting begins the 

 inner layers fall behind, since the outer layers for a time absorb 

 large quantities of heat, passing very little to the interior. 

 Expressed in terms of temperature, the retardation will be 

 n—1 times the (original) time-lag times the rate. 



This result, however, as already indicated, applies strictly 

 only to an infinitesimal charge, since it assumes a complete 

 homogeneity, which the melting itself destroys. In the actual 

 case, while the body is melting the outer layers will have a 

 higher temperature and therefore a greater specific heat than 

 the inner. This, it can readily be shown, will diminish the 

 temperature difference between center and surface and there- 

 fore the time lag, while an increase of conductivity due to 

 melting will probably act in the same direction. The retarda- 

 tion of the center will thus really increase less rapidly than the 

 square of the radius, and for a very large crucible will not 

 even approach the formulae just given. 



As soon as the outward layer of the charge is fully melted, 

 the whole course of the phenomena changes. The virtual 

 specific heat of the substance while melting is usually from 50 

 to 100 times what it is before or after, hence the heat capacity 

 of the whole depends for a time almost entirely on the still 

 unmelted core. As this diminishes the relative heat supply to 

 it increases, increasing the obliquity of the critical end-portion 

 of the curve. Nor is the resulting distortion, like that from 

 uneven heat supply, above described (page 461), merely a 

 general increase in steepness at the end. It is a rapidly accel- 

 erated increase, changing the form of the curve in that region. 

 In large crucibles, it often masks entirely the break at the end 

 of the melting, substituting for it a premature break a degree 



