10 PROCEEDINGS OF THE AMERICAN ACADEMY. 



_ dQi 



do . 



approximately, where -pJ, is the actual rate of cooling at the beginning 



of transformation. Therefore 



For safety, 



2 (^1 - U) < T, 



otherwise the irregularity in 62 will lie wholly above the temperature 

 of transformation. 

 Therefore, for safety, 



do. 



2 





1 



dT dT 



dQ d.Q 



For slow cooling -^ = -j— approximately. Then 



For rapid cooling -7^ > -7^ throughout most of the temperature 



range covered, and our formula becomes 



L 



62 — Gi « ^, 



which is meaningless. 



For slow cooling, then, the cooling curve will give us the correct 

 temperature of the melting point, providing the temperature lag is less 

 than the ratio between the latent heat of melting and the average 

 specific heat of the metal during the transformation. This value for 

 the specific heat is about equal to the average between the specific 

 heats corresponding to the liquid and solid states, and therefore in 

 general more than the specific heat of the solid. This ratio always 

 gives a fairly large value for 63 — Gi, so we may be fairly sure of 

 obtaining the correct temperature of melting, even though the temper- 

 ature lag is considerable. 



In general an incwrect curve gives incorrect data. — However, in 

 the case of many transformations, such as a change of allotropy, the 

 latent heat of transformation is small, so the ratio L/S is small, and 



