HAYES. — ERRORS IN COOLING CURVES. y 



cooling curve. How erroneous can the cooling curve be and still give 

 the temperature of transformation with considerable accuracy 1 



For simplicit}^, let us take the case of finding the melting point of a 

 pure metal. In this case the cooling curve for that portion of time in 

 which transformation takes place is a straight line parallel to the time 

 axis. In Figure 1 let the line abc'd represent the true cooling curve, 

 while line abc represents the cooling curve if no transformation takes 



place. Let the line ah'c'd' represent the cooling curve given by the 

 couple inside the protection tube, and the line ah'e the corresponding 

 curve if no transformation takes place. Then the temperature lag at the 

 beginning of transformation is 02 — 0i, and the corresponding time lag 

 is ti — ^1. The time through which transformation takes place is 

 tfi — t\i while Gi — 00 is the number of degrees through which the melt 

 would cool if no transformation takes place. 

 It will be seen that 



®2 ®1 — "7777 ■ 2 (^2 *\h 



(IT 



lf/0 



if we assume that — ™ is the averate rate of cooling during the period 



required for to drop to the temperature of transformation, and that 



r/0., 



-TTyl is the rate of cooling at the beginning of transformation. Also, 



J/(0i-0o)-6'=il/X, 



where M is the mass in grams of the melt, H is the average specific 

 heat, and L is the latent heat of melting. But 



