HAYES. — ERRORS IN COOLING CURVES. H 



the value of ©a — ©i must be small if the transformation temperature 

 is to be given with accuracy. This requires that the cooling curve 

 must be nearly correct. Yet Curve 3 shows that for comparatively 

 slow cooling the temperature lag is 45 degrees for quartz protection 

 tubes, and much more for porcelain tubes. The conclusion follows that 

 the ordinary method for taking cooling curves fails to give with 

 accuracy the temperature of such transformations as involve slight 

 absorption or evolution of heat. 



Ordinary method of correcting for temperature lag. — This error due 

 to temperature lag has been long recognized, and the following method 

 employed to correct it. Both a cooling and a heating curve is taken. 

 The cooling curve gives a temperature above, while the heating curve 

 gives a temperature below the temperature of transformation. Assum- 

 ing that the rate of change of temperature is constant, and that the lag 

 is proportional to the rate of change of temperature, then the correct 

 temperature c^n be obtained as follows : 



Let e,. be the transformation temperature given by the cooling curve, 

 e, " " " " " " heating " 



a " rate of cooling, assumed uniform, 

 b " " heating, 



k " temperature lag for unit rate of cooling, 

 © " correct temperature of transformation. 



« 



" k 



Then ©« = © + ^a 



G/, = © — kb 



© — ©,._ a 

 ©-©/. ~ " b' 



Therefore e = — —7 e, + — ^ ©^. 



a + a + b 



This method erroneous. — The value of this formula dejiends upon 

 the correctness of the two assumptions upon which it is based. The 

 rate of change of temperature can be regarded as fairly constant over 

 a considerable period of time when the cooling is slow. The accuracy 

 of the second assumption — that the temperature lag is proportional 

 to the rate of change of temperature — can be tested by the aid of 

 Curves 1' and 2 (Plate 1), for we can readily find the temperature lag 

 at any time, and also the rate of cooling, and hence the value for k. 



