8 PEOCEEDINGS OF THE AMERICAN ACADEMY. 



tube, and ©i be the temperature of that junction. Let E2 and Q^ be 

 the e. m. f. and temperature respectively of the other junction at the 

 same instant. Then 



(01 - 62) = (a/4 bE^ + a' - a/4 hE^ + a=^)/2 h, 



the maximum temperature lag through quartz and porcelain protection 

 tubes for different rates of cooling, is given in Table II. This is 

 computed from the curves of the accompanying plate (Plates 1 to 6). 



No simjyle relatioti between the two curves. — These results show that 

 the error in the cooling curve as usually taken (i. e. by means of a 

 thermo-couple placed inside a protection tube) is large, especially if the 

 rate of cooling is at all large. The question then arises : Is it possible 

 to find a relation between the correct curve and the incorrect curve 

 such that the correct curve can be obtained from the incorrect one, 

 i. e. from the curve taken. Curve 8 (Plate 5) enables us to answer 

 this question. 



In taking this curve, time coordinates of which were three seconds 

 for one space, the copper block was first dipped for an instant to a 

 depth of two inches in ice-water, then removed, then redipped, then 

 removed, etc. The lower line, which is very irregular, as we should 

 expect, is the correct cooling curve. The upper one is the curve ob- 

 tained by the ordinary method, a junction inside a protection tube. 

 The relation between the two curves is far from simple, and any for- 

 mula giving this relation must needs be complicated. Thus far no 

 formula has been found. 



Incorrect curve may give correct temperature of transformation. — 

 Much of the information, however, that comes from a cooling curve can 

 be had from a curve that is not absolutely correct ; for this information 

 comes from the irregularities of the curve, not from the regular parts. 

 In general, any change in the constitution of a metal is accompanied 

 by a liberation or absorption of heat, thereby causing a kink in the 



