HAYES. — ERRORS IN COOLING CURVES. 7 



graphs, show this lag for both quartz and porcelain protection tubes 

 for different rates of cooling. These curves are reduced to one fifth 

 the original size. The highest temperature in each case was about 550 

 degrees centigrade. 



tSimilariti; of the thermo-couples and calibration. — Curve 1, Plate 1, 

 which traverses the sheet four times, due to four revolutions of the 

 drum, was taken at a very slow rate of cooling, the time of exposure 

 being about four hours. In place of the ordinary protection tube closed 

 at the end, the tube used in this case was open at the lower end except 

 for a thin film of mica. Here the temperature lag between the two 

 junctions must have been practically zero, because of the slow rate of 

 cooling and because of the thinness of the film separating them. The 

 curve, which is in reality double, shows that the two couples were 

 practically identical throughout the temperature range covered. 



A calibration curve for one of these couples was obtained by taking 

 the melting points of pure tin, lead, zinc, and aluminum, also the 

 boiling point of water. These results are given in Table I. 



Melting aluminum 657 33.70 33.70 



The third column, marked Millivolts (calc), was obtained by apply- 

 ing the well-known formula connecting temperature and electromotive 

 force, 



E=ae + be\ 



Here B is the e. m. £ in millivolts and e is in degrees centigrade. 

 Substituting in this equation the values of B and G, as found for boiling 

 water and melting Al, the values of a and b were found to be 0.0362 

 and 0.0000229 respectively ; and since the variation between the ob- 

 served and calculated results lies within the limit of error, the curve 



E= 0.0362 8 + 0.0000229 e^ 



has been taken as the calibration curve for the two junctions. 



Referring to this formula, it is comparatively easy to find the differ- 

 ence in temperature between the two junctions at any instant during 

 the cooling. Let L\ be the e. m. f of the junction within the protection 



