196 PROCEEDINGS OF THE AMERICAN ACADEMY. 



hot junction varies, then w t" becomes a constant, and it will be 

 convenient to denote this constant by /3 when t = 273° abs. =: 0° C. So 

 that for this special case where the cold junction is at 0° C. and the hot 

 junction at f C, we have 



2^e=:mT"-/3. (7) 



This expression is not advanced as a possible natural form of the 

 function y(y^,c). It is essentially empirical, and is not designed to 

 account separately for the several distinct components entering into 2 e. 

 The fact that it closely fits the experimental data arises chiefly from 

 the well known adaptability of the exponential equation to represent 

 limited portions of curved lines. The equation also leads to certain 

 inferences which appear inconsistent with the known thermo-electric 

 laws, and fails to explain some known phenomena. 



The evaluation of the constants m, ?i, and [i is unfortunately 

 attended by considerable labor. No application of the method of 

 least squares readily presents itself, but by a method of successive 

 approximations the values can be obtained with any desired degree of 

 exactitude. Only two measured pairs of values of 2j e and t are 

 necessary for this approximation method, the third required pair 

 being furnished by SqC = and < = 0; although, of course, by the 

 employment of three pairs of values well distributed in the data, a 

 more closely fitting equation might frequently be obtained. The 

 calibration of a thermo-couple for pyrometric work can thus be 

 affected by the employment of but two known temperatures, and this, 

 on account of the uncertainty of our knowledge of high melting points, 

 is of great importance in high temjierature work. 



Let ^0 = 0^ C, <', and t" be the selected observed temperatures 

 from which to compute the constant, so that tq = 273°, t' —t' -\- 273°, 

 t" = t" 4- 273° abs. And let Sj" e = 0, 2o' e, 2u" e, be the correspond- 

 ing observed emfs. of the couple. Then, by substituting these in equa- 

 tion (7), and combining the three expressions, or their logarithms, 

 we easily deduce 



^-//y_/ (8) 



_ log (2^" e + ^) - log (2;' g + jg) . (^9) 



n = 



log T — log 





