468 Prof. Silas W. Holman on 



If in any instance, as is frequently the case in measurements, 

 the temperature of the cold junction is maintained constant 

 while that of the hot junction varies, then mrr n c becomes a 

 constant, and it will be convenient to denote this constant by 

 /3 when t=273° abs. =0° 0. So that for this special case 

 where the cold junction is at 0°C, and the hot junction at 

 i° C, we have 



2j*=mT w -£. . . . . . • (7) 



This expression is not advanced as a possible natural form 

 of the function f(h, c). It is essentially empirical, and is not 

 designed to account separately for the several distinct com- 

 ponents entering into 2#. The fact that it closely fits the 

 experimental data arises chiefly from the well known adapta- 

 bility 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, n, and ft is unfortunately 

 attended by considerable labour. 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 2q£ and t are necessary for this approximation 

 method, the third required pair being furnished by Xo<? = 

 and £ = ; 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 calibra- 

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

 effected 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 tempera- 

 ture work. 



Let £ =0°C, t 1 , and t" be the selected observed tempera- 

 tures from which to compute the constant, so that t =273°, 



^ = £' + 273°, T"=*"+273°abs. And let 2?«=0, 2j«, 2?«, 

 be the corresponding observed E.M.F's. of the couple. Then, 

 by substituting these in equation (7), and combining the 

 three expressions, or their logarithms, we easily deduce 



e 



e=%r—> (8) 



(1)1 



\T A / 



