226 PROCEEDINGS OF THE AMERICAN ACADEMY. 



one junction of the couidIo is kept at 0° C, and the other is at any 

 other temperature t C, or t = ^ + 273° absolute ; m and n are constants, 

 different for the two expressions; 2*e denotes the resultant thermal 

 emf. of the circuit, viz. that which is the object of direct measurement. 

 The first, called the exponential equation, is 



2o e = m t" — (3 (where /3 = ?7i tq = m X 273"). 



The second expression, called the logarithmic equation, is 



^qC =:: m f\ or log 2o e = ?« log t + log m. 



Both formulas have been applied to (he data of the present investi- 

 gation given in Table I., with results shown below. The Avenarius 

 formula has also been applied for purposes of comparison. 



To evaluate the constants tn and 7i of the exponential equation (for 

 method, consult the paper referred to) it is necessary to have values 

 of 2o e at three known temperatures. Of these, however, one may be 

 2o e = 0, at T = 273°, i. e. with both junctions in ice. It therefore 

 remains to fix upon two other temperatures between which to inter- 

 polate, or, in other words, two other temperatures which shall be 

 assumed as known. In looking over the ground it seemed that the 

 boiling point of sulphur, being so high and so accurately determined 

 by Callendar and Grifiiths,* 



444.53 -f 0.082 (H — 760), 



was pre-eminently one of these points. The other must be much 

 higher, and the melting point of pure gold seemed to be almost, if not 

 quite, the only one upon which reliance could be placed. 



Apart from freedom from oxidation, and its conveniently high 

 point of fusion, gold seemed the more suitable because its melting 

 point had recently been so carefully measured by Holborn and Wien, 

 and because the metal could be obtained of the necessary purity. 

 Add to these considerations the fact that its melting point in a state of 

 at least fairly high purity has been measured by more experimenters 

 than that of any other high melting metal, so that it serves as an 

 excellent connecting link between their work, and we have claims 

 which no other substances can at present offer. The fusion point of 

 gold was therefore chosen as the second reference or calibration tem- 

 perature. As to the figure to be assumed as the melting point of 

 gold there is room for differences of opinion. The claims of the work 



* Phil. Trans. CLXXXII, 119, 157 (1891). 



