Thermo-electric Interpolation Formula. 467 



purely empirical expression for the same temperature ranges 

 applies, and with the same closeness, so that it is unnecessary 

 to test more than one of the first four expressions against any 

 one set of data. Also the fact that the Avenarius and Tait 

 equations approximately conform to the observed data does 

 not necessarily in any material degree strengthen the hypo- 

 theses which are adduced to show that these equations are a 

 natural expression of the law. 



Without attempting here a further analysis of the com- 

 ponents making up the resultant E.M.F. ^e, which is the 

 measured E.M.F. of the thermo-couple, the proposed interpo- 

 lation formulae will be merely developed and applied. It 

 may, however, be suggested in passing, that there seems to 

 the writer to be little hope of arriving at a close approxima- 

 tion to the natural law except through an expression which 

 shall contain separate terms representing the temperature 

 function of the component arising at the contact of the 

 dissimilar metals, and that arising from the inequality of 

 temperature of the ends of each (homogeneous) element 

 (Thomson E.M.F.). The parabolic and Avenarius formulae 

 would comply in part with this requirement on the supposi- 

 tion that the E.M.F. at contact varied as the first power, and 

 the Thomson E.M.F. in both wires as the square of the 

 temperature. And looked at from that point of view, the 

 neutral point would seem to have an explanation materially 

 different from that usually accorded to it. 



The Proposed Formulas. 



Exponential Equation. — The significance of this proposed 

 expression may be thus stated. Suppose the cold junction of 

 the couple be maintained at the absolute zero of temperature, 

 t=0°, and its E.M.F. to be consequently zero. Let the other 

 (hot) junction be at any temperature r h ° absolute. The pro- 

 prosed equation is based on the assumption that the total 

 E.M.F of the couple would then be representable by 



e f = m,T^. 



where m and n are numerical constants. If then the cold 

 junction were raised to any temperature t c °, there would be 

 introduced an opposing E.M.F. e", which would be expressible 

 ty e" = niT\ 



The resultant E.M.F % h c e would then be e'-e", and there- 

 fore expressible by 



X h c e = mTl-mT n c (6) 



2K2 



