HOLMAN. — THERMO-ELECTRIC FORMULA. 195 



one of the first four expressions against any one set of data. Also 

 the fact that the Avenarius and Tait equations approximately con- 

 form to the observed data does not necessarily in any material degree 

 strengthen the hypotheses which are adduced to show that these equa- 

 tions are a natural expression of the law. 



Without attempting here a further analysis of the components 

 making up the resultant emf. 2'!e, which is the measured emf, of the 

 thermo-couple, tlie proposed interpolation formulaa 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 

 approximation 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 (homo- 

 geneous) element (Thomson emf.). The parabolic and Avenarius for- 

 mulre would comply in part with this requirement on the supposition 

 that the emf. at contact varied as the first power, and the Thomson 

 emf. 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 Formula. 



Exponential Equation. — The significance of this proposed expres- 

 sion may be thus stated. Suppose the cold junction of the couple be 

 maintained at the absolute zero of temperature, r = 0°, and its emf. 

 to be consequently zero. Let the other (hot) junction be at any tem- 

 perature t\ absolute. The proposed equation is based on the assump- 

 tion that the total emf. of the couple would then be representable by 



e' ^=z m r". 



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

 were raised to any temperature t° there would be introduced an 

 opposing emf. e" , which would be expressible by 



The resultant emf. S^e would then be e' — e", and therefore expressible 



by 



2* e = m T^ — m T^. (6) 



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

 perature of the cold junction is maintained constant while that of the 



