Thermo-electric Interpolation Formulas. 485 



mean line M M is almost identical in form with the line K K 

 for alloy A. Relatively to the Holborn and Wien formula 

 (line H H), the exponential possesses a similar advantage, 

 with also the merit of greater simplicity of form. 



It may therefore be affirmed that for interpolation between 

 450° and 1450° in the H. and W. data the exponential equation 

 is abundantly exact. For extrapolation above 1450° it would 

 not be entirely safe, although presumably better than the 

 others, since the departure between 0° and 450°, and the 

 similarity of the form to others, make a systematic departure 

 sufficiently certain. 



Applied to the Chassagny and Abraham data, 0°-l 00°, and 

 to the Noll data, 0°-218° (see diagram), the Avenarius and 

 exponential formulae show about equal deviations, but with 

 the advantage slightly on the side of the former. In the case 

 of the Noll data, the line indicates that the systematic error 

 is slightly greater for the exponential than for the Avenarius 

 expression. The average deviations in Table IX., on the 

 contrary, show that for each individual equation the concor- 

 dance is greater for the exponential than the Avenarius. This 

 discrepancy is due to the fact that, in order to eliminate local 

 accidental errors, the equations (both Avenarius and expo- 

 nential) are not all made to coincide with the data at the 

 same temperatures, so that the process of averaging by which 

 the data for the Noll plots is obtained is not numerically rigid. 

 This does not, however, sensibly affect the general form of 

 the curve. The greater ease of computation of the numerical 

 constants of the Avenarius expression, and its applicability 

 where both t and t change, ought not to be overlooked. For 

 extrapolation the exponential would be safer, for the reason 

 that it has been shown above that for long ranges its syste- 

 matic error is less. 



The logarithmic equation fits the Noll data very badly, as 

 shown by the deviation in Table IX. (not plotted), and also 

 is much less close to the Chassagny and Abraham data than 

 are the others. 



The general conclusion as to applicability, then, seems to 

 be that, while the Avenarius expression may be equally good 

 or better than the exponential for interpolation over short 

 ranges, yet for interpolation over long ranges and for extra- 

 polation above the observation limits the exponential is decidedly 

 preferable. The exponential form is also preferable to the 

 remaining expressions with the exception noted. 



The logarithmic form, although closely applicable to the 

 Barus data, is of more doubtful general value, yet on account 



