214 PROCEEDINGS OF THE AMERICAN ACADEMY. 



of itself alone any inference of systematic departure, especially when 

 the mean line MM from all the couples is considered. It will be 

 noted as an important confirmation of both the exactness of the 

 electrical measurements in the investigation and the applicability of 

 the exponential formula through a considerable range of alloys (and 

 therefore of values of m and n) that this mean line 3IM is almost 

 identical in form with the line KK iov alloy A. Relatively to the Hol- 

 born and Wien formula (line HH), the exponential possesses a simi- 

 lar 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 abun- 

 dantly 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, makes 

 a systematic departure sufficiently certain. 



Applied to the Chassagny and Abraham data, 0°-100°, and to 

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

 tial formulas 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 devia- 

 tions in Table IX., on the contrary, show that for each individual 

 equation the concordance 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 

 exponential) 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. Tlie 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 above shown that for long ranges its 

 systematic 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 ybr interpolation over short ranges, yet for inter' 



