484 Prof. Silas W. Holman on 



normal scale by an amount and system roughly indicated by 

 the above residual plots. 



The latter inference, suggested by Chassagny and Abraham 

 in the interpretation of their results, does not seem to possess 

 much weight, notwithstanding the urgent need of renewed 

 elaborate experimental investigation of the relation between 

 the hydrogen, air, and thermodynamic scales of temperature. 



As to the relative usefulness of the various expressions for 

 purposes of interpolation and extrapolation some further 

 inspection is necessary. The Barus equation 3, line C D, 

 shows slightly smaller deviations on the plot than do the 

 Avenarius and exponential, lines E E and F F. This, how- 

 ever, is due to the fact that the data against which 3 is 

 tested are mean interpolated values, and hence have a sensibly 

 less variable error than those against which the other equations 

 are tested. An approximate exponential equation showed 

 less deviations than 3 against the same data. There seems, 

 therefore, to be no advantage in this equation sufficient to 

 offset the difficulty of evaluation of its constants. 



Applied to the Barus data from 350° to 1250°, the ex- 

 ponential equation shows deviations considerably less than one 

 half as great as those of the Avenarius, while those of the 

 logarithmic equation are so small as to lie far within the 

 range of the variable errors, and they moreover show no clear 

 evidence of systematic error between these limits of tempera- 

 ture. For interpolation in the Barus data, therefore, the 

 logarithmic equation is far preferable, and must be conceded to 

 be representative of the data. For extrapolation it is un- 

 doubtedly better than the Avenarius, which (as would the 

 exponential in less degree) would certainly give above 1000° 

 extrapolated values of %e too large, or of t too smalL The 

 advantage due to its simplicitjr is also to be noted. 



Applied to the Holborn and Wien data from 400° to 1450° 

 the exponential equation shows (line KK) the same sort of 

 superiority to both logarithmic (line L L) and Avenarius 

 (line 1 1) that the logarithmic shows to the others with the 

 Barus data, but in a still more marked degree. Within the 

 limits 450° to 1450°, in fact, the distribution of the residuals 

 to the exponential is such as not to warrant of itself alone 

 any inference of systematic departure, especially when the 

 mean line M M 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 



