HOLMAN. — THERMO-ELECTRIC FORMULiB. 213 



One of two inferences is therefore warranted : — 



1. That neither the parabolic, Avenarius, Barus, exponential, nor 

 logarithmic equation is the natural expression of the function. 



-2. Or that the scale of temperature to which the vaUies of t are 

 referred in the foregoing investigations departs from the 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 thermo- 

 dynamic 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 OD, shows slightly smaller deviations on 

 the plot than do the Avenarius and exponential, lines EE and FF. 

 This, however, 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 oflfset the difficulty of evalua- 

 tion of its constants. 



Applied to the Barus data from 350° to 1250°, the exponential 

 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 temperature. 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 undoubtedly better 

 than the Avenarius, which (as would the exponential in less degree) 

 would certainly give above 1000° extrapolated values of 2 e too 

 large, or of t too small. The advantage due to its simplicity 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 LL) and Avenarius (line IT) that the logarith- 

 mic shows to the others with the Barus data, but in a still more 

 marked degree. Within the limits 450° to 1450°, in fact, the dis- 

 tribution of the residuals to the exponential is such as not to warrant 



