198 PROCEEDINGS OF THE AMERICAN ACADEMY. 



may be computed, or a plot of log 2 e and log t may be made, and a 

 straight line be drawn through them. Graphical interpolation on this 

 line will then of course yield the values of lug t and hence of t corre- 

 sponding to observed values of 2 e, and vice versa, and, if desired, the 

 constants m and ?i. The expression for ^ as a function of 2 e is, of 

 course, 



t = n/(%er, or t= (^)»- 



This formula is well adapted to pyrometric work not of the very 

 highest grade of accuracy, and has been advantageously emplo^-ed in 

 connection with the Le Chatelier thermo-electric pyrometer in a 

 method to be described in a later article. 



Test of Formulae. 



This will be made by applying the several formula3 to the experi- 

 mental data of Barus, Holborn and Wien, Chassagny and Abraham, 

 and Noll. These investigators employed modern methods of ther- 

 mometry and of electrical measurement. Temperatures are either 

 made in or reduced to the scale of the hydrogen (C. & A.), or of the 

 air thermometer (B., H. & W., N.). Constants for the formulae will 

 be deduced, and the residuals or deviations of the data from the equa- 

 tions (i. e. 8 = data-equation) will be computed for the observed 

 Doints. For discussion these deviations will be expressed in per- 

 centages, viz. 100 ^, rather than in microvolts or degrees. This is 

 preferable because the process of measurement of the emf., and to some 

 extent at least of the temperature, is such as to yield results of a 

 nearly constant fractional or percentage precision at all temperatures 

 rather than of a constant number of microvolts or degrees. Thus by 

 comparing percentages we eliminate a complication arising otherwise 

 from the increasing value of 5 as < increases. Incidentally there are 

 also other well recognized advantages frequently attending the com- 

 parison of percentages rather than of absolute quantities. 



The Barus Data. — Taking the data in the order of priority, those 

 of Barus will be first employed. The measurements to be used con- 

 sist of very elaborate and painstaking direct comparisons of several 20 

 per cent irido-platinum thermo-couples with several porcelain bulb air 

 thermometers used under the constant pressure method. 



Quotations of, or rather interpolations in, his original data* are 



* Barus, C. U. S. Geol. Surv. Bull., No. 54 (1889). Phil. Mag., XXXIV. 1 

 (1892). 



