466 Prof. Silas W. Holman on 



of scientific importance, but is urgently needed in the develop- 

 ment of the art of pyrometry. At present even a satisfactory 

 empirical formula for interpolation is lacking, the best still 

 being probably that of Avenarius and Tait. 



The existing formulae are the five following : — 



Ordinary or parabolic : 



tU=at + bt 2 + cf + (1) 



This is, of course, merely a series in ascending powers of t, 

 where one junction is at any temperature t° C, and the other 

 at 0° C, a, b, and c being constants. A more general form 

 for the case where the cold junction is at any constant tem- 

 perature, ti°, is 



2^ = a(i-^ 1 )H-^ 2 -f 1 2 ) + c(i 3 -^ 1 3 )+ . . . 



These expressions may, of course, be inverted, giving t as a 



function of 2 e. 



Avenarius : ^ h 



X h c e={h-c){a + b(h + c)\ .... (2) 



in accordance with the foregoing notation. 



Thomson: , r h + T c \ 



where t is the absolute temperature, r being that of the 

 " neutral point/' 



Tait : f 



$U=(k'-k)(T h -T e )\ Tn -?*+I?.} ... (4) 



Both of the last two, by the substitution of £ + 273 for t, 

 obviously reduce to the Avenarius form. 



e4 + , c =10 p +^ + 10 p ' +Q, °, .... (5) 



where e h represents the thermal E.M.F. of the hot junction 

 and e c that of the cold junction. In view, however, of the 

 existence of the Thomson effect, these symbols can strictly be 

 interpreted only as having the meaning that e h — e c =%*e. 



Bote. — With regard to the Avenarius, Thomson, and Tait 

 expressions, it may be remarked that they are not only 

 mutually equivalent, but that if t c or r, becomes 0° C. they 

 reduce at once to the ordinary parabolic form of two terms : 



tU^at + bt' 2 . 

 They are all, therefore, forms which must apply if the latter 



