194 PROCEEDINGS OF THE AMERICAN ACADEMY. 



The existing; formuloe are the five foUowincr. 

 Ordinary or parabolic : 



^'^e = at + ht^ + ct'^ -}- (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 temperature, ti° , is 



2,\e = a{t-t^) + b (t- - ti") + c (t' - t{) + 



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

 of 2e. 



Avenarius 



2^ e = (h — c) {a + b (h + c)}, (2) 



in accordance with the foregoing notation. 

 Thomson : 



2^ = a(r,-x.)-[r„-Ii + I-«|, (3) 



where t is the absolute temperature, t„ being that of the " neutral 

 point." 

 Tait: 



2^^e=(k'-k) (r,-r,)^r„-Z^Y (4) 



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

 reduce to the Avenarius form. 

 Barus : 



e^ + e, = 10 ^+ «'' + 10 ^' + «''•• (5) 



where e,, represents the thermal emf. of the hot junction and e^ that of 

 the cold junction. In view, however, of the existence of the Thom- 

 son effect, these symbols can strictly be interpreted only as having 

 the meaning that e^, — e<, — ^c ^- 



Note. — With regard to the Avenarius, Thomson, and Tait expres- 

 sions it may be remarked that they are not only mutually equivalent, 

 but that if t^ or r^ becomes 0° C. they reduce at once to the ordinary 

 parabolic form of two terms : 



%:=at-\-bt^. 



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

 empirical expression for the same temperature ranges applies, and 

 with the same closeness, so that it is unnecessary to test more than 



