HOLMAN. — THERMO-ELECTRIC FORMULAE. 215 



polatlon over long ranges and for extrapolation above the observation 

 limits the exponential is decidedly preferable. The exponential form 

 is also preferable to the remaining expressions with the exception 

 noted. 



The logarithmic form, although closely applicable to the Barus data, 

 is of more doubtful general value, yet on account of its great con- 

 venience it may find application in industrial pyrometry, as will be 

 elsewhere indicated. Although failing below 300° or 400°, it may 

 probably be applied to the irido- or rhodo-platinum couple between 

 400° and 1200° C. with a maximum error not exceeding about 5°. 

 If extended to cover 400° to 2000° the error might rise to 15° or 20°. 



More in detail it may be briefly noted by way of summary : — 



That the logarithmic equation fits the Barus data between 400° 

 and 1250° with scarcely sensible systematic error, and within the 

 limits of variable errors of the data. 



That the exponential equation similarly fits the Holborn and Wien 

 data within the limits 400° to 1445°. 



That when made to coinci^le with the data at about 450° and 1200° 

 tlie systematic deviations of the exponential equation from the Barus 

 data, and of the logarithmic equation from the Holborn and Wien 

 data, are in general of opposite sign and of roughly equal magnitude. 



Barus Melting and Boiling Point Data. 



From the foregoing demonstration of its applicability, it seems 

 proper to apply the logarithmic formula to the Barus thermo-electric 

 data on melting points.* 



Whether the extrapolation above 1000° by the logarithmic formula 

 is entitled to any great weight may be questioned, but there is no 

 obvious reason why it is not more reliable than by any of the others. 

 I have employed the equation given on page 202, which repre- 

 sents very closely Barus's high temperature air thermometer com- 

 parisons, calculating thence the temperatures t corresponding to the 

 values of 1^ e given by Barus for the various points, assuming Barus's 

 value S-y'e = 150 mv. The results are given in column three of 

 Table X. Column four quotes the most reliable previous determina- 

 tions of the same points by other observers. As to which of the two 

 columns of results best represents Barus's work there can be little 

 doubt from the above evidence that below 1000° it is the second, that 



* Amer. Jour. Sci., XLVIII. 332 (1894). 



