538 Adams and Johnston — Standard Scale of Temperatures. 



equation of the form t=Ae + Be 2 + Ce % \* but they can, as we 

 found, be fitted very closely by the inverse form of function, 

 e=At+Uf+Cf. Accordingly, on this basis a least square 

 solution for all the points in Table I was made ; this resulted 

 in the equation 



e =38-105 £ + 0-04442 £ 2 — 0*00002856 f, 

 from which the figures in the third column of Table I have 

 been computed. The agreement is excellent ; it cannot, how- 

 ever, be used as a valid argument in favor of the accuracy of 

 either the temperature scale or of the measurements, as any- 

 one can readily convince himself by working with a number of 

 similar cubics. Incidentally, it may be noted that in making 

 such a least square solution, it is inadmissible to lighten the 

 work by dividing through by t, which would necessitate only 

 the least square solution of a quadratic ; for the solution 

 obtained by proceeding in this way, although apparently a 

 cubic equation, is that appropriate to the condition that the 

 deviation of the curve from the values of e/t (instead of e) 

 shall be a minimum. 



By means of this equation, values of e and of de/dt for each 

 10° up to 360° were computed ; the slight irregularities being 

 evened out by adjustment of the successive differences. By 

 interpolation from these results, and adjustment of the suc- 

 cessive differences again, a table was constructed giving t for 

 each 100 microvolts ; this is presented in Table II,f to which 

 are also appended the E. M. IVs corresponding to the fixed 

 reference points. 



This table may be used for any copper-constantan element 

 with the aid of its deviation curve, which is obtained by 

 plotting at several;}; known temperatures the differences 

 between the readings of the element in question and the stand- 

 ard curve.g Its use thus saves much recalculation of thermo- 

 element curves. The absolute uncertainty of temperatures 

 deduced from the above table should, we believe, not now 

 exceed 0*1° ; temperature differences over a small range are 

 probably accurate at least to 0-02°. For this reason the values 

 of temperatures and differences in Table II are given to 

 hundredths of degrees. 



The Identity of the Readings of Thermoelement and Resistance 

 Thermometer at Roiling Points and Melting Points. 



The initial series of measurements gave differences between 

 the freezing point of tin and the naphthalene point on the one 



* This was tried because its use would have saved so much trouble in cal- 

 culating the most convenient form of table — that giving t for round values 

 of e. 



f This table replaces Table I of the previous publication (loc. cit., p. 510). 



^For accurate work, comparison at a number of temperatures is advisable, 

 since the slope of the deviation curve is likely to change sign once or oftener. 



§ This matter is more fully treated by Sosman, this Journal, xxx, 7, 1910. 



