Prof. H. L. Callendar on Platinum Thermometry. 203 



For work at low temperatures, it would be most conveuient to 

 select the boiling-point of oxygen for the determination of 

 either difference-coefficient. The two formulae are so similar 

 that they cannot be distinguished with certainty over a 

 moderate range of temperature. But if the values of the differ- 

 ence-coefficients are calculated from the S.B.P., the balance 

 of evidence appears to be in favour of the original formula (2). 

 Formula (4) appears to give differences which are too large 

 between 0° and 100° C; and it does not agree nearly so 

 well as (2) with my own air- thermometer observations over 

 the range 0° to 650° C. It appears also from the work of 

 Heycock and Neville to give results which are too low at high 

 temperatures as compared with those of other observers. 



It is obvious, from the similarity of form, that the differ- 

 ence-formula (4) in terms of pt corresponds, as in the case of 

 formula (2), to a parabolic relation between the temperature 

 and resistance, of the type 



^-^H-a'R/^ + Z/CR/R^^a'XR/^-lJ+^^R/R -!) 2 . (5) 



When R = 0, t = - t° = -(<*"-&"). Also V= b", and 

 a'=a"-2&". 



The values of the fundamental coefficient c, and of the fun- 

 damental zero pt°, are of course the same on either formula, 

 provided that they are calculated from observations at 0° and 

 100° C, but not, if they are calculated from observations 

 outside that range. The values of the coefficients a" and h" 

 are given in terms of d' ', and either pt°, or c, by the relations 



a" =pt° (1 - d'/lOO) = ( 1 - d7 100) /c, and d! = 10,0006V. 



Formulae of this general type, but expressed in a slightly 

 different shape, have been used by Holborn and Wien for 

 their observations at low temperatures, and recently by 

 Dickson for reducing the results of Fleming and other 

 observers. But they do not employ the platinum scale or 

 the difference-formula. 



Maximum and Minimum Values of the Resistance and 

 Temperature, — It may be of interest to remark that the dif- 

 ference-formulae (2) and (4) lead to maximum or minimum 

 values of pt and t respectively, which are always the same 

 for the same value of d, but lie in general outside the range 

 of possible extrapolation. In the case of formula (2), the 

 resistance reaches a maximum at a temperature t= —a/'lb — 

 (5000/d) (l + d/100). The maximum values of pt and R are 

 given in terms of d and c by the equations 



pt (max.) = (1 + d/100) t/2 = (2500/rf) (1 + d/lOO)*, 



R/R° (max.) =l+pt (max.)//rf?=l+ (2500c/d) (l+^/lOO) 2 . 



