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



This formula is so simple and convenient, and agrees so 

 closely over moderate ranges of temperature with the ordinary 

 difference-formula, as to be well worth discussion. I have 

 been in the habit of using it myself for a number of years in 

 approximate reductions at moderate temperatures, more par- 

 ticularly in steam-engine and conductivity experiments, in 

 which for other reasons a high degree of accuracy is not 

 required. It has also been recently suggested by Dickson 

 (Phil. Mag., Dec. 1897), though his suggestion is coupled 

 with a protest against platinum temperatures. 



The value of the difference- coefficient oV in this formula 

 may be determined as usual by reference to the boiling-point 

 of sulphur, or it may be deduced approximately from the 

 value of the ordinary difference-coefficient d by means of the 

 relation 



d'=d/(l--077d), or d=d'/{l + '077d'). 



If this value is chosen for 

 ence-formulae will of course 



the coefficient, the two dii 



at 0°, 100 c 



and 445° C, 

 The order of 



but will differ slightly at other temperatures, 

 agreement between the formulae is shown at various points of 

 the scale by the annexed table, in which t represents the 

 temperature given by the ordinary formula t—pt=l'50p(t), 

 and t' the temperature calculated by formula (4) for the same 

 value of pt, choosing the value d'= 1*695, to make the two 

 formulae agree at the S.B.P. 



Table I. 

 Comparison of Difference-Formulae, (2) & (4). 



t 



-300° 

 -4° -5 



-200° 

 -l°-95 



-100° 

 -0°-54 



+•50° 

 +•050° 



200° 



-•23° 



300° ! 

 -•42° 



t-v ... 



t 



400° 

 -•25° 



600° 



+2°-2 



800° 

 +9°-3 



1000° 

 +22° -9 



1200° 

 +46°-6 



1500° 



+97°'2 



t-t' ... 



It will be observed that the difference is reasonably small 

 between the limits — 200° and + 600°, but that it becomes 

 considerable at high temperatures. A much closer agreement 

 may be readily obtained over small ranges of temperature by 

 choosing a suitable value of d' . The two formulae become 

 practically indistinguishable between 0° and 100°, for in- 

 stance, if we make d f = d. For steam-engine work I generally 

 selected the value of d f to make the formulae agree at 200° C. 



