282 ADAMS AND JOHNSTON: STANDARD TEMPERATURE SCALE 



could be desired. This concordance shows further that if we derive an 

 interpolation formula for the resistance thermometer based on all of the 

 points excepting sulfur, and calculate by means of this formula the boiling 

 temperature of sulfur, we obtain a result identical with the direct gas 

 thermometer determination of this fixed point. 



If we recalculate the above temperatures using a fixed value of 8 

 based on the newer determinations of the sulfur point, we obtain results 

 which are practically identical with those of column II (Table IV) 

 except at the silver and copper points, which would on this basis be 

 lower by 0?6 and 0?9 respectively. This silver point would stiH be 

 within the limits of accuracy of the gas thermometer measurements at 

 that point, but the divergence at the copper point (1?3) is somewhat 

 greater than the probable error. 



This raises the question of the range through which the simple, 

 and very convenient, Callendar formula is applicable in accurate 

 work. It does not hold for impure platinum or for palladium; 13 

 nor does it hold for pure platinum at all temperatures below 0°C. 

 Indeed Travers and Gwyer say: "A standard scale of tempera- 

 ture, based on Callendar's three fixed points, using standard wire, 

 and taking 1.5 for the value of 5, would obviously lead to absurd 

 results at low temperatures; and the converse may be said of our 

 own observations;" 14 and conclude that the Callendar formula 

 cannot be made use of except for interpolation. There is thus 

 ground for believing that the accuracy of the results calculated 

 from the change of resistance of pure platinum by means of the 

 simple Callendar formula is to some extent fortuitous. The 

 small variation of 8 introduces uncertainties which would appear 

 to be too great for the most accurate work except over the tem- 

 perature range included between the -fixed calibration points 

 (0°-444?55), and a short region beyond (perhaps to 750°). ,5 On 

 the other hand it must be admitted that the cubic term (which 

 expresses the variation of 8 with the temperature) is very small— 

 so small that its effect is scarcely greater than the uncertainty in 

 the gas thermometer determinations at the higher temperatures. 



13 Waidner and Burgess, Bu'l. Bureau Standards, 6: 176, 183. 1910. 



14 Proc. Roy. Soc. London, 74: 538. 1904-5. 



16 The effect of slight changes of 5 on the calculated temperatures may be gauged 

 from the following: that a change of 0?2 in the boiling point of sulfur changes 5 

 by 1 per cent (and proportionally for other small changes); this in turn affects 

 temperatures of 300° or lower by 0?1 or less, but affects the antimony point by 0?5 

 and the copper point by 1?6. 



