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



the formula as the product of three factors, because the sub- 

 traction (7/100 — 1) can be safely performed by mental 

 arithmetic. The whole process can then be performed by 

 one application of the slide-rule, instead of two, and it is 

 unnecessary to write down any intermediate steps on paper. 



The Parabolic Function. — It is convenient to have an 

 abbreviation for the parabolic function of t vanishing at 

 0° and 100°, which occurs so frequently in questions of 

 thermometry. I have found the abbreviation p(t) both sug- 

 gestive and useful for this purpose. The formula may then 

 be written in the abbreviated shape, t=pt-\-dxp(t). 



The "S.B.P." Method of Reduction.— -Assuming the differ- 

 ence-formula, the value of the difference-coefficient d may be 

 determined by observing the resistance B", and calculating 

 the corresponding value of the platinum temperature pt" . at 

 some secondary fixed point t n , the temperature of which is 

 known on the scale of the gas-thermometer. The boiling- 

 point of sulphur (S.B.P.) is generally the most convenient 

 to use, and has been widely adopted for this purpose. As- 

 suming that this point is chosen for the purpose, and that the 

 height of the barometer at the time is 760 + A millims., the 

 corresponding temperature is given by the formula 



t" =444-53 + -082 h, 



provided that h is small, and the corresponding value of the 

 parabolic function by the formula 



p(t") = 15*32 + -0065 h, 



whence d=(t"-pt // )[p(t // ). 



With the best apparatus it is possible to attain an order of 

 accuracy of about 0*1 per cent, in the value of d obtained by 

 this method, at least in the case of thermometers which are 

 not used at temperatures above 500°. At higher temperatures 

 the exact application of the formula would be more open to 

 question, and it may be doubted whether the value of the 

 difference-coefficient would remain constant to so small a 

 fraction of itself. 



Other Secondary Fixed Points. — For very accurate work 

 between 0° and 100° C. it might be preferable to use a value 

 of d determined at 50° C, either by direct comparison with 

 an air-thermometer or by comparison with a standard platinum 

 thermometer. The latter comparison would be much the 

 easier and more accurate. Although the most careful com- 

 parisons have hitherto failed to show that the value of d 

 obtained by assuming the S.B.P. does not give correct results 



