In order to determine the value of δ, it is necessary to measure the resistance of the wire at 0°, 100°, and a third temperature, which should be considerably above 100°. The readings at 0° and 100° are requisite to establish the platinum scale of temperatures; the third reading is required to calculate the value of δ, as p and t are equal at 0° and 100°, these points forming the basis of both scales. An example is appended to make this matter clear.
Example.—A platinum wire has a resistance in ice of 2·6 ohms; in steam, 3·6 ohms; in boiling sulphur, 6·815 ohms. To find the value of δ, the boiling point of sulphur being 444·5 on the gas scale.
Since an increase of (3·6 - 2·6) = 1 ohm is produced by 100°, the increase observed in boiling sulphur, (6·815 - 2·6) = 4·215 ohms, will represent a temperature, on the platinum scale, of (4·215 × 100)⁄1 = 421·5° p.
Applying Callendar’s formula,
(444·5 - 421·5) = δ { (444·5⁄100)2 - (444·5⁄100) }
the value of δ is found to be 1·5.
Callendar, in his experiments, employed the boiling point of sulphur for the third point, and determined this temperature on the gas scale with great accuracy, The necessity for extreme precision in applying this formula is made clear by noting the effects on the value of δ resulting from small differences in the figures chosen in the above example. If, for instance, the boiling point of sulphur on the gas scale were taken at 2° lower, or 442·5, the value of δ would work out to 1·37; and the error at 1200° C. thus caused would amount to 17°. The same discrepancy would be observed if the resistance in boiling sulphur were taken as 6·835 ohms, an error of 0·02 ohm; and a still greater error would result if the difference in resistance at 0° and 100° were measured as 0·99 ohm instead of 1 ohm. From an extensive experience of the difficulties attendant on correctly determining the value of δ, the author has found that no reliable result can be obtained unless measuring instruments of the highest precision are used, and elaborate precautions taken to ensure the exact correction for alterations in the boiling points of water and sulphur occasioned by changes in atmospheric pressure. Unless the necessary facilities are at hand, an operator would be well advised to standardize a resistance pyrometer by taking several fixed points and drawing a calibration curve, after the manner recommended for a thermo-electric pyrometer.
If a resistance pyrometer be calibrated so as to read in platinum-scale degrees, and the value of δ be known for the wire, the correct gas-scale temperatures may be calculated from Callendar’s formula. The table on next page gives the results of a number of calculations made in this manner.
Changes in Resistance of Platinum when constantly Heated.—The resistance of platinum undergoes a gradual change when the wire is kept continuously above a red heat; and if the temperature exceed 1000° C. the change becomes very marked after a time, leading to serious errors in temperature indications when used in a pyrometer. The alteration under notice is due, as shown by Sir William Crookes, to the fact that platinum is distinctly volatile above 1000° C., and hence the diameter of the wire diminishes. This variation constitutes a serious drawback to the use of resistance pyrometers for temperatures exceeding 1000° C.
Comparison of Gas and Platinum Scales.
δ = 1·5.