where x is the temperature of the surroundings receiving the radiations. As previously pointed out ([see Example on page 140]), the term x4 may be ignored for the range of high temperatures measured by a radiation pyrometer, hence E1 = K T14, and E2 = KT24; and therefore E1 / E2 = T14 / T24. But, as shown above, readings in millivolts on the indicator are directly proportional to the energy received, and if R1 and R2 = millivolts due to E1 and E2, the relation R1/R2 = T14/T24 is then obtained.
In order to prepare a temperature scale from this relation, it is necessary to take one correct reading at a known temperature, after which the remainder of the scale may be marked by calculation, as shown in the example appended:—
Example.—A tube closed at one end is at 927° C. (1200° abs.), and gives a deflection corresponding to 2 millivolts on the indicator. To find the temperatures which would yield deflections due to 1, 3, 4, and 5 millivolts.
Taking the case of 1 millivolt and applying in the formula
R1⁄R2 = T14⁄T24 ; 2⁄1 = 12004⁄T24
from which T24 = 12004⁄2 and T2 = 1009° abs. = 736° C. Similarly, 3 millivolts represent 1055° C.; 4 millivolts = 1154° C.; and 5 millivolts = 1236° C. These values are readily obtained by the use of four-figure logarithms.
Having calculated the temperature corresponding to each whole millivolt, a curve may be plotted to represent millivolts against corresponding temperatures, and intermediate values deduced from it. Evidently, the standard reading must be taken with great accuracy, as the whole scale hinges upon it; and for this purpose an accurate resistance or thermo-electric pyrometer may be used, placed inside the tube of an electric furnace, and the radiation pyrometer sighted on a thin sheet of iron placed just in front of the naked junction. A check at the higher readings of the scale is necessary, as an exact realisation of the fourth-power law is seldom obtained in practice. This may be taken in the same manner, as thermocouples may now be calibrated directly against the gas scale up to 1550° C., thus enabling the gas-scale reading to be transferred to the radiation pyrometer. For delicate readings over a given range, the scale of a mirror galvanometer may be calibrated in this manner, sufficient resistance having first been added in series to ensure that at the highest temperature employed the spot of light will remain on the scale.
Fig. 54.—Record obtained with Radiation Pyrometer.