=Calibration of Indicators for Radiation Pyrometers.=—The deflections on the indicators are due to the E.M.F. generated, which is proportional to the difference in temperature between the hot and cold junctions. If both these are at the same temperature—say, 20° C.—the deflection is zero; and on allowing the radiations to fall on the hot junction its temperature is raised by an amount depending upon the intensity of the radiations—say, to 90° C. The deflection produced is then due to a difference of (90-20) = 70°, the radiations having raised the temperature of the hot junction 70° above its surroundings. If the surroundings (including the cold junction or junctions) had been at 15° to commence with, the hot junction under the same conditions would have risen to 85°, giving again a difference of 70°, and thus causing the same deflection as before. Provided both hot and cold junctions are located so as to attain the same atmospheric temperature in the absence of radiations, a given quantity of energy impinging on the hot junction will always produce in it the same _excess_ temperature, and will therefore give rise to the same deflection at all ordinary atmospheric temperatures. As the junctions are so arranged in radiation pyrometers as to fulfill this condition, no correction for fluctuations in the cold junctions is necessary. The deflections, therefore, correspond to excess temperatures of the hot junction, which in turn are directly proportional to the energy received by the junction. Readings in millivolts on the indicator thus represent directly the proportions of energy received by the hot junction, 4 millivolts corresponding to twice the energy, which produces 2 millivolts, and so on; and hence the millivolt scale becomes an energy scale. In order to translate energy into corresponding temperatures, the fourth-power law must be applied. If E_{1} correspond to an absolute temperature T_{1} on the part of the black body from which radiations are received, and E_{2} correspond to another temperature T_{2}, the following relations will hold good: E_{1} = K(T_{1}^4 - _x^4_), and E_{2} = K(T_{2}^4 - _x^4_), where _x_ is the temperature of the surroundings receiving the radiations. As previously pointed out (see Example on page 140), the term _x^4_ may be ignored for the range of high temperatures measured by a radiation pyrometer, hence E_{1} = KT_{1}^4, and E_{2} = KT_{2}^4; and therefore E_{1}/E_{2} = T_{1}^4/T_{2}^4. But, as shown above, readings in millivolts on the indicator are directly proportional to the energy received, and if R_{1} and R_{2} = millivolts due to E_{1} and E_{2}, the relation R_{1}/R_{2} = T_{1}^4/T_{2}^4 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:—