where E is the total energy radiated; T_{1} the absolute temperature of the black body; T_{2} the absolute temperature of the receiving substance, and K a constant depending upon the units chosen. If E be expressed as watts per square centimetre, the value of K is 5·6 × 10^{-12}; if in calories per square centimetre per second, the value is 1·34 × 10^{-12}. The introduction of the temperature of the receiving substance, T_{2}, is rendered necessary by the fact, previously cited, that energy will be radiated back to the hot body, and the net loss of energy will evidently be the difference between that which leaves it and that which returns to it from the receiving substance. If T_{2} were absolute zero, the energy leaving the black body would be KT_{1}^4; whereas if T_{2} were equal to T_{1}, the loss of energy would be nil, as a substance cannot cool by radiation to a lower temperature than its surroundings. The temperatures T_{1} and T_{2} refer to the thermodynamic scale (page 9), but as the gas scale is practically identical, Centigrade degrees may be used, measured from absolute zero, or -273°. An example is appended to illustrate the application of the law:— _Example._—To compare the energy radiated through an opening in the side of a furnace at temperatures of 527°, 727°, and 927° C. respectively, to surroundings at 27° C. The quantities will be as K(800^4 - 300^4) : K(1000^4 - 300^4) : K(1200^4 - 300^4). since 273 must be added to each temperature to convert into absolute degrees. Dividing each by K, and expanding in each case, the ratio becomes (4096 - 81) × 10^8 : (10000 - 81) × 10^8 : (20736 - 81) × 10^8. Dividing each by 10^8 and subtracting, the result is 4015 : 9919 : 20655, or 1 : 2·47 : 5·12. It will be noted in the above example that the effect of the surrounding temperature, taken as 27° C., is small in quantity, and becomes proportionately less as the temperature of the furnace increases. If T_{2} had been ignored in the calculation, the amounts of energy radiated would have appeared as 1 : 2·44 : 5·06. It will be seen later, that in calculating the temperature scale of a radiation pyrometer, the temperature of the surroundings is for this reason not taken into account. Fig. 43 is a graphic illustration of the fourth-power law. [Illustration: FIG. 43.—ENERGY RADIATED BY A BLACK BODY AT DIFFERENT TEMPERATURES.]