The determination of the intrinsic brightness of the heated substance by a photometric method naturally suggests itself as a possible means of ascertaining temperatures by optical means, and it will be found that all the optical pyrometers used for industrial purposes are based on this procedure. The law connecting the intensity of the whole of the light waves emitted with temperature, for a given solid, is approximately given by Rasch’s formula:— ┌ ┐_x_ I_{1} │ T_{1} │ ───── = │ ───── │ I_{2} │ T_{2} │ └ ┘ where I_{1} and I_{2} are the intensities corresponding to absolute temperatures T_{1} and T_{2}; and the exponent 25000 _x_ = ───── . T_{1} Hence at 1250° abs. the brightness increases as the 20th power, and at 2500° abs. as the 10th power of the temperature. This rapid increase in brightness for a small rise in temperature enables small increments to be readily observed; but a difficulty arises in practice owing to vast differences in brightness displayed by different substances at the same temperature. For example, the light emitted by an incandescent gas-mantle, which consists of thorium oxide, is vastly greater than that given out by a metal, such as platinum, at the same temperature; and it is therefore evident that the luminosity of a substance depends not merely upon its temperature, but also upon its nature. It is possible, however, to obtain indications for any substance in terms of a black body; thus if a heated solid possessed the same intrinsic brightness as a black body at a temperature of T, the “apparent” or “black-body” temperature of the solid would also be called T. All that this would signify would be that the condition of the solid was such that the light radiated was equal in intensity to that emitted by a black body at temperature T; and to obtain the true temperature of the solid, T must be multiplied by a factor which expresses the ratio of its emissive power to that of a black body.