In all photometric methods a standard light is employed, which should not vary in brightness, and with which the light from the source is compared. In optical pyrometers no attempt is made to measure the illumination in terms of candle-power; all that is necessary is to bring the standard and the source to the same degree of brightness by suitable adjustments. Amongst the standards employed are carbon-filament electric lamps, amyl-acetate lamps, and for higher temperatures the centre of an acetylene gas-flame; each of which is capable of producing a fixed degree of brightness when used under specified conditions. A black body, at known temperatures, is compared with the standard used, thus furnishing a scale of “black-body” temperatures to which the indications of a given source may be referred, as explained in the previous paragraph. Above 1000° C., however, the light becomes too dazzling to enable a proper comparison of the standard and source to be made, and absorbing glasses must then be used to reduce the brightness. Any coloured glass, taken at random, might not reduce the standard and source equally; but if a monochromatic glass be used—that is, a glass which transmits light of one wave-length only—a well-defined relation is found to exist between the intensity of the transmitted light and the temperature of the source. As optical pyrometers are used for temperatures above 1000° C. in most cases, involving the use of such glass, it will be necessary briefly to consider the relations between the wave-lengths of light and the temperature of the radiating substance, which in all cases will be assumed to be a black body. =Wien’s Law.=—When the temperature of a substance increases, the enhanced brightness which results is shared by all parts of its spectrum; and if the substance were viewed through a glass prism, it would be noticed that every portion was brighter than before. Taking a ray of wave-length λ, the relation between its intensity and the temperature of the (black-body) source is given by Wien’s formula:— J = _c_{1}_λ^{-5} × _e_^{-_c_{2}_/λT} (1) where J = energy corresponding to wave-length λ; _e_ = the base of the natural system of logarithms; T = absolute (thermodynamic) temperature of the black-body source, and _c_{1}_ and _c_{2}_ are constants, the values of which may be found by measuring J at two known temperatures for light of a known wave-length. Experiment has shown that this formula is correct for wave-lengths which lie in the visible spectrum, but does not hold for longer waves; and modifications of Wien’s equation have been given by Planck and others which are of more extended application. For the purposes of optical pyrometry, however, using red light of wave-length about 65 millionths of a centimetre, Wien’s law may be applied with great accuracy; and a calibration based upon this law agrees closely with the values obtained by other pyrometric methods. Wien’s formula may be written in the form—