The emission constants of metals in the near infra-red

Abstract

In the far infra-red, the reflecting power, R, of a metal at a wave-length, λ, is connected with its specific resistance, ρ, by the Hagen-Rubens relation, 1 - R = k √ρ/λ, where k is a constant with the value 0·365 when λ is measured in μ., and ρ is the resistance of a rod of the metal 1 metre in length and 1 sq. mm. in cross-section. The relation has only a restricted range of validity: for it is based theoretically on the electromagnetic theory, which does not embody the modern conceptions of the electron theory; and a restriction for a lower wave-length limit is made in the deduction of the formula itself. Hagen and Rubens have subjected the formula to a rigid test by a series of emission measurements. At wave-lengths of 25·5 and 8·85 μ, the calculated and observed emissivities agreed usually to within about 10%. Further experiments at the same wave-lengths showed, moreover, that the emissivity changed with temperature in the manner demanded by the relation. It follows that the emissivity of a metal at sufficiently long wave-lengths is roughly proportional to the square-root of its absolute temperature.