FIG. 23.
By means of Langley's bolometer the distribution of energy in the spectrum has been measured accurately, with the results of confirming and amplifying the general results just stated. The energy in the spectrum of even the hottest of terrestrial radiators is mostly in the longer waves of the infra-red, but the position of the maximum of energy moves to shorter and shorter wave-lengths as the temperature rises, and so more of the shorter waves make their appearance. The sun is not a full radiator, but is nearly so, and its temperature is so high that the maximum of energy in its spectrum is in the visible part near to the red end.
Fig. 23 shows the results obtained by Lummer and Pringsheim, and brings out clearly the shift of the maximum with rising temperature and also the position of the greatest part of the energy in the infrared region.
Wien's Laws.—Examination of the results also shows that the wave-length at which the maximum energy occurs is inversely proportional to the absolute temperature and that the actual energy at the maximum point is proportional to the fifth power of the absolute temperature. These two results have both been derived theoretically by Wien[[2]] in a similar way to that in which Boltzmann derived Stefan's fourth power law, i.e. by imagining a space filled with the radiation to be taken through a cycle of compressions and rarefactions.
[[1]] Wied. Ann., 46, p. 633; 52, p. 132.
Wien derived an amplification of the last result by showing that if a wave-length in the spectrum of a full radiator at one temperature and another wave-length in the spectrum at another temperature are so related as to be inversely proportional to the two absolute temperatures, they may be said to correspond to each other, and the energy in corresponding wave-lengths at different temperatures is proportional to the fifth power of the absolute temperature.
We see therefore that if the distribution of energy in the spectrum of the full radiator be known at any one temperature it may be calculated for any other temperature by applying these two laws of corresponding wave-lengths and the energy in them.