So many attempts have been made to establish, by one or other of these two methods, the relation between the quantity of heat radiated and the temperature, that it is impossible to give even a passing reference to most of them. Unfortunately, the results do not show the agreement with one another which we would like, but probably the most correct result is that stated by Stefan in 1878, after a close inspection of the experimental results of Dulong and {48} Petit. He stated that the quantity of heat radiated per second by a full radiator is proportional to the fourth power of its absolute temperature.[1] Thus the quantity of heat radiated by one square centimetre of the surface of a full radiator whose absolute temperature is T, is equal to ET(sup)4, where E is some constant multiplier which must be determined by experiment and which is called the radiation constant. If the absolute temperature of the enclosure in which the surface is placed is T, then the rate at which the surface is losing heat will be E(T(sup)4-T(sub)1(sup)4), for it will receive heat at the rate ET(sub)1(sup)4 and will radiate it at the rate ET(sup)4. [1] See page 56. Stefan's fourth power law has been verified by a number of good experiments, notably those of Lummer and Pringsheim (_Congrés International de Physique_, Vol. II. p. 78), so that although some experiments do not agree with it, we are probably justified in taking it as correct. In 1884 Boltzmann added still further evidence in support of this law by deriving it theoretically. He applied to a space containing the waves of full radiation the two known laws which govern the transformation of energy, by imagining the space to be taken through a cycle of compressions and expansions in just the same way as a gas is compressed and expanded in what is known as Carnot's cycle. +Variation of Spectrum with Temperature.+--The variation of the character of the spectrum of a full radiator has been determined mainly by the use of Langley's bolometer, but the general nature of the change may be readily observed by the eye. {49} As the temperature of a full radiator rises it first gives out only invisible heat waves; as soon as its temperature exceeds about 500° C. it begins to emit some of the longest visible rays; and as the temperature rises further, more and more of the visible rays in the spectrum are emitted until, when the radiator is white hot, the whole of the visible spectrum. is produced. Thus the higher the temperature of the radiator the more of the shorter waves are produced. [Illustration: FIG. 23.]