RADIATION 215 ments. To this we will recur.) His desire to escape the difficulties of surface-reflexion led him to consider the radia- tion inside an imperfectly transparent body in the enclo- sure above spoken of. He thus arrived at an immediate proof of the existence of internal radiation, which recruits the stream of radiant heat in any direction step by step precisely to the amount by which it has been weakened by absorption. Thus the radiation and absorption rigorously compensate one another, not merely in quantity but in quality also, so that a body which is specially absorptive of one particular ray is in the same proportion specially radiative of the same ray, its temperature being the same in both cases. To complete the statement, all that is necessary is to show how one ray may differ from another, viz., in intensity, wave-length, and polarization. 14. The illustrations which Stewart brought forward in support of his theory are of the two following kinds. (1) He experimentally verified the existence of internal radiation, to which his theory had led him. This he did by show- ing that a thick plate of rock-salt (chosen on account of its comparative transparency to heat-radiations) radiates more than a thin one at the same temperature, surrounding bodies being in this case of course at a lower temperature, so that the effect should not be masked by transmission. The same was found true of mica and of glass. (2) He showed that each of these bodies is more opaque to radia- tions from a portion of its own substance than to radiation in general. Then comes his conclusion, based, it will be observed, on his fundamental assumption as to the nature of the equilibrium radiation in an enclosure. It is merely a detailed explanation that, once equilibrium has been arrived at, the consequent uniformity of radiation throughout the interior of a body requires the step-by-step compensation already mentioned. And thus he finally arrives at the state- ment that at any temperature a body's radiation is exactly the same both as to quality and quantity as that of its absorption from the radiation of a black body at the same temperature. In symbolical language Stewart's proposi- tion (extended in virtue of a principle always assumed) amounts to this : at any one temperature let E be the radiation of a black body, and eR (where e is never greater than 1) that of any other substance, both for the same definite wave-length; then the substance will, while at that temperature, absorb the fraction e of radiation of that wave-length, whatever be the source from which it comes. The last clause contains the plausible assumption already referred to. Stewart proceeds to show, in a very original and ingenious way, that his result is compatible with the known facts of reflexion, refraction, &c., and arrives at the conclusion that for internal radiation parallel to a plane the amount is (in isotropic bodies) proportional to the refractive index. Of course, when the restriction of parallelism to a plane is removed the internal radiation is found to be proportional to the square of the refractive index. This obvious completion of the statement was first given by Stewart himself at a somewhat later date. 15. So far Stewart had restricted his work to "dark heat," as it was then called ; and he says that he did so expressly in order to confine himself to rays " which were universally acknowledged to produce heat by their absorp- tion." But he soon proceeded to apply himself to luminous radiations. And here he brought forward the extremely important fact that " coloured glasses invariably lose their colour in the fire " when exactly at the temperature of the coals behind them, i.e., they compensate exactly for their absorption by their radiation. But a red glass when colder than the coals behind appears red, while if it be hotter than they are it appears green. He also showed that a piece of china or earthenware with a dark pattern on a light ground appears to have a light pattern on a dark ground when it is taken out of the fire and examined in a dark room. Hence he concluded that his extension of Prevost's theory was true for luminous rays also. 16. In this part of the subject he had been anticipated, for Fraunhofer had long ago shown that the flame of a candle when examined by a prism gives bright lines (i.e., maxima of intensity of radiation) in the position of the constituents of a remarkable double dark line (i.e., minima of radiation) in the solar spectrum, which he called D. Hallows Miller had afterwards more rigorously verified the exact coincidence of these bright and dark lines. But Foucault 1 went very much farther, and proved that the electric arc, which shows these lines bright in its spectrum, not only intensifies their blackness in the spectrum of sun- light transmitted through it, but produces them as dark lines in the otherwise continuous spectrum of the light from one of the carbon points, when that light is made by reflexion to pass through the arc. Stokes about 1850 pointed out the true nature of the connexion of these phenomena, and illustrated it by a dynamical analogy drawn from sound. He stated his conclusions to Sir W. Thomson, 2 who (from 1852 at least) gave them regularly in his public lectures, always pointing out that one con- stituent of the solar atmosphere is certainly sodium, and that others are to be discovered by the coincidences of solar dark lines with bright lines given by terrestrial sub- stances rendered incandescent in the state of vapour. Stokes's analogy is based on the fact of synchronism (long ago discussed by Hooke and others), viz., that a musical string is set in vibration when the note to which it is tuned is sounded in its neighbourhood. Hence we have only to imagine a space containing a great number of such strings, all tuned to the same note. Such an arrangement would form, as it were, a medium which, when agitated, would give that note, but which would be set in vibration by, and therefore diminish the intensity of, that particular note in any mixed sound which passed through it. 17. Late in 1859 appeared Kirchhoff's first paper on the subject. 3 He supplied one important omission in Stewart's development of the theory by showing why it is necessary to use as an absorbing body one colder than the source in order to produce reversal of spectral lines. This we will presently consider. Kirchhoff's proof of the equality of radiating and absorbing powers is an elaborate but unnecessary piece of mathematics, called for in con- sequence of his mode of attacking the question. He chose to limit his reasoning to special wave-lengths by introduc- ing the complex mechanism of the colours of thin plates (LIGHT, vol. xiv. p. 608), and a consequent appeal to Fourier's theorem (HARMONIC ANALYSIS, vol. xi. p. 481), instead of to the obviously permissible assumption of a sub- stance imperfectly transparent for one special wave-length, but perfectly transparent for all others ; and he did not, as Stewart had done, carry his reasoning into the interior of the body. With all its elaboration, his mode of attack- ing the question leads us no farther than could Stewart's. Both are ultimately based on the final equilibrium of tem- perature in an enclosure required by Carnot's principle, and both are, as a consequence, equally inapplicable to exceptional cases, such as the behaviour of fluorescent or phosphorescent substances. In fact (see THERMODYNAMICS) Carnot's principle is established only on a statistical basis of averages, and is not necessarily true when we are deal- ing with portions of space, which, though of essentially finite dimensions, are extremely small in comparison with the sentient part of even the tiniest instrument for measur- ing temperature. 1 L'lnstitut, 7th February 1849 ; see Phil. Mag., 1860, i. p. 193. 2 Brit. Assoc., President's address, 1871. 3 Pogg. Ann., or Phil. Mag., I860.
