way of this theory arise from the fact that nearly all radiation
is more or less selective in character, as regards the quality
and frequency of the rays emitted and absorbed. It was shown
by J. Leslie, M. Melloni and other experimentalists that many
substances such as glass and water, which are very transparent to
visible rays, are extremely opaque to much of the invisible
radiation of lower frequency; and that polished metals, which
are perfect reflectors, are very feeble radiators as compared
with dull or black bodies at the same temperature. If two
bodies emit rays of different periods in different proportions,
it is not at first sight easy to see how their radiations can balance
each other at the same temperature. The key to all such
difficulties lies in the fundamental conception, so strongly insisted
on by Balfour Stewart, of the absolute uniformity (qualitative
as well as quantitative) of the full or complete radiation stream
inside an impervious enclosure of uniform temperature. It
follows from this conception that the proportion of the full
radiation stream absorbed by any body in such an enclosure
must be exactly compensated in quality as well as quantity
by the proportion emitted, or that the emissive and absorptive
powers of any body at a given temperature must be precisely
equal. A good reflector, like a polished metal, must also be a
feeble radiator and absorber. Of the incident radiation it absorbs
a small fraction and reflects the remainder, which together with
the radiation emitted (being precisely equal to that absorbed)
makes up the full radiation stream. A partly transparent material,
like glass, absorbs part of the full radiation and transmits part.
But it emits rays precisely equal in quality and intensity to
those which it absorbs, which together with the transmitted
portion make up the full stream. The ideal black body or perfect
radiator is a body which absorbs all the radiation incident on it.
The rays emitted from such a body at any temperature must be
equal to the full radiation stream in an isothermal enclosure at
the same temperature. Lampblack, which may absorb between
98 to 99% of the incident radiation, is generally taken as the
type of a black body. But a closer approximation to full radiation
may be obtained by employing a hollow vessel the internal
walls of which are blackened and maintained at a uniform
temperature by a steam jacket or other suitable means. If
a relatively small hole is made in the side of such a vessel, the
radiation proceeding through the aperture will be the full radiation
corresponding to the temperature. Such a vessel is also a
perfect absorber. Of radiation entering through the aperture an
infinitesimal fraction only could possibly emerge by successive
reflection even if the sides were of polished metal internally.
A thin platinum tube heated by an electric current appears
feebly luminous as compared with a blackened tube at the same
temperature. But if a small hole is made in the side of the
polished tube, the light proceeding through the hole appears
brighter than the blackened tube, as though the inside of the tube
were much hotter than the outside, which is not the case to any
appreciable extent if the tube is thin. The radiation proceeding
through the hole is nearly that of a perfectly black body if the
hole is small. If there were no hole the internal stream of radiation
would be exactly that of a black body at the same temperature
however perfect the reflecting power, or however low the
emissive power of the walls, because the defect in emissive power
would be exactly compensated by the internal reflection.
Balfour Stewart gave a number of striking illustrations of the qualitative identity of emission and absorption of a substance. Pieces of coloured glass placed in a fire appear to lose their colour when at the same temperature as the coals behind them, because they compensate exactly for their selective absorption by radiating chiefly those colours which they absorb. Rocksalt is remarkably transparent to thermal radiation of nearly all kinds, but it is extremely opaque to radiation from a heated plate of rocksalt, because it emits when heated precisely those rays which it absorbs. A plate of tourmaline cut parallel to the axis absorbs almost completely light polarized in a plane parallel to the axis, but transmits freely light polarized in a perpendicular plane. When heated its radiation is polarized in the same plane as the radiation which it absorbs. In the case of incandescent vapours, the exact correspondence of emission and absorption as regards wave-length of frequency of the light emitted and absorbed forms the foundation of the science of spectrum analysis. Fraunhofer had noticed the coincidence of a pair of bright yellow lines seen in the spectrum of a candle flame with the dark D lines in the solar spectrum, a coincidence which was afterwards more exactly verified by W. A. Miller. Foucault found that the flame of the electric arc showed the same lines bright in its spectrum, and proved that they appeared as dark lines in the otherwise continuous spectrum when the light from the carbon poles was transmitted through the arc. Stokes gave a dynamical explanation of the phenomenon and illustrated it by the analogous case of resonance in sound. Kirchhoff completed the explanation (Phil. Mag., 1860) of the dark lines in the solar spectrum by showing that the reversal of the spectral lines depended on the fact that the body of the sun giving the continuous spectrum was at a higher temperature than the absorbing layer of gases surrounding it. Whatever be the nature of the selective radiation from a body, the radiation of light of any particular wave-length cannot be greater than a certain fraction E of the radiation R of the same wave-length from a black body at the same temperature. The fraction E measures the emissive power of the body for that particular wave-length, and cannot be greater than unity. The same fraction, by the principle of equality of emissive and absorptive powers, will measure the proportion absorbed of incident radiation R′. If the black body emitting the radiation R′ is at the same temperature as the absorbing layer, R = R′, the emission balances the absorption, and the line will appear neither bright nor dark. If the source and the absorbing layer are at different temperatures, the radiation absorbed will be ER′, and that transmitted will be R′ − ER′. To this must be added the radiation emitted by the absorbing layer, namely ER, giving R′ − E(R′ − R). The lines will appear darker than the background R′ if R′ is greater than R, but bright if the reverse is the case. The D lines are dark in the sun because the photosphere is much hotter than the reversing layer. They appear bright in the candle-flame because the outside mantle of the flame, in which the sodium burns and combustion is complete, is hotter than the inner reducing flame containing the incandescent particles of carbon which give rise to the continuous spectrum. This qualitative identity of emission and absorption as regards wave-length can be most exactly and easily verified for luminous rays, and we are justified in assuming that the relation holds with the same exactitude for non-luminous rays, although in many cases the experimental proof is less complete and exact.
40. Diathermancy.—A great array of data with regard to the transmissive power or diathermancy of transparent substances for the heat radiated from various sources at different temperatures were collected by Melloni, Tyndall, Magnus and other experimentalists. The measurements were chiefly of a qualitative character, and were made by interposing between the source and a thermopile a layer or plate of the substance to be examined. This method lacked quantitative precision, but led to a number of striking and interesting results, which are admirably set forth in Tyndall’s Heat. It also gave rise to many curious discrepancies, some of which were recognized as being due to selective absorption, while others are probably to be explained by imperfections in the methods of experiment adopted. The general result of such researches was to show that substances, like water, alum and glass, which are practically opaque to radiation from a source at low temperature, such as a vessel filled with boiling water, transmit an increasing percentage of the radiation when the temperature of the source is increased. This is what would be expected, as these substances are very transparent to visible rays. That the proportion transmitted is not merely a question of the temperature of the source, but also of the quality of the radiation, was shown by a number of experiments. For instance, K. H. Knoblauch (Pogg. Ann., 1847) found that a plate of glass interposed between a spirit lamp and a thermopile intercepts a larger proportion of the radiation from the flame itself than of the radiation from a platinum spiral heated in the flame,
