indicates, moreover, that the true absorption bands in a gas
of sufficiently low density must be extremely narrow. There
is direct evidence that many of the more permanent gases do
not sensibly emit light on being subjected to high temperature
alone, when chemical action is excluded, while others give
in these circumstances feeble continuous spectra; in fact,
looking at the matter from the other side, the more permanent
gases are very transparent to most kinds of radiation, and
therefore must be very bad radiators as regards those kinds.
The dark radiation of tiames has been identified with that
belonging to the specific radiation of their gaseous products
of combustion. There is thus ground for the view that the
impacts of the colliding molecules in a gas, or rather their
mutual actions as they swing sharply round each other in
their orbits during an encounter, may not be sufficiently violent
to excite sensibly the free vibrations of the definite periods
belonging to the molecules. But they may produce radiation
in other ways. While the velocity of an electron or other
electric charge is being altered, it necessarily sends out a stream
of radiation. Now the orbital motions of the electrons in an
actual molecule must be so adjusted, as appears to be theoretically
possible, that it does not emit radiation when in a
steady state and moving with constant velocity. But in the
violent changes of velocity that occur during an encounter
this equipoise will be disturbed, and a stream of radiation,
without definite periods, but such as might constitute its share
of the equilibrium thermal radiation of the substance, may be
expected while the encounter lasts. At very high temperatures
the energy of this thermal radiation in an enclosure entirely
overpowers the kinetic energy of the molecules present, for the
former varies as T4, while the latter measures T itself when
the number of molecules remains the same. The radiation
which can be excited in gases, confined as it is to extremely
narrow bands in the spectrum, may indeed be expected to
possess such intensity as to be thermally in equilibrium with
extremely high temperatures. That the same gases absorb
such radiations when comparatively cold and dark does not,
of course, affect the case, because emissive and absorptive
powers are proportional only for incident radiations of the
intensity and type corresponding to the temperature of the
body. Thus if our adiabatic enclosure of § 3 is prolonged into
a tube of unlimited length which is filled with the gas, then
when the temperature has become uniform that gas must send
back out of the tube as much radiation as has passed down the
tube and been absorbed by it; but if the tube is maintained
at a lower temperature, it may return much less. The fact
that it is now possible by great optical dispersion to make the
line-spectra of prominences in the middle of the Sun’s disk
stand out bright against the background of the continuous
solar
spectrum, shows that the intensities of the radiations of these prominences correspond to a much higher temperature than that of the general radiating layer underneath them; their luminosity would thus seem to be due to some cause (electric or chemical) other than mere temperature. On the other hand, the general reversing gaseous layer which originates the dark Fraunhofer lines is at a lower temperature than the radiating layer; it is only when the light from the lower layers is eclipsed that its own direct bright-line spectrum flashes out. It is not necessary to attribute this selective flash-spectrum to temperature radiation; it can very well be ascribed to fluorescence stimulated by the intense illumination from beneath. When the radiation in a spectrum is constituted of wide bands it may on these principles be expected to be in equilibrium with a lower temperature than when it is constituted of narrow lines, if the total intensity is the same, in the cases compared; this is in keeping with the easier excitation of band spectra (cf. the banded absorption spectra), and with the fact that various gases and vapours do appear to emit band spectra more or less related to the temperature.
15. Constitution of Spectra.—In the problem of the unravelling of the constitutions of the very complex systems of spectral lines belonging to the various kinds of matter, considerable progress has been made in recent years. The beginning of definite knowledge was the discovery of Balmer in 1885, that the frequencies of vibration (n) of the hydrogen lines could be represented, very closely and within the limits of error of observation, by the formula n ∝ 1 − 4m2, when for m is substituted the series of natural numbers 3, 4, 5, . . 15. Soon afterwards series of related lines were picked out from the spectra of other elements by Liveing and Dewar. Rydberg conducted a systematic investigation on the basis of a modification of Balmer’s law for hydrogen, namely, n=no−N/(m+μ)2. He found that in the group of alkaline metals three series of lines exist, the so-called principal and two subordinate series. whose frequencies fit approximately into this formula, and that similar statements apply to other natural groups of elements; that the constant N is sensibly the same for all series and all substances, while no, and μ have different values for each; and that other approximate numerical relations exist. In each series the lines of high frequency crowd together towards a definite limit on the more refrangible side; near this limit they would, if visible, constitute a band. The principal or strongest series of lines shows reversal very readily. The lines of the first subordinate series are usually nebular, while those of the second subordinate or weakest series are sharp; but with a tendency to broaden towards the less refrangible side.
In most series there are, however, not more than six lines visible: helium and hydrogen are exceptions, no fewer than thirty lines of the principal series of the latter having been identified, the higher ones in stellar spectra only. But very remarkable progress has recently been made by R. W. Wood, by exciting fluorescent spectra in a metallic vapour, and also by applying a magnetic field to restore the lines sensitive to the Zeeman effect after the spectrum has been cut off by crossed nicols. The large aggregates of lines thus definitely revealed are also resolved by him into systems in other ways; when the stimulating light is confined to one period, say a single bright line of another substance, the spectrum excited consists of a limited number of lines equidistant in frequency, the interval common to all being presumably the frequency of some intrinsic orbital motion of the molecule. In this way the series belonging to some of the alkali metals have been obtained nearly complete.
Simultaneously with Rydberg, the problem of series was attacked by Kayser and Runge, who, in reducing their extensive standard observations, used the formula n=A+Bm−2+Cm−4, higher terms in this descending series being presumed to be negligible. This cannot be reconciled with Rydberg’s form, which gives on expansion terms involving m−3; but for the higher values of m the discrepancies rapidly diminish, and do not prevent the picking out of the lines, the frequency-differences between successive lines then varying roughly as the inverse squares of the series of natural numbers. For low values of m neither mode of expression is applicable, as was to be expected; and it remains a problem for the future to ascertain if possible the rational formula to which they are approximations. More complex formulas have been suggested by Ritz and others, partly on theoretical grounds.
Considered dynamically, the question is that of the determination of the formula for the disturbed motions of the system which constitutes the molecule. Although we are still far from any definite line of attack, there are various indications that the quest is a practicable one. The lines of each series, sorted out by aid of the formulae above given, have properties in common: they are usually multiple lines, either all doublets in the case of monad elements, or generally triplets in the case of those of higher chemical valency; in very few cases are the series constituted of single lines. It is found also that the components of all the double or triple lines of a subordinate series are equidistant as regards frequency. In the case of a related group of elements, for example the alkaline metals, it appears that corresponding series are displaced continually towards, the less re frangible end as the atomic weight rises; it is found also that the interval in frequency between the double
