lines of a series diminishes with the atomic weight, and is proportional to its square. These relations suggest that the atomic weight might here act in part after the manner of a load attached to a fundamental vibrating system, which might conceivably be formed on the same plan for all the metals of the group; such a load would depress all the periods, and at the same time it would split them up in the manner above described, if it introduced dissymmetry into the vibrator. The discovery of Zeeman that a magnetic field triples each spectral line, and produces definite polarizations of the three components, in many cases further subdividing each component into lines placed usually all at equal intervals of frequency, is explained, and was in part predicted, by Lorentz on the basis of the electron theory, which finds the origin of radiation in a system of unitary electric charges describing orbits or executing vibrations in the molecule. Although these facts form substantial sign-posts, it has not yet been found possible to assign any likely structure to a vibrating system which would lead to a frequency formula for its free periods of the types given above. Indeed, the view is open that the group of lines constituting a series form a harmonic analysis of a single fundamental vibration not itself harmonic. If that be so, the intensities and other properties of the lines of a series ought all to vary together; it has in fact been found by Preston, and more fully verified by Runge and others, that the lines are multiplied into the same number of constituents in a magnetic field, with intervals in frequency that are the same for all of them. When the series consists of double or triple lines the separate components of the same compound line are not affected similarly, which shows that they are differently constituted. The view has also found support that the different behaviours of the various groups of lines in a spectrum show that they belong to independent vibrators. The form of the vibration sent out from a molecule into the aether depends on the form of the aggregate hodograph of the electronic orbits, which is in keeping with Rayleigh's remark that the series-laws suggest the kinematic relations of revolving bodies rather than the vibrations of steady dynamical systems.
According to Rydberg, there is ground for the view that a natural group of chemical elements have all the same type of series spectrum, and that the various constants associated with this spectrum change rapidly in the same directions in passing from the elements of one group to the corresponding ones of the following groups, after the manner illustrated in graphical representations of Mendeléeff's law by means of a continuous wavy curve in which each group of elements lies along this same ascending or descending branch; the chemical elements thus being built up in a series of types or groups, so that the individuals in successive groups correspond one to one in a regular progression, which may be put in evidence by connecting them by transverse curves. Illustrations have been worked out mathematically by J. J. Thomson of the effect of adding successive outer rings of electrons to stable vibrating collocations.
The frequencies of the series of very close lines which constitute a single band in a banded spectrum are connected by a law of quite different type, namely, in the simpler cases n2= A-Bm2. It may be remarked that this is the kind of relation that would apply to a row of independent similar vibrators in which the neighbours exert slight mutual influence of elastic type. If ξ denote displacement and x distance along the row, the equation d2ξ+k2ξ=-gd2ξ would represent the general features of their vibration, the right-hand side arising from the mutual elastic influences. If the ends of the line of vibrators, of length l, are fixed, or if the vibrators form a ring, the appropriate type of solution is ξ∞sin μx sin pt, where; μl=mπ and m is integral; further - p2+k2=gμ2, hence p2=k2-gπ2m2, which is of the type above stated. Dynamical systems of this kind are illustrated by the Lagrangean linear system of connected bodies, such as, for example, a row of masses fixed along a tense cord, and each subject to a restoring elastic force of its own in addition to the tension of the cord. A single spectral line might thus be transformed into a band of this type, as the effect of disturbance arising from slight elastic connexions established in the molecule between a system of similar vibrators. But the series in line-spectra are of entirely different constitution; thus for the series expressed by the formula p2=p02-Bm-2 the corresponding period-equation might be expressed in some such form as sin k(p2-p02)-½=constant, which belongs to no type of vibrator hitherto analysed.
Authorities.—The experimental memoirs on the constitution of radiation are mostly in the Annalen der Physik; references are given by P. Drude, Lehrbuch der Optik, Leipzig, 1900; cf. also reports in the collection issued by the International Congress of Physics, Paris, 1900. See also Lord Rayleigh's Scientific Papers, in various connexions; and Larmor, in Brit. Assoc. Reports, 1900–1902, also the Bakerian Lecture, Roy. Soc. Proc., 1909, for a general discussion of molecular statistical theory in this connexion. Planck's Theorie der Wärmestrahlung, 1906, gives a discussion from his point of view; there is a summary by Wien in Ency. Math. Wiss. v. (3) pp. 282-357; also a lecture of H. A. Lorentz to the Math. Congress at Rome, 1908, and papers by J. H. Jeans, Phil. Mag., 1909, on the partition of energy. In spectrum analysis Kayser's extensive treatise is the standard authority. Winckelmann's Handbuch der Physik, vol. ii. (by Kayser, Drude, &c.), may also be consulted. (J, L *)
RADICAL (Lat. radix, a root), in English politics, a term applied to politicians who desire to make thorough, or radical, changes in the constitution and in the social order generally. Although it had been used in a somewhat similar way during the reign of Charles II., the term Radical, in its political sense, originated about the end of the 18th century, probably owing its existence to Charles James Fox, who, in 1797, declared that “ radical reform ” was necessary. The ideas of the first Radicals were borrowed largely from the authors of the French Revolution. The word was more generally employed during the disturbed period between the close of the Napoleonic wars and the passing of the great Reform Bill of 1832, and was applied to agitators like Henry Hunt and William Cobbett. After the Reform Bill had become law, the advocates of violent change were drawn into the Chartist movement, and the Radicals became less revolutionary both in speech and object. Thus in 1842 an observer writes:—“ The term Radical, once employed as a name of low reproach, has found its way into high places, and is gone forth as the title of a class who glory in their designation.” About this time many members of Parliament were known as Radicals, among these men being George Grote and Joseph Hume. The Radicals never formed a distinct party in the House of Commons, and subsequently they formed simply the advanced section of the Liberal party. For a few years in the 19th century the wearing of a white hat was looked upon as the distinguishing mark of a Radical, a hat of this colour having been worn by Hunt when addressing meetings.
See W. Harris, History of the Radical Party in Parliament (1885); S. Bamford, Passages in the Life of a Radical (new ed., 1893); C. B. Roylance Kent, The English Radicals: an Historical Sketch (1899).
RADIOACTIVITY. The subject of radioactivity deals with phenomena exhibited by a special class of bodies of high atomic weight of which uranium, thorium, radium and actinium are the best known examples. These substances possess the property of spontaneously emitting radiations of a special character which are able to penetrate through matter opaque to ordinary light. The beginning of this subject dates from 1896, and was an indirect consequence of the discovery of the X rays made a few months before by Röntgen. It was known that the production of X rays in a vacuum tube was accompanied by a strong phosphorescence of the glass, and it occurred to several investigators that ordinary substances made phosphorescent by visible light might emit a penetrating radiation similar to X rays. Following out this idea, H. Becquerel (1), a distinguished French physicist, exposed amongst other substances a phosphorescent compound of uranium, uranium-
- These numbers refer to papers noted under References (below).