The modern theory of dispersion, the foundation of which was laid by W. Sellmeier, is based upon the assumption that an interaction takes place between ether and matter. Sellmeier adopted the elastic-solid theory of the ether, and imagined the molecules to be attached to the ether surrounding them, but free to vibrate about their mean positions within a limited range. Thus the ether within the dispersive medium is loaded with molecules which are forced to perform oscillations of the same period as that of the transmitted wave. It can be shown mathematically that the velocity of propagation will be greatly increased if the frequency of the light-wave is slightly greater, and greatly diminished if it is slightly less than the natural frequency of the molecules; also that these effects become less and less marked as the difference in the two frequencies increases. This is exactly in accordance with the observed facts in the case of substances showing anomalous dispersion. Sellmeier’s theory did not take account of absorption, and cannot be applied to calculate the dispersion within a broad absorption band. H. von Helmholtz, working on a similar hypothesis, but with a frictional term introduced into his equations, obtained formulae which are applicable to cases of absorption. A modified form of Helmholtz’s equation, due to E. Ketteler and known as the Ketteler-Helmholtz formula, has been much used in calculating dispersion, and expresses the facts with remarkable accuracy. P. Drude has obtained a similar formula based on the electromagnetic theory, thus placing the theory of dispersion on a much more satisfactory basis. The fundamental assumption is that the medium contains positively and negatively charged ions or electrons which are acted on by the periodic electric forces which occur in wave propagation on Maxwell’s theory. The equations finally arrived at are
where λ is the wave-length in free ether of light whose refractive index is n, and λm the wave-length of light of the same period as the electron, κ is a coefficient of absorption, and D and g are constants. The sign of summation Σ is used in cases where there are several absorption bands, and consequently several similar terms on the right-hand side, each with a different value of λm. This would occur if there were several kinds of ions, each with its own natural period.
In a region where there is no absorption, we have κ = 0 and therefore g = 0, and we have only one equation, namely,
which is identical with Sellmeier’s result. As λm, is a wave-length corresponding to an absorption band, this formula can be used to find values of λm which satisfy the observed values of n within the region of transparency, and so to determine where the absorption bands are situated. In this way the existence of bands in the infrared part of the spectrum has been predicted in the case of quartz and detected by experiments on the selective reflection of the material.
References.—For the theory of dispersion see P. Drude, Theory of Optics (Eng. trans.); R. W. Wood, Physical Optics; and A. Schuster, Theory of Optics. For descriptive accounts, see Wood’s Physical Optics, T. Preston’s Theory of Light, E. Edser’s Light. The last work contains an elementary treatment of Sellmeier’s theory. (J. R. C.)
D’ISRAELI (or Disraeli), ISAAC (1766–1848), English man of letters, father of the earl of Beaconsfield (q.v.), was born at Enfield in May 1766. He belonged to a Jewish family which, having been driven by the Inquisition from Spain, towards the end of the 15th century, settled as merchants at Venice, and assumed the name which has become famous; it was generally spelt D’Israeli until the middle of the 19th century. In 1748 his father, Benjamin D’Israeli, then only about eighteen years of age, removed to England, where, before passing the prime of life, he amassed a competent fortune, and retired from business. He belonged to the London congregation of Spanish and Portuguese Jews, of which his son also remained a nominal member until after Benjamin D’Israeli died at the end of 1816.
The strongly marked characteristics which determined Isaac D’Israeli’s career were displayed to a singular degree even in his boyhood. He spent his time over books and in long day-dreams, and evinced the strongest distaste for business and all the more bustling pursuits of life. These idiosyncrasies met with no sympathy from either of his parents, whose ambitious plans for his future career they threatened to disappoint. When he was about fourteen, in the hope of changing the bent of his mind, his father sent him to live with his agent at Amsterdam, where he worked under a tutor for four or five years. Here he studied Bayle and Voltaire, and became an ardent disciple of Rousseau. Here also he wrote a long poem against commerce, which he produced as an exposition of his opinions when, on his return to England, his father announced his intention of placing him in a commercial house at Bordeaux. Against such a destiny D’Israeli’s mind strongly revolted; and he carried his poem, with a letter earnestly appealing for advice and assistance, to Samuel Johnson; but when he called again a week after to receive an answer, the packet was returned unopened—the great Doctor was on his death-bed. He also addressed a letter to Dr Vicesimus Knox, master of Tonbridge Grammar School, begging to be received into his family, that he might enjoy the benefit of his learning and experience. How this application was answered we do not know. The evident firmness of his resolve, however, was not without effect. His parents gave up their purpose for a time. He was sent to travel in France, and allowed to occupy himself as he wished; and he had the happiness of spending some months in Paris, in the society of literary men, and devoted to the literary pursuits in which he delighted.
In the beginning of 1788 he returned home, and in the next year he attacked Peter Pindar (John Wolcot) in The Gentleman’s Magazine in a poem in the manner of Pope, “On the Abuse of Satire.” The authorship of the poem was much debated, and it was attributed by some to William Hayley, upon whom it was actually avenged, with characteristic savageness, by its victim. It is greatly to Wolcot’s credit that, on learning his mistake, he sought the acquaintance of his young opponent, whose friend he remained to the end of his life. Through the success of this satire D’Israeli made the acquaintance of Henry James Pye, who helped to persuade his father that it would be a mistake to force him into a business career, and introduced him into literary circles. D’Israeli dedicated his first book, A Defence of Poetry, to Pye in 1790. Henceforth his life was passed in the way he best liked—in quiet and almost uninterrupted study. In 1802 he married Maria Basevi, by whom he had five children, of whom Benjamin (afterwards Lord Beaconsfield and Prime Minister of England) was the second. He was able to maintain his strenuous habits of study till he reached the advanced age of seventy-two, when he was forced, by paralysis of the optic nerve, to give up work almost entirely. He lived ten years longer, and died at his seat at Bradenham House, Buckinghamshire, on the 19th of January 1848.
Isaac D’Israeli is most celebrated as the author of the Curiosities of Literature (1791, subsequent volumes in 1793, 1817, 1823 and 1834). It is a miscellany of literary and historical anecdotes, of original critical remarks, and of interesting and curious information of all kinds, animated by genuine literary feeling, taste and enthusiasm. With the Curiosities of Literature may be classed D’Israeli’s Miscellanies, or Literary Recreations (1796), the Calamities of Authors (1812–1813), and the Quarrels of Authors (1814). Towards the close of his life D’Israeli projected a continuous history of English literature, three volumes of which appeared in 1841 under the title of the Amenities of Literature. But of all his works the most delightful is his Essay on the Literary Character (1795), which, like most of his writings, abounds in illustrative anecdotes. In the famous “Pope controversy” he supported Byron and Campbell against Bowles and Hazlitt by a defence of Pope in the form of a criticism of Joseph Spence’s Anecdotes contributed to the Quarterly Review (July 1820). In 1797 D’Israeli published three novels; one of these, Mejnoun and Leila, the Arabian Petrarch and Laura, was said to be the first oriental romance in English. His last novel, Despotism, or the Fall of the Jesuits, appeared in 1811, but none of his romances was popular. He also published a slight sketch of Jewish history, and especially of the growth of the Talmud, entitled the Genius of Judaism (1833).
He was the author of two historical works—a brief defence of the literary merit and personal and political character of James I. (1816), and a learned Commentary on the Life and Reign of King Charles I. (1828–1831). This was recognized by the University of Oxford, which conferred upon the author the honorary degree of D.C.L. As an historian D’Israeli is distinguished by two characteristics. In the first place, he had small interest in politics, and no sympathy with the passionate fervour, or adequate appreciation of the importance, of political struggles. And, secondly, with a laborious zeal then less common than now among
