| a1, b1, c1 |
| a2, b2, c2 | = 0.
| a3, b3, c3 |
(See Determinant.)—Bibliography: Burnside and Panton, Theory of Equations; Salmon, Higher Algebra.
El´iot, George, the assumed literary name of Mary Ann, or, as she preferred to write the name in later years, Marian Evans, English novelist. She was the daughter of a Warwickshire land-agent and surveyor, was born at Griff, near Nuneaton, on 22nd Nov., 1820, and died on 22nd Dec., 1880. She received at Coventry an excellent education, comprising the classical and modern languages, and shortly after her twenty-first year became a convert to Rationalism. Her first literary undertaking was the completion of Mrs. Hennell's translation of Strauss's Life of Jesus (1846). Towards the end of her task she seems, however, to have wearied of it, and when the work appeared she declared herself 'Strauss-sick'. After spending two years abroad, she boarded at the house of John Chapman, editor of the Westminster Review, of which she became sub-editor. It was not, however, until January, 1857, that she came prominently into public notice, when the first of a series of tales entitled Scenes from Clerical Life appeared in Blackwood's Magazine. The series came to an end in Nov., 1857, and in the following year the publication of Adam Bede placed her in the first rank of writers of fiction. It was succeeded by The Mill on the Floss (1860), Silas Marner (1861), Romola (1863), Felix Holt (1866), Middlemarch (1872), and Daniel Deronda (1876). In addition to those prose works she published three volumes of poems, The Spanish Gypsy (1868), Agatha (1869), and The Legend of Jubal (1874). Her last work published during her life was the series of essays entitled The Impressions of Theophrastus Such (1879), but a volume of mixed essays was issued posthumously. For many years she was happily associated both in life and work with George Henry Lewes, though a legal union was impossible during the lifetime of Mrs. Lewes. In May, 1880, after Lewes's death, she married Mr. John Cross, but did not survive the marriage many months, dying rather suddenly at Chelsea.—Bibliography: Haton, George Eliot in Derbyshire; J. W. Cross (editor), George Eliot's Life as Related in Her Letters and Journals (3 vols.); O. Browning, Life of George Eliot; Deakin, The Early Life of George Eliot; Sir Leslie Stephen, George Eliot (in English Men of Letters Series).
Eliot, Sir John, one of the ablest of the popular leaders of Charles I's reign, of an old Cornwall family, born in 1592, died in 1632. He entered Parliament in 1614 as member for St. Germans, winning immediate reputation as an orator. As vice-admiral of Devon he was energetic in suppressing piracy. In the three Parliaments of 1623, 1625, 1626, he made his way to the front of the constitutional party, joined Hampden and the rest in refusing contributions to the forced loan, and took a prominent share in drawing up the Remonstrance and Petition of Right. He was imprisoned in the Tower in 1629, and died in confinement. During his imprisonment he wrote a work on constitutional monarchy entitled The Monarchie of Man. Among his other works are: An Apology for Socrates, and Negotium Posterorum (an account of the Parliament of 1625).
E´lis, a maritime state of ancient Greece in the west of the Peloponnesus, bordering on Achaia, Arcadia, and Messenia, and watered by the Rivers Alphēus and Penēus. Of its capital Elis (now Kaloskopi) there are few traces. Olympia, where the famous games were held, was near the Alpheus. Since 1899 Elis forms a nomarchy of Greece.
Eli´sha, a Hebrew prophet, the disciple and successor of Elijah. Many miracles of prediction and cure, and even of raising the dead, are ascribed to him, but his figure is less original and heroic than that of his master. He held the
office of prophet for fully sixty-five years, from the reign of Ahab to that of Joash (latter half of ninth century B.C.).
Elix´ir, a word of Arabic origin (al iksir, the philosopher's stone), applied by the alchemists to a number of solutions employed in attempting the transmutation of metals into gold, and also to a potion, the elixir vitæ, or elixir of life, supposed to confer immortality. It is still used for various popular remedies, for the most part composed of various aromatic and stimulative substances held in solution by alcohol.