No sooner had peace been concluded than there broke out the so-called African or Libyan War. It was a most formidable mutiny or insurrection. Hamilcar’s mercenaries on their return looked for the pay which he had promised them, but had not been able to furnish while he was cooped in within his lines on Mount Eryx. The stupidity of the home Government soon caused trouble. The peace party at Carthage, headed by Hanno, who hated Hamilcar, was foolish enough to raise a dispute about the pay of the troops. The result wa3 a furious mutiny, which Hanno, who was sent to quiet them, could not appease. The men to the number of 20,000 began to march on Carthage itself, and encamped near Tunis. The mutineers were led by Spendiαs, a fugitive slave from Campania, and by Matho, an African who had served with distinction under Hamilcar in Sicily. These two men incited all the neighbouring tribes to rise against the dominion of Carthage. Carthage itself was soon cut off from all communication with the interior. Hanno was called to take the command, but it was only to meet with defeat and disaster. The rebels surprised and captured his camp. The Government was now thoroughly frightened, and begged Hamilcar to save them from the consequences of their own folly. With a force of only 10,000 men he had to face what must now have grown into a very formidable host. It would seem that his personal influence led many of the rebels to return to his standard, and he was also skilful enough to secure the friendship and aid of the Numidian sheiks. One especially, Naravas, helped him very materially; and with his assistance he was able to achieve a decisive victory over the mutineers. At last he so effectually hemmed in Spendius within his camp near Tunis that the rebel leader was obliged to throw himself on his mercy. With nine of his brother leaders he sought an interview with Hamilcar. Hamilcar’s demand was the surrender of ten of the rebels, whom he was to name himself. This being agreed, he seized Spendιus and his nine companions, a proceeding which the mutineers furiously resented. But they were soon surrounded and cut off to a man, to the number, it is said, of 40,000. The war, which had lasted three years and four months, was now over in the year 238 B.c.

One would have supposed that Hamilcar would be at once recognized as the right man to direct the future policy of the state. But it was not so. Hanno’s party, the peace party, was as shortsighted as ever, and actually dared to say that Hamilcar had been the cause of the late war by having made promises which he was not able to fulfil. But by this folly they injured and weake.∖ed themselves. The patriotic party, the “Barcine faction,” as it was called by its opponents, prevailed so far as to raise their leader to a position answering as nearly as possible to a dictatorship among the Romans. Hamilcar was made commander-inchief of the Carthaginian army in Africa, and invested with a power which could be taken from him only by the popular assembly. He was still a young man, under thirty years of age. For a short time he employed himself in overawing the Numidian tribes bordering on Carthaginian territory, but his main object was to form the nucleus of an efficient army out of his Libyan mercenaries. Meanwhile he was maturing a great plan which soon afterwards on his own responsibility he carried into execution, Spain was a country the coasts of which at least were well known to the Carthaginians. Spaniards too had served among Hamilcar’s troops. To Spain he decided to go; there, he felt sure, he could find material for an army and abundant means of providing pay. He had now three sons, the “lion’s brood,” as he called them, Hannibal, Hasdrubal, Mago. Wishing with all his heart that they should be like minded with himself, he made the eldest, Hannibal, then a little boy of nine, swear on the altar of the supreme Carthaginian deity eternal hatred and enmity to Rome. This was just before he left Carthage, probably in the spring of 236 b.c. Suddenly there came tidings to the home Government that their commander-in-chief was, without their orders, carrying on war in Spain. He had, however, done his work so thoroughly in Africa that the troublesome Numidian tribes were now submissive to Carthage, and for the most part paid tribute. He never returned. The last eight years of his life he devoted to the great work of reducing Spain to a Carthaginian province. He penetrated into the interior of the country, subduing some of the tribes by force of arms and drawing others into friendly relations by negotiation. It was not to mere conquest that he aspired; he did his best to win the good-will of the Spaniards and to attach them to Carthage. Spain was to be a compensation to Carthage for the loss of Sicily and Sardinia. But, above all, its possession was to be subordinate to Hamilcar’s great design of some day renewing the war with Rome. For this he would have felt himself prepared when, in addition to his Numidian cavalry, he had organized a force of Spanish infantry. Had his life been prolonged, he would doubtless, as Livy says (xxi. 2), have invaded Italy at the head of a Carthaginian army. What he accomplished in Spain so much impressed the elder Cato, who less than half a century afterwards saw the traces of his work, that he declared that there was no king like Hamilcar Barca. In the prime of his years he fell in battle in 228 b.c., fighting, it would seem, somewhere between the Tagus and the Douro. Spain was now left in the hands of his son-in-law Hasdrubal. (w. j. b.)

Immediately east of the town is Hamilton palace, the seat of the duke of Hamilton and Brandon, premier peer of Scotland. The present palace was commenced in 1822. Its front is a specimen of the enriched Corinthian architecture, with a projecting pillared portico after the style of the temple of Jupiter Stator at Rome, 264 feet in length and 60 feet in height. The interior is richly decorated and contains one of the most valuable collections of paintings in Scotland. Within the grounds, which comprise nearly 1500 acres, is the mausoleum erected by the tenth duke, a structure resembling in general design that of the emperor Hadrian at Rome, being a circular building springing from a square basement, and enclosing a decorated octagonal chapel. About 2 miles south-east of Hamilton, on the summit of a precipitous rock 200 feet in height, the foot of which is washed by the Avon, stand the ruins of Cadzow Castle, the original seat of the Hamilton family, conferred on the chief of that family immediately after the battle of Bannockburn, having been previously a royal residence for at least two centuries. The castle has been made the subject of a spirited ballad by Sir Walter Scott. Near it is the noble chase with its ancient oaks, the remains of the Caledonian Forest, where are still preserved some of the old Scotch breed of wild cattle. Opposite Cadzow Castle on the other side of the Avon is Chatelherault, consisting of stables and offices, and imitating in outline the palace of that name in France. A magnificent double avenue stretches between it and Hamilton palace.

HAMILTON, a city of Canada, the chief town in the county of Wentworth, province of Ontario, is advantageously situated on the south side of Burlington Bay, a large and beautiful basin of water connected with Lake Ontario by a short canal, which forms one of the safest and most commodious harbours on the lake. It is also connected with the town of Dundas by the Desjardins Canal, about 4 miles in length. Hamilton holds an important position at the head of the navigation on Lake Ontario, and in the centre of one of the finest agricultural districts of the Dominion. It is the headquarters of the Great Western Railroad, and is connected by other lines of railway with Lake Erie, Lake Huron, and the Georgian Bay. The site on which it is built rises gradually from the bay to the foot of a lofty bluff called “The Mountain,” the summit of which commands an extensive and beautiful view. The streets are well laid out, and planted with shade trees, and the houses and public buildings are substantially constructed of stone and brick. The court-house and county buildings, recently completed, are the finest in Canada. Among the other public buildings are the provincial lunatic asylum, the Anglican and Roman Catholic cathedrals, and handsome places of worship of other denominations, the collegiate institute, the Wesleyan female college, the mechanics’ institute, the banks, the city hospital, and other charitable institutions. The city water-works, by means of which a constant supply of pure water is brought from Lake Ontario, have been completed on a scale amply providing for the future growth of the city, at a cost of about $1,000,000. The industries, include iron rolling mills, iron foundries, the manufacture of agricultural implements, sewing machines, musical instruments, carriages, glass, pottery, <kc., tobacco manufacture, and brushmaking. The total value of imports at the port of Hamilton for the fiscal year 1878-9 was $3,992,123; and the duty collected amounted to $839,153. The total tonnage entered at the port was 160,666 tons; but this is exclusive of a much larger amount of goodä brought by railway, including foreign importations, on which the duty has already been paid at Quebec or Montreal, and of which therefore no entry is made. Daily lines of steamers run in the summer months between Hamilton, Toronto, Kingston,, and Montreal; and an extensive trade is carried on with the maritime provinces. Hamilton was founded in 1813,. and incorporated in 1833. The population in 1836 was 2846; in 1851, 10,248; in 1861,19,096; in 1871, 26,716; and in 1879 it is estimated at 35,000. It is the seat of the Anglican bishop of Niagara, and of a Roman Catholic bishop. It returns one member to the provincial parliament of Ontario, and two members to the Dominion parliament, or House of Commons.

HAMILTON, a township and post village of Madison county, New York, U.S., is situated on the Chenango canal, and on the Utica branch of the New York and Oswego Midland Railway, 30 miles S.W. of Utica. The village is the seat of Madison university, chartered in 1846, in connexion with which there are a theological seminary of the Baptist denomination opened in 1820, and a preparatory academy opened in 1832 under the name of Colgate Academy, and chartered in 1853 as the grammar school of the university. The university has 10 professors, has both a scientific and a classical course, and is attended by upwards of 100 students. The other educational institutions are a female seminary and a union graded school. The village possesses a foundry, a tannery, and manufactories of sashes and blinds, doors, waggons, cigars, and cheese. The population of the village in 1870 was 1529, and of the township 3687.

HAMILTON, a city of the United States, capital of Butler county, Ohio, is situated on both sides of the Great Miami river, on the Miami and Erie canal, and at the junction of several railways, 23 miles N. of Cincinnati. The water-power for manufacturing purposes is obtained by an hydraulic canal which secures a fall of 30 feet; and the situation of the city in the heart of the Miami valley, a rich agricultural district, is very favourable to the development of commercial enterprise. It possesses two public parks, twelve churches, two national banks, a complete graded system of public schools, an orphans’ home, and a free library. Its industries are of a varied kind, and are represented by paper and woollen factories, flourmills, foundries, breweries, distilleries, bleaching works, machine shops, and manufactories of carriages and waggons, reaping machines, ploughs, and other agricultural implements, sashes and blinds, railroad supplies, and machinery. Hamilton received a municipal charter in 1853, at which time the portion on the west side of the river formerly called Rossville was incorporated with it. The population, which in 1860 was 7223, and in 1870 11,081, of whom 3062 were foreigners, was estimatedin 1879 at 17,000.

HAMILTON, the principal town in the western district of Victoria, Australia, is situated on the Grange Burne Creek, in 37° 45' S. lat. and 142° 1' E. long. It was proclaimed a borough in 1859, the area of the municipality being 5280 acres. It has several elegant buildings—a hospital and benevoleut asylum, a town-hall, a treasury and land office, and a public library. Its educational institutions include the Hamilton and western district college, the academy, and the Alexandra college for ladies, besides a state school with accommodation for 500 pupils. It possesses a fine race-course covering 120 acres, and pastoral and agricultural exhibitions are held annually, the surrounding district being chiefly devoted to sheepfarming. The population of the town and suburbs on the 1st January 1879 was estimated at 4400. The railway from Melbourne to Portland passes through the town.

HAMILTON, Anthony or Antoine (1646-1720), a French classical author, who is especially noteworthy from the fact that, though by birth he was a foreigner, his literary characteristics are more decidedly French than those of many of the most indubitable Frenchmen. His father was George Hamilton, younger brother of James, second earl of Abercorn and head of the family of Hamilton in the peerage of Scotland, and sixth duke of Châtellerault in the peerage of France; and his mother was Mary Butler, sister of the duke of Ormonde. He was born in 1646, but the place of his birth has not been ascertained. According to some authorities it was Drogheda, but according to the London edition of his works in 1811 it was Roscrea in Tipperary county. From the age of four till he was fourteen the boy was brought up in France, whither his family had removed after the execution of Charles I. The fact that, like his father, he was a Roman Catholic, prevented his receiving the political promotion he might otherwise have expected on the Restoration, but he became a distinguished member of that brilliant band of courtiers whose most fitting portraiture was destined to be the product of his pen. His connexion with France was always maintained, and the marriaere of his sister to the Comte de Gramont rendered it more intimate if possible than before. On the accession of James he found his religious disabilities transformed into advantages. He obtained an infantry regiment in Ireland, and was appointed governor of Limerick. But the battle of the Boyne, at which he was present, brought disaster on all who were attached to the cause of the Stewarts, and before long he was again in France—an exile, but at home. The rest of his life was spent for the most part in the châteaux of his friends. With the duchess Ludovise of Maine he became an especial favourite, and it was at her seat at Sceaux that he wrote the Mémoires that made him famous. The ill-advised expedition of 1708 was the last political enterprise in which he shared, and he died at St Germain-en-Laye, August 6, 1720.

It is mainly, as has already been indicated, by the Mémoires du Comte de Grammont that Hamilton takes rank with the most classical writers of France. The work was first published anonymously in 1713 under the rubric of Cologne, but it was really printed in Holland, at that ti'-Je the great patroness of all questionable authors. An English translation by Boyer appeared in 1714. Upwards of thirty editions have since appeared, the best of the French being Renouard’s (1812) and Gustave Brunet’s (1859), and the best of the English Edward’s (1793), with 78 engravings, and Malleville’s (1811), with 64 portraits by Scriven and others. The original edition was reprinted by Pifteau in 1876. In imitation and satiric parody of the romantic tales which Galland’s translation of The Thousand and One NightshaA brought into favour in France, Hamilton wrote Le Bélin, Fleur d Épine, Zénéyde, and Les Quatre Facardins, which are characterized by the graceful ease of their style and the successful extravagance of their incidents. The first three tales appeared at Paris in 1730, ten years after the death of the author, and a collection of his Oeuvres Diverses in 1731 contained the unfinished “Zénéyde.” A collected edition of Hamilton’s works was published in six volumes in 1749, and was reprinted in 1762, 1770, 1776, and 1777. A translation of Pope’s Essay on Criticism, which procured the author a complimentary acknowledgment from the poet, is still in MSS., with the exception of a fragment printed in the 1812 edition of the works. In the name of his niece, the countess of Stafford, Hamilton maintained a witty correspondence with Lady Mary Wortley Montagu. See Notices of Hamilton in the 1862 edition of his works, and in Lescure’s edition of the Contes, Sainte-Beuve’s Causeries du Lundi (tom. i.), and Sayou’s Histoire de la littérature française à V étranger, 1853.

HAMILTON, Elizabeth (1758-1816), novelist and miscellaneous writer, was born at Belfast, of Scotch extraction, 25th July 1758. Her father’s death in 1759 left his wife so embarrassed that Elizabeth was adopted in 1762 by her paternal aunt, Mrs Marshall, who lived in Scotland, near Stirling. There Elizabeth spent her youth and received a good education,—at first at school, afterwards in private, and latterly for some months under masters at Edinburgh and Glasgow. In her 15th year she made a tour in the Highlands with some friends, and wrote a journal of it for her aunt’s perusal, which was inserted, unknown to the authoress, in a provincial magazine. In 1780 Mrs Marshall died, and Miss Hamilton was prevented by household cares from using her pen; but in 1785 she made her first voluntary contribution to the press in the shape of a letter to the Lounger, of which paper it forms the 46th number. On the death of Mr Marshall in 1788, Miss Hamilton lived for a time with her brother, Captain Charles Hamilton, who was engaged on his translation of the Hedaya. Prompted by her brother’s associations, she produced her Letters of a Hindoo Liajah in 1796, and soon after, with her sister Mrs Blake, settled at Bath, where she published in 1800 the Memoirs of Modern Philosophers, a kind of satire on the admirers of the French Revolution. In 1801-2 the Letters on Education appeared, her most valuable though not her most popular work. After travelling though Wales and Scotland for nearly two years, the sisters took up their abode in 1803 at Edinburgh. In 1804 Mrs Hamilton, as she then preferred to be called, published her Life of Agrippina, wife of Germanicus ; and in the same year she received a pension from Government. About this time she consented to take charge for six months of a widowed Scotch nobleman’s family; and to his eldest daughter were addressed Letters on the Moral and Religious Principle, published in 1800. Her next publication of importance, The Cottagers of Glenburnie, appeared in 1808. This work, to which the authoress owes most of her fame, is an admirable description of the failings of the Scotch peasantry in their home life, and, while graphic and telling, is “saved from caricature and absurdity.” Sir Walter Scott describes it as “a picture of the rural habits of Scotland, of striking and impressive fidelity;” and Lord Jeffrey reviewed it very favourably in the Edinburgh Review (vol. xii.). Her subsequent works were a supplement to her Letters on Education, under the name of Popular Essays on the Elementary Principles of the Human Mind (1812), and Hints addressed to the Patrons and Directors of Public Schools (1815). She died at Harrogate, July 23, 1816.

Memoirs of Mrs Elizabeth Hamilton, by Miss Benger, were published in 1818. A notice of her literary life and labours, attributed to Miss Edgeworth, appeared in the Monthly Magazine for September 1816.

HAMILTON, James (1769-1831), the author of the Hamiltonian system of teaching languages, was born in 1769 and died October 31, 1831. The first part of his life was spent in mercantile pursuits. Having settled in Hamburg and become free of the city, he was anxious to become acquainted with German and accepted the tuition of a French émigré, General D’Angelis. In twelve lessons he found himself able to read an easy German book, his master having discarded the use of a grammar and translated to him short stories word for word into French. As a citizen of Hamburg Hamilton started a business in Paris, and during the peace of Amiens maintained a lucrative trade with England; but at the rupture of the treaty he was mιde a prisoner of war, and though the protection of Hamburg was enough to get the words efface de la liste des prisonniers de guerre inscribed upon his passport, he was detained in custody till the close of hostilities. His business being thus ruined, he went in 1814 to America, intending to become a farmer and manufacturer of potash; but, changing his plan before he reached his “location,” he started as a teacher in New York. Adopting his old tutor’s method, he attained remarkable success in New York, Baltimore, Washington, Boston, Montreal, and Quebec. Returning to England in July 1823, he was equally fortunate in Manchester and elsewhere. His system attracted general attention, and was vigorously attacked and defended. In 1826 Sydney Smith devoted an article to its elucidation in the Edinburgh Review :—“We are strongly persuaded,” he said, “that, the time being given, this system will make better scholars, and, the degree of scholarship being given, a much shorter time will be needed” than in the ordinary system. As text-books for his pupils Hamilton printed interlinear tr anslations of the Gospel of John, of an Epitome historiae sacrae, of Aesop’s Fables, Eutropius, Aurelius Victor, Phaedrus, &c., and many books were issued as Hamiltonian with which he had nothing personally to do. The two master principles of his method, which has left its traces on our modern linguistic discipline, are that the language is to be presented to the scholar as a living organism, and that its laws are to be learned from observation and not by rules.

See Hamilton’s own account— The Principles, Practice, and Results of the Hamiltonian System for the last Twelve Years, Manchester, 1829; Alberte, Ueber die Hamilton’ sehe Methode ; C. F. Wurm, Hamilton und Jacotot, 1831.

HAMILTON, Patrick (1504-1528), son of Sir Patrick Hamilton, well known in Scottish chivalry, and of Catherine Stewart, daughter of Alexander duke of Albany, second son of James II. of Scotland, was born in the diocese of Glasgow, probably at his father’s estate of Stonehouse in Lanarkshire. Of his early boyhood and education nothing is known. In 1517 he was appointed titular abbot of Ferne, Ross-shire; and it was probably about the same year that he went to study at Paris, for his name is found in an ancient list of those who graduated there in 1520. It was doubtless during this period that he received the germs of the doctrines he was afterwards so nobly to uphold. From Ales we learn that Hamilton subsequently went to Louvain, attracted probably by the fame of Erasmus, who in 1521 had his headquarters there. Returning to Scotland, the young scholar naturally selected St Andrews, the capital of the church and of learning, as his residence. On the 9th June 1523 he became a member of the university of St Andrews, and on the 3d October 1524 he was admitted to its faculty of arts. There Hamilton attained such influence that he was permitted to conduct in the cathedral a musical mass of his own composition. But the Reformed doctrines had now obtained a firm hold on the young abbot, and he was eager to communicate them to his fellow-countrymen. Early in 1527 the archbishop Beatoun’s attention was directed to the heretical preaching of the young priest, whereupon he ordered that Hamilton should be formally summoned and accused. Hamilton fled to Germany, first visiting Luther at Wittenberg, and afterwards enrolling himself as a student, under Francis Lambert of Avignon, in the new university of Marburg, opened May 30, 1527, by Philip, landgrave of Hesse. Frith and Tyndale were among those whom he met there. Late in the autumn of 1527 Hamilton returned to Scotland, bold in the truth of his principles. He went first to his brother’s house at Kincavel, near Linlithgow, in which town he preached frequently, and soon afterwards he married a young lady of noble rank, whose name has not come down to us. Beatoun, avoiding open violence through fear of Hamilton’s high connexions, invited him to a conference at St Andrews. The reformer resolutely accepted the invitation, and for nearly a month was permitted to preach freely. At length, however, he was summoned before a council of bishops and clergy presided over by the archbishop; and though he clearly and calmly answered all the written charges brought against him, his replies gave ground for new accusations of heresy. The council eagerly convicted him, and handed him over to the secular power. The sentence was carried out on the same day (February 29, 1528) lest he should be rescued by his friends, and he was burned at the stake as a heretic. His courageous bearing attracted more attention than ever to the doctrines for which he suffered, and greatly helped to spread the Reformation in Scotland.

Hamilton left a short treatise showing the antithesis between the law and the gospel. Frith’s translation of it, under the name of “Patrick’s Places,” is to be found in Foxe’s Acts and Monuments. Patrick Hamilton, the first Preacher and Martyr of the Scottish Reformation, by the Rev. Peter Lorimer, was published at Edinburgh in 1857.

HAMILTON, Robert (1743-1829), an able writer on political economy and finance, was born at Pilrig, Edinburgh, on the 11th June 1743. He was of good family, his grandfather, William Hamilton, professor of divinity and afterwards principal of Edinburgh University, having been a cadet of the family of Preston. He received an excellent education, and specially distinguished himself in the classes of mathematics at the university of Edinburgh, then under Professor Matthew Stewart. Although desirous of following a literary life, he was induced to enter the banking-house of Messrs Hogg in order to acquire a prae-tical knowledge of business. In 1766 lie was disappointed in his effort to obtain the mathematical chair at Aberdeen university, but three years later he gave up business pursuits and accepted the rectorship of Perth academy. In 1779 he was presented to the chair of natural philosophy at Aberdeen university. For many years, however, by private arrangement with his colleague Professor Copland, Hamilton taught the class of mathematics. In 1817 he was presented to the latter chair. For some years before his death in July 1829 he had retired from the active business of his chair, and quitted his privacy only at rare intervals to take part in important affairs concerning the college.

Hamilton’s most important work is the Essay on the National Debt, which appeared in 1813 and was undoubtedly the first to expose the economic fallacies involved in Pitt’s policy of a sinking fund. It is still of value. A posthumous volume published in 1830, The Progress of Society, is also of great ability, and is a veιy effective treatment of economical principles by tracing their natural origin and position in the development of social life. Some minor works of a practical character {Introduction to Merchandize, 1778; Essay on JVar and Peace, 1790) are now forgotten.

HAMILTON, Thomas (1789-1842), the author of Cyril Thornton, was the younger brother of Professor Sir William Hamilton, Bart., and was born in 1789. In his early years he acquired a thorough mastery of the classics, and notwithstanding that he entered the artillery and was engaged in active service throughout the Peninsular and American campaigns, he continued to cultivate his literary tastes. On the conclusion of peace he withdrew, with the rank of captain, from active professional duties, and amused his leisure hours with the congenial pastime of literature. He was a frequent contributor to Blackwood’s Magazine from its commencement, his papers manifesting great variety and versatility of talent, and embracing both prose and poetry. The most important and popular of his contributions to that periodical was the military novel Cyril Thornton, whose deficiency of plot is sufficiently compensated for by the interest of its details, its vivacity of movement, its truthful and clever delineation of character, and its easy, fresh, and graceful style. His Annals of the Peninsular Campaign, published originally in 1829, and republished in 1849 with additions by Frederick Hardman, though too condensed to leave room for graphic description, is written with great clearness and impartiality. His only other work, Men and Manners in America, published originally in 1832, is the result of much careful observation, and its criticisms, though frank and outspoken, and somewhat coloured by British prejudice, are always expressed with courtesy and good taste. He died at Pisa, December 7, 1842.

HAMILTON, Sir William, Bart. (1788-1856), one of the most eminent of Scottish metaphysicians, was born in Glasgow, on the 8th March 1788. His father, Dr William Hamilton, had in 1781, on the strong recommendation of the celebrated William Hunter, been appointed to succeed his father, Dr Thomas Hamilton, as professor of anatomy in the university of Glasgow; and when he died in 1790, in his thirty-second year, he had already gained a reputation that caused his early death to be widely and deeply regretted. William Hamilton and a younger brother (afterwards Captain Thomas Hamilton, noticed above) were thus brought up under the sole care of their mother,—a woman, fortunately, of considerable ability and force of character. William received his early education in Scotland, except during two years which he spent in a private school near London, and went in 1807, as a Snell exhibitioner, to Balliol College, Oxford. There he pursued his studies zealously, though for the most part independently,— devoting himself chiefly to Aristotle, but in other directions also laying the foundations of that wide and profound scholarship with which his name is associated. In November 1810 he took the degree of B.A. with first-class honours, after an examination so much above the usual standard in the number and difficulty of the works which it embraced that the memory of it was long preserved at Oxford. He had been intended for the medical profession, but, soon after leaving Oxford, gave up this idea, and in 1813 became a member of the Scottish bar. Henceforward Edinburgh was his place of residence, and, except on occasion of two short visits to Germany in 1817 and 1821, he never again quitted Scotland. Neither his ambition nor his success was such as to absorb his time in professional pursuits. His life was mainly that of a student; and the following years, marked by little of outward incident, w ere filled by researches of all kinds, through which he daily added to his stores of learning, while at the same time he was gradually forming his philosophic system. The outward and visible traces of these researches remain in his common-place books, especially in one which, having been in constant use, is a valuable record of his studies from this time onwards to the close of his life. He did not withdraw himself from society, but his favourite companions were the books of his own and of every library within his reach. Among these he lived in a sort of seclusion, from which only now and then, when stirred by some event of the world around, did he come forth, in vigorous pamphlets, to denounce, or protest, or remonstrate, as the case might be.

His own investigations enabled him to make good his claim to represent the ancient family of Hamilton of Preston, and in 1816 he took up the baronetcy, which had lain dormant since the death (in 1701) of Sir Robert Hamilton, well known in his day as a Covenanting leader.

In 1820 he was an unsuccessful candidate for the chair of moral philosophy in the university of Edinburgh. Soon afterwards he was appointed professor of civil history, and as such delivered several courses of lectures on the history of modern Europe and the history of literature. In 1829 his career of authorship began with the appearance of the well-known essay on the Philosojohy of the Unconditioned,— the first of a series of articles contributed by him to the Edinburgh Review. He was elected in 1836 to the Edinburgh chair of logic and metaphysics, and from this time dates the influence which, during the next twenty years, he exerted over the thought of the younger generation in Scotland. Much about the same time he began the preparation of an annotated edition of Reid’s works, intending to annex to it a number of dissertations. Before, however, this design had been carried out, he was struck with paralysis of the right side, which seriously crippled his bodily powers, though it left his mind wholly unimpaired. The edition of Reid appeared in 1846, but with only seven of the intended dissertations,—the last, too, unfinished. It was Sir William’s distinct purpose to complete the work, but this purpose remained at his death unfulfilled, and all that could be done afterwards was to print such materials for the remainder, or such notes on the subjects to be discussed, as were found among his MSS. Considerably before this time he had formed his theory of logic, the leading principles of which were indicated in the prospectus of “an essay on a new analytic of logical forms” prefixed to his edition of Reid. But the elaboration of the scheme in its details and applications continued during the next few years to occupy much of his leisure. Out of this arose in 1847 a sharp controversy with the late Professor De Morgan of University College, London. The essay did not appear, but the results of the labour gone through are contained in the valuable appendices to his Lectures on Logie. Another occupation of these years was the preparation of extensive materials for a publication which he designed on the personal history, influence, and opinions of Luther. Here he advanced so far as to have planned and partly carried out the arrangement of the work; but it did not go farther, and still remains in MS. In 1852-53 appeared the first and second editions of his Discussions in Philosophy, Literature, and Education, a reprint, with large additions, of his contributions to the Edinburgh Review. Soon after, his general health began to fail. Still, however, aided now as ever by his courageous and devoted wife—(he had married in 1829)—he persevered in literary labour; and during 1854-55 he brought out nine volumes of a new edition of Stewart’s works. The only remaining volume was to have contained a memoir of Mr Stewart from his pen; but this he did not live to write. He taught his class for the last time in the winter of 1855-56. Shortly after the close of the session he was taken ill, and-on the 6th May 1856 he died at his house in Edinburgh.

Sir W. Hamilton’s philosophy is presented in writings either more or lese fragmentary in form and occasional in purpose, or else, in whole or in part, prepared for publication by others, not by himself. Hence, not only do some points receive what seems almost a superfluity of attention, while others of equal importance are treated with barely enough of detail, but there is no complete statement of the latest results of his thinking in their mutual relation®. It may be that this imperfection of the outward form has tended to obscure the real harmony of his system, and in part led to its being pronounced —as it has too often been—an assemblage of contradictory doctrines. How far this is from being the case, and how closely the various parts are connected, becomes apparent when it is seen how they are all developed from the central conception of consciousness. In the following sketch that conception will be used as a point from which briefly to view the system as a whole, and to trace the bearing on one another of its leading doctrines.

Consciousness is regarded by Hamilton under three chief aspects: — (1) as it is in itself; (2) as realized under actual conditions; (3) as a source of truth.

1. Consciousness in itself is to Hamilton but another name for immediate or intuitive knowledge. For such knowledge is a relation between a subject (knowing) and an object (known), which, as it is viewed from the side of the one or the other term, is properly called consciousness or knowledge: there are two aspects, but the thing itself is one. Immediate knowledge or consciousness involves the existence of both subject and object,—it is the affirmation by the subject implicitly of its own existence, explicitly of that of the object. In this relation as realized in the primary judgment, that which knows is conceived as the ego or self,—that which is known, either as a mole of the ego or self, or as a mode of the non-ego or not-self. Thus we have, in the terms of the relation, a division of cvisteηοe into the noumenon self and the contrasted phenomena of mind ani of matter; while the relation itself yields a division of knowledge into philosophy, corresponding to its subjective, and science, corresponding to its objective, phase,—the latter being further subdivided into the sciences of mental and those of material phenomena.

2. Hamilton adopted the division of mental phenomena (not as states but as elements) into the three groups or classes of cognition, feeling, and conation. Cognitions he classified according to the different relations between subject and object, calling these relations,— as subjective, powers or faculties,—as objective, forms or stages, of knowledge. Under these, cognition is either immediate or mediate, i.e., either consciousness itself or the datum of consciousness. The first of the faculties, therefore, is of immediate knowledge,—the acquisitive or presentative power, which yields perception (external and internal). The second is of that form of mediate knowledge which is representative of an individual object. Here Hamilton distinguished three moments or phases, which he termed the retentive, the reproductive, and the representative powers,—distinguished them perhaps too widely, but at the same time indicated their essential unity. The third is of that form of mediate knowledge in which a number of objects receive a factitious unity from being thought under a common relation. This he named the elaborative or discursive faculty. Here, where he had to deal with consciousness in the form of experience, realized under actual conditions and comprehending every variety of mental life, Hamilton showed, in the first place, how the mutual action and reaction of the several elements produces the complexity which the phenomena present. Reminiscence, imagination, and judgment are all, as acts of which we are conscious, and which imply a prior immediate knowledge, contained in self-perception. But, on the other hand, our knowledge or perception even of self could not be what it is, did processes of reminiscence, imagination, and judgment not enter into its composition. Consciousness includes all the particular forms of knowledge; yet its development into a whole is the effect of the agencies which make up its content. In the next place, he showed the laws of mental action in the conditions under which consciousness is exercised. From the variety and the limitation of consciousness, under the relation of time, arises the successive variation of its units,—in other words, the train of thought. By the limitation of consciousness is meant the limited number of objects to which it can at one time be directed, but this issues in a farther limitation, consisting in the disproportion between consciousness and the whole sum of mental modifications. Sir W. Hamilton held that consciousness is the mental modes or ‘ ‘ movements, rising above a certain degree of intensity,” and that “the movements beyond the conscious range are still properties—and effective properties —of the mental ego.” This doctrine he used to explain not only the phenomena of ordinarily latent knowledge and of forgetfulness but also those of the abnormal recovery of apparently lost knowledge and of the formation of habits and dexterities. The units (or rather groups of units) of the train—partly former thoughts again present, partly thoughts for the first time present to the mind—follow one another according to what Hamilton called the law of integration, i.e., “only as they stand together as relativo parts of the same common whole.” Of this supreme law subordinate phases determine more special consecutions of thought. The reappearance of former thoughts (reminiscence voluntary or involuntary) is governed by the laws of (1) redintegration and (2) repetition. “Thoughts tend to suggest one another which are coidentical (1) in time or (2) in mode.” New wholes of thought are framed by successive analyses and syntheses. Under the law of integration these analyses are effected by means of attention and abstraction, i.e., by consciousness being continuously and repeatedly concentrated on certain parts or aspects of objects and withdrawn from others. The syntheses of thought are infinitely diverse in character, yet possess in common an invariable form. This process of forming new wholes, by discrimination and comparison, out of the materials supplied by perception and recollection, is the one kind of mental activity recognized by Hamilton in the various products of thought, from the simplest to the most complex. In other words, he regards judgment as the fundamental act of mind, the proposition, or expressed judgment, as its primary product.

3. Hamilton’s theory of consciousness in its third aspect, i.e., as a source of principles, is embodied in his doctrines of the conditioned and of common sense. The former is so called because it professes to be a demonstration that “the conditionally limited (what we may briefly call the conditioned) is the only possible object of knowledge and of positive thought.” The name of the latter was adopted by Hamilton, not as in itself a good one, but as sanctioned by the usage of philosophers in general and of Scottish philosophers in particular. The doctrine itself is that the primary data of consciousness are, as such, i.β,, as facts, and solely on the authority of consciousness, to be accepted as true. The two doctrines are complements of each other, as severally explications of the principle of the relativity of human knowledge, which, common to both, is manifested in the one through that which we cannot know,—in the other through the inexplicable character of our fundamental cognitions.

The primary data of consciousness Hamilton held to be of two orders, otherwise diverse, but in this the same, that they are known merely as facts. These are—(1) truths of perception—theconviction of the reality asmodes of self of our own thoughts and feelings, and the allied conviction that in sense-perception we come into contact with a reality external to the mind'; and (2) truths of reason—the fundamental laws of logic, the necessary forms of thought or relations of existence C.e., quality, and quantity in its threefold aspect as time, space, degree), the causal judgment, the principle of substance and phenomenon, &c.

Now here it was Hamilton’s peculiar contribution to philosophy that he placed,the data of perception along with the data of thought, and affirmed that both classes alike are inexplicable, yet as facts clear; that both rest on the same authority; and that, if the one be accepted as true, so also should be the other. He was a realist, because he held realism to be the dictate of consciousness. Evidently here the ground of the view is of even more importance than the view itself, and so to Hamilton the question of realism versus idealism was momentous chiefly from its connexion with that of the authority of consciousness. He was fully aware that, since he claimed so high an authority for the primary data of consciousness, it was necessary to supply the means of deciding whether any given cognition is or is not entitled to be placed among such; and to this end he laid down certain criteria of alleged primary facts of consciousness. These criteria are (1) simplicity, (2) universality and (subjective) necessity, (3) comparative evidence and certainty, (4) incomprehensibility. In other words, no cognition is an original datum of consciousness which is not simple (i.e., incapable of being resolved into another), not held by all men as a self-evident and necessary truth, and not in itself inexplicable. Now the doctrine of the immediate knowledge of the non-ego will, Hamilton affirmed, stand all these tests. It is the simple residuum of truth in the crude and erroneous beliefs of men as to what they perceive through their senses; it is the spontaneous conviction of all (as to this lie cited as witnesses philosophers who regarded the belief as a mistake and a delusion); and it does not admit of being made comprehensible. That this is so can hardly be denied. Practically, indeed, all acknowledge that consciousness does intuitively affirm what he alleges it to affirm; and, the question being one of fact, a practical acknowledgment is quite as good as a theoretical one.

Here let it be remarked in passing that Hamilton’s doctrine of common sense is wholly misrepresented when held up as an appeal to the belief of the unthinking multitude versus the judgment of philosophers. Rather it carries the appeal into a sphere where the philosophic and the vulgar have ceased to be distinguished; it shows that not the mind of the philosopher, and not the mind of the vulgar, but the mind of man, is what philosophy has to deal with, and that its office is to resolve current beliefs into their elements, not satisfied till it has reached the final and absolutely pure deliverance of consciousness.

P>ut it may be said, as it often has been said, that consciousness is not competent to affirm immediate knowledge of the non-ego, because to discriminate the non-ego from the ego is beyond its power. Hamilton’s answer is that, if knowledge be, as he holds, essentially relative, self cannot be known except with and through uot-self, and that natural realism is but a corollary of the general principle of the relativity of knowledge. On that principle he held that “we think one thing only as we think two things mutually and together,” and that, self being inherently a relative notion, we should never interpret by it facts of our experience, if experience did not come before us under a relation that needs both terms (self and not-self) for its expression. Hamilton certaiuly implies, if he does not expressly say, that, had we no knowledge of a not-self, we could never objectify self so as to know it as such at all. To him a knowledge of the ego alone would be absolute, not relative— such a knowledge, that is, as he held to be impossible. But, viewing knowledge as a relation between an existing subject and an existing object, he saw no reason why the object should not be what it is knoιon as— sometimes a mode of self, sometimes a mode of not-self,—and why consciousness of the ego should not include also that which stands in relation with it.

But that there has been so amazing an amount of misconception on the point, it might seem hardly needful to say that Hamilton did not hold that in perception we know the thing-in-itself. His doctrine of relativity included phenomenalism, though it was more than phenomenalism; and not only his oft-repeated assertions that there can be no such object of knowledge, but the whole tenor of his philosophy, are directly against this inteηu , eta-tion. In passages where he speaks of “the thing” as directly known, the word is obviously used, not for nournenon or the thing in itself, but for the real as opposed to the ideal in phenomena. There can be no doubt that he held the object in sense-perception to be a phenomenon of the non-ego; and arguments that proceed upon a different supposition are of no effect against his theory.

The relativity of perception on that theory is, indeed, not open to doubt. According to him, we perceive phenomena alone,—such alone as we have faculties to apprehend,—such alone as stand in relation to our organs of sense; and we perceive only under the contrast of self and not-self. There is thus in every act of perception a twofold relation—(1) between the thing and the organ, manifested in sensation being a condition of perception, and (2) between self and not-self, manifested in consciousness and perception being different names for the same thing. This of itself should show that he cannot be expected to state definitely what is the object in perception,—as it has often been said that he does not do, or does differently in different places. The object of intuition or perception does not admit of being definitely stated. For individual objects cannot as such be conceived, still less named, till knowledge has risen above the intuitive or perceptive stage. On this, as on all points relating to perception, Hamilton’s mature and carefully expressed view is to be found in his dissertations appended to Reid’s works. There he divides the qualities of body into three classes,—primary, secondary, and secundo-primary. He shows that sensation and perception proper, though up to a certain point inseparable, are not only distinct, but above that point actually in the inverse ratio of one another; that sensations proper (identical with the secondary qualities) are merely subjective affections of the animated organism, and afford no knowledge of external reality; that in perception proper the material organism, which is to be regarded as an external reality, is presented under those relations which constitute its extension, i.e., we know its primary qualities; and that in sensation and perception together we know the secundo-primary qualities, i.e., objects external to the body become known, as directly τelated, through various modes of resistance, to the organism in motion. The object in perception is, then, according to him, a primary quality of the organism, or the quasi-primary phase of a secundoprimary quality. It is a fundamental point of Hamilton’s doctrine that the organism is differently related to the ego in perception proper and in sensation proper. In his own words—“the organism is the field of apprehension to both, but with this difference, that the former views it as of the ego, the latteι ’ as of the non-ego,—that the one draws it within, the other shuts it out from, the sphere of self.” On this distinction is partly founded his doctrine of the twofold character of space, as at once an a priori conception and an a posteriori perception. He held with Kant that space is a necessary condition of thought, and as such not derived from experience; but he at the same time held that through sense we have a perception of something extended, i.e., of extension. Now the cognition of extension is a cognition of relations,— properly therefore realized by a simple energy of thought ; but the facts that sensation is an essential condition of this cognition, and that what is known as extended is the organism, which is as much external to the ego as any other part of the material world, seemed to him to justify these relations being regarded not as subjective but as objective.

Hamilton’s doctrine of the conditioned relates to the second group of primary truths or original data of consciousness. Relativity, as a general condition of the thinkable, he asserts, is brought to bear under three principal and necessary relations :—the first (subjective) the contrast of self and not-self, the second (objective) quality, and the third (objective) quantity. Quality is realized under the twofold aspect of substance and phenomenon. Quantity has three phases :—time (protensive), space (extensive), degree (intensive). Now the doctrine of the conditioned is (1) that under these relations—specially those of quality and time—we must think everything; (2) that the unconditioned as such is either the unconditionally limited—the absolute, or the unconditionally unlimited—the infinite; (3) that, under the necessary relations of thought, we are unable positively to conceive either unconditional limitation or unconditional illimitation; e.g., an absolute whole or part of existence in time or in space or in degree is inconceivable, so is infinite increase or division; absolute quality is inconceivable, quality infinitely undetermined is so equally. Thus this doctrine claims to demonstrate the limited range of positive thought, by showing that the mind is tossed from the one to the other of two contradictory extremes, unable to conceive either, yet compelled to believe that one or other is actual. The kind of inconceivability of the two extremes is indeed different, and it may be regretted that, in his expositions of this part of his philosophy, Hamilton did not more explicitly recognize that fact. It seems true that to combine the absolute with existence regarded quantitatively, i.β., in time or in space or in degree, or the infinite with existence regarded qualitatively, is impossible, not only as beyond but as against thought, i.e., as involving a contradiction; and therefore that, in respect of one of the two extremes, the mind is not simply impotent, seeing it rejects it as that to which there can be nothing answering in actual existence. But then it does so only to find itself face to face with an alternative which, while it must be inferred to be actual, can by no effort be realized in thought. So that, even if this objection be allowed, the doctrine still remains intact as a demonstration how limited is the sphere of human thought as compared with that of existence, and how little human powers of conception are to be made the measure of truth.

Its significance becomes still more apparent in the original and ingenious application made of it by Hamilton to the solution of such philosophic problems as the origin of the principles of cause and effect, substance and phenomenon, &c. That the sum of existence of one set of modes has passed into another mode is, according to him, what we mean by saying that an event had causes. Consciousness is a knowledge of existence only as conditioned in time, and we are impotent—(it matters not how)— to conceive the forms of existence within our experience as having had an absolute commencement; therefore we conceive them as having existed in other forms, in other words, as caused. Thus it is in order to escape from the necessity of thinking an absolute beginning for existence in time that we view all things as a series of causes and effects. In like manner, it is because we can think neither that which exists in and for itself nor that which exists merely in and through something else that we recognize all objects under the double aspect of substance and phenomenon,—knowing nothing but the latter, yet always supposing the former. ®

Having showed that the original data of consciousness, however different in other respects, are alike in this, that they are as facts—but only as facts—clear and certain, and as cognitions relative, more properly indeed, beliefs than cognitions,—Hamilton claims for all that, on the sole authority of consciousness, they be accepted as truths. This is the point to which the whole of his philosophy leads up; hence he offers no arguments in its support. He only asks—If the authority of consciousness be disallowed, what other warrant of truth remains? Where else will a source of certainty be found? He saw no alternative between absolute scepticism and implicit reliance on consciousness. But his reliance was no absolute and blind belief. He claimed implicit credence for consciousness only after having investigated and laid down the conditions of its credibility. The inexplicability that is to him a mark of truth must be proved to be that which springs from the fundamental character of the cognition. While the establishment of principles on which belief may be sure, rational, and consistent is the ultimate aim of his philosophy, groundless or inconsistent belief he sweeps away wherever he meets with it. Thus he will not allow the validity of belief in an external reality which, ex hypothesi, is not known. Be it noted too, that it is consciousness, i.e., reason, for which he claims supreme authority. His position is best understood through the mutual relation (already referred to) of his doctrines of the conditioned and of common sense. The former extends the bounds of existence as much as it narrows those of thought, and so makes room for belief; while the latter shows belief to be the condition on which alone even primary and fundamental truths can be apprehended. Thus, for example, on the ground of both, he held that freedom of will and necessity are alike inconceivable, but that we are not entitled to reject the testimony of consciousness to the fact that as moral agents we are free, on account of the speculative difficulties with which it is surrounded. These two doctrines Sir W. Hamilton did not himself apply to theology, and in themselves they have no direct theological bearing, since the one is concerned with the infinite and the absolute merely as notions, and the other with simple forms of thought long prior to those of theology. But his references to this subject indicate clearly what he considered to be the true relation of theology to philosophy, and show that, in the one as in the other, he held wisdom to lie in such a conviction of human ignorance as disposes the mind to accept harmony with the facts of consciousness as evidence of truth.

Of the three classes into which, as we have seen, Hamilton divided mental phenomena, the third—the phenomena of conation —is not treated of in his Beehives, and his other works contain only fragmentary discussions of particular ethical points. Several lectures, however, are devoted to the consideration of the phenomena of feeling and the development of a theory of pleasure, founded chiefly on that of Aristotle, which is. in substance that pleasure is the reflex in consciousness of the spontaneous and unimpeded exercise of power or energy,—pain being, on the other hand, the consciousness of overstrained or repressed exertion. ®

The logic λvith which Sir W. Hamilton’s name is associated is a purely formal science. Nothing else indeed did he consider properly to be called logic. For it seemed to him an unscientific mixing together of heterogeneous elements to treat as parts of the same science the formal and the material conditions of knowledge. He was quite ready to allow that on this view logic cannot be used as a means of discovering or guaranteeing facts, even the most general, and expressly asserted that it has to do, not with the objective validi

HAMILTON, Sir William (1730-1803), antiquary and patron of the fine arts, was born in 1730 of a noble but needy Scottish family. Of his early life and education we know nothing beyond the fact that he was equerry to Prince George, afterwards George III., whose foster-brother he is said to have been; but in his twenty-fifth year he married a young and beautiful heiress, whose fortune placed him in affluence. In the first parliament of George III. Hamilton sat as member for Midhurst; and in 1764 he was accredited ambassador to Naples, an office which he retained till 1800. On proceeding to his post his attention and interest were at once awakened by the discoveries at Pompeii and Herculaneum, and he took up the study of antiquities with ardour. The Porcinari collection of Greek and Etruscan vases, purchased in 1765, was the nucleus of a valuable collection of his own, now for the most part in the British Museum. Engravings and descriptions of the most valuable pieces are given in the famous Antiquités Etrusques, Grecques, et Domaines, tirées du Cabinet de Μ. Hamilton, edited by D’Hancarville, and published at Naples in 1766-67. Hamilton also contributed liberally to the museum at Portici, and gave much attention to the MSS. and other valuable articles rescued from the buried cities; but his efforts were almost nullified by the inertness of the Neapolitan court, which was even suspicious of his zeal. Natural history and science also were not neglected by him. Between 1764 and 1767 Hamilton paid numerous visits to Vesuvius, Etna, and the Lipari Islands, accompanied by a young artist, Pietro Fabris, who made drawings of the noteworthy objects and appearances under Hamilton’s directions. The result of these excursions, first sent as letters to the Royal Society, of which he became a member in 1766, was afterwards expanded into two works,— Observations upon Mount Vesuvius, Mount Etna, and other Volcanoes of the Two Sicilies, published at London in 1772, and Campi Phlegraei, a collection of plates illustrating the volcanic phenomena, accompanied by concise descriptions in English and French, published at Naples in 1776-77. A Supplement to the latter described the eruption of Mount Vesuvius in 1779. Hamilton’s daughter died in 1775, and his first wife in 1782. In 1772 he was made K.C.B., and in 1791 privy councillor. His continued interest in art and antiquity is manifested by his contributions to the Philosophical Transactions of the Royal Society from 1767 to 1795, and to the Arch<xologia in 1777, as well as by his generosity to artists and antiquaries, such as Morghen, Winckelmann, and Piaggi. Recalled in 1800, he died April 6, 1803.

Sir William Hamilton’s second wife, Emma Lyon or Harte, whose name is so notoriously associated with that of Nelson, was born of very humble parents at Preston in Lancashire, about April 26, 1764. Her youth was spent in domestic service, and it was first as attendant on a lady of fashion that she learned to develop her talent for singing and mimicry. Having lost this situation she became waitress in a tavern frequented by actors, and soon entered upon a gay and dissolute career. Her beauty attracted among others the painter Romney, who depicted her in no fewer than twenty-three of his works. Sir William Hamilton married her in 1791; and, going with him the same year to Naples, she speedily acquired an ascendency over the mind cf the queen, which at the instigation of Nelson she used for the advantage of the British fleet. On the death of Sir William she lived in a house at Merton Place, provided for her by Nelson, but on his death in 1805 she soon squandered the modest fortune left her by her husband, and after being imprisoned for debt, retired with Nelson’s daughter Horatia to Calais, where she died, January 16,1815. Her Memoirs appeared in the year of her death.

HAMILTON, William (1704-1754), a minor Scottish poet, the author of The Braes of Yarrow, was born in 1704, probably at Bangour in Linlithgowshire, the second son of James Hamilton of Bangour, a member of the Scottish bar. It is supposed that he studied at the university of Edinburgh; and it is certain that he received an education which enabled him to enjoy the classical writers of Greece and Rome, and to be a congenial associate in after years with such men as Allan Ramsay and Henry Home. As early as 1724 we find him contributing to Ramsay’s Tea Table Miscellany. In 1745 Hamilton joined the cause of Prince Charles, and, though it is doubtful whether he actually bore arms, he certainly celebrated the battle of Prèston-pans in an ode beginning—“As over Gladsmuir’s bloodstained field.” After the disaster of Culloden he lurked for several months in the Highlands, and at length escaped to France; but in 1749 the influence of his friends at home procured him permission to return to Scotland, and in the following year he obtained possession of the family estate of Bangour. In 1751 he married for the second time, but the state of his health was such that he soon afterwards went abroad, and he died at Lyons on 25th March 1754.

Hamilton has left behind him a considerable number of what are best described as poetical effusions, manyof them pleasing and tasteful, but none of them except the Braes of Yarrow of striking originality. The first collection of his pieces was published without his permission or even knowledge by Foulis (Glasgow, 1748), and introduced by a preface from the pen of Adam Smith. Another edition with corrections by himself was brought out by his friends in 1760, and to this was prefixed a portrait engraved by Sir Robert Strange. Though the poems have been since reprinted in Anderson’s British Poets (vol. ix. ), in Sharpe’s Collection of the British Poets, and in Chalmers’s English Poets (vol. xv.), there was no separate edition between 1760 and 1850, when James Paterson edited The Poems and Songs of William Hamilton. This volume contains several poems till then unpublished, and presents a bibliographical introduction and life of the author.

See also James Chalmers’s ‘ ‘ Notices of Life of William Hamilton” in Transactions of Society of Scottish Antiquaries, vol. iii., 1831; and Charles Mackay, The Poetical Works of Allan Ramsay, with Selections from the Scottish Poets before Burns.

HAMILTON, Sir William Rowan (1805-1865), one of the really great mathematicians of the present century, was born in Dublin, August 4, 1805. His father, who was a solicitor, and his uncle (curate of Trim), migrated from Scotland in youth. A branch of the Scottish family to which they belonged had settled in the north of Ireland in the time of James I., and this fact seems to have given rise to the common impression that Hamilton was an Irishman.

His genius displayed itself, even in his infancy, at first in the form of a wonderful power of acquiring languages. At the age of seven he had already made very considerable progress in Hebrew, and before he was thirteen he had acquired, under the care of his uncle, who was an extraordinary linguist, almost as many languages as he had years of age. Among these, besides the classical and the modern European languages, were included Persian, Arabic, Hindustani, Sanskrit, and even Malay. But though to the very end of his life he retained much of the singular learning of his childhood and youth, often reading Persian and Arabic in the intervals of sterner pursuits, he had long abandoned them as a study, and employed them merely as a relaxation.

His mathematical studies seem to have been undertaken and carried to their full development without any assistance whatever, and the result is that his writings belong to no particular “school,” unless indeed we consider them to form, as they are well entitled, to do, a school by themselves. As an arithmetical calculator he was not only wonderfully expert, but he seems to have occasionally found a positive delight in working out to an enormous number of places of decimals the result of some irksome calculation. At the age of twelve he engaged Colburn, the American “calculating boy,” who was then being exhibited as a curiosity in Dublin, and he had not always the worst of the encounter. But, two years before, he had accidentally fallen in with a Latin copy of Euclid, which he eagerly devoured; and at twelve he attacked Newton’s Arithmetica Universalis. This was his introduction to modern analysis. He soon commenced to read the Principia, and at sixteen he had mastered a great part of that work, besides some more modern works on analytical geometry and the differential calculus.

About this period he was also engaged in preparation for entrance at Trinity College, Dublin, and had therefore to devote a portion of his time to classics. In the summer of 1822, in his seventeenth year, he began a systematic study of Laplace’s Mecanνjue Celeste. Nothing could be better fitted to call forth such mathematical powers as those of Hamilton; for Laplace’s great work, rich to profusion in analytical processes alike novel and powerful, demands from the most gifted student careful and often laborious study. It was in the successful effort to open this treasure-house that Hamilton’s mind received its final temper. “Dès-lors il commença à marcher seul,” to use the words of the biographer of another great mathematician. From that time he appears to have devoted himself almost wholly to original investigation (so far at least as regards mathematics), though he ever kept himself well acquainted with the progress of science both in Britain and abroad.

Having detected an important defect in one of Laplace’s demonstrations, he was induced by a friend to write out his remarks, that they might be shown to Dr Brinkley, afterwards bishop of Cloy ne, but who was then royal astronomer for Ireland, and an accomplished mathematician. Brinkley seems at once to have perceived the vast talents of young Hamilton, and to have encouraged him in the kindest manner. He is said to have remarked in 1823 of this lad of eighteen,—“This young man, I do not say will be, but is, the first mathematician of his age.”

Hamilton’s career at college was perhaps unexampled. Amongst a number of competitors of more than ordinary merit, he was first in every subject, and at every examination. His is said to be the only recent case in which a student obtained the honour of an optime in more than one subject. This distinction had then become very rare, not being given unless the candidate displayed a thorough mastery over his subject. Hamilton received it for Greek and for physics. How many more such honours he might have attained it is impossible to say; but he was expected to win both the gold medals at the degree examination, had his career as a student not been cut short by an unprecedented event. This was his appointment to the Andrews professorship of astronomy in the university of Dublin, vacated by Dr Brinkley in 1827. The chair was not exactly offered to him, as has been sometimes asserted, but the electors, having met and talked over the subject, authorized one of their number, who was Hamilton’s personal friend, to urge him to become a candidate, a step which his modesty had prevented him from taking. Thus, when barely twenty-two, he was established at the Dublin Observatory. He was not specially fitted for the post, for although he had a profound acquaintance with theoretical astronomy, he had paid but little attention to the regular work of the practical astronomer. And it must be said that his time was better employed in grand original investigations than it would have been had he spent it in meridian observations made even with the best of instruments,— infinitely better than if he had spent it on those of the observatory, which, however good originally, were then totally unfit for the delicate requirements of modern astronomy. Indeed there can be little doubt that Hamilton was intended by the university authorities who elected him to the professorship of astronomy to spend his time as he best could for the advancement of science, without being tied down to any particular branch. Had he devoted himself to practical astronomy they would assuredly have furnished him with modern instruments and an adequate staff of assistants.

In 1835, being secretary to the meeting of the British Association which was held that year in Dublin, he waβ knighted by the lord-lieutenant. But far higher honours rapidly succeeded, among which we may merely mention his election in 1837 to the president’s chair in the Royal Irish Academy, and the rare and coveted distinction of being made corresponding member of the academy of St Petersburg. These are the few salient points (other, of course, than the epochs of his more important discoveries and inventions presently to be considered) in the uneventful life of this great man. He retained his wonderful faculties unimpaired to the very last, and steadily continued till within a day or two of his death (September 2, 1865) the task (his Elements of Quaternions) which had occupied the last six years of his life.

The germ of his first great discovery was contained in one of those early papers which in 1823 he communicated to Dr Brinkley, by whom, under the title of Caustics, it was presented in 1824 to the Royal Irish Academy. It was referred as usual to a committee. Their report, while acknowledging the novelty and value of its contents, and the great mathematical skill of its author, recommended that, before being published, it should be still further developed and simplified. During the next three years the paper grew to an immense bulk, principally by the additional details which had been insetted at the desire of the committee. But it also assumed a much more intelligible form, and the grand features of the new method were now easily to be seen. Hamilton himself seems not till this period to have fully ιmderstood either the nature or the importance of his discovery, for it is only now that we find him announcing his intention of applying his method to dynamics. The paper was finally entitled “Theory of Systems of Rays,” and the first part was printed in 1828 in the Transactions of the Royal Irish Academy. The second and third parts have not yet been printed; but it is understood that their more important contents have appeared in the three voluminous supplements (to the first part) which have been published in the same Transactions, and in the two papers “On a General Method in Dynamics,” which appeared in the Philosop)hical Transactions in 1834-5. The principle of “Varying Action” is the great feature of these papers; and it is strange, indeed, that the one particular result of this theory which, perhaps more than anything else that Hamilton has done, has rendered his name known beyond the little world of true philosophers, should have been easily within the reach of Fresnel and others for many years before, and in no way required Hamilton’s new conceptions or methods, although it was by them that he was led to its discovery. This singular result is still known by the name “Conical Refraction,” which he proposed for it when he first predicted its existence in the third supplement to his Systems of Rays, read in 1832.

The step from optics to dynamics in the application of the method of “Varying Action” was made in 1827, and communicated to the Royal Society, in whose Philosophical Transactions for 1834 and 1835 there are two papers on the subject. These display, like the ‘ ‘ Systems of Rays,” a mastery over symbols and a flow of mathematical language almost unequalled. But they contain what is far more valuable still, the greatest addition which dynamical science had received since the grand strides made by Newton and Lagrange. Jacobi and other mathematicians have developed to a great extent, and as a question of pure mathematics only, Hamilton’s processes, and have thus made extensive additions to our knowledge of differential equations. But there can be little doubt that we have as yet obtained only a mere glimpse of the vast physical results of which they contain the germ. And though this is of course by far the more valuable aspect in which any such contribution to science can be looked at, the other must not be despised. It is characteristic of most of Hamilton’s, as of nearly all great discoveries, that even their indirect consequences are of high value.

The other great contribution made by Hamilton to mathematical science, the invention of Quaternions, is fully treated under that heading. It is not necessary to say here more than this, that quaternions form as great an advance relatively to the Cartesian methods as the latter, when first propounded, formed relatively to Euclidian geometry. The following characteristic extract from a letter shows Hamilton’s own opinion of his mathematical work, and also gives a hint of the devices which he employed to render written language as expressive as actual speech. His first great work, Lectures on Quaternions (Dublin, 1852), is almost painful to read in consequence of the frequent use of italics and capitals.

“I hope that it may not be considered as unpardonable vanity or presumption on my part, if, as my own taste has always led me to feel a greater interest in methods than in results, so it is by methods, rather than by any theorems, which can be separately quoted, that I desire and hope to be remembered. Nevertheless it is only human nature, to derive some pleasure from being cited, now and then, even about a ‘ Theorem especially where the

∙quoter can enrich the subject, by combining it with researches of his own.”

The discoveries, papers, and treatises we have mentioned might well have formed the whole work of a long and laborious life. But, not to speak of his enormous collection of MS. books, full to overflowing with new and original matter, which have been handed over to Trinity College, Dublin, and of whose contents it is to be hoped a large portion may yet be published, the works we have already called attention to barely form the greater portion of what he has published. His extraordinary investigations connected with the solution of algebraic equations of the fifth degree, and his examination of the results arrived at by Abel, Jerrard, and Badano, in their researches on this subject, form another grand contribution to science. There is next his great paper on Fluctuating Functions, a subject which, since the time of Fourier, has been of immense and ever increasing value in physical applications of mathematics. There is also the extremely ingenious invention of the Hodograph (q. V. ). Of his extensive investigations into the solution (especially by numerical approximation) of certain classes of differential equations which constantly occur in the treatment of physical questions, only a few items have been published, at intervals, in the Philosophical Magazine. Besides all this, Hamilton was a voluminous correspondent. Often a single letter of his occupied from fifty to a hundred or more closely written pages, all devoted to the minute consideration of every feature of some particular problem: for it was one of the peculiar characteristics of his mind never to be satisfied with a general understanding of a question; he pursued it until he knew it in all its details. He was ever courteous and kind in answering applications for assistance in the study of his works, even when his compliance must have cost him much valuable time. He was excessively precise and hard to please with reference to the final polish of his own works for publication; and it was probably for this reason that he published so little compared with the extent of his investigations.

Like most men of great originality, Hamilton generally matured his ideas before putting pen to paper. “He used to carry on,” says his elder son, “long trains of algebraical and arithmetical calculations in his mind, during which he was unconscious of the earthly necessity of eating; we used to bring in a ‘ snack ’ and leave it in his study, but a brief nod of recognition of the intrusion of the chop or cutlet was often the only result, and his thoughts went on soaring upwards.”

For further details about Hamilton (his poetry and his association with poets, for instance), the reader is referred to the Dublin University Magazine (Jan. 1842), the Gentleman's Magazine (Jan. 1866), and the Monthly Notices of the Royal Astronomical Society (Feb. 1866); and also to an article by the present writer in the North British Review (Sept. 1866), from which much of the above sketch has been taken.

The census of 1872 gives a population of 529,137—276,196 males and 252,941 females. The Hindus numbered 493,877, and the Mahometans 33,658. The Chandels and Bundelas, the old dominant classes, have now sunk to 548 and 612 respectively; most of these still cling to the neighbourhood of Mahoba, the seat of their former supremacy. The district contains 6 towns with a population of more than 5000 souls—namely, Rath, Hamirpur, Mahoba, Maudha, Sumerρur, and Jaitpur. The staple produce of the district is grain of various sorts, the most important being gram. Cotton is also a valuable crop, whose cultivation le on the increase. Out of a total area of 1,464,641 acres, 762,212 are under cultivation. Irrigation is practised on only 16,000 acres, chiefly in the south, where water can be obtained from the artificial lakes. Agriculturists suffer much from the spread of the kdns grass, a noxious weed which overruns the fields and is found to be almost ineradicable, wherever it has once obtained a footing. The district is little subject to blight or flood; but droughts and famine are unhappily common. The scarcity of 1837 and 1868-69 was severely felt in Hamirpur. Commerce is chiefly carried on by means of its great river highway, the Jumna. Cotton and grain, the main exports, are carried downwards; while rice, sugar, tobacco, and Manchester goods constitute the principal imports upwards. The manufactures consist of coarse cotton cloth and soapstone ornaments. There is only one metalled road, that between Hamirpur and Naugaon, 70 miles in length. The gross revenue in 1870-71 was £184,646; expenditure, £116,416. In 1871 the police force numbered 534 men, supplemented by 1953 village watchmen {chaukid<irs), maintained at a cost of £8058. The district contains only one jail: the average number of prisoners in 1850 was 400; 1860, 72; and 1870, 129. In 1870 the number of schools was 112, with 3066 pupils; the cost, £1354. The district is divided into 8 fiscal divisions {pargands}. The climate is dry and hot, owing to the absence of shade and the bareness of soil, except in the neighbourhood of the Mahoba lakes, which cool and moisten the atmosphere. The rainfall in 1869-70 was 37 ’ 1, and in 1870-71 38T inches.

History.— From the 9th to the 14th century this district was the centre of the Chandel kingdom, with its capital at Mahoba. The raj as adorned the town with many splendid edifices, remains of which still exist, besides constructing the noble artificial lakes already described. At the end of the 12th century Mahoba fell into the hands of the Mussulmans, who retained possession of it for 500 years. In 1680 the district was conquered by Chhatar Sal, the hero of the Bundelas, who assigned at his death one-third to his ally the peshwa of the Mariettas. Until Bundelkhand was constituted a British district in 1803, there was constant warfare between the Bundela princes and the Marhatta chieftains. The land had been impoverished by the long war carried on under Chhatar Sal, overrun and ravaged during the Marhatta aggression, and devastated by robber chiefs, so that in 1842 it was reported to be utterly valueless. On the outbreak of the mutiny, Hamirpur was the scene of a fierce rebellion. All the principal towns were plundered by the surrounding native chiefs. Since then the condition of . the district seems to have improved; but it has not yet recovered from the long anarchy of Marhatta rule.

Hamîrpur, the administrative headquarters of the above district, in 25° 58' N. 1at. and 80° 11' 50" E. long., is situated on a tongue of land at the confluence of the Betwa and the Jumna, on the right bank of the latter river. It was founded, according to tradition, by Hamir Deo, a Karchuli Râjput expelled from Ulwar (Alwar) by the Mahometans. The town possesses little importance; there are no manufactures, and quite a limited trade in grain. Population in 1872, 7007.