Hamilton Sentence Examples

Oxford is served by the Cincinnati, Hamilton & Dayton railway.

Early in 1787 King was moved by the Shays Rebellion and by the influence of Alexander Hamilton to take a broader view of the general situation, and it was he who introduced the resolution in Congress, on the 21st of February 1787, sanctioning the call for the Philadelphia constitutional convention.

William Lithgow (1582-1645), the traveller, William Smellie (1697-1763), the obstetrician and Gavin Hamilton (1730-1797), the painter, were born at Lanark.

The fixed given points of intuitionalism furnish Hamilton with one of his arguments in his unexpected development towards a sceptical or " faith philosophy."

As late as 1566 ticalJuris= Archbishop Hamilton of Glasgow, upon his appointment, had restitution of his jurisdiction in the probate Scotland.

From Persia much new information was supplied by Jean Chardin, Jean Tavernier, Charles Hamilton, Jean de Thevenot and Father Jude Krusinski, and by English traders on the Caspian.

Archbishop Hamilton, however, who now granted the decree, had himself obtained a papal dispensation for the marriage, 1 and in consequence it is extremely doubtful whether according to the Roman Catholic law Bothwell and Mary were ever husband and wife.

It is served by the Chicago, Indianapolis & Louisville, the Cincinnati, Hamilton & Dayton, the Cleveland, Cincinnati, Chicago & St Louis (New York Central System), the Lake Erie & Western (New York Central System), the Pittsburg, Cincinnati, Chicago & St Louis (Pennsylvania System) and the Vandalia (Pennsylvania System) railways.

James Hamilton, 3rd marquess of Hamilton, was the king's commissioner; and when the Assembly insisted on proceeding with the trial of the bishops, he formally dissolved the meeting under pain of treason.

In 1891 Hamilton Bower made his famous journey from Leh to Peking.

Among his articles may be mentioned those which he wrote for the ninth edition of this Encyclopaedia on Light, Mechanics, Quaternions, Radiation and Thermodynamics, besides the biographical notices of Hamilton and Clerk Maxwell.

The next work on the husbandry of Scotland is The Countryman's Rudiments, or an Advice to the Farmers in East Lothian, how to labour and improve their Grounds, said to have been written by John Hamilton, 2nd Lord Belhaven about the time of the Union, and reprinted in 1723.

The scanty leisure of his first recess had been devoted to writing his St Andrews rectorial address on higher education and to answering attacks on his criticism of Hamilton; of the second, to annotating in conjunction with Bain and Findlater, his father's Analysis of the Mind.

The promenade of Hamilton Terrace commands a fine view of the broad expanse of the Haven with its various towns and forts.

Greville, nephew of Sir William Hamilton, who in 1790 laid out a town on this spot, the advantages of which as a convenient port for the Irish traffic he clearly recognized.

The hostility of Arran and his brother Archbishop Hamilton forced Mary into friendly relations with the lords who favoured the Protestant party.

She was reconciled with Archbishop Hamilton, and took up arms against the Protestants of Perth, who, incited by Knox, had destroyed the Charterhouse, where many of the Scottish kings were buried.

Green, Lives of the Princesses of England (6 vols., London, 1849-1855); The Hamilton Papers, ed.

Hamilton, "the measurement of a number of tails of the [European] wild cat and of the domestic cat gives a range between 11 in.

Messrs Hamilton Hume and Hovell set out from Lake George, crossed the Murrumbidgee, and, after following the river for a short distance, struck south, skirting the foothills of what are now known as the Australian Alps until they reached a fine river, which was called the Hume after the leader's father.

Meanwhile behind his back the royalists had risen all over England, the fleet in the Downs had declared for Charles, and the Scottish army under Hamilton had invaded the north.

Immediately on the fall of Pembroke Cromwell set out to relieve Lambert, who was slowly retreating before Hamilton's superior forces; he joined him near Knaresborough on the 12th of August, and started next day in pursuit of Hamilton in Lancashire, placing himself at Stonyhurst near Preston, cutting off Hamilton from the north and his allies, and defeating him in detail on the 17th, 18th and 19th at Preston and at Warrington.

Several of the leading United Irishmen, including Reynolds and Hamilton Rowan, immediately fled the country; the papers of the United Irishmen were seized; and for a time the organization was broken up. Tone, who had not attended meetings of the society since May 1793, remained in Ireland till after the trial and suicide of Jackson in April 179.

It is now known that the influence of Nelson and of the British ambassador, Sir William Hamilton, and Lady Hamilton precipitated the rupture between Naples and France.

Sir William Hamilton was subsequently recalled in a manner closely resembling a disgrace, and his place was taken by Paget, who behaved with mote dignity and tact.

In this body he served in 1789-1796, supported Hamilton's financial measures, Washington's neutrality proclamation and the Jay Treaty, and became one of the recognized leaders of the Federalist party.

It is served by the Cleveland, Cincinnati, Chicago & St Louis, the Cincinnati, Hamilton & Dayton, the Cincinnati Northern (New York Central system), and a branch of the Cincinnati, Lebanon & Northern (Pennsylvania system) railways.

Early in 1881 he was appointed assistant prosecuting attorney of Hamilton (disambiguation)|Hamilton county (in which Cincinnati is situated), but resigned in 1882 on being appointed collector of internal revenue of the United States for the first district of Ohio.

From 1885 to 1887 he served as assistant solicitor of Hamilton county, and in the latter year was appointed judge of the Superior Court of Ohio to fill a vacancy.

The Federalist Party, which may be regarded as definitely organized practically from 1791, was led, leaving Washington aside, by Alexander Hamilton and John Adams. A nationalization of the new central government to the full extent warranted by a broad construction of the powers granted to it by the constitution, and a correspondingly strict construction of the powers reserved to the states and the citizens, were the basic principles of Hamilton's policy.

He corresponded with Hamilton of Bangour (q.v.), Somerville, Gay (q.v.) and Pope.

Hamilton's Colonial Mobile (Boston and New York, 1898), and the Colonization of the South (Philadelphia, 1904) are standard authorities for the French and English periods (1699-1781).

His philosophical influence was exerted largely through the writings of Dugald Stewart and Sir William Hamilton.

Hamilton's edition of Reid also contains an account of the university of Glasgow and a selection of Reid's letters, chiefly addressed to his Aberdeen friends the Skenes, to Lord Kames, and to Dr James Gregory.

Like Kant, too, Reid finds in space the source of a necessity which sense, as sense, cannot give (Hamilton's Reid, p. 323).

The relativism or phenomenalism which Hamilton afterwards adopted from Kant and sought to engraft upon Scottish philosophy is wholly absent from the original Scottish doctrine.

But since Hamilton's time the most typical Scottish thinkers have repudiated his relativistic doctrine, and returned to the original tradition of the school.

Stewart's Memoir prefixed to Hamilton's edition of Reid's works.

Having attained his majority in 1805, he married on the 28th of July Catherine Elizabeth Hamilton, daughter of John James, 1st marquess of Abercorn.

His eldest son, George John James, succeeded as 5th earl; his second son was General Sir Alexander Hamilton-Gordon, K.C.B.; his third son was the Reverend Douglas Hamilton-Gordon; and his youngest son Arthur Hamilton, after holding various high offices under the crown, was created Baron Stanmore in 1893.

He succeeded in escaping from the Tower, but was again captured, was condemned to death by the new "high court of justice" on the 8th of March 1649, and was beheaded together with the duke of Hamilton and Lord Holland the next day.

His earliest work dealt mainly with mathematical subjects, and especially with quaternions (q.v.), of which he may be regarded as the leading exponent after their originator, Hamilton.

He was the author of two text-books on them - one an Elementary Treatise on Quaternions (1867), written with the advice of Hamilton, though not published till after his death, and the other an Introduction to Quaternions (1873), in which he was aided by Professor Philip Kelland (1808-1879), who had been one of his teachers at Edinburgh.

His next treatise, The Subjection of Women, was not published till 1869.1 His Examination of Hamilton's Philosophy, published in 1865, had engaged a large share of his time for three years before.

The great canal was not begun; irrigation works were started but were soon given up. The letters of Kleber and Menou (the successors of Bonaparte) show that the expenditure on public works had been so reckless that the colony was virtually bankrupt at the time of Bonaparte's departure; and William Hamilton, who travelled through Egypt in 1802, found few traces, other than military, of the French occupation.

Differences of opinion with regard to the policies to be pursued by the new government gradually led to the formation of two well-defined political groups - the Federalists and the Democratic-Republicans - and Adams became recognized as one of the leaders, second only to Alexander Hamilton, of the former.

In 1796, on the refusal of Washington to accept another election, Adams was chosen president, defeating Thomas Jefferson; though Alexander Hamilton and other Federalists had asked that an equal vote should be cast for Adams and Thomas Pinckney, the other Federalist in the contest, partly in order that Jefferson, who was elected vice-president, might be excluded altogether, and partly, it seems, in the hope that Pinckney should in fact receive more votes than Adams, and thus, in accordance with the system then obtaining, be elected president, though he was intended for the second place on the Federalist ticket.

Moreover, factional strife broke out within the party itself; Adams and Hamilton became alienated, and members of Adams's own cabinet virtually looked to Hamilton rather than to the president as their political chief.

The United States was, at this time, drawn into the vortex of European complications, and Adams, instead of taking advantage of the militant spirit which was aroused, patriotically devoted himself to securing peace with France, much against the wishes of Hamilton and of Hamilton's adherents in the cabinet.

The largest cities are Cleveland, Cincinnati, Toledo, Columbus (the capital), Dayton, Youngstown, Akron, Springfield, Canton, Hamilton, Zanesville and Lima.

There he probably met Patrick Hamilton, and was joined by John Frith.

Mount Hamilton, which lies north of the waterparting, is over 9000 ft.

Silver Spring and Blue Spring in Marion county, Blue Spring and Orange City Mineral Spring in Volusia county, Chipola Spring near Marianna in Jackson county, Espiritu Santo Spring near Tampa in Hillsboro county, Magnolia Springs in Clay county, Suwanee Springs in Suwanee county, White Sulphur Springs in Hamilton county, the Wekiva Springs in Orange county, and Wakulla Spring, Newport Sulphur Spring and Panacea Mineral Spring in Wakulla county are the most noteworthy.

Wise, prudent and conservative, Gallatin made few changes in Hamilton's arrangements, and for twelve years administered the national finances with the greatest skill.

It is served by the Baltimore & Ohio South-Western, the Chicago & Alton, the Chicago, Peoria & St Louis, the Illinois Central, the Wabash, and the Cincinnati, Hamilton & Dayton railways, and by inter-urban electric lines.

Franklin's opinions we have already indicated; and Madison, Hamilton, and Patrick Henry all reprobated the principle of the system.

On the death of James in December 1542 he attempted to assume office as one of the regents for the infant sovereign Mary, founding his pretensions on an alleged will of the late king; but his claims were disregarded, and the earl of Arran, head of the great house of Hamilton, and next heir to the throne, was declared regent by the estates.

He burned Patrick Hamilton and other heretics, and died at St Andrews in September 1539.

Lord Aberdeen made no secret of his dislike for the Turks, and openly expressed his disbelief in the reality of their reforms; and in January 1853 the tsar, in conversation with Sir Hamilton Seymour, the British ambassador at St Petersburg, spoke of the Ottoman Empire as " the Sick Man," and renewed the proposals for a partition made in 1844.

In 1796 he began the study of law, completing his preparation in 1802 at New York, where he studied under William Peter Van Ness (1778-1826), an eminent lawyer and later Aaron Burr's second in the duel with Alexander Hamilton.

Bowling Green is served by the Cincinnati, Hamilton & Dayton and the Toledo & Ohio Central railways, and by the Toledo Urban & Interurban and the Lake Erie, Bowling Green & Napoleon electric lines, the former extending from Toledo to Dayton.

When Charles visited Scotland to give his formal assent to the abolition of Episcopacy, Montrose communicated to him his belief that Hamilton was a traitor.

It had indeed been alleged, on Clarendon's authority, that he proposed to murder Hamilton and Argyll; but this is in all probability only one of Clarendon's many blunders.

Hamilton's impracticable policy of keeping Scotland neutral for long stood in the way of Charles's consent.

Hamilton is situated in a productive agricultural region, and has a large trade in hops; among its manufactures are canned vegetables, lumber and knit goods, There are several valuable stone quarries in the vicinity.

Hamilton is the seat of Colgate University, which was founded in 1819, under the name of the Hamilton Literary and Theological Institution, as a training school for the Baptist ministry, was chartered as Madison University in 1846, and was renamed in 1890 in honour of the Colgate family, several of whom, especially William (1783-1857), the soap manufacturer, and his sons, James Boorman (1818-1904), and Samuel (1822-1897), were its liberal benefactors.

The fauna shows striking analogies with that of the Bokkeveld beds of South Africa on the one hand and of the Hamilton group of North America on the other.

The work of Cobden, and what is now called "Cobdenism," has in recent years been subjected to much criticism from the newer school of English economists who advocate a "national policy" (on the old lines of Alexander Hamilton and Friedrich List) as against his cosmopolitan ideals.

The symbol e 0 behaves exactly like i in ordinary algebra; Hamilton writes I, i, j, k instead of eo, el, e2, es, and in this notation all the special rules of operation may he summed up by the equalities = - I.

In the applications of the calculus the co-ordinates of a quaternion are usually assumed to be numerical; when they are complex, the quaternion is further distinguished by Hamilton as a biquaternion.

Kuhn (1750-1751) and Jean Robert Argand (1806) were completed by Karl Friedrich Gauss, and the formulation of various systems of vector analysis by Sir William Rowan Hamilton, Hermann Grassmann and others, followed.

This was accomplished by French and his subordinate, Colonel (Sir) Ian Hamilton, in the action of Elandslaagte on the 21st of October (British losses, 258 all ranks).

The main advance was taken with one cavalry and three infantry divisions (the cavalry commanded by French, and the infantry divisions by Generals Tucker, PoleCarew and Ian Hamilton).

These, under Sir Archibald Hunter and Sir Leslie Rundle, successfully herded Prinsloo with 4000 Free Staters into the Brandwater Basin (July 29) - a very satisfactory result, but one seriously marred by the escape of De Wet, who soon afterwards raided the Western Transvaal and again escaped between converging pursuers under Kitchener, Methuen, SmithDorrien, Ian Hamilton and Baden-Powell.

The reverse at Bakenlaagte was repaired by a force under Bruce Hamilton.

In January Bruce Hamilton continued his successful night marches, and late in the month General Ben Viljoen was captured in the Leydenburg district.

The entire text of the London MS. was published by Land in the third volume of his Anecdota syriaca; and there is now an English translation by Hamilton and Brooks (London, 1899), and a German one by Ahrens and Kruger (Leipzig, 1899).

He graduated at Hamilton College, Clinton, N.Y., in 1820, and at the Princeton Theological Seminary in 1823, was ordained as a Presbyterian minister by the presbytery of Elizabethtown, New Jersey, in 1825, and was the pastor successively of the Presbyterian Church in Morristown, New Jersey (1825-1830) and of the First Presbyterian Church of Philadelphia(1830-1867).

It appears to have been used by James Bradley, but for its practical development we are mainly indebted to Sir William Rowan Hamilton, who published an account of it in the Proceedings of the Royal Irish Academy, 1846.

His literary capacity was early shown in the remarkable fiction of his Memoirs of Arthur Hamilton (1886) under the pseudonym of "Christopher Carr," and his Poems (1893) and Lyrics (1895) established his reputation as a writer of verse.

The principal Canadian ports are Kingston, at the head of the St Lawrence river; Toronto, where the harbour is formed by an island with improved entrance channels constructed both east and west of it; and Hamilton, at the head of the lake, situated on a landlocked lagoon, connected with the main lake by Burlington channel, an artificial cut.

But Sir Ian Hamilton judged it to be inexpedient to initiate land operations at once.

Hamilton contemplated two distinct major operations.

Hamilton ordered a further attack for the 28th.

It is true that Hamilton was expecting the arrival of the 42nd Division and of the 2nd French Division within a few days; but his losses had been extremely heavy, there were no depots at hand from which these losses could promptly be made good, and he was inferior to ` the Turks in artillery both as regards calibre of guns and as regards ammunition.

Hamilton made Imbros his headquarters, and troops also were sometimes collected there owing to its vicinity both to Helles and to Anzac. Within the Dardanelles the battleship " Goliath " had been torpedoed by the Turkish destroyer " Muavenet-i-Milliye " on May 13; on the other hand British submarines were performing invaluable service, diving under the mine-fields, causing havoc amongst enemy craft in the channel itself and higher up, and threatening Ottoman communications with the peninsula.

Hamilton's orders - eight now that the 52nd had arrived - in reality gave a very misleading impression of the strength of the force; his Majesty's Government had, however, during the course of the month decided to dispatch large reinforcements to this theatre of war, and the Allied commander-in-chief had been cheered by the tidings that five further divisions, the loth, 11th, 13th, J3rd and 54t h, had been placed under orders for the Aegean, and would join him between July 10 and Aug.

Hamilton, and he framed his plans well in advance.

This part of Hamilton's programme was, indeed, carried out most successfully, for, although Liman von Sanders was aware of the arrival of large bodies of British troops in the islands, he remained entirely ignorant of his rival's real design until this was actu ally in execution.

Hamilton's plan was completely exposed, and so victory definitely decided itself in favour of the defenders early on the Toth.

Hamilton, however, still entertained hopes of effecting some improvement in his position in this area.

Hamilton had cabled home asking for reinforcements and for very large drafts that were needed to bring the depleted units under his command up to their war establishment.

Hamilton's orders were transferred to Salonika.

Hamilton was, however, invited to give his views concerning the question of evacuating the peninsula and abandoning the enterprise against the Straits.

Hamilton's army was ready to land, the defenders should be in a position to bring it to a standstill.

After his return he became the first head of St Stephen's House, Oxford (1876-1878), and then, after presiding for two years over the Theological College at Salisbury, where he acted as his father's chaplain, he accepted the college living of Great Budworth in Cheshire in 1880, and the same year married Alice, the daughter of his father's predecessor, Walter Kerr Hamilton.

Airdrie unites with Falkirk, Hamilton, Lanark and Linlithgow in sending one member to parliament.

Sir William Hamilton regarded him as "the real founder of the Scottish school of philosophy."

It is in Mill's Examination of Sir William Hamilton's Philosophy that the classical statement of the Relativity of Knowledge is to be found.

Hamilton Street, the principal business thoroughfare, extends over 2 m.

It is served by the Cincinnati, Hamilton & Dayton, and the Pittsburg, Cincinnati, Chicago & St Louis railways, and by interurban electric lines connecting with Cincinnati, Dayton and Toledo.

The valley in which Hamilton is situated is noted for its fertility.

A hydraulic canal provides the city with good water power, and in 1905, in the value of its factory products ($13,992,574, being 31.3% more than in 1900), Hamilton ranked tenth among the cities of the state.

The town was renamed, in honour of Alexander Hamilton, about 1796.

In 1803 Hamilton was made the county-seat; in 1810 it was incorporated as a village; in 1854 it annexed the town of Rossville on the opposite side of the river; and in 1857 it was made a city.

In 1908, by the annexation of suburbs, the area and the population of Hamilton were considerably increased.

Hamilton was the early home of William Dean Howells, whose recollections of it are to be found in his A Boy's Town; his father's anti-slavery sentiments made it necessary for him to sell his printing office, where the son had learned to set type in his teens, and to remove to Dayton.

It is served by the Baltimore & Ohio, the Cincinnati & Muskingum Valley (Pennsylvania Lines), the Detroit, Toledo & Ironton, and the Cincinnati, Hamilton & Dayton railways.

Blanco White, " the rationalist A'Kempis," who had dared to appear as " a religious sceptic in God's presence," had found a biographer and interpreter in Martineau's friend and colleague, John Hamilton Thom.

In the first part Spencer's argument rests on Mansel's Limits of Religious Thought and Hamilton's" philosophy of the conditioned "(and so ultimately on Kant), and tries to show that alike in scientific and religious thought the ultimate terms are" inconceivable "(not by him distinguished from" unimaginable ").

Dayton is served by the Erie, the Cleveland, Cincinnati, Chicago & St Louis, the Pittsburg, Cincinnati, Chicago & St Louis, the Cincinnati, Hamilton & Dayton, and the Dayton & Union railways, by ten interurban electric railways, centring here, and by the Miami & Erie canaL The city extends more than 5 m.

In 1788 he joined his son-in-law Alexander Hamilton, John Jay and others in leading the movement for the ratification by New York of the Federal constitution.

The Tory party and the established church were defended in the Critical Review (1756-1817), founded by Archibald Hamilton and supported by Smollett, Dr Johnson and Robertson.

The industry was founded by Baron Hamilton in 1761.

He had been chosen to meet Hamilton in controversy, with a view to convincing him of his errors, but the arguments of the Scottish proto-martyr, and above all the spectacle of his heroism at the stake, impressed Alesius so powerfully that he was entirely won over to the cause of the Reformers.

This must be so, for Lennox's letters of the 11th of June were intercepted by his foes, the Hamiltons, and were found in the Hamilton Muniment Room.

He completed his university successes by winning the TyndallBruce scholarship, the Hamilton fellowship (1872), the Ferguson scholarship (1872) and the Shaw fellowship (1873).

Hamilton (Discussions, p. 197) allows greater sagacity to Collier than to Berkeley, on the ground that he did not vainly attempt to enlist men's natural belief against the hypothetical realism of the philosophers.

It has monuments to Patrick Hamilton, the martyr, and Thomas Hog (1628-1692), the Scottish divine, for some time a prisoner on the Bass.

Patrick Hamilton became titular abbot in 1517, and after his martyrdom the abbey was added to the bishopric of Ross.

The death of his patrons, the duke of Richmond and the marquess of Hamilton, and of King James put an end to his hopes of political preferment; moreover he probably distrusted the conduct of affairs under the new reign.

In taking root in England idealism had to contend against the traditional empiricism represented by Mill on the one hand and the pseudo-Kantianism which was rendered current by Mansel and Hamilton on the other.

St George was the capital till the senate and courts of justice were removed by Sir James Cockburn to Hamilton, which being centrally situated, is more convenient.

Hamilton, which is situated on the inner part of the Great Sound, had a population in 1901 of 2246, that of St George being 985.

The Bermudas are a British crown colony, with a governor resident at Hamilton, who is assisted by an executive council of 6 members appointed by the crown, a legislative council of 9 similarly appointed, and a representative assembly of 36 members, of whom four are returned by each of nine parishes.

It was intended that young Grover should be educated at Hamilton College, but this was prevented by his father's death in 1852.

He graduated from Hamilton College in 1878, was admitted to the bar in 1880, and practised in Utica until 1907.

He received his early education at the grammar-school of Hamilton, and he appears to have subsequently attended some classes at the university of Glasgow.

During his residence at Hamilton, besides the arduous duties of medical practice, he found time to devote to the study of the natural sciences, and especially of chemistry.

The principal forest area is in the Adirondack region where the state has a forest preserve (in Clinton, Essex, Franklin, Fulton, Hamilton, Herkimer, Lewis, Oneida, St Lawrence, Saratoga, Warren and Washington counties) containing (1909) 1, 53 0, 559 acres, and there is as much or more in private preserves and in tracts owned by lumbermen.

Those popularly known as " bluestones " belong to the Hamilton period of the Devonian formation and occur mainly between the Hudson and Delaware rivers.

Their places, however, were taken by Andrew Hamilton, speaker of the Assembly of Pennsylvania and a lawyer of great reputation in the English colonies.

In support of the constitution, however, there arose the Federalist party under the able leadership of Alexander Hamilton.

But others were won over by the news that it had been ratified by New Hampshire and Virginia or by the telling arguments of Hamilton, and on the 26th of July the motion to ratify was carried by a vote of 30 to 27.

The Clintons were most popular among the independent freeholders; the Livingstons had increased their influence by numerous marriage alliances with landed families; and the Schuylers had General Philip Schuyler and Alexander Hamilton, his son-in-law.

Hamilton's action in counselling Federalists not to vote for Burr for governor just as he had counselled them not to support Burr against Jefferson in 1800, was one of the contributary causes of Burr's hostility to Hamilton which ended in the duel (July 1804) in which Burr killed Hamilton.

Hamilton's death marked the end of the Federalists as a power in New York.

In 1906 sugar refineries were projected at Hamilton, Kalispell, Chinook, Laurel, Missoula, Dillon and Great Falls; and in 1907 the crop was so large that 12,000 freight cars were needed to carry it and the railways had a car and coal " famine."

Olney is served by the Baltimore & Ohio South-western, the Illinois Central, and the Cincinnati, Hamilton & Dayton railways, and is a terminus of the Ohio River Division of the last.

He edited The Works of Alexander Hamilton (9 vols., 1885-1886) and The Federalist (1891).

The theological application and development of Hamilton's arguments in Mansel's Bampton Lectures On the Limits of Religious Thought marked a still more determined attack, in the interests of theology, upon the competency of reason.

Most of these railways use the Union Station; the Pennsylvania and the Cincinnati, Hamilton & Dayton, have separate stations.

The attempts of a powerful faction among the Federalists to secure the election of Burr failed, partly because of the opposition of Alexander Hamilton and partly, it would seem, because Burr himself would make no efforts to obtain votes in his own favour.

Hamilton had opposed Burr's aspirations for the vice-presidency in 1792, and had exerted influence through Washington to prevent his appointment as brigadier-general in 1798, at the time of the threatened war between the United States and France.

Smarting under defeat and angered by Hamilton's criticisms, Burr sent the challenge which resulted in the famous duel at Weehawken, N.J., on the 11th of July 1804, and the death of Hamilton on the following day.

After the expiration of his term as vicepresident (March 4, 1805), broken in fortune and virtually an exile from New York, where, as in New Jersey, he had been indicted for murder after the duel with Hamilton, Burr visited the South-west and became involved in the so-called conspiracy which has so puzzled the students of that period.

North British or Caledonian railway or both, are Bothwell Park, Carfin, Chapelhall, Bellshill (pop. 8786), Holytown, Mossend, Newarthill,Uddingston (pop. 7463), Clydesdale, Hamilton Palace, Colliery Rows and Tennochside.

With a company of volunteers Clark captured Kaskaskia, the chief post in the Illinois country, on the 4th of July 1778, and later secured the submission of Vincennes, which, however, was recaptured by General Henry Hamilton, the British commander at Detroit.

In the spring of 1779 Clark raised another force, and recaptured Vincennes from Hamilton.

Sidney is served by the Cleveland, Cincinnati, Chicago & St Louis, the Cincinnati, Hamilton & Dayton, and the Western Ohio (electric) railways.

The formations most widely recognized are the Helderberg limestone, the Onondaga limestone and the Hamilton shale.

The Hamilton fauna which followed represents the admixture of the resident Onondaga fauna with new types which are thought to have come from South America, showing that faunal connections for marine life had been made between the interior of the United States and the lands south of the Caribbean Sea, a connection of which, before this time, there was no evidence.

The late Devonian fauna of the interior represents the commingling of the Hamilton fauna of the eastern interior with new emigrants from the north-west, a union which was not effected until toward the close of the period.

William Hamilton Maxwell (1792-1850), the Irish novelist, wrote, in addition to several novels, a Life of the Duke of Wellington (1839-1841 and again 1883), and a History of the Irish Rebellion in 1798 (1845 and 1891).

There are two Italian marble monuments in honour of Confederate soldiers, and monuments to the Southern poets, Paul Hamilton Hayne and Richard Henry Wilde (1789-1847).

Affiliated with the university, but not receiving state funds, are three preparatory schools, the South Georgia Military and Agricultural College at Thomasville, the Middle Georgia Military and Agricultural College at Milledgeville, and the West Georgia Agricultural and Mechanical College at Hamilton.

In 1581 he issued a pamphlet against John Hamilton and other Catholics, who had, he said, driven him from his country.

Sherman was not a deep and original thinker like James Wilson, nor was he a brilliant leader like Alexander Hamilton; but owing to his conservative temperament, his sound judgment and his wide experience he was well qualified to lead the compromise cause in the convention of 1787.

He describes his belief in an unknowable absolute as " carrying a step farther the doctrine put into shape by Hamilton and Mansel."

He develops this belief in an absolute in connexion with his own theory of evolution into something different both from the idealism of Hume and the realism of Hamilton, and rather falling under the head of materialism.

It was counteracted to some extent by the study at the universities of the deductive logic of Aristotle and the inductive logic of Bacon, by parts of Mill's own logic, and by the natural realism of Reid, Stewart, and Hamilton, which met Hume's scepticism by asserting a direct perception of the external world.

But natural realism, as finally interpreted by Hamilton, was too dogmatic, too unsystematic, and too confused with elements derived from Kantian idealism to withstand the brilliant criticism of Mill's Examination of Sir William Hamilton's Philosophy (1865), a work which for a time almost persuaded us that Nature as we know it from sensations is nothing but permanent possibilities of sensation, and oneself only a series of states of consciousness.

His theory of "attuition," by which he supposes that we become conscious of objects outside ourselves, is his " return to dualism," and is indeed so like natural realism as to suggest that, like Ferrier, he starts from Hamilton to end in Hegel.

As, however, he does not suppose that we have a direct perception of something resisting the organism, such as Hamilton maintained, it becomes necessary to state exactly what he means by " attuition."

Hamilton went still further; he tried to combine the oil of Reid with the water of Kant; and converting.

Hamilton's views both on the absolute and on perception affected Mansel and Spencer.

Hamilton, in fact, made the double mistake of limiting knowledge to what we can conceive, and confusing the determinate with the finite or limited.

He edited two editions of Hamilton Moore's Navigation, and in 1802 published a valuable work, New American Practical Navigator, founded on the earlier treatise by Moore.

Wyndham as chief secretary for Ireland was included in the cabinet; Lord Selborne remained at the admiralty, Mr St John Brodrick (afterwards Lord Midleton) war minister, Lord George Hamilton secretary for India, and Mr Akers-Douglas, who had been first commissioner of works, became home secretary; Lord Balfour of Burleigh remained secretary for Scotland, Lord Dudley succeeded Lord Cadogan as lord lieutenant of Ireland, and Lord Londonderry became president of the Board of Education (with Sir William Anson as parliamentary secretary in the House of Commons).

But Mr Chamberlain's new programme for a general tariff, with new taxes on food arranged so as to give a preference to colonial products, involved a radical alteration of the established fiscal system, and such out-and-out Unionist free-traders in the cabinet as Mr Ritchie and Lord George Hamilton, and outside it, like Lord Hugh Cecil and Mr Arthur Elliot (secretary to the treasury), were entirely opposed to this.

On the 16th of September Mr Balfour published a pamphlet on "Insular Free Trade," and on the 18th it was announced that Lord George Hamilton and Mr Ritchie had resigned, Lord Balfour of Burleigh and Mr Arthur Elliot following a day or two later.

This manifesto was at first taken, not only as the platform of the government, but also as that from which its resigning free-trade members had dissented; and the country was puzzled by a statement from Lord George Hamilton that Mr Balfour had circulated among his colleagues a second and different document, in fuller agreement with Mr Chamberlain.

He used all his influence to hamper the president and to advance the political interests of Alexander Hamilton, until he was dismissed, after refusing to resign, in May 1800, Returning to Massachusetts, he served as chief justice of the court of common pleas of Essex county in 1802-1803.

In 1876 Tyndall married Louisa, daughter of Lord Claud Hamilton.

Thorold, of the India Medical Service, and a native sub-surveyor, Captain Hamilton Bower, I.S.C., set out from Leh on the 1st of June 1891, and crossed the Lanak la and the Ladak frontier on the 3rd of July.

See Hamilton (disambiguation) for articles sharing the title Hamilton.

Hamilton originated in the 15th century under the protecting influence of the lords of Hamilton, and became a burgh of barony in 1456 and a royal burgh in 1548.

The latter rights were afterwards surrendered and it was made the chief burgh of the regality and dukedom of Hamilton in 1668, the third marquess having been created duke in 1643.

Immediately east of the town is Hamilton palace, the seat of the duke of Hamilton and Brandon, premier peer of Scotland.

Each of the twelve pillars of the portico is a single block of stone, quarried at Dalserf, midway between Hamilton and Lanark, and required thirty horses to draw it to its site.

The interior is richly decorated and once contained the finest collection of paintings in Scotland, but most of them, together with the Hamilton and Beckford libraries, were sold in 1882.

They were planned in 1583 by John Hamilton, an ancestor of Lord Belhaven, and now belong to Lord Ruthven.

The castle had been a royal residence for at least two centuries before Bannockburn (1314), but immediately after the battle Robert Bruce granted it to Sir Walter FitzGilbert Hamilton, the son of the founder of the family, in return for the fealty.

Hamilton Benn and four French were attached for smoke screen, inshore and rescue work, and the whole force was under Commodore Hubert Lynes.

Hamilton Benn were busy laying a smoke screen, supported by the "Faulknor" (flying Commodore Hubert Lyne's broad pendant), "Lightfoot," "Mastiff," "Afridi," "Swift" and "Matchless."

The hapless and worthless bridegroom had already incurred the hatred of two powerful enemies, the earls of Morton and Glencairn; but the former of these took part with the queen against the forces raised by Murray, Glencairn and others, under the nominal leadership of Hamilton, duke of Chatelherault, on the double plea of danger to the new religion of the country, and of the illegal proceeding by which Darnley had been proclaimed king of Scots without the needful constitutional assent of the estates of the realm.

A bond was drawn in which Darnley pledged himself to support the confederates who undertook to punish "certain privy persons" offensive to the state, "especially a strange Italian, called Davie"; another was subscribed by Darnley and the banished lords, then biding their time in Newcastle, which engaged him to procure their pardon and restoration, while pledging them to insure to him the enjoyment of the title he coveted, with the consequent security of an undisputed succession to the crown, despite the counter claims of the house of Hamilton, in case his wife should die without issue - a result which, intentionally or not, he and his fellow-conspirators did all that brutality could have suggested to accelerate and secure.

Thence they rode to Seton's castle of Niddry, and next day to Hamilton palace, round which an army of 6000 men was soon assembled, and whither the new French ambassador to Scotland hastened to pay his duty.

But on the day when Mary arrived at Hamilton Murray had summoned to Glasgow the feudatories of the Crown to take arms against the insurgent enemies of the infant king.

A third "Farmer's Letter" replied to Hamilton's View of the Controversy between Great Britain and her Colonies, in a broader and abler treatment than in the previous pamphlets.

To this third pamphlet Hamilton replied with The Farmer Refuted (1775).

His grandfather, William Hamilton, principal of Edinburgh University, had been a professor of divinity.

For many years, however, by private arrangement with his colleague Professor Copland, Hamilton taught the class o £ mathematics.

Hamilton, then a boy of ten, was made abbot, and the abbacy and monastery were erected into a temporal lordship ih his favour in 1587.

The chapel contains the tombs of abbot John Hamilton and of the children of the 1st lord Paisley, and the recumbent effigy of Marjory, daughter of Robert Bruce, who married Walter, the Steward, and was killed while hunting at Knock Hill between Renfrew and Paisley (1316).

His son, Paul Hamilton Hayne (5830-5886), was a poet of some distinction, and in 1878 published a life of his father.

William Hamilton, was mainly due to Aristotle, Kant and Reid.

Like Hamilton, Mansel maintained the purely formal character of logic, the duality of consciousness as testifying to both self and the external world, and the limitation of knowledge to the finite and "conditioned."

Consciousness, he held - agreeing thus with the doctrine of "natural realism" which Hamilton developed from Reid - implies knowledge both of self and of the external world.

The south-western part is naturally divided into two tracts by the Niagara escarpment, a line of cliffs capped by hard Silurian limestones, running from Queenston Heights near the falls of Niagara west to the head of Lake Ontario near Hamilton, and then northwest to the Bruce Peninsula on Georgian Bay.

London, for example, is built on the old shore of Lake Warren, the highest of the extinct lakes; and St Catharines, Hamilton and Toronto are on the old shore of Lake Iroquois, the lowest.

Canals of Greenwich 88 Longitude West important cities are Ottawa (the capital of the Dominion) (59,9 28 in 1 9 01), Hamilton (52,634), London (37,981), Kingston (17,961).

The borough of South Trenton was annexed in 1850; the borough of Chambersburg and the township of Millham in 1888; the borough of Wilbur in 1898; and parts of the townships of Ewing and Hamilton in 1900.

His father, Sir James Dalrymple, Bart., of Hailes, in the county of Haddington, auditor-general of the exchequer of Scotland, was a grandson of James, first Viscount Stair; and his mother, Lady Christian Hamilton, was a daughter of Thomas, 6th earl of Haddington.

One of these is the portrait of Frederick the Wise of Saxony, formerly in the Hamilton collection and now at Berlin; the second, much disfigured by restoration, is the Dresden altarpiece with a Madonna and Child in the middle and St Anthony and Sebastian in the wings.

Although inferior in intellectual quality to Alexander Hamilton's Report on Manufactures, presenting the case against free trade, it is regarded as the most powerful attack upon the protection system which has ever been made in an American state paper.

He edited the North British Review from 1850 to 1857, and in 1856, having previously been a Free Church minister, he succeeded Sir William Hamilton as professor of Logic and Metaphysics at Edinburgh University.

In 1836 Sir William Hamilton was appointed to the chair of Logic and Metaphysics, and Fraser became his pupil.

He himself says, "I owe more to Hamilton than to any other influence."

The father returned to Connecticut in 1837 and the son graduated at Hamilton College (Clinton, N.Y.)in 1847.

Those of British-Colonial birth were most numerous in Edinburgh (with 0.933%), and foreigners in Glasgow (with 0.890), Leith (with 0.741) and Hamilton (with 0.720).

On his death the nobles, notably Fleming, Livingstone, Crawford, Hamilton and Boyd, made a band for securing power and place.

The princess Mary was divorced from her Boyd husband and married Lord Hamilton.

Never was marriage so fruitful in tragedies as the wedding of Lord Hamilton and the princess Mary.

The facts may be found in contemporary English despatches printed in the Hamilton papers.

She also restored Archbishop Hamilton to his consistorial jurisdiction, but withdrew her act, in face of presbyterian opposition.

But on the 23rd of January, Murray was shot dead, in the street of Linlithgow, by a Hamilton, with the approval and aid of Archbishop Hamilton and other heads of the house.

On the 2nd of April 1571 Mary's party lost Dumbarton castle, which Crawford of Jordanhill took by a daring night surprise; and Archbishop Hamilton, a prisoner, was hanged without trial.

James Stewart received the Hamilton earldom of Arran, and under him and Lennox the young king began his long strife with the kirk and his halfhearted dealings with the Catholics and his mother.

Charles drove on the bishops, who better understood the situation, and he sent the half-hearted Hamilton to negotiate and threaten in Edinburgh, where the Covenanters were blockading the castle.

In 1639 he was as active in arms in the north as Hamilton, on the king's side, was dilatory and helpless in the south.

Montrose kept his word, while Hamilton stooped to sign the Covenant.

All that is known of Montrose, in this matter, is that from prison he had written thrice to Charles, and that Charles had intended to show his third letter to Argyll, Hamilton and Lanark, on the very day when they, suspecting a plot, retired into the country (12th of October).

Lanark, from Oxford, fled to join the Covenanters; Charles imprisoned Hamilton in Cornwall; Montrose was made a marquis; Leslie, with a large Scottish force and 4000 horse, besieged Newcastle.

A strife arose between Hamilton, who wished to disband the Covenanting army, and Argyll, and gradually the struggle was between Hamilton and the sympathizers with the imprisoned king and Argyll at the head of (or under the heels of) the more fanatical preachers and Presbyterians.

The Scottish commissioners in England, with Lauderdale, and with the approval of Hamilton's faction, signed, at the end of 1647, " The Engagement " with Charles, and broke away from the tyranny of the preachers.

In August 1648, they crossed the border, leaving the fanatics to arm in their rear, but Cromwell, by a rapid march across the fells, caught and utterly routed them at Preston and on the line of the Ribble, taking captive the infantry and Hamilton, who was sent to the block.

After six weeks the plundering clansmen were withdrawn, and in the spring of 1678, also of 1679, Hamilton with his allies carried their complaints to Charles.

The murderers rode to the west, joined the company of Robert Hamilton, defeated Graham of Claverhouse with a small force of horse at Drumclog, occupied Glasgow, and proved the total inability of the regular forces to cope with a rising.

For president, Hamilton, who had been in opposition from 1673 to 1682, was preferred to Atholl by a small majority, but it soon appeared that William's friends were in the ascendant.

Mar, Queensberry, Stair (of Glencoe) and Argyll (Red John of the Battles) were the leading statesmen of the Unionist party; being opposed by Hamilton, Atholl and Lockhart of Carnwath as Jacobites; by Fletcher of Saltoun as an independent patriot; by popular sentiment, by mob violence, and by many of the preachers, though not by the General Assembly.

The final debates of 1706 were conducted under apprehensions of an invasion of Edinburgh by highlanders and wild western fanatics of the Covenant; but the astuteness of Harley's agent in Edinburgh, de Foe, the resolution of Argyll and the tact of Queensberry, who easily terrified the duke of Hamilton, carried the measure into haven.

The fatal duel in which Hamilton was slain by Mohun, when on the eve of going as ambassador to France, with the interests of James in his eye, was a blow to the Jacobites; as were the death of Anne, the fall of Bolingbroke and the unopposed succession of George I.

Knox, like Bishop Burnet, needs to be read critically and in the light of contemporary documents; especially those in the Hamilton Papers, The Border Papers and English State Papers (Foreign).

Up to this time, John Quincy Adams was regarded as belonging to the Federalist party, but he now found its general policy displeasing to him, was frowned upon, as the son of his father, by the followers of Alexander Hamilton, and found himself nearly powerless as an unpopular member of an unpopular minority.

An inscription on the tomb of Thomas Abbott Hamilton in the churchyard is by the poet Cowper, who lived in the neighbouring town of Olney.

The town is under the control of a council with provost and bailies, and combines with Airdrie, Hamilton, Lanark and Linlithgow (the Falkirk group of burghs) to return a member to parliament.

At Polmont, farther east, which gives the title of baron to the duke of Hamilton, is the school of Blair Lodge, besides coal-mines and other industries.

Alexander Hamilton was secretary of the treasury.

These two men, antipodal in temperament and political belief, clashed in irreconcilable hostility, and in the conflict of public sentiment, first on the financial measures of Hamilton, and then on the questions with regard to France and Great Britain, Jefferson's sympathies being predominantly with the former, Hamilton's with the latter, they formed about themselves the two great parties of Democrats and Federalists.

Separation from European politics - the doctrine of" America for Americans "that was embodied later in the Monroe declaration - was a tenet cherished by Jefferson as by other leaders (not, however, Hamilton) and by none cherished more firmly, for by nature he was peculiarly opposed to war, and peace was a fundamental part of his politics.

To this reaction Hamilton explicitly appealed in the convention of 1787; and of this reaction various features of the constitution, and Hamiltonian federalism generally, were direct fruits.

Hating as he did feudal class institutions and Tudor-Stuart traditions of arbitrary rule, 2 his attitude can be imagined toward Hamilton's oft-avowed partialities - and Jefferson assumed, his intrigues - for British class-government with its eighteenth-century measure of corruption.

In short, Hamilton took from recent years the lesson of the evils of lax government; whereas Jefferson clung to the other lesson, which crumbling colonial governments had illustrated, that governments derived their strength (and the Declaration had proclaimed that they derived their just rights) from the will of the governed.

As Hamilton was somewhat officious and very combative, and Jefferson, although uncontentious, very suspicious and quite independent, both men holding inflexibly to opinions, cabinet harmony became impossible when the two secretaries had formed parties about them and their differences were carried into the 1 It was at this period of his life that Jefferson gave expression to some of the opinions for which he has been most severely criticized and ridiculed.

Party feeling in America has probably never been more dangerously impassioned than in the three years preceding 3 Hamilton wrote for the papers himself; Jefferson never did.

Better counsels, however, prevailed; Hamilton used his influence in favour of Jefferson as against Burr, and Jefferson became president, entering upon his duties on the 4th of March 180 1.

The only just judgment of these notes is to be obtained by looking at them, and by testing his suspicions with the letters of Hamilton, Ames, Oliver Wolcott, Theodore Sedgwick, George Cabot and the other Hamiltonians.

His rhind, no less trenchant and subtle than Hamilton's, was the most impressible, the most receptive, mind of his time in America.

He published anonymously (though without succeeding in concealing the authorship) An Address to the People of New York, in vindication of the constitution; and in the state convention at Poughkeepsie he ably seconded Hamilton in securing its ratification by New York.

Hamilton was stoned at a public meeting in New York while speaking in defence of the treaty, and Washington was grossly abused for signing it.

In politics he was throughout inclined toward Conservatism, and after the rise of parties under the federal government he stood with Alexander Hamilton and John Adams as one of the foremost leaders of the Federalist party, as opposed to the Republicans or Democratic-Republicans.

From 180 9 onwards Stewart lived mainly at Kinneil House, Linlithgowshire, which was placed at his disposal by the duke of Hamilton.

In Ipswich were originally included the present townships of Hamilton (1793) and Essex (1819).

Hamilton's Philosophy, and there is no doubt that the empirical school owed a great deal to his sound, accurate thinking, untrammelled by any reverence for authority, technique and convention.

His influence largely shaped the form of the final draft of the constitution, but the labour was not finished with this draft; that the constitution was accepted by the people was due in an eminent degree to the efforts of Madison, who, to place the new constitution before the public in its true light, and to meet the objections brought against it, joined Alexander Hamilton and John Jay in writing The Federalist, a series of eighty-five papers, out of which twenty certainly, and nine others probably, were written by him.

It is very probable that Jefferson's influence over Madison, which was greater than Hamilton's, contributed to this result.

Madison now opposed Hamilton's measures for the funding of the debt, the assumption of state debts, and the establishment of a National Bank, and on other questions he sided more and more with the opposition, gradually assuming its leadership in the House of Representatives and labouring to confine the powers of the national government within the narrowest possible limits; his most important argument against Hamilton's Bank was that the constitution did not provide for it explicitly, and could not properly be construed into permitting its creation.

Madison, Jefferson and Randolph were consulted by Washington, and they advised him not to sign the bill providing for the Bank, but Hamilton's counterargument was successful.

On the same constitutional grounds Madison objected to the carrying out of the recommendations in Hamilton's famous report on manufactures (Dec. 5, 1791), which favoured a protective tariff.

He found in Washington's attitude - as in Hamilton's failure to pay an instalment of the moneys due France - an "Anglified complexion," in direct opposition to the popular sympathy with France and French Republicanism.

Here Sir William Hamilton did a real service to logic in pointing out that " Logic postulates to be allowed to state explicitly in language all that is implicitly contained in the thought."

On the other hand, we may go too far in the opposite direction, as Hamilton did in proposing the universal quantification of the predicate.

It is remarkable that in Barbara, and therefore in many scientific deductions, to think the quantity of the predicate is not to the point either in the premises or in the conclusion; so that to quantify the propositions, as Hamilton proposes, would be to express more than a rational man thinks and judges.

Beneath Hamilton's postulate there is a deeper principle of logic - _A rational being thinks only to the point, and speaks only to understand and be understood.

Lotze's mistake is the same as that of Hamilton about the quantification of the predicate, and that of those symbolists who held that reasoning ought always to exhaust all alternatives by equations.

It is because of the failure of this endeavour to bring the technique of induction within the setting of his Humian psychology of belief that the separation of his contribution to the applied logic of science from his sensationism became necessary, as it happily 1 Mill, Examination of Sir William Hamilton's Philosophy, cap. 17.

Stuart Mill, despite of his relation of antagonism to Hamilton and Mansel, who held themselves to be Kantian in spirit, is still wholly pre-Kantian in his outlook.

Among them it is on the whole impossible not to include the names of Hamilton and Mansel.

Hamilton's significance for the history of logic lies in the stimulus that he gave to the development of symbolic logic in England by his new analytic based upon his discovery or adoption of the principle of the quantification of the predicate.

And he was a clearer thinker than Hamilton.

By means of the doctrine of the quantification of the predicate, in which with his Leibnitzian conception of identity he anticipated Beneke and Hamilton alike, universal and particular judgments are made to pull together.

Hamilton was probably influenced by the recollection of its Greek equivalent, the Pythagorean Tetractys (TerpaKrt, the number four), the mystic source of all things.

Hamilton was led to his great invention by keeping geometrical applications constantly before him while he endeavoured to give a real significance to .,I - i.

He gave, in fact, the theory of what in Hamilton's system is called Composition of Vectors in one plane i.e.

Servois (Gergonne's Annales, 1813) a very remarkable comment, in which was contained the only yet discovered trace of an anticipation of the method of Hamilton.

Hamilton took this grand step, but, as we have already said, without any help from the previous work of De Moivre.

Hamilton, like most of the many inquirers who endeavoured to give a real interpretation to the imaginary of common algebra, found that at least two kinds, orders or ranks of quantities were necessary for the purpose.

Hence the simplest form of a set is a " couple "; and it was to the possible laws of combination of couples that Hamilton first directed his attention.

But Hamilton's special object required that these laws should be such as to lead to certain assumed results; and he therefore commenced by assuming these, and from the assumption determined how the separate time-steps must be involved in the couple.

Hamilton, still keeping prominently before him as his great object the invention of a method applicable to space of three dimensions, proceeded to study the properties of triplets of the form x+iy+jz, by which he proposed to represent the directed line in space whose projections on the co-ordinate axes are x, y, z.

But the interpretation of ij presented a difficulty - in fact the main difficulty of the whole investigation - and it is specially interesting to see how Hamilton attacked it.

Hence Hamilton was at first inclined to think that ij must be treated as nil.

Hamilton at once found that the Law of the Norms holds, - not being aware that Euler had long before decomposed the product of two sums of four squares into this very set of four squares.

Hamilton, having gone thus far, proceeded to evolve these results from a characteristic train of a priori or metaphysical reasoning.

Hamilton seems never to have been quite satisfied with the apparent heterogeneity of a quaternion, depending as it does on a numerical and a directed part.

Hamilton was not the only worker at the theory of sets.

The year after the first publication of the quaternion method, there appeared a work of great originality, by Grassmann," in which results closely analogous to some of those of Hamilton were given.

Hamilton and Grassmann, while their earlier work had much in common, had very different objects in view.

Hamilton had geometrical application as his main object; when he realized the quaternion system, he felt that his object was gained, and thenceforth confined himself to the development of his method.

But his claims, however great they may be, can in no way conflict with those of Hamilton, whose mode of multiplying couples (in which the " inner " and " outer " multiplication are essentially involved) was produced in 1833, and whose quaternion system was completed and published before Grassmann had elaborated for press even the rudimentary portions of his own system, in which the veritable difficulty of the whole subject, the application to angles in space, had not even been attacked.

But it is to be observed that Grassmann, though he virtually accused Cauchy of plagiarism, does not appear to have preferred any such charge against Hamilton.

He does not allude to Hamilton in the second edition of his work.

But in 1877, in the M athematische Annalen, xii., he gave a paper " On the Place of Quaternions in the Ausdehnungslehre," in which he condemns, as far as he can, the nomenclature and methods of Hamilton.

More general systems, having close analogies to quaternions, have been given since Hamilton's discovery was published.

When that is done, the full value of Hamilton's grand step becomes evident, and the gain is quite as extensive from the practical as from the theoretical point of view.

Hamilton, in fact, remarks, 2 " regard it as an inelegance and imperfection in this calculus, or rather in the state to which it has hitherto been unfolded, whenever it becomes, or seems to become, necessary to have recourse.

And one of Hamilton's earliest advances in the study of his system (an advance independently made, only a few months later, by Arthur Cayley) was the interpretation of the singular operator q()q1, where q is a quaternion.

Even in Hamilton's earlier work it was shown that all such questions were reducible to the solution of linear equations in quaternions; and he proved that this, in turn, depended on the determination of a certain operator, which could be represented for purposes of calculation by a single symbol.

Here, then, is a case specially adapted to the isotropy of the quaternion system; and Hamilton easily saw that the expression i d x +j - + k dz could be, like ix+jy+ kz, effectively expressed by a single letter.

In octonions the analogue of Hamilton's vector is localized to the extent of being confined to an indefinitely long axis parallel to itself, and is called a rotor; if p is a rotor then wp is parallel and equal to p, and, like Hamilton's vector, wp is not localized; wp is therefore called a vector, though it differs from Hamilton's vector in that the product of any two such vectors wp and coo- is zero because w 2 =o.

At the lower end of the west water-front, facing the Narrows, are a United States reservation and the harbour defences of Fort Hamilton.

Here are hotels, large apartment-houses, many private residences and a number of clubs, including the Brooklyn, the Crescent, the Hamilton, the Jefferson and the Germania.

From the same entrance Fort Hamilton Parkway extends 41 m.

After graduating at Hamilton College in 1818, he assumed the management of the vast estate of his father, Peter Smith (1768-1837), long a partner of John Jacob Astor, and greatly increased the family fortune.

Brodick Castle, the ancestral seat of the dukes of Hamilton, is a splendid mansion on the northern shore of Brodick Bay.

Virginia and Maryland promised such a cession; President Washington was known to be in favour of a site on the Potomac, and in July 1790 Alexander Hamilton, in return for Thomas Jefferson's assistance in passing the bill for the assumption of the state war debts by the Federal government, helped Jefferson to pass a bill for establishing the capital on the Potomac, by which the president was authorized to select a site anywhere along the Potomac between the Eastern Branch (Anacostia) and the Conococheague river, a distance of about So m., and to appoint three commissioners who under his direction should make the necessary surveys and provide accommodations for the reception of Congress in r800.

In 1848 he was nominated for governor of New York by the Free Soil party, but was defeated by Hamilton Fish.

Bossuet and the old-fashioned divines had believed in an elaborate system of checks and balances - popes, councils, bishops, temporal sovereigns each limiting and controlling the other - just as Montesquieu and Alexander Hamilton had believed in a careful separation of the executive from the legislative power.

In April 1754 Townshend was transformed from the position of a member of the board of trade, which he had held from 1749, to that of a lord of the admiralty, but at the close of 1 755 his passionate attack against the policy of the ministry, an attack which shared in popular estimation with the scathing denunciations of Pitt, the supreme success of Single-Speech Hamilton, and the hopeless failure of Lord Chesterfield's illegitimate son, caused his resignation.

The consequence was that the two leading members of the cabinet, Alexander Hamilton and Thomas Jefferson, exponents for the most part of diametrically opposite political doctrines, soon occupied the position, to use the words of one of them, of "two game-cocks in a pit."

The people of South Carolina were not satisfied, and Calhoun in a third political tract, in the form of a letter to Governor James Hamilton (1786-1857) of South Carolina, gave his doctrines their final form, but without altering the fundamental principles that have already been stated.

Hamilton was appointed agent to the governorgeneral.

James Sharp, Fairfoul, James Hamilton (1610-1674) and Robert Leighton were the new bishops; Sharp and Leighton having to be ordained as deacons, then as priests, before the consecration, and the party travelling to Scotland in state, though Leighton left them before crossing the border.

Troy is served by the Cleveland, Cincinnati, Chicago & St Louis and the Cincinnati, Hamilton & Dayton railways, and by the Dayton & Troy and the Springfield, Troy & Piqua electric inter-urban lines.

James V., the '"Commons' King" had put himself into the hands of the Beatons, who in 1528 burned Patrick Hamilton.

Knox's objections to the "regiment of women" were theoretical, and in the present case he hoped at first for the best, favouring rather his queen's marriage with the heir of the house of Hamilton.

In 1550 he was sent to Rome in the interests of John Hamilton, archbishop of St Andrews, and attracted the notice of the highest authorities, who, when his failing health drove him back to Scotland in 1558, nominated him papal nuncio to inquire into the spread of heresy in that country.