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In 1720 Colin Maclaurin, the successor of James Gregory in the mathematical chair at Edinburgh, published his "Geometrical Organica," a treatise on curves; in 1742 his admirable treatise on Fluxions; and in 1748 his treatise on Algebra. Dr. Robert Simson, professor of mathematics at Glasgow, published a restoration of the "Loci" of Apollonius, and an English translation of Euclid, which continued down to a late period in use, both in Scotland and England. In 1717 James Stirling published a Latin treatise on lines of the third order, and another on Fluxions, called "Methodus Differentialis," in 1730. William Emerson, a mathematician and mechanist, wrote on fluxions, trigonometry, mechanics, navigation, algebra, optics, astronomy, geography, dialling, etc., but a considerable portion was only in part published during this period. Thomas Simpson, a weaver, of Market Bosworth, at the age of seven-and-twenty suddenly discovered himself as an extraordinary mathematician, and went on till his death, in 1761, publishing works on fluxions, the nature and laws of chance, on mixed mathematics, on the doctrine of annuities and reversions, on algebra, elementary geometry, trigonometry, etc. James Ferguson, also, the son of a day-labourer, in Banffshire, studied mathematics whilst tending sheep, and published a number of works on the phenomena of the harvest moon, astronomy, mechanics, hydrostatics,[154] pneumatics, and optics. Ferguson had a remarkably lucid and demonstrative style, both in writing and lecturing, and his example excited a keen spirit of inquiry amongst the working classes, so that he is said to have diffused the knowledge of physical science amongst the class from which he sprang more than any other man.

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DEPARTURE OF THE BRITISH TROOPS FROM ALEXANDRIA. (See p. 539.)Napoleon, seeing that Bernadotte was become King of Sweden contrary to his secret will and to his expectations, determined, however, that he should still serve him. He gave him no respite. He demanded incessantly, and with his usual impetuosity, that Bernadotte should declare war against Great Britain and shut out of the Baltic both British and American merchandise. Alexander regarded him first with suspicion but his spies soon dissipated his fears. They soon perceived that Bernadotte was not disposed to be at once master of a powerful kingdom and the vassal of France. Alexander made offers of friendship; they were accepted by Bernadotte with real or affected pleasure, and his course became clearer. For the next two years there was a great strife to secure the alliance of the Crown Prince; and the proud, disdainful, imperious temper of Napoleon, who could not brook that one who had been created by him out of nothing but a sergeant of marines should presume to exercise an independent will, threw the prize into the hands of the more astute Russian, and decided the fate of Europe and of himself.But, scarcely had Howe posted himself at Wilmington, when Washington re-crossed the Schuylkill and marched on the British left, hoping to imitate the movement of Cornwallis at the Brandywine which had been so effectual. Howe, aware of the strategy, however, reversed[239] his front, and the Americans were taken by surprise. In this case, Howe himself ought to have fallen on the Americans, but a storm is said to have prevented it, and Washington immediately fell back to Warwick Furnace, on the south bank of French creek. From that point he dispatched General Wayne to cross a rough country and occupy a wood on the British left. Here, having fifteen hundred men himself, he was to form a junction with two thousand Maryland militia, and with this force harass the British rear. But information of this movement was given to Howe, who, on the 20th of September, sent Major-General Greig to expel Wayne from his concealment. Greig gave orders that not a gun should be fired, but that the bayonet alone should be used, and then, stealing unperceived on Wayne, his men made a terrible rush with fixed bayonets, threw the whole body into consternation, and made a dreadful slaughter. Three hundred Americans were killed and wounded, about a hundred were taken prisoners, and the rest fled, leaving their baggage behind them. The British only lost seven men.
ONE:These vexatious proceedings, including a great number of debates and divisions, led to the passing of an Act for more clearly defining the privileges of the House of Commons, which had made itself unpopular by its course of proceeding towards the sheriffs, who had only discharged duties which they could not have evaded without exposing themselves to the process of attachment. On the 5th of March, accordingly, Lord John Russell moved for leave to bring in a Bill relative to the publication of Parliamentary papers. He said, in the course of his speech, that at all periods of our history, whatever might have been the subjectwhether it regarded the privileges of Parliament or the rights of the Crown or any of the constituted authoritieswhenever any great public difficulty had arisen, the Parliament in its collective sense, meaning the Crown, Lords, and Commons, had been called in to solve those difficulties. With regard to the measure he was about to propose, he would take care to state in the preamble of the Bill that the privilege of the House was known only by interpretation of the House itself. He proposed that publications authorised by either House of Parliament should be protected, and should not be liable to prosecution in any court of common law. Leave was given to introduce the Bill by a majority of 149, in spite of the opposition of the Solicitor-General, Sir Thomas Wilde; the House went into committee on the Bill on the 13th of March, and it passed the third reading on the 20th of the same month. It was read a second time in the Lords on the 6th of April; and the Royal Assent was given to it by commission on the 14th of the same month. THREE:In America, all at the opening of the campaign seemed to favour the English cause. The army of Washington, still suffering the utmost extremities of cold and starvation, began in earnest to mutiny. A Pennsylvanian division of one thousand three hundred men marched out of their camp at Morristown, and proceeded to Princeton, carrying with them six field-pieces and their stores, and their demands were granted by Congress. The success of this revolt encouraged others to repeat the man?uvre. On the night of the 20th of January a part of the Jersey brigade, stationed at Pompton, marched to Chatham, and made precisely the same demands. But now seeing that, if this were suffered, the whole army would quickly go to pieces, Washington sent General Howe after them, with orders to surround them, and shoot them down, if they did not surrender; and if they did surrender, immediately to seize the most active ringleaders, and execute them. Howe readily accomplished his mission; he reduced the mutinous, and shot their leaders.In the debate on this subject, George Canning, who on many occasions had shown himself capable of better things, breathed the very language of Toryism. He declared the representation of Parliament perfect, and treated the most moderate proposals for Reform as only emanations from the mad theories of the Spenceans. The message of the Prince Regent came down on the 3rd of February, ordering certain papers to be laid before the House, "concerning certain practices, meetings, and combinations in the metropolis, and in different parts of the kingdom, evidently calculated to endanger the public tranquillity, to alienate the affections of his Majesty's subjects from his Majesty's person and Government, and to bring into hatred and contempt the whole system of our laws and institutions." Lord Sidmouth endeavoured to guard the House of Peers against the belief that the insult to the Regent had any share in the origination of this message, but the House of Lords, in its Address, directly charged this event as an additional proof of the public disaffection. Unfortunately, the Regent had two Houses of Parliament only too much disposed to make themselves the instruments of such vengeance. The message was referred to a secret committee in each House, and on the 18th and 19th of February they respectively made their reports. Both went at great length into the affair of the Spa Fields meeting, and the proceedings and designs of the Spenceans were made to represent the designs of the working classes all over the kingdom; that such men as Thistlewood, who not long after suffered for his justly odious conduct, were conspicuous among the Spenceans, and that there had been an affray in Spa Fields, were circumstances to give ample colouring to the reports of these committees. The Lords' report stated"It appears clear that the object is, by means of societies, or clubs, established, or to be established, in all parts of Great Britain, under pretence of Parliamentary reform, to infect the minds of all classes of the community, and particularly of those whose[124] situation most exposes them to such impressions, with a spirit of discontent and disaffection, of insubordination, and contempt of all law, religion, and morality; and to hold out to them the plunder of all property as the main object of their efforts, and the restoration of their natural rights; and no endeavours are omitted to prepare them to take up arms, on the first signal, for accomplishing their designs."
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FORE:It was proposed also to form, in certain districts, relief committees, which should be empowered to receive subscriptions, levy rates, and take charge of donations from the Government; and that out of the fund thus raised they should establish soup kitchens, and deliver rations to the famishing inhabitants. Sir John Burgoyne, Inspector-General of Fortifications, was appointed to superintend the works. Lord John Russell referred to measures for draining and reclaiming waste land in Ireland, and to advances of money for this purpose to the proprietors, to be repaid in instalments spread over a number of years. On a subsequent day, in answer to questions from Mr. Roebuck, the noble lord gave a statement of the sums that had already been advanced. 2,000,000 had been issued on account of the Poor Employment Act of the last Session. He expected that not less than 500,000 or 600,000 a month would be spent from the present time until August, and he calculated the whole expenditure would not be less than 7,000,000. There was great difference of opinion on the subject of the Government plans. A counter-scheme for the establishment of reproductive works deserves to be noticed for the interest it excited and the attention it occupied for years afterwardsnamely, the railway plan of Lord George Bentinck. Acts of Parliament, he said, had been passed for 1,582 miles of railway in Ireland, of which only 123 miles had then been completed, while 2,600 miles had been completed in England. In order to encourage the formation of Irish railways, therefore, he proposed that for every 100 expended by the companies 200 should be lent by the Government at the same interest at which they borrowed the money, Mr. Hudson, who was "chairman of 1,700 miles of railroad," pledging his credit that the Government would not lose a shilling by the transaction. By adopting this plan they could give reproductive employment to 109,000 men in different parts of the country, for earth-works, fences, drains, and watercourses connected with the lines. This would give support of 550,000 souls on useful work, tend to develop the resources of the country, and produce such improvement that the railways constructed would add 23,000,000 to the value of landed property in twenty-five years, and would pay 22,500 a year to the poor rates. The purchase of land for the railways would moreover place 1,250,000 in the hands of Irish proprietors, for the employment of fresh labour, and 240,000 in the hands of the occupying tenants for their own purposes. The Government also would reap from the expenditure of 24,000,000 on railways in Ireland, an enormous increase of revenue in the augmented consumption of articles of excise and customs. The noble lord's speech, which lasted two hours and a half, was received with cheers from both sides of the House. Leave was given to bring in the Bill, though it was strongly objected to by Lord John Russell, Mr. Labouchere, and other members of the Government. It was also opposed by Sir Robert Peel, who exposed the unsoundness of the economic principles involved in it. The Bill was rejected by a majority of 204, the numbers being 118 for the second reading, and 322 against it. Notwithstanding this decision, loans were subsequently advanced to certain Irish railways, amounting to 620,000, so that the objection of the Government was more to the extent than to the principle of Lord George Bentinck's measure.

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FORE:Lord John Russell was immediately summoned from Scotland, and on the 11th arrived at Osborne, where he received her Majesty's commands to form a Government. On the ground that his party were in a minority in the House of Commons, Lord John Russell at first declined the honour presented to him; but on a paper being placed in his hands by the Queen, in which Sir Robert Peel promised, in his private capacity, to aid and give every support to the new Ministry in settling the question of the Corn Laws, he undertook the task. There was no amicable feeling between the new and the retiring Minister. Lord John Russell's letter, published a few days before, had excited as much attention for its bitter sarcasm against Sir Robert Peel as for the important change in the Whig policy which it announced. Lord John Russell held communication with the late Government, but through Sir James Graham. It was of importance to him to know more clearly the nature of that support which Sir Robert Peel's memorandum seemed to promise; and he was, therefore, anxious to know what the latter would consider a satisfactory settlement. This proposal, however, to the late Minister to become responsible for the measures of his successors was declined. Sir James Graham communicated to Lord John Russell the information as to the state of the country on which they acted; but Sir Robert Peel, through his colleague, declined to state the details of the measures which had lately been contemplated. Lord John Russell then gave, in writing, an outline of the measures which the new Cabinet would propose, and invited the opinion of the late Minister. Sir Robert Peel, however, still declined to take part in the plans of his opponents; and in a letter to the Queen, on the 17th of December, he stated the constitutional grounds on which he considered it improper that any one, not an adviser of the Crown, should take a part in the preparation of Ministerial measures. Lord John Russell thereupon immediately proceeded with his negotiations with his own party. It soon, however, appeared that the task he had proposed to himself was beyond his power. Earl Grey, who had agreed to take the Secretaryship of the Colonies in the new Ministry, suddenly declared that he would not join any Administration in which Lord Palmerston should hold the office of Secretary for Foreign Affairs. This unexpected accident was regarded by Lord John Russell as decisive. On the 20th of December he communicated the facts to the Queen, and begged to be relieved from the task he had undertaken.

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FORE:Pitt had returned to office in anything but promising circumstances. Britain was at war with a great nation, and as yet the coalition which he was laboriously building up was far from being complete. Pitt's health was failing: his energies were prematurely worn out by the gigantic task that was forced upon him; his end was fast approaching, and his majority was shrunk and attenuated to an alarming degree. The Fox and Grenville opposition held together firmly, and Addington had carried a strong party along with him on retiring. Pitt felt his situation keenly and the king was sensibly alarmed at it. He attempted to conciliate Grenville, but, as Fox could not be accepted too, that failed. He then turned to Addington, and as the king was favourably disposed to his old minister, he warmly recommended this coalition. It was effected, and Addington was made a peerViscount Sidmouth, of Sidmouth. This was one of those rapid political promotions of George III.'s reign in which politics were made to ennoble men of no particular mark or abilities; and certainly the son of Pitt's father's doctor had never shown those splendid talents or rendered those brilliant services which justified such an elevation. But, as Pitt would take the lead in the Commons, it was, no doubt, felt more convenient that one who had lately been Prime Minister should not serve under the present Prime Minister, but should represent the Cabinet in the Upper House. There were some other changes at the same time. The Duke of Portland, who was growing old and infirm, retired from the post of President of the Council, which Sidmouth took up. Lord Harrowby, a warm friend of Pitt, retired, in consequence of continued illness, from the Foreign Department, and Lord Mulgrave took it, the Earl of Buckinghamshire succeeding to Lord Mulgrave's post as Chancellor of the Duchy of Lancaster.

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FORE:At length, after much mischievous delay, the Government ventured to lay hands upon the disseminators of sedition and the organisers of rebellion. On the 13th of May John Mitchel was arrested and committed to Newgate. On the 15th, Mr. Smith O'Brien, who had been previously arrested and was out on bail, was brought to trial in the Queen's Bench, and arraigned on ex officio information as being a wicked, seditious, and turbulent person, and having delivered a speech for the purpose of exciting hatred and contempt against the Queen in Ireland, and inducing the people to rise in rebellion. He was defended by Mr. Butt, a Conservative barrister, who spoke of the ancient lineage and estimable character of the prisoner, concluding thus:"Believe me, gentlemen, all cannot be right in a country in which such a man as William Smith O'Brien is guilty, if guilty you pronounce him, of sedition." At the conclusion of this sentence the majority of the bar, and of the people in court, rose from their seats and loudly cheered, the ladies in the galleries waving their handkerchiefs. The jury were locked up all night without refreshments, but they could not agree. The next day Meagher was tried, with a similar result, and was hailed by a cheering multitude outside, whom he addressed from a window in the Nation office. Mitchel, however, was tried, found guilty, and sentenced to transportation for fourteen years; he was immediately conveyed in the police prison van to a small steamer which waited in the bay, and then to a man-of-war which conveyed him to Bermuda.

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Napoleon dispatched Murat with his cavalry, Junot, Ney, and Davoust, in pursuit of the Russians, whom they overtook at a place called Valoutina, where a desperate battle was fought, and many men were killed on both sides; but the Russians moved off again without the loss of guns, prisoners, or baggage. Buonaparte, on proceeding to the spot, blamed Junot, imputing to him want of activity in the action, and threatening to deprive him of his command. The whole road between Smolensk and Valoutina was strewn with the dead and wounded; and as he entered the city on his return, he met whole tumbrils of amputated limbs going to be thrown away at a distance. The scene is said to have overcome even his senses, so long hardened to human suffering. On the 24th of August he marched forward to Gjatsk, where his advanced guard had halted. There he learned, to his great satisfaction, from a Frenchman long resident in Russia, that the people and the new levies, impatient of continual retreat and the ravage of their country, had demanded that Barclay de Tolly, a German, whom they imagined not sufficiently careful of Russian property and interests, should be superseded by the old general, Kutusoff, and that they should stand and fight. This was precisely what Buonaparte wanted, and the prudent De Tolly knew to be little better than madness, as it must cause a fearful loss of life, and would not rid the country of the invader, who was better left to starvation and the elements. But Alexander, though of De Tolly's opinion, gave way, and the Russians entrenched themselves on the heights of Borodino, De Tolly most magnanimously continuing to serve under Kutusoff. There, after a march of two hundred and eighty versts in seventeen days, the French came up with them; and, after a halt of two days, they attacked the Russian lines.In the trying circumstances in which they were placed, Lord Grey and his colleagues displayed a firmness and courage which entitled them to the everlasting gratitude of the country. The pluck of Lord John Russell in particular had quite an inspiriting effect on the nation. Replying to a vote of thanks to him and Lord Althorp, which had been passed by the Birmingham Political union, the noble Paymaster of the Forces used an antithetical expression, which has become historical, and which, considering that the faction to which he alluded was the majority of the order to which he himself belonged, must be admitted to be one of extraordinary boldness. He said: "I beg to acknowledge with heartfelt gratitude the undeserved honour done me by 150,000 of my countrymen. Our prospects are now obscured for a moment, and I trust only for a moment. It is impossible that the whisper of faction should prevail against the voice of the nation." Colonel B. Heneker, a regiment, and 3,500 a-year for his seat.
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