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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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The fire raged with unabated fury from the 14th till the 19thfive days. Then the city lay a heap of burning ashes. All the wealth which was left behind was burnt or melted down. But there could be no stay at Moscow, for all their provisions had to be brought from distant districts by water carriage in summer, and on sledges in winter. But, as the Russian population had fled, the Russians were only too glad to starve out the French. Not a single article of food came near the place. Alexander returned no answer to Buonaparte's letter. The pledge which he might have made some concessions to redeem had been destroyed by his own orders, and Buonaparte had now nothing to offer worthy of his attention. He and his army were awaiting the attack of the wintry elements to join them in the extermination of the invaders. Buonaparte dispatched General Lauriston to Alexander with fresh offers; but Alexander refused to see him, and turned him over to Kutusoff, who flattered him with hopes and professions of desire for peace, in order to put off the time, for every day nearer to winter was a[48] day gained of incalculable importance. But he said that he must send Napoleon's letter to St. Petersburg, to the Czar, and await his reply. This was on the 6th of October, and the reply could not be received before the 26th; there was nothing for it but to wait, and Lauriston waiteda fatal delay for the French!The noble marquis was regarded by Mr. Peel with the most sincere respect and esteem, which were cordially reciprocated. In a letter dated January 30th, 1828, Lord Wellesley wrote to him thus:"Your most acceptable letter of the 29th instant enables me to offer to you now those assurances of gratitude, respect, and esteem which, to my sincere concern, have been so long delayed. Although these sentiments have not before reached you in the manner which would have been most suitable to the subject, I trust that you have not been unacquainted with the real impressions which your kindness and high character have fixed in my mind, and which it is always a matter of the most genuine satisfaction to me to declare. I am very anxious to communicate with you in the same unreserved confidence so long subsisting between us on the state of Ireland."

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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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The fire raged with unabated fury from the 14th till the 19thfive days. Then the city lay a heap of burning ashes. All the wealth which was left behind was burnt or melted down. But there could be no stay at Moscow, for all their provisions had to be brought from distant districts by water carriage in summer, and on sledges in winter. But, as the Russian population had fled, the Russians were only too glad to starve out the French. Not a single article of food came near the place. Alexander returned no answer to Buonaparte's letter. The pledge which he might have made some concessions to redeem had been destroyed by his own orders, and Buonaparte had now nothing to offer worthy of his attention. He and his army were awaiting the attack of the wintry elements to join them in the extermination of the invaders. Buonaparte dispatched General Lauriston to Alexander with fresh offers; but Alexander refused to see him, and turned him over to Kutusoff, who flattered him with hopes and professions of desire for peace, in order to put off the time, for every day nearer to winter was a[48] day gained of incalculable importance. But he said that he must send Napoleon's letter to St. Petersburg, to the Czar, and await his reply. This was on the 6th of October, and the reply could not be received before the 26th; there was nothing for it but to wait, and Lauriston waiteda fatal delay for the French!The noble marquis was regarded by Mr. Peel with the most sincere respect and esteem, which were cordially reciprocated. In a letter dated January 30th, 1828, Lord Wellesley wrote to him thus:"Your most acceptable letter of the 29th instant enables me to offer to you now those assurances of gratitude, respect, and esteem which, to my sincere concern, have been so long delayed. Although these sentiments have not before reached you in the manner which would have been most suitable to the subject, I trust that you have not been unacquainted with the real impressions which your kindness and high character have fixed in my mind, and which it is always a matter of the most genuine satisfaction to me to declare. I am very anxious to communicate with you in the same unreserved confidence so long subsisting between us on the state of Ireland."
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THREE:Whilst these movements had been progressing, very different ones had been in development in the north. The British Government, with the fatality which distinguished nearly all its counsels in this war, had thought proper to take the command of the army destined to operate by way of Canada on the northern colonies, from Sir Guy Carleton, and to confer it on General Burgoyne. The campaign had been plannednot by experienced military men on the spot, capable of estimating the difficulties of the enterprise, but in the Cabinet at home, directed by defective maps, and still more defective information.
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THREE:Howe, who, with seven thousand soldiers and more than one thousand sailors, did not feel himself safe at New York till the new reinforcements should arrive, sailed away to Halifaxa circumstance which gave the appearance of a retreat to his change of locality, and had thus a bad effect in more ways than one. Washington, who was informed of his final destination, immediately marched with the greater part of his army to New York, and thence went himself to Philadelphia to concert future measures with the Congress. This body, in commemoration of the surrender of Boston, ordered a medal to be struck in honour of it, and that it should bear the effigy of Washington, with the title of the Asserter of the Liberties of his Country. The medal was cast in France.
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THREE:SCENE AT THE "SURRENDER" BANQUET IN DERRY. (See p. 287.)The active mind, strong will, and philanthropic spirit of Mr. Stanley, now transferred from Ireland to the Colonial Secretaryship, found an important field for their exercise in the Colonial Office. He applied his energies to the abolition of negro slavery in the West Indies, and was happily more successful in that work than in his attempt to tranquillise Ireland. The time had arrived when the labours on behalf of the negro race, of Clarkson, Wilberforce, Mackintosh, Brougham, Buxton, Lushington, and William Smith were to be followed with success, by the abolition of slavery in the British West Indian colonies. The Society of Friends, as became that philanthropic body, led the van in the movement which began in 1823, when Wilberforce presented a petition from them in the House of Commons. Soon afterwards, when Mr. Buxton brought forward a resolution condemning slavery as repugnant to Christianity and to the British Constitution, Mr. Canning moved a counter-resolution as an amendment, recommending reforms in the system, which, he alleged, might be safely left to the West Indian Assemblies; and if they refused to do their duty, the Imperial Parliament might then interfere. These resolutions were carried, although any one acquainted with the history of the West Indies might have known that they would be perfectly futile. No amelioration of the system could be rationally expected from the reckless adventurers and mercenary agents by whom many West Indian plantations were managed. The infamous cruelty of which the missionary Smith had been the victim showed that, while the colonial laws allowed the most horrible atrocities, there existed among the planters a spirit of brutality which did not shrink from their perpetration. Time was when such barbarities might have escaped with impunity; when in Great Britain it was maintained in high places, and even by the legislature, that slavery was defended by an impregnable fortress, that property in human flesh was not only expedient for the good of the commonwealth, and beneficial for the negro, but also a sacred institution, founded on the authority of the Bible. But, thanks to the indefatigable labours of the friends of the negro race, such abominable dogmas had been long reprobated by public opinion, and at the period now referred to no man ventured to promulgate such heresies in England. The moral sense of the nation had condemned slavery in every form. The missionaries had, in the midst of tremendous difficulties and cruel persecutions, enlightened the West Indian slaves with regard to their rights as men and their privileges as Christians; and while they inculcated patience and meek submission even to unjust laws, they animated their crushed hearts with the hope that the blessings of liberty would soon be enjoyed by them, and that humanity and justice would speedily triumph over the ruthless tyranny under which they groaned.
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THREE:Meanwhile the aspect of foreign affairs was hardly reassuring. Britain was at war with China and Afghanistan, and within measurable distance of war with France and the United States. Postponing for the present our review of the first Afghan war and the differences with America, which will be dealt with more properly under the history of Sir Robert Peel's Ministry, we proceed to give a short sketch of the Chinese war and the Syrian crisis. The exclusive right of the East India Company to trade with China ceased on the 22nd of April, 1834, and from this time dates the great dispute about the opium traffic. The first free-trade ship sailed from England on the 25th of the same month. Lord Napier was sent out to China to superintend British commerce, and arrived at Macao on the 15th of July. He died soon after his arrival, and was succeeded by Mr., afterwards Sir, John Davis. But the Chinese were not disposed to recognise the authority with which he was vested. During 1835 and 1836 matters went on peaceably under the superintendence of the second and third Commissioners, Mr. Davis and Sir T. Robinson, the former of whom returned to England, and the latter was superseded by Captain Elliot, R.N., who in vain renewed the attempt to establish an official connection with the Chinese authorities. The opening of the trade in 1834 gave a powerful stimulus to all kinds of smuggling, and especially in opium, the importation of which into China was prohibited by the Imperial Government, in consequence of its deleterious qualities. During the following years, however, the supply of that drug was increased enormously, and the smuggling trade was carried on along the coasts of the northern provinces, in defiance of the laws of the country. The Imperial Government was naturally indignant at these encroachments, and became, moreover, seriously alarmed, perhaps not so much for its demoralising effects, as for the continued drain of specie which it occasioned. In March, 1839, Lin arrived at Canton, as Imperial High Commissioner, to enforce the laws in this matter. He immediately issued an edict requiring that every chest of opium on the river should be delivered up, in order to be destroyed; and that bonds should be given by traders that their ships should never again bring any opium, on pain of forfeiture of the article and death to the importer. Lin having taken strong measures to carry this edict into effect by blockading the British merchants, Captain Elliot proceeded to Canton, and issued a circular letter to his countrymen, requiring them to surrender into his hands all the opium then actually on the coast of China, and holding himself responsible for the consequences. On the 21st of May the whole of the opium, to the amount of 20,283 chests, was given up to the Chinese Government, and immediately destroyed. But even this great sacrifice did not propitiate Commissioner Lin. On the 26th of November he issued another interdict, ordering the cessation of all trade with British ships in a week; and in January, 1840, an Imperial edict appeared directing that all trade with Britain should cease for ever. Further numerous outrages were committed by the Chinese against British sailors. In consequence of these proceedings an armament was sent forth to teach the Chinese the principles of international law. The first part of the armament reached the Canton river in June, 1840, under the command of Captain Elliot. Having established a rigorous blockade in the river, the British, on the 5th of July, took possession of the large island of Chusan, in the Eastern Sea. It proved very unhealthy, and one man out of every four died. Proceeding still farther to the mouth of the Peiho, in the Yellow Sea, Captain Elliot attempted to overawe the Chinese. But the sea was too shallow to enable him to land his troops, and he was forced to put back to Chusan.
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    TWO:Yet, on the first view of the case, the selection of the Swedes augured anything but a Russian alliance; and showed on the surface everything in favour of Napoleon and France, for it fell on a French general and field-marshal, Bernadotte. The prince royal elect made his public entry into Stockholm on the 2nd of November. The failing health of the king, the confidence which the talents of Bernadotte had inspired, the prospect of a strong alliance with France through himall these causes united to place the national power in his hands, and to cast upon him, at the same time, a terrible responsibility. The very crowds and cries which surrounded him expressed the thousand expectations which his presence raised. The peasantry, who had heard so much of his humble origin and popular sentiments, looked to him to curb the pride and oppression of the nobles; the nobles flattered themselves that he would support their cause, in the hope that they would support him; the mass of the people believed that a Republican was the most likely to maintain the principles of the Revolution of 1809; the merchants trusted that he would be able to obtain from Napoleon freedom for trade with Great Britain, so indispensable to Sweden; and the[7] army felt sure that, with such a general, they should be able to seize Norway and re-conquer Finland. Nor was this all. Bernadotte knew that there existed a legitimist party in the country, which might long remain a formidable organ in the hands of internal factions or external enemies. How was he to lay the foundation of a new dynasty amid all these conflicting interests? How satisfy at once the demands of France, Britain, and Russia? Nothing but firmness, prudence, and sagacity could avail to surmount the difficulties of his situation; but these Bernadotte possessed.
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At the point at which our former detail of[316] Indian affairs ceased, Lord Clive had gone to England to recruit his health. He had found us possessing a footing in India, and had left us the masters of a great empire. He had conquered Arcot and other regions of the Carnatic; driven the French from Pondicherry, Chandernagore, and Chinsura; and though we had left titular princes in the Deccan and Bengal, we were, in truth, masters there; for Meer Jaffier, though seated on the throne of Bengal, was our mere instrument.There remain only the trials of Hunt and his associates in the meeting at Manchester to close the events which arose out of circumstances originating under the reign of George III. These took place at York spring assizes, whither they had been prudently removed out of the district where both parties were too much inflamed for a fair verdict to be expected. During the time that they lay in prison the conduct of Hunt had greatly disgusted his humble associates. He[156] showed so much love of himself that Bamford says he began to think that he could never have really loved his country. The Government had found it necessary a second time to lower its charge against the Manchester prisoners. At first it was high treason, then it subsided to treasonable conspiracy, and now, at last, it was merely "for unlawful assembling for the purpose of moving and inciting to hatred and contempt of the Government." Of this they were all convicted, and were confined in different gaols for various periods, and were called upon to give substantial security for good behaviour in future before being set at liberty. Hunt was imprisoned for three years in Ilchester gaol. It is only justice to him to state that though, during this imprisonment, he was continually sending to the newspapers complaints of ill treatment, he was instrumental in making known to the public some flagrant malpractices going on in the gaol, and which, through these exposures, were afterwards corrected.[77]The campaign in Flanders commenced with the highest expectation on the part of England. Cumberland had now obtained the great object of his ambitionthe command of the Allied army; and the conqueror of Culloden was confidently expected to show himself the conqueror of Marshal Saxe and of France. But Cumberland, who was no match for Marshal Saxe, found the Dutch and Austrians, as usual, vastly deficient in their stipulated quotas. The French, hoping to intimidate the sluggish and wavering Dutch, threatened to send twenty thousand men into Dutch Flanders, if the States did not choose to negotiate for a separate peace. The menace, however, had the effect of rousing Holland to some degree of action. When the vanguard of Saxe's army, under Count L?wendahl, burst into Dutch Flanders, and reduced the frontier forts of Sluys, Sas-van-Ghent, and Hulst, the Dutch rose against their dastardly governors, and once more placed a prince of the House of Nassau in the Stadtholdership. William of Nassau, who had married Anne, daughter of George II. of England, was, unfortunately, not only nominated Stadtholder, but Captain-General and Lord High Admiral; and, being equally desirous of martial glory with his brother-in-law, the Duke of Cumberland, he headed the Dutch army, and immediately began to contend with Cumberland for dictation as to the movements of the army. In these disastrous circumstances, the Allies came to blows with the French at the village of Laufeldt, before Maestricht. The Dutch in the centre gave way and fled; the Austrians on the right, under Marshal Batthyani, would not advance out of their fortified position; the brunt of the whole onset, therefore, fell upon the English. Cumberland found himself engaged with the whole French army, directed by the masterly mind of Saxe, and animated by the presence of Louis himself. The dispositions of Cumberland were bad, but the bravery of the British troops was never more remarkable. Though it was impossible for them to prevail against such overwhelming numbers, they did not retreat before they had, according to Saxe's own acknowledgment, killed or wounded nine thousand of the French.The Government of Spain was sunk into the very deepest degradation and imbecility. Charles IV. was one of the weakest of Bourbon kings. He was ruled by his licentious wife, Maria Luiza, and she by Manuel de Godoy, a young and handsome man, who, about the year 1784, had attracted her eye as a private in the Royal Guards. By her means he was rapidly promoted, and at the age of twenty-four was already a general. He was soon created a Grandee of Spain, and the queen married him to a niece of the king. He was made Generalissimo of all the Spanish Forces, and, in fact, became the sole ruling power in the country. He was styled the Prince of the Peacea title acquired by his having effected the pacification of Basle, which terminated the Revolutionary War between France and Spain. By the subsequent Treaty of St. Ildefonso he established an offensive and defensive alliance with France, which, in truth, made Spain entirely subservient to Napoleon.ALEXANDER I.
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