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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.[See larger version]
THREE:It must be confessed that it was impossible to keep peace with a nation determined to make war on the whole world. Perhaps on no occasion had the pride of the British people and their feelings of resentment been so daringly provoked. War was proclaimed against Britain, and it was necessary that she should put herself in a position to protect her own interests. The country was, moreover, bound to defend Holland if assaulted. But though bound by treaty to defend Holland, Great Britain was not bound to enter into the defence of all and every one of the Continental nations; and had she maintained this just line of action, her share in the universal war which ensued would have been comparatively insignificant. Prussia, Russia, and Austria had destroyed every moral claim of co-operation by their lawless seizure of Poland, and the peoples of the Continent were populous enough to defend their own territories, if they were worthy of independence. There could be no just claim on Britain, with her twenty millions of inhabitants, to defend countries which possessed a still greater number of inhabitants, especially as they had never been found ready to assist us, but on the contrary. But Britain, unfortunately, at that time, was too easily inflamed with a war spirit. The people as well as the Government were incensed at the disorganising and aggressive spirit of France, and were soon drawn in, with their Quixotism of fighting for everybody or anybody, to league with the Continental despots for the purpose not merely of repelling French invasions, but of forcing on the French a dynasty that they had rejected.

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THREE:Affairs had now assumed such an aspect that the different sections of the Opposition saw the necessity of coalescing more, and attending zealously; but still they were divided as to the means to be pursued. A great meeting was held on the 27th of November at the Marquis of Rockingham's, to decide on a plan of action. It was concluded to move for a committee on the state of the nation, and Chatham being applied to, advised that the very next day notice should be given that such a motion should be made on Tuesday next, the 2nd of December. The motion was made, the committee granted, and in it the Duke of Richmond moved for the production of the returns of the army and navy in America and Ireland. Whilst Lord Northwho, if he had been his own master, would have resignedwas refusing to produce the necessary papers, the Lords consented to this measure; and at this very moment came news of the surrender at Saratoga, which was speedily confirmed.

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THREE:

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TWO:It was agreed between the Catholic Powers that the Papal territory should be invaded at the same time by Neapolitan, Austrian, and French troops. France was determined to have the chief part, and, if possible, all the glory of the enterprise. Odillon Barrot, President of the Council, explained the objects of the French expedition, on the 16th of April. The Minister demanded extraordinary credit for the expenses of the expedition. It was promptly voted without any opposition, save some murmurs from the Left. An expedition was immediately organised, and an army, 6,000 strong, was embarked at Marseilles, with astounding celerity, on the 22nd of April, 1849, under the command of General Oudinot. But the Romans had no confidence in their professed protectors. On the contrary, they set about making all possible preparations for the defence of the city. In consequence of the hints he had got, however, Oudinot sent forward a reconnoitring party, which was saluted with a fire of artillery, certainly not meant as a feu de joie. The French general then ordered an attack upon two gates, the Portese and San Pancrazio, both on the right bank of the Tiber. The Romans repelled them at both points with a discharge of grape-shot, and they were compelled to retire with heavy loss; General Garibaldi, with his Lombard legion, having surrounded a retreating column, and made 200 prisoners. After this mortifying repulse, Oudinot retired to Palo, near Civita Vecchia, to await reinforcements, in order to enable him to vindicate the honour of the French arms, which could now be done only by the capture of Rome; and the French Government were probably not sorry to have this pretext for their unwarrantable course of aggression. In the meantime reinforcements were rapidly sent from Toulon. During this period a Neapolitan army, 16,000 strong, commanded by the king in person, had entered the States of the Church. Garibaldi, disregarding the orders of Roselli, went forth to meet the invaders, fell upon them with the suddenness of a thunderbolt, won a victory over them, and compelled them to retreat. All negotiations having failed, the French general commenced a regular siege. The city was cannonaded from the 11th to the 21st of June, when Garibaldi assured the Triumvirs that the defence was no longer possible. So Pius IX. was restored by foreign bayonets. Shortly after, the Pope issued a decree, proprio motu, containing a programme of "liberal institutions," so far as they were compatible with an absolute authority, enjoyed in virtue of Divine Right. The people were up for a brief period; they were now down, and would be kept down, if possible. They had presumed to think that they were the source of political power; that they could give their representatives the right of making laws and dethroning kings; but they must now learn that their business was to obey, and submit to anything which their superiors might think proper, of their own will and pleasure, to ordain.
THREE:[See larger version]

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THREE:SCENE AT THE "SURRENDER" BANQUET IN DERRY. (See p. 287.)

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THREE:Previous to this, however, Chatham had thought over several decisive measures, and sketched out a scheme of foreign and domestic policy, which marked how far above the intellectual grasp of most of his contemporaries was that of his mind. He determined, if possible, to form an alliance of European states against the Family Compact of the Bourbons in France and Spain; to reform the Government of Ireland, which greatly needed it, and that of India.

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THREE:But though the 21st of January was to be the day of the grand attack on the Ministry, the battle was not deferred till then. Every day was a field-day, and the sinking Minister was dogged step by step, his influence weakened by repeated divisions, and his strength worn out by the display of the inevitable approach of the catastrophe. The first decided defeat that he suffered was in the election of the Chairman of Committees. The Ministerial candidate, Giles Earle, was thrown out by a majority of two hundred and forty-two to two hundred and thirty-eight, and the Opposition candidate, Dr. Lee, was hailed by a shout that rent the House. Other close divisions followed. The fall of Walpole was now certain, and he would have consulted both his dignity and comfort in resigning at once. This was the earnest advice of his friends, but he had been too long accustomed to power to yield willingly. He was oppressed with a sense of his defeats, and the insolence of enemies whom he had so long calmly looked down upon without fear. He was growing old and wanted repose, but he still clung convulsively to his authority, though he had ceased to enjoy it.

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The Swedes cursed the less than half assistance of their British allies, and Gustavus endeavoured to fight his way without them. He continued to win victory after victory on land; but Catherine soon brought down on his squadron of galleys, which attended his march along the coast to keep up his supplies, an overwhelming fleet of galleys[354] of her own. A desperate battle ensued, but the Swedish galley-fleet was at length overcome. Gustavus was thus greatly embarrassed, and compelled to stand merely on the defensive, till it was time to go into winter quarters. He continued for twelve months to do battle with Russia, and, though with insufficient forces, threatened the very capital of that country. A little support from Britain, Prussia, and Holland, would have enabled Sweden to regain its territories on the eastern shores of the Baltic, to curb the power of Russia, and to assume that station in the North which is essential to the peace of Europe. These countries, however, had not the statesmanship to appreciate this point, or the friendly feeling to effect it, and Gustavus was left to struggle on alone.IRISH TRAMPS.The state of the Church of England was one of the most surprising deadness and corruption. Vast numbers of the churches had no minister resident, except a poor curate at a salary of some twenty pounds per annum, who, therefore, was compelled to do duty in two or three neighbouring parishes at once, in a manner more like the flying tailor of Brentford than a Christian minister; and the resident incumbents were for the most part given up to habits of intoxication, inherited from the last reign. Some of these ruling pastors held three or four livings, for the licence as to the plurality of livings was then almost unbounded.SEIZURE OF SIR WILLIAM MACNAGHTEN. (See p. 495.)
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