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Until the beginning of the nineteenth century the state of mathematical science was very low in England. The commencement of a better era originated with Woodhouse at Cambridge and Playfair in Edinburgh, by both of whom the Continental methods were introduced into the studies of their respective Universities. About 1820 the translation of La Croix's "Differential Calculus," superintended by Sir John Herschel and Dean Peacock, came into use as a text-book. Soon afterwards the writings of Laplace and Poisson were generally read in the Universities; and a few men of active and daring minds, chiefly of the Cambridge school, such as Professor Airy and Sir John Lubbock, grappled with the outstanding difficulties of physical astronomy; whilst a larger number applied themselves to the most difficult parts of pure analysis, and acquired great dexterity in its use, in the solution of geometrical and mechanical problems.

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ONE:The next morning, the 6th of December, the retreat commenced; but the soldiers and the inferior officers little dreamed that it was a retreat. They imagined that they were going to fight the Duke of Cumberland, and marched out in high spirits. The morning was foggy, and for some time the delusion was kept up; but when the fog cleared away, and they perceived that they were retracing their former route, their disappointment and rage became excessive. The retreat was rapidly continued through Preston, and on to Lancaster, which they reached on the 13th. On the 18th Oglethorpe and Cumberland, accompanied by a mob of country squires and mounted farmers, attacked Lord George Murray's rear near Penrith; but the countrymen were speedily put to flight by a charge of the Glengarry clan, and Oglethorpe fell back to the main body. They came up again, however, in the evening near the village of Clifton, and Lord George perceived, by the fitful light of the moon, the enemy forming behind the stone walls, and lining every hedge, orchard, and outhouse. Just as the royal troops commenced their charge they were stopped by a cross-fire of the concealed Highlanders, and, whilst affected by this surprise, Lord George cried, "Claymore! claymore!" and rushing down upon them with the Macphersons of Cluny, attacked them sword in hand. Being supported by the Stuarts of Appin, they compelled the English to retreat.
THREE:FIGHTING AT THE BARRICADES IN PARIS. (See p. 551.)But Ministers were too sensible of the unconstitutional character of their deeds to rest satisfied with the mere justification of an accepted report. A Bill of Indemnity was introduced to cover "all persons who had in 1817 taken any part in apprehending, imprisoning, or detaining in custody persons suspected of high treason, or treasonable practices, and in the suppression of tumultuous and unlawful assemblies." Thus Ministers were shielded under general terms, and to avoid all appearance of personal movement in this matter by those in the Cabinet the most immediately active, the Bill was introduced by the Duke of Montrose, the Master of the Horse.
THREE:Still the affairs of Wilkes continued to occupy almost the sole thought and interest of the Session. On the 23rd of November the question of privilege came up; and though he was absent, having been wounded in a duel, it was actively pushed by the Ministers. Mr. Wilbraham protested against the discussion without the presence of Wilkes, and his being heard at the bar in his defence. Pitt attended, though suffering awfully from the gout, propped on crutches, and his very hands wrapped in flannel. He maintained the question of privilege, but took care to separate himself from Wilkes in it. The rest of the debate was violent and personal, and ended in voting, by two hundred and fifty-eight against one hundred and thirty-three, that the privilege of Parliament did not extend to the publication of seditious libels; the resolution ordering the North Briton to be burnt by the hangman was confirmed. These votes being sent up to the Lords, on the 25th they also debated the question, and the Duke of Cumberland, Lord Shelburne, and the Duke of Newcastle, defended the privilege of Parliament as violated in the person of Wilkes. In the end, however, the Ministers obtained a majority of a hundred and fourteen against thirty-eight. Seventeen peers entered a strong protest against the decision. On the 1st of December there was a conference of the two Houses, when they agreed to a loyal address to the king, expressing their detestation of the libels against him.
THREE:The real fact was, that exertions equally strenuous were all this time being made on the part of the Pretender. As the state of Anne's health became more and more precarious, both parties increased their efforts to secure their ground, and there was a most active and incessant struggle going on round the throne to enable the head of either party to step into it the moment it became vacant. It was considered essential for the claimant to be on the spot, and, therefore, every means was used to induce the queen to admit the Pretender as well as a member of the Electoral House to Court. It was a scheme of the Duke of Berwick, which he communicated to Oxford through the Abb Gualtier, that the queen should be induced to consent to do her brother justice; that he should go to St. James's, and that on the understanding that he consented to allow liberty of the subject and of religion, the queen should pass such Acts as were necessary for the public security on these heads, and that then she should suddenly introduce him in full Parliament.
TWO:Whilst Washington man?uvred to prevent Howe from crossing the Schuylkill above him, the English General crossed below on the 22nd of September, and thus placed himself between Philadelphia and the American army. It was now necessary for Washington to fight, or give up that city; but the condition of his troops, deficient in clothes and shoes, owing to the poverty of the commissariat department, with wretched arms, and fatigued by their recent exertions, forbade all hope of maintaining even the defensive. He therefore fell back, and Cornwallis, on the 27th, advancing from Germantown, entered Philadelphia amid the welcome of the loyal inhabitants. Cornwallis occupied the city with four regiments, but the body of the British army encamped at Germantown, ten miles distant. But, though the Americans had evacuated the city, they still held the command of the Delaware below it, and thus cut off the supplies of the British army by sea, and all communication between the army and the fleet, except by the circuitous course of Chester, liable to capture by the enemy.

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TWO:The first place that reeled under the electric shock of the French Revolution was Glasgow. On the 5th of March, in the afternoon, a body of 5,000 men suddenly assembled on the Green in that city, tore up the iron railings for weapons, and thus formidably armed, they commenced an attack on the principal shops, chiefly those of gunsmiths and jewellers. The police, apprehending no outbreak of the kind, were scattered on their beats, and could afford no protection until forty shops had been pillaged and gutted, and property to the value of 10,000 carried off or destroyed. Next morning about 10,000 persons assembled on the Green, armed with muskets, swords, crowbars, and iron rails, and unanimously resolved"To march immediately to the neighbouring suburb of Calton, and turn out all the workers in the mills there, who, it was expected, would join them; to go from thence to the gas manufactory, and cut the pipes, so as to lay the city at night in darkness; to march next to the gaols and liberate all the prisoners; and to break open the shops, set fire to and plunder the city." They immediately set out for the Calton mills, meeting on their way fourteen pensioners in charge of a prisoner. These they attempted to disarm, but the veterans fired, and two men fell dead. Instantly the rioters raised the cry, "Blood for blood!" and were wresting the muskets from the soldiers, when a squadron of cavalry galloped up with drawn swords. The people fell back, and the riot was suppressed. It afterwards transpired that the Chartists in all the manufacturing towns of the west of Scotland only awaited the signal of success from Glasgow to break out in rebellion. The prompt suppression of the movement was therefore a matter of great importance.

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THREE:The death of the Princess Charlotte left the prospect of the succession to the Crown equally serious. Of the numerous sons and daughters of George III. not one had legitimate issue. It might be necessary soon to look abroad in Germany or in Denmark for an heir to the Crown. This consideration led to a number of royal marriages during the earlier part of this year. The first of these marriages was not of this description. It was that of the Princess Elizabeth, his Majesty's third daughter, to the Landgrave and Hereditary Prince of Hesse-Homburg, on the 7th of April. As the princess was already nearly eight-and-forty, no expectation of issue in that quarter was entertained. On the 13th of April Lord Liverpool brought down a message from the Regent to the Peers, and Lord Castlereagh to the Commons, announcing treaties of marriage in progress between the Duke of Clarence and the Princess Adelaide Louisa, of Saxe-Meiningen; and also between the Duke of Cambridge and the Princess Augusta Wilhelmina, of Hesse, youngest daughter of the Landgrave of Hesse. The House of Commons was also asked to add an additional ten thousand pounds a year to the allowance of the Duke of Clarence, and six thousand pounds a year each to those of the Dukes of Cumberland and Cambridge, and to that of the Duke of Kent,[136] if he, too, should marry. Ministers intimated that it had been the intention to ask much larger sums, but they found that it was necessary to reduce the sum asked for the Duke of Clarence. It was a matter of notoriety that the duke had already a large family by the actress, Mrs. Jordan, and probably the feeling of the House was influenced by his desertion of that lady; but there was a stout opposition and the sum was reduced to six thousand pounds. Loud acclamations followed the carrying of this amendment, and Lord Castlereagh rose and said, after the refusal of the sum asked, he believed he might say that the negotiation for the marriage might be considered at an end. The next day the duke sent a message declining the sum granted; yet, after all, his marriage took place. The Duke of Cumberland was already married to the Princess Frederica Sophia, the daughter of the Duke of Mecklenburg-Strelitz, who had been divorced from Frederick Louis, Prince of Prussia. The Duke of Cumberland was one of the most unpopular men in the whole kingdom, for there were rumours of very dark passages in his life, and Parliament had rejected an application for an additional allowance on his marriage; and it now rejected this application amid much applause. The sum asked for the Duke of Cambridge was carried, but not without considerable opposition. The spirit of reform was in the air.
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THREE:Sir Henry arrived at Calcutta in September, 1844. He found that tranquillity prevailed throughout the empire, and applied his energies to the formation of railways. But he had soon to encounter the exigencies of war. Notwithstanding the stringent injunctions he had received to cultivate the most amicable spirit with the Sikhs, he was obliged to tax the resources of the empire in maintaining with them one of the most desperate conflicts recorded in Indian history. The Sikhs were a warlike race, distinguished not less by fanaticism than bravery. They were bound together and inspired by the most powerful religious convictionsa tall, muscular, and athletic race of men, full of patriotic ardour, elevated by an ancient faith. They were confederated in various provinces, to the number of about 7,000,000. They were accustomed to ride upon fleet horses, and had organised an effective cavalry, while their infantry had been disciplined by French and Italian officers. They could, if necessary, bring into the field 260,000 fighting men; but their regular army now consisted of 73,000 men with 200 pieces of artillery. Settled chiefly in the Punjab, a country of extraordinary fertility, they also abounded in Mooltan, Afghanistan, and Cashmere, celebrated from the most ancient times as the favoured abode of manufacturing industry, social order, wealth, and happiness. This warlike race had been governed by Runjeet Singh, a chief of extraordinary ability, energy, and determination. He had but one eye; he was deeply marked with the small-pox; his aspect was repulsive, and his manner rude; yet was he looked up to by this great people with respectful homage, and obeyed with implicit trust. While he lived he maintained an alliance with the British Government; but after his death the Sikhs were divided into two factionsone headed by Gholab Singh, and professing to be favourable to the British; the other by the Ranee, who yielded to the clamours of the unpaid soldiers to be led against the English. Accordingly the[597] military forces of the Sikhs were ordered to march down to the Sutlej. But their intended attack was prevented by the astrologers, who declared that the auspicious day for marching had not yet arrived. Sir Henry Hardinge, however, in common with the most experienced officers of the Indian Government, did not think the Sikh army would cross the Sutlej with its infantry and artillery, or that they would have recourse to offensive operations on a large scale. Up to this period it had committed no act of aggression. In 1843 and 1844 it had moved down the river from Lahore, and after remaining there encamped a few weeks, had returned to the capital. These reasons, and, above all, his extreme anxiety to avoid hostilities, induced him not to make any hasty movement with his army, which, when the two armies came into each other's presence, might bring about a collision. This moderation, however, was misconstrued by the Sikhs. They supposed that the British were afraid to encounter them. Accordingly, on the night of the 9th of December, 1845, a portion of the Sikh army appeared within three miles of the Sutlej; and information was received by our garrison at Ferozepore that preparations were making on a large scale for the movement of infantry, artillery, and stores from the Sikh capital, Lahore. On the 12th of December the Sikh army crossed the Sutlej, and concentrated in great force on the British side of the river. The British reserves, meanwhile, were advancing to meet this formidable enemy; but they were still far off, and Ferozepore had but a garrison of 9,500 men to withstand an army of 60,000 with 100 guns! Sir Charles Napier wrote in his "Memoirs" that he did not think history would let off Sir Henry Hardinge for allowing such an army to cross the river unmolested, and entrench itself on the other side. It is quite certain that Sir Charles would not have given them such an advantage. But their generals did not know how to use it. Sir Henry Hardinge had hastened in person to assist General Gough in conducting the operations against the enemy, and both putting themselves at the head of the advanced guard, they were followed by the reserves, marching at the rate of twenty-six miles a day, full of excitement at the prospect of more fighting.
THREE:His plan for his chef-d'?uvre, St. Paul's, like his grand plan for the City, with its principal streets ninety feet wide, its second-rate streets sixty, and its third-rate thirty, was rejected. This cathedral was a composition compact and simple, consisting of a single general octagonal mass, surmounted by a dome, and extended on its west side by a portico, and a short nave or vestibule within. The great idea of Wren was to adapt it to Protestant worship, and therefore he produced a design for the interior, the parts of which were beautifully grouped together so as to produce at once regularity and intricacy, yet without those long side aisles and recesses, which the processions and confessionals of Roman Catholic worship require. The whole long period of Wren's erection of this noble pile was one continued battle with the conceit, ignorance, and dogmatism of the commissioners, who made his life a bitter martyrdom; and when we read the admired inscription in St. Paul's, "Si monumentum requiris, circumspice," we behold, on obeying its injunction, only what Wren did, not what he suffered in doing it.
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The elections were now carried on with all the fire and zeal of the two parties. The Tories boasted of their successful efforts to stem the tide of expenditure for the war, to staunch the flow of blood, and restore all the blessings of peace. The Whigs, on the contrary, made the most of their opposition to the Treaty of Commerce, which they represented as designed to sacrifice our trade to the insane regard now shown to the French. To show their interest in trade, they wore locks of wool in their hats; and the Tories, to show their attachment to the Restoration and the Crown, wore green twigs of oak. Never was shown more completely the want of logical reason in the populace, for whilst they were declaring their zeal for the Protestant succession, and whilst burning in effigy on the 18th of NovemberQueen Bess's daythe Pope, the Devil, and the Pretender, they sent up a powerful majority of the men who were secretly growing more and more favourable to the Pretender's return. Never, indeed, had the chances of his restoration appeared so great. General Stanhope, on the close of the elections, told the Hanoverian minister that the majority was against them, and that if things continued ever so short a time on the present footing, the Elector would not come to the Crown unless he came with an army.This decided repulse ought to have shown the prince the violence that he was doing to the public sense of decency, and the mischief to his own character; but the disappointment only the more embittered him and increased his miserable obstinacy. Time had no effect in abating his unnatural resentment. Though this parliamentary decision took place in February, he continued so much in the same temper, that the very last day of the following May, his wife being seized with symptoms of labour, he suddenly determined to remove her from Hampton Court, where all the Royal Family then were, and hurry her off to London.
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