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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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Such were the advantages now possessed by the British over the French commander, that both the Portuguese and people at home were impatient that Wellington should at once attack and annihilate Massena's army. But Wellington knew better. He knew that a great battle, or battles, must vastly reduce his own as well as Massena's army. He knew that France could readily march down eighty or a hundred thousand fresh men into Portugal at extremity, but that Great Britain could not so readily do that; and, should the Whigs come into power, as was probable, he could not calculate on any support at all. The king now hopelessly insane, the Prince of Wales must be soon appointed Regent, and then, perhaps, would come in his friends the Whigs. There were many other considerations which made Wellington refuse to accede to a general attack on the French at present. He had, as it was, trouble enough with the Junta; but, should any reverse occur, his situation then would be intolerable. Just now the Portuguese troops were in good spirits for fighting, but defeat would ruin all the progress yet made with them. He knew that the winter would do for the French army all that he expected without any cost to himself, and he waited for that, ready then to follow up the advantages it would give him. It was his great plan of operations which already reduced them to the dilemma in which they were, and now came winter and did the rest, fully showing his superior sagacity. In November the weather became and continued wretched in the extreme. The country was flooded, cutting off the precarious supplies of the French, but adding strength to the encampment of Torres Vedras. The cross roads were impassable for artillery, and all but impassable for waggons bringing provisions, which had to be hunted for far and wide, with incredible hardships and little success. Leaving the hostile armies in this position till the spring, we must notice other important matters.Within a few days of taking Philadelphia, Lord Howe raised three batteries on the side of the river. On the 3rd of October Washington issued from his camp on the Schuylkill, about fourteen miles from Germantown, having heard that two British detachments had been withdrawn thence to attack the forts on the Delaware. He had been reinforced by militia from Maryland and New Jersey, and determined to surprise the British camp at Germantown. Two columns of Continental troops, led by Greene and Sullivan, were to gain the front of the British, and attack it; whilst two other columns of militia were to attack the rear. This force marched all night, and entered Germantown about sunrise, and all seemed likely to favour their enterprise. A fog prevented the discovery of their approach. But, at the first surprise, Colonel Musgrove threw himself into a storehouse, and kept up such a fire from the windows as checked the assault of the Americans, and gave time for the rest of the British force to get under arms. The village of Germantown consisted of one long street. Across this street the British army had encamped, and stoutly resisted the advance of the Americans. Musgrove was summoned to surrender; but he continued his fire from the house without taking any notice, and, before artillery could be brought up to batter the house, General Greig and Brigadier Agnew came up to his assistance. The Continental troops in front, led on by Washington himself, made a brisk attack, but were repulsed at all points, and were badly co-operated with by the militia in the rear. Washington was compelled to fall back to his camp at Skippack Creek, leaving behind him about eight hundred killed and wounded, and four hundred prisoners. So far, however, was Sir William Howe from availing himself of this opportunity to follow up the attack on Washington, and disperse his army, that he, as usual, thought only of getting into snug winter quarters.The Duke brought this letter to Mr. Peel, who read it in his presence, and then at once told him that he would not press his retirement, but would remain in office, and would propose, with the king's consent, the measures contemplated by the Government for the settlement of the Catholic question. Immediately after this decision was taken he attended a meeting of the Cabinet and announced his determination to his colleagues. One of these, Lord Ellenborough, could not refrain from writing to express his admiration of his conduct, dictated by true statesmanlike wisdom; adding that he had acted nobly by the Government, and in a manner which no member of it would forget. On the day that the king got the paper, those of the Ministers who had uniformly voted against the Catholic question had each a separate interview with the king, and individually expressed their concurrence in the course Mr. Peel recommended. The Ministers werethe Duke of Wellington, Lord Lyndhurst, Lord Bathurst, Mr. Goulburn, and Mr. Herries. The king, after this interview, intimated his consent that the Cabinet should consider the whole state of Ireland, and submit their views to him, not pledging himself, however, to adopt them, even if they should concur unanimously in the course to be pursued. The king was not convinced by Mr. Peel's arguments. He admitted it to be a good statement, but denied that it was an argumentative one.
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FORE:It was now the turn of the French to triumph, and of the Allies to suffer consternation. Louis, once more elate, ordered Te Deum to be sung in Notre Dame, and all Paris was full of rejoicing. He declared that God had given a direct and striking proof of the justice of his cause and of the guilty obstinacy of the Allies. His plenipotentiaries assumed at Utrecht such arrogance that their very lacqueys imitated them; and those of Mesnager insulted one of the plenipotentiaries, Count von Richteren, and Louis justified them against all complaints. In such circumstances, all rational hope of obtaining peace except on the disgraceful terms accepted by England vanished.
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Lord Advocate Jeffrey, who had introduced the Scottish Reform Bill as early as the 19th of January, moved the second reading on the 21st of May. He had, in the previous Session, proceeded on the principle that the old system was to be regarded as utterly incurable, and not to be patched or mended, but abandoned and destroyed. They could not decimate its abuses, or cut off its vicious excesses; its essence was abuse, and there was nothing that was not vicious about it. He gloried in the avowal that no shred, or jot, or tittle of the old abomination should remain. Indeed, it is a matter of astonishment that the Scottish people could have so long borne a state of things so humiliating to a nation which originally formed a kingdom by itself, which still retained its own laws, religion, interests, feelings, and language; which was full of generally diffused wealth; in which education had for ages been extended throughout the very lowest ranks; and whose people were peaceable, steady, and provident, possessing all the qualities requisite for a safe exercise of the franchise. The Scots had literally no share whatever in the representation of the Imperial Parliament. The qualification for a voter in Parliament was at least thirty or forty times higher than in any other part of the empire, and above a hundred times beyond the general qualification in England. Consequently a vote became a dear article in the Scottish market. Some persons bought votes as a good investment. The average price was about 500, but it frequently rose to double that sum. Shortly before the passing of the Reform Bill six Scottish votes were exposed for sale in one day, and brought 6,000. The electors were, therefore, cut off from the rest of the public, and set aside to exercise a high and invidious privilege, which they regarded not as a trust for the people, but as a privilege to[354] be prized for its pecuniary value or for its influence in procuring Government situations.In America, the belligerents were early afoot this year; but the attention and the forces of the English were drawn from the States to the West Indies by the determined attempts of the French to make themselves masters of our islands there. D'Estaing, who was joined by another French squadron under the Marquis de Vaudreuil, was early opposed by Admiral Byron, who arrived at St. Lucia from the American coast on the 6th of January. This Admiral Vaudreuil, on his way, had visited our settlements on the coast of Africa, and taken from us Senegal; but Sir Edward Hughes soon arrived there, and took their settlement of Goree, so that it was a mere exchange of territory. In June Admiral Byron was obliged to escort our merchant fleet to a certain distance, and D'Estaing seized that opportunity to make himself master of St. Vincent and Grenada, where the garrisons were weak. On the return of Byron, on the 5th of July, he came to an engagement with D'Estaing off Grenada; but the French admiral, after an indecisive action, took advantage of the night to sail away, boasting of a great victory. He now made for Georgia and Carolina, to assist the Americans in endeavouring to wrest from us our recent conquest of Savannah, in Georgia.[282]
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