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THREE:To procure peace, Madison now sought the good offices of the Emperor Alexander of Russia with Great Britain, and these offices were readily accepted, for the latter had never willingly gone into or continued this unnatural war. A Congress was appointed at Gothenburg, and thence transferred to Ghent. There, on the 24th of December, 1814, a loose and indefinite peace was concluded, in which every principle on which the war had been begun was left to be settled by commissioners; and some of which��such was the difficulty of negotiating with the Americans��were not settled for many years. On these points alone were the two Powers agreed��that all hostilities between the contracting parties and the Indians should be put an end to, and that both parties should continue their efforts for the suppression of the slave-trade. Such was the joy of the north-eastern States of America at the peace that the citizens of New York carried the British envoy, sent to ratify the treaty, in triumph through the streets.Even now, had the Russians and Austrians possessed the spirit which the circumstances of the time demanded of them, they were far from being in a hopeless condition. Buonaparte was at an immense distance from his country. Besides the army still remaining with the two Emperors��at least sixty thousand in number��there were the strong forces of the Archdukes Charles and John in Hungary, and of Prince Ferdinand in Bohemia. By bold and skilful man?uvres they might have cut off his communications with France and Italy, and have harassed him, without committing themselves to a decided battle, till he must have found himself in a most perilous position. But Francis of Austria gave up the struggle in despair; he sent Prince John of Lichtenstein to propose a suspension of arms. Buonaparte insisted that they should first break with the Russians, and Lichtenstein said that Francis was quite willing, and to treat with Napoleon for a separate peace, but that he must claim for the Emperor Alexander the privilege of retreating into his own country without molestation. Buonaparte granted this as a favour, and added words so complimentary to Alexander, that they betrayed a wish to complete an agreement also with him. He returned to Vienna, and again occupied the palace of Sch?nbrunn. There he and Talleyrand concerted the demands which should be made; and an armistice was signed, on these terms, with Prince John of Lichtenstein, on the 6th of December. The final treaty was signed by the Emperor Francis, at Pressburg, on the 26th of December, a fortnight after Austerlitz. By this treaty Austria surrendered to Buonaparte all her territories in Italy, as well as her Venetian provinces of Dalmatia and on the coast of Albania. She surrendered her only seaport on the Adriatic, Trieste, and thus reduced herself to a mere inland power. She was compelled to cede to her rival, Bavaria, the Tyrol��a country most faithfully attached to the House of Hapsburg,��the bishopric of Passau, and other regions. Bavaria and Würtemberg, for their hostility to their own German race, were elevated into kingdoms, and Baden, for the same unpatriotic services, into a grand duchy. Thus France and her allies, or rather subjects, were now in possession of Switzerland, Italy, and the Tyrol on one side, and of Holland and Belgium on the other, so that she had everywhere an open high road into Germany,[507] and nations of tributary princes, which were to aid in further enslaving it. Prussia had made up her mind on hearing of the victory of Austerlitz, and Haugwitz appeared at Sch?nbrunn, not to declare war on Buonaparte, but to compliment him on his victory. Buonaparte could not conceal his contempt for this despicable conduct. He said, "Ah! this compliment was intended for others, but fortune has transferred it to me;" but as he still intended to make use of Prussia, and could humiliate George III. by her means, he concluded a treaty with Haugwitz, by which he handed over Hanover to our late ally, and claimed Anspach in lieu of it. He then strengthened the Confederation of the Rhine, of which he was Protector, and so completely broke up the old federation of Germany, that Francis of Austria soon abandoned the title of Elective Emperor of Germany, and assumed that of Hereditary Emperor of Austria.

THREE: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.