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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.TWOPENNY PIECE OF GEORGE III.

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THREE:

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THREE:"THE POLLING."[See larger version]

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TWO:It was very generally understood that it had been definitely arranged that Lord Londonderry should represent England at the Congress of Verona, and it was universally believed, as we have seen, that this fact weighed on his mind and led to his suicide; but Mr. Gleig states that in consequence of the reluctance expressed by Lord Londonderry to undertake the mission, it had for some time been settled that England should be represented there by the Duke of Wellington, and that he had begun to make his preparations, when a severe illness fell upon him, from which he did not sufficiently recover to set out upon his journey till after Lord Londonderry's death. The Duke of Wellington started for his mission when Mr. Canning had been only forty-eight hours in office. Stress has been laid upon the fact that he received his instructions from Mr. Canning, and this has been declared to be the turning-point in our foreign policy, when England began to disengage herself from the Holy Alliance. She was not formally a party to that alliance, but the despots composing it had counted on her aid and influence in keeping down the nations which they oppressed. But Mr. Gleig states that Lord Londonderry himself had compiled a letter of instruction for the representative of England at the Congress, and that this was transferred without a single alteration to the Duke of Wellington. It is, he says, "a very interesting document. It touches upon every point which could be expected to come under consideration at the Congress, and it handles them all so as to guard with scrupulous care not only the honour of Great Britain, but the rights of foreign peoples as well as of their Governments. It assumes that the subjects of general discussion would be three: first, the Turkish question, external and internal; secondly, the Spanish question, European and American; and, thirdly, the affairs of Italy. With this last question the representative of England was directed not to concern himself at all. As England had been no party to the military occupation of Naples and Sardiniaas she had merely acquiesced in it with a view to prevent worse thingsso she felt herself precluded from advising upon the arrangement now that it was complete, lest by so doing she should appear to admit the justice of a proceeding against which from the outset she had protested. The representative of Great Britain was therefore instructed to hold aloof from all meetings at which Italian affairs were to be discussed, and, if possible, to avoid connecting himself with the Congress till these should have been settled."

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The English Government, instead of treating Wilkes with a dignified indifference, was weak enough to show how deeply it was touched by him, dismissed him from his commission of Colonel of the Buckinghamshire Militia, and treated Lord Temple as an abettor of his, by depriving him of the Lord-Lieutenancy of the same county, and striking his name from the list of Privy Councillors, giving the Lord-Lieutenancy to Dashwood, now Lord Le Despencer.Whilst these violent dissensions had sprung up from the French Revolution, Wilberforce and his coadjutors had been active in their exertions to abolish the Slave Trade. Thomas Clarkson, now devoted heart and soul to this object, was, with Dr. Dickson, sent out by the parent Anti-Slavery Society through the country, to call into life provincial societies and committees, and found themselves zealously supported and warmly welcomed by philanthropists, and especially by the Society of Friends. They circulated the evidence taken before the House of Commons' Committee, and made a great impression. On the other hand, the French Revolution proved as antagonistic to the cause of the abolitionists as it had to the friendship of Burke and Fox. The dreadful insurrection in St. Domingo was attributed to the formation of the Society in Paris of Les Amis des Noirs, and many otherwise enlightened men took the alarm, lest similar scenes in our West Indian colonies should be the result of the doctrines of the abolitionists. Few persons could be found willing to entertain the idea of immediate abolition of the trade in slaves; and even Dr. Parr, though a great Whig and adherent of Fox, declared that these Utopian schemes of liberty to blacks were alarming to serious men. Wilberforce was earnestly entreated to reconsider his plan; he was assured that immediate abolition would not pass the Commons, nor even gradual abolition the Lords. Wilberforce, however, could not be deterred from bringing on the question. On the 18th of April he moved for leave to bring in a Bill to prevent the introduction of any more slaves into our colonies. Besides showing the cruelties practised in the collection and transmission of negroes, he brought forward evidence to prove that, so far from this trade being, as had been represented before the Committee of the Commons, the nursery of British seamen, it was their grave. He showed that of twelve thousand two hundred and sixty-three men employed in it, two thousand six hundred and forty-five had been lost in twelve months. This was calculated to produce far less effect than the surrender of hundreds of thousands of negroes, inasmuch as profit and loss was a more telling argument with the slave traders than mere humanity; and they exerted all their influence in defence of their traffic. Wilberforce added that even had this trade really been a beneficial one as regarded mere political economy, there was a smell of blood about it that all the perfumes of Arabia could not disguise. He was ably supported by Fox and Pitt; but, on this occasion, the Prime Minister could not command[381] his large majority; the motion was lost by one hundred and sixty-three against eighty-eight.We return now to the American campaign. Sir Henry Clinton, at the close of the year 1779, proceeded to carry into effect his plan of removing the war to the Southern States. The climate there favoured the project of a winter campaign, and, on the day after Christmas Day, Sir Henry embarked five thousand men on board the fleet of Admiral Arbuthnot. But the weather at sea at this season proved very tempestuous, and his ships were driven about for seven weeks. Many of his transports were lost, some of them were taken by the enemy; he lost nearly all the horses of the cavalry and artillery, and one vessel carrying the heavy ordnance foundered at sea. It was the 11th of February, 1780, when he landed on St. John's Island, about thirty miles from Charleston. He then planned the investment of Charleston with Admiral Arbuthnot; but he was not on good terms with that officer, and this threw great impediments in the way of prompt action. It was the 1st of April before they could break ground before the city. Once begun, however, the siege was prosecuted with vigour. Lord Cornwallis was sent to scour the country, and so completely did he effect this, that Lincoln was compelled to offer terms of surrender. These were considered too favourable to the Americans, and the siege continued till the 11th of May, when the English were doing such damage to the town, and the inhabitants suffering so much, that they threatened to throw open the gates if Lincoln did not surrender. In this dilemma, Lincoln offered to accept the terms proposed by Clinton before, and the British general assented to his proposal. On the 12th of May the Americans grounded their arms. The news of this blow, which laid the whole south open to the English, carried consternation throughout the States; and, arriving in England at the close of the Gordon riots, seemed to restore the spirits of the British.Great Britain, which had amassed so vast a debt in aiding the Continental sovereigns against Napoleon, played the magnanimous to the last. She gave up her share of the public indemnities, amounting to five million pounds, to the King of Holland and the Netherlands, to enable him to restore that line of fortresses along the Belgian frontiers which our Dutch king, William III., had planned, and which Joseph II. of Austria had suffered to fall to decay, thus rendering invasion from France especially easy. Nor was this all: she advanced five million pounds to enable the different sovereigns to march their troops home again, as she had advanced the money to march them up, the money demanded of France not being ready. Truly might Napoleon, in St. Helena, say that England, with her small army, had no business interfering in Continental wars; that "with our fleet, our commerce, and our colonies, we are the strongest power in the world, so long as we remain in our natural position; but that our gains in Continental wars are for others, our losses are for ourselves, and are permanent."
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