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FORE:[18]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. THREE:The construction of public roads has been greatly improved in the United Kingdom by the general adoption of the plan of Mr. Macadam, who gave his name to the process of substituting stones broken small for the old rough pavement. We read with astonishment of the state of English roads a century ago, of carriages breaking down and sticking fast in deep ruts, and of days passed in a journey which now only occupies as many hours. Yet in early times England was better off in this respect than other countries. Of all the proofs of social progress which the country now exhibits to such a marvellous extent on every side, there is nothing more decisive or more wonderful than the rapidity with which we have improved and extended our internal communication. From 1818 to 1839 the length of turnpike roads in England and Wales was increased by more than 1,000 miles. In the former year England and Wales contained paved streets and turnpike roads to the extent of 19,725 miles. Scotland also made great progress in the construction of highways from the commencement of the century, and roads were thrown across the wildest districts in Ireland. By the improvement of the common roads, and in the construction of vehicles, stage coaches increased their speed from four to ten miles an hour. Upon the Stamp Office returns for 1834 a calculation was based which showed that the extent of travelling on licensed conveyances in that year would be equal to the conveyance of one person for a distance of 597,159,420 miles, or more than six times the distance between the earth and the sun. There were, in 1837, in England, fifty-four mail coaches drawn by four horses each, and forty-nine by two horses each, drawn at an average speed of nine miles an hour. Ireland had at the same time thirty four-horse mails, and Scotland ten.As this rout was taking place, Bulow, who had beaten back the French battalions from Frischermont and Planchenoit, was approaching La Belle Alliance, and Blucher with the main army soon after appeared following him. At a farmhouse called Maison Rouge, or Maison du Roi, behind La Belle Alliance, the Duke of Wellington and Blucher met and felicitated each other. Blucher, in the Continental manner, embraced and kissed the victorious Duke; and it was agreed that, as the army of Wellington had been fighting hard for eight hours, the Prussians should make the pursuit. Blucher swore that he would follow the French whilst a horse or a man could move, and, with three cheers from the British, he set forward with his troops in chase. So far from "the Guards dying, but not surrendering," these brave men flew now before the stern old Prussian, and immediately in the narrow passage at Genappe they abandoned to him sixty pieces of their cannon. Amongst other spoil they captured the carriage of Napoleon, and found in it, amongst other curious papers, a proclamation for publication the next day at Brussels. As it was moonlight, the Prussians continued the chase till late into the night, slaughtering the fugitives like sheep. Numbers quitted the road and fled across the country, seeking shelter in the woods, where many of them were afterwards found dead or severely wounded. The highway, according to General Gneisenau, was covered with cannon, caissons, carriages, baggage, arms, and property of every kind. The wounded were humanely sent to Brussels, but those who could continue their flight did so till they had reached France, where they sold their horses and arms, and dispersed themselves to their homes. The grand army was no more, with the exception of the division of Grouchy, who made good his retreat to Paris, only to be upbraided by Buonaparte as the cause of his defeat. In this battle and retreat the French lost more men than at Leipsic, the killed and wounded exceeding thirty thousand.