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in a workmanlike manner. A people who could build such perfect ships would certainly not waste time and labour in constructing a trench which would be any longer or deeper or wider than was absolutely necessary.

      Now the shortest canal possible would be that in which he was just able to drag his vessels round without destroying the banks. In other words, if a circular canal began at C B, and if we drew an imaginary circle round the middle of the canal, what was required was that the chord D F, forming a tangent to the middle circle, should be at least as long as the longest vessel. Now (see diagram) —

AD² – AE² = DE²

      If r is the radius, AD and 2a the breadth BC, and 2b the length of the chord DF —

r² – (ra)² = b² ∴ r = (a² + b²)/2a

      This represents the length of the radius in terms of the length and breadth of the largest vessel in the fleet, and is therefore the smallest radius possible for getting the ships through. Now, the ship of Gokstad, already described, was undoubtedly one of the finest of the vessels used by Danes and Normans. The poets certainly speak of larger ships, but as a marvel. Nothing is said about Cnut bringing over ships of very great size. Now, that vessel was 66 feet in length, considering the keel, which is all we need consider; 16½ feet in breadth, and 4 feet in depth. She drew very little water; therefore a breadth of canal less than the breadth of the vessel was enough. Let us make the chord 70 feet in length, so that b = 35. Let us make the breadth of the canal 12 feet. Therefore 2a = 12 or a = 6 and r = 105 feet very nearly. Measuring, therefore, 105 feet on either side of London Bridge, we arrive at a possible commencement of Cnut's work. That is to say, if he made a semicircular canal, in that case the length of the canal would be 320 yards, which is certainly an improvement on four miles and a half, or even three miles and three-quarters.

      THE GOKSTAD SHIP

      There is, however, more to consider. Why should Cnut make a semicircle when an arc would serve his turn? All he had to do was to draw an arc of a circle with the radius just found, to clear any obstacles in the way of approach to the Bridge, and use that arc for his canal. This is most certainly what he did: I am quite certain he adopted this method, because it was the only sensible thing to do. He would thus get off with a canal about fifty yards long, of which the only difficulty would be the cutting through the Embankment and the Causeway.

      What would be the depth of the canal? Look at this section of the Gokstad ship. With her breadth of sixteen feet, she had only four feet in depth; without her company and crew, and their arms and provisions, she would thus draw no more than a few inches – certainly not more than eight inches or so. Freeman's deep canal therefore comes to eight inches at the most. But there is still another consideration which lessened the labour materially. The ground behind the Embankment was a little lower than the river at high tide: the Danes, therefore, had only to construct a low wooden containing-wall of timber on each side in order to make their canal without excavating an inch. When that was done, the cutting of the Embankment let in the tide and did the rest. In this simple manner do we reduce Cnut's colossal work of a deep canal, four miles and a half long, into a piece of construction and demolition which would take a large body of men no more than a few hours.

      If, however, there actually was any digging to be done, we must remember that the ground was a level; that there were no stones or rocks in the way, and that it consisted of a soft black humus, the result of ages of successive growths of sedge and coarse grass, formerly washed twice a day by the brackish waters of a tidal river. The object of the canal once attained, the ships drawn back again, Cnut, of course, left the place to be repaired by any who pleased. The broken Embankment let in the tide; the broken Causeway cut off any approach to the river; but Southwark was deserted. When things settled down a little, workmen were sent across from London, and the broken places were repaired. Then all traces of the canal disappeared.

      Thirty-six years later, in 1052, Earl Godwine arrived at Southwark with a fleet and an army. He had no difficulty in passing the Bridge; he waited till flood-tide, and then sailed through 'on the south side.' It is quite impossible to explain this statement, or to make it agree with the difficulty felt by Cnut. The Bridge may have sustained some damage; there may have been a drawbridge; or Godwine's ships may have been smaller: one knows nothing. I merely state the fact as the Chronicler gives it.

      One more glimpse of the Bridge from Southwark before we pass on to more modern times.

      After Hastings, William marched northwards. Arrived near London, he advanced to Southwark, where he found the Bridge closed to him – closed, I believe, by knocking away some of the upper beams. This, of course, he expected; his friends within the City, of whom he had many, kept him acquainted with the changing currents of popular opinion. It is commonly stated that the citizens were terrified by the sight of Southwark in flames at his command. Southwark in flames! A few fishermen's huts were all that remained of the suburb, whose population since the time of the Pax Romana had been so precarious and so changeful. Five hundred years of battle, war between kings and tribes, invasion and ravage by Dane and Norseman, had not left of Southwark, once so beautiful a suburb, anything more than these poor huts and ruins of huts. William's soldiers burned them, because wherever a soldier of that period appeared, the thatch always caught fire spontaneously. William saw the flames, and regarded them not, any more than he regarded the flames that followed in his track all the way from Senlac. He gazed across the river, and remembered that twice had London defied all the strength of Swegen; that three times had London beaten off the great King Cnut when all England had surrendered; that in six sieges London had always been victorious; he knew, because his friends in the City would allow no mistake on that point, that the spirit of the citizens was as high now as it had been then; that they still remembered with pride the defeat of Cnut; and that not a few were anxious to treat William the Norman as they had treated Cnut the Dane. One knows not, exactly, what things went on within the walls; what exhortations, what wild talk, what faction fight; how the citizens rolled, and surged, a mass of wild faces, about their Folk-mote by St. Paul's. But of one thing we may be quite certain: that William did not expect the citizens to be afraid of him; and that, in fact, they were not afraid of him, whether he set fire to the huts of Southwark or not; they were not afraid of William, whatever the historians say. As for the Bridge, the old Roman Bridge, by this time there could hardly have been a single pile remaining of the original structure; yet it was constantly repaired.

      We may restore to Norman London, therefore, not only the grey wall rising out of the level ground, without any ditch or moat outside, but also the Bridge of wooden piles with the transverse girders and beams for additional security, so that the old Bridge contained a whole forest of timbers like those which support the roof of an ancient hall. It was continually receiving damage. In the year 1091, a mighty whirlwind blew down a good part of London, houses and churches and all. It has been assumed that the Bridge was also destroyed; but the 'Chronicle' is silent on the subject. In 1092 there was a great fire in London; it is again assumed that the Bridge was destroyed, but again the 'Chronicle' is silent. In 1097, however, it is plainly stated that the Bridge had been almost washed away, and that it was repaired.

      In 1136 the most destructive fire ever experienced by London, save that of 1666, spread through the whole City, from London Bridge, which it greatly damaged, all the way to St. Clement Danes on the west, and Aldgate on the east. One wonders what ancient monuments – walls of Roman churches, villas, and baths, still surviving halls and chambers of the Forum – were destroyed in this fire; Saxon houses of the better sort, with their great halls and courtyards; small Saxon churches of wood or stone, with low towers and little windows. Possibly there was no great loss: it was already seven hundred years since Augusta was deserted. Roman remains must have been scanty; the City was chiefly built of wood, with thatched roofs; the splendour of the latter centuries had not yet commenced. The Bridge, however, was either wholly or in part destroyed. It was repaired, because, fifty years later, FitzStephen, in his description of the City, speaks of the citizens watching the water sports from the Bridge. Indeed, the Bridge was now absolutely necessary to the City. A hundred years of order in the City – with the seas cleared of pirates, the Danes kept down,

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