462 H A K B U 11 S It may in some cases be found better, in designing a sea wall for protecting a sinuous coast, to carry the bulwark straight across ledges of rock which extend landwards, than to follow the line of the high water margin. For although with the straight wall we may have to encounter a greater depth of water and a heavier surf, still with the other we may have to oppose the waves with a wall which has at some places a concave horizontal curvature, by which the force is concentrated and rendered more destructive. More over, the straight wall may be considerably shorter than the curved. jrtical The general gradient of a fragmentary beach depends ofile of upon the size and nature of the particles, and the force of llls the sea. The dissimilarity between its slopes near the levels of high and low water arises from a decrease in the force of the waves, caused by their being broken before they reach the high water mark. The great object, there fore, is to design the profile of the wall so as to alter as little as possible the symmetry of the beach. For the reasons already stated, it is plain that unless near high water mark a vertical wall is in most cases unsuitable for a sandy beach. Instead of altering the direction of the wave at a distance from its foundation, the whole change is produced at that very point ; and, unless the wall be founded at a considerable depth, its destruction is all but certain. A curved profile will prevent to a considerable extent the danger of reaction, by causing the alteration in the direction of the wave to take place at that part where the wall is strongest, and which is also at the greatest possible distance from the toe or curb course. But a very serious objection to all forms of curved walls, unless the radius be large, is the weakness which results from the use of wedge-shaped face-stones. The impact of the sea on materials of that form may be compared to a blow directed upwards against the intrados of a stone arch the direc tion of all others in which the voussoirs are most easily dislocated. This action can only be resisted by very careful workmanship in the dressing and setting of the backing. Another objection, applicable to all except tideless seas, such as the Mediterranean, arises from the varying level of the surface of the water ; for what may be best at one time of the tide cannot be equally suitable at another, iduc- When a wave encounters an obstacle such as a break water, the portion which strikes it is either entirely destroyed or reflected seawards ; while the portion which is not so intercepted passes onwards, and spreading later ally under lee of the barrier suffers a reduction of its height. From a very few observations in the sea under lee of the breakwater at Wick, and from some experi ments made in a brewer s cooling vat by Mr Thomas Stevenson, it appeared that after passing an obstruction the reduction in the height of a wave varies as the square root of the angle of deflexion. When x represents the ratio of the reduced to the unreduced wave and a the angle of deflexion, the formula, which must however, be regarded as only approximate, is z=roo--o6v;r. The measurements of the distances of high water mark from the centre of divergence, in sandy bays which are under lee of promontories, seem to show that this formula, or one for a logarithmic spiral, represents the effect of lateral divergence very fairly. Providing the materials of the beach are homogeneous and easily moved, the incursions of the waves into the land will be measures of the forces, all of which become nil at the high water mark. The fol lowing table shows measurements of the finely curved storm and tide marks traced out on the sandy beach under the lee of the promontory at North Berwick, and the results of the formula. Angles of Deflexion. Distances from centre of Divergence at end of Promontory to High Water Mark. Ratios of Measurements. Results of Formula.
1150 i-oo i-oo 10 1000 87 87 20 920 80 73 30 840 73 67 40 735 64 62 45 700 Gl 60 50 675 59 58 60 600 52 53 70 570 50 50 80 555 49 46 90 530 46 43 The tranquillity of close harbours with the same exposure depends on the relative widths of the entrance and the interior, the depth of water, and the form and direction of the entrance in relation to the line of maximum exposure, A formula for the reductive power of harbours has been given by Mr Thomas Stevenson (Edin. Phil. Journal for 18.53). "Where the piers are liigli enough to protect the enclosed area from the wind, and the width of entrance not very great in comparison with the breadth of the wave, the quay walls nearly vertical, and the distance from the entrance to place of observation not less than 50 feet, then- Reduc- tlon of passing into close VB where II height of wave at entrance, J = breadth of entrance, B= breadth of harbour at place of observation, D = distance from mouth of harbour to place of observation, x=-- height of reduced or residual wave at place of observation, all in feet. If II be taken as unity, x will be a fraction representing the reductive power of the har bour. Actual measurements at the harbours of Kingstown, Snnderland, Macduff, Fisherrow, and Buckle gave the mean of observations (which at Buckle alone numbered upwards of 2000) = 2 64 feet, while that of results calculated by the formula gave 2 62 feet. The size as well as the ratio of widths of entrance and basin must also bear a proper relation to the height of waves to which the harbour is exposed. The formula for the reductive power assumes that the waves after being reduced by lateral expansion shall have time to sink and be ultimately destroyed. But if instead of this they are again reflected towards the entrance, such recoil will destroy the tranquillity of the basin and prevent vessels from answering their helm when taking the entrance. Also where a spending beach which is only partially effective in destroying the waves is formed very near the entrance, it may do little or no good by causing a back wash or recoil wave which will injuriously affect vessels when entering. As before mentioned, it is essential when the exposure is great that there be either a considerable internal area, or else a separate basin opposite the entrance to the inner basin, for the waves to destroy or spend themselves. Such a basin should, if possible, enclose a portion of the original shore for the waves to break upon, and when circumstances preclude this there should be a flat talus wall of at least 3 or 4 to 1, as recommended by the late Mr Bremner of Wick. Mr Scott Russell has found that talus walls of 1 to 1, or steeper, will not allow the waves to break fully, but will reflect them in such a manner as might in some cases make the entrance difficult or even dangerous of access, and the berthage within unsafe. The following cases in which traffic has been successfully carried on at quays unprotected by covering piers, may be found useful as a guide : At Scrabster the quay is at right angles to a fetch of 6 miles. At Invergordon there is a fetch of 5 miles ; at Burntisland, 6 ; Kil- creggan, 4; Londonderry, 1J; Greenock, 6; Albert Quay, Greenock, 7 miles. The last two arc, however, somewhat sheltered by the low-water banks near Greenock. Five miles is probably not far from the limit that should be ob served, which by the ordinary formtflft, & = 1 - 5VD, gives a wave of Size ot harbon to mas nitude of wav( Stillinj basins, Places tected"
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