This process, continually in operation during the several hours of the tides, is sufficient to account for the removal of an immense amount of material. Allowing fifteen waves to the minute, there are no less than 3600 impulses during the period, taken at 4 hours, that each tide is sufficiently high to act on a shingle-bank.

Thus, while the smaller pebbles are carried back by the retiring waves from the line of high water, there is always a certain quantity of pebbles carried on the crest of the highest wave above the reach of the retiring waves and there left stranded.

In addition to the movement of individual stones, the whole of the face of the bank, above the line reached by the water under the pressure of the wave, is forced upwards, and the top of the bank is thus raised considerably above the level of high tides.

It is difficult to follow for any length of time the movement of individual pebbles, as, owing to the constant shifting in position, a marked stone becomes buried amongst the others; but when this can be done it will be found, on carefully watching, that the material moved varies from coarse sand and small pebbles weighing 1 or 2 ozs., up to stones weighing 5 or 6 lbs.

The average size moved by these tidal wavelets is about 4

or 5 ozs.

When watching the effect of the incoming tide with a perfectly calm sea and the absence of any wind, when small boats in the offing were lying motionless, the author has repeatedly observed, on shingle-beaches in sheltered positions, numbers of pebbles moved by these tidal wavelets upward and forward along the beach, which weighed more than 4 ozs. when out of the water, and single stones weighing as much as 6 lbs., and, shortly before high water, pebbles weighing 1 lbs. rolled upward and forward and left on the bank. Also, on a shore with an inclination of 5 degrees, consisting of coarse sand and shingle, stones containing 6 to 18 cubic inches were moved upward 6 feet, and forward 4 feet in the course of six waves; and with a perfectly calm sea, the wavelets being from 6 to 9 inches high, a piece of tile drifted 9 feet in a quarter of an hour; and half a brick carried 30 yards in two hours, and on another occasion half-bricks drifted 25 yards in 11 hours.

The ebb tide also retires from the beach with an oblique waveaction, the direction of these waves being the same as on the flood; and although the waves roll down most of the pebbles that they carry up, there is always a certain quantity of material

which is moved upwards and remains, pebbles of considerable size being raised by the tidal wavelets and left on the bank above the reach of the falling water.

Although the ebb acts for the same period on a bank as the flood, as the shingle is situated generally high up the beach, it is not able to reverse the movement of the material. The waves

lack the momentum of the rising tide, and each series of waves, instead of rising to a higher level as on the flood, is continually falling, and fails to reach the stones deposited on the flood.

The quantity finally lifted and added to the bank forms only a very small proportion of that moved backwards and forwards by the waves, as the stones carried back by the retreating waves form the larger proportion of those rolled up, and this especially applies to the sand and smaller pebbles.

The material lifted by the incoming wave is moved in an oblique direction, as the water of the retiring wave moves normal to the bank, and the pebbles have not only therefore to descend, in place of being moved upwards, but the distance of travel is less.

There are so many varying conditions that affect the breaking of the waves, such as the slope of the shore, the amount of friction due to the material of which the beach is composed, the angle at which the wave breaks and the obstructions with which it comes in contact, that it is not possible to calculate with accuracy the force exerted by these wavelets on the materials composing the beach.

An approximation of the tidal energy may, however, be obtained.

The volume of water displaced by the breaking wave is the product of the depth of the water in repose, before being affected by the wave, by the length of the wave and any given width.

As a result of a great number of observations, the following may be taken as the mean conditions of the wavelets of a spring tide, having a rise and fall of from 15 to 20 feet, flowing up a beach composed of rough sand and shingle, with an inclination of 5 degrees, or about 1 in 10. The height of the breaking wavelet from trough to crest, 1 foot; depth of water in repose, 6 inches; the length of the wave, 10 feet; and the number of waves, 15 per minute. Taking the weight of sea-water at 64 lbs. per cubic foot, the weight of the volume of moving water would be, for a given width of 1 foot of the shore

ft. ft. ft. lbs. lbs. ton

10 x 1 x 0·5 × 64 = 320 = 0.142

Taking the mean height that the water of the wave falls as 6 inches, the kinetic energy of the wave would be

320 × 0.5 = 165 foot-lbs. = 0.074 foot-ton

that is to say, the energy due to each wave would be capable of raising 165 lbs. of pebbles a height of 1 foot.

Taking the weight of stone in water as 100 lbs. per cubic foot, and that a pebble 2 inches in diameter weighs 0.25 lb., the force of each wave would be capable of moving 660 pebbles of this size, or 9900 a minute and.2,376,000 in a tide. If the whole energy were absorbed in moving the face of the bank, it would be capable of raising the pebbles of which it was composed to a depth of 1.65 feet over a width and height of 1 foot

Allowing 15 waves to the minute, and the tide to be sufficiently high for 4 hours to act on the bank, the energy developed by every tide on each foot of width of the beach would be equal to raising 266 tons 1 foot high

The whole energy of the wave is not, however, available for lifting and transporting the pebbles of which the bank is composed, a large proportion being absorbed by friction, but the above calculation is sufficient to give some indication as to the enormous power that is developed by tidal action, day by day, on the coasts, and the capability of the wavelets due to the tides for building up shingle-banks and for drifting material along the beach.

CHAPTER IV.

SEA-WALLS.

THE walls dealt with in this chapter are those required for the protection of low-lying land from the incursion of the sea, where the beach is not sufficiently high to prevent the tides from washing over; for the preservation of cliffs where the land above is of sufficient value to warrant the cost of protection; and those at seaside towns, where the formation of roads and promenades along the sea-front necessitates the construction of retaining walls for holding up and protecting them from damage by waves.

The walls for these purposes may be divided into two classes, sloping and upright; the former being most commonly used for land defence, and the latter for the maintenance of roads and promenades.

A difference of opinion exists amongst engineers as to the respective advantages of two kinds of wall for sea-coast protection. In England the upright wall has in most cases been adopted, while in Holland and Belgium the sloping form is more commonly in use.

The relative merits of sloping and upright walls for harbour purposes was the subject of investigation by the commission appointed to inquire into the proposal to construct a harbour of refuge at Dover in 1846, and the opinions of all the principal engineers and nautical experts were obtained. A perusal of this evidence with the light of subsequent events will be of great value to an engineer engaged in the construction of sea-walls. At that time there was no example of the construction of an upright wall in 40 feet of water, and the attempt to carry out such a work was regarded more or less as an experiment. In fact, several of the witnesses gave evidence to the effect that the construction of such a wall was practically impossible, and that a sloping mound, such as had then been constructed at Plymouth

and Cherbourg, was the most suitable form. The majority of the evidence, however, preponderated in favour of an upright wall, and it was contended by the witnesses who were in favour of this form that the percussive effect of waves was far less violent on an upright wall than on a sloping face, on which the waves were changed from undulations to breakers.

This evidence has been justified by the manner in which the Admiralty Pier at Dover has weathered all the gales which have occurred since its construction half a century ago, as compared with the constant damage which occurred after every gale for many years to the breakwaters at Cherbourg and Plymouth, and the great cost incurred in repairs; and also the destructive effect of the waves on the wall at Alderney, the completion of which was finally abandoned.

There seems, however, to be a consensus of opinion that, for deep-water purposes, an upright wall resting on a sloping base is more subject to the destructive effect of the waves than either of the other two.

The different effect of upright and sloping walls on waveaction may be best realized by watching the sea break with violence in a storm on a sloping breakwater; while within a short distance, where the slope terminates at the entrance into the harbour in an upright wall, and where the depth of the water is great, the waves only rise and fall with gentle undulations.

A distinction must be drawn as to the action to which walls constructed parallel with the coast for protective purposes are subject as compared with those built for break waters. The former have to act as retaining walls to the land behind, and to contend with the pressure of the earth at the back. These walls at one period are free from any pressure in front, while at other times they are subject to the impact of waves which have broken on the shallow shore in front; whereas the walls of breakwaters are not subject to land pressure, and have water on both sides, and when built in deep water, the waves which come in contact with them on the outside have more the character of waves of undulation than of progression, unless the profile of the wall is such as to change the character of the wave.

The force to be encountered by sea-walls for coast protection consists-(1) of the statical pressure due to the head of water brought against the wall by the upward projection of the waves; (2) the percussive force due to the momentum of a large mass of