jetties which project out from the shore. This effect, however, only extends within the range of the shallow water in which the waves break.

In the discussion on the author's paper on Bars, read before the Institution of Civil Engineers in 1890, it was stated by Mr. Mann that he had frequently seen quantities of fine sand on the east coast of Ireland, estimated at from 15,000 to 20,000 tons, carried away during a single tide from the zone lying between high and low-water mark, in easterly gales, from a length of less than a quarter of a mile, and deposited in a similar position on the foreshore further to the northward.

On more than one occasion at Plymouth during the construction of the breakwater, large blocks of stone, some of them weighing 7 to 9 tons, were removed from the sea-slope of the breakwater at the level of low water, carried over the top, a distance of 138 feet, and piled up on the inside. In one night 200,000 tons of stone were thus removed, and on another occasion 9000 tons.

At Peterhead, where a breakwater is being extended out into deep water for the harbour of refuge, and where the sea exposure is very great, waves of 30 feet in height and from 500 to 600 feet in length are occasionally encountered during heavy gales. On three occasions during storms, blocks weighing over 40 tons each have been displaced at levels below low water varying from 17 to 36 feet, and the water thrown upwards 120 feet.

At Cherbourg blocks of concrete weighing 4 tons were lifted by the waves during a north-east gale, and taken over the top of the wall, and upwards of 200 of these blocks were deposited inside the breakwater ; many blocks weighing 12 tons being moved from their places, and turned upside down.

These instances occurred in deeper water than has to be encountered in works for coast protection, and are only given as showing the enormous force exerted by waves.

Force of Impact of Waves. It is not practicable, owing to the fluid character of water, to reduce to a mechanical calculation with any exactness the force of the impact with which breaking waves strike a cliff, or other vertical face, with which they are brought in contact. If the wave be treated as a solid body moving with a certain velocity, its kinetic energy, or power to move material, would be the product of the weight and the height from which it had descended. The mean height from which the

water of a wave may be taken as descending is half that of the height from the trough to the crest. Taking a wave 10 feet high, and the depth of water where it breaks, in repose, at 5 feet; the weight of sea-water as 64 lbs. per cubic foot; the length of the wave as 30 feet; the velocity of movement due to the head of 5 feet, as 18 feet a second; the weight of the water in movement, for 1 foot in width, would be

30 × 1 × 5 × 64 = 9600 lbs.

= 4.27 tons

The kinetic energy would be the product of 4-27 tons falling from a height of 5 feet, or 21:35 tons, or 4.27 tons per foot super. That is to say, each wave would be capable of moving about 21 tons of material, eroded from the cliffs, to a height of 1 foot.

The force of the impact of the blow on the wall would be, however, reduced in proportion to the angle at which the wave struck the face, either horizontally or vertically according to the law previously given.

Experiments made by the late Mr. Thomas Stevenson with the marine dynamometer, which he constructed for the purpose of ascertaining the force of the impact of waves on harbour-walls and exposed piers, give a very much lower result than that shown by the above calculation. With waves 10 feet high, the mean pressure recorded was 1:36 ton per square foot, or about one-third of that given.

Experiments carried out with a dynamometer by Mr. Frank Latham on the sea-wall at Penzance, showed that with the wind blowing with a force of from 15 to 18 lbs. per square foot, and with a depth of 10 feet of water, the pressure of the water on the wall due to the waves striking it at right angles was from 18 to 20 cwt. per square foot; the spray rising above the wall, which was nearly vertical, to a height of from 25 to 30 feet.

From experiments made at Cherbourg during the construction of the breakwater, it was found that the force of the waves in storms varied from 3000 to 4000 kilogrammes per square metre, equal to about 600 to 800 lbs. per square foot.

In designing the sea-wall at Scheveningen, 3000 kilogrammes per square metre was allowed for wind-waves, and 5000 kilogrammes for ground-swell, equal to about 600 and 1000 lbs. per square foot respectively.

In addition to the effect of the horizontal movement of the wave, there is also a vertical action of the water on the face of the beach, which has a material effect in its disintegration. When the waves strike a cliff or sea-wall and the water is deflected upwards, in its descent it cuts out and loosens the beach.

Assuming that half the volume of the 10-feet wave described above to be thus deflected, a column of 213 tons of water would be projected upwards a mean height of 5 feet, the summit of the column reaching 10 feet above the beach. The weight of this column of water would exert a statical pressure on each square foot of the beach of 0.28 ton; and falling from a mean height of 5 feet, with a velocity of 18 feet a second, would produce an impact of 5.18 tons on each square foot. If this calculation be reduced in the same proportion as the other result obtained by the dynamometer, the blow would still be equal to about 12 tons on the square foot, repeated with each wave, at the rate probably of ten or twelve a minute.

Approximately, and under ordinary conditions, breaking waves are reflected from a vertical face upwards equal to the height of the wave.

During very heavy ground-swells, with a long fetch in exposed positions, this limit is very considerably exceeded. Mr. Stevenson has given an instance at the Bell Rock Lighthouse, where the water was thrown upwards 106 feet, and instances have occurred at the Skerries, where the water and spray have been projected 60 feet upwards, carrying with it pieces of stone on to the lighthouse roof, 240 yards from the face of the rock, one of these going through the roof, which was 50 feet above the sea.

At the breakwater at Alderney the water from the waves breaking on it is reported to have been thrown upwards to a height of 200 feet.

Even when the depth of water in front of a sea-wall or cliff is only that due to the rise of the tide, water from waves that break is thrown to very great heights. Thus at Hastings, where the beach at the foot of the sea-wall is dry at low water, and the depth of the water is only that due to a rise of 15 feet at high water, during a heavy gale in the winter of 1898 the broken water was thrown as high as the top of a large hotel, as shown in the frontispiece, which is taken from a photograph made by Blomfield of Hastings-and shingle was lifted off the beach and carried

across the promenade into the bedrooms of the houses fronting the sea. At Peterhead, as already mentioned, the water due to a rise of tide on the foreshore of only 7 or 8 feet has been known to strike the wall with such force as to be thrown upwards 100 feet.

CHAPTER III.

LITTORAL DRIFT.

THE term "littoral drift " is intended to describe the movement of the material, that is always taking place along the shores of a tidal coast, due to the action of the waves.

This material may be classed as rock fragments, boulders, shingle, sand, and alluvium. The two former, in course of time under the action of the waves, become reduced to shingle, and this finally to sand of varying degrees of fineness.

This material is sorted by wave-action, the stones and pebbles being deposited at the top of the beach above the level of mean high water, the sand being placed below this, and the alluvial matter carried to the depths of the sea. Owing to the sorting action of the waves, material of different sizes, shingle and sand, may be carried on the same beach and at the same time in opposite directions, the former towards the land and the latter seaward; while the finer alluvial matter will remain in suspension until it is carried seaward beyond the reach of wave-action.1

Although shingle and sand have accumulated in some places in great and apparently unlimited quantities, it must be borne in mind that these accumulations are the product of a vast period of time, and that the great bulk of the material was placed under different conditions from those that now prevail. An examination of the coasts of this country will show that the quantity of shingle drifting along the beach is by no means inexhaustible, but, on the contrary, is limited in quantity; and that the wear and tear of the sea-cliffs does little more now than supply the waste which is always going on from the perpetual action of the waves.

Source of Supply.-The present shape of the cliffs and their

1 Further particulars as to the movements of beach material will be found in a paper by Dr. Vaughan Cornish in the Geographical Journal of May and June,