waves in a given period is an indication of their size, and fewer large waves break on a shore in a given time than small ones. With small waves the number frequently reaches from fifteen to twenty in a minute.

As already stated, any disturbance of the water caused by wave-action rapidly dies out as the depth below the trough of the wave increases.

The depth to which the agitation extends is in the ratio the length bears to the height. Thus a wave 30 feet long and 10 feet high would affect the water 6 inches at a depth of 10 feet below the bottom of the wave; whereas a wave of the same height and three times the length would agitate the water 18 inches below the bottom of the wave.

The heavy seas which break on the sloping mounds of stones at such breakwaters as Plymouth, Portland, Holyhead, and Cherbourg cease to have effect at about 15 feet below low water. Beyond this the stones remain at their natural angle of repose, or at a slope of from 1 to 1 to 1; while above this within the range of the breaking waves they become shaped to a slope of from 7 to 12 to 1, or about the same inclination that a shingle beach assumes after a gale.

This depth, however, may be exceeded when a form of breakwater is adopted that lends itself to increasing the effect of the breaking waves.

At Alderney, where the breakwater consists of a rubble mound surmounted by an upright wall, it was found that the stones of the mound remained undisturbed at a depth of 15 feet below the surface previous to the upper wall being built. After this was constructed, the destructive action of the waves was so great that the mound was affected at more than 20 feet below low water, and a clean breach was made through the wall between the level of high and low water.

Tynemouth north pier consisted also of a rubble mound foundation, on which was built an upright masonry wall, the depth at low water on the sea side being from 28 to 30 feet, the top of the rubble mound being 9 feet below low water, and the rise of a spring tide being 16 feet.

The waves broke on this mound with such force in heavy storms as to cause the water to be thrown upwards above the pier to a height of 160 feet, and the percussive action of the waves on the wall was so great that a breach was made through the wall,

and the structure generally so damaged that it was found necessary to reconstruct the outer portion.1

Movement of Material at Great Depths.-Any movement of sand, stones, and shells that takes place in water of considerable depth is due to tidal currents, and not to wave-action. A column of water several fathoms in depth, moving with a velocity of 3 or 4 knots, is fully sufficient to account for the displacement of materials of considerable size lying on the bed of the ocean.

It is well known that there is a movement at the bottom of the deep-water channels that intersect the sands lying off the shore, but the sand is only drifted backwards and forwards with the flood and ebb tide.

When there is considerable wave-motion on the surface of the sea, at a depth at which divers are able to work the water is found to be motionless. On the other hand, where the tidal currents run strongly, divers are unable to hold their ground on the bed of the sea.

As to the effect of tidal currents on the movement of submerged sand-beds in tidal channels, and, as showing that this movement is one of oscillation and not transportation, an instance may be recorded which occurred at the mouth of the Gironde. A steamer was sunk by a collision opposite Verdon, and rested on her keel at the bottom of the channel in 6 fathoms at low water, the masts and chimney only showing. At the end of the ebb tide the sand was so scoured as to leave a space under the keel at both ends, leaving the hull only supported in the middle; at the end of the flood tide the vessel was again completely buried in sand; the sand-bed extending 100 yards fore and aft of the vessel and 50 yards from each side."

Power of Waves.-The power of waves due to heavy gales in drifting material on a beach, in moving heavy stones, or in the destructive effect due to percussive action on cliffs and sea-walls is almost incredible.

Stones of considerable size are frequently cast on to the top of shingle banks 8 to 10 feet above high water. At Brighton it is recorded that in south-west gales the shingle has been thrown on to the road 18 feet above high-water level.

1 Further information as to the action of waves on seawalls will be found in "The Designing and Construction of Harbours," by T. Stevenson. Edinburgh, 1874. "Harbours and Docks," by L. F. Vernon-Harcourt. London, 1885.

"Étude sur les Rivières à Marée," Partiot. Paris, 1892.

During a heavy gale from the south-west, from measurements made by Sir John Coode, on one occasion he ascertained that 3 million tons of shingle had been torn down from the Chesil Bank and carried seaward by the waves, and on another occasion 4 million tons were scoured out, three-fourths of which was removed back after the gale ceased.

During a heavy gale in the winter of 1824, a laden sloop of 100 tons burden ran on the Chesil Bank, and was carried by a wave and cast on the top of the bank at a place where it was more than 30 feet above ordinary high water.

At Hove it was calculated that 27,000 tons of shingle were removed from the beach in a heavy gale during one set of spring tides, and that 10,000 tons were drifted along the beach in two tides on another occasion.

In the Solent, near Hurst Castle, a shingle bank, 2 miles long and 12 feet high, consisting principally of flints resting on a clay base, was moved forwards in a north-easterly direction 40 yards, during a storm in 1824.

The Northam pebble ridge, which extends for 2 miles in a north-easterly direction from Westward Ho, has on more than one occasion, during very heavy gales from the west and northwest, been moved shorewards a distance of 30 feet, and the clay base on which it rested exposed on the seaward side. This bank is composed principally of large boulders, many of which, 12 inches and upwards in diameter, and weighing from 40 lbs. to 50 lbs., are on the top of the bank, which is about 6 feet above the line of ordinary high water; and many as large as this were thrown over the bank and some distance inland during the gale referred to.

This bank also affords a good illustration of the forces at work in drifting material along the coast for long distances. Rockfragments from Hartland Point and the cliffs on the coast between there and Abbotsham have been rolled along the beach in the form of boulders, each weighing from 10 lbs. to 150 lbs., for a distance of from 10 to 15 miles, and piled up into banks of from 100 to 150 feet wide and 20 feet high, the top being from 6 to 9 feet above high water.

On the coast of France, where extensive deposits of sand are heaped upon the beach, during very heavy westerly or easterly gales large quantities of this, amounting sometimes to as much as from 25,000 to 40,000 cubic yards, are thrown, in the course of a few days, into the channel at the end of the windward side of the

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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.