or other artificial works, the supply of beach material has been arrested; and this has been followed by the denudation of the coast to the leeward.

The protection of sand-dunes has also been deemed a matter of sufficient importance to warrant legislative interference to prevent the abstraction of the plants, which prevent it from drifting.

The protection of "marram grass was held to be of so much importance that in an Act passed in the reign of George II. (15 Geo. II. c. 33), after reciting that certain lands on the north-west coast of the kingdom were prevented from being overflowed by the sea by sandhills composed of such loose sand that in dry weather the sand was blown upon the adjacent land, to the damage of the land and the destruction of the banks, and that it was found by experience that the best way of preserving the hills was to plant them with a rush or shrub called star or bent grass, which was found to be an effectual means of keeping the banks firm; and that the sandhills were frequently damaged by persons cutting, pulling, and taking away the grass for making mats and brooms: it was therefore enacted that any person convicted of cutting or removing the grass without the consent of the owner, or unlawfully having such grass in their possession within five miles of the sandhills, should be liable to a penalty of twenty shillings, or in default of payment three months' imprisonment, and for a second offence one year's imprisonment. A similar enactment which had been passed in 1695 for the protection of bent grass in Scotland was confirmed.

CHAPTER II.

THE ACTION OF SHORE WAVES.

As waves are one of the chief factors which have to be dealt with in works for sea-coast protection, it is necessary to have a clear idea of their motion in the shallow water which prevails on coasts, and as to the manner in which they act on a beach or sea-wall.

Although the waves in the shallow waters near the coast do not attain the dimensions or the magnificent grandeur of those in the open sea, yet during a storm the shore presents a most impressive scene, and affords a striking example of the enormous power set in motion by natural causes.

Shore or littoral waves are of a different character, and to some extent are governed by different laws from those in the open ocean.

The waves which have to be considered in connection with coast destruction and protection are-tidal waves, wind waves, ground swells, breaking waves.

1. Tidal Waves. In the great majority of cases the waves which affect beaches, cliffs, and sea-walls are those which occur when the rise of the tide affords the necessary depth of water for their formation.

The great tidal wave of the ocean, which causes the rise and fall of the water on the coast, is therefore an element that has to be taken into consideration.

The maximum effect due to the tidal wave is felt at the time of high spring tides, when accompanied by heavy on-shore gales.

The height to which the water rises above the beach is considerably increased during gales. The effect of gales is greatest when the wind, after blowing along the coast in the same direction as the main stream of the flood tide, changes about the time of high water to an on-shore direction.

The increase above the normal height due to gales varies from

3 to 4 feet, and under exceptional conditions to 5 feet and even 7 feet.1

There are also the small but constant and ever-present waves derived from the swelling of the tide on the shore, which have a material effect on the movement of beach material.

When the tide is rising, the water for some distance from the coast is flowing towards the shore, and when falling is flowing from it.

The tidal wave moves along the deep water of the open sea with greater velocity than in the shallow water near the coast. The crest of the wave in the open sea is therefore in advance of that near the shore, resulting in an oblique lateral movement along the shore. The water is also slightly heaped up in the centre of the channel, assuming a convex shape on the flood, and being concave on the ebb.

The tidal wave, being a wave of translation, when it encounters the obstruction caused by the shoaling of the shore, is reflected back and a series of small oscillations or waves is set up, which break when they reach the low-water line.

Observations of the flowing or ebbing tide, on even the flattest beach, will show that when there is an entire absence of wind or other disturbing cause, the rise and fall of the tide is not effected by a mere vertical swelling and depression, or rising and fall of the water, but is accompanied by a series of small waves varying in height according to the condition of the tide and the beach, from 6 to 24 inches, which break on the beach at the rate of ten to twenty a minute, one of the series reaching a maximum height.

These wavelets are never absent from the shore, except when absorbed by the larger waves due to gales.

The height of these wavelets is greater when the beach rises rapidly. Up to a certain point, these tidal wavelets are increased by a wind blowing on-shore, but if the wind-force is great, the tidal wave becomes lost in that due to the wind.

As these wavelets break on the shore the particles of water assume a horizontal motion, and the wavelet becomes a vehicle for the transmission of mechanical force, and capable of transporting material.

1 "Effect of Wind and Atmospheric Pressure on the Tides," by W. H. Wheeler, M.I.C.E. Paper read at the British Association Meeting, Ipswich, 1895, and Report of Committee, 1896.

Wind Waves.-Waves produced directly by the wind blowing on the surface of the sea.

These waves are pure undulations. The form of the wave is transmitted towards the shore, but there is no forward progressive movement of the water until the margin of the shore is reached.

There are two motions operating in the formation of wind waves -one horizontal, due to the wind which generates the undulation; and the other vertical, due to the force of gravity. These two motions take place within a defined orbit, the limit of which is regulated by the force of the wind which produces the undulation and the depth of the water in which it takes place.

The particles of water in the crest or upper half of the undulation, or that above the level of the water when in repose, move upwards and forward in the same direction as the travel of the wave, those contained in the lower portion, or the trough, moving downwards and backwards. The maximum horizontal motion takes place at the top of the crest and bottom of the trough, and is at zero at the centre of the undulation, where the motion is only vertical.

The common form of wind waves in the open sea is cycloidal, but the shorter shore waves assume more the form of an ellipse.

Although a wave completes its undulation within a given orbit, the height of which is measured from the crest to the trough, the particles of water below the trough must to a certain degree be disturbed, the amount of this disturbance rapidly vanishing as the depth below the trough of the wave increases.

Waves moving towards the coast along a shoaling shore show that they feel the effect of the shoaling by altering their shape. The form becomes gradually more abrupt, the crest more raised, the length decreased, the orbit more elliptical, and the whole mass begins to change from a wave of simple oscillation to one of translation. Finally, when the depth is not sufficient for the complete formation of the undulation, the bottom of the wave is retarded by encountering the friction of sea-bed, the top is thrown forward and the vertical oscillation is changed into a horizontal movement, the water contained in the wave being thrown forward on to the beach.

A purely oscillating wave cannot cast any material lying seaward of its plunge or breaking-point on to the shore. If two floating substances be thrown into the water, one immediately beyond the wave breaking on the shore, and the other within

J

its range, the former will flow away with the tidal current, while the latter will be thrown on to the beach.

Although the wave immediately in the rear of the one that breaks retains its undulating character, any floating substance within its range simply rising and falling and getting no nearer to the shore, while a substance contained in the shoreward wave is thrown forward beyond the water-line, yet the particles of water below the rear wave have a certain amount of translatory movement due to the effect which the shoaling of the bed has on the water below the wave's orbit.

This horizontal motion of the particles below the wave in shallow water is proved to be sensible by the broken water that occurs on the surface over a reef of rocks or on the edge of a shoal lying below the orbit of the wave.

When a wave meets a barrier projecting from the bed of the sea the water is thrown upward, and the wave which comes in contact with this obstruction attains an increased height.

The translatory movement of the particles of water below the wave accounts for substances being thrown, during heavy gales, on to the beach from greater depths than the height of the wave breaking on shore would appear to warrant.

This translatory movement, however, only extends for a short distance from the shore-line. Beyond this the waves, being mere undulations, are incapable of conveying material towards the land.

In order to find out the depth at which waves act on the seabed, an experiment was made in Lake Ontario, where in storms the waves are of considerable dimensions, by anchoring four empty boxes on the sloping sand-bed of the lake at equal distances over a length of 650 yards, in depths of 6 feet, 12 feet, 18 feet, and 20 feet. After storms it was found that the first box in the shallow water became filled with sand; the box in 12 feet of water half full; in the one at 18 feet there was very little sand; and at 20 feet there was no sand in the box.

In storms or heavy ground swells waves will break in depths that are great in comparison with their height, where the bottom is abrupt or uneven, or where there is sudden shoaling.

Ground-swell waves which are of great length, although of small height, break in depths where ordinary waves would remain undulations.

This translatory movement of the water below the wave itself