Much of the region in which the true hurricane or typhoon occurs is not ordinarily subject to long-period swells, and when such are observed it is desirable that seamen should have precise data for judging the force of wind which produced them, for if very great it is certainly associated with these whirling storms which are so disastrous to shipping. If the navigating officer will note the number of seconds occupied by the subsidence and up heaval of a patch of foam as it falls and rises with the swell and multiply the number by 31 he will know at once that the product is only a few miles an hour less than the velocity of the wind which produced the swell, and will therefore be able to place the distant disturbance in its category in Beaufort's scale of force with greater precision than if he rely upon "sea sense" unaided by measurement.
In order to realise the process of wave transmission of ter the wind has dropped, let us picture the profile of a wave from one trough to the next following trough. The water between the first trough and the crest is rising, that between the crest and the next trough, falling. The continual rise of front is the advance of the wave; in the subsiding back of the mound we see the action of the propelling agent, which is the force of gravity. The less the depth of water participating in the transmission, the slower will be the progress of the rising front, and for any given depth of water there is a limiting speed of transmission which can be calculated from the force of gravity. A strong gale in the North Atlantic produces waves more than Boo feet from crest to crest travelling 45 miles an hour, and after the wind drops the speed is maintained as long as the depth of water is comparable with the wave-length, but when the depth is reduced from Boo to 8 feet the speed is diminished to about one quarter, and the distance between crests reduced to 200 feet. Thus the league-long crests, widely separated, of the ocean swell travelling swiftly up the English Channel are bent back near the coasts of France and Eng land, upon which rollers, ranged nearer to one another advance more slowly but reach the shore at intervals of time equal to the period of the swell.
When the depth of water below the troughs is comparable to the height -of the waves from trough to crest we can no longer say that there is definite depth in which the wave as a whole is being transmitted, and in fact the rate of transmission is con siderably greater at crest than trough. The ridges then cease to be symmetrical, become steep-fronted and cusped, and at last the cusp curls over in a scroll and falls.
Beaches.—At Eastbourne during the larger, or spring, tides near the times of new and full moon the difference of level be tween high and low water is about twenty feet. At high water on a calm day the sea is a few feet below the top of the bank of shingle. At low water the whole bank of shingle and an almost level stretch of sand beyond lies exposed. At high water on a rough day there is sufficient depth for large rollers to hold to gether until near the shore, so that a spectator on the beach can watch the process of steepening and curling over from close quar ters. The relation of the depth of water in which a wave breaks
to the height of the wave varies somewhat with the slope of shore and direction of wind, but the facts may be expressed in a general way by saying that a wave crest is on the point of break ing when its height above the trough behind it is equal to the depth of water below that trough. The depth of water in front of the wave which is about to break upon a sloping shingle beach depends upon the amount of backwash which it happens to en counter from the surge of the preceding breaker and it may even fall upon bare shingle.
Shingle beaches are the wave's own making, for wherever the conditions of supply cause a pile of pebbles to gather on the shore, the stones flung up by the waves tend to collect. These are driven up in the full depth of the surge flung by the breaker, but the settlement of water in the crevices of the shingle dimin ishes the depth of the backwash and consequently many stones are stranded. The stranding action is most marked with buoyant materials, hence the wrack of driftwood, sea-weed and shells which forms a line at the highest reach of the surge.
The seaward slope beyond low-water mark of spring tides at Eastbourne is extremely slight. This has two consequences, first that a large wave breaks far out from the shore, secondly that its discharge is not dissipated as a surge but initiates a new kind of wave which is transmitted to the shore across the inter vening sheet of shallow water. The new wave is the perfect type of a bore, the foaming front very steep, the slope behind so gradual as to escape the notice of the eye. The foaming ridge travels steadily towards the shore with unchanging form but diminishing height. If we fix our attention upon a particular patch of foam we shall see that it is left behind by the foaming front as long as the water has some inches depth, but when the depth is reduced to about one inch the foam of the overfall is pushed along by the advancing ridge, accumulating in a scroll of froth which is finally left stranded on the sandy beach. These foaming ridges, sometimes called waves of translation, can be followed by the eye without difficulty, their individuality being persistent, but among deep-sea waves individuality is strangely elusive. The eye is attracted by and follows trustfully the wave which is larger than its fellows but soon finds that it is no longer looking at the largest wave, which is now the next behind, the first having outrun the supply of energy. This elusive effect is best illustrated in a group of waves in smooth water such as that produced by throwing a stone into a pond. The front wave of the group flattens out until it ceases to be visible while at the rear of the group a new wave appears. In water which is deep as compared with the wave-length the rate of advance of the group is only one half the speed of the individual waves, which travel through the group. In shallower water the waves do not so quickly outrun the energy and when the depth is very small in proportion to the the two rates of transmission are the same, and we have the typical bore, or wave of translation.