been driven over the land at heights much greater than that at which vegetation commences and far above the ordinary run of the surf. vel of The level below the surface of low water at which mud ul a reposes will be found of very considerable value in judging asure o f t ^ e eX p OSU re of a coast. It may appear unlikely that the sur " e disturbance of the surface of the sea occasioned by storms should be propagated to great depths, but there is no want of evidence on this head. Sir G. B. Airy, the astronomer- royal, has shown, on theoretical grounds, that at a depth equal to the length of the wave the motion is T Jv- of that at the surface, and mentions that heavy ground swells break in a depth of 100 fathoms. Sir J. Coode found, from under water examinations made with the diving dress, that the shingle of the Chesil Bank was moved during heavy winter storms at a depth of 8 fathoms ; and Captain E. K. Calver, R.N., has seen waves 6 or 8 feet high change their colour Pitching r *~ WAT E R tt/t S
- ! 2
- / 6 o
(Jf a LOW I ^ f^ lie a rl i n <j <& C 1 | 1 Wf J I Paul ^ n ^ Roadwati } Pitching Cofr HP<I rt in tff/f* /*/} Fig. 3. from the abrasion of the bottom after passing into water of 7 or 8 fathoms. Captain Cialdi maintains that waves may excavate the bottom at a depth of 655 feet in the ocean, of 163 feet in the Mediterranean, and of 132 feet in the English Channel and Adriatic From these statements it may easily be inferred that in exposed situations mud can not repose near the surface. Applying su:h a test to the German Ocean, it is found that in Shetland mud lies in from 80 to 90 fathoms below low water, and its level gradually rises till, on the coast of Holland, it is found at a depth of from 16 to 12 fathoms at the mouth of the Elbe. Now, the violence of the waves upon the shores of the German Ocean certainly corresponds with the rise in the level of the mud, there being a gradual decrease as we come from Shetland and the north of Scotland where, as will be afterwards shown, wonderful energy is displayed by the sea to the coasts of Holland, where the waves are much modified. Although it is no doubt true that the flat- bottom vessels of the Dutch are built purposely for resist ing a heavy surf, still the fact of their being able to take the open beach in nearly all weathers without any protection from harbours proves that the waves are very much reduced before they reach the Dutch coast. Mr Hyde Clarke says " On the coast of Zealand the Dutch reckoned 8.V feet as the greatest height to which any wave would be thrown." Tn comparing an existing harbour with a proposed one, perhaps the most obvious element is what may be termed the line of maximum ejcposztre, or, in other words, the line of greatest fetch or reach of open sea, and this can be easily measured from a chart. But though possessed of this information, the engineer still does not know in what ratio the height of the waves increases in relation to any given increase in the line of exposure. In 1852, in the Edin b uryh New Philosoph. Journal, Mi- Thomas Stevenson stated as the result of experimental observation that the heights of the waves were most nearly " in the ratio of the square roots of their distances from t/tc u indward shore;" or, hcn h = height of wave in feet, d distance in miles, and a a coefficient varying with the strength of the wind, then Ths truth of this law has since then been variously tested. 1 The accompanying table contains some of the observations made in 1850-52, as well as later observa tions on the effects of heavy gales which could only be made at long intervals of time : Lino of maxi mum o> postnv. Law of ratio of square roots of tlic dis tances from Hi wind ward shore. Place of Ol>S-Tv r ation. Length of Fetch in Miles Nautical. Observed Height of Wave. Height due to Fetch, calcu lated from Formula h= Wd. Height due to Fetch, calculated from Formula h = l-5/d + (2-5 -I d). Vide p. 4.">7. Scalpa Flow 1-0 13 o-o 9-0 9 10-0 11-0 110 24-0 30-0 31 380 38-0 40-0 44-5 4i fi 05-10 11-1 -0 100 Mean 40 IS 40 2-0 40 4<l 40 5 4"2 35 5-0 r K C 5 8-2 70 7-0 8-0 80 80 100 10-12 15-0 1 .-> 1-8 2-9 4-1 4-r, 4-9 6-0 5*0 5 li 8 2 84 9-2 9-2 9 :>r> 10-02 10-20 120 16-0 l J-3 30 32
- -75
- ..,|
4 4 iiC 525 5 5 5-7 0-1 7-7 8-37 8-5 9-2 9*2 9.5 99 100 15-25 18-15 Firth of Forth Clyde Glenkioe J!:iy Lake of Geneva, ^ stated by Minurd 2 Buckie Macduff Douglas, Isle of i Man, St George s - Channel ) Sunderlai d, dis ) (mice measured - fromHiokc-n Bank j 159-7 153-07 102 -G8 G3 697 7-,"9 Some of those earlier results have also been laid down in fig. 4, GO as to form a storm curve, but since the dia gram was made many more observations have been obtained which corroborate the law. The formula h= 1 5 Jd is represented by the parabolic curve in the diagram, which indicates pretty nearly the height of waves during heavy gales, at least in seas which do not greatly differ in depth from those where the obser vations were made. This formula is of course inapplicable where the water is not of sufficient depth to allow the 1 It follows from this law that the heights of embankments of reser voirs above the water surface should, eceteris parfbus, Le proportional to the square roots of the lengths of water over which the wind acts. 2 Cours de Construction des Ouvrages Hydrauliqiics, Lioge, 1852, p. 8. 3 Mr Mallet, who made these observations, said that the extreme
waves appeared to be about twice this height.
