Page:Encyclopædia Britannica, Ninth Edition, v. 11.djvu/479

waves to be fully formed, or where it becomes so shallow as to reduce their height after they are formed. It must be observed that in short fetches, as in narrow lochs or arms of the sea, waves are raised higher during very violent gales than the formula indicates ; though it does not appear that such waves go on progressing in height in the same high ratio for any considerable distance. Vertical Scoile,. Fig. 4. For short reaches and violent squalls, the formula given in column 5 of the foregoing table will be found more suitable, viz. : 7t = l-5 */ d + (2 5-t/d) For all ordinary situations the results in the following table will be found sufficient as a general guide. Table showing ajrproximate Heights of Waves due to lengths of Maximum Fetch bij the Formula. Miles. Heights. Miles. Heights. Miles. Heights. Miles. Heights. 1 3-0 20 7 1 39 9-4 130 17-1 2 3 4 21 7-2 40 9-5 140 377 3 3-8 22 7 4 41 9 6 150 18-4 4 41 23 7-5 42 97 160 19-0 5 4-3 24 7-6 43 9 8 170 19-5 6 4-6 25 7 8 44 9 9 180 20-1 7 4 8 26 7-9 45 10-0 190 207 8 5-0 27 8 46 10-2 200 21-2 9 5-3 28 8-1 47 10-3 210 217 10 5-6 29 8-3 48 10-3 220 22-2 11 57 30 8-4 49 10-5 230 227 12 5-9 31 8-5 50 10-6 240 23-2 13 6-0 32 8-6 60 11-6 250 237 14 6-2 33 8-8 70 12-5 260 24-2 15 6-3 34 8-8 80 13-4 270 24 6 16 6-5 35 8 9 90 14-2 280 25-1 17 67 36 9-0 100 15-0 290 25-5 13 6-8 37 9 2 110 157 300 26-0 19 7-0 38 9-3 120 16-1 xposure -ob- The Comte de Marsilli, in 1725, observed waves 14 feet 10 inches in height where the longest possible fetch is 600 miles. At Wick, with much the same exposure, waves of about 40 _ feet have been seen to strike the breakwater. But the highest which are known to have been accurately measured were by Dr Scoresby in the Atlantic, where they attained the height of 43 feet above the hollow. Cialdi gives observations of others which were from 60 to 108 feet high, but he does not state how the heights were ascertained. It does not follow, however, that the line of the maximum exposure is in every case the line of maximum effective force of the waves, for this must depend, not only on the length if fetch, but on the angle of incidence of the waves on the walls of the harbour. What may be termed the line of maximum effective exposure is that which, after bein" corrected for obliquity of impact, produces the maximum result, and this can only be ascertained from the chart by successive trials. Let x= the greatest force that can assail the pier, h= height of j waves which produce (after being corrected for obliquity) the maxi- mum effect, and which are due to the line of maximum effective exposure, o = azimuthal angle formed between the directions of pier and the line of exposure ; then, when the force is resolved normal to the line of pier, x <xh siu -a ; but if the force be again resolved in the direction of the waves themselves, the expression becomes x a h sin 3 . It should not, however, be forgotten, in connexion with this subject, that in some cases there are modifying elements to which special attention requires to be given. The waves, for example, when approaching the land obliquely, alter their direction when they get close to the shore, in consequence of the change of depth, and from this cause they approach more nearly at right angles to the general line of the beach, and thus strike with greater force than the line of maximum effective exposure would lead us to expect. The extraordinary difference between waves which impinge at right angles and others which have even a very slight amount of obliquity has been shown in the most unmistakable man ner at the Wick breakwater, where all attempts to make the work stand when exactly at right angles to the waves have hitherto been unsuccessful. It was found by ob servation that while waves coming from the direction of S. by E. struck the outer part at normal incidence, they struck the landward end of the same kant at an angle of 81, giving 9 of obliquity. This small measure of relief was found to make a great difference in the impact upon the wall. The value of the line of effective exposure varies in certain localities with the geographical configuration of the land, as in Loch Fyne, where the wind seems to alter its direction with the winding of the loch, so that the effective fetch is greater than the width of free water at the place. On the other hand, where the channel expands, the height of the waves is decreased, as at Craignure in Mull, where the highest wave observed during the winter of 1853-4 was very much less than the formula indicates. In a case such as represeute 1 in fig. 5, the waves which enter the entrance channel or harbour mouth B, though generated appa rently in the fetch AB, are largely due to the fetch CB. For the waves generated in the length CA pass round the point A, and are thereafter subject to the impulse of the wind along the line AB. The waves then which enter the harbour mouth, instead of having their point of genesis at A, really Fig. 5. take their origin at C, and their height is due to the fetch CB, though reduced by a deflexion round the point A. Lateral friction is due to the passage of the end of the Later wave along the face of a vertical wall, while lateral erosion frictic is due to the end of the. wave breaking as it passes along and . the face of long talus walls or sloping beaches. Force of Waves. Smeaton, in referring to the propriety of using joggles in the masonry of the Eddystone Lighthouse, says " When we have to do with and to endeavour to control those

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