BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF 1891 590" Cornell University Library QB 415.W56 A practical manual of tides and waves. 3 1924 012 318 915 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924012318915 A PRACTICAL MANUAL OF TIDES AND WAVES BY THE SAME AUTHOR TIDAL RIVERS; their Hydraulics, Improvement and Navigation. Price i6s. net. 1893- THE SEA-COAST; Destruction, Lit- toral Drift and Protection. Price 10;. 6d. net. 1902. LONGMANS, GREEN, AND CO. 39 Paternoster Row, London, E.G. THE DRAINAGE OF FENS AND Lowlands by Gravitation and Steam Power. Price I2J. 6d. 1888. E. & F. N. SPON, Ltd. 125, Strand, London, W.C. THE HISTORY OF THE FENS OF SOUTH LINCOLNSHIRE. Price 15 j. i8g6. SIMPKIN, MARSHALL, AND CO., Ltd. 4, Stationers' Hall Court, London, E.C. fSIK ISAAC NF.WTOX. A PRACTICAL MANUAL OF TIDES AND WAVES BY W. H. WHEELER, M.Inst.C.E. ~* author of "tidal eivers," "the sea-coast," etc., etc. WITH ILLUSTRATIONS LONGMANS, GREEN, AND CO. 39 PATERNOSTER ROW, LONDON NEW YORK AND BOMBAY 1906 AU rights reserved r PREFACE The investigation of the Tides has occupied the attention of some of the greatest mathematicians who have ever lived; and a scientific study of the theory requires an intimate knowledge of the laws of Physical Astronomy. There is, however, a practical side to the question. The fact of the existence of the Tides and the raising and lowering of the water of the sea twice every day affects a very large number of people engaged in maritime pursuits, to many of whom the cause of the tidal phenomena that is so intimately associated with their daily lives must have some interest ; as also to those having the designing or maintenance of Harbours, Elvers, and Docks, or of Sea-Coast protection. It has been the endeavour of the Author of this book to give as practical an account as possible, and free from all mathe- matical demonstration, of the action of the sun and moon in producing the tides; and also of the physical causes by which the tides are affected after their generation, and of their propagation throughout the tidal waters of the earth. As a matter of general interest one chapter is devoted to the history and development of tidal science. As the time of the tide and the depth of water in tidal channels varies from day to day, it is essential to every mariner who has to pilot a vessel over a bar, or along a tidal river, or into a dock, to ascertain what depth of water he may count on to carry the vessel under his charge to its destination. For this purpose he has to consult a tide table, and if the weather be normal he may rely on the information there furnished him. The method of recording tides and constructing tide tables is fully explained. If, however, storms prevail, the depth of water vi PREFACE. may be affected to a considerable extent. He has then to rely on his own judgment as to the effect of the prevailing gale on the tides. To assist in this, the result of investigations as to the effect of wind and atmospheric pressure on the time and height of the tides as calculated is given. The laws relating to the formation of tidal currents as distinguished from tidal waves is explained, and their effect on navigation dealt with. The action of waves is explained, and an account given of the remarkable results due to cyclones and seismic disturbances, generally known as " tidal waves." The other chapters deal with the mean level of the sea and tidal ranges ; river tides and bores ; tidal gauges and the construction of tide tables ; the use of tidal action in producing mechanical power ; also secondary undulations and seiches. The Author disclaims any attempt to deal with the difficult subject of the tides in a scientific way. His object has been to bring together information and facts relating to the tides, contained in many scattered papers, reports, and publications, which, though known to those who have made a study of tidal science, are not easily accessible ; and to produce a handbook that may be of interest and practical service to those who have neither the time nor the opportunity of investigating the subject for themselves. Some of the facts relating to the tides will be found recorded in more than one place. This has been necessary in order to make the subjects dealt with in the separate chapters complete, but repetition has been avoided as far as possible. W. H. WHEELER. Boston, Lincolnshire. CONTENTS CHAPTEK j.^,5^ Preface ... v I. Introdcction J II. Development op Tidal Science 5 III. The Sun, the Moon, and the Earth 33 IV. The Making op the Tides .... 41 V. Propagation of the Tidal Wave .... 56 VI. Tidal Currents , . es VII. Mean Level of the Sea and Eange of the Tides 69 VIII. Effect of Wind and Atmospheric Pressure on the Tides . 7i IX. KiVEB Tides 89 X. Wind Waves . 107 XI. Seismic and Cyclonic Storm Waves . 129 XII. Tidal Bores in Rivers j 141 XIII. Tide Tables and Tide Gauges .... 15g XIV. Secondary Unddlations and Storm Warnings 16i XV. The Tides as a Soueob of Power I70 APPENDICES 1. List of Books, Papers, Reports and IPamphlets relating to Tides AND Waves consulted in the preparation of this Book . . . 175 2. Velocity of the Tidal Wave . 182 Table 1. Velocity in the Open Sea 182 „ 2. Velocity of breaking Shore Waves 182 „ 3. Examples of the Velocity of Tidal Waves obtained BY Observation and by Formula 183 viii CONTENTS. PAGE 3. Tidal Data ... 184 Table 1. Variation in the Mean Level op the Sea bound the English Coast • • 184 „ 2. Datum of L.W.S.T. used for the Admiralty Tide Tables 185 „ 3. Data fob Tidal Observation and Charts in Great Britain and the Continent of Europe . ... 186 „ 4. Table givino the Height of the Mean Level fob European Seas, compared with the Mediterranean at Marseilles 187 4. Table 1. Showing approximately the Hourly Kisb and Fall of the Flood and Ebb Tide ... 188 „ 2. Foe asoeetaining the Height of the Tide at Any Hour during Ebb and Flood .... . . . . 188 5. Table 1. Formula for Velocity of the Tidal Wave in Kivebs 190 „ 2. Example of Velocity of Waves as observed and as calculated by the Formula . 191 6. Table 1. Proportion of Ocean Waves . 194 „ 2. Showing the Velocity of the Wind with befeeence to the Size and Proportion of Waves . ... 194 7. English and French Nautical Measuees 195 Index ... .... 197 LIST OF ILLUSTRATIONS FIS. PAGE PoBTEAiT OF SiR IsAAC Newton Frontispiece 1. DiAGBAM OF Moon in Pebigee and Apogee .... ... 36 2. Poem of Tidal Wave . . . 45 3. Tidal Wave 46 4. 5, 6. Position op Sun, Moon, and Eaeth, in Conjunction and Opposition .... 48 7. Height op Speing and Neap Tides 49 8. Chabt of the Wokld with Time and Height op the Tides [To face 57 9. Diageam op Tidal Ccebents . . 65 10. Bange of Speing and Neap Tides .71 11. DiAGBAM OP. Wave Poem . 108 12. Teoohoidal and Ctoloidal Wave 116 13. Bebaking Wave . lyj 14. Cyoloidal Wave 118 15. Chaet showing Position op "Tidal" Waves .... . 134 16. EsTUAEY AND EivEE Tsien-Tang-Kiang . 143 17. DiAQEAH op Boke in Bay op Fundy .... 149 18. Boee in the Eivee Tbent 152 19. Bivee Severn ... 153 A PRACTICAL MANUAL OF TIDES AND WAVES CHAPTEE I. INTRODUCTION. CONSIDEEING the great length of sea-coast that surrounds these islands, the essentially maritime nature of the trade of this country, and the importance of the tidal rivers and harbours to its commerce, a general knowledge of the tides cannot fail to be of interest. To mariners and pilots engaged in navigating their vessels into and out of the narrow channels by which this country is intersected and to ports situated far up tidal channels ; and to the engineer who has to design harbours and docks and works of coast protection, a practical knowledge of tides and waves may be considered as essential. Apart from those whose professional duty may lead them to desire practical information about the tides, even an intelligent observer on the seashore who watches the gentle ebb and flow of the water ; or the great waves of the ocean breaking on the cliffs, or on a sea-wall, cannot but desire some explanation of the remarkable phenomenon that day by day comes under his observation. But while an observer of the tides may be conscious that day by day the vast body of water that bathes the shores with per- sistent regularity, gradually advancing shorewards and covering the beach, previously dry, to a considerable depth, and then as gradually retiring ; or that with equal regularity the almost dry bed of a river becomes at intervals, though varying in their times, covered with water to a depth which is sufficient to allow vessels of considerable size to navigate the channel, it is perhaps seldom realized that this tide has been propagated from a tidal "JC B 2 TIDES AND WAVES. wave generated by the action of the sun and moon in an ocean several thousand miles distant ; that from this sea two tide waves are daily propagated over more than 16,000 miles of ocean, and thence through many hundreds of miles of smaller seas and estuaries, and up all the rivers and creeks connected with them, involving the movement of every particle contained in all the tidal waters of the world, which in some parts extend to depths which are measured in miles. It is not easy to realize the vastness of the terrestrial mechanism by means of which the forces primarily imparted by the sun and moon are emj)loyed in the transmission of these tidal waters ; or of the gigantic forces employed by nature in making and propagating the tides. It is only by the aid of the tides that vessels of the largest size are able to pass along many rivers, and enter the docks, which otherwise would be unnavigable except for small boats, and that they are thus enabled to deliver their cargoes at ports situated far inland. Thus London is situated 46 miles from the sea; Hull, on the Humber, is 23 miles, and Goole 46 miles, from the North Sea ; Bristol is 50 miles from the Irish Sea ; Rouen, 77 miles up the Seine ; Hamburg, 60 miles up the Elbe ; Rotterdam, 20 miles up the Maas; Antwerp, 45 miles up the Scheldt ; and Bordeaux, 75 miles up the Gironde. The numerous small harbours that indent the coast and which form the homes of the fishing fleet only exist by the aid of the tides ; and the fishermen are largely indebted to the tides for taking them into and out of harbour. Many large and important rivers devoid of tidal flow, although of much greater magnitude, and draining vastly greater areas, are practically unnavigable for vessels of any size for want of sufficient depth of water. The Mississippi, draining a million and a quarter square miles, or two hundred times as much as the Thames, and which is 50 feet deep a few miles from its junction with the Gulf of Mexico, had only a navigable depth at its lower end where it entered the Gulf of Mexico of 13 feet before extensive training and dredging works were carried out a few years ago; the Danube, draining 316,000 square miles, had in its natural condition a navigable depth of from 7 to 12 feet along the best of its outlets ; the Rhone, one of the principal rivers of Europe, had in its natural condition a depth over the shoal places of 6 feet, and was only INTRODUCTION. 3 rendered navigable by means of a canal connecting it with the sea ; the Neva has not, except in floods, more than 13 feet ; the Volga, the longest river in Europe, has during a great part of the year only 8 feet navigable depth along its entrance to the Caspian Sea ; and the Nile, one of the largest rivers in the world, is only navigable for craft of light draught. All these are practically tideless rivers. They may be contrasted with the tidal river Thames, which comparatively is only a small river, yet is the highway to the Port of London, and which in its natural condition provides accommodation for the largest class of vessels constructed, and has the largest amount of shipping of any port in the world. The river Mersey, which is the approach to Liverpool and Manchester, with a tidal rise of 27 feet, stands only next to London in importance as a shipping centre, and provides a water- way for the great American liners, is in itself a very small river with a drainage area of only 1748 square miles. The Avon, leading up to Bristol, has only a depth of 3 or 4 feet at low water, yet owing to its great tidal rise of 32 feet enables vessels of over 2000 tons to get up the river. In non-tidal rivers the quantity of water is restricted, and varies considerably at the different seasons of the year. Their capacity for improvement is therefore limited. In tidal rivers, on the other hand, the amount of tidal water to be obtained from the seas with which they communicate being unlimited, they possess very great capacities for improvement. Thus the Clyde, with a rise of tide of 11 feet, and a drainage area of 1580 square miles, in its original state was only capable of affording navigation to the smallest class of boats. By deepening the channel, and so admitting a greater volume of tidal water from the Atlantic, the means were secured of developing Glasgow into a first-class port, which has become the birth-place of some of the largest vessels afloat. Without an unlimited supply of tidal water, this development of its navigable capacity could not have taken place. The problem as to how the tides are caused and the theory of their making cannot be regarded as altogether satisfactory. Although tidal science has engaged the attention of some of the ablest mathematicians of the last two centuries, for all practical purposes the theory remains as Newton left it. Both the 4 TIDES AND WAVES. theories that have been adopted are based upon assumptions involving arbitrary conditions that do not exist in nature. In the Preface to the Tide Tables issued by the Admiralty so late as 1903 it is stated that, " although a great deal has been done by observation to advance our knowledge of the tides at many ports both at home and abroad, there are perhaps few physical subjects which are still at the present time on the whole more unsatisfactory." While it is accepted that the tides are due to the universal gravitation of matter, yet owing to the imperfect state of the science of hydrodynamics, no mathematician has yet been able to deduce a law by which information can be furnished for any given port as to the time at which the tides will arrive, or the height to which they will rise. By the aid of Newton's theory and an examination and analysis of tidal records, however, it has been made practicable to deduce data by which this information can be supplied, and to calculate the time and height of the tides for long periods in advance, "according to the stamp first set upon them by the action of the sun and moon," for every port in the world. It may therefore be assumed that although from a strictly scientific point of view the theory of the tides has not been brought up to date, and that there is room for further investiga- tion, yet as it exists it is sufiicient for all practical purposes. CHAPTER II. DEVELOPMENT OF TIDAL SCIENCE. Four namsa sta.nrl mit, pvnmiTipnfly in fhn rlmrnlnpnipnt n f tidal science. Copernicus. Kepler. Galileo, and Newto n. ^ Copernicus was the first to place the sun in its true place as the centre of the solar system, instead of the earth as previously believed, and to prove that the earth in common with the other planets revolves round the sun. I As the result of long and patient observations, Kepler was able to show that planets, including the earth, move in elliptical orbits with the sun in one focus ; the same law applying to the moon's movement round the earth. Galileo taught the relation between space and time of falling I bodies under the attraction of gravity, and the true laws of motion. Newton, by the aid of mathematical research, formulated the laws of gravity, and proved that every particle of matter attracts every other particle with a force proportional to the mass of each, and to the inverse square of the distance between them; and applying this law to the sun, earth, and moon, was able to ex- plain how their differential attraction acting on the water of the ocean surrounding the earth accounts for the phenomena of the tides. Tidal science does not segT^i to Tia.ve received any fyreat amount of att ention from the ancient astronomers. T his was no doubt dii e to the fact that the chie f centres o_f J_earning and comm erce. Egvpt. Gree cft, an^ ;i;^,nnift. were gituafesd on an jljmost tide] ess aaa. The PhffiTii f^.ifl.Ti Tiria.rinera. howev e r ^hn navigfltprl hpYnnrl..t he Me^iter fflnean to the coasts of Spain and Franc e, and even as far as Great Britain, where they came to trade for the tin obtained from the mines in Cornwall , must have had an acquaintance with tba.ph.fti;inmfiTia.i of tllfi tlfies. 6 TIDES AND WAVES. The Eoman mariners in their voyages to Spain and Gaul and this country must also necessarily have become familiar with the tides. It is recorded that when Caesar effected his first landing at Eichborough his captains chose a night when the moon was full, because there were at that time the greatest risings of the water in the ocean. It is also recorded that when crossing from Calais to invade Britain, the south-west wind dropping as he crossed the channel, his vessels were drifted a long way by the tide ; and that in a subsequent invasion during a storm and high tide his galleys were carried up on to the shore and stranded. So far as the phenomena of the tides was dealt with at all by the astronomers of those days, the conclusion appears generally to have been arrived at that the moon had relation to the exciting cause. It was recognized that the flowing of the tide was always concurrent with the passage of the moon across the heavens, and that the water rose highest about the periods of new and full moon ; and became later and less in height each day until the moon was in the quarters, when it began again gradually to increase ; but they do not appear to have advanced further than this or to have arrived at the knowledge as to why this should be so. The earliest refexfiace to the tides is to be found i n the description of Egypt by Herodotus. 445 B.C.. where-lie _sp,eaks of the water on the coast as ebbing and flowing daily., ..Later,, Pliny, A.D. 79, ascribes its ebb and flow to the action, iif. tlie_s.ucL_ajad moon. Pytheas, a Greek merchant resident at Marseilles, and who also had voyaged across the water to the tin mines in Cornwall, not only made observations on the action of the tides, but obtained information from the mariners and fishermen. Besides the change of the tide concurrent with that of the moon, he noted that the greatest tide was always two days after the full or change of the moon, and the smallest at a similar interval after the quarters ; also that the retardation of the tides was not uniform, but was greater at or about the quadratures. Posidonius, as quoted by Strabo, partly from his own obser- vations, and also from the information obtained by dwellers on the coast of Spain, described the phenomena of the tides and their connection with the moon in some detail. He also noted that there was a variation in the height at the equinoxes and at the solstices. DEVELOPMENT OF TIDAL SCIENCE. 7 The tides were also the subject of investigation by the Chinese, and were ascribed to the breathing of the earth ; and so far back as the fourth century an attempted explanation is given of the cause of the variation in the height of the tides. In the thirteenth century an Eastern author in a treatise on the tides ascribed their ebb and flow to the alternate heating and cooling of the water by the sun and moon causing expansion and contraction ; which also was the cause of breezes on the shore of the sea ; and that as to the flow of the sea at the time of the rising of the moon, its rays penetrating to the rocks on the bed of the sea heated and rarified the water, which, seeking greater space, rolled in waves towards the shore, retreating as the moon's rays disappeared, and the rocks cooled down.^ Passing on to more recent times, Bede, who resided at Tynemouth, in the eighth century, and had full opportunity of watching the tides off the coast of Northumberland, in his work " De Eatione Temporum," says, " The tide is driven forward as if by certain influences of the moon, and again it is pushed back to its natural bounds when the force alluded to ceases, and as the moon daily recedes 12 degrees from the sun, so, on an average, the tides are daily retarded 4 points or 48 minutes in their approach to the shore. Some days before a conjunction they seem to increase. From the 5th to the 12th and from the 20th to the 27th they continually diminish. The graduations of increase and decrease not being, however, regular, which variation may be ascribed perhaps to the resistance or impulse of the winds, but most probably to the agency of some unknown power." Jlhe ^enjexal-jijationJJiaiJJia._siia_.ig, Jh^._cg^ round whic h the otl^ OJ p laao ^revolve appears to hav e been first fdre- shadowed b^F ythagora s^who lived 54P,B.C.,,in his system of the "uniyerseXwhich conceived a kosmos consisting of ten heavenly bodies revolving round a central fire, the hearth or altar of the universe ; but it was not until the siKteenth century that the Ptolemai c theory which iimdoJlJieueajthJlia ceiiks.., ^the sy stem ancTwhich was theniBiixvei'ariJx-accapted-. a,s correct, was shown to be wrong by( Copeffi ifiaa^>,Ma. work " De JBejelutionibus Orbitum-..Gelfgti um^^ ufaiished in 1542. in which_he for ever settled the tjBL,e„place jof. the sun as th®, centre of the celestial system, with the ea(E.th-.and .planets moving round it at regular iijtervals. ' " The Tides and Kindred Phenomena." — Darwin. 8 TIDES AND WAVES. ^ A few years after the death of CopernicusCKeple^jfter a long vseries of investigations of the movement of theEeavenly bodies, jwas able to complete the Copernican system, and formulated in 1609 his laws of their movements, and showed that all planets move in elliptical orbits with the sun in one focus ; that the line joining the sun and the planets swept out equal areas in equal times; and that the square of the revolutions of each planet is proportional to the cube of its mean distance from the sun. It is t he tides. He also completed the tables of planetary motion commenced by Tycho Brahe. These were the first reliable tables available for navigators, and were the precursors of the present nautical almanack. Ha ftmm p,iaffirl t.TiR ]p.w tViRt. if t.bfirft arp two bodies plaged- .jaiit->s^ ^ Althnn p ^ Galiletyfailed to gras p the true connection between the ti^ea pi Tifl tbft ftctign o f .grayfty TSs researches ^nTl^CiSs^® nf mntigp. flnfl nf fi?JIirigLbn.difis_i which, as afterwards formulated by Newton, were one. of the principal steps in deterin,iningj^ laws- of the t^ue- th«ory .loLth&itiides. /^ These laws of motion may be thus summarized — / (1) If a body be set in motion, it will continue to move I uniformly in the same direction and with the same velocity as originally imparted to it, unless hindered by some contrary impediment. (2) That when another force acts, the motion changes both I in speed and velocity proportional to the magnitude of the force. lo . TIDES AND WAVES. (3) That where one body exerts force on another, the latter reacts with equal force. Action and reaction are equal and opposite. It was not, however, till nearly the end of the seventeenth century (1687), when Newton had reduced the knowledge of universal gravitation to a practical form, that a reasonable theory of tlje-caB^ of the tides was established. Newto^reated the water rotating with the earth once a day somewhat as if it were a satellite acted on by perturbing forces. The moon as it revolves round the earth is perturbed by the sun ; the ocean, held to the earth by gravitation just as the moon is, being perturbed by both sun and moon; the moon being the more powerful of the two disturbing bodies. Having determined by mathematical calculation the relative gravitational and centrifugal forces of the sun, moon, and earth, he assumed for the sake of argument that a channel was cut all round the circumference of the earth containing water, the water being accelerated and retarded in its motion by turns, and ebbing and flowing in its channel after the manner of the sea. This acceleration and retardation he ascribed to the unequal attraction of the sun and moon; and showed that without this unequal attraction of the luminaries there would not be any motion of flux and reflux of the waters covering the earth. By the sum of the gravitational and centrifugal forces the sea is raised at the syzygies in such places as are directly under the luminaries, and also in those places which are directly opposite ; and the water is depressed at the quadratures in those places that are 90 degrees from the luminaries. From the diurnal motion of the earth and the attractions of the sun and moon the sea rises and falls twice every day ; and the water rises in the open sea at that time in which the force of the luminaries to raise is greater, and falls at that time in which the force is less ; the time of the greatest rise at any place being reckoned from the appulse of each luminary to the me- ridian of the place. * Owing to the varying position of the luminaries with regard to the earth, there results two mixed motions. When the luminaries are in conjunction or opposition their forces are conjoined, and bring on the greatest flood and ebb. In the quadratures the sun raises the water which the moon depresses. DEVELOPMENT OF TIDAL SCIENCE. n and depresses the water which the moon raises, and from thfe .result of the differences of forces the smallest tides follow. Owing to the reciprocal motion of the water the greatest tides do not occur at the syzygies, but fall on the third day after new or full moon. ^ The effect of the luminaries depends upon their distances from the earth in the triplicate proportion of their apparent diameters. The sun in winter, being then in its perigee, has the greater effect, and makes the tides at the syzygies greater, and those in the quadratures less, than in the summer season. Also the moon when in perigee raises greater tides than when in apogee ; and hence the two highest tides do not follow one another on two immediately succeeding syzygies. The luminaries also increase their distance from the equator by north and south declinations ; and as such distances increase they by degrees lose their force, and on this account excite lesser tides in the solstitial than in the equinoctial syzygies. In the solstitial quadratures greater tides are raised than in the quadratures about the equinoxes, because the effect of the moon, then situated in the equator, most exceeds the effect of the sun ; therefore the greatest tides fall out in those syzygies, and the least in those quadratures which happen about the time of both equinoxes; the greatest tide in the syzygies being always suc- ceeded by the least tide in the quadratures. Because the sun is less distant from the earth in winter than in summer, the greatest and least tides more frequently appear before than after the vernal equinox, and more frequently before than after the autumnal. The sea being divided into two hemispherical floods, the northern and southern, opposite to one another, comes by turns to the meridian of all places after the interval of twelve lunar hours ; and as the northern countries partake more of the northern flood, and the southern countries of the southern flood, the tides are alternately greater and less in all places without the equator in which the luminaries rise and set. When the moon changes its declination, that which was the greater tide is changed into the lesser, and the greatest difference of the floods falls out about the time of the solstices. As an example he quotes the tides at Plymouth when the morning tides in winter exceed those of the evening. In the "Principia" Newton calculated "that since the 12 TIDES AND WAVES. centrifugal force of the parts of the earth arising from the earth's (Jiurnal motion, which is to the force of gravity as 1 to 289, raises the water under the equator to a height exceeding that under the poles by 85,472 Paris feet, the force of the sun, which is as to the force of gravity as 1 to 12,868,200, and therefore is to that of centrifugal force as 289 to 12,868,200, or as 1 to 44,527, will be able to raise the water in the places directly under and opposed to the sun to a height exceeding that in the places which are 90 degrees removed from the sun only by 1 Paris foot and llgi„- inches." The force of the moon to move the sea he deduced from its proportion to the force of the sun as collected from the proportion of the motions of the tides in the Eiver Avon about three miles below Bristol, and from this he calculated that the force of the sun to that of the moon is as 1 to 4*815 ; and as the water excited by the sun rises to the height of 1 foot 11 3^0 inches, the moon's force will raise the same 8 feet 1^^ inches, and the joint forces of both raise the same to 10^ feet, and when the moon is in perigee to the height of Vl\ feet. These figures, however, he modified in his " System of the World," where he gave the force of the sun as able to raise tides as 9 inches, and the moon's force as 5^ times that of the sun. The moon's force, therefore, being 4497 feet, the combined force would give a tide of 5-247 feet. This, however, does not appear consistent with the fact after- wards stated, that the rise of the tides in the open sea does not exceed 3 feet. / Newton, however, admitted that the result thus ascertained was subject to modification when the proportion of the bodies of the moon and earth one to the other was more exactly defined, and the circumference of the earth more accurately determined than it had been up to that time. It has since been found that the relative forces of the sun, moon, and earth vary from those given by Newton. He pointed out that the theoretical effect thus obtained is subject to modifications owing to wind, and also to different con- ditions of the various seas throughout which the tides are propa- gated. While in the open sea the rise of the tide is not more than 2 or 3 feet, yet on the shores of continents the tides may be three or four times greater, especially if the motions propagated from the oceans are by degrees contracted into narrow spaces, or where DEVELOPMENT OF TIDAL SCIENCE. 13 the water is forced to flow and ebb with great violence through shallow places. He instances the tides at Chepstow and those in the Channel Islands, where the water is raised and depressed from 20 to 50 feet and, more ; and also those in long and shallow straits that open to the sea with mouths wider than the rest of their channel, where the tides more intend and remit their course and therefore rise higher, and are depressed lower. y He also pointed out that the tides may be propagated from the oceans through diflferent channels towards the same part, and may pass quicker through some channels than through others, in which case the same tide may be divided into two or more succeeding one another, and may compound new motions of different kinds with two greater tides and two less. Newton's theory, as amplified by Bemouilli. is general ly ^nown _a§jthgJ'Jj]qui1ihi;JMJ"tt.ihat>..JlJ3.&.iadea -mighJL to be, dealt jyith as a problem of gsciUatioa- -rarth'es— than ~t>f .equilibrium ;„ and as .Qal^io-be solved by 1rh-e-~priiteiple9— »f dynamics.. , This theory, is -gBneraUy, known as the ■■'^Dynamieftl^' asadistinctionjfrom.ihe..iJJBquilibEium..'.' thaocjf. /" In order, however, to make the application of mathematics practicable, he started with two suppositions. (1) That the earth is entirely covered with water; and (2) that the depth of this water is the same throughout the whole extent of any parallel of latitude ; both of which suppositions are inapplicable to the state of the earth. The principle adopte d by Lap lace is generally c onsidered a s more_a£ienlifLcally. CQirect_tJian_that_of Newton, b ut it is em - barrassed with inxesMgatians at) .nbspju:fi-tbat-.0.a following mathe - matician in thisi:im uitiyJiasjaad&.jis&jQ£.it. In fact. Airy in his article on the tides in the " Encyclopaedia Metropolitana," when dealing with this theory, was obliged to substitute an equivalent for it, as he considered that it would be useless to attempt to offer it in the same shape as Laplace had given it. It would be quite impossible to give any.intelligihla analysis of it in a work of this kind. -' It does not afford any consequences that Newton does not supply *with equal certainty and greater simplicity, and it fails in giving any aid in dealing with the modifications of the tides produced by the sun and moon due to physical causes, such as the varying depths and boundaries of the sea, or in explaining the peculiarities of estuary and river tides. Whewell expressed the opinion, with regard to this theory, that the " results obtained by precarious assumptions, and upon arbitrary hypothesis, were fatal to it even as a first approximation." DEVELOPMENT OF TIDAL SCIENCE. 17 Lubbock considered that Laplace's analysis is far from being complete, and as contributing but little to unravel a question which Laplace himself considered as the most intricate of physical astronomy. Airy, after describing this theory as " one of the most splendid works of the greatest mathematician of the past age," and placing it " far before that of Newton's, as being more scientific," admits that " under the suppositions the theory is far from being one of practical application," and that though this theory was based on sounder principles than Newton's, it has far too little regard to the actual state of the earth to serve for the explanation of the principal phenomena of the tides. Darwin, in his article in the " Encyclopaedia Britannica," says that this theory is far from representing the tides of our ports. Observations show, in fact, that the irregular distribution of land and water, and the variable depth . of the ocean, produce an irregularity in the oscillations of the sea of such complexity that the rigorous solution of the problem is altogether beyond the power of analysis. X The first complete observations on the tides were made a t ^rest and Bochefort early in the eightgfintk_Cfiiitiu:y_jt_jth,e y insti gation of the A cademy of Paris, ,and,.cQBtiaUfid-£aE.ja.4ieiaDd I of "'si x years . These records were examined and analyzed by ^ Cassini, and he deduced from them certain general laws of the tides, and made it possible to assort and combine the variety in the height and time of the tides, and to throw them' into classes to be compared with the aspect of the sun and moon according to the Newtonian, theory. In 1834 , in compliance with a suggestion made by Mr. (after- wards Sir J. W. ) Lubbock. F.B.S. . a series "f giTm^]|nTiPQiig observations of the ti des were made at the, preventive ..afijadce stations on the^ coasts jiL^jiglaad, jreland, and- Scotland, by "cTifectiaa^ of the Admiralty, with^..:&a.jBllififiL-^.Jissg£taiBixig whethejcjihere are general ir regularities whict.alBect..,the. tid« at all places alongjiErextensiyeJiae^of coast ; and the conclusion arrived at was, that the tide is^notjiffectgd by distant and general Irregularities in the^^tlagtiCj^ut thj,t such irregulajitiea^rejiiie to cauies which operate locally, such, as the effect of the wind andT the form of the land. Similar Simultaneous tidal observations were carried out on c i8 TIDES AND WAVES. the coast of Ireland in the year 1850 at twelve stations by direction of the Committee of Science of the Eoyal Irish Academy, for the purpose of affording data for the separation of the effects of the sun and moon on the diurnal tide ; and the result of these observations was given in a paper by the Eev. S. Haughton in the Transactions of the Royal Irish Academy for 1854. ^/- Between 1831 and 1837, Lubbock was engaged in making very important investigations into the tidal conditions on the east and west coasts of England, his object being to ascertain whether the variation in the time and height of the tides as actually (occurring are in accord with the changes due to the varying position and distances of the sun and moon, and with the laws ^laid down by the Equilibrium theory. This work consisted in the examination of 24,592 observations of the time and height of high water at London, as recorded at the Wapping entrance of the London Docks over a complete period of nineteen years, commencing in 1809, or one complete cycle of the moon's nodes ; and of 13,391 observations at Liver- pool docks for a similar cycle, commencing with 1774 ; and in making an analysis of the effects of the changes, transit, parallax, and declination of the sun and moon, and evolving the relative value for each factor. In the analysis of this mass of observations Lubbock was assisted by Mr. Dessiou, of the Nautical Almanack Office. The result obtained proved the nnrrectni^ijfi pf the laws to in the Equi librium theory ; and shawed ihat. any changes inihg ti me-or hei ght of the tides due^_the_vajjing_distancfia.j2Lihe sun andjQooii, and which. affeGti..t.h&m^i]i.thfiii; pTaf^e nf origin, tha-Sotuiheia. Ocean, are propag^ated thrauffhout^Ahdi- . wlinlft course, of. thousands of miles alo ng.^ thj3.-A=tlaii.tie> and roiHiiiie^ , coasts fif &reat Britain,, according ^ta the form first imjaessfid. on them by the luminaries ; and these variations are proportionately developed, whether the rise of the tide is 21 feet, as at London, -or 27 feet, as at Liverpool. The result of the investigation is embodied in papers con- tributed to the Philosophical Transactions for 1831, " On the Tides of the Port of London, 1836," and " On the Tides," 1837. With the -data-- thus obtaiuied . and following on the lines suggested by Bernoulli in his investigations of the tidal data at Brest, Lubbock was able Jo pl§ice the jaeieiice.of-tideaja£L§312]i DEVELOPMENT OF TIDAL SCIENCE. 19 a basis as to make it.j3ra.c ticable to calcula te in a^vfmngjhmr t ime and height at any port i n.Jhe.worJd, provided the necessary ^^sL^-da^jaa JbQ» ^ A li m!flZa^^ the .m^Qft's JsmaJkjSr thej^ j at ah l i s h . m aat-'' of ih^-'pe#r^Hts».baaB..aiacejtaine d ; and ha s enabled the Admiralty to issue annually, and give in advance the time and height of the two tides of every day at 25 ports in Great Britain, with constants for 181 other places by means of which the tides there may easily be calculated. In the absence of disturbing causes from gales or atmospheric pressure thesgjiables are thoroughly reliable. ^^ r-'They also give the time and height of the tide at full and change of the moon at nearly all the principal places on the coasts of the earth ; with parallax and declination tables ; and "remarks on the tides on the coast of Great Britain. These tide tables have been described as " The Text Book for the Seamen of all Nations." Bpt.wPPTi 1S.q.q anrl 1S4 the Eev. W Whpwpll -PT?.S n»r, tributed a series of articles cnrniected with tbfi tidpg in the PUlo- sophiccd Transactions. The prinmpa.1 purpono nf thnnn papnyn wit; tn tiVirr tlir pin pagat loil.Qf..the tidal yavfis alnng' thp nPAflns nf flig earthy J?ith their variations in timg and^^twe^i^and 'aj^wcrerrt'-anomalies', 'and t o cmnp aie-ih^^^ ma i tTOiia- , roa i d e-ky jxkaiij3fiia~Anji.-athers. with the de :!gdflped..;ateoE^fc ef ■■ .jag »« t ft ta€a^ .. to Jbhe-effect ofjhe sun and mQrt0..nn thft.j£atfilLSa£e]a3ag-tha.-ear-th. The observations that had been made by Lubbock of the tides at the ports of London and Liverpool, and also of the returns made by the coastguards of different stations in Great Britain and Ireland, were investigated. Generally agreeing with Lubb ock. he arrived..-a t. tke^^dnelaeiea- that, noteithataruJing^Jhe great irregularities to whi ch the tides are subi^fit., .the results of the means of large masses of observations accord with the theoretical formula with a precision not far below that of other astronomical phenomena, and that there exists this simple general law of the tides, namel ^J^at.it>]aeJlJiei.at.M^-4ilacaj3i^^ as if tiieocean i mitated , the-ibi m.. of equilibrium corresponding to a ^PTfain a.ntfif>fidfiTi|. fi^'n^e . . . and th at the ec[uilibrium theory expresses with ver y remarkable exactness most of,i he cir CT5as|^ ^^the ^^gsJE^Ifl^iSsS" That the tides at Liver- pool agreewith an equilibrium tide produced in the Southern 20 TIDES AND WAVES. Ocean 37^ hours previously to the moon's transit at that port, and transmitted thither unchanged ; and that the changes of lunar parallax and declination are very well represented by the Equilibrium theory. He defined the " establishment " of a port as the interval of time by which the time of high water follows the moon's transit on the day of new or full moon, which being ascertained and the mean height of spring tides above low water, the time and height for every other day may be calculated. In the first series of his papers given in the Transactions of 1833, and in the sixth series for 1836, the tide is traced step by step along the coasts of the Atlantic and round Great Britain ; and with less detail the tides of the Pacific are given. He also dealt with littoral currents and river tides. With these facts before him, he constructed two "cotidal charts," one a general map of the world, and the other of the British Isles. On these charts is given the time of the tide on the opposite shores of the seas at different intervals, these being connected by lines so as to show the rate of propagation of the tide, and the time at which high water arrives at the different ports of the earth. Although these cotidal lines can only be regarded as approxi- mations, they are interesting and instructive. With the exception of some slight modifications subsequently made by Airy, no recent attempt has been made to construct more accurate charts of a similar character. The first charts are given in the TraTisactions of 1833, and an amended edition in the sixth series, 1836. In the sixth, seventh, and eighth series, Whewell gave the laws relating to the diurnal inequality of the tides so far as they could be traced from an examination of the high water at London and Liverpool, and on the coasts of America and Europe. His conclusions may be summarized as follows : — Wh ^n t.hg^moon is on the Eq uator^^thfi..Jw_o„tideg. of the day are equal. The maxmum^ difference between,.ilia.Jjya occurs, when. Jt,fee_mpon ^as_gEgaifiat.-declination ; but although it corresponds _s«ith, it is^iig.t.necessarily^-simultaneous-j "-when the moon is soutt. of the equatorj^the equilibmini tide corresponding to her upper trainsit at any place having sauthem. latitude is greater than- 4he Jide corresponding to her lower transit ; when she is north of the equator, the contrary is the case." The, inequality of the-EfiigliJLs- will depend ito a certain extent on local ™circ]inisiances. The DEVELOPMENT OF TIDAL SCIENCE. 21 effect du e to the p innn'f! rlBo1inn.tirm.Jji_mAt-f.pU af, 3,1^ y ravtiAnlgv latitude until such time has elapsed, gs_.it JaJ£fia~.^(E~tlie_spaTe deiwed frdm-ffieSiBEilSrQcean to reachihatlatitude.- It is-.not possible to give the law of this inequality as making the morning tides at one time of the year, and the evening tides at another as being greater or less." An examination of the tides along the coast of the Atlantic, and those on the American coast, showed that the diurnal inequality changes almost simultaneously with the change of declination of the moon ; on the coast of Spain, Portugal and France the diurnal equality is steady and well marked, and is not felt till two or three days after the moon has crossed the Equator. On the coast of Cornwall and Ireland it is well marked for part of the lunation, and then vanishes ; the rule being for these coasts that the tide which follows the superior transit of the moon when she has south declination, and the inferior transit when she has north declination, is the greatest. In the North Sea the inequality is less marked. The subject of wave action was d galt^ witLas-fiarlji-.as-.JJie fifteenth centur y. Leonardu irlia...i.Kinpiy-3aib#-i8 genejaUyJiaowm 8'^--2Bj£j8llJ^.gXSaitaXtalian,»paJa.t6BS>efe'fee^£teeffl..tb' century ,.Jazt ^«^ifeMi. *^l,.Sfe>.of .jn^in£^i^_ffiBd-ii^ of work»«in Tu^aayj and who lived from 1452-1519, explauiai.,tlie-giaBeiral principle of wave action on lines wWch^^ h^e s^^gJjggjj^aslQptPd a£LCOir.e5t."T[e"showed that the crests of waves are as much raised above the level of the water in repose as the troughs are depressed below it; that the crest of the wave is raised by the action of the wind, and the trough depressed by the action of gravity; that sometimes waves have greater velocity than the wind, and sometimes the velocity of the wind is greater than that of the waves. He explained how a wave is a change of form and not of horizontal movement of the water, and illustrated this action by the undulations caused by the wind in a field of corn ; that wave motion does not create a current, as instanced by the fact that a floating body only rises and falls without moving forward under the influence of the wave. He described the action of breaking waves, and those of incidence and reflection ; and how waves, striking an object and breaking, are thrown upwards ; and the effect of the back-wash in eroding the shore ; also ground swells ; and how waves of equal size coming from different 22 TIDES AND WAVES. r directions do not penetrate one another, but that each wave keeps its separate course ; that waves which augment in length diminish in height ; that if waves of unequal form meet, the weaker is joined to the stronger, but when of equal force they retire backwards.^ The subject of wave action was also treated by Lagrange in his Meeanique Analytiqm, published in 1787, where he showed that the velocity of propagation of waves is the same as that which a heavy body will acquire in falling from a height equal to half the depth of the water in which the wave is propagated when the water is horizontal. In 1824 M. Bidone published the result of experiments relating to the production of waves in a canal having a current of water passing through it, the waves being produced by the sudden closing of a sluice door. From these experiments he evolved a formula which coincides with that afterwards adopted by Scott Eussell.^ A treatise on waves giving the results of researches into wave action was published at Leipsic, 1825, by the brothers Weber.^ This treatise was described by Scott Eussell in his subsequent report to the British Association, as " containing nearly all that has ever been written on waves since the time of Newton, and that as a book of reference alone it is a valuable history of wave research." Between 1836 and 1844 Scott Eussell was engaged in in- vestigating and experimenting on the nature of waves, and in verifying the correctness of the theory of Lagrange, and at the meeting of the British Association at York in 1844 he presented a report embodying the results of his researches : " On varieties, phenomena, and laws of waves, and the conditions which effect their genesis and propagation." The researches of Scott Eussell were, however, made quite independent of what had been done by the brothers Weber, as his attention was not called to their work until his own report had been made. He claims that their work and his do not in the ' Account of Leonardo da Vinoi in the Bulletin de l' Encouragement pour L'Indmtrie National. Paris, Dec. 1902. ' " Eeoherches Hydrauliques." Memoir, L'Institut Imperial de France. Paris, 1865. 2 " Wellenlehere auf Experimente gegrundet oder uber die Wellen tropfbarer Flussigkeiten mit Anwendung auf die Sohall und Liohtwellen von den Bruder Weber." Leipsic, 1825. DEVELOPMENT OF TIDAL SCIENCE. 23 least degree supersede or interfere with each other ; but rather as being supplementary the one to the other. The Webers did not recognize the existence of the great soli- tary wave of the first order, nor did they examine its phenomena, and Scott Kussell claims to be the first to direct attention to this particular class of large waves, which he designates as "waves of translation" or waves of the first order as distinguished from waves of oscillation of the second order, the two classes of waves "differing essentially from each other in the circumstances of their origin, as transmitted by different forces; existing in different conditions and governed by different laws." The wave of the first order he describes as " furnishing the model of a terrestrial mechanism by means of which the forces primarily imparted by the moon and sun are taken up and em- ployed in the transport of tidal waters to distant shores, and their distribution in remote seas and rivers, which they continue in succession to agitate long after the forces employed in the genesis of the wave have ceased to exist." He points out that in the transit of the wave of translation the particles of the fluid are transported forward in the direction of the motion of the waves ; there is no retrogradation, no oscil- lations, and the movement extends throughout the whole sea from the surface to the bottom ; while with wind waves, or waves of oscillation, there is a partial displacement at the surface, a vertical rise and fall of the particles of water, but no forward movement. He also adopted the law laid down by Lagrange, that the velocity of waves of the first order is as the square root of half the depth of the water in which they are propagated. About thirty years later, in 1857-1859, MM. Darcy and Bazin conducted experiments on the movement of waves on a larger scale than that used by Scott Eussell on a reach of the Canal de Bourgogne, about a quarter of a mile in length, the width of the waterway being 54 feet, and the depth of the water 2 feet. The waves were formed by the admission of water through a sluice. The results obtained confirmed the correctness of the formula of Lagrange, V = \/ 1g X s- ^"^ account of these experiments is given in the memoir of the Imperial Institute of France, 1865. The subject of deep-sea waves was investigated by Dr. Scoresby, who made a series of observations of Atlantic stor 24 TIDES AND WAVES. waves, during a voyage to and from Australia by the Cape of Good Hope, and round Cape Horn. The results are given in the Report of the British Association for 1850 ; and in the Report for 1842 is also a paper on the same subject by Mr. Walker. Very numerous observations on deep-sea waves have also been made by Lieut. Paris, an officer of the French Navy, during voyages extending over the years 1867-1870, when he recorded daily the state of the sea and the force of the wind. The result of these observations was given in the Revue Maritime, vol. 31. In 1874, M. Antoine presented to the Societe Academique at Brest a memoir on deep-sea waves, and as to the proportions of these waves, obtained from a very large number of observations made in vessels of the French Navy taken over a considerable period in different seas, in which he founded certain formulae as to length, height, and velocity of the waves, and their relation to the velocity of the wind. These results were published in 1879.^ The most recent explanation of the modern theory of deep- sea waves is to be found in Sir W. H. White's Manual of Naval Architecture, where the trochoidal curve which these waves assume is explained and illustrated. In 1834, a committee of the British Association voted the sum of £500 for the purpose of taking a series of levels from Bridgewater and Portishead in the Bristol Channel to Axmouth in the English Channel, with the view of determining the mean level of the sea. These levels were taken by Mr. T. C Bunt. The results are given in the Reports of the British Association for 1838, 1839, and 1841. An account of these levels will be found in chapter vii. on the range and height of the tides. About the year 1842, Mr. G. B. Airy, the Astronomer Royal (afterwards Sir G. B. Airy), contributed an elaborate paper on waves and tides to the " Encyclopsedia Metropolitana," which has since been accepted as the standard article on the subject. This article is almost entirely theoretical, and is not based on any observations or tidal investigations made by himself, and is likely to be more appreciated by mathematicians than by the practical student of tidal science. Out of 153 quarto pages of which the article consists, 100 are occupied with mathematical demonstrations. ' Bet Lames de Haute Mer. Par Oh. Antoine. Paris, 1879. DEVELOPMENT OF TIDAL SCIENCE. 25 In tHs article, Airy entered at some length into the mathe- matical theories and the experimental observations applying to tides and waves of water. The relative effect of the sun and moon on the tides is investigated, and an explanation of the Equilibrium theory is given, and an equivalent to Laplace's Dynamical theory as it appeared in the Mecanique Celeste. Considering neither of these theories as satisfactory, he pro- pounded a third, " that of the motion of the tidal waters, supposing them to run in the manner of ordinary waves in canals." As, however, this theory does not apply to every part of the sea, he considered it also imperfect. He also gave a general explanation of waves, and the theory of wave motion, and laid down certain laws as to their lengths, periods, and velocities. The tide wave due to the immediate action of the sun and moon he described as a " fixed " wave ; and the other coexistent with this, produced originally by the action of the sun and moon, he termed the " free tide wave." He showed that in wind waves the motion is only sensible near the surface. He also dealt with the phases of shore and river waves. The experiments conducted by Scott Kussell were criticised, and he considered that the method adopted for measuring the velocities of the waves as very ingenious, and on the whole, as given in the report made to the British Association, that they constituted the most important body of experimental information in regard to the motion of waves then in existence. He described the methods used for observing the tides and for reducing the observations ; and dealt with tides in bays, estuaries, and rivers ; and the phenomena of tidal bores. Airy's article is accompanied by a chart of cotidal lines, similar to that given by Whewell already referred to. With the more perfect information as to the mass of the earth and moon, which he took as being in the proportion of eighty to one. Airy showed that according to the Equilibrium theory of Newton the force of the sun to raise the water following the moon is 0*542 feet on the side next to and furthest from the sun, which is about three inches less than Newton's calculation ; and that its greatest action in depressing the water in the inter- mediate points ninety degrees away is 0271 feet. The whole difference between the elevation of high and low water due to the moon's attraction he calculated as being 2-0325 feet. 26 TIDES AND WAVES. In order to facilitate the calculations required in the con- struction of tide tables, Sir W. Thompson (now Lord Kelvin) initiated the system of harmonic analysis, and this subject was referred to a committee of the British Association appointed in 1867, and carried on from year to year till 1876 with the aid of grants of money. The subject was also dealt with by Darwin in the. Beports of the British Association for 1883 and 1885. The complicated motions of the tides as traced by the self- registering tide-gauge are by this process analyzed into a series of simple harmonic motions in different periods with different amplitudes of range. To supersede the laborious arithmetical calculation required in analyzing the tides, Sir W. Thompson also constructed a tidal harmonic analyzer, or tide-predicting machine, by means of which these calculations can be made mechanically. An illustration and description of this machine is given in the Minutes of Broceedings of the Institution of Civil Engineers, vol. Ixv., 1881. Mr. T. K. Abbot, Fellow of Trinity College, Dublin, having previously contributed articles on the subject in the Bhilosophical Magazine of 1871 and 1872 and in the Quarterly Journal of Mathe- matics of 1872, published in 1888 a short treatise on the theory of the tides, the object of which is to prove that but for friction low water would be under the moon, and high water in the quad- ratures ; and that friction accelerates the time of high and low water; that in addition to the oscillatory motion of the water there is a constant current produced by the action of the moon ; and that the effect of friction on this is to increase the length of the day. He supposes, for the sake of his argument, that the tides are generated in an equatorial canal ; the moon being sup- posed to be on the Equator. For the purpose of establishing the above, he states " that it must be admitted that the ocean is in a state of equilibrium under the moon's action, that it is absolutely at rest (relatively to the moon) while the earth rotates, which would imply an apparent translatory movement of the whole body of water with a velocity equal and opposite to that of the earth's rotation, that is, that at the Equator there would be an apparent current of about 1000 miles an hour." It is difScult to realize the correctness of a theory which is DEVELOPMENT OF TIDAL SCIENCE. 27 admitted to be founded on facts so widely different from those that exist. _Professor G-. H. Darwin., has contributed^ to-ihe ilsEfileEment o LtidaL ac ienea .bjt his -eontributions. ta^-the S&HosopIdcal.J^W'^- actions otH a&^uaif^l. Society ; by his reports to the British Asso- ciation in 1883 and 1885 on the Harmonic Analysis of the Tides ; the article in the " Encyclopaedia Britannica " on the tides ; and also by his book " The Tides and Kindred Phenomena in the Solar System," being the substance of lectures delivered at the Lowell Institute in 1897. This bflflkmffffitt-tftiinifjr- an explanation of the tlig(K$ua£i'ttt@> tides, aodddeal^ with some- othes^'kindred subjects. He also contributed the article on the " Tides " in the " Admiralty Manual of Scientific Enquiry," the object of which is to show the best use to be made for scientific purposes of a short visit of a surveying ship to any port and the method of making tidal observations of high and low water. H,e cm^ijidera tha,t there are grounds for^conjecturing that the moonjs-Cfliaposed. of .fragmentaof the pirxmitisie planet, now called the, Earth„.whieh>were .JJetaebBdwhen.tha-planet spun very swiftly, and- tha t aft e fw ei r ds^-ese'faeeaitte' consolidated. r>gxwin .^as-~ G ¥el » ed " -4be»-tbe€>ry (Philosophical Transactions, 1879, 1880, 1881) that, -a&jiLjiu»iiig«s5Js4em^jdbifih. are subject to friction gradually co me to rest . th,e.eariih!ajaitatioiLand moon's revol ution must bc- retarded, by tidal friction, and, conse.quently, |,Tint Vint.h tiio (lay Qjid-,±kQ. .Trinp-th are bewg lengthened. This loss of speed, however, is insignificant ; the day at the present time being about one eighty-fourth part of a second longer than it was at the beginning of the Christian Era. He calculated that the tidal retardation of the earth's rotation varies as the inverse sixth power of the distance, so that if the moon's distance was diminished to a quarter of what it is at the present time the tidal friction would act with 4096 times its present strength. Thus, although the action is insensibly slow now, it must have gone on with much greater rapidity when the moon was nearer to the earth. He found that if the earth was revolving once in three hours instead of in twenty -four, the centrifugal force due to rota- tion would about balance the retaining force of gravitation. If the tidal friction always operated under the conditions most favourable for producing rapid change, the sequence of events from the beginning until now would have occupied 50 to 60 28 TIDES AND WAVES. millions of years. Although unable to find any direct confirma- tion of this theory from geology, he does not consider that it presents any evidence inconsistent with it, nor that the applica- bility of the theory is negatived by the magnitude of the period demanded. According to this theory, the tides on the sea-coast must have had a much wider range and the currents greater speed ; and river-floods have been much greater than they are now. If the tides had a rise and fall many times the vertical height of those now existent, the force of the waves in eroding the shores and the power of the currents to transport material would have been pro- portionately increased ; and the efficiency of the ocean and rivers in making the earth as it now is have been far greater than it is at the present day. In 1898, the Eev. I. H. S. Moxly published two treatises on the tides. After expressing the opinion that the true explanation of the tides in accordance with the laws of Newton has never yet been understood ; and that the great mathematicians and tidal experts have been misled, he severely criticises Darwin's state- ments in his book on the tides ; and proceeds to state a theory " founded on the sure basis of Natural Law, but which may be seen to give a simple and rational account of those tidal phe- nomena that have baffled all attempts to explain them." He claims that his theory is a corrected adaptation of Newton's Equilibrium theory ; considering the principles of dynamics as not being those that govern tide generation, he dismisses Laplace's theory as quite out of court. His contention is that " the tide is caused by the pressure of the earth's gravity acting vertically, this pressure being assisted in a slight degree in one region by the tidal force of the lumin- aries acting vertically, and concentrated to a greater extent over other regions of the earth's surface. A manual for tidal observation by Major Baird, K.E., who was in charge of the tidal and levelling operations for the survey of India, was published in 1886, for the purpose of rendering assist- ance to those engaged in similar work. In 1887, the Government of India issued instructions for systematical tidal observations to be taken at all the principal Indian ports. Major Baird gives an account of the operations generally, and a description of the DEVELOPMENT OF TIDAL SCIENCE. 29 instruments used ; and of the method employed of reducing these observations by harmonic analysis. In 1860, the French Government issued an order fixing the datum of all levels for France on the mean level of the Mediterranean Sea at Marseilles ; and under the general survey of France carried on since 1884 this datum has been connected with the seas round Europe. In 1878, observations were commenced by a committee of the British Association, Mr. J. N. Shoolbred acting as secretary, for the purpose of obtaining information as to the phenomena of the stationary tides in the English Channel and in the North Sea, and connecting these observations with the coast of France ; and also for obtaining records of the tides at the Azores Islands in order that a series of observations might be carried on upon the tides of the North Atlantic. At the instance of the committee a tide gauge was established by the Portuguese Government in the Bay of Funchal ; and a self-recording tide gauge was fixed at Dover in 1880, which is now working regularly; and tidal records kept by the Belgian Government at Ostend were placed at the disposal of the committee. The reports of the committee are given in the British Association Beport for 1878, 1879, 1880, 1881. At a meeting of the British Association in 1885, a committee was appointed to inquire into the tides of Canada, and for representing to the Canadian Government the necessity of establishing tidal stations for continuous lidal observations for the purpose of having reliable tide tables published. The repre- sentations of this committee were backed up by the Eoyal Society of Canada, and by petitions to the Canadian Parliament from 400 masters and officers of vessels engaged in the navigation of the Gulf of St. Lawrence, and the waters of the Atlantic coast of Canada, pointing out that for the want of proper information there were frequent wrecks, and great loss of life and property. After some delay, this survey was undertaken in 1894, and the work entrusted to Mr. Bell Dawson, by whom a series of tidal observations were made, and tide gauges fixed at various points; and when sufficient tidal data had been obtained, reli- able tide tables were issued for the ports of Halifax, Quebec, Charlottetown, Pictou, and St. Paul Island ; and information 3° TIDES AND WAVES. given as to the currents on the south-east coast of Newfound- land. A description of the tide gauges used, and of the method of conducting the survey, is given in the reports issued by the maritime department at Ottawa for the years 1894 to 1904. The method of obtaining a knowledge of tidal action in sandy estuaries by means of working models, was first brought to notice by Professor Osborne Eeynolds, in a paper read before the British Association at Manchester in 1887. In this paper Mr. Reynolds described the results he had obtained from a model of the upper estuary of the Mersey ; and the subject was referred to a committee to investigate, a grant being made from the funds to pay the cost of apparatus and the services of an attendant. Two tanks were fixed at Owens College, Manchester, and were in operation for a period of two years, the results obtained being contained in two reports, one made at the meeting of the Association at Newcastle-on-Tyne, in 1889, and the other at Leeds, in 1890. A model tank was also made at the expense of the French Government of the estuary of the Seine, in which the engineers connected with the proposed works for improving the channel through the sand banks to the sea were able to watch the effect produced by the varying lines of direction. The author, having had several opportunities of watching the original model of Professor Reynolds, and also as a member of the committee, those at Owens College, and also having a tank erected on his own premises, which was operated by water power, is of opinion that models of this character have a great value as a means of instruction, and although the results due to piers, training walls, groynes, or other works obtained by the use of these models, cannot be taken as reliable guides for carrying out such works in an open sea or estuary, yet they are valuable aids as indicating results that may occur, and as affording suggestions that can be followed up and investigated. The effect of atmospheric pressure on the tides was dealt with by Sir J. W. Lubbock in his paper on the tides in the British Assodiation Beport of 1832, and in his paper in the Bhilosophical Transactions of 1837, wherein he gave the results obtained from an analysis of the tides at London, Liverpool, and Bristol. DEVELOPMENT OF TIDAL SCIENCE. 31 The effect of the pressure of the atmosphere on the sea was also investigated by Sir J. Olark Ross when he was icehound at Port Leopold in the Arctic regions in 1848. During this time hourly observations were taken of the level of the water under the ice, and of the barometer, during a period of forty-seven days, and the results given in a paper in the Philosophical Transactions of 1854. This subject was also brought before the Meteorological Society in 1886 and the Shipmasters' Society in 1894, in papers read by Captain Greenwood. The results deduced were based on observations made over a lengthened period of the atmospheric gradients in the Irish Sea from the south of St. George's Channel to Morecambe Bay. On the data obtained. Captain Greenwood prepared a table for use on that part of the coast, showing the effect of the difference of the gradient on the tides. The rise and fall of the tides on the Dutch Coast was investi- gated by a commission appointed by the Government for deter- mining the degrees of the rise and fall of the sea-level during 1889 ; and the Dutch Meteorological Institute also furnished data as to wind and atmospheric pressure. A report was pub- lished in De Ingenieur in 1890, No. 26, published at the Hague. In the same journal for September 26, 1891, No. 39, is a paper " On the Influence of the Wind both in Direction and Pressure upon the Sea-Level," giving the result of observations by E. Engelenborg. In this paper twelve tables are given of the half- tide level, compared with the state of the barometer and the pressure of the wind at Flushing during the years 1887 and 1888. The author read a paper at the British Association meeting at Ipswich in 1895 on " The Effect of Wind and Atmospheric Pressure on the Tides," and at his suggestion a committee was appointed to further investigate the subject, and a report drawn up by him was presented at the Liverpool meeting in 1896. Five ports were selected as fairly representing the tidal conditions round the English coast, and, with the permission of the various authorities, the tidal and meteorological records of the ports of Sheerness, Portsmouth, Liverpool, Hull, and Boston, and the weather reports issued daily by the Meteorological office were examined and analyzed as to the effect produced by gales or atmospheric pressure for the years 1892-1895, the results being given in the Beport. 32 TIDES AND WAVES. The tides of the North Sea have recently formed the subject of investigation, and the results obtained have been given in the Proceedings of the Netherlands Meteorological Institute in three papers by Mr. J. P. Van der Stok.^ The first of these papers contains an analysis of the movement of the level of the sea ; the second gives the results of observations made on board the Netherlands lightships as to the direction of the wind and the currents; and the third, tables of the currents. Mr, Stok more particularly directed his attention to the horizontal move- ment of the water and the rotary character of the tidal currents. The tides have formed the subject of numerous papers in the Philosophical Transactions of the Royal Society, including those of Wallis, Whewell, Lubbock, and Airy, which have already been referred to. Also amongst the records of the British Association are to be found upwards of thirty-five papers or reports that have been contributed to the Proceedings of the Association since 1832, and a total sum of £2717 has been granted for the purposes of tidal research. ' " Etudes des phenomenes de Maree sur les cotes Neerlandaises," parts i., ii., iil., Utrecht. Kemink and Son. 1905. CHAPTEK III. THE SUN, THE MOON, AND THE EARTH. In order to understand how the tides are made, it is necessary to have some idea of the relation of the sun and moon to the earth. The Sun. The sun is one of the tide-producing agents, and is the great centre of attraction round which the earth, with its attendant satellite the moon, revolves in an elliptical orbit once a year (365-25 days). Although other planets may have some slight gravitational effect, the sun and moon are alone taken into account as tide makers. The sun is distant from the earth 92J millions of miles. Its mass is 324,000 times greater than that of the earth, and 26 million times greater than that of the moon. Although the mass of the sun is so much greater than that of the moon, yet, owing to its greater distance from the earth, it is weaker than the moon as a tide-producing agent. The sun at one period of the moon's revolution round the earth acts in conjunction with the moon, and at another period in opposition. Owing to the ellipticity of the orbit of the earth's passage round the sun, it is nearer to the sun at one period, or in peri- helion, and is further away when in aphelion. The difference of the maximum and minimum distance is about ^Jjth of the whole. The periods of perihelion and aphelion are respectively December 31 and July 1. The sun is therefore nearer to the earth in winter than in summer. Equinoxes. — At the vernal and autumnal equinoxes on March 34 TIDES AND WAVES. 20 and September 21, the equator of the earth is vertically under the sun. Declination. — The sun, during the revolution of the earth, moves in a diagonal path across the equator following the ecliptic. At the vernal equinox it declines to the south, and after reaching the maximum south declination on June 21 (summer solstice) it commences moving northward, crossing the equator again at the autumn equinox, September 21, and reaches its northern limit on December 21 (winter solstice). The decliiiation varies from 21-59° to 24'16° north or south. The sun is therefore nearest to that part of the earth where the tides are generated, when the supreme point of southern declination is reached and farthest away at the extreme point of north declination, and, consequently, the declination of the sun has an influence on the tides, and has to be taken into account in calculating the height and time. The Moon. The moon is the principal agent in producing the tides. From the most ancient times the connection of the tides with the moon has been recognized. Long before the time of tide tables and other aids to navigation, mariners and fishermen regulated their times for entering or leaving their harbours by the phases of the moon. New and full moon, or full and change, as it is termed, is still looked upon as the guide for regulating all matters in connection with local tides. Sir E. Ball has remarked in his " Story of the Heavens," " that if the moon were struck out of existence, we should be immedi- ately apprised of the fact by a wail from every sea-port in the kingdom. The rise and fall of the tides would almost cease ; the ships in dock could not get out ; the ships outside could not get in ; the maritime commerce of the world would be thrown into confusion." The fleets of fishing-boats around the coasts time their daily movements by the tides, and are largely indebted to the moon for bringing them in and out of harbour. There appears to be reasonable ground for conjecturing that the moon at one time formed part of the earth, and that as the earth was cooling and contracting from its nebulous condition. THE SUN, THE MOON, AND THE EARTH. 3; the speed of its rotation increased until the length of the day was only three hours, and then a mass equal to five thousand million cubic miles was thrown off the earth's surface by centri- fugal force ; the catastrophe being either a prolonged process, or happening all at one time. This mass subsequently became consolidated, and is now a satellite of the earth. Conjectures hare been made as to the part of the earth from which this mass was torn. It has been suggested that the old and new worlds once formed a single continent, and were rent asunder at some time by a fearful cataclysm. It is certainly a singular feature how nearly the coast lines on the eastern and western sides of the Atlantic resemble one another, and which, if brought together, would very nearly fit. The tendency of the moon is to pursue the direction in which she was originally cast off from the earth, but her distance from the earth, and the velocity at which she now revolves round the centre of gravity of the earth-moon system, is such that the centrifugal force is counterbalanced by the centripetal force of gravity, and the moon is kept revolving in an orbit round the centre of gravity of the earth-moon system. Dimensions. — The diameter of the moon is 2160 miles, or 0*27 that of the earth ; and her mass is about g^o that of the earth, and 3 J^of the sun. She is distant from the earth 240,000 miles, or 60 radii of the earth. The tide-producing effect of the moon is about two-thirds greater than that of the sun. Revolution. — The moon revolves round the earth from west to east in an elliptical orbit once every month, or more accurately once in 27-33 days. The time occupied in completing her phases, that is from new moon to new moon, or one lunation, is 29 '53 days. The difference in time between the revolution round the earth and a lunation is due to the earth having during the period changed its position, and moved on 27 degrees in its annual course round the sun, and nearly two days elapse before the moon can overtake the sun, so as to be seen at new. The time occupied by the revolution of the earth on its axis is 24 hours, but during that time the moon has moved 13 degrees ; it therefore takes on an average 50 minutes longer for the moon to come again over the same meridian of the earth. The length 36 TIDES AND WAVES. of the tide day is therefore on an average 24 hrs. 50 min., and the interval between two tides 12 hrs. 25 min. Phases of the Moon.— The tides follow the phases of the moon. At the time of new or full moon, or " full and change," or at the "syzygies," they are at their highest, or spring tides; at the "quarters," or in the "quadratures," they are at their lowest, or neap tides. The phases of the moon are expressed in tidal almanacks by symbols ; new moon being shown as #, full moon O, first quarter 3 , and last quarter aa. s a a >-Q o o 3 of Wave CD Crest of - Anti Lunar Tide THE MAKING OF THE TIDES. 47 • As the sun and moon are continually changing their posi- tions relative to the earth, returning again to the same places in regular cycles, the tidal ellipsoid from time to time becomes altered in form, causing variations in the height of the tidal wave. The primary tidal waves continually move in one direction from east to west, and have done so ever since the creation of the world. They vary, therefore, from the secondary waves which are propagated from the primary waves, in that they do not oscillate backwards and forwards. Both the primary and the secondary tidal waves vary from the waves due to wind action, which are only surface movements, and do not extend far below the surface, whereas, with the tidal waves, the whole mass of the water from the surface to the bottom is in motion. The interval between two crests is 12 hours 25 minutes, andft the two waves complete the circumference of the earth once in I a lunar day, each crest arriving at the same meridian of the earth 1 again in 24 hours 50 minutes. -^ The mean length of each wave is about 6000 miles, and its rate of movement 563 miles an hour, and the height from trough to crest is approximately two feet. The Southern Ocean cannot be considered as an ideal basin for the true development of the tidal wave ; the contour of the shores is very irregular, especially where the projection of the South American continent occurs, and the variation in the depth has some effect on the velocity of the wave. The information available also as to the tides in this sea is very scanty, and few observations are available as to their rise and fall. Relative EiFect of the Sun and Moon. — The tide-producing effect of the sun and moon not being a direct, but a differential attraction, is inversely as the cube of their distances. The mass of the sun being 26 million times as great as that of the moon, and the distance from the earth 386 times further removed than the moon, the effect of the sun to that of the moon is 26,000,000 _ 0.445 Conjunction and Opposition. — At new moon the sun and moon are on the same meridian and on the same side of the earth. The wave due to the sun is then superimposed on that due to the moon. 48 TIDES AND WAVES. and consequently the tidal wave is at its maximum, low water occurring 90 degrees away. The height of this wave from trough to crest is about 2 feet, of which 0-60 foot is due to the tide-making force of the sun, and 1-40 foot to that of the moon. At this period high tides ensue. Low Water .New Moon 3 SUN Low Water Fig. 4.— Spring Tide, New Moon. The moon proceeding on her course round the earth, and the sun remaining in the same position, at the end of 1\ days the moon has accomplished the first quarter of her journey, and is at " quad- Moon at 1st. Quarter "'^pT Fig. 5.— Neap Tide, let and 3rd Quarters of Moon. rature,'' at right angles, or 90 degrees, away from the sun, the lunar tide being six hours distant from the solar; the sun and moon are then acting in opposition to one another. Two separate Low Water Full Moon Low Water Fib. 6.— Spring Tide, Full Moon. waves are made, one directly under the sun, raising the crest of the solar wave 0*60 foot, and the lunar wave 90 degrees away, superimposed on the trough of the solar wave, and raising its crest l4o foot. The height from the trough to the crest of this wave is therefore only 0"80 foot. At this period low tides occur. THE MAKING OF THE TIDES. 49 After another 1\ days the moon has accomplished the second quarter of her course and is " full," and again in the same meridian of the earth as the sun, only on the opposite side of the earth and 180 degrees away from the sun. The sun and moon are again conjoined in raising the tides ; the sun also acting in conjunction with the anti-lunar force. At this period the tides are again high. At the end of a further period of 1\ days the moon has arrived at the third quarter of her course, and has approached within 90 degrees of the sun. The solar and lunar forces are therefore again in opposition, and low tides occur. At the end of a further period of 7J days the sun and moon are again on the same meridian and on the same side of the earth. The diagrams, Figs 4, 5, 6, show the tidal wave when the sun and moon are acting conjointly, and when they are in opposition. Spring and Neap Tides. — The two tidal waves described above constitute spring and neap tides. The origin of these terms is probably due to the fact that as the moon leaves the meridian of the sun in her orbital transit round the earth and approaches the quarters the tides begin to " fall off," or are " nipped," and neap tides ensue. As she leaves the quarters for the meridian they begin to "lift," or "come on," or "spring up," and when the meridian is reached spring tides ensue. As shown in the diagram. Fig. 7, the rise of spring tides is 2 feet, and of neap tides 140 foot, the range of neap tides being 0-80 foot. H.W.S.T. L.W.S.T. Fig. 7.— Dtagram showing Relative Heights of Spring and Neap Tides. The proportion between springs and neaps due to the action of the sun and moon, as above described, is maintained in the costal tides propagated from the great primary tide, neap tides being about three-fourths the height of spring tides above low water of spring tides, and their range from neap low water to neap high water being about half that of springs. The time of the high tides which at springs coincide with 50 TIDES AND WAVES. the moon's transit of the meridian at noon and midnight in the Southern Ocean, is later on the coasts of other seas, in pro- portion to the time taken for the derivative wave to reach them. In the seas of the British Isles this time varies from three- quarters of a day at the mouth of the English Channel, to one and a half day at the mouth of the Thames. Age of the Tide. — The interval between new or full moon and the time when the spring tides occur at any place away from the Southern Ocean is called the age of the tide. Declination. — Both the time and height of the tides are affected by the declination of the sun and moon north and south of the equator. The change of declination of the sun takes place twice a year at the vernal and autumnal equinoxes in March and September, and the limit of the northern declination is reached on December 21, and of the southern declination on June 21. The extreme variation in time is five minutes. The declination of the moon, north or south of the equator, changes every fourteen days. The time at which she crosses the equator, or of extreme declination, may coincide with either spring or neap tides or any period between ; or with apogean or perigean tides. Declination of the moon differs at each succeeding equinox until a period of nineteen years has elapsed. At the end of this period the moon again assumes the same relative position with respect to the sun and earth, and the tides recommence in the same sequence. The effect on the tides due to the moon's declination in the Southern Ocean is communicated to the derivative tides and re- produced at the different parts of the earth ; an interval elapses between the original effect and that reproduced, depending on the distance between the local tide and the place of origin. The maximum effect on the tide in time due to the moon's declination is about twelve minutes, and on the increase or de- crease in height between extreme north and south declination is about 0'066 foot for each foot of rise. The greatest effect in raising the tides is when the moon is from 2° to 6° away from the equator. After 15° is reached the effect is a minus quantity. Diurnal Inequality. — There is a variation in the height of the two tides of the day or " diurnal inequality," which varies with the declination of the sun and moon. THE MAKING OF THE TIDES. 51 Lunar diurnal inequality is absent when the moon is on the equator, and the effect increases as her declination increases. This feature of the tides is produced in the ocean where the tides are generated, and is communicated thence to the derivative tides. The law governing the diurnal tides may for some months produce the effect of making the evening tides greater than the morning, or vice versa. Generally, if the day tides are higher at one time of the year, they are lower at another. As a matter of experience it is generally found that when latitude and the sun's declination are of the same name, the day tides are highest, and when of different names the night tides are the highest ; that is to say that north of the equator, when the moon has north declination, the day tides are greater than with south declination and vice versa. New and Full Moon Tides. — The tides following the new moon when the sun and moon are together on the same side of t' earth, are higher than those following the full moon^TaEing an average over a year of three ports on different sides of England, the new moon tides are 4 inches higher than those of the full moon. The configuration of the coast line and local circumstances in some degree modify the effect produced on the primary tide. Aphelion and Perihelion. — The time and height of the tides is affected by the horizontal parallax of the sun, or its varying distance from the earth when in perihelion or aphelion. The tides are increased during the sun's perihelion in December and diminished at the aphelion in July. The maximum difference in time between the extreme limits of the elliptic orbit is 3 minutes, and in height for each foot of rise about 0*009 foot. Apogee and Perigee. — One of the chief causes of inequalities ^ of the tides depends on the eccentricity of the moon's orbit, that is, on its horizontal parallax, or on the moon being in perigee or apogee. The highest and lowest elliptic tides due to apogee and perigee occur at intervals of 13f days, the tides being increased every 27^ days, and halfway between decreased, The waves due to perigee and apogee do not coincide with the phases of the moon. The crests follow one another at ( intervals of 12-66 hours, and as the interval of the principal lunar j 52 TIDES AND WAVES. tide is 12-42 hours, the elliptic tides fall behind by 14^ minutes each tide. They may, therefore, happen at new or full moon and coincide with spring tides, or at the quarters and coincide with neaps. If the moon is in perigee at new or full moon, the height of the corresponding tides will be increased, and the following spring tides diminished, as the moon will then be near the apogee. The neap tides between will be normal. If the moon changes at her mean distance between apogee and perigee, the spring tides are normal, but one neap tide will be higher than the following. The difference in time due to the extreme range in apogee or perigee is about 9 minutes. The difference in the height of the tides due to this cause at the extreme range of apogee and perigee for each foot of rise is about 0092 foot. Priming and Lagging. — The earth completes its revolution on its axis, and the same meridian is brought again under the sun, in a solar day of 24 hours ; therefore if the sun alone acted, the interval between two tides would be 12 hours. The moon, however, in the mean time has advanced one day on its transit round the earth, and to bring the same meridian again under the moon occupies on an average 50 minutes. The interval between two tides is, therefore, 12 hours 25 minutes. The solar waves, therefore, follow one another more quickly than the lunar waves, and while the solar wave "primes" the lunar wave " lags " behind, the tidal day on an average being 50 minutes longer than the solar day. The time of high water is accordingly about 50 minutes later each day. The intervals are not regular. At new and full moons the tide day is 24 hours 35 minutes long, and at the quadratures 25 hours 25 minutes ; the interval varying from 19 to 58 minutes, the mean being 50. If springs occur when the moon is in perigee, the tide day following the perigean tides is 24 hours 17 minutes, and following the apogean spring tides 24 hours 33 minutes. At neap tides the day is 24 hours 15 minutes and 25 hours 40 minutes respectively. The mean interval between successive high tides being thus more than 12 hours, it follows that on two days in each lunation, or period between one new moon and the next, there is only one high water during the 24 hours constituting the solar day. THE MAKING OF THE TIDES. 53 For example, if high water occurs at 11.45 p.m. on Monday, or shortly before midnight, then the succeeding tide will occur on Tuesday at 0.10 p.m., and there will not be any tide on Tuesday morning. Height of the Tidal Wave.— As already stated, the theoretic difference in the level of the water following the sun and moon is about 2 feet. Observations made in the Southern Ocean are of too limited a character to enable it to be stated with accuracy what is the actual rise and fall of the water there ; but taking the heights given in the Admiralty Tide Tables at the islands in the open ocean, the rise and fall given above is borne out by experience. The mean level of the sea and range of the tides generally is dealt with in Chapter VII. The height of the spring tides varies at different times of the year. They are at a maximum at the equinoxes in March and September, when the sun is on the equator, especially if the moon crosses the equator at full and change, these being known as equinoctial tides. They are at a minimum in June, when the sun is furthest from the equator. The summer tides are sometimes called "bird tides," because they occur about the time when the sea-fowl are laying their eggs and breeding their young on the salt marshes, which are not flooded when the tides are low. It may be noted that as a rule the higher the tides rise the lower is the ebb. When the successive tides of the same day are very unequal, the ebb which follows the greater of these tides is lower than that which follows the less. The hourly rise of the tide is not regular. It is least at the first hour of either flow or ebb, increases at the second and third hours, and is greatest at half flood and half ebb, and there is a period of slack water at low and high water which lasts generally only a few minutes, but in some cases this extends to hours. (See Appendix IV.) In the open ocean the period of the rise and fall occupies the same time, but as a rule in the restricted channels of the confined seas and estuaries the ebb lasts longer than the flood. Tides composed of Separate Waves. — The tides which reach the coasts of the earth during the course of a year are thus due to a number of disturbing causes arising from the varying distances, and different periods, of the tide-producing agents, and of the 54 TIDES AND WAVES. changes of certain elements in their orbits. The tidal wave may therefore be regarded as the result of the superposition of a number of smaller waves generated at different periods and of varying heights, but although these waves co-exist they are not separately manifest. Eight waves practically represent the changes due to astro- nomical causes, but if great accuracy be required there are other minor waves depending on the nutation, and other perturbations of the sun and moon that have to be taken into account, making up the total number of tidal constituents that are superimposed on each other to twenty-three. The principal waves to be taken into account are — 1. The Lunar tide wave caused by the direct action of the moon. 2. The Anti-lunar or Inferior wave on the opposite side of the earth. 3. The Solar wave generated under the direct action of the sun. 4. The Anti-solar wave on the opposite side of the earth. 5. The wave due to the declination of the sun. 6. The wave due to the declination of the moon. 7. The solar elliptic wave due to the varying distance of the earth from the sun. 8. The lunar elliptic wave. One series of waves is semi-diurnal, the second occurs at intervals of a fortnight, and the third at intervals of six months. The minor waves extend over longer periods, but are confined within a cycle of nineteen years. The effect due to the elliptic motion of the sun and moon and to declination may be calculated approximately as follows, the multiplier for each foot of rise at spring tides being — Mulliplier for each foot of height. Increase. Decrease. Total. Sun's horizontal parallax . . „ declination ... . . Moon's parallax ... . . „ declination . . . . 0-005 0-008 0-018 0-056 0-087 0-004 0-010 0-048 0-036 0-098 0009 0-018 0-066 0-092 0-185 For example, the extreme difference plus or minus from the average rise in a spring tide rising 16 feet due to the above THE MAKING OF THE TIDES. 55 would be 16 x 0185 = 2-96 feet; and for a 40 feet tide 740 feet; and for one rising 6 feet 1-10 foot. Taking the spring tides at Brest over a cycle of 19 years, 1884-1902, the average rise as calculated in the Admiralty Tide Tables is 1930 feet, the highest spring tide during the period being 21-33 feet, and the lowest 16-84 feet, making the maximum difference due to the variation of the sun and moon 4-49 feet. Multiplying the average tide 19 "30 by the constant for decrease for the sun and moon, 0'098, gives the decrease 1'89, and by 0-087 for the increase gives 1-68, or a total effect of 3-60, which is a near approximation considering the minor disturbances are not taken into account. Establishment. — The establishment of any place on the sea- coast is the hour at which high water occurs at that place at new or full moon. This is generally known as the Vulgar EstahUsh- ment. The time of high water does not, however, follow the moon's transit by the same interval at every period of the lunation, this interval being regulated by the distance of the moon from the sun. When the moon and sun are in conjunction the corresponding tide follows the moon by its mean interval, and when the moon is at various hour angles after the sun the follow- ing mean corrections negative and positive have to be applied to find the correction for the establishment : — Honr angle Correction of the of the moon, establishment. Hours. Minutes. . . . . . deduct 1 . . . . . 16 2 . . . . . . ' 31 S . . 41 4 . . . .44 5 . . . ... 31 6 . . .0 7 . add 31 S . . . 44 9 . .41 10 31 11 . .16 12 .... For example, if the establishment corresponding to the new and full moon be at 6 o'clock, the time of the corresponding high water when the moon is one hour from the sun will be 5 hours 44 minutes after the moon's transit ; when the moon is six hours from the sun the time of high water will again reach the mean ; 7 hours after the time will be 6 hours 31 minutes, and so on. CHAPTEE V. PEOPAGATION OF THE TIDAL WAVE. The tidal wave generated by the action of the sun and moon in the Southern Ocean is propagated into the Atlantic, Pacific, and Indian Oceans, and from these into all the smaller seas, estuaries and rivers with which they are connected up to the Arctic latitudes. The tidal wave propagated into these seas being derived from the great primary wave of the Southern Ocean is recognized as a derivative or secondary wave. This derivative tidal wave is governed by different laws from those that regulate the primary wave, and is not affected by the direct action of the sun and moon. The primary tidal wave moves continuously in one direc- tion, while the derivative waves oscillate, moving for 6 hours 25 minutes in one direction, and then returning over the same course for a like period. Owing to the physical conditions which they encounter the derivative waves vary considerably in their rate of propagation, and amount of rise, from the parent wave. Both waves are, however, subject to the law of conservation of energy governing all matter in motion. By the action of the sun and moon an enormous amount of matter, in the form of water, is put in motion, which moves at a great velocity through the ocean in which the tidal wave is generated, and in the seas into which it is propagated. Where the momentum of the mass of moving water is checked by a contraction of area or decrease in depth of the channel through which it is passing, and in some measure by unevenness of the bottom and irregularity of the coast line, the energy is diverted to increasing the height of the wave or its velocity. Owing to the retarding effect of contact with the shores, the wave travels at a less rate along the coast than in the deeper To face page 57.] Fig. 8.— Chart op Tides. Explanation —Greenwich Time marked VI. 20, Rise Spring Tides ,, 17. Depth in Fathoms ,, 3000. PROPAGATION OF THE TIDAL WAVE. 57 water of the open sea, and is thus made to assume a convex form. The wave is also affected in its progress by coming in contact with obstructions due to islands and to headlands projecting from the coast line. Progress of the Tidal Wave. — The only way of tracing the progress of the tidal wave from its generation in the Southern Ocean throughout the seas of the earth is to take the time of high water, or the period at which the crest of the wave reaches any given part of the coast at full or change of the moon, as given in the Admiralty Tide Tables and Sailing Directions, and to reduce the local to Greenwich time. This, however, only gives an approximate result, as, owing to the effect of projections and indentations in the coast line divert- ing the tidal wave, the variations in depth of the ocean, and other disturbing causes, the time and height of the tides along the coast is very irregular, and in some seas difficult to follow. Rate of Propagation. — In the Southern Ocean the mean rate of movement of the crests of the two tidal waves is about 563 miles an hour ; the depth varying from 10,000 to 20,000 feet. In the Pacific the rate of movement of the tidal wave along the American coast is about 600 miles an hour, the depth varying from 9000 to 12,000 feet ; on the west side, along the coast of China, the rate is about 480 miles an hour, the depth being from 12,000 to 18,000 feet ; and from the coast of China to the Arctic Sea 250 miles an hour. In the Atlantic, along the coast of Africa to Cape Eoque, the rate of progress is 660 miles an hour, the depth being about 15,000 feet. North of this, along the coast of Europe to the British Islands, the rate is 300 miles an hour, the depth varying from 500 to 12,000 feet. On the west side of the Atlantic, up to about Long Island Sound, the rate of progress cannot be traced, owing to the varying set of the tidal wave, one wave moving diagonally in a westerly direction from the coast of Africa towards Newfoundland, and the other working along the coast. Around the British Isles, owing to the shoaling of the sea, the rate at which the wave progresses is much slower than in the open sea. From Valentia, along the west coast of Ireland and Scotland, the rate is 194 miles an hour, the depth varying from 300 to 500 feet for 100 miles from the shore. From Scilly to Lundy the rate of progress is 150 miles an 58 TIDES AND WAVES. hour ; and up the Bristol Channel, from Lundy to the mouth of the Avon, 40 miles an hour ; the depth varying from 60 to 30 feet. In the Irish Sea, through St. George's Channel, the rate is 90 miles an hour. From there to Holyhead 22 miles ; and from Holyhead to Moreeambe 45J miles, or an average of 30 miles an hour from Lundy ; the depth varying from 60 to 300 feet. In the north part of the Channel the wave travels at the rate of 90 miles an hour towards the Mull of Galloway ; and thence to Moreeambe the average rate is 190 miles; the depth varying from 240 to 300 feet. In the English Channel, from the entrance between Ushant and the Scilly Islands to a point between Beachy Head and Cape Grisnez, the average rate is 40 miles an hour, the depth varying from 60 to 150 feet over the greater part of the distance. Along the west side of the North Sea, from the north of Scotland to the Wash, the average rate is 52 miles an hour; the depth varying from 240 to 300 feet. From the Wash to Winterton the rate is 20 miles an hour, the depth being 120 feet; and from there to Harwich the rate is 10 miles, with a depth of about 50 feet. Along the coast of Denmark the rate is 70 miles an hour, with a depth of about 100 feet. Along the Belgian and Dutch coasts, from Calais to Ymuiden, the rate is 40 miles an hour. Effect of Expansion and Contraction of the Shore Line. — While the convergence of the shores by which the tidal wave is bounded, and the shallowing of the bottom lead to increase of height, the tidal rise is diminished by diffusion where the shores widen out. Thus, while the normal height of the tide as propagated from its place of generation into the Atlantic is about 2 feet, along the shores of Africa and South America the rise increases to 5 and 8 feet ; and at the most contracted part from 12 to 16 feet. Where the tide enters a converging channel with a gradually rising bed, the width and depth both being thus contracted, the momentum heaps up the water to an abnormal height as in the Straits of Magellan, the Bay of Fundy, the north-west coast of France, and the Bristol Channel. In these seas the rise from low to high water is from 30 to 50 feet. This great rise and fall is due to an alteration in the character of the tidal wave. As it encounters the shoaler water it assumes more the character of a wave of translation. The crest of the wave being driven by the PROPAGATION OF THE TIDAL WAVE. 59 momentum to an abnormal height, gravity seeks to restore the equilibrium, and in this effort the water is carried down the in- clined plane lying between the crest and trough of the wave with such impetus as to scoop out the water below the mean level of the sea as far as the incoming wave raised it above the mean level ; low water being as much depressed below the mean level of the sea as high water is raised above it. Where the sea expands into a widened area, and the water becomes diffused, a reduction in height takes place. An example of this is to be found in the Caribbean Sea and Gulf of Mexico, where the Atlantic expands from a width of 1500 miles between the African and American promontories to double this width; the rise of tide falling from 8 to 12 feet on those coasts to 1 and 2 feet, where the water expands into the bay. Reflected Tides. — In some seas the tides are reflected back from a projecting promontory, and travel along the coast in the opposite direction to that in which the main tidal wave is being propagated. This is the case on both the east and west coasts of South America, where the tide is reflected from the promontories of Brazil and Peru, and travels southward down the coast, while the set of the main tide is northward. An instance of reflected tides also occurs in the English Channel, where the flood tidal wave coming up the Channel strikes the north coast of France at Cape Antifer, and is re- flected back into the mouth of the Seine. Races and Eddies. — Where the coast projects out from the general run of the coast forming headlands and bays, the rapidity of the movement required to transfer the water from one bay into the other, results in greatly increased velocity and conse- quent formation of races and eddies. So also when the tidal wave is forced by its momentum through a narrow channel into another sea races are formed. Eaces are found in the Straits of Magellan and the Straits of Gribraltar ; in Pentland Firth and Sumburgh Head, in the North Sea ; and past such headlands as Portland Bill, and at Alderney and Cape La Hague. Some races get up very suddenly, and the sea becomes in a very turbulent condition almost without warn- ing, the currents running at a rate of from 7 to 10 knots. Surface Ripples and Eddies. — The fact that the undulation of the tidal wave is not a mere surface movement like waves formed by wind, but extends throughout the whole depth of the ocean, 6o TIDES AND WAVES. is shown by the sensitiveness of the moving water ; any sudden alteration in the bed of the sea being indicated on the surface by ripples and broken water. These ripples are sometimes mistaken by mariners as indica- tions of shallow water, but they may occur where there is a great depth of water. Thus, in the Straits of Magellan there is a strong ripple and broken water on the surface, where no bottom is found at a depth of 50 fathoms. Other examples may be found in some of the channels amongst the islands of the Pacific. In Pentland Firth, on the north of Scotland, ripples are observed in depths of from 40 to 50 fathoms, although the varia- tions in the level of the bed of the sea is not more than 20 feet. Double Tides. — In some cases, where the tid6s approach a coast from two different directions, the second tide may arrive later than the first, and so lead to the creation of two periods of high water, or a long period of slack water. Examples of double tides are to be found in the Bay of Cal- vados, at the mouth of the Seine, where high water practically lasts 3^ hours. On the opposite side of the English Channel, between Portland and Selsea Bill, owing to the double set of tides, one to the north and the other to the south of the Isle of Wight, there are also two high waters, the first making high water last from 2 to 4 hours. As the interval between the two high waters increases a second low water is developed. At Marsdiep, on the Holder, where the rise of spring tides is only b\ feet, the tide remains at high water for 3^ hours — the flood lasting 3^ hours and the ebb 6 hours. At spring tides the tidal wave shows two crests with a depression between them. This is due to the meeting of the two tidal waves, one coming from the English Channel and the other down the North Sea. Rotary Tides. — In confined seas and narrow channels the tides have frequently a rotary motion, making a complete circuit of the compass in 12 hours ; in some cases working round from left to right, and in others in the opposite direction. These revolving currents take place generally where the stream of tide separates or meets. Thus, at the Scilly Isles the Atlantic tide stream divides into two branches, one of which runs up the Bristol and St. George's Channels, while the other proceeds along the English Channel. Each of these currents goes through a regular cycle of changes in 12 hours, at one time one branch PROPAGATION OF THE TIDAL WAVE. 6i being more powerful than the other, and during another the other branch having the greater effect, and so the directions of the currents are made to revolye. Kotary tides are frequent in the English Channel and North Sea. Diurnal Inequality. — On some coasts there is a considerable difference in the time and height of the two tides of the day. The difference in height varies, according to the locality, from a few inches to as much as 6 feet ; and in time from a few minutes to there being only one tide in the day. The higher tide in some places occurs with the night tide for one part of the year, and with the day tide during the remainder. This irregularity in the time and height vanishes when the moon is over the equator, and is at a maximum when the declina- tion is greatest. Diurnal inequality is most marked where the tides are small and irregular and their propagation is disturbed by islands and narrow channels. Although the diurnal inequality is to be found in all latitudes from the equator to the polar regions, it is most marked amongst the islands of the Pacific, and in the Caribbean Sea and Gulf of Mexico, where in some places there is only one tide in the day. In the Grulf of Cambray there is a difference in the height of two succeeding tides of from 7 to 8 feet ; and at Singapore, where the rise of spring tides is 10 feet, the diurnal inequality amounts to as much as 6 feet. At Luciparu, in the Banks Straits, and in some parts of the Java Sea there is only one tide in the day, and this is very irregular. On some parts of the Australian coast the evening tides are 2 feet higher than the morning tides, and from October to November the reverse is the case. At Sydney the evening tides are 2 feet higher in June and July, and the reverse in December and January. At Port Darwin, on the north-west coast, where there is a tidal range of 24 feet, the difference in two successive high waters amounts to as much as 4f feet, and at low water to 10 feet. These variations, however, may be partly accounted for by the action of the wind, which blows continuously on or off shore according to the time of the year. In the Bay of Fundy the variation in the range of the tides due to declination is as great as the difference between spring and neap tides. 62 TIDES AND WAVES. In many of these cases it is difficult, if not impossible, to determine how far the irregularities in the time and height of the two tides of the day are due to declination or to the effect of sea and land breezes which vary in direction at different times of the year, or to causes due to the configuration of the coast and set of the tides. On the European coasts the difference between the two tides of the day is less marked, but a difference in both time and height due to the moon's declination can be traced. At Brest there is an average difference in height between the night and morning tides of 5 inches; on the east coast of England, at Hull, the average difference is 4| inches, and on the west coast, at Liverpool, of 8 inches. These differences are, however, partly accounted for by the difference between the lunar and anti-lunar tides. At the east end of the English Channel and south end of the North Sea the diurnal difference vanishes, as the tides there are compounded of two separate tides coming from different direc- tions, one being 12 hours later than the other. CHAPTER VI. TIDAL CUBRENTS. Theee is a very marked distinction between the tidal wave and the tidal current. The ignorance of the set and force of tidal currents has only too frequently been the cause of the loss of vessels, with the lives on board and of valuable cargo. Granville Collins, in his " Coasting Pilot," written in the last century, says, " The next thing that I recommend to your notice is the setting of the tides, which may alter the course to the loss of many ships." ^ Professor Haughton, in the introduction to his "Manual of Tides and Currents," states that a want of proper knowledge of the laws relating to tidal currents is a fertile source of the loss of ships, lives, and property,^ In the open sea a vessel is not affected by tidal drift, the movement of the water being only that due to wave action, except where some special currents prevail. At or near the coast, how- ever, where tidal currents of 3 or 4 knots are met with, a vessel may insensibly be carried several miles out of her course towards the shore or on to a sandbank. It is of service, therefore, for a mariner to have some information as to the conditions under which tidal currents exist and the localities where they are likely to be met with. On all sea margins, except where they consist of precipitous rocks, the sea bed shoals very considerably near the land ; and in most seas there is a costal shelf, which in some cases extends out several miles from the shore, on which the water is comparatively shoal. • " Great Britain's Coasting Pilot," by Captain GrenviUe Collins. London, 1779. 2 " Manual of Tides and Tidal Currents," Eev. S. Haughton. Cassell and Co., London. 64 TIDES AND WAVES. As there exists a relation between the rate of the tidal wave and the depth of the water through which it is propagated it is obvious that the movement must be slower over shoal ground than in the deeper water of the open sea. The axis of the tidal wave follows the deepest line of soundings, causing an overflow and recession of the central volume towards the shore. As this takes place and the wave encounters the shoal platform extending out from the coast, or enters narrow seas or channels, its momentum is checked and its character changes. The height of the wave increases, its length diminishes, and the rate of movement is considerably decreased. The progress being less rapid along the coast than in the centre of the sea, tl^e wave assumes a convex form, and approaches the shore at a varying angle, depending on the amount of shoaling of the water, and configuration of the bottom and sides of the costal shelf. High water may therefore reach a coast much earlier when the tidal wave has approached it directly from the open ocean than when it has come round by the shore. For example, in an embayment the tidal wave reaches the further horn of the bay before that which has proceeded along the shore round the curve, and which curling round meets the shore wave. The tidal wave propagated through the water of the ocean, and extending from trough to crest over a length of from 100 to 200 miles, with a height of only 3 or 4 feet, presents no conditions favourable to the formation of a current ; the inclination of the surface necessary for the horizontal movement of the water, although it exists, is inappreciable ; but when the wave approaches a shore, where the water shoals it feels the effect of this shoaling, and its character begins to assume that due to a wave of transla- tion, and a horizontal movement of the particles of water takes place, sufScient to produce a current running parallel with the shore, or in nautical phraseology, a " tidal stream." Thus, while the crest of the tidal wave is making high water at the rate of 50 to 100 miles an hour, a tidal current may at one period of the tide be running in an opposite direction at the rate of 2 or 3 knots. There is along coasts a tendency for vessels to be drawn out of their course by what is termed by sailors an "indraught," and more correctly a tidal current, the velocity and strength of which are subject to recognized laws, and the direction and time of which are fully described in the Admiralty Sailing Directions. TIDAL CURRENTS. 65 Also rules for calculating the drift of vessels by tidal currents are given in Galbraith and Haughton's "Manual of Tidal Currents." These currents are due to the action of gravity. The surface of the water between the trough and crest of a tidal wave assumes the form of an inclined plane. The amount and continuance of this gradient governs the rate of the currents which, owing to the momentum they acquire, continue to run in the same direction for some time after the commencement of the reversal of the direction of this gradient, in the same way that a pendulum swings upward above the line of gravity to the same height from which it descended on the opposite side. This is shown on the diagram, Fig. 9, where from B to the current is an ascending gradient due to the momentum "acquired while fall- s s ■f s *^ F^«., \. ' """^^ ^^^ ■^ ^ ^^y^ D -^^ — F B ~~— 1 3 6 ,9 12 Fig. 9. — Diagram showing Tidal CurrentB. 15 IS Hours ing from A to B, and the flood current as continuing to run for three hours after H. W. and the ebb for three hours after L. W. The maximum rate of the current is at half tide, and it is slack at high and low water. The effect of gravity due to the general slope of the surface of the water caused by the advance and retreat of the tidal wave leads to the simultaneous change in the direction of the current in confined channels. Tidal currents are governed by the same law that regulates the movement of water in open channels. There being an inclination in the surface of the water between the crest and the trough of the wave, the action of gravity tends to draw the particles of water from the higher to the lower level, causing a horizontal movement. This is retarded by the friction against the sides and bottom of the channel. 66 TIDES AND WAVES. The common formula for ascertaining the velocity of water in open channels V = v^ X 2F, in which V = velocity in feet per second, F the fall in two miles, and E the hydraulic radius, or the area of the channel divided by the perimeter or length of surface covered by the water, may be used for ascertaining the velocity of tidal currents. As the difference in level between the trough and crest of the wave is changing throughout the period of the rise or faU of the tide, half the total rise of tide between the trough and crest represents the fall in this case. The hydraulic mean depth of tidal seas can only be approxi- mately ascertained, and the depth is only that over the shallow water where the currents are formed. The following are therefore only approximate results, but may be taken as some indication of the relation of tidal currents to tidal waves. In the English Channel between Scilly and Hastings the length of the tidal wave is 250 miles, the average depth of the water 120 feet, the difference in level between the trough and crest 20 J feet; the total inclination per mile 0'08 foot. The average rate of the current worked out by the above formula is 2 miles an hour, which agrees very closely with that which pre- vails. The rate of propagation of the tidal wave is 40 miles an hour. In the North Sea from Wick to the Wash : length of wave, 340 miles; average depth of water, 240 feet; height of wave, 16 feet ; surface slope, 0*048 foot per mile ; calculated rate of the current, 2*31 miles an hour. The rate of propagation of the tidal wave, 52 miles an hour. In Boston Deeps, on the north side of the Wash, the distance from the entrance at Skegness to Clayhole at the upper end is 17 miles ; the average depth 28 feet. Else of spring tides, 22 feet ; gradient from high to low water, 1"29 foot per mile. Calculated rate of current, 4 miles an hour, which is about the same as that which occurs at spring tides. In the Irish Channel, between the entrance to the Bristol Channel and Morecambe Bay, the length of the wave, 180 miles ; average depth, 300 feet ; height of wave, 25 feet ; surface slope, 0-14 foot per mile ; calculated rate of the current, 2 miles an hour. The rate of movement of the crest of the tidal wave, 30 miles an hour. TIDAL CURRENTS. 67 In the Bristol Channel the length of the wave is 70 miles ; average depth, 40 feet ; height of the wave, 38^ feet ; surface slope, 0-55 foot per mile ; calculated rate of current, 4-76 miles an hour. The rate of movement of the tidal wave, 40 miles an hour. In Pentland Firth, where the tidal wave changes to a tidal current, the length of the Firth is 13 miles ; the average depth, 204 feet ; height of wave, \\\ feet ; surface slope, 0'88 foot per mile ; calculated rate of the tidal current, 8'84 miles an hour, the same as the rate of propagation of the tidal wave. Tidal currents are most pronounced in narrow and shallow seas, such as those of the British Islands, where currents of from 2 to 3 knots exist ; but they are also to be found on the coasts of the ocean, but generally feeble unless aided by wind. Thus, on the north coast of Spain there is an easterly drift, but it is so slight that a vessel does not feel it, but when a strong westerly wind is blowing, a very considerable current sets into the Bay of Biscay. On the coast of France, in the offing off the island of Ushant, there are strong tidal currents which attain a speed of 6 to 7 knots at springs. Within the last few years there have been several wrecks on this part of the coast owing to vessels having been drifted out of their course by this current. The time of the change of the direction of the tidal current in the offing is seldom coincident with the time of high and low water by the shore. In the oflSng, the change in direction lags behind the commencement of the rise and fall on shore to half tide, so that during one period of the tide the tidal wave and the tidal current may be making in opposite directions. As a general rule, round the coast of Great Britain the tidal current in the offing continues to run for about three hours after high and low water by the shore, and the same is the case off the island of Ushant on the north-west coast of France. In proportion as a channel is obstructed at the further end the flood-current runs for a shorter time after the flood tide ; and in a closed channel the flood-current ends simultaneously with high water. For example, in the English Channel the flood- current continues to run for three hours after high water ; in the Bristol Channel, for only two hours after high water ; while in rivers, with some exceptions, for only a few minutes after. In the seas of the British Islands the turn of the current is simultaneous throughout each sea, and the time of change in 68 TIDES AND WAVES. direction may be referred to one common standard. A know- ledge of this fact is of great service to mariners, as, the state of the tide at one of these standard ports being known, there is no necessity of comparing the motion of the currents with the vary- ing times of high water along the coast. The standard place of reference for the English Channel and the south end of the North Sea is Dover. From the entrance to the English Channel to about Hastings, and in the southern part of the North Sea, the current is running westward and northward when the tide is falling at Dover, and eastward and southward when it is rising there. That is to say, that the stream will always carry a vessel up the English Channel towards Dover when the tide is rising there, and down the Channel when it is falling there. In the North Sea there are four standard places governing the turn of the tidal current : Wick, from the west side of Pent- land Firth ; Leith, from Eattray to the Firth of Forth ; the Wash, from St. Abb's Head to Cromer (Hull is generally recog- nized, as the time of the tide is the same there as at the Wash) ; Dover, from Cromer to the Thames and the North Foreland; and for the east side up to the Hook of Holland. In the Irish Sea, the northern and southern tidal currents practically commence and end in all parts at the same time, and coincide with the rise and fall of the tide at Morecambe Bay or Liverpool. CHAPTEE VII. MEAN LEVEL OF THE SEA AND KANGE OF THE TIDES. Mean Level of the Sea, — The tides are due to a derangement of the water of the ocean, and to the surface being elevated above or depressed below the normal level. The mean sea-level is that condition which would prevail if the sea were in a state of repose, and undisturbed by tidal action or by waves due to meteorological causes. It is the mean plane between high and low water. Ordnance Datum. — In this country the mean level of the water at Liverpool at all conditions of the tide, ascertained from obser- vations spread over a considerable period, has been adopted as the datum for the ordnance levels, and is referred to a permanent mark known as Old Dock Sill, which is 4-67 feet below the ordnance datum. The mean level of the sea as given by the Ordnance Survey does not vary much in the sea round the coast, but in rivers and estuaries it is nearly as much as 2 feet. A table of these differences is given in Appendix III. French Datum. — The datum adopted by the French Govern- ment is the mean level of the Mediterranean Sea at Marseilles, and is known as " the zero of Bourdaloue." This level is approximately two feet below the English Ordnance datum; and has been connected with the Italian, Austrian, Dutch, and German systems which embrace ports on the coasts of the Mediterranean, Atlantic, and North Sea. Practically the mean level of these seas is the same. The connection of the levels of the various seas with the datum of Marseilles is given in Appendix III., Table 4. It has not been found practicable so far to connect with accuracy the mean level between the English and Continental datums ; but from such observations as have been made it may be 70 TIDES AND WAVES. assumed tliat there is very slight variation in the mean level of the seas of Great Britain and those of the Continent. Admiralty Datum. — The datum adopted by the British Admiralty for the soundings given on the charts is the mean low water of spring tides. This also is the datum from which is calculated the rise of spring and neap tides given in the twenty-four standard ports in the Admiralty Tide Tables. In Appendix III., Tables 2 and 3, the level of this with reference to the ordnance datum will be found, and also other tidal data. Mean High Water. — The mean level of high water at any given part of the coast is the average height to which both spring and neap tides rise on the shore as ascertained over a lengthened period. This level is of importance, as it determines the limit of the rights of the Crown to the foreshore, beds of rivers and the tidal creeks as against frontagers; all foreshores below mean high water being claimed by the Crown or the Duchy of Lancaster, except where the right has been alienated by special grants. Although there is very considerable difference in the height to which the tides rise at different parts of the coast of the world, this variation consists in a depression below and elevation above a fixed point, the mean level remaining the same whether the tides rise 40 to 50 feet as in some places, or only 1 or 2 feet as in others. In 1838 a Committee of the British Association, under the direction of Professor Airy, had a series of levels run from Portishead in the Bristol Channel to Axmouth in the English Channel, and also a series of observations of the tides taken at each of these places, in order to determine the difference of the mean level of the surface of the water at tide time at the two places. The result showed that with a mean tide rising 35"74 feet and a spring tide of 41-08 feet at Portishead, and 10 feet and 10'66 feet respectively at Axmouth, the mean level of the sea was only nine inches higher at the former place than at the latter. The high-water level rose 18'60 feet higher at Portishead than at Axmouth, and the low water fell 1214, making a total difference in the level of high and low water of 25-74 feet. The position of the line of levels is denoted by means of marks at the following places, the figures giving the respective levels : — MEAN LEVEL OF THE SEA AND RANGE OF THE TIDES. 71 Level feet. Axmouth (granite block) 83-65 East Quantooks Head (granite block) .... 244:'4i Stolford (granite block) 12511 Portishead 102-58 From further investigations of six years' tides (1833-1838) taken at Plymouth under the superintendence of Mr. Walker, the Queen's Harbour Master, made by Airy, it appeared that the level of mean high water is constant from year to year within two or three inches. At the head of the Bay of Fundy spring tides rise 45 feet, while in Northumberland Straits, which is separated from the bay by a narrow neck of land 18 miles wide, the range of spring tides is only 9 feet. From levels taken across this neck of land for the Chicnecto Ship Eailway it was ascertained that the mean level of the sea is only three inches higher at Bale Verte, in the Gulf of St. Lawrence, than in the Bay of Fundy.^ Eange of the Tides. — The range of the tide is the difference in level between high and low water of any given tide. With spring tides the range and rise denote the same thing. With neap tides the range is the difference between low and high water of neaps, while the rise is that from mean low water of spring tides to high water of neap tides. Tide Gauge xrr XIII XII XI X IX VIII VII VI V rv III II I o I II El Fig. 10.— Diagram showing Eelative Levels of Tides. This will be made clearer by the accompanying diagram (Fig. 10), where represents the mean level of the sea, AE the ' " Survey of Tides and Currents in Canadian Waters," by W. Bell Dawson. RepoH for 1902. ij Mean Level A O.S.T. ^ E Mean Level B O.N.T. ^ E- Half Tide or Mean Level of S.T. & N.T. ^ ^ ~— c Mean Level D L.W. O.N.T. t Mean Level E L.W. O.S.T. E I 72 TIDES AND WAVES. range or rise of a spring tide, EB the rise of a neap tide, and DB the range of a neap tide. The height of high water varies at different periods, depend- ing on changes in the moon's position over a cycle of 19 years. The difference in the rise of the tides is due to astronomical causes, and the variation in the range at different localities to mechanical effects. The rise of a neap tide above mean low water of spring tides is about three-fourths that of spring range, and the range or difference between neap low and high water is about half that of spring range. Low water of spring tides ebbs out lower than low water of neaps in the same proportion as high spring tide rises above high water neap tide. There are, however, exceptions to this rule in estuaries and tidal rivers, examples of which are given in Chapter IX. Hourly Else and Fall. — The rise and fall of the tide is not spread evenly over the time occupied. There is a period of slack water both at low and high water, the length occupied by the slack varying in different situations. The rate of rise or fall at the second and fifth hours is about double that of the first hour, and at the third and fourth hours it is about three and a quarter times as great. In Appendix IV., Tables of constants are given for finding the hourly rise or fall, and the height of a given tide at each hour of the flood or ebb. High Water. — The vertical difference between the crest and trough of the tidal wave, or high and low water, due to the effect of the sun and moon as determined theoretically, is 2 feet at spring tides and 140 foot at neap tides. See diagram, Fig. 7, Chapter IV. At the islands in the middle of the Southern Ocean, Auck- land, St. Paul, Amsterdam, Kerguelen, the Sandwich group, and Georgia, the rise of spring tides is from 2 to 3 feet. At the cluster of islands in the open water of the Pacific the rise is IJ to 4 feet. At the islands of Ascension and St. Helena in the open water of the Atlantic from 2 to 3 feet. Among the West India Islands from 1^ to 2 feet. As the velocity of the wave is checked by the shoaling of the bed of the sea, and by coming in contact with the coast, the rise is considerably increased. Thus, where the tidal wave washes MEAN LEVEL OF THE SEA AND RANGE OF THE TIDES. 73 the coast of Australia and New Zealand, the range at spring tides is from 5 to 10 feet. In the Pacific, along the west coast of America, from 4 to 7 feet, and on the east of America and west shores of Africa from 6 to 8 feet ; along the west coast of Europe from 12 to 16 feet, and on the east coast of North America from 6 to 8 feet. In the shallow water round the British Islands the rise of spring tides varies considerably. At one place on the west coast of Ireland there is scarcely any rise or fall of the tide perceptible, while on the opposite side the rise is from 27 to 28 feet. In the English Channel the variation is from 5 feet between Portland and Swanage to 38 feet on the opposite side in the Gulf of St. Malo, and in the North Sea the variation is from 5 feet to 22 feet. The average rise of the tides round the British Islands is 15 feet at springs, and 11^ feet at neaps, the mean neap range being 7| feet. Examples of extreme variations are to be found in the Straits of Magellan, where spring tides rise in the narrows at the east end from 42 to 44 feet, and in the centre from 21 to 23 feet, while at the Pacific end the rise is only from 4 to 5 feet ; on the north-east coast of South America the rise is 16i feet, and in the Caribbean Sea and Gulf of Mexico the rise is only from 1|- to 2 feet. On the east coast of America, near the entrance to the Bay of Eundy, the rise is from 8 to 12 feet, while in the Bay spring tides range 50|^ feet. The record difference between high and low water occurred at Moncton, in the Bay of Fundy, in 1869, when the " Saxby " tide reached to 53 feet above low water ; and at Chepstow, in the Bristol Channel, when in 1883 the tide reached to 48*55 feet above low water of spring tides. CHAPTEE VIII. THE EFFECT OF "WIND AND ATMOSPHERIC PRESSURE ON THE TIDES. The variation in the calculated time and height of the tides due to wind and changes in the pressure of the atmosphere, is a matter that requires careful attention by pilots and mariners ; and the great increase above the normal rise in the level of high water due to this cause is an element that has to be taken into con- sideration by engineers in charge of sea defences. In order to save a tide and not lose time, pilots are often obliged to navigate vessels over bars and up tidal channels with a very narrow margin of water under their keels. In crossing a bar in calm weather this margin frequently is not more than from 2 to 3 feet ; and in crossing over shoals in an estuary or tidal river, or over a dock sill, a pilot will frequently run with as narrow a margin as six inches. As gales of wind have the effect of increasing or decreasing the depth of the water to the extent of six or seven feet, it is of importance that some data should be afforded as to the extent to which the particular tide of the day may be affected. The changes in the pressure of the atmosphere as recorded by the barometer have a material effect on the height of the tides, but to a much less extent than the wind ; as the barometer and the wind force are generally in sympathy, any effect due to change of pressure is marked by the greater effect of the wind. The effect of the wind may be taken as from 6 to 10 times greater than that due to atmospheric pressure. The direction and force of the wind at any particular port affords, therefore, a much more reliable, although not a certain, guide as to any variation that may be expected in the height of the tides. The effect of atmospheric pressure on the tides has received a considerable amount of attention, and was one of the matters WINDy BAROMETER, AND TIDES. 75 investigated by Sir J. W. Lubbock with reference to the ports of London, Liverpool, and Bristol ; and by Sir T. Clark Boss, in the Arctic regions ; but the influence of the wind has been almost entirely neglected until the matter was brought before the British Association by the author in 1895. The greatest variation in the normal height of the tides occurs when meteorological and astronomical perturbations conjoin. The conditions most favourable to extreme ranges of the tides are a new or full moon tide, with the moon in perigee, and her declin- ation near the equator, a strong gale blowing for some time in the same direction as the flood tide in the open sea, and then changing as the tide is rising to an on shore direction ; and a steep gradient in the barometer falling in the same direction as the flood tide. With the opposite conditions the tides will be correspondingly below their normal level. High tides due to wind force are of frequent occurrence, but extraordinary high tides have occurred only about five times during the last half century. The Wind. — The effect of wind on the tides of any particular port in the open sea depends on its situation and exposure, or fetch. Winds prevailing from the same quarter for long periods may be the cause of a continual current in one direction, which may act coinciding with, or running contrary to, the tidal stream ; in one case increasing and in the other diminishing its rate of flow. The depth to which water may be affected by wind blow- ing from the same quarter for some time was found to extend in the Gulf of St. Lawrence to over five fathoms, and its influence was felt throughout the surface layer sufficiently to affect navi- gation.^ In the tropics there is in many places a regular alternation of breezes towards and off the land, the effect of which is to heap up the water in shore so long as the wind is blowing inland, and to depress the water when blowing off shore. Hence there is a diurnal irregularity in the sea level independent of the tide. At Port Darwin, on the north-west coast of Australia, the water in the harbour is raised two feet higher during the summer than in the winter, due to the action of the wind, which blows persistently during the summer months from the north-west into the harbour, piling the water up, while in the winter time the prevailing wind is from the south-east. 1 « The Currents in the Gulf of St. Lawrence." Ottawa. 1900. 76 TIDES AND WAVES. Wind blowing on any large sheet of water alters the level oi the surface, depressing it on the windward and raising it on the lee side. Thus the author ascertained that a gale blowing on one of the Norfolk Broads, half a mile across, caused a difference of 1\ inches as between one side and the other. In an inland sea the effect of the wind has to be taken into consideration in the navigation and berthing of vessels, a shift of wind having the same effect as a tide and causing either deep or shoal water. Thus in the Caspian Sea the wind raises or depresses the water as much as 6 feet, according to its direction and force, making a total variation of 12 feet.^ In the Lijm Fiord, an extensive sea lake on the north of Jutland, where the spring tides rise from 2 to 3 feet, during east winds after west gales, the ebb runs out for two or more days without intermission, after which the tide makes regularly, changing every six hours. .. On the Zuyder Zee, with heavy west winds the water is lowered 8 feet on the coast and raised correspondingly with east wind. In December, 1904, owing to a heavy gale from the north- east the water in the Baltic Sea, in the course of ten hours, was raised 11 "71 feet above its normal level and inundated a large area of land. On Lake Erie, which is 250 miles long and 60 miles wide, with a depth varying from 30 to 180 feet, a 42-mile south-west gale in December, 1899, raised and depressed the surface so as to cause a maximum difference of level of 47 inches in 18 hours ; the water rising 5 feet during the storm at Buffalo. In Novem- ber, 1900, with a west wind having a maximum velocity of 80 miles, and a mean of 60 miles, an hour lasting for six hours, the level of the lake rose 8i feet at Buffalo, the extreme difference of level between the two ends of the lake being 13 feet. Continuous records of the level of the water have been kept at four stations at different parts of the lake in conjunction with the records of the wind direction and velocity and atmospheric pressure. These indicate that winds blowing parallel to the longer axis of the lake tend to heap up the water at the end towards which they blow and to depress it at the opposite end. Owing to the convergence of the shore lines at Buffalo, the ' " Tidal Kivers : their Hydraulics, Improvement, ahd Navigation." Longmans, Green, and Oo. WIND, BAROMETER, AND TIDES. 77 heaping up of the water under the influence of south-west gales is sometimes sufficient to cause considerable damage to the wharves and shipping, while at the same time the water becomes so shoal at the other end as to interfere seriously with the navi- gation. The undulations in the lake are not propagated, in the ordinary sense of the word, but the whole lake appears to oscillate about a nodal line in the centre where the movement is at zero, and it increases in degree towards both ends. Deductions as to the effect of wind and atmospheric pressure on the Dutch coast from observations made by M. Engelenburg at Flushing, showed that winds blowing off the land cause a decrease in the sea level, and sea winds arise in the half-tide level of 3-8 cm. (1-52 in.), 10-7 cm. (4-28 in.), and 17-3 cm. (6'92 in.) respectively in the summer, equinoctial and winter months. For the barometer, for every increase of 1 inch of mercury, thehalf^tide level is depressed with a land wind 0'6 cm. (240 in.), with a sea wind 0-8 cm. (3"20 in.). The rise of mean tides at Flushing is 13 feet. Gales blowing along the coast in the same direction as the main stream of the flood tide occasion an elevation of the crest of the tidal wave along that coast, and direct on-shore winds a heaping-up of the water. The reverse takes place when the wind is against the flood tide. The amount of variation from the natural or calculated height depends to a certain extent on the range of the tide, the differ- ence being greater where the range is great than when it is small. Thus, on the west coast in the Irish Sea a south-west gale causes a high tide in the Mersey, the Eibble, and the Lune; and when from the opposite direction a low tide. With very strong gales the tide in the Mersey has been raised nearly 7 feet above the normal level, and in the Lune nearly 5 feet. At Eathlin Island, on the north coast of Ireland, where the mean range of spring tide is from 3 to 4 feet, in stormy weather the extreme range varies from 9 feet to a few inches according to the direction of the wind. In the English Channel the tides are raised from 2 to 3 feet with south-west winds and depressed with easterly gales. Among the Channel Islands south-west winds accelerate and raise the tides 2 to 3 feet, while north-east winds operate in the opposite direction. At Guernsey the greatest effect of wind recorded resulted in a tide having a range of 33 feet 6 inches, an ordinary spring tide ranging 26 feet. On this occasion low water ebbed 78 TIDES AND WAVES. out 4 feet 6 inches below mean low water, spring tide. In October, 1883, during a heavy gale the tide rose in the Severn 10 feet above the calculated height. At the east end of the Channel the tides are affected both by the North Sea wave and that coming up the Channel, so that they are subject to variation both from north-east to north-west, and south-west and south-east winds. At Dover and Folkestone, ordinary gales raise or lower the tide from 2 to 3 feet ; and the variation from the normal level has been as much as 6 feet, low water receding 4^ feet below low water, spring tide. On the east coast, north-westerly to north-easterly gales raise the tides from Pentland Firth to the Thames, and even affect them as far as Dungeness, to the extent of from 2 to 3 feet, also causing them to flow earlier. In strong gales the increase at some places is greater than the total height of a normal spring tide. Thus at Yarmouth, during a heavy north-west gale, the tide has been known to rise 12| feet, the ordinary rise of spring tides being 6 feet. In the Humber and the Wash an excess of height of 6^ feet, and in the Thames of 5 feet, has been recorded, and the low water has ebbed out 3 to 4 feet below the normal level. The following table, taken from the Admiralty "Channel Pilot," Part I., shows the average number of heavy gales occur- ring round the British Islands in a year, derived from fifteen years' observations, 1871-85 : — S.W. coast. S. coast. E. coast. Gales of ain kinds / Severe gales N. 3-0 0-3 E. 6-5 0-6 s. 15-7 0-4 121 0-5 Total. 37-3 1-8 N. 1-8 B. 1-3 S. 10-7 0-4 w. 6-6 0-3 Total. 20-4 0-7 N. 3-8 0-2 E. 3-4 0-2 S. 12-5 0-1 w. 3-6 0-2 Total. .23-3 0-7 (South-west coast comprises from Pembroke to Portland ; south, from Portland to Dungeness; east, from Dungeness to Hasborough. North winds include E. by N. ; East, S. by E. ; South, W. by S. ; "West, K. by W.) This Table includes gales blowing with a force of more than eight on the Beaufort scale, and severe gales blowing with force of ten or sixty miles an hour. The tides, however, are materially affected with winds of less force than this, as will be seen by the particulars given further on. Gales which occur during spring tides are generally more violent, and last longer than those which take place during WIND, BAROMETER, AND TIDES. 79 neaps, and they acquire their greatest strength at the beginning of the flood.i On the coast of Holland, at Ymuiden, where spring tides only rise 5j feet, with heavy on-shore gales, that is from the N.W., the tides sometimes rise from 9 to 10 feet ; whereas with the wind off shore they do not rise higher than 3^ feet. Gene- rally wind depresses the low water after high tides on the coast of Holland, as elsewhere, but this rule does not always hold good. Winds from the S.B. have caused two extraordinarily low ebbs to follow one another with a very slight rise between, even this remaining below low-water level. On other occasions it has been found that the effect of gales blowing in the same direction as the flood tide was to raise the level of low water as well as that of high water ; and for corresponding tides on the Clyde the same result ensued.^ The same is recorded also as occurring in the St. Lawrence. On the north coast of France strong N.W. winds raise the tides from 2 to 3 feet above normal level ; and on the west coast they are raised by S.W. winds to the same extent. On the coast of Spain, where the rise of spring tides varies from 10 to 15 feet, gales from S.W. to N.W. raise the tides from 4 to 5 feet ; while with N.E. winds they are depressed 3 feet. In the St. Lawrence during strong N.B. winds in 1894 the tide at Quebec was raised 7 feet above its normal level. In Winyah Bay on the Atlantic coast, during a very heavy N.E. gale in October, 1893, the estimated force of which was 12 on the Beaufort scale, the tide rose more than four times the natural height. When low water was due, the tide was still rising, and reached on the following day to a height of 11 feet 6 inches, or 8^ feet above its normal height. Thus for 24 hours the tide continued to rise owing to the force of the wind. In the La Plata heavy gales from the N.E. to N.W. have caused the water to rise above the soundings shown on the Admiralty Chart 8 feet, and to fall 4 feet lower than the sound- ings, making a difference of 12 feet, or 7 feet more than the rise of a spring tide. In the Gulf oif Mexico, where the rise of tide is only from 7 to 9 inches, long-continued wind from the S.E. raises the tides ■ " Channel Pilot," Part I. = Report Brit. Ass. on the Effect of Wind, etc. 1896. 8o TIDES AND WAVES. 3 feet above the mean, while northerly winds lower as much below mean low water. For the Keport on this subject drawn up for the British Association ^ the author made a careful analysis of the effect of wind on the tides, compiled from the records kept at five ports situated at different parts of the United Kingdom : Sheerness on the south-east, Plymouth for the English Channel, Liverpool for the west coast, and Hull and Boston for the east coast ; and tables are there given of the results at each place. The object of this investigation was the practical purpose of ascertaining whether the records of the wind and atmospheric pressure, as obtained by an observer at any particular port, afforded a reliable guide to pilots and mariners navigating vessels over bars and up the channels of tidal rivers ; and to those engaged in coast work, as to the variations to be expected in the height of the calculated tides as given in the Admiralty Tide Tables. It was there shown that in extreme cases a variation from the tide tables to the extent of 8 feet might occur ; and a difference in the height between two succeeding tides to the same extent. The general conclusions arrived at as given in the Eeport are as follows : — Taking the mean result of the five ports : — One hundred and eighty tides were affected by the wind in a year, or about 26 per cent, of the whole. One hundred and twenty-three were either increased by winds blowing with the tide or depressed by winds against the tide. Sixty-seven were influenced in an opposite way. The mean force of the wind affecting these tides was 4'02 (Beaufort scale). With a mean rise of the tide above low water of spring tides of 1844 feet, the mean variation in the height was 13"89 inches. The mean variation per foot rise of tide due to wind was for force of — Inch. 3 ... 0-76 per foot rise of tide. 4 and 5 . . . . .... 0-80 „ „ 6 0-91 „ 7 to 10 . . . 106 „ Eor example, with a tide due to rise 20 feet by the tide table ' Beport of the Committee on the Effect of Wind and Atmospheric Pressure on the Tides, W. H. Wheeler, Secretary Brit. Asa. Liyerpool,il896. WIND, BAROMETER, AND TIDES. 8i and the wind blowing a gale witk a force of 6, the increase or decrease in the height was 18'20 inches. The author endeavoured to formulate some reliable rule for guidance, available for all ports, as to the variations to be expected with a given force of wind and height of tide. As a rough rule it may be taken that the effect of a moderate gale is to raise or lower the tide according to its direction as many inches as it would rise in feet under normal conditions. The figures in the above table afford some indication as to what may be expected, but they are only approximate, and are not to be universally relied on, as the tides may be affected by different conditions in the sea through which they are propagated from those which prevail in the sea where the port is situated. Table Showing the Extent to which Tides mat be afjeotbd by Wind DURING Gales. The following variafiona from the expected or calculated height are taken from the observatioDS contained in the tables in the report. Rise of spring Variations in Difference Port. tide above low height ot tide due between two water. to gale. succeeding tides. ft. in. ft. in. ft. in. Hull ... 21 6 4 5 Boston 22 5 3 8 8 Lynn ... . ... 22 7 11 11 Yarmouth . 5 8 9 9 3 Gravesend . . 18 6 4 7 7 5 Dover 18 9 6 1 8 Flushing 15 5 1 2 8 Ymuiden 5 3 5 4 1 4 Schokland (Zuyder Zee) . . 9 7 9 1 9 Liverpool 27 6 6 8 7 9 Glasson dock . . . 20 4 9 3 Glasgow 11 3 6 2 3 11 Portsmouth 13 6 3 8 3 1 The following examples show the effect of gales in disturb- ing the tides. Examples of the Eflfect of Gales on the Tides. — Consequent on the gale of November, 1893, with N.E. to N.W. wind with force of 8 to 10, the gradient of the barometer being 0"65 as between Aberdeen and Yarmouth, being lowest at the latter place, the tide was raised 2 feet 9 inches at Sunderland; 3 feet 3 inches at Grimsby ; 5 feet 1 inch at Boston ; 4 feet 9 inches at Yarmouth ; and 2 feet 4 inches at Dover. G 82 TIDES AND WAVES. In the gale of November, 1894, with the wind blowing strongly from N.W., backing on next day to S.W. with force of 7 to 9, the barometer being 0'25 below the mean, with a gradient between Scilly and Ardrossan ; and between Scilly and Denmark of 0*84, being highest in the south and west, the mean result of the effect on fourteen ports round the coast was to raise the tides, which were then at springs, on an average 2-88 feet on the west coast, and to depress them on the east coast 2*82 feet, the greatest variation being a depression in the Wash and the Thames of 3 feet 5 inches ; and at Dover 3 feet 3 inches ; and increase at Holyhead of 4 feet above the height given in the tide table. The gales of December, 1894, caused considerable disturbance in the tides on both sides of the coast. On the east coast the wind on the 20th was N.N.W. with a force varying from 5 to 7 ; on the 23rd the wind had backed to S.W., blowing with a force of 10. On the 28th, 29th, and 30th the wind had veered to W.N.W. with force varying from 6 to 10. The barometer on the 20th was about the average ; on the 22nd it had fallen to 0'97 below the normal height ; on the 28th and 29th it was from 0'52 to 0'72 below the normal height, the gradient between Aberdeen and Yarmouth being 048, the depression being in the north. With these conditions the tide was raised 3 feet 1 inch above the height given in the tide table at Hull on the 20th ; 13 inches on the 22nd, 4 feet 1 inch on the 23rd, 6 feet 4 inches on the 26th, and 1 foot 7 inches on the 30th. The morning tide of the 22nd at Boston was depressed 6 inches, and the other tides for the same dates raised 3 feet 2 inches, 1 foot 2 inches, and 4 feet 4 inches, and on the 28th the morning tide was depressed 3 feet 1 inch, and the evening tide raised 4 feet 3 inches. High water at Boston for the evening tide on the 22nd was 2 hours 33 minutes late, and the morning tide of the 23rd 1 hour 10 minutes early. At Ipswich the evening tide of the 23rd was raised 4 feet 11 inches and flowed an hour longer than its proper time. On the west coast at Liverpool on the 21st, with the wind blowing from the S.W. with force of 4, the tide was normal. On the morning of the 22nd, the wind being nearly due south, with force of 11, the tide rose to 29 feet 6 inches above low water, spring tide, or 6 feet 8 inches above the expected height ; the evening tide was deficient by 13 inches, making a difference of 7 feet 9 inches in the height of two succeeding tides. In November, 1895, the gradient in the barometer being half WIND, BAROMETER, AND TIDES. 83 an inch on the English coast, the depression being in the north ; wind from S.E. to S.W. blowing with force of a gale on the 11th ; at Leith for 12 days the tides averaged 1 foot 4 inches above the normal height. At Grimsby the wind from the 5th to the 17th was blowing principally from the S.W., with mean force for 7 days of 5, the mean increase of the tides being 1-30 foot. At Hull the mean increase was I'lO foot. At Boston with an average force of the wind from the S.W. from the 10th to the 16th 5-10, the gale attaining a force of 10, three tides were depressed an average of 15J inches and three raised an average of 14 inches. At Ipswich the morning tide on the 11th was depressed 3 feet 9 inches. At Dover from the 10th to the 17th the wind was blowing from the S.W. with an average force of 4*80, two tides were depressed 15 and 20 inches, one tide was raised 2 feet 1 inch, and the others were about 10 inches above normal height. At Portsmouth on the 18th, with N.W. wind, force 6, one tide was raised 13 inches, and the other 10 inches, and on the following day both tides were raised 18 inches. At Avonmouth on the 6th and 7th, with wind N. to N.W., force 7 to 10, the mean increase in the tides was 9 inches, the maximum being 18 inches. At Liverpool from the 2nd to the 7th the tides were all high, the mean increase being 2 feet 8 inches, and the maximum 3 feet 5 inches; the wind was W.S.W. to W., mean force 6*80 and maximum 9. At Holyhead, 2nd to 7th, wind W. to S.W., mean force 6 '40, maximum 7, mean increase of tides 1"14 feet, maximum 2 feet 1 inch. Belfast, 1st to 6th, wind W.S.W., mean force 6*80, maximum 8, mean increase in tides 1 foot 4^ inches, maximum 8 feet 1 inch. Glasgow on 4th, wind W.S.W., force 6, increasing to 8 on 5th, and continuing to blow from S.W. to 6th; mean increase in height of tides 3 feet 9 inches, maximum 6 feet 2 inches, the normal rise above low water of spring tide being 10 feet 10 inches, and actual rise 17 feet ; the barometer fell 072 inches. The gale of November, 1897, had the effect of raising the tides on the south-east coast to an abnormal extent, causing them to overflow the sea banks, and doing an enormous amount of damage all along the coast, from the Humber to the Thames. The wind on the previous days had been blowing strongly from the S.W., a condition favourable to increasing the height in the English Channel; it then flew to the N.W., a quarter which tends to raise the tide in the North Sea. The continued influence 84 TIDES AND WAVES. of the winds from these two opposite quarters, therefore, operated to concentrate the full effect of the tide along the south-eastern coast. This gale fortunately occurred 5 days after the full moon, or the disasters that occurred would have been greatly aggravated. On the 27th the wind was blowing round the south and east coasts strongly from the S.W., the force varying from 5 to 7. It then changed to N.W. with force of 10, and backed again to S.W. with force 3 to 6 ; the barometer varied from 29-92 at Spurn to 30-32 at the North Foreland. Next day it had fallen to 29-49 at Spurn and 2976 at the North Foreland, continuing to fall to 29-10. The falling gradient at first was 0-40 from north to south, and later was reversed to 027 from south to north. At Sunderland the tides were increased 2 feet 10 inches ; at G-rimsby the morning tide of the 29th rose 5 feet 11 inches above the tide table height; the next day the tide being 1 foot 9 inches deficient, making 8 feet 9 inches difference in the two succeeding tides. At Boston the morning tide was increased 5 feet 3 inches, the difference between this and the succeeding tide being 8 feet 8 inches ; at Lynn the increase was 7 feet and the difference in the two tides 11 feet 11 inches,*the effect of the N.W. wind being more felt here than on the other side of the Wash. The increase at Yarmouth was 8 feet, or 2 feet more than the rise of a spring tide, the difference between the two succeeding tides being 9 feet 3 inches. At Ipswich the increase in the tide was 6 feet 6 inches. At Dover the afternoon tide of the 29th was increased 6 feet 1 inch, the difference between this and the succeeding tide being 8 feet. In the Thames at Gravesend the tide rose to 3 feet 4 inches above Trinity High Water Mark, or within 5 inches of the highest previously recorded tide. The difference between the two tides here was 7 feet 5 inches. At the Victoria and Albert Dock the increase was 4 feet 5 inches, the difference in height of the two tides being 7 feet 4 inches. At Blackfriars Bridge the tide rose 4 feet 9 inches above Trinity High Water Mark, and at Hammersmith 4 feet 6 inches. At Eichmond the tide flowed over the towing path and the Twickenham Embankment. In February, 1903, owing to a heavy gale from S.W., with force of 9, the tide at Boston was 5 feet 1 inch below the normal height ; and in October, 1904, with strong wind from W.N.W., the force 7, the tide was increased 4 feet 3 inches, the difference in two succeeding tides being 6 feet 9 inches. WIND, BAROMETER, AND TIDES. 85 In December, 1904, owing to a heavy gale from the N.W. with force of 9, during neap tides, the tide continued to flow at ' Boston for 3 hours after the proper time, the excess over the tide-table height being 3 feet 9 inches ; the following tide being 5 feet 7 inches in excess. At Grimsby the morning tide was raised 6 feet 10 inches^ the difference between that and the succeeding tide being 6 feet. At Hull the tide was raised 5 feet. In the Thames the tide at Westminster Bridge rose 5 feet above the ordinary level. Barometer. — The sea may be regarded as a great barometer, the amount of pressure on the water being inversely as the rise or fall of the mercury. In an inland sea, bordered on all sides by land and having no outlet, a variation of pressure over the whole surface could not have any effect in raising or lowering the surface, as water is prac- tically incompressible. If the pressure were confined to the area of the water, and there was an outlet, the level would be depressed by its escape ; if the pressiire were unevenly distributed, being greater over one part than the other, the water would accordingly be depressed in one part and raised over the other ; in the same way that the level is altered by the pressure of a gale of wind blowing continuously in one direction. The pressure to which the surface of the sea is subject with the barometer standing at 30 inches is 14*70 lbs. on the square inch, equal to about 26|^ million of tons on a square mile. It is estimated that a difference of 1 inch in the barometric column or about half a pound of atmospheric pressure will cause over 1 foot difference in the elevation of the surface of the sea.^ As the atmospheric pressure frequently varies considerably over even such a limited area as that covered by the British Islands, it can readily be seen that the height of the tides may be affected to a certain extent by the variation in the pressure on the surface of the seas by which these islands are surrounded. In stormy weather, owing to the force of the wind varying with the alternate cyclones and anticyclones prevailing over different areas, the gradient of pressure in gales blowing over the British Islands varies as much as an inch over a distance of 300 ' " Kelation between Barometric Pressure and the Strength and Direction of Ocean Currents," by Lieut. H. Beebler, U.S. Navy. Chicago Meteorological Con- gress, 1893. 86 TIDES AND WAVES. or 400 miles, the result being that there may be a Tariation of pressure on the surface between the upper and lower end of the gradient of more than three-quarters of a million tons per square* mile. For example, in the gale of November, 1893, there was a difference in the barometer of 0*65 inch between Yarmouth and Aberdeen ; in the gale of November, 1895, of 0*94 inch between Scilly and Ardrossan. In the great anticyclone which occurred over the South of Europe in 1882, the level of the water of the Mediterranean at Antibes on North West coast was lowered 1 foot, owing to the exceptionally high pressure. It is also recorded that in the Gulf of St. Lawrence a difference of atmospheric pressure tends to produce a flow from the higher to the lower pressure, and the flow of water through the inlets of that gulf. In January, 1894, a drop of over an inch in the barometer in 24 hours over the area of the Gulf was accompanied by a rise in the tide at Quebec of 6 feet above the normal tide.^ In the Gulf of Mexico also, with a high barometer, and a lower pressure on the ocean outside, the speed of the Gulf Stream is appreciably affected. Investigations of the tides at Brest by M. Daussy led him to the conclusion that 1 inch variation in the height of the barometer resulted in a depression of 14 inches in the height of the tides. In the French Annuaires de Marees, a table is given of deductions to be made from the calculated height of the tides in each centimetre of rise in the mercury from SO'OO to 30"70 inches, the total allowance for the 0-70 inch rise being 10^ inches. No calculation is given for any other height of the barometer. The analysis of the tides at London and Liverpool by Sir J. W. Lubbock,^ caused him to come to the conclusion that at Liverpool, when the barometer fell 0"91 inch, the heieht of the WIND, BAROMETER, AND TIDES. 87 The investigation made by Sir J. C. Eoss at Port Leopold in the Arctic Sea in 1854, showed that a decrease in the pressure of 0'668 inch caused a rise of 9 inches in the water. Captain Greenwood, as the result deduced from observations made over a lengthened period, of the atmospheric gradients in the Irish Sea, from the south of St. George's Channel to Morecambe Bay, found that the mean gradient over this distance of 240 miles was 0-043 inch, and he prepared a table for use on that part of the coast from which the effect of the variation of the pressure as shown by the barometer on the level of the tides could be ascertained. A difSculty arises in attempting to obtain results solely from the reading of the barometer in excluding the element of wind. In the great majority of cases a low or high barometer is accom- panied by sufficient wind to affect the tides. For this reason the data given by Sir J. W. Lubbock are less valuable than they otherwise would be, as, although stated to be taken from the tides unaffected by wind, no force of wind being given, it is not known what was taken as the standard of a calm. From an analysis of two years' tides recorded at Boston Dock on the east coast, the author prepared the following table, all occasions on which the wind was blowing with a force of 3 being excluded, and all tides where the variation was six inches and upwards being taken. The first column gives the number of tides, the alteration in which may fairly be assumed as due to the pressure of the atmosphere. The second the average height above low water of the tides affected. The third column gives the variation from the calculated height; and the last, the variation of the barometer from the average. Number of tides. Average height of tide in feet. Variation in height of tide in inches. Variation in barometer from average in inches. 55 36 19-8i 20-53 12-71 below 110 above 0-36 above 0-42 below 45 16 22-45 20-36 11-0 above 12-0 below 0-36 above 0-38 below Mean 152 21-01 11-68 0-38 From an analysis by the author of the tide tables of five representative ports it was found that in calm weather, that is 88 . TIDES AND WAVES. with a wind force not exceeding 3 of the Beaufort scale, taking all tides raised or depressed six inches or more above the normal height, 56 per cent, of these tides were depressed when the barometer stood above the average, and 44 per cent, were influenced in the opposite direction. The results indicated that it is not possible to lay down any general law applying to all parts of tidal waters as to the effect of atmospheric pressure on the height of the tides. The effect can only be local. Taking the coasts of England, a study of the daily weather charts issued by the meteorological committee at once shows, that when any great disturbance takes place there is a steep gradient in the pressure as between one part of the coast and another, and that a high barometer in the north or east will be found to correspond with a low reading in the south or west. The effect, therefore, on the tidal wave on the north or east coasts is different to that on the others. To forecast what the variation of the range of tide for the day is going to be, it is therefore essential to know what the atmospheric gradient is, and this can only be ascertained by consulting the weather charts. These would not be available on board a vessel, or at most ports until the effect of the tide was over. Although, therefore, the variation of pressure may be a primary cause of the alteration in the height of the tides, both by its direct action in depressing the crest of the wave in one locality and raising it in another, and indirectly being the cause of the gale, the wind invariably setting from the region of high reading to that of the depression, yet the wind is a safer and more ready guide for the immediate purpose of navigation. OHAPTEE IX. EIVEE TIDES. The action that takes place in tidal rivers is a compound one, consisting of: (1) the ebb current, due to the water supplied from the area which the river drains, which moves in a downward direction; (2) the tidal wave, coming from the sea, which is propagated up the river with a velocity proportionate to the depth of water in the channel ; (3) the tidal current, which is attained when the tide has risen sufficiently in the lower part of the river to reverse the inclination, which moves in an upward direction. When the tidal wave of the sea arrives opposite the mouth of a river, the line of the wave under ordinary conditions revolves round the promontory which forms the opening of the river, and then assumes a direction at right angles to the direction of the tidal wave. As the parent passing wave rises, it throws off a branch which flows into and up the river. As the tide continues to rise at the mouth, the branch wave is propagated further and further up the river, the distance to which the wave action extends depending on the condition of the channel and the depth of the low-water stream. Propagation of River Tides. — The propagation of the tides up the channels of rivers, and the tidal wave rising to a higher level at the upper end than at the mouth, is due to the principle of the conservation of energy. When any quantity of matter is in motion its momentum is capable of carrying every particle of the mass to a height pro- portionate to the distance which it must have fallen to have acquired the velocity with which it is moving. This momentum is a compound of weight and velocity, and hence the value of a deep low-water channel, owing to a greater mass of water being set in motion. If the area into which the water is propagated only allows of a smaller quantity of water being poured into it, 90 TIDES AND WAVES. this decrease ia quantity is compensated by increase in height, that is to say, if the energy has a smaller quantity of matter to move, it can move it to a greater height ; and so the crest of a tidal wave up a converging estuary or river channel, in spite of the declining gradient which it has to overcome, is frequently higher than the crest of the wave from which it was originally propagated. As the tide from the passing ocean wave is propagated into a river, it encounters the ebb current which checks its downward movement. As the water in the channel gradually rises the down-flowing ebb-water is ponded back, and a " slack of the ebb " occurs ; then the direction of the gradient becomes reversed and the upward movement of the flood tide wave is established, and continues until the slack of high water is reached. The up-flowing salt water mixes with the down-flowing land water, the tidal wave being composed of an amalgamation of the fresh and salt water. Thus, although the tidal wave in a river is entirely due to the salt water sent into it from the sea, yet owing to the ponding back of the ebb current, the tidal wave at the upper end may consist entirely of fresh water. The original force imparted to a river tide is gradually absorbed by the effort required in propelling the water up the channel and in overcoming the friction of the water on the sides and bottom, and from eddies. At the first quarter of the flood, the action of the ebb having to be reversed, and the water in which the tide is propagated being shallower than later on, the velocity of propagation and of the entering tidal current is less than at half flood, when the tidal wave attains its maximum velocity. And so with the ebb : on the turn of the tide at the first quarter ebb, the direction of the water has again to be reversed, and the inclination is less than that which occurs later ; in the middle period, or half ebb, the water therefore moves with the greatest velocity. The rise and fall also at half flood and half ebb is nearly twice as much as during the first and last quarters. The ebb has an advantage over the flood, inasmuch as the flood has to create its own head. The flood tide, on the other hand, having arrived at the slack period at high water, the natural action of gravity of the ebb water which has been ponded back asserts itself, and the water flowing from a higher level then is instru- mental in carrying the ebb downwards. RIVER TIDES. 91 Owing to these conditions the duration of the flood in rivers is invariably less than that of the ebb. In large rivers, such as the Humber or the lower part of the Thames, the difference is not more than an hour, or as 5| hours flood to 6^ hours ebb. This difference increases as the distance from the mouth lengthens, and the frictional resistance to the progress of the tidal wave is increased, due to the shallowing of the water and the narrowing of the channel. In the middle reaches of a moderate-sized river the flood seldom exceeds 3 hours unless the channel has been deepened by dredging and training; and as the tide extends further up the river the duration of the tide may gradually decrease to a few minutes. Where the channel of a river has been improved and the low- water depth increased by the admission of a greater quantity of sea water, as in the Clyde, the duration of the flood and ebb is increased correspondingly. Thus at Glasgow the flood tide lasts 5 h. 40 m. and the ebb 6 h. 50 m. ; the periods at Port Grlasgow being for the flood 6 h. 17 m. and the ebb 6 h. 2 m. Double Flow. — It occasionally happens, when a heavy gale has been blowing over the adjacent sea, that the tide in a river having reached high water, and commenced to ebb for some time, again flows up the river to a greater height than before, and much above its calculated height. These are usually known as "blown tides." The following quaint account of a double flow of the tide in the Thames as it was observed at London Bridge in the middle of the seventeenth century is given in a pamphlet in the British Museum : — " Friday, February 4th, 1641, it was high water at one of the clock at noon — a time by reason so accommodated for all employ- ments of water, or land, very fit to afford witness of a strange and notorious accident. After it was full high water, and that it flowed its full time, as all almanacks set down, watermen, the unquestion- able prognosticators in that affair, with confidence maintain it stood a quiet, still, dead water a full hour and a half, without moving or returning in any way never so little ; yea, the water- men flung in sticks to the stream as near as they could guess, which lay in the water as upon the earth, without moving this way or that. Dishes, likewise, and wooden buckets, they set a swimming; but it proved a stilling, for move they would not any way, by force of stream or water, so that it seemed the water 92 TIDES AND WAVES. was indeed asleep or dead, or had changed or borrowed the stability of the earth. The watermen, not content with this evidence, would needs make the utmost of the matter, and with more creditable confidence, they took their boats and launched into the stream, or yery channel ; but the boats that lay hauled up on the shore moved as much, except when they moved their oars; nay — a thing worthy the admiration of all men — they rowed under the very arches, took up their oars and slept there, or, at least, lay an hour very near ; their boats not so much as moved through any way, either upward or downward, the water seeming as plain, quiet, even and stable as a pavement under the arch, where, if anywhere in the Thames, there must be moving by reason of the narrowness of the place. In this posture stood the water a whole hour and a half, or rather above, by the testimony of above five hundred watermen on either side of the Thames, whom not to believe in this case were stupidity, not discretion. At last when all men expected its ebb, being filled with amazement that it stood so long as hath been delivered, behold, a greater wonder — a new tide comes in ! A new tide with a witness. You might easily take notice of him ; so loud he roared that the noise was guessed to be about Greenwich when it was heard so not only clearly, but fearfully to the bridge ; and up he comes tumbling, roaring, and foaming in that furious manner that it was horror unto all that beheld it. And as it gave sufficient notice to the ear of its coming, so it left sufficient satisfaction to the eye that it was now come, having raised the water four foot higher than the first tide had done— four foot by rule, as by evident measure did appear, and presently ebbed in as hasty, confused, unaccustomed manner. See here reader ! a wonder that, all things considered, the oldest man never saw or heard the like." Low Water of Spring Tides and Neap Tides. — As a rule, low water of spring tides ebbs out lower than that of neap tides, the differ- ence being about the same as that to which the high water of spring tides exceeds that of neap tides. There are, however, rivers where this is not the case. Thus in the Severn, Admiral Beechey stated in his report on this river that " from Lidney downwards to the sea the low water of spring tides follows the general rule of being lower at such times than at neaps, but above Lidney the reverse takes place, the low water at springs being higher than at neaps. This no doubt is occasioned by the tide at springs throwing more water into RIVER TIDES. 93 the river than can escape before the return of the following tide."i In the Trent the ebb of neap tides near the junction with the Humber is 2 feet lower than that of springs. Captain Jarrad in his report ^ gives the same reason for this as that given by Captain Beechey. In some rivers, owing to the swing of the tide, the level of low water is lower at the upper part of the river than at the mouth. Thus on the G-ironde at Bordeaux, 59 miles from the mouth, low water of neap tides is about 3'60 feet lower than at the Point de Grave ; and in the Loire the level of low water of neap tides is lower at St. Nazaire than at the bar 5 miles lower down. At spring tides the low water level is the same at both places. Velocity of Propagation. — When the depth of water is sufficient, the propagation of the tidal wave in a river obeys the same law as in the open sea, its velocity being equal to that which a heavy body would acquire under the influence of gravity in falling from a height equal to half the depth of the water in which it is propagated, with this difference, that the velocity of the ebb current which it encounters has to be deducted from the foot of the wave ; and the mean depth of the ebb water has to be increased by half the rise of the tide in calculating the velocity of the head of the tide.^ The formula then becomes for the foot of the tidal wave and for the head V 15 X (^ + I where V = the velocity in statute miles per hour, d = the depth of low water in feet, V = the velocity of the ebb in miles per hour, h = the range of the tide in feet. In Appendix V. will be found several examples of tidal rivers ' Bemarhs on the Tidal Phenomena of the Biver Severn. J. W. Beeohey, 1849. ^ Beport on the Slate and Condition of the Lower Beaohes of the Trent, 1885. ' M. Patriot and other French writers on tides describe the two waves as those of " Basse Mer " and " Pleine Mer," or as " La T^te du Flot " and " Le Sommet du riot." English writers, on the other hand, have adopted the term for the wave of first of flood " foot of the wave," and for the high water wave the " head of the tide." 94 TIDES AND WAVES. where the Telocity of propagation has been calculated on this formula compared with the velocity obtained from observation. From this it will be seen that the rate of propagation of the foot of the tide varies from 22-66 to 4-87 miles per hour, the ebb current in these rivers running 3 to 5 miles an hour ; and of the head from 6-50 to 35'16 miles an hour. The mean rate of propaga- tion of the foot of the tide, as found from observation in seven rivers, is 14 miles an hour, and by the formula 13-71 ; and of the head, by observation, 19-74 miles an hour, and by the formula 19-03. The following table of the tides in the Seine shows the effect of deepening a channel on the propagation of the tidal wave. 1820. 1856. Locality. Depth in feet. Rate of propa- gation. Miles per hour. Depth in feet. Bate of propa- gation. Miles per hour. Hode to Quillebceuf . . . Quilleboeuf to Villequier . Villequier to Eouen . . . 5-90 1214 22-30 9-80 12-79 23-94 17-71 21-97 25-25 16-40 21-32 24-30 Average . . . 13-44: 15-15 21-64 20-67 Distance to which Tides are propagated. — The distance up which rivers are affected by the tides varies with their magni- tude. Thus, for example, in the Amazon, which is the largest tidal river in the world and has a width equal to many large estuaries, and a depth as great as many small seas, the tide occupies several days in ascending. It was calculated by Lalande that there are eight separate waves oscillating up and down this river at the same time. At Obydos, 500 miles from the mouth, there is a sensible rise and fall of the tide ; and the tide is even felt as far as Tapagos, 530 miles from the main stream and 900 miles from the sea. In the St. Lawrence the tides, which range from 3 to 4 feet in the Gulf, penetrate for 450 miles up the river, with a range of from 9 to 18 feet, the rate of propagation up to Quebec, 350 miles from the mouth, being 83 miles an hour. In the Orinoco, according to Humboldt, the tides, which only range 2 to 3 feet at the mouth, at equinoctial tides in April, when the fresh water is at the lowest, range a foot and a half at 180 miles up the river, and extend as far as Angostura, 255 miles from the mouth. RIVER TIDES. 95 In the Hooghly tlie tide is propagated for 181 miles from the mouth, the range at spring tides varying from 18 feet at the lower end to 3 feet at the end of the tide, the rate of propagation of the foot of the tide for the first 40 miles being about 14-80 miles an hour, and of the head 2309 miles. In the Seine the tidal flow is stopped by a weir 96 miles above the mouth of the river at Havre. The mean depth over this distance is 17 feet, and the range at spring tides 12-60 feet ; the mean rate of propagation of the foot of the tide is 13-72 miles an hour, and of the head 17-30 miles. In the Gironde and G-aronne the tidal influence continues up the channel for a distance of 93 miles from the mouth of the river. The average depth at low water up to the end of the tide at Castets is 12-22 feet, the mean range at spring tides 13-24 feet, and the velocity of propagation of the foot of the tide 9-80 miles an hour, and of the head 17-31 miles. In the Thames the tidal effect is stopped by the weir at Teddington, 62| miles from the mouth of the river. The average depth between the Nore and London Bridge, 46 miles, is 18-33 feet, and the mean range of tide 14-33 feet. The mean rate of propagation of the foot of the tide is 18-40 miles an hour, and of the head 30-66 miles. On the Humber the tide extends up its two large tributaries, the Ouse and the Trent. In the Ouse the tide is stopped at Naburn Lock, 72 miles from the mouth of the Humber; the mean depth at low water up to Hull is 43 feet, the range of spring tides 20J feet, and the rate of propagation of the foot of the tide 22 miles an hour. Between Hull and Naburn the mean depth is 8^ feet, the range 13 feet, and the velocity of propaga- tion of the foot of the tide 12-83 miles an hour. In the Severn the tide is partially stopped by the weir at Gloucester, 48 miles from its mouth. The mean depth of the water over this distance is 12*40 feet, the range at spring tides 12-76, and the average rate of propagation of the foot of the tide 8-60 miles an hour, and of the head 14-27 miles. In the Clyde, which may be considered an artificial channel, the mean depth between Port Glasgow at the mouth and Glasgow, 17J miles, is 18-33 feet, and range of the tide 11 feet ; the mean rate of propagation of the foot of the tide is 10-53 miles an hour, and of the head 17-71 miles. Tides highest at the Upper End of Rivers. — In some rivers the 96 TIDES AND WAVES. flood tide is propelled to a greater height up the river than at the mouth. Thus, in the Thames the level of high water at London Bridge is nearly 4 feet higher than at the Nore. Above this to Teddington the surface at high water is practically level. In the Humber the surface of high water of spring tides is 2 feet higher at Hull than at Spurn. In the Clyde the level of high water is 2 feet 3 inches higher at Glasgow than at the mouth of the river at Port Glasgow. In the Seine the level of high water at Tancarville, 18 miles from the mouth, is 18 inches higher than at Havre. In the St. Lawrence the range at the mouth is 9 feet, and increases to 14 feet at Father Point, and 18 feet at Quebec. Tidal Currents. — A distinction has to be dra'mi between the propagation of the tidal wave up a river and the tidal current. While the rate of the tidal wave as shown above varies from 15 to 30 miles an hour, the rate of the tidal current runs from 1\ to 3 miles an hour, seldom exceeding 4 miles. The tidal wave in a river, as in the ocean, consists of a change of form in the water, with the addition of a damming back of the ebb current. In this wave there is not much horizontal move- ment or translation of the particles of the water, and no motion capable of carrying any floating substance, or matter in suspen- sion, up the river. The tidal current, on the other hand, consists in a transfer of the particles of the water a certain distance up the river on the flood and downwards on the ebb. The tidal current is therefore capable of carrying with it for a certain distance material in suspension. The flood current extends up a river as far as the tide extends. In some rivers the tidal current continues to run up the river after high water has been reached, and after the water has com- menced falling. Thus in the Humber the current continues to run up past Hull for 1 hour after high water ; and at Gains- borough for 1^ hour after, though with diminished velocity. The flood current generally commences to run up the sides of a river while the ebb is still running down in the centre. The sea water which enters a river on the rising tide, being of greater specific gravity than the fresh water of the ebb, the first of the flood pushes its way up the river in a wedge-shaped form under the descending fresh water, the flood making up the river at the bottom while the ebb is running down at the surface, until the salt and fresh water become diffused. RIVER TIDES. 97 In the measurements of the currents in Boston (U.S.A.) Harbom- it was found that the early flood tide set in with greater strength near the bottom, the tide turning from ebb to flood near the bottom from 10 to 20 minutes earlier than at the surface.^ This effect is also shown by the use of surface and submerged floats which, with the early flood tide, will be seen moving in opposite directions, the former continuing downwards with the fresh water of the ebb current, and the latter moving upwards with the bottom current of salt water. Also if two vessels are lying at anchor, the one of shallow, the other of deep, draught, the latter will begin to swing up with the incoming current before that having the shallow draught. Transport of Material. — The tidal current in a river runs from 5 to 5|- hours in the lower reach nearest the sea, the average velocity throughout the flood tide being from 2 to 4 miles an hour. The flood tide is, therefore, only capable of carrying upwards sea water, material in suspension, or a floating body, for a distance of 12 to 15 miles in one tide. On a high spring tide, as a greater quantity of water enters the river during the same period, the velocity and the distance of transport is correspond- ingly greater, while with a neap tide the distance is less. Professor Unwin, in a paper on the movement of tidal water,^ has shown that the rush of water up a tidal river as the channel fills, and the shrunken look at the end of the ebb, both convey the impression of a change so large that the possibility of a simple flux and reflux of the same water does not naturally occur to the observer; and it is only when the great length over which the tidal wave extends during the period of the tidal flow is realized that it becomes obvious that some other action must take place beyond the mere flow of the water from the sea. As a means of arriving at the displacement involved in the phenomena of a tidal river, he takes the Thames as an example, in which the tidal action extends to Teddington Lock, 64 miles from the sea. He divides the river into reaches, and gives a diagram showing the sectional area of each reach, which increases from 10,000 feet at Teddington to 400,000 at Sheerness. He assumes that the ' " Report of the Committee appointed to consider the advisability of constructing a dam across the Charles Biver." Boston, Mass. 1903. ' "The Movement of the Water in a Tidal River," by W. Cawthorne Unwin. E. and F. N. Spon. London. 1883. H 98 TIDES AND WAVES. direct effect of the upland water is to displace a quantity of water below it by a distance which in each reach is equal to the length of the channel it would occupy. The mean volume of upland water during.one tide he takes at 2000 cubic feet a second, or 90 million cubic feet each tide, and the diagram shows that this would occupy 30,000 cubic feet at Putney, 50 miles from Sheemess ; 15,000 at London Bridge, 40 miles distant ; 7500 at Greenwich, 20 miles, and only 450 feet at Sheemess. The relative value of the upland water thus rapidly diminishes as the sectional area of the channel increases and the sea is approached. The mean horizontal displacement per tide in the lower part of the river below Woolwich he calculates by this method at 1200 feet per tide, and as the distance to sea is about 30 miles, it would take, if the travel seaward were due to upland water alone, about 130 tides, or say 65 days for a particle of water, or matter in suspension, passing Woolwich to reach the sea. This rate would, of course, vary with the flood, or dry weather, flow. He points out that the primary and main effect of the tidal water entering the river at Sheerness is to drive back the water which at the end of the ebb occupies the river channel. By means of another diagram it is shown that the water on the flood tide is driven back for a distance of 10| miles at spring tides, and very much less at neap tides, and, apart from any mixing action, no sea water that enters at Sheerness could reach a higher point in the river ; the horizontal oscillation through each reach varying from 10^ to 5 miles. The general conclusion being that the tidal action alone does not directly effect any change in the material water in the river, which merely undergoes a reciprocating oscillation over a limited reach. Thus the water in the river at low water is driven back a certain distance, and then travels back the same distance plus the displacement due to the upland water ; and so the particle of upland water and matter in suspension gradually works seaward. Eepeated experiments with submerged floats in the Thames, the Clyde, the Seine, and other rivers demonstrate the fact that these progress a certain distance up the river on the flood, then descend again on the ebb to some place lower than the starting point, due to the ebb lasting longer than the flood, and to the reinforcement of the influence of the tidal ebb water by that of the down-flowing fresh water. Experiments with floats have been made in the Thames on RIVER TIDES. 99 several different occasions in connection with the discharge of the sewage of the metropolis. Floats 6 feet long put in at Barking 31 miles from the sea, under the direction of Mr. Phillips, in 1852, and started after high water, after being carried about 10 miles down the river on the ebb, returned on the flood to a point either above or below the starting-place, depending on the condition of the tide or the proportion of land water coming down on the ebb; the permanent downward progress after oscillation up and down during one set of spring and neap tides was 5 miles in 1.5 days, or a third of a mile a day. Sir Joseph Bazalgette subsequently gave as the result of his investigations the length of the tidal oscillation as 12 miles, and that approximately any substance in suspension works up the river a mile a day at each high water as the spring tides strengthen, and down the river 2 miles a day as they fall off. In 1882, seven distinct sets of observations were made under the direction of Mr. Baldwin Latham with floats 12 feet long, put into the river at Barking. These were kept under observa- tion for periods of 30 to 45 days, giving a complete range over springs and neaps. The maximum range at spring tides was 18 miles on a tide, and the minimum at neap tides 7 miles ; the mean of the whole being 12J miles. The average progression downwards was one-third of a mile a day. The duration of the ebb current in the Thames at the lower part of the river was 7 hours, and of the flood h\ hours. The quantity of land water passing over Teddington Weir when these experiments were made was rather under the ordinary summer flow.^ These floats only acted over a limited reach at the lower part of the river. Mr. Baldwin Latham calculated that with an ordinary dis- charge over Teddington Weir of 1390 cubic feet a second it would take 42 days to reach the mouth of the river, a distance of 63| miles, whereas if the quantity of fresh water were increased sixfold by a land flood to about 8000 cubic feet a second the rate of travel would be 14 days over the same distance, thus showing the effect of land water in the upper reach of a river in transporting material to sea. On the Clyde experiments made by Mr. James Deas in June, 1881, when only the ordinary amount of fresh water was running down the river, showed that floats put in at G-lasgow Bridge ' Report Boyal Commission on Metropolitan Sewage Discharge, 1882, and Minutes of Evidence. Byre and Spottiswoode. 1884. 100 TIDES AND WAVES. reached 23-5 miles down the river in ten tides, or at the rate of 2'35 miles a tide. The rate of progress is much greater in the upper part of a river, where the land water has most influence, than at the lower end, where the sea water predominates. M. Belleville, in his treatise on the Seine,^ gives a diagram of the downward course of a particle of water over the whole length of the tidal Seine, which shows that a particle leaving Rouen at high water would not reach Havre, a distance of 112 miles, in less than %\ days, or at the rate of about 18 miles a day. Observations made by the author on separate occasions in the tidal river Witham, with wooden floats, showed that the rate of travel of a submerged float on the flood tide was 1*99 mile an hour, and on the ebb 1*12 mile. The results obtained in this case were due entirely to the action of tidal water. The river Witham is canalized above Boston, the water being held up by a lock and sluices placed across it, 1^ mile above the entrance to the dock, where the flow of the tide is stopped. During the time the observations were being made no fresh water was passing downwards through these sluices. The depth of water at low water was about 3 feet at the upper end, increasing to 10 feet at the lower end ; the rise of tide being 18 feet at the upper end and 22 at the lower. The float, which was 6 feet long and 12 inches square, and weighted so that there was only 6 inches above the surface, left the entrance to Boston Dock half an hour after high water and reached Clayhole in the estuary, 2 miles below the mouth of the river, a distance of 6'66 miles, in 6 hours 21 minutes. It then remained stationary an hour and returned to the dock in 3^ hours, arriving there one hour before high water. Subsequent observation confirmed this rate of travel. As regards the distance that material brought into the river by the flood tide will travel up it, this depends on the condition of the ebb current. Sand or material not put in suspension but driven along the bed of the river by the flood current will be rolled back by the ebb, which will have the advantage that it lasts longer than the flood and is greater in volume, and is moving on a down instead of an up gradient. Finer particles of matter which are carried in suspension become diffused throughout the combined salt and fresh water. The ' " Regime Hydraulique de la Seine Maritime." RIVER TIDES. loi water in the section nearest the sea all passes out of the river on the ebb and carries with it any matter in suspension. In the next section, where the greater bulk of the water consists of ebb water ponded back, a partial displacement only takes place ; and in the upper part, where no sea water reaches, and the transport of matter in suspension is not affected by tidal influence, there is a gradual descent of solid matter seawards. In all rivers there is a certain quantity of solid matter, either washed off the land with the rainfall or eroded from the banks of the river and its tributaries, which is carried down in sus- pension, which travels downwards at the same rate as the ebb current until it meets with tidal oscillation, and then its progress is increasingly retarded the further it travels downwards. There are, however, rivers where the matter brought down in suspension remains within a certain zone lying between the points where the influence of the tidal and fresh water respectively have the greater influence, oscillating backwards and forwards when the freshets are weak, and moving seaward when they increase in quantity and velocity. Instances of this are to be found in the Trent and Ouse, where advantage is taken of this circum- stance to utilize the water for warping the low land on their margin during the summer months ; ^ and in the Parrett, where the matter in suspension over a length of about 8 or 9 miles when deposited is used for making Bath bricks.^ Where the flow of the tidal water is stopped in a river by a weir or sluice, the back action of the freshets being reduced, and in some instances entirely suspended in dry seasons, solid material driven up along the bottom by the flood tide remains at the head of the tidal run and accumulates until the winter freshets become sufficiently powerful to carry it seaward. Instances of this are to be found in the Witham, where the tides are stopped by the Grand Sluice, and in the Yorkshire Ouse at Naburn Lock. In both these rivers deposits of from 5 to 10 feet have taken place in dry seasons.^ Salinity of River Water. — Ploats, although they give some indication as to the distance solid matter, either sent into a river ' " Tidal Rivers," chapter vi., " On tlie Physical Condition of Rivera." Longmans. 1893. == Report on River Parrett. Wheeler. 1896. = " Tidal Rivers," chapter iv., " On the Transporting Power of Water." Wheeler on the River Witham. Min. Froc. Instit. C. K, vol. 28, 1868. I02 TIDES AND WAVES. from sewage discharge, or brought down by the land water, will travel, yet fail to show the movement of the finer particles of solid matter in suspension, or of matter in solution, such as salt. These undergo a mixing process, and become diffused over greater lengths than floats are carried. There is no actual line of demarcation between the sea and land water, but under all conditions the quantity of salt in the water diminishes as the river is ascended. The cause of the mixing action by which the salt water becomes diffused over a greater length than floats indicate, is due to the way in which the water moves. Owing to the friction of the sides and bottom of the channel, the particles of water are constantly being projected from the sides and from the bottom to the surface ; the sea water, owing to its greater specific gravity, on entering the channel first works its way upwards underneath the ebb water and causes a constant mixing process ; any changes in the direction of the axis of the channel or of its area lead also to changes in the velocity and to eddies. There is, consequently, a mixing or diffusing action always going on between the salt and the fresh water owing to the oscillation of the tides, and salt may, therefore, be traced at a greater distance up a river than floats indicate. The propagation of the tidal wave up the river does not, therefore, result in a filling up of the space that exists between high and low water with sea water, although this area may be the measure of the quantity poured in from the sea, but a combined action of lifting up the ebb water and filling up these areas, resulting in the mixing and diffusion of the two waters. Pure river water above tidal influence has a specific gravity of I'O, and contains 3'16 grains of salt in a cubic foot. Sea water has a specific gravity of 1'026, and contains from 6230 to 6853 grains in a cubic foot, or nearly one pound of salt. The presence of salt in water may be ascertained by adding to a sample a small quantity of nitrate of silver, which has no effect in colouring water in which salt is absent, but where salt is present turns the water milky white ; and if a solution of bichromate of potash be added, the fresh water turns maroon colour and the salt water orange, the depth of the tint increasing with the quantity of salt. The quantity of salt may be ascer- tained by evaporating the water. RIVER TIDES. 103 The normal amount of salt in the water being ascertained in the sea at the mouth of the river, and that in the river above the influence of the tides, the quantity found in any part of the river between these points determines how far the salt water has pene- trated up the river under the influence of tidal action. In the Humber, where the tide has a run of 1\\ miles to Naburn Lock, the proportion of salt in the water declines from 2445 grains in a cubic foot at the mouth of the river, to 1220 grains at Hull, 22 miles up, and to 264^ grains at Whitton, 35 miles from the mouth. Between this place and Goole, or about 5 miles further, the water is generally fresh.^ In the small river Bure in Norfolk, which discharges into the North Sea at Yarmouth, and where there is only a rise of 6 feet at spring tides, the salt water penetrates 15 miles up the river, and with very high tides to 19 miles. This mixing action can be definitely traced where large volumes of crude sewage are poured into a river, as was at one time the case in the Thames. Instead of this sewage being all carried out to sea with the ebb current, a part of it remained in the river and was driven upwards with the flood tide, the pro- portion gradually accumulating as the quantity of land water coming down decreased, and becoming weaker when land floods prevailed. It was estimated that sewage discharged at Barking, 31 miles from the sea, took about 30 days in dry weather before it finally reached the sea. The results of a very elaborate series of experiments were produced before the Royal Commission on Thames Sewage in 1882, showing the amount of chlorine existing in the different reaches in the Thames. The chlorine included small quantities of other matter in solution, besides salt (chlorate of sodium). The tables given in this Eeport ^ showed that with the land water passing over Teddington Weir in September, 1882, being 25 per cent, below the normal summer discharge, and with a land flood when the quantity of fresh water was 4J times above the normal discharge, the quantity of chlorine was as follows at high water in grains per cubic foot : — 1 " Eeport on the Eiver Humber," by G. N. Abernethy and W. H. Wheeler. 1905. '^ " Keport of Eoyal Commission on Metropolitan Sewage Discharge." 1882. 104 TIDES AND WAVES. Dry weather. River in flood. Graius in Per cent, of Grains in Per cent, of cubic foot. sea water. cubic foot. Bea water. lu the estuary .... 8550 100 8550 100 Southend 8458 98-5 7818 911 Gravesend 160 6578 76-5 — — Erith 26-8 4516 52-6 1375 17-7 Deptford 394 1909 22-2 88 0-8 St. Paul's pier .... 43-4 920 10-7 12 Chiswiok 530 20 0-2 8 Teddington 62-5 H 8 The ayerage duration of the flood tide over the lower part of the river was 5^ hours, and ebb 7 hours. At Teddington, 2 hours flood and 10 hours ebb. The mean velocity of the flood was 2*25 miles an hour, and of the ebb 1'80 mile. The range of the spring tide was 14-36 feet at Southend and 3"70 feet at Ted- dington. Samples of water taken in the river Seine at difierent places in March, 1855, showed that at a little above Quilleboeuf, 22 miles from the sea, at the time of low water hardly a trace of sea water could be found ; samples taken a little after high water at Mailleraye, 38 miles from Havre, did not show a trace of sea water. M. Belleville subsequently, dealing with the same river, gives some graphic tables showing the amount of salt at different parts and at different distances below the surface, which show as the result of his observations that the proportion of salt decreased rapidly as the distance from the sea increased. He found that at spring tides the sea water did not extend beyond Villequier, 21 '72 miles above Havre ; at neap tides it only reached Quille- boeuf, 20^ miles at high water. At low water no sea water was found above La Eisle, 12 miles from the sea. He further shows by diagrams the relative proportion of salt and fresh water in the Seine at high water, which varies with the range of the tides and with the quantity of fresh water coming down. Taking an average of 706 tides, the proportion of sea water carried into the river on the flood tide was 75 per cent, of the area lying between high and low water ; and the volume of sea water carried into the river on the flood tide was about three times the fresh- water discharge of the Seine. In the following table constructed from these diagrams the RIVER TIDES. 105 quantity of chlorine in solution in the Seine is given for both spring and neap tides with the equivalent English measures ^ : — Distance from the sea. Miles. Maximum quantity of chlorine. Locality. Grammes per litre. Grains per cubic foot. Spring tides. 1 Kcap tides. Spring tides. Neap tides. English Channel . . Opposite Havre Honfleur Riale ... Quillebceuf . Vienx Port . 5-50 12-0 21-72 26-72 18-20 — 18-0 1 18 17-0 j 8 13J ! 3J 60 7951 7864 7427 5898 2621 7864 3495 1529 In the Scheldt, which has a tidal run of 110 miles and a range of 15 feet at Antwerp, the salt, as a rule, does not penetrate beyond Antwerp, 47 miles from the mouth. At the junction of the Eupel, 12 miles further, the water remains fresh always. The specific gravity of the water at high water at the mouth is 1-025 ; at Flushing, 1-020 ; at Terneuzen, 13 miles up, 1-018 ; at Bath, 32 miles, 1-014 ; at Antwerp, 1-002. M. Comoy considers that in a tidal river the motion of a particle of salt water is compounded of that of the average rate of propagation of the tidal wave and the velocity of the flood current, and gives the following formula for ascertaining the distance any given particle of water will ascend a tidal river from the sea on the flood tide : — L = T where L = the distance travelled by the particle, T = the time between the first of flood and high water, V = the mean rate of propagation, v = the mean velocity of the flood current, the time being in seconds and the other dimensions in metres. The following examples are given of the distance travelled by a particle of salt water as by the above formula and the dis- tance from the sea that salt is found in the water, reduced to English measures in miles and hours, the limit of the salt water being at PauUiac on the Gironde, Migron on the Loire, and Caudebec on the Seine ^ : — ' " Regime Hydraulique de la Seine Maritime." M. Belleville. "- " Les Mare'ee." M. Comoy. Paris. 1881. 1889. io6 TIDES AND WAVES. Duration of tide. Hours. Velocity of propagation. Miles per hour. Velocity of current. Miles per hour. Distance by formula. Miles. Distance by observation. Miles. TheGironde . . The Loire . . . The Seine 6-lG 5-25 5-41 26-88 12-32 19-04 4-25 2-91 4-03 31-11 20-61 22-47 32-22 21-00 23-52 Applying this formula to the Thames, the salt water should not reach further up the river than 1942 miles, and in the Humber further than 21 miles. In both these rivers, however, the distance to which the sea water reaches exceeds these limits. CHAPTEK X. WIND WAVES. The action of the water when broken up into waves is difficult to realize. An observer standing on the sea margin and watching the waves receives the impression that the crest of the wave is rolling into the shore, and that it must bring every floating substance with which it comes in contact with it. If, however, a log of wood or any substance floats at sufficient distance from the point where the wave actually breaks, it will be seen that it makes no advance forward, but only rises and falls as the crest of the wave passes. So with a vessel lying at anchor in a sea much disturbed by waves. As the crest of the wave approaches the vessel it has all the appearance of either submerging it, or break- ing the moorings and carrying the ship in the direction in which the wave appears to be travelling, whereas the only result is a vertical rise of the vessel as the crest passes, and the reappearance of this some distance away as the vessel descends to the trough of the wave. In a wave of oscillation the moving forward or travel of the particles is thus more apparent than real. The crest and trough change places, and so the form moves, but the particles of water do not travel beyond the orbit of the wave, or from the crest to the trough. While the wave form moves forward, each of the particles of water remains behind. A particle of water, being at rest, starts, rises, is accelerated, is then slowly retarded, and finally stops still, describing a circular orbit during the transit of the wave. In the diagram (Fig. 11), EF represents the surface of the still water, AC the crests of the wave, and ac the troughs; the dotted lines show the altered position of the wave after an undulation. To effect this change of position, the water at A has sunk to a, and that at B risen to b. It will thus be seen that the io8 TIDES AND WAVES. advance of the form of the wave has been produced without any advance of the water, by the particles rising and falling in a vertical direction. Wave motion was described by Scott Kussell as the transference of motion without the transference of matter ; of form without the substance ; of force without the agent. This wave motion has frequently been illustrated by the action that takes place in a field of standing corn waving with the wind. Each gust, as it passes across the field, bends and crowds the stalks, causing a wave-like motion on the surface, while the lower part of the stalks retain their position in the ground. In this case the surface of the ground may be regarded as the undis- turbed sub-surface of the water which is unaffected by wind waves. It has also been compared to the action of a chain made fast at one end, the other end being held in the hand. If a jerk be Fig. 11. — Diagram of Wave Form. given to the chain, a wave-like motion runs along it, but neither the chain nor the individual links make any advance, but alternately rise and fall in their places. The propagation of waves occasions two distinct motions, the velocity of the propagation which measures the rapidity of the transmission of the undulatory movement, and the velocity of the horizontal displacement of the particles of water. Classification of Waves. — Waves may be divided into two main classes : Tidal waves and Wind waves. The first class may be subdivided as follows : — 1. The great primary tidal wave generated by the sun and moon in the Southern Ocean. 2. The tidal waves propagated from the primary wave into the oceans and seas that cover the earth. 3. Tidal shore waves. Wind waves are classified for the purpose of this chapter as follows :— WIND WAVES. 109 1. The deep waves of the ocean, where unlimited depth and space are provided for the making of the wave. 2. Waves found in the smaller seas, where the depth, and the fetch of the wind, is limited. These are shorter and steeper than deep sea waves. 3. Rollers and ground swells. 4. Shore and breaking waves, or waves of translation. Definition of Waves. — The following are the definitions of a wave : — The length of a wave is its measurement from crest to crest. This is generally expressed in feet. The height is the vertical measurement from the crest to the trough. This is generally given in feet. The word '' amplitude " is used by Scott Eussell and Airy to denote the length of a wave. By French engineers, and generally by English writers, this word denotes the height. The velocity is the rate at which the successive crests pass a fixed point, this being given either in feet per second, statute miles per hour, or in knots. The period is the time occupied by the crest traversing a distance equal to the length of the wave, expressed in seconds. Ocean waves are those formed in the Southern, Pacific, Indian, and Atlantic Oceans; sea waves, those found in enclosed seas with restricted areas and depths, such as those round the British Islands. Tidal Waves. — The great primary tidal wave generated by the sun and moon in the Southern Ocean varies from other tidal and wind waves in being an undulation without oscillation, always moving in one direction without any retrograde motion. The primary tidal waves are constant and unchangeable, obeying well-defined laws as to their height and period. Their proportions bear no comparison with those of wind waves. The length is magnificent as compared with wind waves, extending to over 500 miles, but their height is insignificant, being only about two feet, while their periods are to be measured by hours instead of seconds. The tidal waves derived from the parent wave, which are pro- pagated through all the tidal seas of the world, are true oscillations regularly moving in alternate directions at fixed periods. Tidal waves, although true waves consisting of a movement of form over a given length without a transference of the particles no TIDES AND WAVES. of water, Tary from wind waves, which only affect the sea for a short distance below the surface, whereas the tidal wave operates in moving the whole mass of the water from the surface to the bed of the sea. The rate at which these waves are propagated is affected by friction, the amount of which is governed by the depth of the water and the form of the coast line ; and their height varies as the progress of the wave is hastened or retarded by the increase or diminution of the area of the channel through which they oscillate. By a series of experiments on a small scale Scott Russell showed the correctness of the theory put forward by Lagrange, that the velocity of propagation of tidal waves is in proportion to the square root of half the depth of the water in which they are propagated, the formula for ascertaining this velocity being — V = s/g X d where V is equal to the velocity of the tidal wave in feet per second ; g the velocity which a body falling fully under the influence acquires in one second, namely, 32"16 feet ; and d the depth in feet of the water through which the wave is propagated. The principle as applied to water in a channel of regular section and depth on a small scale, where the depths are measured by inches, can hardly be expected to give the same results with accuracy when applied to the varying conditions of the tidal seas of the earth, where the depths extend to thousands of feet, and where the figures for use in the formula can only be approxima- tions based on averages ; nevertheless, the agreement between the figures as ascertained from charts and from those due to calcu- lations are very remarkable. In Appendix II. is given a comparison of the movement of the tidal wave in the great oceans of the earth, and in the seas round the British Islands, as compared with the velocity of propa- gation as obtained from the above formula. Tidal Shore Waves. — With regard to the third class of tidal waves, a fuller explanation is necessary, as previous to the descrip- tion of tidal shore waves by the author in his book on " The Sea Coast " these waves had not been recognized. These shore or littoral waves are of a different character, and to some extent are governed by different laws from the wind or WIND WAVES. Ill tidal waves of the open sea. They are small in size, but constant and ever present on every shore washed by the tides. When the tide is rising in the sea the water for some distance from the coast is flowing towards the shore, and when falling, 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 in the offing and near the shore, causing the water to advance with an oblique lateral movement towards the coast. It changes its character in the shoal water on the beach to a wave of transla- tion, ' and breaks where it meets the low-water line on the shelving shore. It is then reflected back, and a series of small oscillations or wavelets are set up. Even with an entire absence of wind or other disturbing cause, the rise and fall of the tide on the shore does not consist of a mere vertical swelling and depression of the water, but is accompanied by a series of wavelets, varying in height accord- ing to the condition of the tide and the form of the beach from 6 to 24 inches. These break on the shore at the rate of 10 to 20 in a minute. These wavelets are never absent from the shore, except when absorbed by larger waves due to gales. The height of these waves is greatest where the beach rises rapidly. Up to a certain point they are increased by a gentle wind blowing obliquely on shore. When, however, the wind force is great, the tidal wavelet becomes destroyed by the wind wave. As the wavelets break they become a vehicle for the trans- mission of mechanical force, and are capable of transporting material. It is by this agency that shingle is transported along the coast, and shingle beaches are formed. The energy contained in a wavelet only 1 foot in height is capable of lifting 2\ millions of average-sized pebbles 1 foot in height in a single tide, and allowing 15 wavelets in a minute, the energy developed by every tide over 1 foot of width of a shingle beach is equal to raising 266J tons 1 foot high.^ Although in storms shingle may be drifted in a different ■direction, the regular and continuous movement that is always ' "The Sea Coast," Destruction: Littoral Drift and Protection. W. H. Wheeler. Longmans and Co. London. 1902. 112 TIDES AND WAVES. going on is invariably in the same direction as the set of the flood tide. With the wind blowing in the same direction as the flood tide, the drift of the shingle is increased ; with a direct onshore gale shingle banks are pulled down by the back wash of the waves, and the shingle spread over the beach. In calms and winds off shore the shingle is drifted back up the beach by the action of the flood tide, and the banks built up. Although the shingle is always being rolled up and down the bank, the flood tide is the active agent in its drift along the shore, and the ebb is not capable of pulling down or carrying back all that the flood tide has lifted up. The height to which the shingle has been raised by the flood tide may always be seen by the ridge of pebbles left at the highest point reached by the wave. On sandy shores a line of detached pieces of seaweed and floating debris or " wrack " is always to be found, which has been drifted up by the flood tide and left stranded at high-water mark, and which the ebb has not again carried seaward. Where shingle is absent, and the beach consists of sand, the flood tide making along the shore erodes and stirs up the sand, which being thus placed in suspension, is drifted along by the tidal current and deposited during the slack of high water. Both shingle and sand, therefore, tend to travel in the same direction along the coast as the flood tide. The velocity of these waves is the same as that which a heavy body would acquire under the influence of gravity in falling from a height equal to that measured from the crest to the level of the water in repose or half the height of the wave, the for- mula for the velocity being V = 8^/^, where V = the velocity in feet per second, h = height of the wave in feet. For example, a wave 1 foot high would have a velocity of 560 feet a second ; wave 2 feet high, 8 a second. These tidal wavelets breaking on a beach are, therefore, much more powerful, and have much more effect in transporting material than tidal currents. These wavelets in calm weather vary from 10 to 12 in a minute ; their length from 15 to 20 feet, with average of 18 feet ; height from 6 inches to 2 feet, average 1'50 foot, or -^., of the length ; velocity, 489 feet a second ; period, 3. These tidal shore waves or wavelets occur in series, one of WIND WAVES. 113 the series assuming a maximum height, and the others declining until a minimum is reached, when they begin again to increase in size. Waves due to Wind : Ocean Waves. — These are such as are to be found in the great oceans of the earth, where there is un- limited space for their generation, and where the depth of water is so great that the disturbance produced by the wave extends to a comparatively short distance below the surface. Such waves may be the result of a gale blowing in one direc- tion for a long period ; or they may have been generated from diiferent sources, and meeting, may coalesce, or move indepen- dently of each other. If a wave proceeding from a certain direction comes in contact with another wave coming from a different direction, the first wave, instead of coalescing with the second, may continue its original course, each portion of one wave successively encounter- ing and passing through the other wave. The two may combine as they pass to form one billow of greater height, and then separating, each pursuing its own course. To this cause may be ascribed the fact, frequently noticed at sea, of an occasional wave, or one in a series, being higher than the others. Generally waves are composed of two or more series existing simultaneously. When two or more sets of waves, due to different actions, travelling in different directions, meet and pass through each other, they make a very confused and cross sea. This occurs during cyclones, when the wind is blowing in a circuit over the sea. The resultant action of wave motion under the influence of cyclones transmitted in all directions is to give a peculiar up- and-down motion, the sea rising and falling in large pyramids like a boiling cauldron. When this is the case " the sea is appalling in appearance and very dangerous." ^ The effect of winds blowing in cyclones is sometimes felt in the seas surrounding Great Britain, although in a very reduced form to that experienced in the tropics. In crossing the North Sea from Norway to the Humber on one occasion the author encountered one of these cyclonic disturbances. Soon after leaving the coast of Norway a gale was met blowing heavily from the south-east. As the vessel progressed, there was a lull, followed by the wind blowing from the opposite direction, or from ' " Handbook of Cyclonic Storms in the Bay of Bengal." J. Eliot. 1890. I 114 TIDES AND WAVES. the north-west, with a force of from 7 to 8. The result of the wind blowing from opposite directions was to make a short sea with waves only 50 to 60 feet long and from 5 to 6 feet high, but with sufScient effect to cause a 2000-ton steamer to roll at an angle of from 30 to 40 degrees. The disturbance of the sea by wav6s does not always depend on wind that has been blowing over that particular locality, but may be the result of winds which have been blowing at a long distance away, the effects of which have been transmitted during or after the gale. Even in a regular sea, for causes already explained, the waves are not all alike, and there may be considerable range in the length and height of successive waves ; and occasional waves of exceptional size, as compared with their neighbours, may occur, either as solitary waves or at intervals. Size of Waves. — There is considerable diversity of opinion as to the size of the great ocean waves. Some of the largest waves have been met with in the Southern Ocean. Scoresby recorded waves here extending to between a quarter and half a mile in length, with a period of 23 seconds ; and Eoss measured one 1920 feet long. The largest wave that has been recorded is one measured by Mottez, of the French Navy, in the North Atlantic, which had a length of 2750 feet from crest to crest, its period being 23 seconds. The Hydrographic Bureau at Washington, as the result of inquiries instituted as to the length and height of waves, found that the longest wave observed had a length of half a mile and a period of 23 seconds, and the extreme limit of height to be 48 feet. Scoresby recorded, as the result of his observations, Atlantic waves from 18 to 20 feet, with maximum of 28 feet. On one occasion during a " grand storm scene," when there was a mag- nificent example of wave action, he measured waves 43 feet high. Generally, it may be taken that during storms the length of the wave does not exceed 600 feet. If the wind continues blow- ing for some time in the same direction, this length may be increased to 1000 or 1500 feet. The ocean waves of rough weather in the Atlantic may be taken as having a length of 250 to 300 feet, or about half the length of a modern liner. Action of the Wind in making Waves. — Waves are the result WIND WAVES. 115 of the action of the wind on the sea. The wind, blowing with steady force for some time in the same direction obliquely on the surface of the water, causes a depression and consequent elevation. Owing to this impact of the wind and its frictional resistance, waves are formed. As these elevations and depressions increase in size, the wind, acting on the slope of the depression, becomes more effective, and the waves increase in size. A wind moving at a low velocity will cause the surface of the water to be covered with small waves, or " catspaws," two or three feet long and an inch or two high. As these wavelets unite the waves gradually increase in size, and continue to enlarge their dimensions and the depth to which they cause disturbance of the water, until large well-defined waves become formed. The wind is more effective in driving forward the particles of the water that are above the mean plane at the top of the undu- lation than at the bottom. This excess of force in the direction the wave is travelling tends to push the top of the wave over and to break the crest. This limits the height to which the water can be raised. When the wind first begins to form waVes, these are short and steep. With a continuance of the wind the length of the wave gradually increases. Lieutenant Paris, of the French Navy, gives an instance of this off the Cape of Good Hope, where, with a wind blowing continuously in one direction for 4 days, the height of the wave only increased from 20 to 23 feet, while the length had more than doubled, having increased from 370 to 770 feet. So long as the velocity of the wind relatively to that of the wave is capable of accelerating the motion of the particles of water, the size of the wave increases in length, height, and velocity, until a balance of forces is reached and the wind is no longer capable of producing further acceleration. As the gale drops the waves gradually decrease in magnitude and finally die out, friction absorbing the energy imparted by the wind. Formation of Waves. — In all water in motion the mass does not move solidly, but every individual particle is in motion. As the water moves the particles roll round one another in orbits varying in dimensions according to the depth and sectional area of the channel in which they are moving. This same law applies to wave motion. There are two motions operating in the formation of wind waves, one horizontal, or nearly so, due to the wind which ii6 TIDES AND WAVES. generates the undulation ; and the other vertical, due to the force of gravity. The weight of the particles of water heaped up by the wind tends to press forward those in front, but these are resisted by the water there. Under the action of these two opposite forces the particle is driven upward and forward, until the particle which has displaced it has made room for itself ; then it sinks, and finally comes to rest a little in advance of the place from which it started. These motions take place within a defined orbit, the height of which is measured from the trough to the crest, and the limit of which is regulated by the force of the wind which produces B 1 ____ . ^ * 1 \ \ */, F \ ^ ,, ^ ^^ H\ '6 'X"xr>^^>^?=^ !NV Sea Level ,_ / \ V. V v._v: y\u\ \^ i\ lE 1 i r ,upr K A^ )} b 1 V KyA2^y\yA J\>^ >\ave motion is once set up in the ocean it continues for a ' "The Prevalence of Gales on the Coast of the British Isles, 1871-1900." F. J. Brodie. Journal Eoyal Meteorological Society, 1902. WIND WAVES. 121 considerable time after the exciting cause has ceased, and until the energy imparted to the wave by the wind is absorbed by the effect of gravity, or the friction of the particles of water. This wave action may be extended over a wider space than that covered by the original cause of disturbance. Thus frequently there is a heavy ground swell on the coast without any corresponding local gale. As waves due to distant gales travel across the ocean shore- wards, they coalesce and form long low undulations. The effect of a ground swell extends to a greater depth than that of ordinary waves ; and they exert a greater power of trans- mission near the bottom than shorter waves in the same depth. When these waves have travelled beyond the limit of the wind that raised them, they lose the steepness of slope, and become low undulations scarcely noticed in deep water, but become again ap- parent on approaching shoal water. As these long waves approach the shallow water where the depth is constantly diminishing, and the space for their volume is contracted, the momentum contained in the moving water sensibly raises the height of the wave and increases the velocity. These waves, therefore, are more powerful and exert a great percussive effect on cliffs or sea walls, and the backwash is more destructive to a beach than ordinary wind waves. Amongst the islands of the South Atlantic and Pacific Oceans rollers are frequent. They come with little notice, and do not last long. They generally prevail at the same time of the year. They break in from 6 to 7 fathoms as far as 3 miles from the shore. Sometimes without warning, and in the absence of any gale, a high swelling wave is suddenly developed rolling towards the land like a ridge of water. Out at sea these rollers are long and flat, and hardly noticeable, but on entering the shallow water the crest gets steeper, until it forms a wall of water which combs over and falls on the shore with a loud roar. These are generally the remains of a spent storm which has been previously blowing over the ocean, a long distance from the shore. Ground swells having a height of 5 to 10 feet, that fall upon a flat sandy beach, break at some distance from the shore and form surf waves. Where the beach is very flat they may break as much as a mile seaward ; the water then gathers again to form lesser breakers, making a wide belt of tumbling water. Frequently the wave motion travels at a greater rate than that 122 TIDES AND WAVES. of the movement of the wind that causes the disturbance, in which case a ground swell precedes and becomes the harbinger of a coming gale. This part of the subject will be found dealt with in the Article on Storm Warnings (Chapter XIV.). Breaking Waves. — While the waves of the ocean have a special interest for mariners, waves breaking on the coast take the atten- tion of engineers, and those engaged in the protection of the coast, or in the construction of sea walls, breakwaters, and harbours. To design and carry out works which have to contend with the waves of the sea, it is essential that their characteristics should be fully inquired into and known. The wave assumes its most dangerous and destructive action when it breaks in shoal water. Where the water has considerable depth, waves will harmlessly rise and fall against a vertical sea wall, when the same sea will break with violence on a sloping mound having shoaler water in front of it. Waves break when, owing to the water becoming shallow, they are no longer able to complete their undulation ; and the water of the wave is thrown forward on to the beach with a violence pro- portionate to the momentum it has acquired (Fig. 13, p. 117). The depth of water in which a wave ceases to be an undulation and breaks varies with circumstances. The least depth in which a wave can complete its undulation is when it reaches water the depth of which in repose is only equal to half the height of the wave from trough to crest. The general result of observation of coast waves shows that, as a rule, and under ordinary conditions, a wave breaks when it enters water the depth of which is equal to, or little exceeds, its height, from trough to crest. On flat sandy beaches waves break at a great distance from the shore, a succession of smaller waves being formed, decreasing in height from less and less to nothing until low water is reached, the space between the deep water and the shore becoming a mass of broken water. Waves are known to break in heavy gales, and where the fetch is very extended, in depths considerably greater than their height. Mr. Shield records that he has measured unbroken waves at Algoa Bay 21 feet in height from trough to crest in water 23 feet deep, the bed of the sea shoaling to where the observation was made at the rate of 4 feet a mile.^ ' " Principles and Practice of Harbour Construction." W. Sliield. London. 1895. WIND WAVES. 123 At Peterhead he observed waves 26 feet in height which crested and broke in 5^ fathoms. The laws relating to waves breaking on shore are different to those which apply to the deep water of the ocean. As a wave moves over a shoaling shore it changes its character. It grows gradually shorter in length and steeper. 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 the 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. 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. The particles of the water below the rear wave have, however, 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. Colonel Emy, in his treatise on waves,^ considered that the destructive effect of the sea on maritime works is considerably increased by the action of what he termed " Flot de Fond." He assumed that as waves approach the shore and begin to feel the effect of shoaling, the undulatory movement of the lower particles of the water is changed into a horizontal one, independent of the undulatory movement of the upper part of the wave ; and where the bed of the sea rises abruptly, this horizontal or translatory movement accumulates with each successive wave, the wave itself being thus raised above the level which it would otherwise obtain. By this means the depth and volume of the water that finally breaks on the shore, or on a sea wall, is increased, and consequently the force and destructive effect with which the water strikes. 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 the obstruction attains an increased height. ' " Du Mouvement des Ondca et des Travaux Hydrauliques Maritime. " Paris. 1831. 124 TIDES AND WAVES. 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. Ground-swell waves which are of great length, although of small height, break in depths that are great in comparison with their height where the sea bed is abrupt or where there is sudden shoaling. Waves that break on shore and that have to be considered in harbour construction and coast defence are governed to a certain extent by the amount of exposure to which the coast is subject, or the " Fetch." Mr. Stevenson, after a series of observations in 1850, calculated that the height of the wave in feet in gales under such conditions was equal to one and a half times the square root of the length of the fetch in nautical miles, H = 1'5^L, where L is equal to the length of the fetch in nautical miles.^ This he showed to be correct by giving the result of an analysis of 23 waves breaking on the shore of the North Sea in Scotland, of which the fetch varied from 1 to 165 miles ; and the observed height of the waves 6-97 feet, as against 6"30 obtained by the formula. For waves of this character having a height of 4 to 5 feet the velocity of motion varies as the depth of water in repose, and is the same as a heavy body would acquire when falling freely from a height equal to that measured from the centre of gravity of the wave to its lowest part, or a height equal to that from the crest to the level of water when in repose. Approximately V = 8 \J ^ when h is the total height of the wave from trough to crest, and V the velocity in feet per second. It is a subject of common observation to those who have to do with the sea and its beach, that waves break on a beach in series, and that each series has one wave larger than the others. On some beaches the fishermen returning from their fishing realize this fact when they wait for this larger wave to carry their boats up on to the beach. On some coasts one wave in every four is held to prevail, but the general experience is that each tenth wave is higher and longer than the others. Impact and Force of Waves. — When a wave is checked by ' "The Design and Construction of Harbours." T. Stevenson. Edinburgh. 1874. WIND WAVES. 125 coming in contact with a cliff or sea wall, it expends a considerable amount of force on the opposing object. Experiments made by the late Mr. Thomas Stevenson with a marine dynamometer,^ constructed for the purpose of ascertaining the force of the impact of waves on harbour walls and exposed piers, ascertained that the maximum force excited by an Atlantic wave, as recorded by this instrument, was 3 tons per square foot ; and at the Bell Eock in the North Sea, with a wave 20 feet high, 1'33 tons ; at Buckie, 3 tons ; and Dunbar, 3^ tons. Mr. Erank Latham has recorded, as the result of observations made with a dynamometer on a sea wall at Penzance, that with the wind blowing with a force of 15 to 18 lbs. on the square foot, and with a depth of 10 feet of water, the pressure on the wall due to the waves striking at right angles was from 0"90 to 1 ton per square foot, the spray rising above the wall, which was nearly vertical, to a height of 25 to 30 feet. It was estimated by the French engineers that the force of the waves on the breakwater at Cherbourg was 2 "67 to 3"50 tons per square foot. 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 of waves. If the wave be treated as a solid body moving with a certain velocity, the kinetic energy exerted would be the product of the weight by the height from which it descended. The mean height from which the water of a wave may be taken as falling is half that of the height from trough to crest. Taking a wave 10 feet high, and the depth of water where it breaks when 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 weight of the water in movement for 1 foot of width would be — 30 X 1 X 5 X 64 ^ ^.27 ^ j,g fQQ^, 2240 ^ ^ The kinetic energy would be the product of 4-27 tons falling from a height of 5 feet — 4*27 X 5 = 21 '35 tons per foot super The force of the impact of the blow on the wall would be reduced in proportion to the angle at which the wave struck the face. Where waves strike a cliff or sea wall the water is deflected • " Design and Construction of Harbours." 126 TIDES AND WAVES. upwards, and in falling exerts a vertical force on the surface of the beach at the foot of the wall, which tends to disintegrate the beach and expose the foundations. Approximately, and under ordinary conditions, breaking waves are reflected from a vertical face upwards to a height equal to the height of the wave from trough to crest, but with long ground swells in exposed positions this limit is very largely exceeded. Mr. Stevenson has given an instance at the Bell Rock Light- house where the water was thrown upwards 106 feet, and instances have occurred at the Skerries, where the water and spray have been projected 60 feet upwards, carrying with it pieces of stone on to the lighthouse roof, 240 yards from the face of the rock, one of these going through the roof, which was 50 feet above the sea. At the breakwater at Alderney the water from the waves breaking on it was reported as being thrown upwards to a height of 200 feet. At Peterhead, where the sea exposure is great, having a fetch of 300 miles, waves of 30 feet in height and from 500 to 600 feet in length have been recorded, and the water has struck the breakwater with such force as to be thrown upwards 120 feet, blocks of concrete weighing 40 tons having been displaced at levels of 17 to 36 feet below low water. At Tynemouth during a storm in 1901, the waves striking the breakwater were projected upwards from 90 to 100 feet. The depth of the water outside the breakwater just clear of the rubble mound was 30 feet at low-water spring tide. The fetch in a north-easterly direction is 350 miles. According to Stevenson's formula this would give a wave of 18 "70 feet in height. Even where the exposure is not great and the water shallow, the water in gales is thrown to great heights. Thus at Hastings, where the beach at the foot of the wall is dry at low water, and the size of the waves is only that due to the rise of tide of 15 feet, during a heavy gale in 1898, the broken water was thrown on the top of a large hotel, and shingle was lifted off the beach and carried across the promenade into the bedrooms fronting the sea. An illustration of this wave is given in the author's book on the sea coast.^ 1 " The Sea Coast : Destruction, Littoral Drift and Protection." Longmans, Green, and Co. London. 1902. WIND WAVES. 127 During the construction of Plymoutli breakwater in a heavy gale, blocks of stone weighing from 7 to 9 tons were removed from the sea slope at the level of low water and carried over the top, a distance of 138 feet, and deposited on the inside ; the fetch here, in a north-westerly direction, to the coast of France is about 120 miles, but the breakwater lies open to the Atlantic. At Cherbourg breakwater, upwards of 200 blocks of concrete, weighing 4 tons, were lifted by the waves in a north-easterly gale, and taken over the top of the mound and deposited inside. Blocks of 12 tons were moved from their place and turned upside down. The fetch here to the north-west is not more than 60 or 70 miles. At Wick during one storm, two stones, weighing 8 and 10 tons each, were thrown over the parapet of the breakwater, the top of which was 21 feet above high water. Blocks of concrete, weighing respectively 1350 and 2500 tons, were displaced. But in this case there is some doubt as to whether the movement was entirely due to wave action. The fetch in a north-easterly direction is about 300 miles. At the Bishop Eock lighthouse, off the Scilly Isles, an iron column weighing over 3 tons was thrown up 20 feet in a storm by the waves and landed on the top of a rock. This lighthouse is exposed to the full force of the Atlantic waves. At Ymuiden breakwater, on the coast of Holland, one of the blocks of concrete weighing 20 tons, placed on the outside of the harbour walls to act as wave-breakers, was lifted by a wave to a height of 12 feet vertically and landed on the top of the pier, which was 5 feet above high water. The fetch in a north-westerly direction is about 350 miles. At the harbour works at Bilbao, in a storm in 1894, a solid block of the breakwater weighing 1700 tons was overturned from its place and dropped into the water. During the construction of the harbour works at Genoa, it was stated that during a storm in 1898, waves 29| feet high broke on the jetty, causing the water to be thrown 98J feet high. Part of the wall under construction was displaced, weighing 800 tons. The effect of the waves did not damage the work below 19^ feet. Sir John Coode, in his paper on the Chesil Bank, records that during a gale in 1824, a sloop of 100 tons burden, laden with 128 TIDES AND WAVES. guns, ran directly under canvas on to the bank on the top of a sea, and was landed on the top 30 feet abore high-water spring tide, whence she was subsequently launched into Portland roads. Numerous other instances of a similar character could be quoted, but the above are sufficient to show the enormous force exerted by breaking waves. CHAPTEE XL SEISMIC AND CYCLONIC STORM WAVES.^ At occasional intervals records are furnished of abnormal waves breaking on the coast and causing an enormous amount of damage, and of immense solitary waves being met with in the open sea. These waves are commonly but erroneously called " tidal waves." These so-called " tidal waves " are of three descriptions — 1. Where, owing to some great submarine seismical disturb- ance, one or more waves roll in an unbroken mass of water, in some cases from 70 feet to 80 feet in height, having a steep front to the coast, and there break, overwhelming and sweeping away every- thing in their course. Seaward the wave rapidly dies down, but the impulse is felt throughout the ocean for thousands of miles. These have been termed " seaquakes." 2. Where a huge solitary wave is met with at sea, often in otherwise perfectly calm water, which, sweeping over the unfortu- nate vessel by which it is met, causes both loss of life and damage to the ship ; and probably in some cases sending the vessel and all on board to the bottom of the sea. The last class (3) consists of enormous waves generated by cyclones, which, travelling with the centre of the storm towards the land, break on the coast with most disastrous results. With regard to the first class of waves, Professor Milne has shown that these submarine disturbances generally occur where the bed of the sea has a slope from the land less than 1 in 50. In Japan, where submarine disturbances have been most frequent and disastrous, the sea bed slopes from the shore at the rate of 1 in 25, and on the Peru coast slopes as sharp as 1 in 16 are found. Earthquake Waves. — The first great earthquake wave, of which ' A great part of the contents of this chapter appeared in an article by the author in the Engineer of April 7, 1903. K 13° TIDES AND WAVES. there is any record, occurred, according to tradition, in 1099, when an abnormal wave broke over the south-eastern coast of England, and over Scotland and Flanders, the result of which was, according to Boetius, that 4000 acres of low land, belonging to Earl Godwyn, and which was protected from the sea by a wall, were inundated by the water, and became the much-dreaded Goodwyn Sands. There is a record of a heavy rolling sea following on the shock of an earthquake which broke upon the coasts of the island of Jamaica in 1692. At Port Eoyal the frigate Swan lying close to the wharf was borne some distance inland by the wave. The most wide-spreading in its effect of any of the examples of the first class, or seaquakes, is that which occurred during the great Lisbon earthquake of 1755. The seismical disturbances to which this wave was due occurred under the sea off the coast of Portugal, in 30° N. lat. and 11° W. long. The coast is recorded to have suddenly sunk 600 feet, causing the water to be drawn out from the land to such an extent that the bed of the river Tagus was left dry, this being followed by a series of waves from 30 feet to 60 feet high, which broke on the shore and, sweeping over the land, caused the death of 100,000 persons and enormous destruc- tion of property. These waves extended along the coast, engulfing the villages for several miles to the south, and reaching as far as Morocco, where there was considerable inundation. The shock was felt at Oporto, Cadiz, Madrid, and Fimchal, and waves were propagated throughout the Atlantic to the coasts of this country and America. At Cadiz the wave rose 60 feet, and at Madeira 12 feet above its normal height, and the sea was so disturbed at 120 miles west of St. Vincent that vessels were violently shaken, and men standing on the deck were thrown down. The shock in the English Channel extended to Havi-e and Portsmouth — the water rising 8 feet on the coast of Cornwall. In the North Sea the dis- turbance was noticed at Amsterdam and Yarmouth ; it aifected the Humber ; and in the Trent there was a continued rise and fall of the water at short intervals — three tides being recorded as having occurred in twenty-four hours. A similar incident occurred after an earthquake on the same coast of a less serious character in 1815. The water in the Scotch lakes along the valley that extends through Scotland from south-west to north-east was agitated, and waves were propagated along the lakes in large furrows. The effect was felt in Morayshire in the form of a volcanic wave, which swept the coast and washed away a flock of sheep which were SEISMIC AND CYCLONIC STORM WAVES. 131 grazing far beyond tlie ordinary reacli of the waves. This dis- turbed effect extended to the fiords in Sweden and Finland and the lakes in North America. The rate at which the wave of dis- turbance travelled between Portugal and this country was about 900 miles an hour. The Lisbon earthquake of March 31, 1761, the focus of which was put in lat. 43° N., long. 11° W., was felt by a ship at sea 80 leagues off the coast, and by a vessel off Cape Finisterre, lat. 44° N., and at Madeira and the south of Ireland. The great earthquake at Lima on October 28, 1724, was marked by a withdrawal of the water from the coast, followed by a wave which is reported to have been 80 feet high, and which swept over Callao. Twenty-three ships in the harbour were sunk and four carried far inland, and the same phenomenon occurred after the earthquake of 1746. On the coast of Chili, in 1835, after the shock of earthquake was felt, the sea retired, and then returned in a series of three waves 20 feet high, the reflex action of which swept everything towards the sea. In 1854, after an earthquake that occurred on the coast of Japan, a wave was propagated across the Pacific, and the disturb- ance was recorded on the gauges at San Diego and San Francisco. Also, after an earthquake on the coast of Peru, in August, 1868, which was due to a submarine disturbance, large waves were gene- rated and the country was inundated several miles inland ; 25,000 lives were lost, and several towns destroyed. At Arica, one of the United States war vessels, the Wateree, was carried a quarter of a mile inland, from which position she was removed still further inland by a wave of inundation due to a submarine landslip in 1877. This disturbance was propagated throughout the Pacific, and was felt at Japan, 9000 miles distant, the time occupied for the propagation being only twenty-four hours. At Hakodate, where observations were recorded, the sea rose and fell at short intervals for a period of five or six hours, there being a difference in the sea level of 10 feet, an ordinary tide rising only about 2^ feet. Accompanying the great earthquake at Iquique, in South America, on May 9, 1877, the water was withdrawn from the shore for a distance of about 70 yards, after which the coast was devas- tated by waves, which in some places are stated to have been from 20 feet to 80 feet high. This disturbance extended all over the South Pacific as far as Japan ; to the Samoa Islands, where the sea 132 TIDES AND WAVES. rose from 6 feet to 8 feet ; at New Zealand and AustraKa, where the sea oscillated from 3 feet to 20 feet ; and at Japan, where the oscillations were from 5 feet to 10 feet. In 1883, which was the year of the great disturbance at Krakatoa, owing to a submarine landslip the coast of Java and Sumatra was inundated and 36,000 lives lost. In 1896, on June 15, a tremendous seismic disturbance and submarine earthquake occurred on the north-east coast of Japan, and the wOrld was shaken from pole to pole. This seaquake is supposed to have occurred near the Tuscarora Deeps, where the water is 4000 fathoms deep, the rocky bed of the sea being fractured. Three successive waves rolled on the shore, the largest being 50 feet in height, and the coast was inundated over a length of 300 miles. A two-masted schooner was washed 500 yards inland. The destruction of life and property was very great, 30,000 persons having been reported as killed. The disturbance was not felt by boats at some distance out at sea, the fishermen knowing nothing of the disaster that occurred on the land imtil their return to the shore — but waves were recorded as having spread over the Atlantic and Pacific Oceans. On September 3, 1899, following the earthquake that occurred in Alaska, when a chasm was opened near the shore, the sea became very disturbed, the water rising and falling at short intervals, and a wave 30 feet high broke on the shore. On August 17, 1902, owing to a submarine earthquake, the town of Atlata, in the Gulf of California, was swept by a wave which rolled completely over the houses near the shore, doing damage to the extent of £200,000. This wave was seen to approach from a distance estimated at 10 miles out at sea. Occasionally there are reports of disturbances of the sea on the coasts of this country, the water rising and falling at short intervals. These no doubt are due to unrecorded submarine disturbances. Thus, Mallet records that on March 2, 1856, the sea rose and fell over a considerable length of the coast of Yorkshire. At Whitby the tide ebbed and flowed at intervals of ten minutes, and this to such an extent as alternately to place vessels in the harbour aground and afloat. A similar phenomenon occurred on the coast of Wexford on September 16, 1864, where the water ebbed and flowed at intervals of about twenty minutes. In October, 1873, a large solitary wave broke across Filey Bay, and swept two persons off the rocks at a place which is hardly ever covered SEISMIC AND CYCLONIC STORM WAVES. 133 by the tide, the time of the occurrence being within one and a half hour of low wat^r. In 1887 an extraordinary solitary wave broke over the pro- menade at Bridlington, at a part where no wave before or since cast its spray. This wave was also experienced on other parts of the coast. In 1901 the sea was much disturbed at Bournemouth, the waves breaking on the shore every two or three minutes, although the sea was calm. At the same time an unusual movement of the sea in Alum Bay, in the Isle of Wight, was recorded, the waves breaking on the shore at intervals of from two to three minutes, and reaching from 20 feet to 30 feet further up the beach than the ordinary waves ; the sea at the time was calm. A slight shock of earthquake was felt about the same time at Torquay, and the sea was disturbed there. In January, 1901, a large wave, the highest ever known, broke over Staithes, on the north-east coast, and washed over a house on the shore. The subject of disturbances in the ocean is dealt with in the reports of Mr. Mallet to the British Association, and by Professor Milne in Chapter IX. of his book on " Earthquakes." Solitary Ocean Waves. — With regard to the second class of abnormal solitary waves met with in mid ocean, the opinion has been expressed, that these are due to a building-up process, carried on by the joint action of large and small wind-waves approaching each other from different directions and coalescing; or of one large wave having its size continually increased at the expense of the smaller ones ; or of the occasional grouping of three or four waves due to heavy gusts of wind ; in each case forming a single wave of much greater magnitude than the originals from which they were produced. The action of waves, so far as known, does not lend itself to this theory. That two or more waves might coalesce and form one large wave, under the conditions named, is quite possible, and the combined energy of the two waves might result in lifting the joint waves higher than the originals, but not to the extent of the solitary waves as described by those who have encountered them. Against this theory is also to be set the fact that these solitary waves are frequently to be met with in calm weather and with an undisturbed sea. On the other hand, they generally occur in places which are known to be in the line of volcanic eruptions. 134 TIDES AND WAVES. From an investigation into this subject by M. Danny, it was ascertained that submarine disturbances were located in the Atlantic in 0° 20' S. lat. and 22° W. long., which lies in the direc- tion of places subject to seismic disturbances. Facts were col- lected showing that a large number of shocks had been felt by vessels in this locality. On the accompanying chart (Fig. 15), it will be seen that the great majority of the solitary waves that have been recorded are in the North Atlantic, in the track of vessels passing between Fig. 16.— Chart showing Kecorded Tidal Waves. Europe and America, on a line between Iceland, the Azores, Cape Verde Islands, and other places subject to volcanic activity ; but the fact of the greater number appearing in this locality may simply be due to the trafSc being greater here than in any other part of the ocean. Abnormal waves occasionally break on the coast of Madeira. Thus, on January 6, 1891, in lat. 32° 46' N. and long. 16° 55' W., a wave burst with violence on the shore for some distance along the coast, the sea being previously calm and the wind light. The wave appeared to come from the south-east, and a submarine SEISMIC AND CYCLONIC STORM WAVES. 135 cable was broken in deep water 18 miles to the south. This wave was not felt at Teneriffe. In some instances, also, shocks are felt by passing vessels without any unusual disturbance of the sea being noticed. These shocks are described as giving a sensation of a trembling motion of the vessel, and as if the keel had passed over and grated on a reef or rocky bottom. Mallet, in his report to the British Association in 1850, records an instance which occurred in 1796, of a British ship, when 11 leagues from Manilla, feeling a shook from below so sharp and sudden as to unship and splinter the mainmast. On November 1, 1893, a vessel named the Grown of India, when in lat. 17° N., and long. 28° W., felt a shock which made the ship tremble ; and on May 6, 1897, the captain of the Zoe, when in lat, 44° N. and long. 29° W., reported a similar event. The following are examples of solitary abnormal waves : — In 1873, October 3, off Ushant, the s.s. Chimhorazo encoun- tered a solitary wave and shipped a heavy sea which carried away seven boats, the smoking saloon, and everything on the spar deck. In 1881 the s.s. Bosario, on her voyage to New York, was struck by a solitary wave, which swept away all hands on deck. In the same year the Bosina encountered a solitary wave which swept the vessel while the crew were shortening sail, and every man was carried away except a sick seaman lying in his bunk. In 1882, off the Cape of Good Hope, the Loch Torridor, a four-masted sailing vessel, was struck by a fearful and unexpected sea. The master and half the crew were carried away. In 1884, February 2, the s.s. Faraday, in lat. 46° 11' N. and long. 27° 5' W., encountered a solitary wave, which was visible like a line of high land, five minutes before it struck the vessel. In 1886, July 18, the s.s. Khyber, in lat. 40° N. and long. 32° W., encountered a tremendous solitary sea, which rolled over the vessel, doing great damage. In 1886, December 27, the s.s. Westernland, in lat. 47° 59' N. and long. 43° 57' W., was met by a huge wave, which rose to a great height just in advance of her. No other similar waves were met with. In 1887, July 26, the s.s. XJmhria, in lat. 50° 50' and long. 27° 8', encountered two large waves — the first broken ; the second, green, broke on the ship from north-west direction. 136 TIDES AND WAVES. In 1891, February 18, the s.s. Ormites, in lat. 36° 12' K and long. 32° 50' W., encountered a huge ware, which broke over the vessel forward while steaming in smooth water. In 1894, in January, the s.s. Normania encountered an enormous wave, which was observed " mast-head high," and swept the decks like a solid wall, reaching as high as the bridge. It smashed the cabin on the promenade deck, and carried away the music-room and o£Scers' quarters. A stiff gale which had been blowing had moderated. In 1894, November 16, the s.s. Festina Lente, in lat. 50° 12' N. and long. 35° 23' W., had a steep sea fall on board from both sides. In 1894, November 16, the s.s. Manhattan, in lat. 51° 26' and long. 27° 31', had a mountainous wave break on board from the north-west. The sea was high but fairly true. In 1894, November 21, off west coast of Ireland, in lat. 53° 9' and long. 9° 52', the s.s. Diamond was completely submerged by a wave which was estimated to be 40 feet high. In 1895, the s.s. Teutonic, on her homeward voyage from New York, during a gale encountered gigantic waves which swept the decks. Passengers and crew were thrown down by the shock and injured. In the same year the s.s. Montgomery Castle, when 300 miles west of the Azores, shipped a solitary sea which washed overboard the master, both mates, and five seamen. In 1896, March 3, the s.s. Cascapedia, in lat. 48° 8' N. and long. 8° W., was struck by a solitary wave. The sea rose suddenly and swept over the ship. The wave was estimated to be 50 feet high. In 1896, January 15, the s.s. TJiermopylce came up with three heavy swells, into which the vessel pitched with forecastle under. The sea was quite smooth, with a light south breeze. In 1896, December 23, the s.s. Madeleine, in lat. 39° N. and long. 73° W., during a north-west gale was struck by a high broken sea which nearly threw the vessel on her beam ends. In 1897, September, the s.s. Wooloomooloo, in lat. 34° S. and long. 103° E., with moderate breeze, encountered a heavy sea, described as like a moving square lump of water, which broke on board and carried away four men and the whole of the port bulwarks. In 1903, October, the Cunard liner Mruria, six hours after SEISMIC AND CYCLONIC STORM WAVES. 137 leaving Sandy Hook on her homeward voyage, was suddenly struck on her lee-side by a wave reported to be 50 feet high. The captain's port bridge was carried away, the iron stanchions which held the ship's boats were dislodged and twisted, and everything movable was washed overboard. Several of the passengers were severely injured, one dying from the harm he had received. The weather was rough, but gave no indication of the heavy sea by which the vessel was struck. In 1905, October, the Cunard liner Gam^pania, on her outward journey to New York, was struck by an enormous wave as she was passing the Grand Banks of Newfoundland. There was a fresh gale blowing, but nothing that gave the slightest warning, when suddenly the steamer lurched over and scooped an enormous sea, the water sweeping over the deck several feet deep, washing overboard five passengers and seriously injuring twenty-nine others. The wave that struck the ship reached as high as the ship's funnels. Cyclonic Storm Waves. — The third class of solitary abnormal waves has no connection with seismic disturbances, but is due to the force of the wind during cyclones, and these are generally known as storm waves. The water forming the waves is both raised by the wind blowing on the surface and is sucked up in the centre of the cyclone, a large storm wave being thus generated which, travelling in a circular direction with the centre of the cyclone, breaks with overwhelming force on the land with which it comes in contact. Cyclones are due to large barometric depressions causing vast revolving eddies or whirls of the atmosphere. At the bottom of the eddy, at the earth's surface, there is a difference of pressure which is greatest in the middle or interior of the eddy, the pressure decreasing from the outskirts to the centre. In a large cyclonic storm a vast mass of air, 200 or 300 miles in diameter, and from a half to 3 miles in height, is kept whirling round in a complicated spiral form.^ The rate of motion of cyclonic storms differs very considerably even for storms of the same class, and also for the same storm at different periods of its existence. In the earlier stages of cyclonic storms in the Bay of Bengal the velocity is generally less than 4 miles an hour. After they have fully formed they advance, in ■ " Oyclonio Storms in thei Bay of Bengal," T. Elliot. Government Printing Office, Calcutta. 138 TIDES AND WAVES. some cases, with a velocity which is uniform during the remainder of their progress at sea ; but in other cases with a velocity which increases rapidly as they approach land. The average velocity of fully formed storms appears to be from 10 to 12 miles an hour ; some severe storms have reached 15 miles when approaching land, and on one occasion 25 miles an hour. These storms are the cause of strong currents. In the open part of the Bay of Bengal the direction of the currents coincides with that of the wind ; the drift near the centre during a severe cyclone reaching 6 to 8 knots. The waves produced by the winds of a cyclonic storm pass outwards beyond the storm area and produce a very observable swell at distances of 400 and 500 miles away from the centre. Among the islands of the Pacific the water is abnormally raised during cyclones, which are frequent. In 1869, 1879, and 1886 cyclones passed over the Fiji Islands causing inundations, when several lives were lost and much property destroyed. On these occasions waves 10 feet above the ordinary sea level broke on the shore and inundated the coast. The fiercest cyclones are those in the Bay of Bengal, and on the coasts of that bay the most damaging storm-waves have occurred. In September, 1855, during a cyclone, one of these storm-waves broke on the Orissa coast, in the neighbourhood of False Point Harbour, and rolled in one wide, unbroken wave, more than 20 feet high, over the low country, submerging villages, and carrying away before it, with irresistible force, human beings, houses, and cattle, and destroying crops. In 1864, during a cyclone, a storm-wave was driven up the Hooghly to Calcutta, arriving two hours before the time of high water. The wave was described " as rising suddenly, as if by magic." It was estimated by the pilots that the water was 40 feet above the normal level. The whole of the low-lying land was flooded, vessels were driven from their moorings and left high and dry on the land ; thirty-six were totally destroyed, and ninety- seven damaged. The P. and 0. steamer Bengal, of 2185 tons, was stranded, and left high and dry on Shalinar Point. The damage to ships and cargo was estimated at a million pounds, and 50,000 persons lost their lives. A great part of the town of Calcutta was flooded, and 1500 square miles of land were inun- dated. This wave took 5^ hours to traverse the distance from Cowcally to Calcutta, 83 miles, equal to a rate of 15| miles SEISMIC AND CYCLONIC STORM WAVES. 139 an hour. The rate at which the crest of the tidal wave moves over the same distance is 236 miles an hour. In October, 1876, the most extensive and fiercest cyclone of the century occurred, when an enormous storm-wave was driven over the islands and low lands in the neighbourhood of Backer- gange, in the Bay of Bengal, the water rising from 30 feet to 40 feet in less than half an hour, and inundating all the low-lying country, causing the loss of life of 100,000 persons. In September, 1900, a great part of the town of Gralveston, in the Gulf of Mexico, was destroyed during a tornado by a series of waves, 15 feet high, being thrown on to the shore, killing 3000 persons and destroying 4000 houses. Just before the water broke on shore there appeared to be an abnormal wave 4 feet high, which, mounting on the top of the water blown into, the bay, caused the town to be flooded from 6 feet to 10 feet. On January 13, 1903, the Society Islands, in the South Pacific, were devastated by enormous waves breaking over them, causing the loss of 1000 lives, and destroying great quantities of pearl shells, copra, and other property. A hurricane had been raging for several days, and when the centre of the cyclone reached the shore, several abnormal waves broke on it, each being higher than its predecessor, until, according to the description given, a wall of water, 40 feet in height, rushed across the islands, covering them with water for miles. In September, 1898, a cyclone which passed 18 miles south of Barbadoes, swept over the southern half of the island of St. Vincent, then took a north-westerly direction towards Aves Island, its rate of progress being 7J miles an hour. From here it pursued a northerly course for 450 miles, passing from Puerto Eico and the Windward Islands ; it then swerved north-west for 600 miles, and afterwards recurved to the north-east. The direction of travel was traced for 3000 miles at an average speed of 8 miles an hour during the first part of its course, and 24 miles when the recurving commenced. The high sea due to this cyclone and abnormal wave damaged Kingstown, the shipping was destroyed, a great many lives were lost, and great destruction of property caused at St. Vincent. Occasionally the tides on the British coast are abnormally raised by cyclonic storms. In February, 1904, during the period of the spring tides a deep cyclonic depression was situated in the Atlantic off the coast of the British Islands and north-west 140 TIDES AND WAVES. coast of Europe, the centre of which slowly moved for three days, in an easterly direction towards the English Channel. The centre of this cyclone remained almost stationary for half a day in the neighbourhood of the Scilly Islands. The wind was blowing strongly from the south-west, and the barometer fell to 29 inches. An abnormally high wave swept up the English Channel and broke all along the south coast, doing an enormous amount of damage. At St. Mary's, the chief port of the Scilly Islands, the water poured over the quays and inundated many of the fields where early potatoes and bulbs are grown. At Penzance the waves broke over the promenade and flooded the hoiises in the vicinity. At Bude, in Cornwall, the heavy sea breaking into the harbour destroyed the lock gates and emptied the canal. At Chesil, near Portland, the sea, which was reported as running " mountains high," broke over the Chesil Bank and inundated the village three feet deep, covering the streets with boulders, some weighing as much as a hundredweight. The lower parts of Appledore, Weymouth, Pevensey, Portsmouth, and other towns were flooded. At Dover the water rose nearly to the top of the quays ; while at Hastings the waves broke over the promenade, the broken water rising as high as the top of the houses and inundating several of the streets, a large gap being made in the sea defence works at St. Leonards. In the Thames the tide rose to 3 feet 8 inches above Trinity high water mark, the highest recorded tide since 1901, and the water ran level with the embankment. On the coast of Brittany the wave broke through the sand dunes near Quimper. At Saint Pierre, Saint Guenole and Kerity more than three hundred houses were flooded, and the water penetrated \\ mile inland, inundating a large area of land. Many of the fishing boats were dashed to pieces on the shore, and pieces of rock, some weighing more than a ton, were moved from their places and carried a distance of three hundred yards. CHAPTER XII. TIDAL BOBES IN EIVEES. The propagation of the tide into the maritime portion of rivers is sometimes accompanied by a remarkable phenomenon. At the entrance of the river, in place of a gradual rise of the water, the arrival of the tide is made manifest by a breaking wave with a crest several feet in height which, when formed, advances rapidly up the channel. This wave is known as a "Bore," "Aeger," or "Hygre" in this country ; in France as a " Mascaret ; " and in South America as a Proroca.^ The bore is not found in all rivers ; and where it does occur it is of variable intensity, and is only produced at spring tides. The deepening and improving of tidal channels results in the disappearance of tidal bores. For example, the river Witham, which extends out of the upper end of the Wash on the east coast of England, was formerly approached by the tide through a tortuous, shallow channel, passing through shifting sands. The tidal wave, coming up Boston Deeps, being checked on entering this channel, developed into a bore which proceeded up the river with a crest from one to two feet high. When a new cut at the entrance of the river was made, and the channel deepened, the bore entirely disappeared. In the River Nene, owing to the obstruction to the tidal wave from shoals and sandbanks at the mouth of the river, the tide formerly used to rush up the channel with a considerable bore, raising the tide at Wisbech suddenly from 4 to 5 feet. When a new cut was made, and the river deepened and improved, the bore ceased. The bore in this river was described in 1680 as a " most terrible flush of water that came up the river with a terrible noise ' The word "bore" ia supposed to be derived from the Scandinavian word " bara," a billow; Aeger is the name of a Saxon river god; or this name may be derived from " Eau Guerre," water war. The word " Proroca " means " the destroyer." 142 TIDES AND WAVES. and with sucli violence that it sunk a coal vessel in the town. Each wave surmounted the other with terrible violence." A bore is due to the same cause as that which makes waves break on a shore, when, the water becoming too shoal for the complete formation of the wave, the bottom is tripped up and the upper part rolls over. In the one case, however, the breaking wave is reflected back, while in the case of the bore the first wave is overtaken by others following, and thus three or more waves may become superimposed. As the depth of water increases by these succeeding waves, the accumulated volume forms a head, or crest, which, as soon as the bar or shoal on which the wave has broken is overcome, rushes up the channel with great velocity and turbulence. The conditions necessary for the full development of a bore are : — a considerable rise of tide ; a converging channel with a rising bed, the depth of the water decreasing as the channel is approached, its progress being impeded by sandbanks or shoals through which one or more shallow channels are kept open by the ebb current ; or a sand bar, over which there is not sufficient depth of water to admit of the passage of the approaching tidal wave. In the Thames, the Humber, the Mersey, the Clyde, the lower part of the Gironde and the Loire, these conditions are absent and there is no bore ; while they exist in the Severn, the Trent, the Ouse, the Dee, the Seine, the Garonne, and many other rivers. The Tsien-Tang-Kiang Bore. — The most remarkable example of a bore is to be found on the Tsien-Tang-Kiang river in China. This bore has been described "as the most sensational and fascinating tidal phenomenon in the world." Here the conditions necessary for the development of a bore exist. The river discharges into an estuary encumbered with a large area of sand, and is favourably situated for the reception of the tidal wave from the Pacific. The range of spring tides on this part of the coast is about 12 feet, but as the wave becomes compressed in advancing towards the head of the estuary, it increases to 25 feet at ordinary springs, and 34 feet when an on- shore gale is blowing at the same time that the moon is in perigee at the time of full and change. The flood and ebb tide each run for 6 hours at Chang-Fau ; at Haining the flood runs 3 hours and the ebb 9 iours ; while at Hangchau there is only 1\ hour flood, all of which is bore. TIDAL BORES. 143 The shores of the estuary converge (Fig. 16) so that at its head the width is only about one fifth of what it is at the mouth. At low water the river is a mile wide. There is a bar across the estuary. The wave enters the river at first through narrow channels which run through the sand shoals, and meets with a strong ebb current, which trips up its foot and causes an overfall ; then, as the tide continues to flow, and as the succeeding waves are superimposed on those preceding, the water rises and forms Shanghai of 5; Chafu^ # Hangchau Bay M, Haining Mouth o/fl''"e^\^g2SI\ Rise W/i /*^^^oi?||s HangchajU^^f here. ^ \ «g© Rise of tide 12.0'. i^KaupuJ ^m^^^^. w^^^frotn mouth Bore e'xtend's a ^ Rise e ft. 30 miles furtherM t up the riiier.^ ^ ^^ ^^ % Fig, 16. — Estuary and RiTer Tsien-Tang-Kiang. the bore. There are two branches of the bore over the sand flats which unite 4 miles outside the river. At the time the two branches join there is a difference of level of 19 feet at springs between the water on the outside of the bar and that in the mouth of the river, a distance of 20 miles. The flood tide thus enters the river with a falling gradient of a foot in a mile. The bore enters the river with a concave transverse surface 1800 yards wide, and passes Haining at the rate of 21 feet a second, or 14^ miles an hour, the rise of the tide during the first hour being 10 feet. 144 TIDES AND WAVES. The front of the bore is described as a "gleaming white cascade of bubbling foam 8 to 12 feet high, the steepest and highest part being over the deepest part of the river." It maintains its breadth, height, and velocity for 12 or 15 miles above the mouth of the Tsien-Tang. The approach of the bore can be heard on a still night for -a distanpe of 14 or 15 miles, and an hour and twenty minutes before its arrival, and it rushes past Haining with a noise like the roar of the rapids below Niagara. It has been estimated that IJ million tons of water pass Haining in one minute. As the great wave approaches it appears to overrun the swift, down- running, brown-coloured stream which it meets, and to hurl itself against, and break over, the ebb current, and then to race up the river at the rate of 13 to 14 miles an hour. An old writer described the bore thus : " The surge rises like a hill, and the wave like a house ; it roars like thunder, and as it comes on it appears to swallow the heavens and bathe the sun." A more modern observer describes this bore as being pre- ceded by " a soft, long, rolling undertone that grows louder as the bore approaches nearer. As it sweeps past with the fury of a whirlwind, the noise may be compared to that made by the tramp of a charge of cavalry ; and when it moves along, the resemblance ;is more that of the pounding of surf upon a coral reef, the booming, dashing reverberation of waves breaking without cessation, beating the mighty diapason of the sea. A salt, fresh smell of the sea, the breath of the ocean, accompanies this awful tide, succeeded by a ghastly mist." The bore decreases in height as it rolls on up stream, the crest diminishing to 5 feet at Hangchau, where the flood tide only lasts 1^ hour; and gradually dying away, till the last ripples of the highest bore reach 18 miles above the city, or 42 miles from its formation at the mouth of the river. At neap tides it is not felt at 15 miles above Haining. The largest bores take place at the equinoctial spring tides ; and the effect is much increased if the moon happens to be in perigee at that time : and still further, if an on-shore gale is driving the water out of the Pacific into the Bay of Hangchau.^ The Amazon. — The bore of the Amazon is chiefly distinguished ' " The Bore of the Tsien-Tang-Kiang," by W. Osborne Moore, E.N., Min. Pro. Instit. Civil Engineers, vol. xcix., 1889. "The Marvellous Bore of Hang- Chan," by E. K. Scidmore ; Century Magazine, 1900. TIDAL BORES. 145 for the great distance it travels up the river. The particulars to be obtained of this river are very scanty, and principally derived from the account of the travels of La Condamine.^ The Amazon enters the Pacific on the north coast of South America. The general rise of the tide along this part of the coast is from 6 to 10 feet, the range being from 10 to 11 feet at Para, at the mouth of the river. The mouth of the estuary into which the river proper dis- charges between Cape de Norte and Cape Magoari is 150 miles wide, the entrance to the river being 180 miles from the coast line. This estuary is very much encumbered by a number of islands. The characteristics of the river Amazon, owing to its great width and depth, resemble more those of an estuary than a river channel. The approach of the bore is announced by a great roar. At the equinoxes during three consecutive days bores of from 12 to 15 feet in height rush up the river with each high water, so that along the course of the channel for 200 miles from its mouth no less than eight tide-waves are simultaneously advancing, and as many as five bores are at the same time in progress.^ At Abydos, 523 miles from the mouth, the effect is felt in a tide of 18 feet. The Hooghly. — There is a bore of some magnitude in the Eiver Hooghly, the navigable branch of the Ganges. The velocity of the tidal flood current and of the ebb in this river, when freshets are running, is about the same, or from 5 to 6 miles an hour. The average navigable depth of the channel at ordinary low water, apart from floods, is from 14 to 15 feet. The bore is first manifest at the entrance to the river at Buffalo Point, where the estuary is contracted to one-fifth of the width of what it is a short distance below this point. The crest has a height of 4 feet at Buj Buj, 30 miles higher up, and 5 to 6 feet at Chinsnrah, 17 miles above Calcutta, or 67 miles from its commencement, increasing under favourable circumstances to 7 feet ; from here the height decreases, and the bore dies out about 20 miles below the termination of the tidal wave near Nadia, or about 112 miles from its commencement. ' " Etude sur la Navigation des Eiviferes \ Marees." M. Bouniceau. Paris. 1845. ^ " Physical Geography." Herschel. 145 TIDES AND WAVES. The crest advances at the rate of 20 miles an hour. This river is situated at the head of a long sandy estuary, which is 15 miles wide where it joins the Bay of Bengal, and contracts to about 5 miles at Balari, 42 miles from the mouth, and to 1 mile at Buffalo Point, a little above Diamond Harbour, and 53 miles from the mouth of the estuary. Here the tidal river may be said to begin. At Calcutta, 50 miles from its com- mencement, the river has decreased to \ mile in width. The tidal flow continues to a little above Nadia, 88 miles above Cal- cutta, and 138 miles from the mouth of the river. The river at its commencement, for the first 7 miles, between Diamond Harbour and Hooghly Point, is much encumbered with sandbanks over which the tide has to force its way. The range of spring tides is 11 feet in the Bay of Bengal, which increases to 16 feet at the commencement of the river at Buffalo Point, and is 12 feet at Calcutta, and 2 feet at Nadia. For about 10 miles below where the bore first makes its appearance there is a depth at low water of about 50 feet ; there is then a bar at Buffalo Point with only 30 feet, and at Hooghly Point of 15 or 16 feet, the mean depth above this nearly to Kidderpur being about 30 feet. There are here conditions favourable to the formation of a bore ; a converging estuary channel ; a tide increasing in height from 11 to 16 feet at the entrance to the river ; and a channel encumbered with a mass of sandbanks when the tide first enters it.^ The Seine. — There is a considerable bore or "mascaret" on the river Seine. The estuary of this river between Havre and Villerville is 5i miles wide, decreasing at Berville, 12 miles from the sea, and where the river commences, to 3f miles. This estuary is a mass of sandbanks, amongst which the flood and ebb currents work their way through a shoal and tortuous channel. Above Berville the river has been trained and confined to a channel with a uniform width; and the depth has been considerably increased since these works were carried out. The bore is only developed at spring tides, and attains its maximum at the autumn equinox. It commences at 30 miles ' Bruce, " Kidderpur Docks," Min. Pro. Instit. Civil Engineers, vol. xxi. Vernon HarcoTU't, " The River Hooghly," ibid,, vol. cix. Bouniceau, " Riviferes I, Mare'es." 1845. TIDAL BORES. 147 from the mouth of the estuary and runs for about 40 miles up the river in a crescent shape with a crest from 6 to 7 feet high. This bore was described by M. Eobin, Inspector of Fonts et Chaussees, in 1826, before the works of improvement were carried out, as first appearing during high spring tides at 3 miles from the mouth of the bay, but as not being fully developed till Berville was reached, 3 miles further up, and as presenting " an imposing spectacle." The velocity with which it advanced was the same as that of the flood tide, the average rate of travel being : between La Eoque and Quilleboeuf, 4| miles an hour ; between Quilleboeuf and Vieux Port, 9 miles ; and between Yainville and Eouen, 18| miles an hour.^ An account of the bore as observed by M. Partiot in 1856, after the river had been improved, showed that the propagation of the tidal wave between Havre and Tancarville was then much retarded by the sandbanks, the difference in level of the -wave between Havre and Quilleboeuf being 8-20 feet. The velocity was only 740 miles an hour ; the mass of water when it got over these shoals falling with violence into the deeper water and forming a bore. The wave advanced towards St. Jacques, which is situated at the head of the estuary, 12 miles from its mouth, with a crest 6^ feet high, followed by 5 or 6 other waves, the crests of which reached 10 feet in height. In two minutes the level of the water was raised 5| feet above low water, the depth in the channel before the bore arrived being 115 feet.^ Another description given in 1861 put the height of the crest of the bore at 7 feet. The velocity of the bore in the upper part of the river was considerably increased by the deepening of the channel consequent on the training works. The mouth of the river formed a bay 5J miles wide at Honfleur, diminishing towards Quilleboeuf to where the bay terminated. Above Maillerai the channel was not much altered. The following table shows the alteration in the propagation of the tidal wave that took place as between 1826 and 1856 :— ^ 1 " R^oberches Hydrauliques." M. H. Darcy. Paris. 1865. * " Etude sur le mouvement des Maries dans la partie maritime des fleuves." M. E. Partiot. Paris. 1861. ^ " Becherches Hydrauliques." M. H. Darcy. " Tidal Rivers, their Hydraulics, Improvement, and Navigation." W. H. Wlieeler. Longmans. 1893. 148 TIDES AND WAVES. Miles. 1826. 1856. Places. Depth of cbanael. Feet. Velocity of wave. Miles per hour. Depth in feet. Velocity of ■wave. Miles per hour. Hode to Quillebceuf . . Quilleboeuf to Villequier Villequier to Kouen . . 11-8 11-8 44-6 5-9 12-14 22-30 6-72 8-69 16-22 17-71 22-0 25-25 10-23 14-58 16-66 M. Comoy, in his treatise on tidal rivers, published in 1891,^ describes the bore as commencing at Villequier, 31 miles above the mouth of the estuary, and as attaining its greatest height of 7*22 feet at Caudebec, 4 miles further up the river, at the same time that the tidal wave attains its maximum height at the mouth of the estuary. The first crest is followed by ten other waves having a height of 4'59 feet. At Bouille, 35 miles from the commencement of the bore, the height diminishes to 3"18 feet, and it finally disappears between there and Rouen. The level of the water after the passage of the bore was raised 4-50 feet. The velocity of the crest of the mascaret is given as 14-50 miles an hour. The velocity of the flood current after the bore has passed varies from 2*24 to 5'60 miles an hour. Garonne and Dordogne. — There is no bore in the Gironde, for, although there is a bar at its mouth, the depth of water over it and up the river as far as the junction with Garonne and Dordogne is sufficient to allow of the free propagation of the tidal wave. When the tidal wave enters these two tributaries, owing to its being obstructed in its course by the contraction of the water-way, both in width and depth, a bore appears at spring tides. The bore or mascaret in the Garonne first appears about a third of a mile above its confluence with the Gironde, 44| miles from the mouth of this river. At Bee d'Ambes, a short distance above where it is first seen, the height is about 2^ feet. In the autumn equinoctial tides it reaches as far as Bordeaux, about 14 miles above where it begins, and then dies out at Postel, 13 miles further up the river. In the Dordogne the bore first shows itself at Le Port de Plague, 7 miles above its junction with the Garonne, and from ' Comoy, "Etude Pratique sur lea Maries Fluyiales, et notamment sur le Mascaret," Paris. 1891. TIDAL BORES. 149 here increases in height to Saint Pardon, where it attains a maximum height of 3-28 feet, and dies out about 2 miles above Branne.^ Bay of Fundy. — The Petit Codiac Eiver is connected with the Bay of Fundy by an estuary 32 miles long. The estuary at Monckton, 19 miles from its mouth, is half a mile wide, the channel at low water being about 500 feet in width, running through mud flats which are dry at low water. The rise of spring tides at the head of the Bay of Fundy is 45 feet, and at Monckton 47 feet. The rising tide first assumes the character of a bore at Stoney Fe et 9 8 7 ^ [-^ 6 J' r-"""^ 5 ^....y^ 4 A r""^ 3 f 2 1 , 1 . , . 1 1 . . . 1 - , ., _ Minutes '<. 35 40 45 50 1 1 1 1 1 1 I 1 1 1 1 1 1 1 2 Fie. 17.— Bore in the Bay of Fundy. Creek, 8 miles below Monckton, where the estuary bends at almost right angles, and continues for 21 miles to the head of the estuary. The bore arrives at Monckton at half-tide. The observations of the bore on which this notice is founded were taken in the months of August, September, and October, 1898, four days after full moon, and the fifth tide after the highest spring tide. The approach of the bore was made known by a noise described as being like the sound of an approaching railway train, which was heard 11 minutes before the bore appeared; which, as it came nearer, developed into the hissing and rushing sound of broken water in a rapid river. The greatest heigth observed was 4 feet, at the second tide after full moon ; the 1 Comoy, " Etude Pratique sur les Maries Fluviales." , ISO TIDES AND WAVES. average height being about 3 feet 3 inches. Other observers fix the height at 5 feet 4 inches. The rate of advance was 847 miles an hour.^ The diagram (Fig. 17) is taken from those given in the report of Mr. Bell Dawson. At neap tides there is only a heavy ripple a few inches high. The only other place in the Bay of Fundy at which a bore occurs is in the upper part of Cobequid Bay, but here it is little more than a large ripple. The Trent and Ouse. — There is a considerable bore on the river Trent a little above its junction with the Humber. This bore is formed under circumstances somewhat varying from other rivers. The Trent is a tributary of the Humber, and joins that river about 16 miles above Hull and 40 miles from the North Sea. The width of the Trent at the junction is from 2500 to 3000 feet at high water and 550 feet at low water, diminishing to 70 feet at 1^ mile from the junction. This wide space is encumbered with a mass of sandbanks. The width of the Humber below the junction averages about 4500 feet, and this channel also feeds the Ouse, which is a continuation of the Humber. This width is double that of the Trent and Ouse com- bined. The rise of spring tides at Trent mouth varies from 15 feet at ordinary spring tides to 19 feet at equinoctial tides. The tide has a run of 47 miles up the Trent, the flood lasting 3 hours and the ebb 9 hours, and reaches to 87 miles from the North Sea. The bore, or " aeger," as it is locally called, is caused by the check of the tidal flow through the shoal water over the sand- banks, and the contraction of the waterway, the tidal current overrunning the transmission of the foot of the wave. It first assumes a crest somewhere between Burton Stather, 3 miles from the mouth of the Trent, and Amcotts, 2 miles further on, depending on the condition of the tide, the water rising almost instantaneously 3 feet. In ordinary spring tides the bore does not extend more than 7 or 10 miles above Gainsborough. In high spring tides it diminishes to a foot in height at Torksey, 35 miles from the mouth of the river, and then gradually dies out. The author had an opportunity recently of observing this bore under favourable conditions at Gainsborough, which is 1 " Survey of the Tides in Canadian Waters." Eeport by W. Bell Dawson, 1898. TIDAL BORES. 151 25 miles from the mouth of the Trent. The time was during the equinoctial spring tides at the end of October, 1905, on the second and third days after new moon. The tides were laid down in the Admiralty Tide Tables for the Humber as the largest of the year. The moon was in perigee on September 29, and had 11° 21' south declination. The wind was from the N.E. to N.W., a direction which brings the largest tides on the east coast, and was blowing in the North Sea at Spurn with a force of from 6 to 7 of the Beaufort scale. Inland the force was only about 3. There was a limited quantity of fresh water running down the river, the Telocity at low water being 2 miles an hour. The depth in the channel between Gainsborough and the Humber at the time was about 6 feet, but there were several shoals with not more than 2 or '1\ feet over them. Owing to the strong north winds in the North Sea the tide was exceptionally high, rising in the Humber at Hull 271 feet above an ordinary spring tide, and within 10 inches of the record tide of March, 1883. The bore could be heard approaching about half a mile from the place of observation, and passed with a crest in the middle of the river of from 4 to 4^ feet, extending across the full width of the river, which is here about 200 feet wide at high water. At the sides the breaking wave rolled along the banks 6 or 7 feet high. The crest was followed by 5 or 6 other waves of less height, terminat- ing in a mass of turbulent broken water for a distance of 100 yards. The velocity of the wave, as nearly as it could be measured, was about 15 miles an hour, the current running up after the bore had passed at the rate of 4J miles an hour, and at its maximum, about half flood, 5 miles an hour. The tide rose 4 feet in the first 4 minutes after the arrival of the bore, 5 feet in the first half hour, and 8 feet in 2 hours, when it attained its maximum height, and commenced to fall, but the tide continued running up the river for another hour after this at the reduced velocity of 2 miles an hour. There were some steamers and barges lying at the wharves, and a row-boat in the middle of the river. These rose with the wave and suffered no harm. These bores were considered by the men on the river as fair specimens of those which come with high tides, and as not ex- ceeded in height to any extent. When the river is full of fresh water and the ebb is heavy the bore is less pronounced, and does not show at all on neap tides. IS2 TIDES AND WAVES. It was reported that at Owston Ferry, which is eight miles nearer the Humber than G-ainsborough, the crest of the aeger was 8 feet ; a row-boat which was in the middle of the river when the wave came was for an instant completely out of the sight of a spectator on the bank. The photograph from which the illustration (Fig. 18) is taken is by Mr. E. W. Carter, of Gainsborough, and is copyright.' Fig. 18.— Bore in the River Trent. In the Ouse during spring tides there is a less pronounced bore. In ordinary spring tides it commences at a shallow reach in the river at Sand Hall, 2 miles above Goole, attains its greatest height 4 miles above Selby, and then gradually dies out after a run of from 25 to 30 miles. In high spring tides it commences below Goole. The crest of the bore is from 2 to 3 feet, and the breaking wave at the sides 6 or 7 feet. Since the improvement of the channel of the river below Goole these aegers have become smaller. Severn. — There is a bore on the river Severn, at the head of the Bristol Channel (Fig. 19). The tide runs up the Bristol Channel with considerable velocity ; the channel is funnel-shaped, decreasing from a width of 10 miles opposite Minehead to 5 miles at Kingroad, where the estuary of the Severn begins. The rise of the tide here is 40 feet. ' This account of the wave is taken from an article by the author in Nature, of November 9, 1905. TIDAL BORES. 153 The Severn estuary extends for a distance of 27 miles,, to within 3 miles of Newnham, where the channel abruptly contracts to about a quarter of a mile at high water, the width at low water being about 200 yards, decreasing a few miles further up to 80 yards between the river banks. This estuary is much encumbered with sandbanks, through which the low water channel winds about. The tide runs up as far as Gloucester, 48 miles from the mouth, above which the river is semi-tidal ; neap tides not extending as far as this, but high spring tides running further up the river. The depth of the channel at low water up to Beachley is from 30 to 40 feet ; above this it varies from 5 to 11 feet, the average being 8 feet. This is increased in floods to 18 or 20 feet. The bore is formed by the tide being checked by the sandbanks, and passes Sharpness with a crest from 4 to 5 feet high in a con- tinuous wave 90 yards wide. In 1849 Captain Beechy, E.N., made an investigation of the tides of the Severn, and several particu- lars relating to the bore are given in this report.^ At this time the average velocity of the propaga- tion of the tidal wave between Beachley and Gloucester was 1427 miles an hour, while the average ' " Bemarks upon the Tidal Phenomena of the Biver Severn," by Captain F. W. Beechy, B.N. 1849. 154 TIDES AND WAVES. rate of travel of the bore from Sharpness was 8-69 miles an hour, the maximum rate being 14'05 miles an hour in the contracted part of the channel. The velocity between the different reaches is given in Table II. in Appendix V. He describes the first appearance of the bore as commencing in the small channels between Inward Point and G-uscar; but, there being no outlet for these channels until the tide had risen considerably, these small waves expended themselves upon the sands about Gruscar. The bore next appeared above Brimspill, when it took its course up the Nouze Channel, and rolled on, increasing in height, to Hoc Crib, where it became an angry breaking wave. The height of the crest he gave as from 5 to 6 feet at the sides, and 3 feet 6 inches in the centre. The level of the low water when these observations were made was 2 feet above ordinary summer level, and the ebb current was running down at the rate of 3 miles an hour. In the Admiralty Sailing Directions for the West Coast of England it states that " the Hygre or bore rushes up the Severn with considerable noise and a front of 4 or 5 feet ; it is experienced in the several channels from about 2 miles above Sharpness, but not in a continuous wave from shore to shore, until past Longney, 9 miles below Gloucester, where the river is 90 yards in breadth. It is observed in the highest about the fifth flood after full and change, and is occasioned by the contractions of the stream below." Dr. Vaughan Cornish, in a letter to Nature} gave the height of this bore, as the result of an inspection in 1900, at Newnham, as from 3 to 4 feet, and the velocity as 7 to 8 miles an hour. Mr. Whitwell gave the speed at a higher part of the river as over 17 miles an hour, and the height as from 5 to 7 feet.^ Both the velocity of the bore and its height depend on the state of the tides, being greater with equinoctial tides and those raised by a gale from the south-west. With low tides in summer the height is often not more than 2 feet, and the velocity falls to 5 miles an hour. Parrett. — There is a small bore developed out of the Bristol Channel up the Eiver Parrett which passes Bridgewater, 13 miles from the mouth of the river, in spring tides, with a crest from 1 foot to 2 feet. Eiver Dee. — There is a small bore in the river Dee which ' Nature, June 7, 19p2. ^ Nature, February 13, 1902. TIDAL BORES. 155 commences at Eockcliff Hall, one mile below Connagh's Quay, and 17 miles from the mouth of the estuary. It proceeds up the river at the rate of 8 miles an hour, the crest having a height at Sandy Croft of 2 feet. The tidal part of the river Dee commences at the head of a wide estuary 10 miles long, which converges from 7 miles at the mouth to \ mile where the trained channel of the river begins. This estuary is much encumbered with sandbanks; the rise of spring tides is 25 feet, and at equinoctial springs 32 feet. River Mersey. — There is no bore on the Mersey, which branches out of the Liverpool Bay not far from the Dee, although there used to be a sand bar at the mouth, and the tide approached through an estuary 8 miles wide, over which at times there was not more than 9 feet of water, with a rise of the tide at the entrance to the river of 27^ feet. The length of shoal over this bar was a third of a mile, but the tide approached it through a channel having from 20 to 28 feet at low water, the water on the inside deepening to 27 and 50 feet. While, therefore, the tide approached the river channel through a wide sandy estuary, the depth of water was sufficient for the propagation of the tidal wave. Past Liverpool the channel contracts to about \ a mile, with a depth of from 50 to 60 feet, and then expands out into an estuary more than three miles wide. Here the conditions are the reverse of those necessary to the formation of a bore — a narrow channel expanding into a wide estuary. Solway Firth. — In the Solway estuary the first of the tidal wave at spring tides runs up with a bore from 3 to 6 feet high, at the rate of 8 miles an hour, increasing to 10 miles with south- west gales. Its approach is heralded by a deep hoarse roar, which, it is said, can be heard 20 miles away ; this is followed by a " huge wave of foam which is resolved into a great mass of water in violent perturbation." Solway Firth, which opens out of the north-east end of the Irish Sea, is 53 miles long. Its breadth for the first 12 miles is 2J miles. It then opens out to a width of 70 miles. Morecambe Bay. — There is also a bore in this bay which runs up the river Kent, with a crest of about 2 feet. CHAPTER XIII. TIDE TABLES AND TIDE GAUGES. It is obviously an advantage for mariners to have a reliable guide to the time when the water in a tidal river or harbour to which they are bound, or are leaving, will be sufficiently high to enable them to navigate their vessels. For passenger ships especially, which are expected to leave their berths punctually at fixed times, such a guide is a necessity. • For this purpose tide tables, are supplied by the Admiralty giving the time and height of the tide for every day of the year for certain representative ports, with tables of constants of the amounts to be added or deducted for other ports. Datum for Tide Tables. — The datum from which the heights are calculated is the surface of low water of an ordinary spring tide. This level is connected with some fixed datum; in this country the ordnance datum, or mean level of the sea at Liverpool. See Table II. in Appendix III., where also the data for charts and tide gauges in other countries will be found. Tide tables, however, only furnish an accurate indication of the conditions of the tide when the weather is calm and the height of the barometer is normal. Allowance has, therefore, to be made for variations from the calculated height due to these causes. Local Tide Tables. — The connection between the tides and the various phases of the moon is so obvious, that long before the formulation of a satisfactory theory on which to base calculations universally applicable, fairly accurate predictions of the tides for special localities existed. In a paper by Sir J. W. Lubbock, in the Philosophical Transactions for 1837, it is stated that an ancient tide table is in existence in manuscript in the library of the British Museum, with the Codex Cottonianus Julius DVIL, which appears to have been written in the thirteenth century, and to have belonged to TIDE TABLES AND TIDE GAUGES. 157 St. Alban's Abbey. It contains a calendar and other astronomical matters, some of which are the productions of John Wallingford, who died Abbot of St. Alban's, 1213. On one page is a table showing the time of high water at London Bridge, or " flod at London Brigge." Formerly the time of high water at London Bridge was obtained by adding three hours to the moon's southing. In 1668, Phillips gave in the Philosophical Transactions a table showing the variations in the interval between the time of the moon's southing and the time of high water. Shortly after^ wards Flamstead, then Astronomer Royal, having frequent occa- sion to pass between London and Greenwich by water, caused observations to be made over a limited period of the time of high water at those two places, and prepared a tide table showing the time of high water both at the time of the nioon's southing and at the quadratures. Although now the method of preparing tide tables is common property, it was not so regarded formerly, and the secret of the method of preparation was jealously guarded and looked upon as a profitable source of revenue. These local tide tables were con- structed by undivulged methods, which in some instances were handed down from one generation to another. Thus at Liverpool, where the tides for both night and morn- ing had been recorded for many years by Mr. Hutchinson, the harbour-master, the Rev. C. Houlden, by an analysis of these, was able to compile a tide table for the port of Liverpool, which was published annually, and relied upon by mariners for all the ports on the west coast of England. The Construction of Tide Tables. — In 1740, D. Bernoulli, who obtained the prize offered by the Academy of Paris for the best essay on the tides, made an analysis of the tides from the records which had been kept at the port of Brest ; and thus was able to show that to whatever degree the tides as originally generated under the influence of the sun and moon were affected by tbe perturbations or variations of the tide-producing agents, this was accurately reproduced on the coast of France. Taking the equilibrium theory of the making of the tides as his basis, he was thus able to calculate the time and height of the tides at Brest. The tide tables thus prepared by Bernoulli furnished the model on which tables at other ports were prepared, and formed the basis on which those now in use are constructed. 158 TIDES AND WAVES. In 1831 and subsequent years, Lubbock undertook a most laborious investigation of the tidal observations which had been made at his instigation by the coastguards all round the coast of this country ; and also of the records of the height and time of the tides in the Thames kept at the London Docks over a complete cycle of nineteen years, 1809-1828; and subse- quently of those which had been recorded at Liverpool. With the assistance of Mr. Dessiou of the Admiralty, nearly forty thousand tides were analyzed, and it was ascertained to what extent they were relatively affected by the varying position of the sun and moon. Evolving the relative value of each factor, and disentangling the various forces in operation, he was able to assign to each their respective values ; and the fact was con- firmed that the smallest variation in the tides in the sea where they are generated is reproduced with absolute accuracy in every other sea to which the tidal wave extends ; the tide at every part of the ocean being equally affected in proportion to the range at that place, whether this be 4 or 40 feet. The time of the establishment of any port — that is, the time at which high water occurs at full and change of the moon, and the height the tide rises above low water — being obtained by observation, it has become possible, with the aid of the Nautical Almanack, by calculation to predict with absolute accuracy the time and height of the tide for that port for any day of the year and for all time to come. With the information thus obtained, the British Admiralty undertook the preparation and issue of tide tables giving the time and height of the morning and evening tides for every day of the year for the following representative ports : — Brest ; Dover ; Sheerness Dockyard ; Chatham Dockyard ; London Bridge ; De- vonport Dockyard; Portsmouth Dockyard; Harwich; Victoria Dock, Hull ; North Dock, Sunderland, Eiver Tees ; Lighthouse, North Shields ; East Pier, Leith ; Scrabster Pier, Thurso ; East Dock, Greenock ; St. George's Pier, Liverpool ; Pembroke Dock- yard; Port Talbot; Portishead Dock; Holyhead Pier; Kings- town; New Dock, Belfast; Ship Bridge, Londonderry; Mul- laghmore in Sligo Bay ; Galway ; Nimmo Pier, Queenstown ; Duncannon Fort, Waterford.^ A table of tidal constants for all the principal seaports on the ' " Tide Tables for the British and Irish Ports," published by the Hydrograpbio Department of the Admiralty. J. D. Potter. London. Published annually. TIDE TABLES AND TIDE GAUGES. 159 coast of Great Britain is also given, by means of wMch, by a simple calculation, the height and time of the tide can be ascertained from the above representative ports. Tables are also given of the height and time of the spring tides for nearly every port in the world. It has been remarked that " the utmost th6,t can be expected of a tide table is that it shall be correct in calm weather and with a steady wind." An analysis of the tides of five ports, situated on different parts of the coast, made by the author for the two years 1893-4, showed that 180 tides in the year out of 730 are affected by the wind, or about 26 per cent, of the whole ; the mean variation in an 18-foot tide being 13'89 inches, the average force of the wind being 4 on the Beaufort scale ; and that 85 tides in the year were affected by the variation in atmospheric pressure, apart from wind influence ; the mean variation of the barometer being 0*40 inch, with a mean tide of 17"85 feet, 11*80 inches.^ Professor Darwin gives a Table of Errors in the tides at Portsmouth for three months, which shows that 50 per cent, differed from the Tide Table to the extent of six inches in height ; 33 per cent, to the extent of 12 inches ; 14 per cent, to the extent of 18 inches ; and 3 per cent, to the extent of 24 inches ; and that, in time, 81 per cent, varied between 5 minutes and a quarter of an hour; 15 per cent, between a quarter and half an hour; and 4 per cent, above this.^ Further information as to the effect of wind and atmospheric pressure on the tides is given in Chapter VIII. In France tidal records were kept at the port of Brest and Eochefort from 1711 to 1715, and a new series commenced in 1806. Sixteen years' tides, commencing 1807, were subjected to analysis and mathematical discussion by Laplace By the direc- tions of the French Government these records were also analyzed by M. Oassini, and a general law deduced for the calculation of the time and height of the tides at the French ports. In 1839 the French Hydrographic Department issued their "Annuaire des Marees des Cotes de France," which has since been issued annually. Tidal Constituents. — In calculating the time and height of the ' " Report on the Effect of Wind and Atmospheric Pressure on the Tides." British Association. By W. H. Wheeler, Secretary of the Committee. 1896. 2 " The Tides," Darwin. i6o TIDES AND WAVES. tides a number of causes affecting the relations of the sun and moon to the earth have to be taken into consideration. The time of the passage of the sun across the meridian of the earth varies from that of the moon. The force of the sun in raising the tides is less than that of the moon. The distance of both the sun and the moon vary at different periods of the year, causing a propor- tionate variation in their gravitational effects ; the sun and moon at one time are over the equator of the earth, both together, and at other periods separately, and they both decline a certain distance to the north and south ; at one time the sun and moon are acting conjointly in raising the tides, and at other times are in direct opposition. There are other minor variations and perturbations both of the sun and moon, which occur in cycles of varying periods, all of which to some extent exert an influence on the making of the tides. All these changes affect the primary tide wave of the Southern Ocean, and are felt in every tidal sea and river. For ascertaining the daily tides at any particular port,, its local conditions have to be also taken into consideration, and the estab- lishment of the port or the time at which at that particular place the moon crosses its meridian, and the height to which the tide rises under normal conditions at that time, has to be determined. For the purpose of the calculations for constructing tide tables, these various factors are considered as so many different waves superimposed on one another. Eight of these waves are sufficient for the purpose of calculating the tides with a fair amount of accuracy, and these, no doubt, were all that were taken into account in the construction of the local tide tables already referred to. The method of reduction of the tidal constituents formerly adopted was by averaging the height and time of these waves in certain selected groups after the manner originally pursued by Bernoulli and Lubbock. When the observed tidal motions have been analyzed into partial tide waves, they fall into three groups, the first the semi- diurnal, where the crests follow one another at intervals of half a day ; the second, the diurnal, following one another at intervals of a day ; the third having periods respectively of a fortnight, a month, half a year, a year, and longer cycles included within a period of nineteen years. In the making of the tide tables of the British Admiralty, and TIDE TABLES AND TIDE GAUGES. i6i also for those prepared for the Indian Government, and for the French and American hydrographical departments, from 20 to 25 waves of sensible magnitude are taken into consideration. These are described as follows : — The lunar monthly and solar annual elliptic waves 2 „ fortnightly and solar semi-annual declination waves . . 2 „ and solar diurnal waves 4 „ „ semi-diurnal 2 „ „ elliptic diurnal . . 7 „ „ „ semi-diurnal 4 „ „ declination semi-diurnal ... 2 • , 23 Harmonic Analysis. — About forty years ago Sir W. Thompson (now Lord Kelvin) suggested that the principle of harmonic analysis might with advantage be applied to the reduction of these tidal constituents and to the simplification of the calcula- tions ; and at the British Association meeting of 1868 he made a report describing his proposed method of procedure. As harmony in music may be described as the union of sounds which individually appear different, but when blended together form a collective chord, or as the flowing together of several sounds into one, so the object of the harmonic analysis of the different tidal constituents is to' reduce "the complicated motions of the tides into a series of simple harmonic motions or waves in different periods and with different amplitudes, or ranges ; and these simple harmonic constituents added together give the aggregate tide." Each inequality of any one of the tidal constituents is regarded as a smaller superimposed tide of period approximately equal, producing with the chief tide a compound effect which corresponds to the discord of two simple harmonic notes in music approximately in unison with one another. Tidal Harmonic Analyzer and Tide Predicter. — The reduction of figures necessary for analyzing, computing and reducing the time and height of the tides involves a very great amount of labour, and to save this Sir W. Thompson, about the year 1872, invented two machines by which the work can be done mechanically. The object of these two machines is thus described by their inventor : " to substitute brass for brain in the great mechanical labour of calculating the elementary constituents of the rise and M i62 TIDES AND WAVES. fall of the tides, according to the system of harmonic analysis." The principle of these machines and the details of construction are described and illustrated in the paper by Sir W. Thompson on Tidal Instruments in Volume LXV. of the Minutes of Proceedings of the Institution of Civil Engineers for 1880-81. The tide predicter, as there described, is a machine for working out the tides for any port for which the tidal con- stituents hare been found by harmonic analysis from tide gauge observations; and for showing by a continuous curve the time and height of the tide at every instant for a year or any number of years in advance. For each tidal constituent there is a separate shaft with an overhanging crank which carries a pulley pivoted on to a parallel axis, adjustable to a greater or less distance from the shaft's axis according to the range of the tidal constituents of the port whose tides are to be worked out. A wire or chain passes over or under all the pulleys, carrying a weight with a pencil attached, which makes the tidal curve on a cylinder covered with paper. This machine can work off the whole of the tides of a port for a year in about four hours. Machines are in use by the Indian Government for computing the Indian tides ; and by the American Hydrographic Department. Tide Gauges in their simplest form consist of a scale of feet marked off on the wall of a lock or other required locality, by which the height of the tide at any period may be obtained by observation. All large ports, however, are provided with an instrument for automatically recording, by a curve traced by a pencil on paper fixed on a cylinder revolved by clock-work, the height of the water above the zero of the gauge at every instant of time. So far back as 1831 a self-registering tide gauge was described by Mr. H. E. Palmer in the Philosophical Transactions. This machine consisted of a float actuated by the tides, which caused a pencil to move horizontally along the summit of a cylinder which turned round slowly and uniformly. In the Transactions for 1838 also there is a description by Mr. J. G. Bunt of a tide gauge erected in 1837 on the banks of the Eiver Avon, and which continued in operation till 1866. This was worked by a clock, and recorded the tides on a cylinder 2 feet long and 4 feet in circumference. An improved form of gauge, in which the recording cylinder TIDE TABLES AND TIDE GAUGES. 163 is moved by clock-work, is described by Sir W. Thompson in the paper already referred to {Min. Froe. Instit. 0. K, vol. Ixv.). One difficulty that has to be overcome with these self-recording gauges is to prevent the float being influenced by disturbances in the water from the agitation caused by steam-boats or other causes ; and also to ensure that the whole range of the tide can be recorded. When the gauge is fixed in a position where there is a sufficient depth at low water to allow full play to the float there is no difficulty, but where the gauge has to be fixed at some point on the coast where there is no wharf or quay, and to which the water does not extend at low tides, other means have to be adopted. Wave motion is most felt where the float acts in shallow water, the records on the gauge being so much afi'ected by this as to give considerable trouble in obtaining the true tide curve. For the tide gauges for the survey of the Grulf of St. Lawrence this . difficulty was overcome by fixing the gauge on shore and leading the tide to it by a trench or piping, the water being admitted to the cylinder in which the float acted through a rose with small holes so arranged as to reduce or efface the motion of waves ; or by sinking a well at high water mark below the level of the lowest tides, and excavating a trench across the shore, the tide being led to the well by means of piping laid along it. This piping consisted of fir logs 12 inches in diameter, with a three-inch hole bored along the centre. A length of old boiler was placed vertically in the well to form an open shaft for the water in which heating was provided to prevent freezing of the water. It was also found necessary at some station^ to construct a small crib of timber, and to fix on this a shelter for the instruments. In these Canadian waters special precautions had to be taken to prevent damage to the machine by floating blocks of ice in winter. The vertical pipe in which the float works is made of galvanized iron tubing 6 inches in diameter, enclosed in a vertical iron cylinder 3 feet in diameter. This iron cylinder is lined inside with wood lagging to make it non-conducting, and is kept warm inside to prevent its freezing by an oil lamp having six wicks. The gauge house also is heated by a small oil heater. A full description of the gauges used for the Canadian survey is given in a paper by Mr. Dawson in Vol. CXLIX. of the Minutes of Proceedings of the Institution of Civil Engineers, 1902 ; and in the Eeports of the Survey of Tides in Canadian Waters for 1895. CHAPTEE XIV. SECONDARY UNDULATIONS AND STORM WARNINGS. Beyond the undulations of the water due to tidal action there are smaller oscillations in bays connected with the sea, and on inland lakes. These secondary undulations, although the subject of much investigation, have not in all cases been satisfactorily accounted for. They may be divided into two classes : (1) those that appear at regular periods and without much variation in height ; (2) those that occur only occasionally, and of varying periods and heights. In some cases these undulations can be directly traced as the result of storm waves which have occurred in the ocean at long distances away ; in other instances they have been traced to variations in the atmospheric pressure; and it has also been suggested that they are due to the slight seismic disturbances that are always more or less going on in the crust of the earth. Seiches. — The phenomenon of these secondary undulations was noted in the middle of the last century by Duillier as occur- ring on the Swiss lakes, the name locally given to them being Seiches. In 1804 an account of them was published by Vaucher, the result at which he had arrived after much investigation being, that they were common to all lakes ; that they recurred at all seasons of the year, but most frequently in spring and autumn, the largest oscillations taking place in summer; and that the periods were from 20 to 25 minutes; that the condition of the atmosphere was the governing cause, the pressure being less over one part of the lake than over the other ; and that if the (Change occurred suddenly the water which thereby had been set in motion did not come to rest until after a number of oscillations. The first systematic observation of these seiches was made by Professor Forel in 1876 at the Port of Merges on Lake G-eneva by means of an instrument called a plemyameter. A small tank SECONDARY UNDULATIONS AND STORM WARNINGS. 165 fixed on the shore was connected with the water in the lake by- means of a syphon having a horizontal glass tube connected at each end respectively with the tank and with the lake by india- rubber tubing. In the glass a weighted cork float was placed, this float indicating when the water was rising or falling in the lake by its position in the tube. This instrument was supple- mented by a very delicate tide gauge, which recorded the amplitudes of the undulations. The observations made with these instruments showed that seiches consist in a rocking of the whole water of the lake throughout its length, breadth, and depth. The oscillation sometimes extended throughout the whole length of the lake, and at other times there were two nodal lines about which the movement occurred. The period of the former was 73 minutes, and of the latter 35. Oscillations across the breadth of the lake were also noted, having periods of ten minutes. The instruments used by Forel showed that vibrations caused by steamers on the lake continued for 2 to 3 hours after they were first caused by the boat, and that they commenced 25 minutes before the boat approached the pier where the gauge was situated and continued until the steamer was six miles distant.^ The theoretic law deduced from the observations for the duration of these seiches was, that the semi-period of an oscilla- tion is equal to the time that a body travelling at the rate which it would acquire falling from a height, under the action of gravity, equal to half the mean depth of the water in the lake, would take to tra,verse the length of the lake. Thus, the duration of a seiche is proportional to the length of the lake, and is inversely propor- tional to the square root of its mean depth. Secondary Undulations. — The author has traced the existence of these pulsations or oscillations in the non-tidal Broads of Norfolk, where he found that there exists a variation in the level of the water from half an inch to 2 and 3 inches, which occurs periodically ; that this ebb and flow is not coincident with the ebb and flow of the tides in the river with which the broad is connected; and that it takes place when the atmosphere is normal. On Loch Trieg, in Inverness, during the British Lakes Survey, Dr. Johnston and Mr. J. Parsons observed a slight periodic variation in the level of the water, the amplitude of which was • "Archives des Sciences Naturelles." Geneva. 1874. 1 66 TIDES AND WAVES. 0-56 inch and the period 9 50 minutes. The attention of the observers was first called to the fact by the periodic covering and uncovering of some small stones on the shore. This loch is 6 miles long and | mile wide, the mean depth being 436 feet. Mr. W. Bell Dawson, who has charge of the tidal survey of the Canadian waters, found ^ that secondary undulations were plainly indicated on the curves shown on the self-registering tide gauges in the Gulf of St. Lawrence, their magnitude being in proportion to the amplitude of the tides. These were specially noticeable in the Bay of Fundy at St. John's, where they have an amplitude of a foot and a period of forty minutes, the range of the tide on this part of the coast being 28 feet. These minor undulations often continue for a week at a time. At Quaco, about 12 miles to the north, the period is only 12^ minutes. At Halifax, on the Atlantic coast, the periods vary from 5 to 25 minutes, with a range of 4 inches ; the range of the tide here being 6 feet. These secondary undulations are almost continuously present at Halifax, and it is exceptional for the tide curve to be free from them. In the Grulf of St. Lawrence the undulations are present at most parts of the coast, but are small and irregular. In January, 1899, the undulations observed were exceptionally large; at Halifax the range being 1-15 to 1-20 foot, the tidal range being at the same time 3-60 feet. At St. Paul Island, in the Gulf of St. Lawrence, the range of the undulation was 0"23 foot, the range of the tide being 2-20 feet. At Yarmouth the range of the secondary undulation was 4-20 to 4-70 feet, and of the tide at the time 1040 feet. At St. John, N. B., the maximum range of the secondary undulation was 1"90 foot, and of the tide at the time 180 feet. The character of the undulations on Lake Superior has been investigated by Mr. Napier Denison, and for the purpose of tracing their curves he had two self-recording gauges constructed, one being fixed at the mouth of the River Humber and the other at the entrance to the Burlington Canal. It was found that a rise and fall of about 4 inches in water level, with 20-minute periods, corresponded with a slight change in the atmospheric pressure. Mr. Denison found that these lake undulations are ' " Secondary Undulations recorded by Self-registering Tide Gauges." W. Bell Dawson, Trans. Boyal Soc, Canada. May, 1895. "Illustrations of Remarkable Secondary Undulations as registered on recording Tide Gauges in the Eegion of Nova Scotia." W. Bell Dawson, Trans. Soyal Soc, Canada. 1899. SECONDARY UNDULATIONS AND STORM WARNINGS. 167 of a more sensitive character than the indications of approaching storms given by the barometer. He came to the same conclusion as Professor Forel, that these oscillations generally are due to the action of atmospheric waves or billows in passing over the surface of the lakes, which tend to form minute undulations upon the surface corresponding in length to these billows, and becoming magnified when they reach narrower and shallower portions until finally they assume the proportions recorded.^ On Lake Huron Mr. Denison found a regular ebb and flow taking place, with a uniform rise and fall of about 3 inches with a period of 18 minutes. On Lake Superior these secondary undulations are very pronounced. They range from 3 to 4 feet, and this variation has been known on some occasions in periods of 10 to 15 minutes. Fluctuations in level of from 6 to 12 inches occur very frequently within a few minutes. Owing to its greater depth, the fluctuations on Lake Superior are not as great as those upon Lake Erie, which is shallower. These are attributed by Graillard to rapid local changes in the atmospheric pressure.^ At Malta the irregular variations of the water in the sea inlets are often sufiiciently great to completely mask the slight undulation of the lunar tide. At certain times in the harbour there is a regular ebb and flow, with periods of 23 minutes, and 15 inches range. This variation in the water level causes a current which changes its direction every half period, or say 11^ minutes. At Bombay the tide gauge shows by irregularities in the curve traced that there are oscillations in the sea with periods varying from 2 to 15 minutes. On Lake Baikal, in Eussia, which is 1561 feet above sea level, and which has a depth of 820 feet and a length of 420 miles, with a width of from 10 to 60 miles, a distinct ebb and flow has been traced. In the enclosed harbour of Sydney, Australia, a 26-minute period undulation has been observed, which is supposed to be due to the combined effect of wind and current influences exerted at a considerable distance. Mr. Napier Denison considers that a study of these secondary 1 " The Great Lakes as a Sensitive Barometer.'' Napier Denison. Canadian Institute. Feb., 1897. 2 " Harbours on Lake Superior." Gaillard. 1904. i68 TIDES AND WAVES. undulations in conjunction with the readings of the barometer and anemometer would be of great assistance in forecasting coming storms. Undulations preceding Coming Storms. — In the American lakes it was found that exceptional secondary undulations which occurred occasionally indicated the presence of some great atmospheric disturbance, and gave warning some time before the barometer of a coming storm. An example is given where the centre of the approaching storm, as indicated by the curve of the undulation, was at the time situated over Florida, 1300 miles distant ; and on another occasion a heavy southerly gale was indicated by the curves three days before it occurred. On Lake Superior fishermen and mariners who live near the Humber observing station have learnt to take advantage of these undulations, and consult the charts before going out to set their nets. In the open ocean wave motion sometimes travels at a greater rate than that of the wind that causes the disturbance, in which case a ground swell precedes and predicts the arrival of a storm. Colonel Eeid, in his book on the " Development of the Law of Storms," states that at Bermuda the hurricane of 1839 was preceded by rollers breaking on the shore three days before the storm reached the island. In a cyclonic storm which devastated Kingstown in Barbadoes, in 1898, the surf was roaring on the coast of St. Vincent 20 hours before the cyclonic centre reached it. The south-west wind, or Pampeiro, on the coast of South America is felt several hours before the storm arrives, the sea beginning to rise and break over the bar at the mouth of the Rio Grande. A very heavy swell occasionally sets into the Bay of Colon in the West Indies without any gale blowing or indication of a storm being given by the barometer. When this is the case a heavy "norther" follows, and no vessel can then remain in safety in the harbour. (West Indian Pilot.) On the coast of the Bay of Biscay a westerly swell is nearly always the prelude to a gale and heavy sea from the north-west, and precedes it sometimes 24 hours. A heavy sea gets up during a calm, rolling in on the shore and breaking in 20 fathoms, closing the ports and estuaries. SECONDARY UNDULATIONS AND STORM WARNINGS. 169 On the south-east coast of Newfoundland and at the entrance to the Bay of Fundy the wind occasionally causes a drift in an opposite direction to that from which it is blowing, and "the current sets into the weather" some time before the arrival of the gale. A strong set to the south-east is recognized by the fishermen as a sign that bad weather will follow from that direction, and if the current continues to run into the wind after it begins to blow it indicates that the gale will be heayy.^ On the coast between North Carolina and Cape Hatteras the currents, which are there largely governed by the wind, begin to run strongly several hours in advance of the wind that causes them. In summer a change of the current from north-east to south-west is always taken as a true indication of an approaching north-east wind. Dr. Vaughan Cornish records that frequently at Bournemouth a long swell breaking on the shore precedes and predicts the arrival of a storm.^ This is probably due to a storm brewing in the Atlantic. In Aberdovey Bay on the west coast a southerly gale is frequently preceded by a heavy sea on the coast. ' " Currents on tlie Coast of Newfoundland." Report Department of Marine. Ottawa. 1904-5. ^ " On the Dimensions of Deep Sea Waves.'' Geographical Journal, May, 1904. CHAPTEE XV. THE TIDES AS A SOUKOE OF POWER. It has often been considered that the tides might be economically utilized for working machinery ; and the prospect has been held out that when our coal supply fails, an unlimited source of energy will be available from this source. The cost of the necessary installation for making use of the rise and fall of the water, and the many obstacles to be encountered, have, however, so far prevented use being made of the tides for this purpose, except to a very limited extent. The difference day by day in the time at which the tides occur, and the variation in the height at springs and neaps, render the adjustment of labour difficult. Any attempt to utilize the tides on a large scale with the existing mechanical appliances, cannot be considered as coming within the lines of commercial economics. There are, however, many examples of small installations in use, principally for grinding corn, for which power is obtained from the tides. The machinery in use for this purpose consists either of water wheels or turbines — in some cases the outflowing water of a reservoir being used — and in other instances both the inflowing and the outflowing tide being made suitable. This was done with the wheels in the side arches of Old London Bridge, used for raising water for the supply of the city. These wheels rose and fell with the tide, and were worked by the current both on the flow and ebb. The rise and fall of floating hulks has also been thought to be a feasible source of power for generating electricity; and schemes have been brought forward for working motors, by compressing the air, in tanks placed near the sea shore by the rising tide. THE TIDES AS A SOURCE OF POWER. 171 The most economic form of reservoir for holding the water is by placing a dam with sluices across the mouth of a tidal creek. The gross power developed by filling and emptying reservoirs between the period of high and low water, may be computed at less than two horse-power for every acre of storage room, or 43,560 cubic feet. Allowing a rise of tide of 16 feet spread over six hours, and taking half this as the average head, and the weight of salt water as 64 lbs. per cubic foot, the result would be — sq. ft. ft. lbs. 43,560 X 8 X 64 = 1-87 6 X 60 X 33,000 If with floating hulks, having a displacement of 1000 tons, the gross power exerted with a rise and fall of a 16-foot tide running for six hours would be — tons lbs. ft. H.P. 1000 X 2240 X 16 ^ 2-07 6 X 60 X 33,000 Tidal Mills or " Axroyenos " for grinding corn have been in existence for a long period in Spain on the marshy shores of Andalusia. The action of these' wheels resembles that of the modern turbine. The wheel, which is generally about 6 ft. in diameter, is fixed horizontally in a cylindrical brick chamber about 8 ft. high, and connected with the mill stone by a vertical spindle. The water is admitted tangentially through an opening in the brick work and impinges on wooden blades about 3 inches deep, hollowed out to catch the water. The tidal reservoir, which holds from a half to a million cubic feet, is formed by embanking the creeks, into which the water is allowed to enter on the rising tide, through an opening 8 feet wide, which is held up on the ebb by a self-acting door. The power exerted on the wheel averages 0-75 H.P. The speed of rotation is fifty revolutions a minute, and a single pair of stones grinds 1^ bushels an hour. The machine only gives off an efficiency of about 10 per cent, of the theoretical power. A more efficient type of wheel is now coming into use, having a diameter of 3 feet, the efficiency being about 0-35, and with a rise of tide of 10 feet developing 2^ H.P.^ In Nicholson's Operative Mechanic, published in 1829, is an account of a tide mill which was erected on the Thames at East » The Engineer, Jau. 13, 1905. 172 TIDES AND WAVES. Greenwich for the purpose of grinding corn. A series of sluices were constructed in the bank of the river having a waterway of 40 feet, which admitted the water on a rising tide to a reservoir having an area of four acres. The inflowing tide operated a water wheel 26 feet wide and 11 feet in diameter, with thirty-two floats. This wheel weighed twenty tons, and being so constructed as to float, was raised and lowered by the action of the tides so as not to become drowned. The rise of the water at spring tides was 20 feet. When the tide began to fall, the water was allowed to run out of the reservoir into the river, the rotary motion being thus increased. Special gearing was provided by which the interior motions of the mill were preserved in the same direction. This installation worked eight pairs of stones. At Bembridge in the Isle of Wight embankments were formed enclosing a large body of water over a tract of low land in the estuary. On the rising tide the water entering through a sluice filled the area. At the turn of the tide the doors of the sluice automatically closed. The impounded water then flowing out through a raceway drove a breast wheel. The same process has been in use in a small tidal creek connected with the Eiver Colne, known as the Eoman River ; and also near Burntisland at a place still known as "Sea Mills." The power here was obtained both on the rising and falling tide. There is a tidal mill near Lubeck in the Bay of Fundy. The bed of the mill pond is about 15 feet above low water. When the tide rises, self-acting gates in a dam across a creek are opened, and the water flows into and fllls the pond; at high water the gates are closed, the pond having been filled with sufficient water to run the mill for 8 hours with a fall of 15 feet. Air compressed by the rising tide in a reservoir built on the margin of the sea coast has also been made available for driving a motor used for pumping water from a well to a reservoir, and for generating electricity. A project has recently been described in the Genie Civil for utilizing the tides of the river Seine as a source of power. The scheme consists of making use of the tidal embankments constructed for guiding the channel through the estuary, and connecting these with the shore on either side, and so forming two large reservoirs. It is proposed that each of the tidal basins so formed should be divided into two parts by a dam — one being a high-water basin, the level of which would vary from high water THE TIDES AS A SOURCE OF POWER. 173 to one third of the tidal range below high water ; and the other a low-water basin, the level in which would be from one-third of the tidal range to low water. The discharge from the high to the low water basins would actuate a series of turbines. The average height of tide available is placed at 10 feet. The area of each of the reservoirs would be about 1000 hectares or 2471 acres, and the H.P. given off during the six hours of the rising tide about 6000 H.P., or 2\ H.P. per acre. The estimate for the division dam, turbines, sluices, and other works is put at £72,000, or £12 per H.P. The annual cost of the upkeep and interest on capital is put at 10 per cent., or £1-20 per H.P. To this has to be added the letting value of the reclaimed land for agricultural purposes at £1 an acre, equal to £40, making the total of £1"60 at which 1 H.P. could be delivered at the turbines. If, however, the scheme is treated independently of the training of the channel through the estuary, the cost of the walls for enclosing the reservoir would have to be added, and this is estimated at £280,000, making the total cost of the installation £352, and the annual cost of the upkeep, interest on capital, and rent of land £6'27 per H.P. It is suggested that the power thus generated could be utilized to work the dynamos for electric lights, and providing power at the ports of Harfleur and Havre, and for industries that might be established on the sides of the reservoirs. A more detailed account of this scheme is given in the Engineer of January 13th and 20th, 1905. Attempts have also been made to utilize the waves breaking on the sea shore to obtain power. A machine for this purpose has been recently erected at Santa Cruz, California, for pumping water. On the cliffs 30 feet above high water two wells were sunk to a depth of 6 feet below low water, communicating at the bottom with the sea. In one well a force pump is placed, and in the other a float weighing 1600 lbs. These are connected with a beam 60 feet long, which is provided on the land end with a pair of small wheels. As the waves roll in the well fills, raising the float ; and as the water recedes the float acts on the piston of the force pump, sending the water 125 feet above sea level. The motor develops 4 H.P.^ ' Tlie Engineer, June 25, 1905. APPENDIX I. LIST OF BOOKS, PAPEKS, EEPORTS AND PAM- PHLETS RELATING TO TIDES AND WAVES CONSULTED IN THE PREPARATION OF THIS BOOK. PHILOSOPHICAL TRANSACTIONS. Papers hy Bev. Dr. Whewell. 1833. Essays towards a first approximation to a map of co-tidal lines. First Series. 1834. On the Empirical Laws of the Tides in the Port of London. Second Series. 1835. Results of Tide Observations. Third Series. 1836. On the Empirical Laws of the Tides in the Port of Liverpool. 1836. On the Solar Inequality and on the diurnal inequality of the Tides at Liverpool. Fifth Series. 1836. On the results of an extensive system of Tide observations made on the coasts of Europe and America in June, 1835. Sixth Series. 1837. Researches on the Tides. On the Diurnal Inequality of the height of the tide, especially at Plymouth and Singapore, and on the mean level of the sea. Seventh Series. 1837. The Progress of the Diurnal Inequality Wave along the Coasts of Europe. Eighth Series. 1838. Ninth Series. 1839. On the Laws of Low Water at the Port of Plymouth, and on the permanency of Mean Water. Tenth Series. 1839. On certain Tide observations made in the Indian Sea. Eleventh Series. 1840. Additional note on the same. 1840. On the Laws of the Rise and Fall of the Sea's Surface during each Tide. Twelfth Series. 176 APPENDIX I. Papers hy Professor G. H. Darwin. 1878. Parts I. and II. On the bodily tides of viscous and semi-elastic fluids, and on the ocean tides upon a yielding nucleus. 1879. Parts I. and II. Secular changes in the elements of the orbit of a satellite revolving about a tidally distorted planet. Part VIII. Review of the tidal theory of evolutions as applied to the earth and the other members of the solar system. 1881. On the tidal friction of a planet attended by several satellites, and on the evolution of the solar system. 1868. On the tides of Bombay and Kurachi, by W. Parkes. Papers hy Sir J. W. Luhhoch. 1831. Tides: Port of London. 1834. On the Tides. 1836. On the Tides of the Port of London. 1837. On the Tides. Papers by Mr. T. G. Bunt. 1838. Description of a new Tide Gauge erected on the bank of the River Avon. 1866. Discussion of Tide Observations at Bristol. 1666. Essay of Dr. John Wallis, exhibiting his hypothesis about the Flux and Reflux of the Sea, taken from the consideration of the common centre of gravity of the earth and moon. 1831. An Account of operations carried on for ascertaining the difference of level between the River Thames at London Bridge and the Sea; and also for determining the height above the level of the sea. J. A. Lloyd. 1831. Description of a Graphical Register of the Tides and Winds. H. E. Palmer. 1842. The Laws of the Rise and Fall of the Tide in the River Thames. G. B. Airy. 1845. The Laws of the Tides on the Coast of Ireland as inferred from the Ordnance Survey. G. B. Airy. 1847. Observations on the Tides of the Irish Sea, and upon the similarity of Tidal phenomenon in the Irish and English Channels. F. W. Beechy, R.N. 1857. Tides in the English Channel and North Sea. F. W. Beechy, R.N. 1854. On the Effect of the Pressure of the Atmosphere on the mean level of the Ocean. Sir J. C. Ross. Part I. APPENDIX I. 177 1861-77. On the Tides of the Arctic Seas. Rev. S. Haughton. Part I., 1861. Part II., 1862. Part III., 1866. Parts IV. and v., 1874. Part VI., 1875. Part VII., 1877. 1866. On the semi-diurnal Tides of Frediksdal, near Cape Farewell in Greenland. Eev. S. Haughton. BRITISH ASSOCIATION REPORTS AND PAPERS. 1832. The Tides. J. W. Lubbock. 1836-7. Recent Observations on the Tides. J. W. Lubbock. 1837-8, 1844. Committee on Waves. J. Scott Russell. 1838. Measurements to Ascertain the Level of Mean High Water. Whewell. 1838. Discussion on Tides. Whewell. 1839. On the Sum Assigned for Tide Calculation. Bunt. 1841. Bristol Tides. Bunt. 1841. Leith Tides. Ross. 1841. Firth of Forth and East Coast of Scotland. J. Scott Russell. 1847. Expedition for the Purpose of Completing Knowledge of Tides. WheweU and Ross. 1862. Tide Observations at the Port of Hull. 1864. Tidal Observations in the Humber and in the Rivers Trent and Ouse. Oldham. 1868, 1870, 1871, 1872, 1876. Harmonic Analysis of Tidal Observations. Thompson. 1875. Tides in the River Mersey. 1878-9, 1880-1. Stationary Tides in the Enghsh Channel and North Sea. Shoolbred. 1883-5. Harmonic Analysis of Tidal Observations. Darwin. 1884-6. Tides in the English Channel and Coast of France. Shoolbred. 1885-6, 1888-9, 1900. Tidal Observations in Canada. 1888. On Certain Laws Relating to the Regime of Rivers and Estuaries, and on the Possibility of Experiments on a Small Scale. Osborne Reynolds. 1889-90. Committee Appointed to Investigate the Action of the Waves' Currents on the Beds of Foreshores and Estuaries by means of Working Models. Osborne Reynolds, Secretary. Ditto. Second Report. 1895. The Effect of Wind and Atmospheric Pressure on the Tides. Wheeler. 1896. Report on the Tides. Wheeler. 1904. Tidal Regime of the Mersey. J. N. Shoolbred. 178 APPENDIX I. MINUTES OF PROCEEDINGS INSTITUTION OF CIVIL ENGINEERS. Description of the River Witham and the Estuary. W. H. Wheeler. Vol. xxviii. 1868. The Tide Gauge. Tidal Harmonic Analyzer and Tide Predicter. W. Thompson. Vol. Ixv. 1881. The Bore of the Tsien-Tang-Kiang. "W. 0. Moore. Vol. xcix. 1889. Tide Gauges in Northern Climates and Isolated Situations. W. Bell Dawson. Vol. cxlix. 1902. ADMIRALTY PUBLICATIONS. Manual of Scientific Enquiry. Article on the Tides. G. H. Darwin. 1886. Tide Tables for the British and Irish Ports. Times and Heights of High Water for Principal Places on the Globe ; with Treatise on Tides by Dr. Whewell. Methods of Calculating Allowances for Declination, Parallax, etc., of Sun and Moon ; Tidal Streams along the British Coast, etc. Published annually. Directions for Reducing Tidal Observations. Burdwood. London. 1865. Sailing Directions for the Various Seas throughout the World, issued in Separate Volumes by the Hydrographic Department of the British Admiralty. Potter. London. G. B. Airy on Tides and Waves. Uncyclopaedia Metropolitana. Gr. H. Darwin on Tides. 1886. Encyclopaedia Britannica. The Mathematical Principles of Natural Philosophy, and System of the World, by Sir Isaac Newton. Translated into English by A. Motte. Edited by W. Davis. London. 1819. Astronomy and the Tides. Robinson's "Mechanical Philosophy." Vol. iii. 1822. Time and Tide. A Romance of the Moon, by Robert S. Ball. Society for Promoting Christian Knowledge. 1889. The Tides and Kindred Phenomena of the Solar System. Substance of Lectures delivered in 1897 at the Lowell Institute. G. H. Darwin. Boston, Mass. London. J. Murray. 1898. On the Propagation of Waves. G. J. Stoney. Dublin. 1861. Tidal Rivers: their Hydraulics, Improvement, and Navigation. W. H. Wheeler. London. 1893. APPENDIX I. 179 The Sea Coast: Destruction; Littoral Drift; Protection. W. H. Wheeler. London. 1902. Chapter II., Action of Shore Waves. Etude sur la Navigation des Riviferes a Mar^e. M. Bouniceau. Paris. 1845. Du Mouvement des Ondes et des Travaux Hydrauliques Maritime. Par A. R. Emy. Paris. 1857. Etude sur les Mouvements de Maries dans la Partie Maritime des Pleuves. M. L. Partiot. Paris. 1861. Etude sur les Rivieres a Maree et sur les Estuaires. H. L. Partiot. Paris. 1892. Do. Complement de 1894. R^cherches Hydrauliques Relatives aux Remous et la Propagation des Ondes. Darcy et Bazin. Paris. 1865. Les Lames de Haute Mer. C. Antoine. Paris. 1879. Etude Pratique sur les Maries Fluviales, notament le Mascaret. Comoy. Paris. 1881. Monographic du Regime Hydraulique de la Seine Maritime. Belle- ville. Congr^s International des Travaux Maritimes. Paris. 1889. Annuaire par le Bureau des Longitudes. Issued annually. Article on the Tides. Paris. 1904. Etudes de Ph&omenes de Maree sur les C6tes Nderlandaises. J. P. van der Stok. Utrecht. Kemink & Zoon. 1905. Great Britain's Coasting Pilot. Granville Collins. London. 1779. Manual of Tides and. Tidal Currents. Haughton. Cassell & Co. London. Elementary Treatise on the Tides. J. Pearson. J. D. Potter. London. 1881. Computation of Tides at Fleetwood. J. Pearson. Royal Irish Academy. 1879 and 1883. Three Years' Observations of the Tides at Fleetwood. Do. 1880. Manual of Tidal Observations and their Reduction by Harmonic Analysis. Baird. 1886. Elementary Theory of the Tides. T. K. Abbott. London. Longmans, Green, and Co. 1888. Solar and Lunar Diurnal Tides on the Coast of Ireland. S. Haughton. Trans. Royal Irish Academy. 1854. The Tides. Evening Lectures, British Association, Southampton, 1882. Sir W. Thompson. Printed in Nature Series, Popular Lectures and Addresses. Vol. iii. Navigational Affairs. London. 1891. A Suggested Improvement of Current Theories of the Tides, by J. H. S. Moxley. Rivingtons. London. 1898. The Tides Simply Explained, with Practical Hints to Mariners, by Rev. J. H. S. Moxley. Rivingtons. London. 1899. i8o APPENDIX I. On the Movement of the Water in a Tidal River, by W. Cawthorne Unwin. 1883. E. and P. K Spon. London. Manual of Kaval Architecture, by W. A. "White. (Chapter V., Deep Sea Waves.) Second Edition. London. 1882. The Dimensions of Deep Sea Waves and their Relation to Meteoro- logical and Geographical Conditions. Vaughan Cornish. Geo- graphical Journal, May, 1904. Report of the Royal Commission upon Determining the Degrees of Rise and Fall of the Sea Level for the Year 1890. Published in Be IngMeur for 1891, No. 26. The Hague. The Influence of the Wind, both in Direction and Pressure, upon the Sea Level. E. Engelenborg. De Ingenieur, September 26, 1891. The Hague. Relation between the Barometric Pressure and the Strength and Direction of Ocean Currents, by Lieut. H. Beehler, U.S. TSTavy. Chicago Meteorological Congress, 1893. An Investigation of the Tides between the Ower and Portland from Observations made during the progress of the Survey on the South Coast of England, by Captain Sheringham, R.N. Nautical Magazine, August, 1851. Notes on the Tidal Stream at the Entrance to the English Channel. P. Aldrich. J. D. Potter. London. 1890. Remarks on the Tidal Phenomena of the River Severn. F. W. Beechy. 1849. Handy Book of the Tides. W. B. Whall. Philip and Son. London. Tide Charts of the English and Bristol Channels and Entrance to the Thames. A. H. Percy. J. D. Potter. London. Tidal Streams for the whole of the British Coasts, Ireland and North Sea. Brown and Son. Glasgow. 1905. The Phenomena of the Tides ; their Prediction, their Cut and Overflow considered in relation to Atmospheric Pressure and Tidal Currents. Paper read before the Shipmasters' Society. London. January 18, 1894. W. N. Greenwood. The Tides of the Bay of Fundy. Transactions of the Nova Scotia Institute of Natural Science, Vol. vii. Part I. 1886-7. M. Murphy. Tides in the Bay of Fundy. Report on Geology, New Brunswick. 1895. R.Chalmers. Tide Levels and Datum Planes in Eastern Canada. W. Bell Dawson. Proceedings Canadian Society Civil Engineers. 1903. Notes on Secondary Undulations recorded by Self-registering Tide Gauges, and on Exceptional Tides in relation to Wind and Barometer. Trans. Boyal Society of Canada, 1895. W. Bell Dawson. APPENDIX I. i8i Reports on the Survey of Tides and Currents in Canadian Waters made to the Department of Marine and Fisheries, Ottawa, by W. Bell Dawson. 1894-1902. Character and Progress of the Tides in the Gulf and River St. Lawrence. W. Bell Dawson. Durie and Son. Ottawa. 1897. The Currents of the Gulf of St. Lawrence. Published by order of the Minister of Marine and Fisheries. Ottawa. 1900. The Currents on the South-east Coast of Newfoundland. W. Bell Dawson. Published by order Department of Marine and Fisheries. Ottawa. 1904. Illustrations of Remarkable Tidal Undulations- in January, 1899, as registered on recording Tide Gauges in the region of Nova Scotia. Trans. Moyal Society, Canada, 1899. W. Bell Dawson. A Probable Solution of the Secondary Undulations found upon Self- recording Tide Gauges. Proc. Canadian Institute, 1897. Napier Denison. The Great Lakes as a Sensitive Barometer. Proc. Canadian Institute, 1897. N. Denison. Seiches in the Bay of Fundy. American Journal of Science, 1897. A. W. Duff Handbook of Cyclonic Storms in the Bay of Bengal. J. Elliott. Government Printing Office, Calcutta. 1890. APPENDIX II. VELOCITY OF PEOPAGATION OF TIDAL WAVES. TABLE I. Deep Sea "Waves. Formula for ascertaining the rate of propagation of tidal waves in the open ocean and smaller seas :— = \/2^ d ^2 = ^32 X d V = velocity of the wave in feet per second, g' = 32 approximately the measure of gravity (32-1908). d = the depth of the water in which the wave is propagated. TABLE II. Shoee or Beeakikg Waves. -^ V = velocity in feet per second. A = the height of the wave from trough to crest. APPENDIX II. 183 TABLE III. Examples op Velocity op the Tidal Wave in the Open Ocean. Distance, Average Velocity tidal wave. Locality. Nautical deptli in Feet per miles. feet. Nautical miles per hour. Feet per seconii. second by formula V = VsrX 2400 15,400 369 623 706 40° S. to the Equator ) Cape St. Vincent to Ioe-\ laud, 15° to 53° . ., 2880 12,000 480 811 619 Indian Ocean : j St. Paul Island to Co4 3000 12,000 300 507 620 lombo,40°S. tolO°N.) Pacific : \ Southern Ocean to 1 Behiiner Strait, 40° S. | 5400 15,780 600 912 710 to50°N j English Channel : \ Entrance to Hastings / 260 246 42 70 88 North Sea : 1 Shetland Islands to[ 420 312 60 101 99 Plambro' Head . . .) Plambro' to Harwich . 150 78 20 34 49 Irish Sea : 1 Smalls Light to MuU 180 288 36 61 96 of Galloway . . . . | Bristol Channel : \ Lundy to Portishead ./ 75 90 37 62 54 APPENDIX III. TIDAL DATA. TABLE I. Variation in the Mean Level op the Sea round the English Coast. Below. Feet. Weymouth . . 0-089 Pembroke. 0-096 Holyhead. 0-188 Torquay . . . 0-217 Dover . ... 0-233 Berwick ... . . 0-261 Scarboro' . . 0-316 Portsmouth .... 0-348 Shoreham .... 0-461 Weston-super-Mare . .... 0-529 Penzance 0-646 Liverpool (local datum obtained from self-register gauge) , , 0-650 Falmouth 0-051 Plymouth. . .... . 1-009 Silloth . . 1-283 Above. Feet. Hull 0-038 Sunderland 0-064 Southampton ... . . . 0-141 Eamsgate . ... 0-324 Shields . 0-340 Lowestoft . 0-732 Sheemess. 0798 Lynn Cobb 0-840 Grimsby . . ... .... 1-164 Harwich ... . . 1-233 London Bridge ... . . . . ... 1-790 APPENDIX III. 185 TABLE II. The Datum op the Level of Low Watee Ordinary Spring Tides USED FOE the ADMIRALTY TiDE TABLES. Port. Above or below. Datum. ft. in. Brest. . . . 4 9 Below L.W.O.S.T. Belfast . . . 12 8 Below level of roadway of old pier Carrickfergus. Chatham . . 7 ^h Below Ordnance Datum. Devonport . . . 8 5 JJ 5) 3> Dover .... 8 5 »> 30 20 2 9-90 261-0 34-80 26-8 7-50 7 Very fresh . . 35 24 3 11-55 304-5 40-40 24-2 7-53 8 Moderate gale . 44 30 5 14-55 382-8 5100 30-6 7-53 9 Strong gale . . 59 40 8 19-47 513-3 68-44 41-0 7-50 10 Very strong gale 95 67 23 31-35 826-5 110-20 66-1 7-50 11 Violent gale . . 118 80 32 The proportioi 18 of these -wa^ es is so 12 Hurricane . . 147 100 50 various that av< srages c innot t e given APPENDIX VII. Table op English and Feench Nautical Measures. Nautical mile . , . 607698 feet = 11509 statute mile. Statute „ 5280-0 „ = 0-868 nautical mile. Kiiot . . . . .1 nautical mile per hour. Fathom (6 feet) . 0547 metre. Cable 5!, nautical mile. Metre . . . 3281 feet . . 0-3048 reciprocal. KUometre . . . 06214 statute mile . 1-6093 „ .... 0-581 nautical mile . 1-821 Feet per second into metres per second . 0-3386 3-281 „ „ statute miles per hour 0-682 1-467 „ „ nautical „ „ 0-592 1-690 Metres per second into statute miles per hour 2-2363 0-447 Kilometres per hour into feet per second . 0-9114 1-097 Nautical miles per hour into statute miles 1-1509 0-8688 Nautical miles. Degree of latitude— at the equator 59-694 Latitude 45° . 59-866 ,. longitude— latitude 1° 59-99 „ 10° 59-09 „ 20° 56-38 „ 30° 51-96 „ 40° 45-96 „ 50° . 58-57 „ 60° 30-90 „ 70° 20-52 „ 80° 10-42 „ 90° 0-00 g =z 32-191in latitude of Greenwich. Velocity in feet per second acquired in one second by a body falling freely under the influence of gravity — V2 = 2grH (head or height) V =8-022/^ n ^' " ~ 64-381 INDEX Abbot, theory of the tides, 26 Admiralty datum, 70 Tide Tables, 19, 1S8 Aeger, 141 Age of the tides, 50 Airy, 24, 14, 16, 17, 24, 25, 118, 176 Amazon, river, 94, 144 Amplitude of waves, 109 Annitaire de Maries, 86 Antoine, 22, 24, 115, 119 Aphelion, 33, 51 Apogee, 36, 51 Arctic Seas, 39 Arroyenos, 171 Atlantic Ocean, 38, 57 Atmospheric pressure and tides, 74, 30, 85 Australian tides, 75 Avon, river, 3 Axmouth, level of sea, 71 B Baikal, Lake, tides, 167 Baird, 28 Ball, 34 Barometer and tides, 85, 30, 74 Bazallgette, 99 Bazin, 23 Bede, 7 Beechy, 93, 153 Beehler, 85 Belleville, 99, 104, 105 Bembridge tidal mill, 172 Bengal, Bay of, storm-waves, 137 Bernoulli, 15, 16, 18, 157, 160 Bidone, 22, 141 Bores, 141 Bouuiceau, 145 Breaking waves, 117, 122 Brest tidal observations, 17 Bristol Channel currents, 67 British Association, 22, 24, 26, 29, 30, 31, 32,70 Brodie, 120 Bruce, 145 Bunt, 24, 162, 175 Bure, river, 101 Caspian Sea tides, 76 Cassini, 17 Cavalleri, 15 Centrifugal force, 42 Chepstow, tides, 73 Chinese theory of tides, 7 Chlorine, 103 Clyde, river, 3, 95, 96, 99, 192 Coastguard, 17 Coast waves, tidal. 111 wind, 117, 122 Collins, Grenville, 63 Comoy, 105, 139, 140 Conjunction and opposition, 47 Coode, 118, 127 Copernicus, 5, 7 Cornish, Vaughan, 154, 169 Costal shelf, 63 Cotidal lines, 20, 25 Currents, tidal, 63 in rivers, 96 , formula for velocity, 66 , standard ports for, 68 Cycles, lunar, 37 Cyclones, 113, 137 Cyclonic waves, 129, 137 Dancbe, river, 2 Darcy, 23, 147 Darwin, 27, 14, 17, 26, 159, 175 Datum for tide tables, 70, 156 — : — for charts, 70 for foreign, 69 — — for ordnance, 69 for French, 29, 68 Dawson, W. Bell, 29, 86, 150, 163, 166, 169 Deas, J., 99 Decimation of sun, 34, 60 of moon, 36, 50 Dee, river, 154 Denison, Napier, 167 Dessiou, 18, 158 Distance tidal ports from sea, 2 Diurnal inequality, 50, 61 Dordogne, nver, 148 o 3 INDEX. Dover standard for tidal cunents, 68 Duiller, 165 Dynamic theory, 16, 14 E Eakth, 37 revolutions, 38 area and depth of water, 38, 39 dimensions, 38 , distance from sun and moon, 33 Earthquake waves, 129 Eddies, tidal, 59 Elbe, river, 2 Elliot, 137 Emy, 122 Engelenborg, 31 Engineer, The, 129, 171, 173 English C!hannel, 29, 38 • tides, 73 • currents, 66 Equilibrium theory, 13, 18, 41 Equinoctial tides, 53 Equinox, 33 Erie, Lake, tides, 76 Establishment, 55 Euler, 15 Fetch, 124 Flamstead, 156 Floats, 99 Forel, 164 Formula, tidal currents, 66 in rivers, 93 , propagation tidal wave in rivers, 93, 190 , ocean waves, 9, 110, 181 , breaking waves, 124, 182 for diffusion salt in rivers, 105 , velocity shore waves, 112 French marine datum, 29, 69 Annuaire des Marees, 159 Fundy, Bay of, tides, 73 , , bore, 149 , , tidal mill, 172 • , , secondary undulations, 166, 169 Galbeaith, 65 Gales, British seas, 78, 81 Galileo, 8, 6, 9 Galveston storm wave, 139 Garonne, river, 95, 148, 192 Gauges, tide, 162 Generation of tides, 39 Geneva, Lake, seiches, 164 Gerstner, 118 Gironde, river, 2, 95, 105, 148, 192 Goodwyn Sands, 130 Goole, distance from sea, 2 Gravity, law of, 42 Greenwood, 31, 87 Ground swells, 120 H Haemonic analysis, 161, 26 Harmonic Analyzer and Tide Predicter, 161 Haughton, 18, 65, 176 Height of tides, 69, 53, 72 Herodotus, 6 High water, spring and neap tides, 71, 72 , mean, 70 in open ocean, 72 on coasts, 72, 73 , British Islands, 73 • , Straits of Magellan, 73 , Bay of Fundy, 73 , Bristol Channel, 73 , English Channel, 73 Hooghly, river, 94, 138, 145, 193 Hull, standard for cvirrents, 68 tides, 81, 82, 83, 85 Humber, river, 2, 95, 96, 101, 191. See also Hun. Huron, Lake, tides, 167 Hygre, 141 Indian Ocean, 38, 39 Indraught of tides, 64 Inland seas, tides, 39 Irish Channel, 73 , propagation tidal wave, 58 , coast tides, 18 , tidal currents, 66 Jamaica, storm wave, 130 Japan, storm wave, 131, 132 Jarrad, 93 Kelvin, Loed, 26, IGl Kepler, 6, 8 Lagging of tides, 52 Lagrange, 110 Laplace, 16 Lakes, effect of tides, 39, 76 , wind, 76 Baikal, 167 Erie, 76 Geneva, 164 Huron, 167 Michigan, 40 Superior, 40, 166 Trieg, 165 , Norfolk Broads, 76, 165 Latham, B., 99 , F., 125 INDEX. 199 Leonardo da Vinci, 22 Level of sea, mean, 69, 29 , high water, 72, 70, 63 Lima, stoim wave, 131 Lisbon, earthquake wave, 131 Littoral, drift and tides, 111 Liverpool standard for currents, 66 tidal datum, 156 tide tables, 157 Loire, river, 105 Low water in rivers, spring and neap tides, 92 Lubbock, 17, 18, 80, 86, 156, 158, 160, 176 M Maclaurin, 15 Magellan, Straits of, tides, 73 Making of the tides, 41 Mallet, 133 Malta, secondary undalation, 167 Mascaret, 141 Mean level of sea, 69 Mersey, river, 3, 155 Metropolitan Sewage Inquiry, 99 Mexico, Gulf of, 73, 79 Michigan Lake tides, 40 Milne, 129, 133 Mississippi, river, 2 Moon, 34 , origin of, 35 , dimension, 35 , phases, 36 , revolution, 35 , apogee and perigee, 36 , horizontal parallax, 36 , declination, 36 , cycles, 37 , perturbations, 37 , relative effect to sun, 47 , opposition and conjunction, 47 Morecambe Bay, 155 Motion, laws of, 9 Mottez, 114 Moxley, 27 N Nature, 152, 154 Neap tides, 49, 48 Nene, river, 141 Neva, river, 2 Newton, 10, 3, 5 Nile, river, 3 Norfolk Broads, 76 North Sea, 29, 30, 38 currents, 66 O Opposition, sun and moon, 47 Ordnance datum, 69 Oronico, river, 94 Ouse, river, 101, 150 P Pacific Ocean tides, 32, 57 Palmer, 162 Parallax, sun and moon, 36 Paris, Lieut., 24, 115, 119 Parrett, river, bore, 154 , brick earth, 101 Partiot, 147 Pentland Firth, 67 Perigee of moon, 35, 51 Perihelion of sun, 35, 51 Period of waves, 109 Phases of moon, 36 Phenomenon of tides, 6 Phillips, 99 Philosophical transactions, 8, 14, 18, 19, 157 Pliny, 6 Port Darwin tides, 75 Portishead, mean level of sea, 70 Ports, distance from sea, 2 Posidonius, 6 Power, tidal, 170, 171 Priming of the tides, 52 Propagation of tidal wave, 56 , rate of, 57 , formula, 110, 182, 183 effect, expansion, and contraction of shore line, 58 in rivers, 89 Proroca, 141 Pythagoras, 7 Pythias, 6 K Baces, tidal, 59 Bange of tides, 71 Reflected tides, 59 Eeid, 168 Keynolds, Osborne, 30 Eipples on surface, 59 Rivers, tidal, 88 Avon, 3 Amazon, 94, 144 Bure, 101 Clyde, 3, 95, 96, 99 Dee, 153 Dordogne, 148 Elbe, 2 Garonne, 95, 148 Gironde, 2, 95, 105, 148 Hooghly, 94, 138 Humber, 2, 95, 96, 101 Loire, 105 Mersey, 3, 153 Mississippi, 2 Nene, 141 Neva, 2 Nile, 3 Oronoco, 94 Ouse, 101, 150 Parrett, 154 Rhone, 2 Saint Lawrence, 86,^94, 166 INDEX. Eivers, tidal {continued) — Scheldt, 2, 105 Seine, 2, 94, 96, 99, 105, 172 Severn, 93, 95, 153 Thames, 2, 91, 95, 96, 97, 99, 101, 170 Trent, 93, 101, 160 Teien-Tang-Kiang, 142 Volga, 3 Witham, 99, 101, 93, 141 Kiver tides, 89 , propagation, 89 , formula, 93 , blown tides, 91 , low water, spring and neap tides, 92 , effect deepening channels, 94 , distance of propagation, 94 highest at upper end, 95 transport of material in suspension, 97 — currents, 96 , salt water in, 96 float experiments, 99 Rochefort tides, 17 EoUen, 120, Romans and tides, 6 Ross, 31 Rotary tides, 60 Russell, J. Scott, 22, 108, 118 Saint Laweence, rirer, 28, 86, 94, 166 Salt, quantity in sea water, 102 , specific gravity, 102 in river water, 101 , test for, 102 , distance extends up, 101 , formula for, 105 Santa Cruz, mill actuated by waves, 175 Saxby tide, 173 Scheldt, river, 105 Science, tidal, 5 Scoresby, 25, 114 Seaquakes, 129 Secondary undulations, 164 Seiches, 164 Seine, river, 2, 94,^96, 99, 105, 145,'172, 192 Seismic waves, 129 Severn, river, 153, 192 Shield, 119, 120, 122, 124 Shoolbred, 29 Shore waves, 110 Solitary waves, 133 Solway Firth, 155 Southern Ocean, 38, 39, 47, 57 Spring tides, 48, 49 Stevenson, 120, 124, 125, 126 Stok, 32 Storm warnings, 164, 168 Storm waves, 137 Strabo, 6 Stream, tidal. See Cukeent Sun, 33, 47 Superior, Lake, 167, 168 Swiss lakes, 164 Syzygies, 36 Thames, river, 2, 91, 95, 96, 97, 99, 101, 170 192 Theory of tides, 16, 3, 10, 41 Thompson. See KELViif Tidal bores, 141 currents, 63, 96 constituents, 159 models, 30 theory, 16, 2, 3, 10, 41 rivers. See Rivers turbines, 173 waves. See Waves miUs, 171 Tides, making of, 41 , value of, for navigation, 2 , generation, 39 , propagation, 5, 66, 67, 89, 110, 182 , , inland seas, 39 , river, 89, 190 , honrlj' rise and fall, 63 , height of, 24, 25, 53 , reflected, 59 , double, 60 , rotary, 60 , range, 71 , effect of wind and barometer, 74, 81 , source of power, 170 , port of London, 18 , Liverpool, 18 , spring and neap, 49 , age of, 50 , new and full moon, 51 , priming and lag^g, 62 , harmonic analysis, 161 , datum, 156 Tide tables, 156, 4, 18 , local, 156 , Gauges, 156, 162 predicting machines, 161 Transport of material by tides, 97 Trent, river, 93, 101, 150 Tsien-Tang-Kiang, river, 142 U United States Hydrographic Depart- ment, 114 Undulations, secondary, 164, 168 Unwin, 97 Vaucher, 164 Vernon Harcourt, 146 Volga, river, 3 W Walker, 24 Wallingford, 156 Wallis, 8, 176 Warping, 101 Water area of earth, 102 Water wheels, tidal, 170 INDEX. 20 1 Wavelets, 111 Waves, 107 Leonardo du Vinci, on, 21 I Lagrange, on, 22, 108 , Scott Russell, on, 22, 108 , Weber, on, 22 Gerstner, on, 118 , Stevenson, on, 120, 124, 125, 126 I classification and definition, 108, 109 , tidal, 109, 33, 44 , propagation, 56, 57 , velocity ol propagation, 110, 182 — , shore, 110 — , effect on littoral drift, HI — , as source of power, 173 , wind, 113, 114 — , breaking, 117, 122 — , trochoidal and cycloidal, 115 — , deptli motion extends, 118 — , proportions and sizes, 113, 114 — , British seas, 120 — , power of, and impact, 124, 125 — , fetch, 124 — , precursors of storms, 168 — , rollers and ground swell, 120 Waves, wind, solitary ocean, 133 , , cyclonic, 129, 1?7 , , seismic, 129 • Weber, 22 Wheeler, 30, 31, 80, 99, 101, 102, 111, 147, 160, 159 Whewel, 19, 14, 16, 20, 175 White, 24 "V\Tiitwell, 154 Wick, 68, 127 Wind, effect of, on tides, 74 , gales round British Isles, 78 Winyah Bay, 79 Witham, river, 93, 99, 101, 141 Yarmouth, tides, 78, 81, 84 ZuTDER Zee, 76 THE END. PRINTEP ET WIIiLTAM CLOWES AKP SONS, LIMITED, LONDON AND BECCLES.