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TIDE (O. Eng. lid, cf. Ger. Zeit, tim...
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See also:TIDE (O. Eng. lid, cf. Ger. Zeit, See also:time or See also:season, connected with See also:root of See also:Sanskrit a-diti, endless) , a See also:term used generally for the daily rising and falling of the See also:water of the See also:sea, but more specifically defined below . I.—See also:GENERAL See also:ACCOUNT OF TIDES AND TIDAL THEORIES § . 1 . See also:Definition of See also:Tide.—When, as occasionally happens, a See also:ship in the open sea meets a See also:short See also:succession of waves of unusual magnitude, we hear of tidal waves; and the large See also:wave caused by an See also:earthquake is commonly so described . But the use of the See also:adjective " tidal " appears to us erroneous in this context, for the tide is a rising and falling of the water of the sea produced by the attraction of the See also:sun and See also:moon . A rise and fall of the sea produced by a See also:regular See also:alternation of See also:day and See also:night breezes, by regular rainfall and evaporation, or by any See also:influence which the moon may have on the See also:weather cannot strictly be called a tide . Such alterations may be inextricably involved with the rise and fall of the true astronomical tide, but we shall here distinguish them as meteorological tides . It is well known that there are strongly marked diurnal and semi-diurnal inequalities of the See also:barometer due to the sun's- See also:heat, and they may be described as atmospheric meteorological tides.' These movements both in the See also:case of the sea and in that of the See also:atmosphere are the result of the See also:action of the sun, as a radiating See also:body, on the See also:earth . True astronomical tides in the atmosphere would be Shown by a ' See also:Lord See also:Kelvin shows that the attraction of the sun on these tides must produce an excessively small See also:acceleration' of the earth's rotation . See Societe de physique (See also:September 1881), or Proc . See also:Roy . See also:Soc . Edin . (1881-188x), p, 396 . regular rise and fall' in the barometer, but such tides are undoubtedly very See also:minute, and we shall not discuss them in this See also:article, merely referring the reader to the Mecanique See also:celeste of See also:Laplace, bks. i. and xiii . We ATides. tmoapherk shall in the See also:present article extend the -term " tide " to denote an elastic or viscous periodic deformation of a solid or viscous: globe under the action of tide-generating forces . § 2 . General Description of Tidal Phenomena.2—If we live by the sea or on an See also:estuary, we see. that the water rises and falls nearly twice a day; speaking more exactly, the. See also:average See also:interval from high-water to high-water is about I2 25m, so that the average retardation from day to day is about Som . The times of high-water are then found to See also:bear an intimate relation with the moon's position . Thus at See also:Ipswich high-water occurs when the moon is nearly See also:south, at See also:London See also:Bridge when it is south-See also:west, and at See also:Bristol when it is See also:east-south-east . For a very rough determination of the See also:time of high-water it is sufficient to add the See also:solar time of high-water on the days of new and full moon (called the " See also:establishment of the See also:port ") to the time of the moon's passage over the See also:meridian, either visibly above or invisibly below the See also:horizon . The interval between the moon's varfabfttty passage over the meridian and high-water varies of/See also:Biel-vat sensibly with the moon's See also:age . From new moon to afterMoon's first See also:quarter, and from full moon to third quarter Transit . (or rather from and to a day later than each of these phases), the interval diminishes from its average to a minimum, and then increases again to the average; and in the other two quarters it increases from the average to a maximum, and then diminishes again to the average . The range of the rise and fall of water is also subject to See also:great variability . On the days after new and full moon the range of tide is at its maximum, and on the day after the first and third quarter at its minimum . The maximum Spdagaad is called " See also:spring tide " and the minimum " See also:neap Neap. tide," and the range of spring tide is usually nearly three times as great as that of neap tide . At many ports, however, especially non-See also:European ones, two successive high-See also:waters are of unequal heights, and the See also:law of variability of the difference is somewhat complex; a statement of that law will be easier when we come to consider tidal theories . In considering any single oscillation of water level we find, especially in estuaries, that the interval from high to See also:low-water is longer than that from low to high-water, and the difference between these two intervals is greater at springs than at neaps . In a See also:river the current continues to run up stream for some considerable time after high-water is attained and to run down similarly after low-water . Much confusion has beenRIverTide.. occasioned by the indiscriminate use of the term " tide " to denote a tidal current and a rise of water, and it has often been incorrectly inferred that high-water must have been attained at the moment of cessation of the upward current . The distinction between " rising and falling and " flowing and ebbing " must be maintained in See also:rivers, whilst it is DIsandIoa unnecessary at the seaboard . If we examine the of Rise and progress of the tide-wave up a river we find that high- See also:Fan from water occurs at the sea earlier than higher up . If, See also:Flood and for instance, on a certain day it is high-water at See also:Bbb . See also:Margate at See also:noon, it is high-water at See also:Gravesend at a quarter past two, and at London Bridge a few minutes before three . The interval from low to high-water diminishes also as we go up the river; and at some distance up certain rivers-as, for example, the See also:Severn—the rising water spreads over the See also:flat sands in a roaring surf and travels up the river almost like a See also:wall of water . This See also:kind of sudden rise is called a "See also:bore "a (q.v.) . In other cases where the difference between the periods of rising and falling is considerable there are, in each high-water, two or three rises and falls . A See also:double high-water exists at See also:Southampton . When an estuary contracts considerably, the range of tide becomes largely magnified as it narrows; for example, at the = Founded on G . B . See also:Airy's " Tides and Waves," in Ency . Metrop . ' See a See also:series of papers bearing on this kind of wave by See also:Sir W . See also:Thomson (Lord Kelvin) in Phil . Mag . (1886-x887) . Roughly speaking, an See also:inch of the See also:mercury See also:column will correspond to about a See also:foot of water, but the effect seems to vary much at different ports.' Mariners and hydrographers make use of certain technical terms which we shall now define and explain . The " establishment of the port," already referred to above, is the average interval which elapses between the moon's transit across Technical the meridian, at full moon and at See also:change of moon, and Terms used the occurrence of high-water . Since at these,tilnes the Sailors. moon crosses the meridian at twelve o'See also:clock either of day or night,- the " establishment's is the See also:hour of the clock of high-water at full and change . It has already been remarked that spring tide occurs at most places a day or a day and a See also:half after full and change of moon.' Now it is more important in the theory of the tides to know what occurs at spring tide than what occurs at full and change of moon . Thus the term " the corrected establishment of the port " is used to denote the interval in See also:hours elapsing at spring tide between moon's transit and high-water . The difference between the See also:ordinary and the corrected establishments is of small amount . At any other See also:state of the moon, except full and change, the " interval " or " lunitidal interval " means the interval between the moon's upper or See also:lower transit and high-water . The average interval elapsing between full or change of moon and spring tide is called the " age of the tide "; as already remarked this interval is commonly about a day or a day and, a half, but it may be twice as great in some places . The use of this term arises from the See also:idea that spring tides are generated at some undefined See also:place exactly at full or change of moon, and take an interval of time denoted the age to reach the place of observation . The term is not altogether satisfactory, since it implies a theory, but it must be referred to as in general use . The average height at spring tide between high and low-water marks is called " the spring rise "; the similar height at neap tides is, however, called " the neap range." " Neap rise " is used to mean the average height between high-water of neap tides arid low-water of spring tides . Thus both at springs and neaps the term " rise " refers to the rise above the level of low-water at spring tide . See also:French hydrographers See also:call half the spring rise " the unit of height." 2 Airy, " Tides and Waves." 2 Ibid . §§ 572-573 . The " diurnal inequality 't ot. t,.thi, • tide,, deaotas the ,f qt that successive . high-waters and successive 1p -waters are ,agikequ ' to one another . In See also:England the diurnal. irtegliality scaft'61 The practice of the See also:British See also:admiralty is to refer their. se% and tide tables to " mean low-water See also:mark of ordinary springtitidelh This datum is found by taking the mean of all the availableobserva' tions of spring tides, excluding, however, from the mean any spring %tides which may be considered abnormal . The admiralty datum is not, then, susceptible of exact scientific definition; but when it has once been fixed with reference to a See also:bench-mark ashore it is expedient to adhere to it, by whatever See also:process it was first fixed.' When new tidal stations are established in See also:India the datum of reference has, since about 1885, been " See also:Indian low-water mark," which is defined as being below mean sea-level by the sum of the semi-ranges of the tides M2, S2, Kr, 0 (see §§ 24, 25 on See also:Harmonic See also:Analysis below) . In ordinary_ parlance sailors very commonly use the term "tide " when they mean what may be more accurately described as a tidal current . § 3 . Tidal Observation: the Tide-See also:gauge—Tidal prediction is only possible when accurate observations have been made of the ,phenomena to be predicted; and the like is true of verification after preAictaon . It was formerly thought sufficient to See also:note the heights of the water at high and low-water, together with the times of those events, aid the larger ' See also:part of the observations which exist are still of this See also:character, but See also:complete investigation of the ;law of tidal oscillations demands that the height of the Water should be measured at other times than at high and low-water . With whatever degree of thoroughness it is proposed to observe the tides the See also:procedure is much the same . The simplest sort of observation is. to note. the height of the water on a' graduated See also:staff fixed in the sea, with such See also:allowance Te-See also:pole . as may be possible for wave See also:motion . It is, however, fax Preferable to sink a See also:tube into the sea into which the water penetrates through small holes; and the wave motion is thus annulled . In the See also:calm water inside the tube there lies a See also:float, to which is attached a See also:cord passing over a See also:pulley and counterpoised at the end . The motion of the counterpoise against a See also:scale is observed . In either case the observations may be made every hour, or the times and heights of high and low-water may be noted . In more careful observations than those referred to above the tidal See also:record is automatic and continuous and is derived by means of an See also:instrument called a tide-gauge . This gauge should be placed in a place where we may obtain a See also:fair See also:representation of the oscillation of the surrounding sea . In such a site a well or tank is built on the. shorecommuni-Tide: gauge eating by a channel with the see at about to ft. below lowest low water mark . In some cases an artificially constructed well may be dispensed with, where some See also:lagoon or See also:pool exists so near to the. sea as to permit junction with the sea by means of a channel below low-water mark . At any See also:rate we suppose that water is provided rising and falling with the tide, without much wave-motion: A cylindrical float, usually a hollow. metallic See also:boa or a See also:block of See also:greenheart See also:wood, hangs and floats in the well, and is of such See also:density as just to sink without support . The float hangs under very See also:light tension by a See also:platinum See also:wire, or by a metallic ribbon, or by a See also:chain . The suspension wire is wrapped See also:round a See also:wheel, and imparts to it rotation proportional to the rise and fall of tide: By a See also:simple gearing this wheel drives another, by which the range is reduced to any convenient extent . A See also:fine wire See also:wound on the final wheel of the See also:train drags a See also:pencil or See also:pen up and down or to and fro proportionately to the tidal oscillations . The pencil is lightly pressed against a See also:drum, which is driven by clockwork so as to make one revolution per day . The pen leaves its trace or tide-See also:curve on See also:paper wrapped round the drum . The paper is fixed to the drum with the edges of the paper at the XII o'clock See also:line, and the record of a fortnight maybe taken without change of paper . Ah eieample of a tide-curve for See also:Apollo See also:Bender, Bombay, from the 1st to the 15th of See also:January 1884, is shown in fig 1 . The curves are to be , read from right to See also:left, and when we reach the left-See also:hand edge of the paper, we re-enter again at the same height on the right-hand edge . The See also:numbers on the successive curves denote the days of the See also:month . We have chosen an example from a sub-tropical region because it illustrates the remarkable regularity of the tides in a region where the weather is equable . Further, if the reader will note the successive high-waters or low-waters which follow one another on any one day, he will see a strongly marked " diurnal inequality," which would have been barely perceptible in a European tide-curve, 3 See J . N . ' Shoolbred on datum levels, Brit . Asset . Reports (1879) entrance of the Bristol Channel the range of spring' tides is about i8 ft., and at See also:Chepstow about 50 ft . This See also:augmentation Augmeara- of the height of the tide-wave is due to the concenion o/ tration of the See also:energy of motion of a large See also:mass of Helgnt In water into a narrow space . At oceanic ports the esraarles. tidal phenomena are much less marked, the range of tide being usually only 2 or 3 ft., and the interval from high to low-water sensibly equal to that from low to high-water The changes from spring to neap tide and the relation of the time of high-water to the moon's transit are, however, the same both on the open See also:coast and in rivers . In See also:long and narrow seas, such as the See also:English Channel, the .tide in See also:mid-channel follows the same law as at a station near the mouth„ of a river, rising and falling in equal times; the current See also:Land- runs in the direction analogous to up stream for three ' locked Seas . hours before and after high-water, and down stream for the same See also:period before and after low-water . But near the sides of channels and near the mouths of bays the changes of the currents are very complex; and near the headlands separating two bays there is usually at certain times a very See also:swift current, termed a " See also:race." In inland seas, such as the Mediterranean, the tides See also:axe nearly insensible except at the ends of long inlets . Thus at See also:Malta the tides are not noticed by the ordinary observer, whilst at See also:Venice they are conspicuous . The effect of a strong See also:wind on the height of. tide is generally supposed to be strongly `marked, especially in estuaries . In the wince case of an exceptional See also:gale, when the wind veered round appropriately, Airy statesi that the water has been known to epatt from its predicted height at London by as much as 5 ft . The effect of wind will certainly be different at each port . The discrepancy of See also:opinion on this subject appears to be great—so much so that we hear Of some observers concluding that the effect of the wind is Armsure, lc insensible . See also:Variations in barometric pressure also Preasuro . cause departures from the predicted height of water, high barometer corresponding to decrease of height of water . §4 . Tide-Tables and the Degree of Accuracy in Tidal Prediction.' —The connexion between the tides and the movements of the Emperkal moon and sun is so obvious that tidal predictions Tide-tables• were regularly made and published long before mathematicians had devoted their See also:attention to them; and these predictions attained considerable success, although they were founded on empirical methods . During the 18th See also:century, and even in the earlier part of the 19th, the See also:art of prediction. was regarded as a valuable See also:family See also:secret to be jealously guarded~from the public . The best example of this kind of tide-table was afforded by See also:Holden's tables for See also:Liverpool, founded on twenty years of observation by a See also:harbour-See also:master named See also:Hutchinson.'the heights and times are tabulated according to the. hour of the clock at which the moon will See also:cross the meridian at the place of observation, distinguishing between the visible and invisible transits . Certain simple corrections have also to be applied . A considerable degree of elaboration has to be given to the table, in See also:order that it may give accurate results, and it would occupy some half-dozen to a dozen pages of a See also:book, its See also:extension varying according to the degree of accuracy aimed at . It might occupy about five minutes to See also:extract a prediction from the more elaborate See also:form. of such a table . There are - many ports of considerable commercial importance where, nevertheless, it would hardly he See also:worth while to incur the great and repeated A.M . Midnight P.M . a -. i i iii ' V 1F III II I xa Xl I]< ` vu v_ Y r u 11 T :u IIIMIIII1UU!IIIIIIIIUII,,0j . ORIN ^h'44AgI 16mr.a . Pr'''Ar'dqVi7"' , . FAlipppwo Kto''42% AmAlbekwal NLI '' MMINIC i; e.-~-~-~~`•~1- :~-: O :!o K4 A~ iWfl4iN4WdP1V4F4 wwqpAwwAmOmomamigolerpirrptirpe WPAINKI/KePiMpMmai '~— lIiIIIII11IIfr4 g 1884, or from 12 Dec .
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See also:Whewell and of Sir See also: In a general tide-table ' References may be given to two papers by G . H . See also:Darwin on this subject, viz . " Tidal Prediction," Phil . Trans., A . (1891) pp . 159-229; and " An apparatus for facilitating the reduction of tidal observations," Proc . Roy . Soc . (t8g2),vol. iii• For a general account with-out See also:mathematics see Darwin's Tides, &c.; this See also:section is founded on chs. xiii. and xiv. of that book . For mathematical methods see See also:Maurice See also:Levy, Theorie See also:des merges (See also:Paris, 1898) . ' Whewell, See also:History of Inductive .$ciences,, ii,248; Darwin's Tides, &c., ch. iv.See also:expenditure involved in the publication of special tables . But this kind of elaborate general table has been used in few cases,' and the See also:information furnished to mariners usually consists either of a full prediction for every day of a future year, or of a meagre statement as to the average rise and interval, which must generally be almost useless . The success of tidal predictions varies much according to the place of observation . In stormy regions the errors are often considerable, and the utmost that can be expected Me' - of a tide-table is that it shall be correct with a steady togkaf Dlabarometer and in calm weather . But such conditions #urbaneof Prediction. are practically non-existent, and therefore errors are inevitable . Notwithstanding these perturbations, tide-tables are usually of surprising accuracy even in See also:northern latitudes; this may be seen from the following table showing the results of com-Amountol Tarison between prediction and actuality at See also:Portsmouth . See also:Amoy at he importance of the errors in height depends, of Portsmouth. course, on the range of the tide; it is well, therefore, to note that the average ranges of the tide at springs and neaps are 13 ft . 9 in. and 7 ft . 9 in. respectively . , Prediction at such a place as Portsmouth is difficult, on account of the instability of the weather, but, on the other hand, the tides in themselves are remarkably simple in character . Let Amount of us now turn to such a port as See also:Aden, where the weather Erroraf , is very See also:uniform, but the tides very complex on account . Aden . of the large diurnal inequality, which frequently obliterates one of two successive high-waters .
The short series of comparisons between actuality and, prediction which we give below may be taken as a fair example of what would hold good when a long series is examined
.
The results refer to the intervals loth of See also: Cases . Error . Cases . om to 5m 69 Inches . 89 o to 6 6m to tom 50 7 to 12 58 IIm to 15m 25 13 to 18 24 16m to 2om IO 19 to 24 6 2Im to ~5m II -- — 26m to 30m 7 31mto35m 4 — — 52m I - - 177 177 Table of Errors in the Prediction of High-Water at Aden in March– April and November-December 1884 . Time . Height . Magnitude of Number of Magnitude of Number of Error . Cases . Error . Cases . om to 5m 35 . Inches . 15 0 5m to tom 32 I 48 10m to 15m 19 2 28 15m to 20m 19 3 14 2om to 25m 5 4 I I 26m and 28m 2 No high water . 33m and 36m 2 — — 56m and 57m 2 — ae . No high water . I — - - 117 — I17 It would be natural to think that when a prediction is ,erroneous by as much as fifty-seven minutes it is a very See also:bad one, but such a conclusion may be unjust . There was one case in which the high-water was completely obliterated by the diurnal inequality, but there were many others in which 'there was nearly complete obliteration, so that the water stood nearly stagnant for several hours., A measure of the, degree of stagnation .is afforded by the amount of rise from low to high-water . Now, on examining all the eleven cases where the error of time was equal to or over twenty minutes, we find five cases in which the range from low to high-water was less than 8 in., and these include the errors of fifty-six and of fifty-seven minutes . There is one case of a rise of 13 in. with an error of See also:thirty-six minutes; one case of a rise of 17 in. with an error of twenty-two minutes;. one of 19 in. rise with thirty-three minutes error . The remaining three cases have rises of 2 ft. lo in., 3 ft . 9 in., 3 ft . II in., and errors of twenty-two, twenty-three, twenty minutes . Thus all the very large errors of time correspond with approximate stagnation, and are unimportant . It is fair to conclude, therefore, that the predictions as to time are very good . The predictions as to height are obviously good, for more than half were within t in., and only eleven had an error of as much as 4 in . When it is considered that the.incessant variability of the tidal forces, the complex outlines of the coast, the See also:depth of the sea, the earth's rotation and the perturbations by meteorological influences are all involved, it should be admitted that the success of tidal prediction is remarkable . If further See also:evidence were needed, we might See also:appeal to tidal prediction as a convincing See also:proof of the truth of the theory of See also:gravitation . § 5 . General Explanation of the Cause of Tides.—The moon attracts every particle of the earth and ocean, and by the law of Tides gravitation the force acting on any particle is directed generatlaj towards the moon's Centre, and is jointly proportional See also:tea• to the masses of the particle and of the moon, and inversely proportional to the square of the distance between the particle and the moon's centre . If we imagine the earth and ocean subdivided into a number of small portions or particles of equal mass, then the average, both as to direction and intensity of the forces acting on these particles is equal to the force acting on that particle which is at the earth's centre . For there issymmetry about. the line joining the centres of the two bodies, and, if we See also:divide the earth into two portions by an ideal spherical See also:surface passing through the earth's centre and having its centre at the moon, the portion remote from the moon is a little larger than the portion towards the. moon, but the nearer portion is under the action of forces which are -a little stronger than those acting on' the farther portion, and the resultant of the weaker forces-on the larger portion is exactly equal to the resultant of the stronger forces on the smaller . If every particle of the earth and ocean were being urged by equal and parallel forces there would be no cause for relative motion between the ocean and the earth . Hence it is the departure of the force acting on any particle from the average which constitutes the tide-generating force . Now it is obvious that on the See also:side of the earth towards the moon the departure from the average is a small force directed towards the moon; and on the side of the earth away,from the moon the departure is a small force directed away from the moon . Also these two departures are very nearly equal to one another, that on the near side being so little greater than that on the other that we may neglect the excess . All round the sides of the earth along a great circle perpendicular to the line joining the moon and earth the departure is a force directed inwards towards the earth's centre .. Thus we see that the tidal forces tend to pull the water towards and away from the moon, and to depress the water at right angles to that direction . D In ' fig . 2 this explanation is illustrated graphically . The relative magnitudes of the tidal forces are given by the numbers on the figure, M is the direction of the moon, V the centre of the. hemisphere of the earth at which the See also:man in the moon would look, I the centre of the hemisphere which would be invisible to him, DD are the sides of the earth where the tidal force is directed. towards the earth's centre . The outward forces at V and I are exactly double the inward forces at D and D . If it were permissible to neglect the earth's rotation and to consider the See also:system as at See also:rest, we should find that the water was in See also:equilibrium when elongated into a prolate ellipsoidal or See also:oval form with its longest See also:axis directed towards and away from the moon . But it must not be assumed that this would be the case when there is motion . For, suppose that the ocean consisted of a See also:canal round the See also:equator, and that an earthquake Theory of or any other cause were to generate a great wave in See also:Equatorial the canal, this wave would travel along it with canal on a velocity dependent on the depth . If the canal Earth . were about 13 See also:miles deep the velocity of the wave would be about moo miles an hour, and with depth about equal to the depth of our seas the velocity of the wave would be about half as great . We may conceive the moon's tide-generating force as making a wave in the canal and continually outstripping the wave it generates, for the moon travels along the equator at the rate of about moo miles an hour, and the sea is less than 13 miles deep . The resultant oscillation of the ocean must therefore be the summation of a series of partial waves generated at each instant by the moon and always falling behind her, and the aggregate wave, being the same at each instant, must travel r000 m. an hour so as to keep up with the moon . Now it is a general law of frictionless oscillation that, if a slowly varying periodic force acts on a system which would oscillate quickly if left to itself, the maximum excursion on one side of the equilibrium position occurs simultaneously with the maximum force in the direction of the excursion; but, if a quickly varying periodic force acts on a system which would oscillate slowly if left to itself, the maximum excursion on one side of the equilibrium position occurs simultaneously with. the maximum force in the direction opposite to that of the excursion . An example of the first is a See also:ball See also:hanging by a short See also:string, which we push slowly to and fro; the ball will never quit contact with; the hand, and will agree with its excursions . If, however, the ball is hanging by a long string we can See also:play at battledore and shuttlecock with it, and it always meets our blows . The latter is the analogue of the tides, for a See also:free wave in our shallow canal Tides goes slowly, whilst the moon's tide-generating Inverted, action goes quickly . Hence when the system is left to See also:settle into steady oscillation it is low-water under and opposite to the moon, whilst the forces are such as to tend to make high-water at those times . If in this case we consider the moon as revolving round the earth, the water assumes nearly the shape of an oblate See also:spheroid or See also:orange-shaped body with the shortest axis pointed to the moon . The rotation of the earth in the actual case introduces a complexity which it is not easy to unravel by general reasoning . We can see, however, that if water moves from a lower to a higher See also:latitude it arrives at the higher latitude with more velocity from west to east than is appropriate td its latitude, and it will move accordingly on the earth's surface . Following out this conception, we see that an oscillation of the water to and fro between south and north must be accompanied by an eddy . The See also:solution of the difficult problem involved in working out this idea will be given below . The conclusion at which we have arrived about the tides of an equatorial canal is probably more nearly true of the tides of a globe partially covered with land than if we were to suppose the ocean at each moment to assume the prolate figure of equilibrium . In fact, observation shows that it is more nearly low-water than high-water when the moon is on the meridian . If we consider how the oscillation of the water would appear to an observer carried round with the earth, we see that he will have low-water twice in the lunar day, somewhere about the time when the moon is on the meridian, either above or below the horizon, and high-water half-way between the Iow waters . If the sun be now introduced we have another similar tide of about half the height, and this depends on solar time, giving low-water somewhere about noon and midnight . The superposition of the two, modified by See also:friction and by the interference of land, gives the actually observed aggregate tide, and it is clear that about new and full moon we must have spring tides and at quarter moons neap tides, and that (the sum of the lunar and solar tide-generating forces being about three times their difference) the range of spring tide will be about three times that of neap tide . So far we have supposed the luminaries to move on the equator; now let us consider the case where the moon is not on the equator . It is clear in this case that at any Diurnal place the moon's See also:zenith distance at the upper transit One of the most remarkable conclusions of Laplace's theory of the tides, on a globe covered with ocean to a uniform depth, is that the diurnal tide is everywhere non-existent . $vnneacenf But this See also:hypothesis differs much from the reality, i¢ ocean vt and in fact at some ports, as for example Aden, uniform the diurnal tide is so large that during two portions Depth' of each See also:lunation there is only one great high-water and one great low-water in each twenty-four hours,. whilst in other parts of the lunation the usual semi-diurnal tide is observed . § 6 . Progress of the Tide-wave over the Ocean and in the British Seas.-Sufficient tidal data would give the state of the tide at every part of the See also:world at the same instant of time, and if the tide wave is a progressive one, like such wave as we may observe travelling along a canal, we should be able to picture mentally' the motion of the tide-wave over the ocean and the 'successive changes in the height of water at any one place . But we are not even sure that the wave is progressive, for in some oceans, such as perhaps the See also:Atlantic, the motion may be only a see-saw about some line in mid-ocean--up on one side and down on the other; or it may more probably be partly a progressive wave and partly a see-saw or stationary oscillation . In contracted seas the wave is undoubtedly predominantly progressive in character, but too little is known to enable us to speak with any confidence as to wider seas . Whewell and Airy, while acknowledging the uncertainty of their data, made the See also:attempt to exhibit graphically the progress of the tide-wave over a large portion of the oceans of the world . In the first edition of this article (Ency . Brit., 9th ed.) we reproduced their See also:chart.' But, since doubts as to its correctness have gradually accumulated, we think it more prudent to refrain from reproducing it again.' As we have already indicated, the tide in British seas has mainly a progressive character, and the general, march of the wave may be exhibited on a chart by what are called cotidal lines . If at the full and change of moon we draw lines on the sea through all the places which have high-water simultaneously, and if we mark such lines successively XII, I, II, &c., being the See also:Greenwich time of high-water along each line, we shall have a succession of lines which show the progress of the wave front hour to hour .. For phases of the moon, other than full and change, the numbers may be taken to represent the interval in hours. after. the moon's transit, either visible or invisible, until the occurrence of high water . But for these other phases of the moon the interval varies by as much as one hour in excess or defect of the number written on any of the lines . Thus when the moon is about five days old, or five days past full, the numbers must all be reduced by about one hour so that I, II, III, &c., will then be replaced by XII, I, Il:, &c.; and when the moon is about ten days old, or ten days past full, the numbers must all be augmented by about one hour, and will read II, III, IV, &c . However, for a rough comprehension of the tides in these seas it is unnecessary to pay attention to this variation of the intervals . Airy in his " Tides and Waves " gives such a chart for Great See also:Britain and the North Sea, and he attempts to complete the cotidal lines conjecturally across the North Sea to See also:Norway, See also:Denmark and the |