Tides, the alternate rising and falling of the waters of the ocean, which is to be observed on all its coasts and estuaries. The rising is designated as the flood, and the highest elevation as high water; the falling is called the ebb, and the lowest depression low water. The duration of high and low water without apparent change of level is known as the stand, and the cessation of the ebb and flood streams or tidal currents is called slack water. The tides of each day occur somewhat later than those of the preceding day, the average retardation from day to day being about 50 minutes. The times of occurrence of high water bear a very close relation to the appearance of the moon in certain positions. Thus at New York high water occurs when the moon is about E. S. E.; at New Castle, on Delaware river, when the moon is nearly S.; at Baltimore when it is rising or setting. These are rude statements, but they are sufficiently accurate for many purposes, and they show at once the close connection between the time of high water and the time of the moon's passage over the meridian.

In fact, so completely is this recognized, that, in order to give the time of high water upon any day, it is usually thought sufficient to state the time of high water on the days of new moon and full moon (or "full and change ") when the moon passes the meridian at 12 o'clock nearly. This time is called the establishment of the port. Then to find (roughly) the time of high water on any other day, it is only necessary to add the establishment to the time of the moon's meridian passage on that day. There will also be another high water on the same day, prej ceding or following that so found by 12h. 26m. nearly. On closer examination it will be found that the interval between the time of the moon's passage over the meridian and the time of high water varies sensibly with the moon's age. At new moon, full moon, first quarter, and third quarter (or rather on the day following each of these phases), the interval between the time of the moon's passage and the time of high water is nearly the same; but from new moon to first quarter, and from full moon to third quarter, the high water occurs earlier than would be inferred by using that same interval; and from first quarter to full moon, and from third quarter to new moon, it occurs later than the same interval would give it.

The height at high water and the depression at low water are not always the same. On the days following new moon and full moon, high water is higher and low water lower than at any other time; these are called spring tides. On the days following the first and third quarters, high water is lower and low water higher than at any other time; these are called neap tides. Thus at New York the rise and fall (that is, the difference in elevation between high water and low water) is about 5½ ft. at spring tides, and 3½ ft. at neap tides. At Boston this variation is from 11¼ to 8½ ft. There is a sensible difference in height between two successive high waters or low waters, one occurring before noon, the other after noon, and these differences are most perceptible when the moon is at her greatest declination N. or S., and disappear when she is near the equator. There are other variations of height depending on other circumstances. In a single tide the interval from high water to low water is greater than that from low water to high water; the difference between these intervals is sensibly greater at spring tides than at neap tides.

The tidal current in the bay runs upward for some time after high water, and after changing its direction continues to run downward for some time after low water, when it again changes its direction, and runs upward. If we further examine the state of the tide in different parts of the same river, or in a bay of great length as compared with its breadth, as for instance Chesapeake bay, we shall find that near the mouth there is very little difference between the interval from high to low water and that from low to high water; also that the current runs up the channel for a long time (sometimes approaching to three hours) after high water, and runs down the channel for as long a time after low water. In going up the bay we find that the high water occurs later and later, but the velocity with which the high water travels is so great as entirely to preclude the idea of explaining the tide by supposing the same mass of water to have been moved all the way up the bay. Thus, high water is 13 hours in travelling from Cape Henry to the head of •Chesapeake bay, 190 m., moving with an average velocity of 15 m. an hour, while the greatest observed current is less than one mile an hour.

High water takes place simultaneously near the head and the mouth of the bay, while it is low water at the same time near the middle. The interval from low water to high water diminishes as we go up the bay, as also the difference between the stand and slack water. At the entrance of the bay the ebb current begins three hours after the high water stand; in the vicinity of Annapolis it is but one hour, and at the head of the bay there is only half an hour between the high water stand and the commencement of the ebb current. - Herodotus speaks of the tides in the Red sea. Plutarch says that Pytheas of Massilia, who had observed them in Britain, ascribed them to the moon. Caesar, in his account of the invasion of Britain, refers to the nature of spring tides as well understood in connection with the moon's age. Pliny explains the phenomena at some length, and ascribes them to the sun and moon dragging the waters along with them. Kepler in accounting for the tides was evidently aware of the principle of gravitation, but not of the law.

Newton laid hold of this class of phenomena as the most incontestable proof of universal gravitation, and showed that according to its law just such periodic fluctuations in the fluid covering of the earth must take place as are actually exhibited by the tides of the ocean. If we conceive the earth to be wholly or in a great degree covered with water, and subject to the attraction of the sun, the force of which is inversely as the square of the distance, it will be obvious that while the whole earth will fall toward the sun with a velocity proportioned to the aggregate attraction upon its solid portions (which is the same as if all the matter were collected at its centre), the water nearest to the sun, being accelerated by a greater force, and being fluid, will approach the sun more rapidly than the solid core. It will thus run from all sides into a protuberance beyond the form of equilibrium of the earth's attraction and rotation, until the pressure of the elevated mass equals the difference in the attraction of the sun. Moreover, a similar protuberance will be formed on the side opposite to the sun, since the particles of water, being solicited by a less force than the solid core, will fall more slowly toward the sun, and as it were remain behind.

Nor does the fact that, on the average, the earth does not lessen its distance from the sun, in the least invalidate the force of this reasoning; for the deviations from the tangential motion of the earth in its orbit are precisely those which the earth would move through if falling toward the sun unaffected by any other impulse. The same considerations hold good in regard to the attraction of the moon upon the earth and the waters surrounding it; for although we are in the habit of considering the moon as simply revolving about the earth, it must be remembered that the attraction is mutual, that both bodies describe orbits about their common centre of gravity, and that while the moon obeys the attractive force of the earth, the latter equally follows that of the former, by which it is at every instant of time drawn from the path which it would pursue if that influence did not exist, by an amount precisely equal to the fall corresponding to the moon's attractive force. As a necessary consequence of the elevation of the water in the regions nearest to and most remote from the attracting body, there must be a corresponding depression below the mean level of the sea at points distant 90° from the vertices of the protuberances, or at the sides of the earth as seen from the sun or moon.

If the latter bodies maintained a constant position with respect to the earth, the effect would therefore be to produce a distortion of figure in the ocean surface (assumed to cover the whole earth) having the form of a slightly elongated ellipsoid, the two vertices of which would be, the one precisely under, the other precisely opposite to the points at which the disturbing body is vertical. But this is not the case; for by the rotation of the earth and the motion of earth and moon in their orbits, the direction of the disturbing forces is constantly changing with respect to any point on the earth's surface. New points arrive at every instant under the zenith and nadir of either luminary, and thus waves are produced which follow them round the globe. The highest points of these waves will remain far behind the verticals of the disturbing bodies, because the inertia and friction of the water prevent the instantaneous change of form required, and because, although the elevating force is greatest under the vertical, it continues to act in the same direction for some hours after the passage of the luminary, with but little diminished force.

This retardation, which would be sensible under the simple supposition of an uninterrupted ocean covering the earth's surface, becomes very considerable under the actual circumstances of the case. - The depth of the sea varies so much, and the form of its basin, taken as a whole, is so interrupted by the land, that it may be doubted whether, were the action of the sun and moon at once suspended, their tide waves would perform even a single revolution with any sort of regularity. Hence it follows that the tides for the time being may be considered as almost completely commanded by the then actual positions and proximities of the sun and moon, the free oscillations of the sea in its bed being quite subordinate to the forced wave generating them. In consequence (as is always the case in forced oscillations), every periodicity in the action of the forcing cause is propagated in the oscillations, and records itself in the recorded height of the tide on every point of the coast, but at each point at a greater or less interval from the culmination of the sun or moon, according to its local position and the more or less circuitous course taken by the tide wave to reach it, which special observation can alone determine. This interval is called the establishment of the place.

The close relation which the times of high water bear to the times of the moon's passage shows that the moon's influence in raising the tides must be much greater than the sun's. In fact, while the whole attraction of the sun upon the earth far exceeds that of the moon, yet, owing to the greater proximity of the latter, the difference between its attraction at the centre of the earth and at the nearest or most remote points of its surface, which produces the tides, is about 2½ times as great as the difference of the sun's attraction at the same points. - There will be two complete lunar tides in every lunar day of 2th. 52m., and also two complete solar tides in every mean solar day. These are known as the semi-diurnal tides, and constitute the principal fluctuations of the sea level. When the sun and moon are in conjunction or opposition, at the time of new or full moon, the effects of both combine to produce the spring tides, when high water is higher and low water is lower than at mean tides by the amount of the solar tide.

At quadratures the high water of the sun will combine with the low water of the moon to produce a less fall, and the low water of the sun with the high water of the moon to produce a less rise, than at mean tides; and we have the neap tides, the range of which is less than the mean range by the amount of the solar tide. Thus, at New York, the rise and fall at syzygies is 5.4 ft., at quadrature 3.4 ft., the former being the sum, the latter the difference of the lunar and solar tides; whence we obtain for the effect of the moon 4'4 ft., and for that of the sun 1 ft., or a ratio of 44 to 10. This proportion does not prove to be the same in all parts of the world, and even varies considerably in places not far distant from each other. At Boston the heights are 11.3 and 8.5 ft. respectively, giving a proportion of 7 to 1. On the Atlantic coast of the United States it averages about 5 to 1, while on the E. side of the Atlantic ocean, on the coasts of France and England, it is in many parts 3 to 1. These differences are to bo ascribed to the fact that the shore and harbor tides which we observe have in every instance acquired a greater magnitude than the ocean tides, and have been modified in form by the varying slope of the bottom and configuration of the shores.

A simple comparison of the range of spring and neap tides will not serve, therefore, as a correct measure of the relative effect of the sun and moon, and hence for a determination of the mass of the moon, which can only be derived from those data by a profound mathematical analysis. - The next variation of the tides to bo considered is that dependent on the moon's declination. Were the moon constantly in the plane of the equator, the highest points of the tide waves would also be in that plane, and would consequently produce a series of equal tides at any place either N. or S. of the equator. But it is evident that when she ascends to the north, the vertex of the tide wave will tend to follow her, giving the highest point of one tide in the northern, and the highest point of the opposite tide in the southern hemisphere. Consequently, when the moon has a northern declination, the tide at any place in the northern hemisphere caused by her upper transit will bo higher than that caused by the lower transit. This variation in the heights has a period of one lunar day, and is called the diurnal inequality; it reaches its maximum when the moon is at its greatest northern or southern declination, and disappears when it is on the equator, and consequently has a half-monthly period.

The variations of height from this cause produce a corresponding inequality in the times of high water. The sun's declination affects the tides in a similar manner, but the amount of the disturbance is very small, and its period extends over half a year. Yet in long series of observations its effect is well marked, both in height and time. The diurnal inequality depending on the moon's declination is on the other hand quite sensible, and in many places constitutes a prominent or even the chief feature of the tides, as on the Pacific coast of North America and in the gulf of Mexico, to the peculiarities of which wo shall recur hereafter. If the tides arrive at the same place by two different channels, and one of them is retarded behind the other by six hours, in consequence of travelling a longer route or in shallower water, the semi-diurnal tides will be destroyed by an interference of the waves, that is, by the high water of one being superimposed on the low water of the other; the diurnal inequality, however, will not be destroyed, but merely modified in height and time, leaving a single tide in the lunar day outstanding, which is always very small in amount.

A further cause of variation in the height of the tides is the variation of the distances of the sun and moon, by reason of the ellipticity of their orbits. The efficacy of a heavenly body in raising tides is shown by theory to be inversely proportional to the cube of the distance. Hence the efficacy of the sun will fluctuate between the extremes 19 and 21, taking 20 for its mean value, and that of the moon between 43 and 59. Taking into account this cause of difference, the highest spring tide will be to the lowest neap as 59 + 21 to 43 - 19, or as 80 to 24, or 10 to 3; leaving out of consideration the local circumstances of access and depth, which greatly modify these proportions. In the North Atlantic the highest tides are observed a day and a half or two days after the syzygies. At New York, the high water which we observe about 8 o'clock in the evening on the days of full or change are those due to the meridian transit of the moon (and sun) on the preceding day, and the highest tide will not occur until the evening of the following day. At Boston this delay, which is called the retard, or age of the tide, is nearly 36 hours.

It is the same at Brest, and the tide wave occupies 10 hours in travelling from Brest up the English channel and Thames to London, making the age of the tide at the latter place 46 hours. This delay, which even at the cape of Good Hope amounts to 14 hours, is still the subject of investigation, and is probably mainly due to friction. The interval between the moon's passage over the meridian of a place and the time of high water, which we have referred to as the establishment of the port, is also called the luni-tidal interval. This interval is constant for each place so far as the lunar tide wave is concerned; but as the actual high water depends upon the combination of the lunar and solar tides, it is subject to a variation which is knowni as the half-monthly inequality in time. On the day after the spring tides the top of the solar tide wave will be nearly an hour in advance of that of the lunar tide wave, and the two waves will combine to make high water earlier than the moon's alone would bring it; hence the luni-tidal interval is shorter.

It will continue to shorten until the moon's transit is later by three hours than when the tide is greatest; it then increases again, passes its mean value when the moon has fallen behind six hours, attains its maximum when it is nine hours later, and again decreases until at the next spring tides it reaches its mean value. The mean of all the luni-tidal intervals for half a month at a port is called its mean or corrected establishment, to distinguish it from the vulgar establishment, which is the luni-tidal interval at full and change. The former is now generally used for finding the time of high water on any given day, and tables are constructed from observations at the principal ports for finding the correction for semi-monthly inequality due to the moon's age. Thus for New York the corrected establishment or mean luni-tidal interval is 8h. 13m., and its least and greatest values are 7h. 52 m. and 8h. 35m. On the Atlantic coast of the United States the range of this inequality is about three fourths of an hour; on the coasts of France and Great Britain it often exceeds an hour and a half.

This difference of the half-monthly inequality in time at different places is analogous to the variation in the proportion of spring and neap tides above noticed, and is due to the same causes. - The motion of the water in the tide wave is totally unlike that in an ordinary surface wave, such as the wind produces. When a narrow wave of the latter kind, or a succession of such waves of equal breadths and heights, is formed in deep water, a light floating body, as a cork, revolves either in a vertical circle or an ellipse not very different from one, having the longer axis vertical. But in the tide wave the movement of each particle may be regarded as performed in an excessively elongated ellipse, the shorter axis of which is vertical. The breadth of the tide wave from crest to crest, supposing all the earth covered, would be half the earth's circumference, or 12,500 miles, in comparison with which the depth of the sea is insignificant; and the slightest consideration suffices to show that, as all the water which goes to form the elevated portion must be brought from that depressed, this can only take place by a lateral approach of the vertical sections of the sea when the water is rising, and their recess from each other when falling (i. e., over a quadrant of the globe in either case, which is only another way of expressing an alternating backward and forward horizontal current at any given place), with this peculiarity, that these currents (the flow and ebb current) run most rapidly at the moments of high and low water; the instants of most rapid rise and fall being those of slack water or no current one way or the other.

In fact, it is obvious that the surface must be rising most rapidly when the water is setting in equally both ways to, and sinking most rapidly when setting out equally both ways from the place; in neither of which cases can there be any current at the place. The tide wave differs also from a wind wave in another very remarkable point. It affects the whole depth of the ocean equally, from the bottom to the surface, while the wind waves, even in the most violent storms, agitate it to a very trifling depth; for the force which acts to produce the former is exerted equally in every portion of the vertical extent of the water, while those producing the latter are strictly confined to the surface. A tide wave of 4 ft. in total height (between high and low water), which is that of the tide at the atolls of the Indian ocean, advancing over a sea 30,000 ft. deep, implies in each particle an alternate advance and recess of 2,800 ft. in its total extent; but this movement, being spread over six hours either way, is nowhere very rapid. , Where a bay or indentation of the coast presents its opening favorably to the tide wave, and decreases in width from the entrance toward its head, the tides rise higher and higher from the mouth upward.

This is due to the concentration of the wave by the approach of the shores, and to the gradual shoaling of the bottom by which a portion of the horizontal motion is transferred into vertical motion, the velocity of the wave being at the same time retarded. This effect is strikingly illustrated by a generalization of the heights of the tides on the Atlantic coast of the United States, developed from the tidal observations made in connection with the United States coast survey. That coast presents in its general outline three large bays : the great southern, from Cape Florida to Cape Hatteras; the great middle, from Cape Hatteras to Sias-conset, Nantucket; and the great eastern, from Siasconset to Cape Sable. Referring to the tide table given below, we find at Cape Florida a mean height of 1.5 ft., and as we follow the coast to the northward a gradually increasing height, reaching 7 ft. at Savannah entrance, then decreasing again, with an exception easily explained, to Cape Hatteras, where it is 2 ft. In the middle bay, following the stations on the coast, and omitting those on the bays and sounds, we have a less regular increase to 4.8 ft. at Sandy Hook, and a decrease to 2.7 ft. at Menemsha bight on Nantucket island.

The configuration of the eastern bay is less regular, and the correspondence of heights requires closer examination. The recess of Massachusetts bay is well marked by the increase in height, reaching 10 ft. at Boston and Plymouth; but the most striking effect of the convergence of shores and shoaling is exhibited in the bay of Fundy. On a line across its mouth, at the Kennebec river as at Cape Sable, the mean height of tide is 8 ft., while at St. John's, N. B., it rises 19 ft., and at Sackville in Cumberland basin, at the head of the bay, 36 ft., attaining to 50 ft. and more at spring tides. When the wave leaves the open sea, its front slope and its rear slope are equal in length and similar in form. But as it advances into a narrow channel, bay, or river, its front slope becomes short and steep, and its rear slope becomes long and gentle. Hence arise the circumstances noticed in the early part of this article, and illustrated by reference to the Chesapeake bay. At the station near the sea the time occupied by the rise is equal to that occupied by the descent; but at a station more removed from the sea the rise occupies a shorter time than the descent.

When the tide is very large compared with the depth of water, this inequality becomes very great; thus in the Severn river, at Newnham, above Bristol (England), the whole rise of 18 ft. takes place in an hour and a half, while the fall occupies 10 hours. As the wave advances over a shoaling bottom, a portion of the horizontal motion is transformed into vertical motion, by which the height of the wave is increased, the most rapid current approaches the greatest rise, and the interval between the stand and slack water is diminished. This exaggeration of the height and current is particularly remarkable whenever the front of the advancing tide wave stretches across the mouth of an estuary with contracting borders, and extensive flats bordering the channel near low-water level; then it produces a bore, or sudden and violent wave of great height, which rushes forward with such impetuosity as to sweep everything before it. Such is the case at the head of the bay of Fundy; likewise in the Hoogly river, in the bay of Bengal; in the Dordogne, where it empties into the Garonne, on the coast of France; and in the Severn river, where at spring tides a bore of 9 ft. in height rushes up stream.

In the river Amazon, at the equinoxes (when the equatorial tide is at its maximum), during three consecutive days bores of 12 or 15 ft. high rush up the river with each high water; so that along the course of the stream, up which for 200 m. from its mouth no fewer than eight tide waves are simultaneously advancing, as many as five bores are.sometimes at once in progress. - It is easily seen that in the smaller seas, which have little or no communication with the ocean, as the Mediterranean, Black, and Caspian seas, and the North American lakes, the tides must be insensible, as the attraction of the moon is at all times very nearly the same for all parts of them. Near the W. end of the Mediterranean, as at Malaga, a small tide is observable, propagated from the Atlantic ocean through the straits of Gibraltar. Tides are also observable at Venice, but the observations have not been discussed so as to determine whether they arise from a small tide wave proper to the Mediterranean, magnified by travelling up the Adriatic sea, although insensible at its mouth, or whether they are variations due to the winds.

Fluctuations of the sea level resembling those of the tides, and causing irregularities in the latter, are often produced by the winds, which in many places have a certain periodicity in their direction and force, as the land and sea breezes in the tropics. They come under consideration here only as complicating the study of the tidal phenomena. - The existing theories, while they suffice for the explanation of the observed facts, are inadequate to the prediction of the phenomena at places where they have not been observed. This arises not from any defect in the principles upon which the theory is based, but from the difficulty of investigating mathematically the motion of fluids, under all the various circumstances in which the waters of the sea and of rivers are found, and from our ignorance of the configuration of the bottom of the sea. The equatorial sea being broken up into three great basins, and open water existing only to the southward of the three great continents, the tides are complicated in a singular way.

In each of these basins the equatorial tide has to take a fresh start from the eastern side with every fresh upper and lower transit of the moon and sun, and is destroyed or confused by reflection on the western coast before the creation of a new wave; while in the open part of the southern ocean the tide wave circulates unimpeded, and spreads into the three oceans up which it runs as a free wave, from S. E. to N. W., overtaking in its progress and compounding with the partial equatorial tides or forced waves proper to either ocean. On approaching the shore, the waves are elevated and retarded by the slope of the bottom, and deflected or crowded together according to the varied configurations of the coasts. It is owing to these complications, together with our ignorance of the laws of friction among the particles of water, and between the water and the bottom, that our theories fail to inform us of the magnitude and time of the tides at any given place. But they determine the periodicity of their phases, and the relative part which each disturbing-force bears to the whole, by which we are enabled, by the analysis of a sufficient series of exact observations at any place, to predict the phases of the tides at the same place for any future time, the knowledge of which is of immense importance to navigation.

It is only since the beginning of the present century that the science of the tides has made any considerable progress in this direction. The theoretical investigations of Laplace, in the Jleca-nique celeste, and his discussions of the tidal observations at Brest, opened the way. Lubbock and Prof. Whewcll contributed largely by the elaborate discussions of large collections of tidal observations, published in the " Philosophical Transactions" of the royal society; and Prof. Airy, in his essay on "Tides and Waves " in the " Encyclopoedia Metropol-itana," has greatly extended our theoretical conceptions of the subject. More recently still important investigations have been published by Prof. W. Thomson and Mr. W. Ferrel. - The tides on the coasts of the United States have been specially investigated by the late Prof. Bache as superintendent of the American coast survey. In connection with that work he organized an extensive system of exact observations, for the purpose of ascertaining the complicated laws which govern the tides.

It will be readily understood that in order to separate the effects of the different causes which modify the phenomena, it is not sufficient to observe merely the heights and times of high and low water, but that a continuous record of the tides is necessary, as the inequalities arc constantly shifting their place and magnitude. For this purpose a self-registering tide gauge is used, by which a continuous curve representing the successive changes in the height of water is traced on paper moved by clockwork, by a pencil acted on by the rising and falling of a float in a vertical box, to which the tide has free access.

The time scale is such that every hour is represented by one inch, and is pricked into the paper by points on the cylinder which moves the paper forward. A continuous sheet, sufficient for the record of a whole month, is put on the tide gauge at one time. A complete description of this instrument will be found in the coast survey report for 1853. Prof. Bache gave in his annual reports on the progress of the coast survey, from 1851 forward, a series of papers on the tides, detailing the processes of discussion, and giving the results as they were from time to time developed. In these are considered the apparent anomalies in the tides in the gulf of Mexico, exhibiting at some places only one tide in 24 hours; the large inequalities in the tides on the Pacific coast; the general progress of the tide wave along our coasts and in the bays and rivers; the influence of the winds in particular localities; and the action of tidal currents on the bars and channels of our harbors. These labors, which are still in progress, have resulted already in the annual publication of "Tide Tables," giving in advance the times and heights of high and low water at all the principal ports of the United States, for every day in the year.

An elaborate discussion of the tides observed at Boston and New York during 19 years, a full lunar cycle, has been made by Mr. William Ferrel of the coast survey, and has resulted in representing the actual tides with unlooked-for precision, yielding moreover a value for the mass of the moon closely approaching that obtained by astronomical methods. - The tides on the coast of the United States, on the. Atlantic, gulf of Mexico, and Pacific, are of three different classes. Those of the Atlantic are of the most ordinary type, ebbing and flowing twice in 24 hours, and having but small differences in height between the two successive high or low waters, one occurring before noon, the other after noon. Those of the Pacific coast also ebb and flow twice during 24 hours, but the morning and afternoon tides differ very considerably in height, so much so that at certain periods a rock which has 3½ ft. of water upon it at low tide may be awash (nearly bare) on the next succeeding low water. The intervals, too, between successive high and successive low waters may be very unequal.

At San Francisco, for example, at a time when the moon has a large southern declination, the high water occurring about 12 hours after the moon's transit may mark 5 ft. on a tide staff; five hours afterward low water will mark 3½ ft., six hours after which the second high water will reach 7½ ft., and seven hours later the second low water will fall to zero. These inequalities depend upon the moon's declination, in the manner which we have explained; they disappear at the time of the moon's declination being nothing, and are greatest about the time of its being greatest. These tides exhibit the normal type, while those at New York and adjacent parts of the Atlantic coast do not exhibit the diurnal inequality. The explanation of this feature is probably to be found in the supposition that the tide wave which advances up into the Atlantic ocean from the continuous tide in the Southern ocean, arrives on our shores 24 hours later than the direct tide wave which crosses the Atlantic from E. to W. In this way the diurnal inequality will be eliminated by the superposition of the two tides, the greater high water of the former coinciding with the lesser of the latter, and vice versa, leaving the semidiurnal tides of equal height.

The tide at Galveston, in the gulf of Mexico, furnishes a case of the elimination of the semi.diurnal tide, leaving only the diurnal inequality. It is to be presumed in this instance that the tides reaching Galveston through the straits of Florida and through the passage between Cuba and Yucatan differ by six hours in their periods, causing the low water of one to coincide with the high water of the other, thus sensibly destroying the semi.diurnal tides, except in so far as they are unequal. This leaves a small tide outstanding, having substantially the form of the diurnal inequality, and producing the appearance of the "single day tide," or one high and one low water in every 24 hours. This residual fluctuation is well marked at times when the moon's declination is considerable on either side of the equator, but disappears almost entirely when the moon is near the equator, since at such times the diurnal inequality disappears. Tides of this class have always a small range; in the gulf of Mexico they rarely exceed 2½ ft., and the average rise and fall is but 1½ ft. The tide gauges being in continuous operation, all other fluctuations of the ocean level, besides that produced by the tides, are likewise registered.

The tide curves of the western coast are frequently found indented by fluctuations arising from earthquakes. A remarkable instance of this kind was furnished by the earthquake that destroyed the city of Shimoda, Japan, in December, 1854. The time required for the transmission of the sea waves from Shimoda to San Francisco was 12h. 3Gm. The distance being 4,500 m., the transmission of the wave was at an average rate of 360 m. an hour. The theory of wave motion teaches us that this velocity will be attained by a free.moving wave in a depth of 1,440 fathoms, which may be taken as the average depth of the Pacific between Japan and California. The crests of the waves occurred at intervals of about 23 minutes, corresponding to a length from crest to crest of 150 m. The height when the waves arrived at San Francisco was about 18 in. from hollow to crest. The great earthquake in Peru in August, 1808, was likewise recorded on the tide gauges at San Diego, San Francisco, and Astoria. The fluctuation of the ocean in this instance was very sensible to casual observation, and was noted in Australia, at the Sandwich islands, and at Kodiak, Alaska. The data obtained from these observations, combined with the result before mentioned, indicate that the average depth of the Pacific ocean is about 1,800 fathoms.

Such waves, originating with an impulse at one definite point, and propagated freely through the ocean in every direction with a velocity depending upon the square root of the depth of the sea, serve as good illustrations of the manner in which tides are propagated as free waves through sounds, bays, and rivers. The rate of motion for different depths is as follows: at 10 ft., 12.2 m. an hour; 60 ft., 30 m.; 100 ft., 38.7 m.; 1,000 ft., 122.3 m.; 6,000 ft., 299.5 m.

* The mean interval in column 2 has been increased by 12h. 26m. (half a mean lunar day) for some of the ports in Hudson river, Delaware river, and Chesapeake bay, so as to show the succession of times from the mouth.