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 GC 301 
 
 c"p, 1 ON TIDES 
 
 TIDAL ACTIOK IN HARBORS, 
 
 BY 
 
 I>ROFESSOR J. E. HILG-j^RD 
 
 OF THE 
 
 UNITED STATES COAST SURVEY. 
 
 EEPBINTED FEOM THE SMITHSONIAN EEPORT EOE 1874. 
 
 WASHIKGTOK: 
 
 aOVEBNMENT PRINTINa OFFICE 
 1875. 
 
11 
 
 I 
 
ON TIDES AND TIDAL ACTION IN HARBORS.* 
 
 By Professor J. E. Hilgard, of the U. S. Coast Survey, Washington, D. C. 
 
 Ladies AND Gentlemen: I propose to eugage your attention this 
 evening with the subject of the tides of the ocean and the influence ex- 
 erted by tidal currents on our harbors. I shall first briefly describe the 
 phenomena of the tides as they present themselves to an observer, then 
 consider the physical causes to which these phenomena are due, next 
 examine more in detail the phases of the tide on our own coasts, and 
 finally describe the tidal hydraulics of the magnificent harbor of New 
 York!! 
 
 The most obvious change in the surface of the ocean to be noticed 
 upon our shores is the alternate rising and falling regularly twice in 
 every day. Closer attention will show that the tides of each day occur 
 somewhat later than those of the preceding day, the average time of re- 
 tardation being fifty-two minutes, and that this retardation corresponds 
 to that of the moon. It will pass as a fair approximation to say, that it 
 is high water at New York with a southeast moon, or similarly for New 
 Castle, on the Delaware, that high water occurs when the moon is south 
 In fact, so closely is the time of tide connected with the position of the 
 moon, that in order to give the time of high water upon any day ap- 
 proximately it is customary to state the time of high water on the days 
 of the new and full moon, when the moon passes the meridian at twelve 
 o'clock, nearly. This time is called the " establishment of the port." 
 Then, to find the time of high water on any other day, it is only neces- 
 sary to add the " establishment " to the time of the moon's meridian 
 passage on that day. 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, called the hmi-tidal interval, varies with the 
 moon's age very sensibly. Moreover, the elevation at high water and 
 depression at low water will not always be the same, but will be great- 
 est about the times of new moon and full moon, and least about the first 
 and third quarters. The details of these variations will be best traced 
 out in connection with the explanation of their causes, to which we will 
 now proceed. 
 
 The popular explanation of the tides, as depending on the law of gravi- 
 tation, is sufficiently simple, although the complete mathematical inves- 
 tigation of the subject, by which we should be enabled to predict their 
 
 * Delivered before the American Institute, January 27, 1871, with revision. 
 
 3 
 
^ 30| 
 
 4 ON TIDES AND TIDAL ACTION IN HARBOES. y\r 
 
 occnrrence and niagiiitiide for any place, is encompassed with difficul- 
 ties, from canses to wbicli we shall hereafter revert. 
 
 If we conceive the earth to be wholly, or for the greater part, covered 
 with water and subject to the attraction of the sun, the force of which 
 varies inversely as the square of the distance, it will be obvious, that 
 while the whole earth will fall toward the suu 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 center,) the water nearest to the 
 siui 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 attrac- 
 tion and rotation, until the pressure of the elevated- mass equals the dif- 
 ference 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 j 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 center 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 ninety degrees from the v^ertices 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 pre- 
 cisely under, the other j)recisely opposite to, the points at which the 
 disturbing body is vertical. This, however, 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 it is that waves 
 are produced which follow them round the globe. The highest points 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 5 
 
 of tbese waves will remain far bebiiul the verticals of the disturbing 
 bodies, liecause the inertia and friction of the water prevent the rapid 
 change of form required, and because, although the elevating force is 
 greatest under the vertical, it still 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 supposi- 
 tion 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 no regular progressive move- 
 ment of the tide- wave can take place, except in the great Southern 
 Ocean. At all points on the coast the phases of the tide will follow 
 the periodicity of the forces causing them, 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. This interval and the actual rise and fall of the 
 tide must be determined for each place by special observation. 
 
 LUNI-SOLAR PHASES OF THE TIDES. 
 
 The close relations which the times of high water bear to the times 
 of the moon-s passage show 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 i)roximity of the latter, the difference between 
 its attraction at the center of the earth and at the nearest or most 
 remote point of its surface, which difference alone produces the tides, 
 is about two and a half times as great as the difference of the sun's 
 attraction at the same points. 
 
 SEMI-MONTHLY INEQUALITY. 
 
 We will now consider the particular phases resulting from the com- 
 bination of the lunar and solar 'tides, and from the varying positions of 
 those bodies. There will be two complete lunar tides in every lunar 
 day of twenty-four hours fifty-two minutes, and also two complete 
 solar tides in every mean solar day of twenty-four hours. These are 
 known as the semi-diurnal tides, and constitute the principal variations 
 of the sea-level. The combined effect of these two fluctuations will be 
 most readily understood by reference to the annexed diagram, in which 
 the lunar tide is represented by dashes, the solar by dots, and the com- 
 bined or actual tide by a full line. At the time of syzygies, or full and 
 change of the moon, the effects of both sun and moon combine together 
 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 quad- 
 ratures the high water of the sun will combine with the low water of 
 
G ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 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 j 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 ]^ew York, the rise and fall 
 at syzygies is 5.4 feet, at quadrature 3.4 feet, the former being the sum, 
 
 SENIl- MONTHLY INEaUALITY 
 
 c 
 
 J*" 0^ f 
 
 
 s'^ 12 
 
 
 ^^'^ 
 
 ^\ 1 
 
 
 03 
 
 X--" 
 
 '^^-X 
 
 
 cl 
 
 /x 
 
 N V 
 
 A 
 
 
 
 
 T^^^ 
 
 
 .-•■'' 4 
 
 CO 
 
 
 
 V 
 
 --y/ 
 
 
 
 
 v-^._ ,-"y 
 
 
 
 
 V. ^ 
 
 NEV/ OR FULL 
 MOON 
 
 QUA.RTER 
 
 OCTAfciT 
 
 the latter the difference of the lunar and solar tides, whence we obtain 
 for the effect of the moon 4.4 feet and for that of the sun one foot, or a 
 ratio of. forty-four to ten. This proportion does not prove to be the 
 same in all parts of the world, and even varies considerably in places 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 7 
 
 not far distant from each other. At Boston the heights are 11.3 and 
 8.5 feet, respectively, giving a proportion of seven to one. On the 
 Atlantic coast of the United States it averages about five to one, while 
 on the east side of the Atlantic Ocean, on the coasts of France and 
 England, it is in many parts as three to one. These differences are to 
 be 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, in consequence of the wave having passed over a sloping bottom 
 and having been greatly retarded by the efl'ect of friction. A comparison 
 of the range of spring and neap-tides, therefore, will not serve as a 
 correct measure of the relative effect of the sun and moon, unless the 
 effect of friction were taken into consideration, which we are at present 
 unable to do for want of a complete knowledge of the configuration of 
 the bottom. 
 
 The interval between the moon's meridian passage and the time of 
 high water is subject to a variation similar to that of the height. On 
 the day after the spring-tides, tlie top of the solar tide-wave will be 
 nearly an hour in advance of the lunar tide-wave, and the two waves 
 will combine to make high water earlier than the moon's alone would 
 bring it. It will continue to be earlier until the moon's transit is 
 later by three hours, or in the first octant. It then falls back until it 
 is latest in the third octant, and again advances, until, at the next 
 spring-tides, it reaches its mean period. The mean of all the luni- tidal 
 intervals for half a month at a port its called its mean estahlisliment^ 
 which is used for finding the time of high water on any given day j and 
 tables are constructed from observations at the principal ports for find- 
 ing the correction for semi-monthly inequality due to the moon's age. 
 Thus, for New York, the mean luni-tidal interval is 8h. 13m., and its 
 least and greatest values are 7h. 52m. and 8h. 35m. On the Atlantic 
 coast of the United States the range of this inequality is about three- 
 quarters of an hour ] on the coasts of France and Great Britain it often 
 exceeds one and a half hours. 
 
 DIURNAL INEQUALITY. 
 
 The next variation of the tides to be considered is that dependent on 
 the moon's declination. Were that body 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 north or south of the equator. But it is evident that, when the 
 moon ascends to the north, the vertex of the tide-wave will tend to fol- 
 low it, giving the highest point of one tide in the northern, and the 
 highest point of the opposite tide in the southern, hemisphere. Conse- 
 quently, when the moon has a northern declination, the tide at any place 
 in the northern hemisphere caused by its upper transit will be higher 
 than that caused by its lower transit. (See diagram of diurnal inequal- 
 ity.) This variation in the heights has a period of one lunar day, and 
 
8 
 
 ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 is called the diurnal inequality; it reaches its maximum whcD 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 
 Tariations of height from this cause produce a corresponding inequality 
 in the times of high water. The sun's declination aftects the tides in a 
 similar manner, but the amount of the disturbance is very small, and its 
 period extends over half a year. In long series of observations its effect 
 is nevertheless well marked, both in height and time. The diurnal in- 
 equality, depending upon the moon's declination, is, on the other hand, 
 quite sensible, and in many places constitutes a prominent feature of 
 the tides, as on the Pacific coast of North America. 
 
 PIURNAL INEQUAUXr *5v^ 
 
 i 
 
 PARALLACTIC INEQUALITY. 
 
 A further cause in the variation of the height of the tides is the varia- 
 tion of the distances of the sun and the moon by reason of the ellipticity 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 9 
 
 of their orbits. The efficacy of a heaveuly body in raising tides is shown 
 by theory to be inversely proportional to the cube of the distance. 
 Hence the efficacy of the suu will fluctuate between the extremes nine- 
 teen and twentv-one, taking twenty for its mean value, and that of tlie 
 moon between"^ forty-three and fifty-nine. Taking into account this 
 cause of difiference, the highest spring-tide will be to the lowest neap as 
 59+21 to 43—19, or as eighty to twenty-four, or ten to three ; leaving 
 out of consideration the local circumstances of access and depth, which, 
 as we have stated, modify those proportions in a marked degree. 
 
 TYPE CURVES. 
 
 "- The three principal forms of tides are illustrated in the annexed dia- 
 gram, which exhibits the tides at New York, San Francisco, and Galves- 
 ton for two days from actual observation. Of these, that for San Fran- 
 cisco may be taken as the normal type, showing the diurnal inequality, 
 while that at New York, as at other ports on the Atlantic coast, is not 
 sensibly affected by it. 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 ar- 
 rives on our shores tw«iw>hours later than the direct tide-wave which 
 crosses the Atlantic froii east to west. In this way the diurnal inequal- 
 ity 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 semi-diurnal tides of equal height. 
 
 TIDE REGISTERS 
 
 gonvAR 
 
 TEXAS 
 
 The tide at Galveston, on the other hand, furnishes a case of the elim- 
 ination of the semi-diurnal tide, leaving as a residual only the diurnal 
 
10 ON TIDES AND TIDAL ACTION IN HAEBORS. 
 
 inequality. It is to be presumed in this instance tliat the tides reaching 
 Galveston through the straits of Florida and through the passage be- 
 tween 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 twenty -four 
 hours. This residual fluctuation is well marked at times when the 
 moon's declination is considerable on either side of the equator, but dis- 
 appears 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 two and 
 a half feet, and the average rise and fall is but one and a half foot. 
 
 The tides on the coasts of the United States have been specially in- 
 vestigated by Professor Bache, the late Superintendent of the American 
 Coast Survey. In connection with that work he organized an extensive 
 system of exact tidal observations, for the purpose of ascertaining the 
 complicated laws which govern the tides of the seas that wash our 
 shores. 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 are constantly shifting their place and magnitude. 
 
 TIDE-aAUGES. 
 
 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 clock-work, by a pencil actuated 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. The scale of heights is so adapted to the 
 range of the tide at the place of observation that the extreme range of 
 the curve will not exceed the width of the sheet — twelve inches. A con- 
 tinuous 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 United States Coast Survey Report for 1853. [The 
 lecturer illustrated the construction of several tide-gauges by means of 
 diagrams.] 
 
 In northern ports interruptions are experienced in winter from the 
 float-box becoming clogged with ice, and various devices have been 
 resorted to for overcoming this difficulty. One of the most effective has 
 been that of maintaining a temperature above freezing within the float- 
 box by means of a simple heating-apparatus. An arrangement of this 
 kind has actually been used on the Fox Islands, in Penobscot Bay. A 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 11 
 
 stream of water flows slowly from an elevated liogsbead tlirongh a coil 
 in a large stove, passes down to the bottom of the float-box and np 
 again into anotber bogsbead, from wbicb it is pumiced up every day by 
 tbe observer into tbe first one. As but a small elevation of temperature 
 is necessary, tbis arrangement bas proved quite sufficient. 
 
 Anotber arrangement, devised by Mr. Batcbelder, of Boston, and 
 called by bim an ^'Arctic tide-gauge," is in use at Boston, and bas com- 
 pared well witb tbe ordinary float-gauge. It consists of a strong iron 
 tube, about four inches in diameter, firmly bolted to a wbarf or pile. It 
 is open at tbe top, and bas at tbe lower end a nipple, to wbicb an India- 
 rubber bag is fastened ; tbe lengtb of tbe tube being sufficient to allow 
 tbe elastic bag to be always submerged at tbe lowest stage of tbe tide. 
 Tbe bag is supported by a suitable sbelf or cage, and is filled witb 
 glycerine, wbicb is poured in at tbe top of tbe tube. When in tbis con- 
 dition tbe glycerine rises and falls witbin tbe iron tube in proportion to 
 tbe varying beigbt and pressure of tbe column of water above tbe rub- 
 ber bag, tbe difference in tbe beigbt of tbe two columns being in pro- 
 portion to tbe difference of tbe specific gravity of tbe water and tbe 
 glycerine. The parts above described insure protection against floating 
 ice^ and prevent congelation within tbe iron tube. 
 
 A copper tube about three inches in diameter, closed at tbe bottom 
 and open at tbe top, is placed within the iron tube, and floats in the 
 glycerine 5 if left free, it would rise and fall witb tbe changing level of 
 tbis liquid. The length of the central tube is a little greater than the 
 whole range of the tide. 
 
 Near the upper end of the outer tube there are three spiral springs, 
 fixed at the top and united at tbe bottom by a plate or disk, from which 
 the central copper tube is suspended. From a stem fixed to the central 
 tube or float, and moving witb it, a string or chain leads over a single 
 pulley, and gives horizontal motion to tbe pencil- carriage of tbe record- 
 ing-apparatus. 
 
 The distance that the central tube is to move vertically is adjusted to 
 agree with the required range of the pencil upon the record-paper by 
 placing within it suitable weights. 
 
 As the glycerine rises or falls in the annular space between the iron 
 tube and tbe central float, the spiral spring at the top is more or less 
 extended, tbe extension being uniform on account of the cylindrical form 
 of the float. 
 
 It is not necessary that the India-rubber bag be inclosed in a perfo- 
 rated box, for tbe purpose of preventing oscillation, as it is always sub- 
 merged, and the pressure upon it is equal to the weight of the column 
 of water, having its base at tbe bag, and its summit at the mean level of 
 tbe surface-waves- 
 
 A tide-gauge, for observations on an open coast, bas been devised by 
 Mr. Henry Mitchell, of the Coast Survey. The graduated scale on the 
 float is read from tbe shore by means of a spy-glass, the top of tbe tube 
 servin gas index-mark. 
 
12 
 
 ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 PREDICTION OF TIDES. 
 
 Self-registering tide-gauges have been kept in operation for a number 
 of years at different points on both coasts of the United States, in order 
 to obtain from them the data for predicting the tides 5 and as a result, 
 tide-tables have been published by the Coast Survey for some years 
 I)ast, giving in advance the times and heights of high and low water for 
 all the principal ports in the United States for every day in the year. 
 In addition to this, the differences are given by which to find the same 
 for intermediate ports. 
 
 A very elaborate discussion of the tides observed at Boston during 
 nineteen 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. By the Introduction of the consideration of 
 friction Mr. Ferrel has also succeeded in deriving a value for the mass 
 of the moon, which appears to compete in exactness with the values 
 obtained by astronomical methods. It is one seventy-seventh part of 
 that of the earth. 
 
 EARTHQUAKE-WAVES. 
 
 The tide-gauges being in continuous operation, all other fluctuations 
 of the ocean-level besides those produced by the tides are likewise reg- 
 istered. The tide-curves of the western coast are frequently found in- 
 dented by fluctuations arising from earthquakes. A remarkable instance 
 of this kind is given in the annexed diagram of earthquake-waves, which 
 
 EARTHaUAKE WAVES AT FORT PT, AS RECORDED ON THE SELF-REGISTERING TIDE GAUGE. 
 
 recorded the earthquake that destroyed the city of Simoda, in Japan, 
 in December, 1854. The upper curve is a reduction from the tide-gauge 
 register, while the lower shows the earthquake-waves separated from 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 13 
 
 tbe tidal wave. The time required for the transmission of the sea-waves 
 from Simoda to San Francisco was twelve hours and thirty-six minutes. 
 The distance being 4,500 miles, the transmission of the wave was at an aver- 
 age rate of 360 miles per 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 Ocean 
 between Japan and California. It will be observed that the crests of 
 the waves occur at intervals of about twenty-three minutes, correspond- 
 ing to a length, from crest to crest, of 150 miles. The height when 
 the waves arrived at San Francisco was about eighteen inches from 
 hollow to crest, the high waves caused by the original impulse having 
 gradually flattened out to that form in their transmission across the 
 ocean. 
 
 The great earthquake which occurred in Peru, in August, 186S, was 
 likewise recorded on the tide-gauges at San Diego, San Francisco, and 
 Astoria. The fluctuation of the ocean was so great in this instance as 
 to be very sensible to casual observation, and was noted in Australia, 
 at the Sandwich Islands, and at Kodiak, in 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. 
 
 MOVEMENT OF TIDAL WAVES. 
 
 The waves above described, originating with an impulse at one definite 
 point, and propagated freely through the ocean in every directioo, with 
 a velocity depending upon the square root of the depth of the sea, may 
 serve as good illustrations of the manner in which tides are propagated 
 through sounds, bays, and rivers. The following table gives the rate of 
 motion for different depths : 
 
 Depth in feet 
 
 ..... 10 
 60 
 
 Miles 
 
 u 
 
 u 
 a 
 
 u 
 
 per 
 
 hour . 
 
 12 2 
 
 a 
 
 30. 
 
 u u 
 
 100 
 
 u 
 
 38. 7 
 
 a (( 
 
 . . .1, 000 
 
 u 
 
 122. 3 
 
 a ci 
 
 6, 000 
 
 ii 
 
 299. 5 
 
 That movement of the ocean, however, which we have designated by 
 the name of tide- wave, does not partake of the nature of a wave in the 
 common acceptation of the term, but it is rather to be conceived as a 
 general movement of the water toward a point under the attracting body, 
 and again away from it. Its periodicity is strictly dependent upon that 
 of the attracting body. The velocity of the movement is about 1,000 
 miles per hour on the equator ; it extends to the bottom of the ocean, 
 the depth of which is inconsiderable compared with the radius of the 
 earth. It is not attended by a sensible elevation of the water in mid- 
 ocean ; and in this respect the characteristic of what we call a wave is 
 absent. The movement may be likened to that of an impulse given to 
 a very long rigid bar, as of iron. In this case, a sensible time will be 
 
14 
 
 ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 required for the transmission of the impulse from one end to the other, 
 and during its transmission the particles will successively approach to 
 each other, by which an infinitesimal elevation and subsidence, after 
 the manner of a wave, will be produced. In the same way the trans- 
 
 riMES AND HEIGHTS OF TIDES ON ATLANTIC COAST OF UNITED STATES 
 
 CAPE/FLORIDA 
 
 mission of the movement through the incompressible water of the sea 
 is attended with an infinitesimal elevation and recession ; but when the 
 movement reaches shallow water, in approaching the shores, the hori- 
 zontal motion is partly translated into vertical motion upon the sloping 
 bottom J and it is thus that the tides attain sensible vertical height. 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 15 
 
 Now, where a bay or indentation of tbe coast presents itself, opening 
 favorably to tbe tide- wave tbus developed, and decreases in width from 
 its entrance toward its head, the tide rises 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. 
 
 This effect is strikingly ilhistrated by a generalization of the heights 
 of the tides on the Atlantic coast of the United States. That coast 
 presents, in its general outline, as represented in the annexed diagram, 
 three large bays : the great southern, from Cape Florida to Cape Ilat- 
 teras ; the great middle, from Cape Hatteras to Nantucket 5 and the 
 great eastern, from Nantucket to Cape Sable, now known as the Gulf 
 of Maine. It will be seen that the tide-wave arrives at about the same 
 time at the headlands, Cape Florida, Cape Hatteras, Nantucket, and 
 Cape Sable, and that at those points the height is inconsiderable com- 
 pared with the rise at the head of the several bays. Thus, at Cape 
 Florida the mean rise and fall is only one and one-half of a foot ; at 
 Hatteras, but two feet ; while at the intermediate entrance to Savannah 
 it reaches seven feet, declining in height toward both capes. Again, at 
 the head of the middle bay, in New York Harbor, it reaches five feet, 
 while on the southeast side of Nantucket Island it is little over one 
 foot. The configuration of the eastern bay is less regular, and the cor- 
 respondence of heights is not so obvious. The recess of Massachusetts 
 Bay is well marked, the increase in height reaching ten feet at Boston 
 and Plymouth. Soiling on eastward along the coast of Maine, it con- 
 stantly increases j but the most striking effect of the convergence of 
 shores is exhibited in the Bay of Fundy. At St. John's the mean height 
 of tide is nineteen feet, and at Sackville, in Cumberland Basin, thirty- 
 six feet, attaining to fifty feet and more at spring-tides. 
 
 When the wave leaves the open sea, its front slope and 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 less inclined. Hence arises the fact that 
 at a 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. Thus, in Delaware 
 Bay and Eiver we have the following relations of the duration and 
 height of rise and fall : 
 
 Station. 
 
 Delaware breakwater 
 
 'Egg Island light 
 
 New Castle 
 
 Philadelphia 
 
 Mean rise 
 and fall. 
 
 Feet. 
 3.5 
 6.0 
 5.5 
 6.0 
 
 Luni-tidal 
 interval. 
 
 h. m. 
 
 8 
 
 9 4 
 11 53 
 13 44 
 
 Mean duration of — 
 
 Flood-tide. Ebb-tide. 
 
 h. m. 
 6 18 
 5 56 
 5 24 
 4 52 
 
 h. m. 
 6 8 
 
 6 30 
 
 7 2 
 7 34 
 
16 ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 Au examination of this table will show, besides the marked increase 
 in the height of the tide due to the contraction of the shores from the 
 capes np to New Castle, a subsequent loss from friction in a narrow 
 channel of nearly uniform character, and correspondingly a rapid propa- 
 gation of the tide-wave through the deep water of the bay, and a com- 
 paratively slow movement along the narrower channel of the river. At 
 the mouth of the bay the duration of rise exceeds that of fall by ten 
 minutes, while at Philadelphia it is less by two hours forty-two min- 
 utes. AVheu the tide is very large compared with the depth of water, 
 this inequality becomes very great ; thus, in the Severn Eiver, at Newn- 
 ham, above Bristol, England, the whole rise of eighteen feet takes place 
 in one and a half hours, while the fall occupies ten hours. 
 
 TIDAL CURRENTS. 
 
 The agency of tidal currents in producing changes in the entrances 
 of bays and harbors is a subject of the first importance to commerce 
 and navigation, and has received full attention in the prosecution of the 
 American coast survey. The laws according to which the changes 
 take place require to be studied by long-continued observation, and 
 when the change is for the worse, the means of counteracting it must 
 be pointed out. 
 
 As on the average the same amount of water moves inward and out- 
 ward with the flood and ebb tides, we might readily suppose that the 
 same amount of material is transported either way, and that no impor- 
 tant change would take place in the configuration of the bottom. But 
 the operation of the flood-stream is very different from that of the ebb- 
 stream. We have, as a general feature, an interior basin of some ex- 
 tent, communicating with the sea by a comparatively narrow passage. 
 The flood-stream, therefore, running with considerable velocity through 
 this channel, will, as it enters the basin, spread out and become slow, 
 depositing the sand and mud it is charged with, and making extensive 
 flats or shoals opposite the entrance. The ebb-stream runs slowly over 
 the flats from all directions toward the opening without removing much 
 of the deposit, and gradually concentrates in definite narrow channels, 
 which it scoops out, and the depth of which will depend in a great de- 
 gree on the proportion of the area of the basin to the outlet, or, in other 
 terms, on the difference of level which will be reached during the ebb 
 between the basin and the ocean, which determines the greatest veloc- 
 ity and transporting power reached by the ebb-stream. 
 
 On the bars of most of the sand-barred harbors on our southern coast, 
 the place and direction of the channel are frequently changed during 
 violent storms j when the direction of the waves happens to be oblique to 
 that of the channel, or when the sea runs directly upon the channel, the 
 depth of water may be considerably diminished for the time being by the 
 sand rolled uj) by the waves. But in all these cases it is found that 
 the normal depth is speedily restored by the scour of the ebb-tide, which 
 
ON TIDES AND TIDAL ACTION IN HAKBORS. 
 
 17 
 
 depends upon the unchanged factors of area and form of basiu, height 
 of tide, and character of the material formiug the bar. 
 
 EFFECT OF SINKING STONE-FLEET ON CH^KLESTON BA[\ 
 
 
 
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 An interesting instance of this maintenance of the depth of channels 
 from a determinate tidal basin is furnished by the effects of the ob- 
 structions placed in the channel over Charleston Bar during the war of 
 the rebellion. On the accompanying diagram is seen the " stone fleet " 
 sunk in the main channel, which at that time had twelve feet of water 
 at low tide where the figure 7 indicates the present depth. There was, 
 moreover, another channel, making out more to the southward, with 
 2 T 
 
18 
 
 ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 nine feet of water, where the figure 3 indicates the present depth. The 
 vessels were placed checker-wise, in such a manner as to impede naviga- 
 tion, while interfering least with the discharge of the water. The effect, 
 nevertheless, was the formation of a shoal in a short time, and the 
 scouring out of two channels, one on each side of the obstructions, 
 through which twelve and fourteen feet can now be carried at low water. 
 The increased water-way thus given to the ebb-tide caused it to aban- 
 don the old nine-foot channel on the less direct course to deep water. 
 We have here the total obstruction of a channel which was of consider- 
 able importance to the southward trade by new conditions introduced 
 at a point four miles distant from where the effect was produced, and 
 we are warned how carefully all the conditions of the hydraulic system 
 of a harbor must be investigated before undertaking to make any 
 change in its natural conditions, lest totally unlooked-for results be pro- 
 duced at points not taken into consideration. 
 
 NEW YORK HARBOR. 
 
 Approaching now more closely to the consideration of the tidal con- 
 ditions in New York Harbor, we will examine the progress of the tide- 
 wave through Long Island Sound from the eastward to its meeting with 
 that entering I^ew York Bay at Sandy Hook. 
 
 TIMES AND HEIGHTS OF TIDES IN LONG ISD. SOUND AND NEW YORK HARBOR. 
 
 """ bl'ock I. 
 
 We see from the annexed diagram that about seven and a half hours 
 after the transit of the moon high water has advanced just within Block 
 Island with an elevation of two feet, and at the same time has just 
 passed Sandy Hook with an elevation of four and a half feet. Travers- 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 19 
 
 jng the sound at a rate indicated by the Eoman figures, with increasing- 
 heights indicated by the Arabic numerals, it reaches Sand's Point 
 eleven and a half hours after the transit of the moon with a height of 
 seven and seven-tenths feet. Tbe observed time of transmission from 
 the Eace to Sand's Point is two hours one minute, and tbe time com- 
 puted from the deptbs, according to the law developed by Airy, is two 
 hours fourteen minutes — a very good approximation, when we consider 
 the irregularities in the configuration of the sound, which could nofc be 
 taken into account. Advancing still farther, the height somewhat de- 
 clines in consequence of the changes of direction in the channel and 
 its shallowness. At Hell Gate this tide-wave is met by that which had 
 entered at Sandy Hook, and advanced more slowly, owing to the nar- 
 rowness and intricacies of the channel, especially in the East River. 
 
 These two tides, which meet and overlap each other at Hell Gate, dif- 
 fering from each other in times and heights, cause contrasts of water- 
 elevations between the sound and harbor which call into existence the 
 violent currents that traverse the East Kiver. The conditions of the 
 tidal circulation through Hell Gate are such, that if there were a parti- 
 tion across it, the water would sometimes stand nearly five feet higher, 
 and at other times five feet lower, on one side than on the other. In the 
 actual case of the superposition or compounding of the two tides the 
 difference of level existing at any time is of course much less; but 
 the difference of one foot is often observed within the space of 100 
 feet in the most contracted portion of Hell Gate, off Hallett's Point 
 Eeferring now more particularly to the diagram representing New 
 York Bay and Harbor, it is important to observe that the entrance from 
 Long Island Sound is a natural depression or arm of the sea, which is 
 not changed by the forces now in operation. The tidal currents which 
 flow through it do not change the channel, but are obliged to follow it 
 in its tortuous course. The Sandy Hook entrance, on the contrary, is 
 characterized by a cordon of sands, extending from Sandy Hook to 
 Coney Island, intersected by channels, which are maintained against 
 the action of the sea, that tends to fill them up, by the scour of the ebb- 
 tide from the tidal basin of New York Harbor. 
 
 Unlike Hell Gate passage, where permanence is the leading charac- 
 teristic, the bar and channels of Sandy Hook have undergone continual 
 changes within the brief period of our history. The advance of Sandy 
 Hook upon the main ship-channel is among the notable and important 
 instances of the effect of tidal currents. Within a century it has in- 
 creased a mile and a quarter. In the place where the beacon on the 
 end of the Hook now stands were forty feet of water fifteen years before 
 it was built. The cause of this growth is a remarkably northwardly 
 current along both shores of the Hook, running both during the flood 
 and the ebb tides with varying rates, and resulting from those tides 
 directly and indirectly. 
 
 The best water over the bar is about two miles east of Sandy Hook 
 
20 
 
 ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 light, in a direct line with the swash channel, which is the second open- 
 iug — shown on the sketch — above the Hook; the shoal lying between 
 the main or Hook channel and the swash channel being known as 
 riynn's Knoll. The greatest depth over the bar is twenty-two feet at 
 mean low water ; and very nearly the same depth can now be carried 
 through the swash channel, which formerly was three feet shallower, 
 
 ENTRANCE TO NEW YORK HARBOR 
 
 •NEWARK 
 
 but has deepened since the cross-section between the Hook and Flynn's 
 Knoll has been diminished by one-third its area by the growth of the 
 Hook. This relative change in the capacity of the channels has not, 
 however, affected the depth on the outer bar, which, according to the 
 principles above laid down, is dependent mainly upon the area of the 
 tidal basin within. 
 
 The depth of twenty-two feet at mean low water, which is now main- 
 tained at the entrance through the sands constantly thrown up by the 
 
ON TIDES AND TIDAL ACTION IN HARBORS. 21 
 
 waves of the sea, may be considered as depending upon tlie following 
 elements: 
 
 1st. The large basin between Sandy Hook and Staten Island, includ- 
 ing Earitan Bay, whicli furnishes more than one-half of the whole ebb- 
 scour 5 
 
 2d. What is called the Upper Bay, including the Jersey flats and 
 Newark Bayj 
 
 3d. The North Eiver, perhaps as far as Dobbs' Ferry, maintaining 
 the head of the ebb-current, although not directly taking part in the 
 outflow ; and, 
 
 4th. A portion of the sound tide, whicli flows in through Hell Gate. 
 
 The proportion of the three first divisions in producing the depth of 
 channel may be approximately estimated by a comparison of the areas 
 and distances from the bar. In order to maintain the depth which we 
 now have, it is important that the area of the tidal basin should not be 
 encroached upon. In proportion as that is diminished the depth of the 
 channels will decrease. 
 
 The flats, just bare at low water, but covered at high tide, form as 
 important a part as any other portion, for it is obvious that it is only 
 the volume of water contained between the planes of low and high 
 water^ — the " tide-prism" — that does the work in scouring the channels. 
 The water on the flats is especially useful by retarding the outflow, 
 thus allowing a greater difference of level to be reached between the 
 basin and. the ocean. 
 
 When we yield to the demands of commerce any portion of the tidal 
 territory to be used for its wharves and docks, we must do so with fall 
 cognizance of the sacrifice we are about to make in tlie depth of water 
 over the bar ; and in order to form any well-founded judgment in re- 
 gard to the effect of such encroachments, it is necessary to be in pos- 
 session of the fullest knowledge of all the physical facts involved in 
 the problem, and no measure of encroachment should be determined 
 upon except in pursuance of the advice of scientific experts. 
 
 A proposition frequently mooted by men of enterprise, and resisted 
 by those interested in the welfare of the city of New York, is the occu- 
 pation of the Jersey flats from Paulus Hook to Bobbins Reef for docks 
 and wharves. Without expressing any opinion as to the relative value 
 of the gain of accommodation for shipping and the loss of depth in 
 the channel, I venture to say that the withdrawal of that area from the 
 domain of the tide would occasion a loss of not less than one foot in 
 the depth of the bar off Sandy Hook, and certainly not more than two 
 feet. 
 
 The i^art which the fourth division in our classification of the basin 
 of New York, that of the East Eiver and Hell Gate passage, plays in 
 the outflow of the ebb-tide through the Sandy Hook channels, depends 
 less upon the area involved than upon the difference in point of time 
 and height of tide in Hell Gate, already adverted to. The westerly 
 
22 ON TIDES AND TIDAL ACTION IN HARBORS. 
 
 current, usually called the ebb-stream, since it falls in with the ebb- 
 stream of New York Harbor, taking place when the sound-tide is 
 highest, starts from a level ot three and a half feet higher than the 
 easterly, and thus a much larger amount of water flows out through 
 the Sandy Hook channels than through the narrows at Throg's Neck. 
 It is apparent, then, that this portion of the ebb-stream^ re-enforcing as 
 it does the ebb-stream of the harbor proper at the most favorable 
 times, performs a most important part in maintaining the channels 
 through the Sandy Hook bar. It may be estimated that the closing of 
 Hell Gate would cause the loss of certainly not less than three feet in 
 the depth of those channels. 
 
 From what has been said with regard to the meeting of the tides in 
 Hell Gate, it will be seen that the violent currents experienced in that 
 locality are due to causes beyond our control. The dangers to naviga- 
 tion arising from these currents, however, by their setting vessels upon 
 the rocks and reefs, may, in a great measure, be done away with by the 
 removal of the obstructions, in which work considerable progress has 
 already been made. The removal of the reef at Hallett's Point, the 
 work upon which is now in progress, will doubtless, in a great degree, 
 do away with the eddies and undercurrents produced by the sharp turn 
 which the channel now takes at that point. It is not improbable that 
 the successful removal of those obstructions will yet cause the souAd 
 entrance to be used in preference to the other by the fleets plying 
 between European ports and the great commercial metropolis of America. 
 
 Note. — The reader who wishes to enter upon the mathematical treatment of the subject 
 of tides is referred to Airy's treatise on tides and waves, and to the memoirs of Whewell 
 and Lubbock, in the Philosophical Transactions of the Royal Society ; and for investiga- 
 tions of the laws of the tides on our own coasts, to the papers on that subject by Bache 
 and others in the annual reports of the Coast Survey. Among the latter, the lecturer is 
 particularly indebteil to the "Report on the tides and currents of Hell Gate," by Henry 
 Mitchell, 1867, in which the complicated problem of the tidal circulation of New York Har- 
 bor is treated with great ability and success. 
 
LIBRARY OF CONGRFSS 
 
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