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CHA1''1ER I INTRODUCTION G. T. RUDE Fo?merly Chief, Division of Tides and Currents, U. S. Coast and Geodetic Survey History arid tidal theories. Fron1 ancie~.~.t times the celestial bodies were suspected of having, art influence of some sort on our planet in causing the tides of the oceans, but only in very recent times has it been known that these forces were of sufficient magnitude to cause a tide : also in the supposedly rigid body of the earth. Ancient philosophers ascribed ocean tides to all courts of fantastic causes; as, for example, that the earth was an animal and the tides were caused by its breathing or by the beating of its pulse. More rational causes were later given for the tidal phenomenon-the heat of the sun, the difference of level of the seas, the water thrown by the winds against one coast and back against another, discharge of rivers into the sea, and finally the forces of gravity exerted by sun and ~noon. It is small wonder though that the ocean tidal phenomenon did not receive a correct explanation from ancient peoples when we consider the mysterious power of these invisible forces Derived from other distant bodies in the universe, as measured by the ordinary units of measure, and their marked effect on another body. This effect first came to the attention of mankind in the ceaseless rising and falling of the sea in answer to the tidal forces of sun and moon acting on the rotating earth, subjecting the surface of the sea to an alternate rising and i'allir.~g brought about by the tides. This alternate elevation and depression of the level of the sea, which at most places occurs twice daily, received a rational explanation only in the latter half of the seventeenth century. Sir Isaac Newton then formulated the law of' gravitation and showed that the ocean tidal phenomenon was one of its necessary consequences, due to the attraction of the sun and the moon upon the rotating earth. Those ancient maritime peoples who have passed down a history of their times, lived on or near the Mediterranean Sea, where the range of tide is small and its regular periodic fluctuations at times are modified or entirely masked by meteorolo<,ical conditions. Since the tidal phe- nomenon had no economic importance in their everyday life, it received very little attention from either practical or theoretical viewpoints. Although the ancient peoples had scant knowledge of the tides, they must have noticed the regular tidal rise and fall early in ancient times, 3

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4 I1'1GURE OF THE EAR TH and must have found it a matter of wonder and speculation. This was undoubtedly tine in alcove regions where the range, or rise and fall of the tide, is large and the phenomenon therefore impressive. Since it was unimpressive in the region around the Mediterranean Sea no direct reference to the tides is made in the;Bible, and classical literature con- tains few such references. It is recorded that the army of Alexander as it approached the mouth of the Indus River (325 B. C.) noted with " amazement and consternation " the rush of water on the incoming tide, not having seen any similar phenomenon in the Mediterranean Sea. An interesting narrative of their experience is given in the History of the Life and Reigns of Alexander.* Just when the true relation of the moon to the making of the tides was first recognized is not known, but as early as the fourth century before the Christian Era, Pytheas of Massilia, who had navigated beyond the confines of the Mediterranean as far north as the British Isles, and probably as far as the Arctic Circle, noted the relationship. Ele is said, too, to have been first to measure the height of the rise and fall of the tide. :Four centuries later Pliny the Elder definitely ascribed to the moon and sun the making of the tide. The rise and fall of the tide was commonly known among the Romans, and Latin-En~,lish lexicons contain such words as " aestus " and "tumesco." ~ Virgil and Horace, before the birth of Christ, mention the phenomenon. In the sixteen centuries following Pliny the Elder there appears to have been no progress toward a solution of the problem of the tides, although the subject received the attention of the leading philosophers. Upon discovery of the law of gravitation by Newton toward the end of the seventeenth century a rational explanation was furnished of the forces exerted by the sun and the moon in bringing about the tides. Newton showed that the tide was a natural consequence of the law of gravitation and having proved it, he left the development of the different theories to scientists following him. Ibis theory, however, furnished the foundation on which subsequent work was based. Daniel Bernoulli de- veloped this theory, known as the Equilibrium Theory, sufficiently to malice it of practical use in the prediction of tides for any particular port when based upon tidal observations previously made at that place. Laplace attempted a solution of the tidal problem as one of fluicl motion; his theory, known as the dynamic theory of the titles, is contained id his Mecanique celeste. Airy approached the problem of a dynamic * Curtius, Bk. IX, Chap. IX. Translated by Pratt. ~ R. A. Harris. Manual of tides, part I, p. 393-394.

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INTROD CCT10N solution in a different manner, treating the rise and fall of the tides as the movement of waves in canals, known as the Canal Theory. TVhewell's progressive wave theory, or Southern Ocean Theory, would have a forced tide wave in the Southern Ocean dominating, the tides of the world, progressive waves setting northward through the various oceans from this primary forced wave. Following Airy a number of mathematicians have added to the further development of the theory of the tides among, them Stokes, Kelvin, Darwin, Rayleigh, Lamb, Hough, Levy, Poincare, Borgen, Whewell and Lubbock, and in America, Ferrel and Harris. The stationary-wave theory, advanced by Harris, is the latest.. This newer theory is opposed to the older ones in-tha.t.it does away with the conception of a single world phenomenon and substitutes regional oscillatory areas in various portions of the.oceans as the origin of the dominant tides, these oscillations being set up and maintained by the. periodic tidal forces of sun and moon. According to this theory, therefore, the tides do not form a general world phenomenon, the tides of any region being caused by the stationary wave oscillation of that particular region, and the tides of areas not capable of sustaining a stationary wave being caused by a progressive wave from an oscillating system of the open ocean. As universally accepted by scientists in the past, the basic theory of the tides, pertaining to the astronomical forces involved, has proved to be a solid foundation for practical work in this subject and tidal pre- dictions for all parts of the world have agreed remarkably well with subsequent actual observations. It is understood, of course, that these predictions are based upon both theory and observations. The manifestations of the astronomical tide-producing forces are complicated by terrestrial conditions which give rise to various secondary theories upon which scientists have not been in entire agreement. The stationary wave theory of Harris seems to be in accord with most of the tidal phenomena as actually observed. ~ There is no known substance that does not yield somewhat when force is applied to it and there is no reason for assuming the substance of which the earth is composed to be in any way exceptional. The earth might conceivably yield like a plastic body and this view was probably the prevailing one, during at least the first half of the nineteenth century, since it conformed to the idea then generally accepted that the earth consists of a molten mass within, covered by a crust too thin to have much effect on the motions of the molten interior. On the other. hand, for reasons of mathematical convenience it was often assumed that the earth acts like a rigid body. Hence there was considerable * This paragraph on earth tides is by W. D. Lambert. (G. T. R.)

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o ^~ on r~ ~ confusion of idea about the subject ~] Lor] Kelvin (tbo~ Sir Waling Ibomsou) v~a tbe hrst to ~Le prominent tbe iJe~ tb~t on tbe o~e band tbe esr~ could hot he ~bsolutely unyicl~ing an] tb~t on ~e otbo1 tbe ~ieldi~g might not be pl~stic b~t el~stic in cb~T~cter. El~sticity im- plies varions ~o~uIi JeGning it ~] ~ltbo~ tbese mo]uli n~douttedl~ v~ry from tbe centgr of tbe e~rtb to tbe sUd~ce, tbere is ~ seuse i~ wbicb we m~y spe~k oT tbe ~a~ a~ac/{~a ~oj~Z~ of ri97~.~ Ibompson estim~te] tb~t tbe mes~ e~ective mo~ulus of rigidity of tbe eartb ~lmosL cert~i~Iy e~ceede] tb~t of gl~ss (for ~icb be took ~ v~lue equiv~leDt to 1.5 x 10ll C. O. S. units) ~] might he eqU~1 to tb~t of steet wbicb is h~e times ~s gre~t. ~piern estim~tes pl~ce tbe me~n e~ective Tigiiit~ even bigher, prot~[ e~ceeiing tvice tb~t of steel. Ibe Iollowi~g ~le tbe ~mplituies in centimetera of tbe rise ~] I~ll of tbe mean lun~r tide ~t tbe eqU~tor for v~rious v41Ues oT tbe mo]UlU~ of rigidity. Ron~e of lunar tid~ S ~ ~ r~i ~. GI~ss 1.5 X 10~- 43 cm. 8teel ~ . 7~ X 10~ ~20 8ubst~nce t~ice ~s diid us steel TS X 10= 12 The n~tUrsl period of tbe e~tb for ~ distortio~ of the tid81 ~po I Ts so sbort in comparison vitb tbe ti]~1 period tb~t tbe e~rth tides ~re bero ~ssUme] to he ~ the equiLbriUm jpe. Ibis ~ssumption ~ppe~s to be ~early correct. 68~ar~z ~7ar677~6 rf 7>a 77~a. Since the tides ~e c~use] hy tbe ~ttr~ction of SUD 8~] ~000 ~ tbe rot~ng e~rtb, it is evident tb~t Ony v~riRtioDs in tbe Jist~nce from tbe e~rtb of tbese t~o tide-pro]Ucing bo~ies, or ~n~ v~ri~tions in tbeir rel~tive positions witb r~fereuce to ~e 4~rtb, ~iI1 tring ~toUt corresponding V~li~tiOuS ~ in tbe tid~1 forces exerted ~nd tbUs ~ perio~ic v~ri~tion in the r~nge oT bee. Ibe moon is the priDcip~1 tide-ploduciDg ~gen~ since it is the closer of tbe two to the e~rtb ~nd since tbe tid~1 Iorces exerted b~ ~ foreign bod~ VR1) directl~ ~s its m~ss ~d inve~sel~ ss tbe c~e of its Jist~uce Ir~m thc e~rtb. When tbe moon is IU11 01 Uew; tbe SUB ~] moon ~io in EDe 1ql~tive 10 tbe e~, ~n] tbeir tid~1 Iorces, ~ctIng tbrougb gr~it~ o~ tbe e~rtb ~] oce~ns, ~e in co~cert ~n] ttiDg ~tout tbe l~rge tides wbicb b~e been Jesign~te] <; Spri~g~ tides. For ~mplici~, especi~lly ip the e~rly discussions of tbe subject, tbe e~rtb ~s ~s~med to be ~co-~hZ~ ~ ~mp~on ~t does not v~i~te tbe gener~1 cb~r~cter of coDclusions reacbed ~s mucb us mi~bt perb~ps be supposed. ~ Represented ly ~ spberic~1 h~rmonic of tbe second degree.

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7~7o) At qU~dr~ture tbe tiJe-~ro3UcT~g bodies (sun a~] moon) themselves uro ~t right sDgles. Tbe Iorces eiecti~e in prodUcing the tides, h~mely, tb~ horizoDt~1 components of tbe ~hole bi~1 forcos, ~re Jirectly opposed, c~cb force terdTDg to minimi%e tbe force oI tbe otber to~y. Ibis 1essening of tbe tiJ~1 Io1ces of e~cb body n~r~ll~ gives rise to sm~ll-~nge tides ~icb b~ve heeD de~ign~te] ~ ne~> ~ tries. Ibese ne~p tides OCCUP every t~o veeks ~hen the moos is in bs htst qu~rter, RD] ~g~Tn ~ben it is in its tbir] qU~rter. Ibe p~tb of tbe moon in its o~it is RD eETpse; its dist~nce f~m ~e e~tb V~)iDg during tbe course oT tbe lun~r month~ ~lso C8USiDg V~TiR- tions in tbe r~nge of the tide. ~en the moon is in ~ position closest to ~ ~ M P M. /.N. M. PM. / 6 . ~ ~ . ~ . ~ ~ ~ ~ z ~ ~ a ~ ~ z 4 6 ~ ~ O Z 4 ~ 8 ~ ~ 2 ~ ~ 8 ~ O P~ ,1 1\1. ,/i~l ~ ~ #) ~ \T /~;~y b1 ~ \y ~ ~ I . , . . . . ~ 3 - jU~ez~/~/3 - ~ [IC l~Thrco types of tide sem~d~ily, d~iIy ~nd mixed. _ _ tbe e~rtb (in <~erigeo~, its tid~1 10rCes 4re strosgest; ~Dd coOverseI~ for its positio~ I~tbest I~om tbe e~tb (in ;; ~pogee ,, ) . Y~li~tions in tbe raDge of tide ~< likewise tro~I ~toUt ty tbe v~r~i~g dist~c~ of th~ e~rth from the SGD ~Ue to its elLptic~1 ortit; tb~t is, ~ben in <' peribelio~ ;, ~] in <; ~pbeliop.~, . Ibe tides i~ tbe v~rioUs p~rts of tbe ~olT] ~ssUme ~ nUmber of di~erebt types RD] form~ yet tbey m~> be convenieDtly cl~sse] ~s tbr~e distinct t~pes, ~itb ~eir di~ere~t Iorms. Tbe gener~1 cl~ssiCc~tiop m~ be m~de ~s d~i~ semi-~ily; ~nJ mixed. tTgure T sbovs ~utom~tic []e g~uge records, ibUsLr~ting tbese simple~t t~pes--tbe semi-~ily ~t Port l~n], ~i~e, tbe d~ily ~t ~nil~; [hiLppi~e Isl~nds; ~nd tbe~mix~d ~t S~n Fr~ncisco. C~lifoini~. TD tte sim~le Iorm of tbe iiil~ t~pe o~e

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8 FIGURE OF THE EARTH Leigh and one low water occur each lunar day. The simple form of the semi-daily type has two high and two low waters during a day, the morning and afternoon tides being very similar; the third, the mixed type, is caused by a combination of the other two types. It is character- istic of this type that two high and two low waters occur each day, but the two dialer both as to :form and height. A.M. M. 10 8 6 4 2 o 0 2 4 6 8 10 12 2 4 ~ = = ~1 1 1 1 7 ~ ~ ~ /~2 ~ ~ \ ~ ~ 6 : =: ~2 =: _4 _ Portland, Me A.M. M. |2 2 4 FM. 6 8 10 0 4 Manila P.l. / \>uos~i~O-~/ j\T ~ ,~ 7 FIG. 2. Variation of.tide curves due to chancing declination of the moon, ex emplified in the tides at Portland, Maine, and Manila, Philippine Islands. Even these simplest types vary during a lunar month, with the char~g- in, declination of the moon, in the heights of consecutive high and low waters, as illustrated in Figure 2, reproducing tidal records at Portland and Manila. The upper graph for Portland is 1:nowr1 as an equatorial-form, whacks occurs when the moon is near the equator in its changing declination from north to south or vice versa. The lower graph for Portland is known as the declinational form, occurring wheel the moon's declination is lar~,e. This variation in the heights of the

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IAN TRODUCT1 ON 9 two high waters and of the two low waters, clurin~, a clay, is known as the diurnal inequality in the tides, and is directly related to the declina- tion of the moon, being least when the moon is on the equator, and greatest when it is farthest north and south of the equator, causing i' tropic tides." At certain times the semi-daily tide approaches somewhat the mixed type, although to a minor degree in comparison with a truly mixed type. Likewise a tide which ordinarily is of the daily type, illustrated by the tide at JIa.nila for June 28 and 29, 1~)15 (Figure 2), may assuage for ~ few days during a lunar month the characteristics of a semi-daily A.r1. ,~0 2 US ~ Dec.7-8, 19/5 . . . . . M. P.M. A.M. M. PM. In 1; ~ 4 6 8 10 0 2 4 6 8 10 12 2 4 6 8 10 o I(J 16 14 12 10 8 6 .! A. 2 :0 3 , ~ ~L L ~- :: ~ - ~ -_ 7 - ~ - 1 1 1 _ ~71 FIG. 3. Different forms of mixed type of tide exemplified by tides at Seattle, Washington, and Honolulu, Hawaii. type when the moon is nearing the equator ancl, therefore, when the semi-daily forces are exerting the dominant influence, illustrated by the tide at Manila for September 11 and 12, 1915 (Figure 2~. In like manner the tide of a port which ordinarily has a mixed type changes for a few days durint, the month to a semi-daily loran when the moon is near the equator. Ill addition to these variations, two distinct -forms of the mixed type occur in some localities, as illustrated, for example, by the tides at Seattle, Washington, and at I-Ionolulu, I-Iawaii (Figure 3~. At Seattle, little diurnal variation occurs in the high waters but considerable vari- ation ocurs in the low waters; while at FIonolulu the tide shows little

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10 FIGURE OF THE EARTH difference in the height of:' the low waters, but a marked difference in. the height o:t' the high waters. I'his cliff'erence in form is due, briefly, to different combinations of the diurnal and semi-cliurnal waves they ~~~~\ \ \ \ // 'aft \ // / ,-~~-~ Use , ~ c~ / ~ ~\ /~//__` r \\ \ lFesu/{c~r~ f ~ \ <~' ~ it ~;/~9 FIG. 4.- Idealized tide curves illustrating various combinations of diurnal and semidiurnal waves which give rise to many different forms of mixed types of tide. may have the same phases and different amplitudes, or both may have different phases and different amplitudes. It is evident, therefore, that they may combine in various waves, ~,i.vin~` forms. rise to many other different

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INTROD UCTION 11 Some of the various combinations of the diurnal and semi-diurnal waves which give rise to these numerous different forms of mixed types of tide are shown in Figure 4. In the upper curve the phases and amplitudes of the diurnal and semi-diurnal waves are such that, their combination results in a mixed type of tide (heavy line) in which both the high and low waters of a day di-f3:er. In the middle graph the combina- tion of the diurnal and semi-diurnal waves results in a mixed type of tide with a marked difference in the high waters of the day and with red 5 4 3 2 1 o / f) FIG. 5.-Tide curves from records at Philadelphia, Pennsylvania, and Albany, New York, illustrating the " River Type Tide." no difference in the low waters. In the lower graph the diurnal and semi-diurnal waves have phases and amplitudes the resultant of which is the " vanishing, tide "; in this type the water of the falling tide remains for several hours at a nearly fixed height at about mean sea level, then falls to the one clearly defined low water of the day. The tide in a river illustrates another type of tide. The tide graph is steep and of a comparatively short period for the flood tide and more inclined and of a longer period for the ebb tide. This is letdown as the " River Type Tide " and is illustrated by the tide at Philadelphia, 2

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12 FIGURE OF THE EARTH Pennsylvania, and at Albany, New York (Figure 5). The range of the tide in a river is not small in comparison with the depth, and therefore the high-water phase of the progressive wave advances upstream laster than the low-water phase of the same wave retreats down stream. In ~ river draining a considerable area the fresh water run-of! still further affects the tide wave. The river type tide is very pronounced in a number of shallow rivers and estuaries which have consi.clerable range of tide and broad flats, bare or almost bare at low water. The extreme case is represented by the " bore ''; the tide rises so rapidly that the depth of the river is not able to accommodate the tide wave as a smooth wave, and the friction of the lower layers of water with the bottom causes the incoming wave to assume the form of a wall of water, at times several -feet high, which rushes up the rivet or the estuar.v. Probably the most famous bore occurs in Tsien-tan~, Kian,,* in China, although smaller ones are found in Turnagain Arm, Alaska; on the Severn and the Wye, in England; on the Seine, in France; on the Hoo,lv, in Inclia, and on the Pet.itcodiac. id Canacla.t :~: Earth tides arc subject to the same inequalities as are oceanic tides :in regard to springs alla neaps, apogean and perigean tides. Since, as has been already noted., the pure earth tides conform to the equilibrium law, the inequalities in height are in the same ratio as the inequalities in the tide-producing forces and the change in phase of the earth tide l~eeps pace with the change in phase of the resulting force. There is no "age " of an inequality, because a variation in force immediately ,oroduces its full. erect. A " pure " earth tide is, however, an abstraction. The varying load of tide of tidal water influences the rising and falling of the earth's crust in an ext.ren~ely irregular mariner, and the varying, gravitational attraction of the water also produces an irregular erect of the same order of magnitude. These secondary effects of the oceanic tides are often several times as large as the " pure " earth tides, especially near coasts where oceanic tides are large. Moreover, these secondary erects are perceptible at surprising distances from the coast. It might be said that no spot on earth is really free from them. The inequalities caused by the presence of both cllurna1 and semi-diurnal elements in the tide do not present quite as many complexities in the case of " pure " in, * For description see, G. H. Darwin, " Tides and kindred phenomena in the solar system," p. 63. t Observations of the bore on the Petitcodiac River have been made at Moncton! N. B., Canada, by Dr. N\. Bell Dawson, formerly Superintendent of the Tidal and Current Surrey of Canada; see Survey of tides and currents in Canadian waters. Ottawa, Ontario, Canada, p. 23. ~ This paragraph on earth tides is by NV. D. Lambert. (G. T. R.)

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INTROS UC TION ~3 earth tides as they do in the case of actual ocean tides, because the difference in phase of the two elements is zero. Ir~stru,mev,ts for observing tides. The first. instruments or means for the observation of ocean tides naturally were simple, the more compli- cated and more efficient means having evolved as have all instruments and labor-saving and time-savin.~, crevices developed by man. The first systematic tide observations were made on a plain graduated tide staff by an observer. In time the necessity for continuous tide observations for considerable periods of time led to the development of automatic or self-registering tide gauges. ~ plain tide staff is a rod or board graduated to units of length and secured in a vertical position to a pile or other support. The staff is usually painted white with the graduations and figures painted black. The more modern stays are made up o:t wrought iron sections covered on both sides with white vitrified enamel, with graduations in black enamel. The position of the zero of such a stay is quite arbitrary, and the staff is usually set at such a height that the zero is below any expected lowest tide and is of such a length as to accommodate the readings of the highest tides of the vicinity, since the staff is not to record the absolute height of the tide at :fi~.ed intervals of time but its varying height during the day as shown by these regular readings. The connection of the zero of the staff with permanent bench marks on shore by means of spirit leveling fixes the elevations of these bench marks in relation to the heights of certain tidal datum planes as determined by the readings of the tide on the staff, such as mean low water, mean sea-level, etc. ~ tape gauge is a modification of a title staff. A flat metal tape, ~radu- ated to feet, tenths and hundredths, is attached at its lower end to a hollow metal float, free to rise and fall with the fluctuations of the tide. This float rests on the water surface in a float well to which the water has access through an opening, near its bottom of a size sufficient to allow free access of the tide and at the same time damp out excessive wind-wave action. The tape passes over a fair-leader or a pulley secured vertically above the center of the float well and thence to a counterpoise weight. The fluctuations of the tide are obtained by readings, made by an observer at fixed intervals of time, of the graduations of the tape opposite a fixed readin, mark. The earliest automatic tide gauge * was devised by an English civil en~i- neer, Henry R. Palmer, to obtain a continuous record of the rise and fall of the tide in the River Trances for ~,ettin3 the effect on the tidal * A paper descriptive of this gauge appears in Philosophical Transactions, Royal Society, 1831.

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~4 FI CURE OF THE EAR TH regimen of the river by the removal of London Bridge, "free," as ex- pressed by Mr. Palmer, "from the inaccuracies and doubts. which the frequent and lon~,-continued observations of individuals through nights and days must be liable." Descriptions and illustrations of all types of gauges devised in the intervening century is beyond the purpose and scope of this paper. Only general descriptions of types representing the fundamental principals will be given. For details of various types the reader is referred to published material to which reference is made in the Bibliography. The fundamental principles embodied in this first automatic gauge are still followed to a large extent and although there are many forms of these gauges, the underlying principle of all is simple. A float is connected by a fine bronze or a nichrome wire, or by a tape, with a record- ing pen or pencil, which, as the tide rises and falls, is made to move at a reduced scale backward and forward across a paper record which is wound on a cylinder, either vertical or horizontal. This paper revolves by means of a clock movement, thus causing the pencil to trace a curve that accurately represents the tide for that locality. In some forms of this type of gauge the record is made on paper in a roll sufficient for a month of record. The paper is wound on a supply roller, is carried over a second roller which is attached to the clocl; movement, and onto a third or receiving roller. The paper may be either plain or cross-section. If cross-section paper is used, the gauge pencil or pen must at all times be set at a reading on the paper corresponding to a plain tide staff reading, in order to connect the marigram curve with the tide, and the time ordinate set with the correct time; if plain paper is used, daily comparative readings must be made on a plain tide stain' to connect the datum line of the record with the tide; and in addition to the motor clock an auxiliary time clock is used with an attachment. for tripping the recording pencil every hour, thus making a break in the record on the hour. The single-roller gauge is somewhat similar to the three-roller gauges described above except that the record is made on a single sheet of cross- section paper which is wrapped around a single large roller, actuated by a motor clock. Another type of gauge, known as a printing gauge, instead of tracing a curve of' the tide, prints in figures on a paper ribbon the height of the tide at frequent regular intervals. A copper ribbon connects the tide i'loat to a drum on which type figures (feet and tenths) are mounted. A carboned ribbon passes over the face of a hammer which, when released by a clock movement at the axed intervals, strikes against the type drum.

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INTRODUCTION The carboned paper ribbon, as it is forced against the drum by the hammer, takes the impression of the type opposite the hammer at that instant. Water stage registers, quite similar to the automatic tide gauge de- scribed, are better adapted to non-tidal river work than to periodic tides since the time scale of this type is rather small for periodic tides, and a large time scale is essential for tidal work. The water stage register, however, has a larger height scale for accommodating extreme fluctuations brought about by freshets and droughts. Another type of tide gauge consists of a sensitive bulb connected with a gauge, somewhat similar to a steam gauge, by means of an air-ti~ht ]ead-covered flexible tube. The change in pressure as the water rises and falls is transmitted to an arm which carries a pen, the pen moving toward the center of a circular graph as pressure decreases, and toward the periphery as the pressure increases. A clock movement turns the circular paper record clockwise for recording the time coordinate. The gauges described hereinbefore are designed for installation on shore on fixed supports. A pressure gauge has been designed for special purposes for which the ordinary type is not suitable. The :Fave " Mare- graphe Plongeur" is an example of this type. This type of gauge is designed for lowering to the ocean bottom, and it records automatically to scale the rise and fall of the tide by registering the change in pressure due to the fluctuating mass of water above the instrument due to the tides. The recording mechanism is enclosed in a watertight metal bowl with a flanged top securely fastened down with nuts to withstand pressure. The pressure is communicated to two metallic plates inside the bowl through a system of tubes and chambers filled with fresh water and fastened to, and forming a part of, the metal top of the bowl. The tubes are packed with cotton to damp the wind-wave action. The two metallic plates in turn transmit the pressure to two points which separate one from the other as the pressure is increased. The registering of the pressure is accomplished by the two points cutting into a very thin gelatins coating of the surface of a glass disc which is made to revolve by means of a clock movement. Two curves are thus obtained at a given time, their distances apart indicating the pressure at that moment. The variation in pressure is read by means of a micrometer instrument. The instrument also registers temperature on the same glass disc by means of two other metallic plates placed side by side in such a manner that any changes in temperature produce a modification in their flexure. The variation in temperature is read in the same manner as the variation in pressure.

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~6 FI GURE OF THE EAR TH * Earth tides are detected by observations of the change in direction of the plumb line with reference to the earth's crust. This change is so small, being of the orals of magnitude of Mel, that early efforts to detect it were not particularly successful on account of the many non- tidal disturbing, influences. The present standard apparatus for measur- irl, changes in the direction is of' two types, the horizontal pendulum, first used with any ma.rl~ecl success by von Rebeur-Paschwitz, although. Lois predecessors in work of this sort had done indispensable preliminary work, and the long water level used by Michelson and Gale. The principle of the horizontal pendulum is that of an ordinary gate swinging freely on its hinges; if the gate-post is thrown even slightly out of the vertical, the gate swings through a considerable arc. Horizontal pendulums are now usually established in deep cellars or mines in order to shield them as far as possible from the effects of diurnal and seasonal changes in temperature. The water level is simply a long horizontal pipe buried in the ground and filled wither water. Oscillations in the direction of the vertical with reference to the earth's crust correspond to changes of' the height to which the water rises at the ends. Since these changes in height are very minute, even when the tube is several hundred feet long, special reading apparatus is necessary. In their preliminary experiments Michelson and Gale used a microscope, in the later experiments an interferometer apparatus. The deflection of' the vertical has two components; hence two horizontal pendulums or two water levels, each measuring the deflection in a differ- ent vertical plane, are needed for a complete determination. Unless there is some special reason to the contrary the meridian and the prime xTert.ical would be the natural planes to choose. Any observed oceanic tide its really the resultant of' the tide in the water and of' the tide in the solid earth. If' one of these could be predicted I'rom theory alone, the other could be deduced from the observed resul- tant. This has been tried in the case of the long-period oceanic tides, the assumption being, made that the oceanic tide conforms to the equilib- riurn law. The assumption has been questioned, and in any case the results at individual tide stations have not been particularly accordant and the whole method is at present somewhat out of favor. Ben cat, r~ar7cs. The simplicity o-t' their definition, as well as the certainty with which they may be reproduced at some future time, gives value to the tidal planes as planes of reference and one of the important phases of' tidal work is the determination and establishment of datum planes based on tidal definition. Surveyors and engineers find necessity ~ This description of earth tide measurement is by TV. D. Lambert. (G. T. R.)

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INTRODUCTION for these planes as rational datums for vertical control of their operations just as they have need :for ~,eo<,raphic positions for horizontal control. The scientist is dependent upon well-established tidal planes to indicate the stability of coast lines. A very accurate determination of the natural standard plane, mean sea level, is of value to him in furnishing the only means for a quantitative measure of a possible emergence or subsi- dence of land. areas. When the determination of sea level has been e2~- tended over centuries, quantitative evidence will be available as to the stability of coast lines of continents by reference to permanent bench marl<-s connected with tide staffs on which this mean sea level datum has been determined. For the preservation of these tidal datum planes established by lone, series of tide observations, these bench marks should be of a permanent character. Such bench marls generally consist of metal discs set into the top of large concrete masses or into the stone foundations of sub- stantial buildings. The principal qualities of ~ <,oocl bench mark are durability, freedom from likelihood of destruction or of chan~,e in ele- v`rtion, and ease of recovery and identification. REFERENCES HISTORY AND TIDAL THEORIES Harris, R. A. Manual of tides. U. S. Coast and Geodetic Surv., pt. I? chaps. 3, 5 G 7, 8. . The tides: their causes and representations. Popular Science Monthly, June, 1909. Mummer, H. A. The problems of the tide. Scientific Monthly, 14: (no. 3), 209-218 (March, 1922). - . The tide. p. 14-60; 130-145. Darwin, G. H. Tides and kindred phenomena in the solar system. p. /1-93; 157-186. Airy, G. B. Tides and waves. Sect. 8. Ferrel, William. Tidal researches. Chap. 8, p. 145-149. Lentz, Hugo. Fluth and Abbe (18~9). Chaps. 1, 2. Guenther. Geophysil<. Vol. 2, pt. 6, chap. 4. GENERAL CHARACTERISTICS OF THE TIDE Harris, R. A. Manual of tides. U. S. Coast and Geodetic Surv., pt. 2, chap. 3. Marmer, H. A. The tide. p. 61-87. . Flood and ebb in New York Harbor. Geogr. Rev. 13: 420 (July 1923). Survey of tides and currents in Canadian waters. Ottawa, Canada, p. 23. Darwin, G. H. The tides and kindred phenomena in the solar system. p. 63; 94-100. (For bibliography of earth tides, we Chapter V.)

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18 FI GURE OF THE EAR TH INSTRUMENTS FOR OBSERVING TIDES Phil. Trans. Roy. Soc., 1831, p. 174-175. Harris, R. A. Manual of tides. U. S. Coast and Geodetic Surv., pt. 2, chap. 1. Darwin, G. H. The tides and kindred phenomena in the solar system. P. 7-20. Rude, G. T. Portable automatic tide gauge. Special Publication No. 113, U. S. Coast and Geodetic Surv. . Instructions for observing tides. Special Publication No. 139, U. S. Coast and Geodetic Surv. Annales hydrographiques. 1908-10, p. 383-437; 1921, p. 193-237. Honda, et al. Secondary undulations of oceanic tides. P. 4-11. Der Hochseepegel. Z. Instrumentenk. p. 331-342 (Nov. 1903) . Measuring tides at sea. Science, April 29, 1904, p. 70~. Accuracy of water level recorders. Trans. Am. Soc. Civ. Eng., 83: 894-903. Tide gauge for deep water. Coast and Geodetic Surv., Report for 1857, p. 403-404. Report on tide gauges. Compt. Rendu. des Seances de la XIV Conference enerale de ['Association Geodesique Internationale, 2 Bd. 1905, Rapports Speciaux, p. 326. IF. S. Coast and Geodetic Survey Reports: 18~53, p. 94-96; 1853, p. 190~191; 1857, p. 402-404; 1858, p. 247-248; 1876, p. 131; 1893, p. 27-28; 1897, Appendix No. 7. U. S. Coast and Geodetic Surv. Bull., No. 12, 1889, p. 143-146. (For bibliography of instruments used in observing earth tides, see Chapter V.)