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C~D IN ALAR Saw H. A. CHARMER A. a. C~6 ~d Oogio~c Spread Wean se~-level ~> be Deanna from two different points of YiOW; Both act landing to solvent ji~ercDt results. With We openly correct a_ _~_= geodcsist we may define it as the e~ipotenti~1 surface which the oceans would assume if unJistnrted By the rise ~] Ian of the Age and t, the eFects of ~in] and bender. Starting with beam se~-level at any given initial point the geoJesist Cal Jetormine, Dy precise spirit levelings such FIG eqUipotc~ti~l surface. geodetically, ~! within the limits of iDStIU- ~ent~1 error, ~11 points on this so~f~ce would he at mean se~-leYel. Egg sc~-level so defined Any tbercCore he c~llc] geodetic ma sc~-l~vel. Gut along the sbolcs w~shc] by the sea me may also JeOne Scan se~Jevel at any point as the ~ct~1 level of the sea at that point Jete~iDe] ty verging the costly cb~ngiDg level at the point over ~ consiJer~ble period of time. Wean sc~-level so determine] may be iistinguishc] Iron geodetic se~-lc~cl by c~lL~g it local or glitch, geographic mean sc~]c~ct #] it is to he notch, Ant st~rti~ from We same it point; geodetic and gcogr~phlc mean se~-le~els Max or may not coincide at other points. For in averaging the varying height of the sea the resultant or act elicits of cb~nging metcorologic~1 conJihons Max Be Ji~ereDt at different places. Thus ~ predominant Ding from ~ given direction gig make se~-level OD the shore from ~bicb it blows lower ~D] OD the other shore bigger. Tn sc~1 use as ~ J~tD~ plane Ion elevations in geopb~sic~1 investTg~- tions, it if g~pb!y mean sc~-l3vcl that is employed. [or geo~phir SPED level lies at lne nose of geodetic mean se~-lc~cl, since the initi~1 se~-level in geodetic leveling must he determine] hy averaging the height of the sea at that initi~I point. Furtbermore, geodetic leveling of clan the biggest precision is subject to instru~e~t~1 errors labia; ~ltbougb very small for moic~te iist~Dces; Mao Become relatively large in leveling . . . bet~ecn widely sep~T~te] points. It is ~erefoTe customary to tape the se~-level determine] t~ averaging the Beirut of the sea at Ji~erent points along the coast as Beaning the mean se~level surI~ce. Tbo level of the sea is at ~11 times disturbed b~ yin] ala tide. Over how long ~ polio] gnat the height oT the sea De ~ver~gc] iU order to give As mean level at that point ~ To answer this question it is obvious that we must first investigate the variations to icy se~-level is subject. so

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AlEAN SEA-LEVEL VARIATIONS IN SEA-LEVEL The most obvious variation in the level of the sea at any place is that clue to the tide. Twice daily, in rhythmic fashion, the sea rises and falls in response to the mighty pulse of the tide-produci:ag forces. These forces, as has been developed in a preceding chapter, may be grouped into three classes; namely, semidaily, daily and long-period forces. The semidaily forces are the principal tide-producin`~ forces, the daily forces are next in importance; and the long-period forces are of such small magnitude as to be of relatively minor importance. The average length of the tidal day is 2a hours and 50.4 minutes. Hence, if at frequent regular intervals during such a period the height of the tide is measured and these heights averaged, the effects of the tide, in so far as the semidaily and daily components are concerned, will be eliminated, and a value of sea-level freed from the disturbing effects of the tide will be obtained. The effects of the long-period tidal forces, as explained above, are so small that for the present they may be disregardecl. In tidal work it is customary to tabulate the height of the tide at the beginning of each hour. Since the length of the tidal day is very nearly So hours, it is obviously more convenient to derive daily sea-level from the hourly heights of the tide as tabulated than from aliquot parts of the tidal day of 2a hours and 30 minutes. Strictly, the first and last hourly heights of the 25-hour period should each be given half weight in deriving daily sea-level; but since daily sea-level is subject to disturbing effects of far greater magnitude, no useful purpose is served by such. refinement. As a matter of' fact it is sufficient to derive daily sea-level as the average of the 24- hourly heights of the tide of the civil day, since this is most convenient. In this connection careful distinction must be made between mean sea- level and half'-tide level. Mean sea-level at any point is defined as the average level of the sea at that point and is determined b.y averaging the height of the sea as measured at frequent intervals, generally every hour. Half-tide level is the plane that lies exactly midway between high water and low water. If the curve representing the rise and fall of the tide were that of a simple sine curve, the planes of mean sea-level and of hall-tide level would coincide. But the tide curve is not a simple sine curve; it is compounded of a number of simple sine curves, some of' which have fixed phase relations with respect to each other. The average rise of high water above mean seat-level is therefore, generally, not exactly the same as the average fall of low water below mean sea-level; and hence mean sea-level and half-tide level generally differ. As determined from day to day the relation of half-tide level to sea- level at any point may differ because of differences in meteorological

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~2 FIGURE OF THE EAR TH conditions. But when averaged over periods of a year or more the relation between the two is very nearly constant. From observations it is found that at certain places half-tide level lies above mean sea-level, while at other places it is below mean sea-level. Thus, as a rule, on the Atlantic coast of the United States half-tide level lies below mean sea-level by about one-tenth of a foot while on the Pacific coast it is above mean sea level by about half that amount. The relation between half-tide level and mean sea-level at any point depends upon the amplitude and phase relations between the various constituents of the tide at that point. A formula expressing this relation quantitatively in the harmonic notation has been given by Harris.t From the formula connecting the two it becomes clear that half-tide level is subject to a variation depenct~ng on the longitude of the moon's node, with a period of 18.6 years. It is obvious, therefore, that although mean sea-level and half-tide level at any point generally do not differ much, the two terms cannot be used as synonymous. If sea-level freed from the tide, as explained above, is derived for a number of days it is found to vary from day to day. In New Yorl: Harbor, for example, during, the winter, sea-level from one day to the next may vary by more than a foot; and within any one month sea-level for two different days may differ by more than two feet. Such changes obviously are to be ascribed to variations in wind and weather, for it is a well-known fact that a wind blowing towards the shore tends to raise sea-level along the shore while a wind blowing from the shore tends to lower it. But not in winter only does sea-level vary from day to day. In summer, too, it varies, though obviously not as much as in winter. During the summer, sea-level in New York Harbor may differ from one day to the next by as much as half a foot; and within one month sea-level for two cliff'erent days may differ by a foot or more. This arises from the fact that both wind and also variations in barometric pressure bring about fluctuations in sea-level. Any arm of the sea may be regarded as a hu~,e inverted water barometer: when the atmospheric pressure over this arm of the sea rises) the level of the water will be depressed, and when the pressure falls, the level of the water will be raised. Owing to effects of wind and weather, sea-level exhibits considerable '' This variation becomes especially marked in regions subject to storms of great intensity, par- ticularly those fronting shallow bodies of water. Thus during the year 1915 a severe storm raised the level of the sea at Galveston, Texas, about 10 feet above its normal level so that during that year the difference between the highest and lowest daily sea-level was more than 11 feet. differences as between one day and another.

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CLEAN SEA-LEVEL ,53 In tidal risers in which there is considerable variation of' -l'resh-water discharge, daily sea-level exhibits greater variation than along an open coast, this variation being especially marked in the upper reaches of the rivers. The Hudson River furnishes an example. From flee open sea- coast to the head of tidewater on the Hudson is a distance of' about 1~0 nautical refiles. In the year 19a the difference between the highest awl lowest values of daily sea-level at the places mentioned below were as I'ollows: open coast near the entrance to New Yorl; Harbor, o.4 feet; Fort Hamilton, within the entrance to New York Harbor, 6.0 feet.; Albany, near the head of tidewater, 15.2 feet. It is obvious that changes in sea-level from day to day must, in general, be much the same at points which are near each other, and subject to similar meteorological conditions. As will be seen later, advantage is taken of this fact in determining the plane of mean sea-level from short series of observations by correcting the sea-level derived from these obser- vations to a mean value. Exactly how far two points may be separated and still exhibit similar sea-level changes depends upon a number o:t' factors. Within a long tidal river subject to considerable variation in fresh-water run-off', the changes in daily river level may be quite different :I'or points relatively near each other. But on the open coast and in tidal waters not sub ject to large variations in fresh-water discharge, the changes in daily sea-level resemble each other closely over areas of' considerable extent. Figure ~ gives, diagrammatically, the daily heights of sea-level for the month of April, 1923, at five stations on the Atlantic coast from Portland, NIaine, to I'ernandina, Florida. A glance shows that at Port- land and Boston the sea-level changes resemble each other closely. At Atlantic City these changes are decidedly different from those of Portland and Boston, and, although the curves for Charleston and Fernandina resemble each other, they differ from the preceding curves. Examining the locations of these stations it is found that, though Boston lies about 100 miles south of Portland, both harbors lie open to the same arm of the sea known as the Gulf of Maine. Atlantic City is about 250 miles south of Boston but lies in a different embayment of' the coast; this fact, together with diff':erences in meteorological conditions, makes the daily sea-level changes at the two places show but little similarity. Charleston and Fernandina are almost exactly the same clis- tance from each other as Atlantic City and Boston, but, lying in the same embayment of' the coast, they exhibit similar chancres in. daily sea-level. From day to day wind and weather may vary widely and thus give rise to relatively wide variations in daily sea-level. But within a Onto such variations obviously tend to balance out. Clearly, if we average the

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a4 FIGURE OF THE EARTH hourly heights of the sea over a period of a month, the level derived will be a much closer approximation to mean sea-level than was daily sea-level. Furthermore, such monthly heights of sea-level should show considerably less variation than daily sea-level. o is lo /5 20 25 30 1 1 1 1 1 1 1 1 1 1 1 1 1 , ~ ~ 1 is, ~ ~;\ ~5 ~? po _ ~ - ~ h~r/es 'cat Fernand/na ~ A I/f~nt/f: ~/-tL \~ FIG. 1. Daily sea-level, Atlantic coast stations, April 1923. An example o:t' the variations to which monthly sea-level is subject is shown in Fissure ~ for the same stations, for which Figure 1 illustrates the variations of daily sea-level. The diagrams give the monthly hei,~,hts of sea-level for each of the months of the years 1"2:3 anl 192-~. For Fernand;~-~a the plotting, stops at the end of J~une 1924, the station

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IDEA SEA-LEVEL having been discontinued at that time. It is seen at once that although the monthly sea-level does not vary as much as daily sea-level, neverthe- less it shows a relatively wide variation. From month to month seat-level varies several tenths of a foot and within a year the monthly height of sea-level may rotary by as much as a foot. /923 Jan ~ Or Ju/u ~ 1 1 1 ~1 i 1 ~ ~ 1 ~ ~ 1 1 ~ 1 1 1 1 ~ 1 MA ~ A, Porf/~nd Feet I /92~ Oct Tom A,c r ua/y Oct Dec Boston A ~ i At/~n tic cite ~ ~-q :\Vl~ / Q \ o 1 ~/~ j >; ~C~ --ton cowl 1~ Fern c~ndin~ FIG. 2.-Monthly sea-level, Atlantic coast stations, 1923-1924. For daily sea-level Figure 1 shows that the variations at Atlantic City are different from those at Boston and Portland. But for monthly sea- level the curves of :Figure 2 show similar cl~arl,es at the three stations with regard to the larger variations. Indeed, with respect to these larger variations there is considerable resemblance in all five of the curves of the figure. In other words, the variations of sea-level from month to month appear much the same over large areas. At first glance the heights of monthly sea-level at any one station shown in :Figure 2 appear to vary in haphazard fashion. A closer examination,

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MEAN SEA-LEVEL Whatever the causes responsible for bringing, about the annual variation in sea-level it is reasonable to suppose that the features exhibited at any place are representative for a considerable area in its vicinity. Observa- tions bear this supposition out. Thus the annual variation of' sea-level at Boston resembles closely that at Portland. Similarly, the annual variation at Atlantic City, New Jersey, and at Baltimore, Maryland, resembles that at New York, while that at Charleston, South Carolina, resembles clearly that at Fernandina. Within tidal rivers subject to wide variations in amount of run-off, especially in the upper reaches, the annual variation may diiT'er consider- ably from that at a near-by point along the open coast. This is due to the fact that in the restricted channel of the river the variation in run-off is the principal factor in the variation of level. Thus, while in New Yorl: TIarbor at the mouth of the Hudson the annual variation in sea-level is . . as shown by the second curve of Figure 3, the high monthly stage coming in the summer and fall, at Albany, near the head of' tide-water, the high stage comes in April, coinciding with freshet conditions in the river. For comparisons with the seasonal variation of' sea-level along the Atlantic coast of' the United States illustrated in lTigure 3, there are shown in Figure 4 the curves of annual variation at several stations on the Gulf and Pacific coasts. Key West, Florida, Pensacola, Florida, and Galveston, Texas, constitute the Gulf coast stations and San Diego, California, San Francisco, California., and Seattle, Washington, the Pacific coast stations. The curves for the three Gulf stations, though they exhibit distinctive individual features, nevertheless resemble each other in many respects. There is also considerable resemblance between them and the curve for Fernandina. The curves for the Pacific coast stations differ markedly from those for the Atlantic and Gulf stations; and it is to be observed, too, that they differ considerably from each other. Without pursuing this phase of:' the subject further it is clear that in the variation of sea-level from month to month there is a large element of' periodicity, and that this periodic annual variation at any place is marked by distinctive local characteristics. Furthermore, at places near each other, or more precisely at places within a given region subject to similar climatic and meteorologic conditions, the annual variation is much the same. If' the height of' sea-level at any place is averaged over a year it is obvious that the periodic annual variation is eliminated. Within a year, too, the effects of varying meteorological conditions, which find reflection in the changes of sea-level from day to day and from month to month, will tend to balance out. Sea-level averaged over a year may therefore be expected to give a much closer approximation to mean sea-level than

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FIGURE OF THE EARTH sea-level derived from a month of observations. tions continued over a number of years bear this out, as may be seen from an inspection of Inure 5 in which the yearly heights of sea-level at The results of observa Feef 2 Jan Fed tour Apr that June Join Auk Sent act //ov Dec . 1 ~ 1 1 1- 1 1- 1 ~1 , hey wes7" >f \ Dolor b of _ _ P~7s~co/ct ~ - 'I :<,,,,~/ Go//vesfon oL ~ own Sun ~r~ncisco ~ my, O \~ ~in/ ~0 ~ So/n D/eJo FIG. 4. Annual variation in sea-le`-el' Gulf and Pacific stations. New YOr~7 Galveston and Ball Francisco for a number of years are shown in di.a~,rammatic form. For New World and San Francisco :Figure ~ gives the heights of sea- level for the 28 successive years from 1899 to 1926. For Galveston the observations begin in 1.904, so that the :-early sea-level heights in the -~,,u~e fun for the 23 year period from 1904 to 1926. For each dia~,ram

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MEAN SEA-LEVEL ~9 the horizontal line represents mean sea-level at that place derived by averaging the height of sea-level over the period of observations shown. As a rule, it is seen that from one year to the next sea-level varies by about ~ tenth of a foot. At times, however, this variation may be as much as a quarter of a foot or even more, as exemplified at each station shown in Figure b. Feet 0.5 0.0 1900 /905 /9/0 /9/5 1920 /925 I T T I T I I /vevl/ it, . L York AFT fit y ~ l I I I T ~4 1 1 1 1 1 1 I G>/~ _ yes ton Get ~ L' l\ \~)1 San Fit ~ \ T ~ 1 ' o/ncisco FIG. 5.-Yearly sea-level. New Yolk, Galveston and San Francisco. A comparison of the diagrams of Figure ~ brings to light the fact that the variations in yearly sea-level at the three places bear no apparent relation to each other. But if we compare New York with other stations on the Atlantic coast of the United States, Galveston with stations off the Gulf coast, and San lTrancisco with stations on the Pacific coast, we find, as a rule, considerable resemblance in the variations of sea-level from year to year. In other words, along ally extended coast line the

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60 FI GURE OF THE EAR TH variation in yearly sea-level is much the same over a wide area. :For the Pacific coast this is illustrated in Figure 6 by the curves of variation of yearly sea-level for San Francisco and Seattle. A glance at Figure 6 shows that notwithstanding the fact that Seattle .~ Alp ~ro~r~icr>~ ore Mars tenon r;r)~) miles snort the variations in sea CUll~L Call ~1 ~11~1~ ~ ~ ~ ^~^ ~^ ~ W 1 ~ ~ level from year to year are In large measure similar. Not that. these changes are exactly the same; but when sea-level during any one year its at a high level phase at Seattle it is, as a rule, also at a high level phase at San Francisco; and similarly with a low level stage. Is the variation in seat-level from year to year accidental, or is it subject to more or less periodicity? Glancing, at Figures ~ and 6 there 1 1 1 Feet 0.5 _ 0.0 -~ /900 /905 /9/0 /9/5 /920 /925 1 1 1 1 1 1 Seo/t +/e l / t I I I I I I I I I M1 1 I- T '\1 \~ \ All/ ~ A ! ~ ~ ' Sari ~,~ FIG. 6. Yearly sea-level, Seattle and ,S;~n Francisco. appear to be evidences of cycles with periods of something like Tour years and nine years respectively. Unfortunately, however, there is not a sufficient body of data from which to draw definite conclusions in the matter. CAUSES OF VARIATION The larger variations in sea-level, whether from day to day, montn to month or year to year, are undoubtedly to be ascribed to changes in meteorological conditions, such as barometric pressure, wind, and rain- fall. bVit.h regard to barometric pressure, a first approximation to the resultant changes in sea-level may be easily derived from general con- siclerat.ions, as follows. Mercury is 13.2 times as heavy as sea water; hence . .,

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lIEAN SEA-LEVEL 61 a change in local barometric pressure of one inch should be reflected by an inverse change of 13.2 inches in the local level of the sea. In round numbers, therefore, the chance in sea-level in feet should be inversely as the change in barometric pressure in inches. The relation of the change in sea-level to change in pressure has been investigated at a number of places. Nearly a century ago the French hydrographer :T)aussy tabulated the sea-level at Brest for different local barometric pressures and found the value 14.? as the ratio of change of sea-level to change of barometer. A few years later Sir John Lubbock obtained a value for this ratio of 11.1 for Liverpool and 7.0 for London. From observations made on his Arctic expedition at Port Leopold in the Arctic Archipelago in 1848, Sir James Foss found the ratio to vary from 11.6 to 13.~. From six years of observations at Boston, Massachusetts, NYm. :Ferrel in 1873 found the ratio to be 7.3. ~ review of these earlier investigations and of the subsequent work to the year 1018 is given by Sir Charles Closed Here it will be sufficient to mention only those of more recent date. In 1924 Alfred Wegener discussed observations made by him during, the winter of 1907 on the northeast coast of Greenland, from which he found the ratio of change in sea-level to cha.n>,e in barometric pressure to be from i! to 12. In the same year, from a comprehensive study of observations at seven stations in the British Isles, A. T. Doodson found this ratio to vary from 6 to 13, and Ogura, from observations at a number of small islands in the western part of the North Pacific, found it to vary from 12 to more than 30. In 1925 Hessen discussed the observations made at the winter station of the German South Polar Expedition in the Gauss in 1902 and found the ratio to be 12. Absolute agreement between the observed value for the above ratio and its theoretical value cannot, obviously, be expected. In the first place, other factors enter which must be evaluated, such as wind and river discharge. And in the second place, the change in level must correspond, not to the local changes in pressure, but rather to the difference between local pressure and the pressure out in the open sea. In other worcls, changes in sea-level are to be correlated with pressure gradients. This procedure was introduced by Witting in 1918, and when this method is employed the observed ratio tends to approximate the theoreti cat static ratio of 13.2. In effect, too, the use of pressure gradients intro- duces correction factors for the wind. The effect of wind on seat-level has been investigated at a number of places. By correlating the observed wind and tide on the coast of Holland F. L. Ort.t 4 in IS07 arrived at a formula for the eject of the wind in terms of velocity and direction. More recently Harold Jefireys,5 by treat

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~2 FIGURE OF THE EARTII in', mathematically the question of the effect of:' a st-eacly wind on that sea-level near a straight shore, arrived at general formula -l'o~: this special case. An interesting phase of the effects of wind and pressure on sea-level leas to do with the time element. Ferrel had noted that at Boston changes in sea-level anticipated changes in barometric Pressure. In lairs paper on . . . . ~ , . . . the meteorological pertur~a.~ons of sea-level and tides, Doodson 6 dis cusses this question briefly and suggests that such anticipations of' vie changes In atmospheric pressure are probably due to the different rates with which disturbances travel through air and through water. :From the preceding discussion it is clear that. in so far as the variat.;on`, in daily seat-level are concerned, the effective causes are to be found primarily in the variations of wind and of barometric pressure. lit places within the influence of rivers carrying, the drainage waters :t'ron:~ large areas, the variation in river discharge is also a -factor of importance. For the change in sea-level from month to month it appears reasonable to fool; to the same causes that were -~:'oun.d responsible for tile ch.a~.~oe in level from day to day. But the variation of' level frown month to month exhibits a large element of periodicity. Can we :6nd a like periocl.;c variation in atmospheric pressure or in wind to account for the annual variation in sea-level? If we examine the annual variation ill atmospheric pressure at ally place along the coast it is found to have a somewhat similar character to the variation In sea-ievet, In so far as phase is concerned; but this ~l~nil~l `~nrinti~n in nro~llrn ;q so small as to be suite inadequate to ~1114~' ~ ~ V ~ ~ ~ ~ 1 ~ account for the annual variation in sea-level. For example, the atmos- pheric pressure at New York is, as a rule, highest in the winter months and lowest in the summer months. This, therefore, corresponds to low sea-level in winter and high sea-level in summer. But the difference in pressure as between winter and summer is only one-tenth of an inch, which would account for an annual variation of but a little more than an inch in sea-level, or less than 20 per cent of the observed periodic variation. In this connection, however, it is of interest to note that an harmonic analysis of the annual variations in sea-level and in atmos- ~heric pressure at New York gave evidence of the existence of like components with periods of a year, a half a year, a quarter of a year, acid a sixth of' a year.7 In attempting, to correlate the annual variation in sea-level with the seasonal variation in direction and force of the wind, the problem becomes complicated when the attempt is made to relate them quantitatively. In certain places, as for example in monsoon regions, the wind must be an important factor in bringing about the annual variation in sea-level.

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~\ =~-~[ ~ a on Ibus, P. 8. Omit Onus ~ very close correlation Between the nub vari- ations in se~-level ~] in the elective velocity and direction of the ~in] in the B~ of ~eng~1~0 also in the Arabian Seam Bowever, ~ is only necessary to refer hack to Figure 3 ~] Dote Ant ~11 along the Atlantic coast of the Pnited States ~ very roIlsiJer~hle cage in se~-level takes place Between the months of October and December, notwithstanding the fact that at grab of the stations the Gino during these months is Irons , . . . . the same phenol 1ng ulTectlon. On investigating the erects of the various causes that m~> he elective in Bringing about the Inn variation of se~-level on the coast of Japan, \o~itsU and Ok~moto concluded Ant the primary I~ctor is the se~son~1 variation in the demise of sea mater Brought about by cb~nges in temper~- ture an] s~linit>. Next in importance was the Satiation of barometric pressure. Together these two ejects were fonn] to Coconut for very nearly all of the actually otae~ve] ~DnU~1 variations in se~-level at the sin Stations OD the coast of Japan investigate]. It is to be note] further abut in regions of strong nontiJ~1 currents the e~rth~s rotation brings about ~ force Enrich is eJective in distn~ting ae~-le~cl. Ibis Iorce, tag so-c~llc] deRecting force of the ebbs rotations tends to msLe the Cater on the right-b~nd bank of ~ stream (looking in the direchon of motion) biter in the northern bem~pbere and lover in the southern bemis~bere. Thence, Where seRsoD~l VRTi~tioDs in the velocity or direction of nontid~1 currents occUr, se~-level cages will take place ~ccordin~y. In regal] to the variations in se~-level Irom bear to dear, it m~ be said abut these UDdoubtedly reRect cages in the yearly values of such factors as barometric pressures wiris, nontiJ~1 currents, and temperature and density of sea mater. Go quantitative studies of this pose of the quest appear to bane been makes tat the causes abut bring about the gaily and annul variations in se~-levet whim mere considered abodes may reasonably Be invoked to account for the variations from gear to gear. As Ads noted TO connection limb the discussion of this variation it is region~1 and not ~ loam pbenomenon, exhibiting similar cb~cteriatirs over large areas. All along the Atlantic coast of the Plaited State the variation in se~-level Irom gear to gear is mUcb the same, sn] ~ simian statement holds with respect to the P~ciCc coast. D,Arcy W. Ibompson found tat this variation lass mUcb the same on the coast of great Britain as on the germ ~nisb ~d Svedisb co~sts> In ascribing tag variations in se~-level at gay point to variations in meteorologir~1 coIIditions and in the pb~sic~1 conditions of the sea mater, it is tacitly assumed that the mean level of the sea as ~ Bole ~em~Tns constant. BUt Any not this mean level of the sea itself Be subject to 5

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~4 FIGURE OF THE EARTH variations ? In answer to this question it may be observed that a change in the mean level of the sea may arise either from a change in the volume of the ocean basins or from a change in the volume of the ocean waters. Earth movements may be cited as a cause adequate to change the volume of the ocean basins. Ancl as causes that may bring about changes in the volume of the water the following may be mentioned: increase of water through volcanic action or through decreased glaciation; decrease of water consequent on chemical binding during the alteration of rocks or on increased glaciation. There can be no question but that during geologic time such changes in the mean level of the sea have taken place consequent on the operation of the causes enumerated. Daly ii has directed attention to the probability of a general lowering of the mean level of the sea, during the humar~ period, of about 20 feet. However, in view of the enormous volume of the ocean waters, changes in the mean level of the sea must be extremely small even over periods measured in scores of years. And in the problem of the determination of mean sea-level as a datum plane, the variations in the mean level of the sea need be considered only in connection with periods measured in centuries. THE DETF,RMI~- XTION OF MEAN SEA-LEVEL In view of the variations to which sea-level is subject, the determinations of mean sea-level involves two different problems. The first is, how lone, a series of observations is required to give an accurate determination of mean sea-level at any point aloe, the coast? The second problem is, how can the sea-level from a short series of observations be corrected to a mean value ? It is clear that, as a general rule, the longer the period of observations the closer will the value obtained for sea-level approximate mean sea- level. In connection with tidal work a period of 19 years is considered as constituting a full tidal cycle, for during this period of time the more important of tidal variations will have gone through complete cycles. It is therefore customary to regard results derived from 19 Rears of tide observations as constituting mean values. Hence sea-level derived from ~ 9 years of observations has frequently been taken as constituting a primary determination of mean sea-level and as giving, accurately the datum of mean sea-level. :For the practical purposes of datum plane determination, 19 years is a considerable period of time. Cannot the period necessary for securing, an accurate determination of mean sea-level be shortened? It will be recalled that in our consideration of the variation in sea-level front year to year, which is illustrated graphically by Figures ~ and 6, there

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MEAN SEA-LEVEL 65 appeared evidences of a cycle with a period of something like nine years. This means that a close approximation to mean sea-level may be derived directly from observations covering a period of nine years. Determina- tions of sea-level front observations covering periods of nine years or more may be denominated primary determinations; those based on less than nine years may be called secondary determinations. Very satisfactory secondary determinations of mean sea-level may be derived from observations coverings, periods of from one to three years, by taking advantage of the fact that the variation in sea-level from year to year is much the same over considerable areas. By comparing with simultaneous observations at a station at which a long series of observa- tions is at hand, corrections may be derived for reducing the secondary determination of sea-level to a mean value. An example will make this clear. Suppose that at the beginning of 1917 it had been desired to secure as accurate a determination of mean sea-level at San Diego, California, as possible from one year of observations. A tide gauge would have been put in operation and the hourly heights of the tide averaged throughout the year, and sea-level that year would have been derived as reading 6.44 feet on the fixed tide staff used in connection with the tide observations. :For that same year sea-level at San lTrancisco read 8.48 feet on the tide staff used at that place. But from 19 years of observations covering the period from 1899 to the end of 1917, mean sea-level on that same staff read 8.~5 feet. Hence seat-level for 1917 was 0.07 foot below the mean value for the 19-year period. And though San Diego its about. 600 miles distant from San Francisco the variations in seat-level from year to tear must be much the same at the two places. Therefore, to correct the 191rY value of sea-level at San Diego to a mean value, a. correction of - 0.07 foot is indicated, which gives the determination of mean seat-level at San Diego as 6.51 feet. Had the observations at San Diego been made the following year, the height of sea-level on the same staff would have read O.69 feet or 0.26 foot higher than the year before. At San lTrancisco, seat-level in 19:18 read 8.70 feet. Comparing this latter height with the height of meaner sea-level of 8.~5 feet, a correction of -0.15 foot is indicated. Applyin, this correction to the 1918 sea-level value of 6.69 feet at San Diego, the value determined for mean sea-level is 6.~4 feet. At San Gino there are continuous observations covering, the 19-year period from 1906 to 192.~. The clirect primary clet.ermination of mean sea-level from this 19-~rear series gives it as 6.~4 feet on the staff. Sea- level for 1917 therefore differed by +0.10 foot from the mean sea-level, and that for 1918 by -0.10 foot. By comparison with simultaneous

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66 FIGURE OF THE EARTH observations at San Francisco, mean sea-level valises. are derived drool each of these years of observations which in the one case agree exactly with the direct determination of mean sea-level and in the other case differ by but three-hundredths of a foot. It is to be observed that, in general, it may be tal~en that when corrected by simultaneous observations at some suitable station not too -far away, a year of observations will give a mean sea-level determination correct to within 0.05 foot and -f:'our years will give it correct to within 0.02 foot. To derive a satisfactory value of mean sea-level from one month of observation, care must be taken to choose a comparison station that is subject to a like annual variation in seat-level. NVhen so compared, a month of observations will give mean sea-level correct to within 0.1 foot. And even one dater of observation, if corrected by comparison with a suitable near-by station, can be depended upon to give mean sea-level correct within a quarter of' a -foot. THE MEAN SEA-LLY]3L SURFACE In the introductory paragraphs to this paper attention was clirectecl to the fact that, starting with mean sea-level at a given initial point, ~,eodetic and geographic mean sea-levels may or may not coincide. In other words, the surface of mean sea-level as determined directly from observations may not he an equipotential surface. Thus Jolly calls atten- tion to the I'act that precise leveling in Great Britain shows that from Newlyn on the English Channel to Dunbar on the North Sea-an air line distance of about 400 nobles, but twice that distance along, the coa.st- `~,eodetiG and '~eo',raphic Clean sea-level diverge 0.81 foot.1'' Avers in a recent study gives the results of precise leveling in the United States which show deviations between geodetic and geographic mean sea-level of very nearly ~ -feet as between tl~e Atlantic and Pacific coasts. ~ r ~ ~ ~ 1 I 1_ _ The i'act that the mean sea-level surface cteterm~nect oy averaging ~e varying height of tl~e sea and the sea-level determined by geoclet.ic levelings, cl.o not coincide means that `~,eo~,raphic mean sea-lex-el does not define ~ strictly level surface. This is not surprising since this mean seat-level at any point reflects the net or resultant effects of climatic and meteorologic conditions, which clearly are different at different places. The deviations of' the mean sea-level surface from a level surface are small, but they introduce a complicating, factor in the ~,eoclesist's work of spreaclin~ nets of precise level lines over large areas. Indeed, it is this leveling, T.': the ~eo~lesist that brings out both the l'act of the deviation ~.~1 its n~,~itt-~ OCR for page 50
MEAT!; SEA-LEVEL RBEERENCES 67 1. Harris, R. A. Manual~of tides, Part III. U. S. Coast and Geodetic Surv. Rept. for 1894, p. 127-187 (1895~). Reference on p. 148. 2. Marmer, H. A. Tidal datum planes. U. S. Coast arid Geodetic Surv. Special Publication No. 135: 1-142 (1927). Reference on p. 70~73. 3. Close, Sir Charles. The fluctuations of mean sea-level with special reference to those caused by variations in barometric pressure. Geogr. J., 52: 51-58 (1918) . 4. Ortt, F. L. The effect of wind and atmospheric pressure on the tides. Nature, 5~;:80-84(1897). 5. Jeffreys, Harold. The effect of a steady wind on the sea-level near a straight shore. Phil. Mag., 46: 114-125 (1923). 6. Doodson, A. T. Meteorological perturbations of sea level and tides. Monthly Notices R. Astron. Soc., Geophysical Supplement, vol. 1, no. 4: 123-147 (1924). 7. Marmer, H. A. Tides and currents in New York Harbor. U. S. Coast and Geod. Surv., Special Publication No. 111: 1-174. Reference on p. 47-48. 8. Galle, P. H. On the relation between wind on current and mean sea level in the Indian and the Atlantic oceans and the adjacent seas. Proceedings of the Koninklijl~e Al~ademie van ~ etenschappen te Amsterdam, vol. 28, no. 10: 90~-918. 9. Nomitsu, Takaharu, and Okamoto, Motojiro. The causes of the annual varia- tion of the mean sea level along the Japanese coast. Memoirs of the Col- lege of Science Kyoto Imperial University, Ser. A, vol. X, no. 3: 12~161 (1927) . 10. Thompson, D'Arcy W. On mean sea level and its fluctuations. Fishery Board for Scotland ScientificInvestigations 1914, No. 4: 1-45' (March 1915). Refer- ence on p. 25~-31. 11. Daly, R. A. A general sinking of sea-level in recent time. Proc. Nat. Acad. Sci., 6: 246-250 (1920). 12. Reference cited under No. 2, p. 63-64. 13. Close, Sir Charles. The second geodetic levelings, of England and TVales, 1912- 1921 (1922): 1-62. Reference on p. 34. 14. Avers, H. G. A study of the variation of mean sea-level from a level surface. Bull. Nat. Research Council No. 61:56-58 (1927).