Observations of the rise and fall of tides.

The first step in the practical design of the sewage works is to ascertain the level of high and low water of ordinary spring and neap tides and of equinoctial tides, as well as the rate of rise and fall of the various tides. This is done by means of a tide recording instrument similar to Fig. 4, which represents one made by Mr. J. H. Steward, of 457, West Strand, London, W.C. It consists of a drum about 5 in diameter and 10 in high, which revolves by clockwork once in twenty-four hours, the same mechanism also driving a small clock. A diagram paper divided with vertical lines into twenty-four primary spaces for the hours is fastened round the drum and a pen or pencil attached to a slide actuated by a rack or toothed wheel is free to work vertically up and down against the drum. A pinion working in this rack or wheel is connected with a pulley over which a flexible copper wire passes through the bottom of the case containing the gauge to a spherical copper float, 8 inches diameter, which rises and falls with the tide, so that every movement of the tide is reproduced moment by moment upon the chart as it revokes. The instrument is enclosed in an ebonized cabinet, having glazed doors in front and at both sides, giving convenient access to all parts. Inasmuch as the height and the time of the tide vary every day, it is practicable to read three days' tides on one chart, instead changing it every day. When the diagrams are taken of, the lines representing the water levels should be traced on to a continuous strip of tracing linen, so that the variations can be seen at a glance extra lines should be drawn, on the tracing showing the time at which the changes of the moon occur.

Fig. 5 is a reproduction to a small scale of actual records taken over a period of eighteen days, which shows true appearance of the diagrams when traced on the continuous strip.

These observations show very little difference between the spring and neap tides, and are interesting as indicating the unreliability of basing general deductions upon data obtained during a limited period only. At the time of the spring tides at the beginning of June the conditions were not favourable to big tides, as although the moon was approaching her perigee, her declination had nearly reached its northern limit and the declination of the sun was 22° IN The first quarter of the moon coincided very closely with the moon's passage over the equator, so that the neaps would be bigger than usual. At the period of the spring: tides, about the middle of June, although the time of full moon corresponded with her southernmost declination, she was approaching her apogee, and the declination of the sun was 23° 16' N., so that the tides would be lower than usual.

In order to ensure accurate observations, the position chosen for the tide gauge should be in deep water in the immediate vicinity of the locus in quo, but so that it is not affected by the waves from passing vessels. Wave motion is most felt where the float is in shallow water. A pier or quay wall will probably be most convenient, but in order to obtain records of the whole range of the tides it is of course necessary that the float should not be left dry at low water. In some instances the float is fixed in a well sunk above high water mark to such a depth that the bottom of it is below the lowest low water level, and a small pipe is then laid under the beach from the well to, and below, low water, so that the water stands continuously in the well at the same level as the sea.

The gauge should be fixed on bearers, about 3 ft 6 in from the floor, in a wooden shed, similar to a watchman's box, but provided with a door, erected on the pier or other site fixed upon for the observations. A hole must be formed in the floor and a galvanized iron or timber tube about 10 in square reaching to below low water level fixed underneath, so that when the float is suspended from the recording instrument it shall hang vertically down the centre of the tube. The shed and tube must of course be fixed securely to withstand wind and waves. The inside of the tube must be free from all projections or floating matter which would interfere with the movements of the float, the bottom should be closed, and about four lin diameter holes should be cleanly formed in the sides near to the bottom for the ingress and egress of the water. With a larger number of holes the wave action will cause the diagram to be very indistinct, and probably lead to incorrectness in determining the actual levels of the tides; and if the tube is considerably larger than the float, the latter will swing laterally and give incorrect readings.

A bench mark at some known height above ordnance datum should be set up in the hut, preferably on the top of the tube. At each visit the observer should pull the float wire down a short distance, and allow it to return slowly, thus making a vertical mark on the diagram, and should then measure the actual level of the surface of the water below the bench mark in the hut, so that the water line on the chart can be referred to ordnance datum. He should also note the correct time from his watch, so as to subsequently rectify any inaccuracy in the rate of revolution of the drum.

The most suitable period for taking these observations is from about the middle of March to near the end of June, as this will include records of the high spring equinoctial tides and the low "bird" tides of June. A chart similar to Fig. 6 should be prepared from the diagrams, showing the rise and fall of the highest spring tides, the average spring tides, the average neap tides, and the lowest neap tides, which will be found extremely useful in considering the levels of, and the discharge from, the sea outfall pipe.

The levels adopted for tide work vary in different ports. Trinity high-water mark is the datum adopted for the Port of London by the Thames Conservancy; it is the level of the lower edge of a stone fixed in the face of the river wall upon the east side of the Hermitage entrance of the London Docks, and is 12 48 ft above Ordnance datum. The Liverpool tide tables give the heights above the Old Dock Sill, which is now non-existent, but the level of it has been carefully preserved near the same position, on a stone built into the western wall of the Canning Half Tide Dock. This level is 40 ft below Ordnance datum. At Bristol the levels are referred to the Old Cumberland Basin (O.C.B.), which is an imaginary line 58 ft below Ordnance datum. It is very desirable that for sewage work all tide levels should be reduced to Ordnance datum.

A critical examination of the charts obtained from the tide- recording instruments will show that the mean level of the sea does not agree with the level of Ordnance datum. Ordnance datum is officially described as the assumed mean water level at Liverpool, which was ascertained from observations made by the Ordnance Survey Department in March, 1844, but subsequent records taken in May and June, 1859, by a self-recording gauge on St. George's Pier, showed that the true mean level of the sea at Liverpool is 0.068 ft below the assumed level. The general mean level of the sea around the coast of England, as determined by elaborate records taken at 29 places during the years 1859-60, was originally said to be, and is still, officially recognised by the Ordnance Survey Department to be 0.65 ft, or 7.8 in, above Ordnance datum, but included in these 29 stations were 8 at which the records were admitted to be imperfectly taken. If these 8 stations are omitted from the calculations, the true general mean level of the sea would be 0.623 ft, or 7.476 in, above Ordnance datum, or 0.691 ft above the true mean level of the sea at Liverpool. The local mean seal level at various stations around the coast varies from 0.982 ft below the general mean sea level at Plymouth, to 1.260 ft above it at Harwich, the places nearest to the mean being Weymouth (.089 ft below) and Hull (.038 ft above).

It may be of interest to mention that Ordnance datum for
Ireland is the level of low water of spring tides in Dublin
Bay, which is 21 ft below a mark on the base of Poolbeg
Lighthouse, and 7.46 ft below English Ordnance datum.

The lines of "high and low water mark of ordinary tides" shown upon Ordnance maps represent mean tides; that is, tides halfway between the spring and the neap tides, and are generally surveyed at the fourth tide before new and full moon. The foreshore of tidal water below "mean high water" belongs to the Crown, except in those cases where the rights have been waived by special grants. Mean high water is, strictly speaking, the average height of all high waters, spring and neap, as ascertained over a long period. Mean low water of ordinary spring tides is the datum generally adopted for the soundings on the Admiralty Charts, although it is not universally adhered to; as, for instance, the soundings in Liverpool Bay and the river Mersey are reduced to a datum 20 ft below the old dock sill, which is 125 ft below the level of low water of ordinary spring tides. The datum of each chart varies as regards Ordnance datum, and in the case of charts embracing a large area the datum varies along the coast.

The following table gives the fall during each half-hour of the typical tides shown in Fig, 6 (see page 15), from which it will be seen that the maximum rate occurs at about half-tide, while very little movement takes place during the half-hour before and the half-hour after the turn of the tide:—

Table I.

Rate of fall of tides.

State of Eqionoctial Ordinary Ordinary Lowest
Tide. Tides. Spring Tides. Neap Tides. Neap Tides.

High water — — — — 1/2 hour after 0.44 0.40 0.22 0.19 1 " " 0.96 0.80 0.40 0.31 1-1/2 " " 1.39 1.14 0.68 0.53 2 " " 1.85 1.56 0.72 0.59 2-1/2 " " 1.91 1.64 0.84 0.68 3 " " 1.94 1.66 0.86 0.70 3-1/2 " " 1.94 1.66 0.86 0.70 4 " " 1.91 1.64 0.84 0.68 4-1/2 " " 1.35 1.16 0.59 0.48 5 " " 1.27 1.09 0.57 0.46 5-1/2 " " 1.06 0.91 0.47 0.38 6 " " 1.04 0.89 0.46 0.37 6-1/2 " " 0.53 0.45 0.24 0.18 Totals…. 17 ft 6 in 15 ft 0 in 7 ft 9 in 6 ft 3 in

The extent to which the level of high water varies from tide to tide is shown in Fig. 7 [Footnote: Plate III.], which embraces a period of six months, and is compiled from calculated heights without taking account of possible wind disturbances.

The varying differences between the night and morning tides are shown very clearly on this diagram; in some cases the night tide is the higher one, and in others the morning tide; and while at one time each successive tide is higher than the preceding one, at another time the steps showing: the set-back of the tide are very marked. During the earlier part of the year the spring-tides at new moon were higher than those at full moon, but towards June the condition became reversed. The influence of the position of the sun and moon on the height of the tide is apparent throughout, but is particularly marked during the exceptionally low spring tides in the early part of June, when the time of new moon practically coincides with the moon in apogee and in its most northerly position furthest removed from the equator.

Inasmuch as the tidal waves themselves have no horizontal motion, it is now necessary to consider by what means the movement of water along the shores is caused. The sea is, of course, subject to the usual law governing the flow of water, whereby it is constantly trying to find its own level. In a tidal wave the height of the crest is so small compared with the length that the surface gradient from crest to trough is practically flat, and does not lead to any appreciable movement; but as the tidal wave approaches within a few miles of the shore, it runs into shallow water, where its progress is checked, but as it is being pushed on from behind it banks up and forms a crest of sufficient height to form a more or less steep gradient, and to induce a horizontal movement of the particles of water throughout the whole depth in the form of a tidal current running parallel with the shore.

The rate of this current depends upon the steepness of the gradient, and the momentum acquired will, In some Instances, cause the current to continue to run in the same direction for some time after the tide has turned, i.e., after the direction of the gradient has been reversed; so that the tide may be making—or falling—in one direction, while the current is running the opposite way. It will be readily seen, then, that the flow of the current will be slack about the time of high and low water, so that its maximum rate will be at half-ebb and half-flood. If the tide were flowing into an enclosed or semi- enclosed space, the current could not run after the tide turned, and the reversal of both would be simultaneous, unless, indeed, the current turned before the tide.

Wind waves are only movements of the surface of the water, and do not generally extend for a greater depth below the trough of the wave than the crest is above it, but as they may affect the movement of the floating particles of sewage to a considerable extent it is necessary to record the direction and strength of the wind.

The strength of the wind is sometimes indicated wind at the time of making any tidal observations. By reference to the Beaufort Scale, which is a graduated classification adopted by Admiral Beaufort about the year 1805. The following table gives the general description, velocity, and pressure of the wind corresponding to the tabular numbers on the scale:—

[Illustration: PLATE III

PERIOD OF SIX MONTHS.

To face page 20]

The figures indicating the pressure of the wind in the foregoing table are low compared with those given by other authorities. From Mutton's formula, the pressure against a plane surface normal to the wind would be 0.97 lb per sq. foot, with an average velocity of 15 miles per hour (22 ft per sec.), compared with o.67 lb given by Admiral Beaufort, and for a velocity of 50 miles per hour (73.3 ft per sec.) 10.75 lb, compared with 7.7lb Semitone's formula, which is frequently used, gives the pressure as 0.005V^2 (miles per hour), so that for 15 miles per hour velocity the pressure would be 1.125 lb, and for 50 miles it would be l2.5 lb It must not be forgotten, however, that, although over a period of one hour the wind may average this velocity or pressure, it will vary considerably from moment to moment, being far in excess at one time, and practically calm at another. The velocity of the wind is usually taken by a cup anemometer having four 9 in cups on arms 2 ft long. The factor for reducing the records varies from 2 to 3, according to the friction and lubrication, the average being 2.2.

The pressure is obtained by multiplying the Beaufort number cubed by 0.0105; and the velocity is found by multiplying the square root of the Beaufort number cubed by 1.87.

A tidal wave will traverse the open sea in a straight line, but as it passes along the coast the progress of the line nearest the shore is retarded while the centre part continues at the same velocity, so that on plan the wave assumes a convex shape and the branch waves reaching the shore form an acute angle with the coast line.