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is called the diurnal inequality; it reaches its maximum when the moon is at its greatest northern or southern declination, and disappears when it is on the equator, and consequently has a half-monthly period. The variations of height from this cause produce a corresponding inequality in the times of high water. The sun's declination affects the tides in a similar manner, but the amount of the disturbance is very small, and its period extends over half a year. In long series of observations its effect is nevertheless well marked, both in height and time. The diurnal inequality, 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.


PARALLACTIC INEQUALITY. A further cause in the variation of the height of the tides is the variation of the distances of the sun and the moon by reason of the ellipticity of their orbits. The efficacy of a heavenly body in raising tides is shown by theory to be inversely proportional to the cube of the distance. Hence the efficacy of the sun will fluctuate between the extremes pineteen and twenty-one, taking twenty for its mean value, and that of the moon between forty-three and fifty-nine. Taking into account this cause of difference, the bighest 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.


"The three principal forms of tides are illustrated in the annexed diagram, which exhibits the tides at New York, San Francisco, and Galveston for two days from actual observation. Of these, that for San Francisco 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 arrives on our shores twelve hours later than the direct tide-wave which crosses the Atlantic from east to west. In this way the diurnal inequality will be eliminated by the superposition of the two tides, the greater high water of the former coinciding with the lesser of the latter, and vice versa, leaving the semi-diurnal tides of equal height.


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The tide at Galveston, on the other hand, furnishes a case of the elimination of the semi-diurnal tide, leaving as a residual only the diurnal

inequality. It is to be presumed in this instance that the tides reaching Galveston through the straits of Florida and through the passage between Cuba and Yucatan differ by six hours in their periods, causing the low water of one to coincide with the high water of the other, thus sensibly destroying the semi-diurnal tides, except in so far as they are unequal. This leaves a small tide outstanding, having substantially the form of the diurnal inequality, and producing the appearance of the “single-day tide," or one bigh and one low water in every twenty-four hours. This residual fluctuation is well marked at times when the inoon's declination is considerable on either side of the equator, but disappears almost entirely when the moon is near the equator, since, at such times, the diurnal inequality disappears. Tides of this class have always a small range; in the Gulf of Mexico they rarely exceed 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 investigated 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-GAUGES. For this purpose a self-registering tide-gauge is used, by wbich 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 bour 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 bas been that of maintaining a temperature above freezing within the floatbox by means of a simple heating-apparatus. An arrangement of this kind has actually been used on the Fox Islands, in Penobscot Bay. A

stream of water flows slowly from an elevated hogshead through a coil in a large stove, passes down to the bottom of the float-box and up again into another hogshead, from which it is pumped up every day by the observer into the first one. As but a small elevation of temperature is necessary, this arrangement has proved quite sufficient.

Another arrangement, devised by Mr. Batchelder, of Boston, and called by him an "Arctic tide-gauge,” is in use at Boston, and has compared well with the ordinary float-gange. It consists of a strong iron tube, about four inches in diameter, firmly bolted to a wharf or pile. It is open at the top, and has at the lower end a nipple, to which an Indiarubber bag is fastened; the length of the tube being sufficient to allow the elastic bag to be always subinerged at the lowest stage of the tide. The bag is supported by a suitable shelf or cage, and is filled with glycerine, which is poured in at the top of the tube. When in this condition the glycerine rises and falls within the iron tube in proportion to the varying height and pressure of the column of water above the rubber bag, the difference in the height of the two columns being in proportion to the difference of the specific gravity of the water and the glycerine. The parts above described insure protection against floating ice, and prevent congelation within the iron tube.

A copper tube about three inches in diameter, closed at the bottom and open at the top, is placed within the iron tube, and floats in the glycerine; if left free, it would rise and fall with the changing level of this 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 the 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 with it, a string or chain leads over a single pulley, and gives horizontal motion to the pencil-carriage of the recording-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 the central float, the spiral spring at the top is more or less extended, the 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 perforated box, for the purpose of preventing oscillation, as it is always submerged, and the pressure upon it is equal to the weight of the column of water, having its base at the bag, and its summit at the mean level of the surface-waves.

A tide-gauge, for observations on an open coast, has been devised by Mr. Henry Mitchell, of the Coast Survey. The graduated scale on the float is read from the shore by means of a spy-glass, the top of the tube serving as index-mark.


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; and as a result, tide-tables have been published by the Coast Survey for some years past, giving in advance the times and heights of liigh 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 obserred 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.


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 avnexed diagram of earthquake-waves, which


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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

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