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1 instead of as in the case of the moon, and being, there1200
1 fore, only 400th that of the moon ; but on account of the mass of the sun being 175 times that of the moon, its actual proportion of effect on the raising of the tides to that of the moon is as 1 to 21.
The moon making her apparent circuit in about 24 hours and 48 minutes, the moon's tidal wave will recur at every 12 hours and 24 minutes. The sun makes his circuit in 24 hours, and his wave will therefore recur at every 12 hours.
The sun making about 30 waves, whilst the moon makes 29, if at the first of these 29, the summits of the two coincide, at the 15th the summit of the moon's will coincide with the hollow of the sun's, and at the 29th the summits of the two will again nearly coincide ; a process very analogous to the well-known
; phenomenon of the recurrence of spring and neap tides, the first of which occur at about every fortnight, and the latter in the intermediate weeks.
When the moon is new she is between us and the sun, and in the south at mid-day when he is, and the two act conjointly in drawing up their respective waves.
When the moon is full she is in the south at midnight, when the sun is due north; here also there is conjoint action, because the moon's nearest wave will coincide with the sun's farthest wave.
In the moon's " quarterings," or intermediate weeks, she is in the east or west when the sun is in the north or south; and the moon's wave will have its summit at a point of the globe at right angles with the sun's wave, and will coincide with the position of the hollow caused by the sun.
Sir Isaac Newton calculated that the height of the tide due to solar attraction would be 2 feet at the equator; the influence of the moon taken at 21 times that of the sun would make this 4} feet, and the spring and the neap tides, being each the sum and difference of the two, would be 61 and 2į. Î'his complete effect of the forces of attraction would, however, be prevented by the velocity of rotation of the earth, even if its surface were completely covered with water.
But on account of the many changes in the relative positions of the three bodies, there are also many modifications in their attractive force, and the following circumstances are observed.
During summer and winter, at new and full moon, the sun and the moon exert their attractive forces together upon alternate belts of the earth's surface, so that the consecutive waves caused by these attractions, although recurring at regular times, or nearly so, will be in themselves different; and it is found that in summer and winter alternate spring tides are high and low, and neap tides nearly regular.
In spring and autumn the attractive forces exert their power upon the equator each time, consequently the consecutive waves will be nearly similar; and during these seasons the spring tides are found regular, and the neap tides alternately vary.
The above modification is called the diurnal inequality of the tide.
Equinoctial tides are the greatest ; at the equinoxes the sun and moon act in concert on the equator, where they have the greatest effect, this being the greatest circle round the earth, and where the centrifugal force exerts its greatest strength; the tide-wave whose summit is in the equator is greater than one with its summit on either side of the equator. This depends on the declination of the sun and moon being greatest when the declination is zero, and least when the declination is greatest, either north or south. On the 21st of March the sun strikes down vertically on the equator, and the sun's declination of zero. On the 21st of June the declination is 231 degrees north ; and on the 21st of December the declination is 23 degrees south. When new or full, the declination of the moon is always nearly the same as that of the sun. In the quarters the moon's declination is greater in spring and autumn, and least in summer and winter.
With regard to the prediction of the tides, the following was the principle of the method adopted by Sir John Lubbock :
He took a series of observations extending over 19 years ; that being the period in which the moon returns into the same position relative to the sun in all respects, and consequently containing a cycle of all varieties of tides ; all amounts of declination, distance, &c., for the different directions of the sun and moon. This
gave him about 14,000 observations as his materials. He divided these 14,000 into 24 groups, the first containing all those tides which occurred on the day of new or full moon, when the moon crossed the meridian, or became exactly south, between twelve and half-past twelve ; the second
contained the tides of the days when the moon was south between half-past twelve and one; the third between one and half.past, and so on for the 12 hours.
Each of these 24 groups contained about 580 observations. Striking an average of all the heights in each group, he found the height to which, on an average, all tides which occur on the day of a certain time of transit of the moon rise, which is as much as to say, that when the sun and moon have their mean declination, and are at their mean distance from the earth, such will be the height of the tide at the different periods of the moon's age.
His next process was to place against the date of each tide, in each group of 580, the declination of the moon when in the meridian on that day. He then divided each group into ll subdivisions, each subdivision consisting of those tides corresponding to a declination of 0° to 3°, 3° to 6°, 6° to 9°, &c., up to 27° to 30°. He then took the averages of the heights in each of these subdivisions, and so found how much the tide at any given period of the moon's age would be affected by the moon's declination. With the moon on the equator the height would be so much ; and the difference would be so much for each three degrees of declination.
Next he took the same 24 groups of 580 tides, and subdivided them accord. ing to the moon's distance from the earth at the time each occurred, making a subdivision for each minute of parallax.* From this he found how much the moon's distance made the height of the tide vary from the mean height at any given age of the moon.
The same process was gone through with the sun's declination and parallax ; and also the declination tables were again subdivided into north and south declinations, or day and night tides, to show how much inequality there was between them for each 3 degrees of declination.
Thus 7 tables were obtained as follows:
I. The average height of the tide corresponding to any half-hour of the moon's transit.
II, The variation from this average caused by the moon's declination. III. The variation caused by the moon's parallax. IV. The variation caused by the sun's declination. V. The variation caused by the sun's parallax. VI. The inequality between two consecutive tides caused by the moon being alternately north and south of the equator.
VII. The same inequality dependent upon the sun.
With these tables therefore, a set of which may be found in the Companion to the British Almanac for 1837, the height of the tide may be predicted for any future day for any place to which the tables are applicable in the following manner.
The Nautical Almanac gives the time of the moon's transit for the day in question. Table I. gives the average height corresponding to such time of transit. The Nautical Almanac further gives the moon's declination for that day. Table II. gives a correction of a few inches to be made to the height given in Table I. In the same way Tables III., IV., and V. give further small corrections according to the parallax and declination for the day as given in the Almanac, and then a height is found which is half-way between the morning and evening tides of that day. Tables VI. and VII. give the correction to be made according as the higher or lower tide of the day is wanted.
This mode of calculation having been compared with observation, it was found to have indicated with remarkable precision the changes which did actually follow in the various heights of the tides. Such discrepancies as appeared were made the groundwork of renewed study, and some corrections were made, especially that in calculating the tide for a certain day, the time
* Astronomical tables give the distance of the sun and moon, not in so many miles, but by their parallax, that is, the size which half the diameter of the earth would appear to be to a person standing on the sun or moon. This would evidently be larger as the sun or moon became nearer. The moon's parallax varies from 54 to 61 minutes ; the sun's from 8.66 to 8.94 seconds.
of the moon's transit of two or three days previous was taken as the startingpoint of the calculation.
In this manner tides have been predicted for every day of the year for all ports at which a sufficient number of observations had been made to found the tables upon, and the predictions have been verified in a most remarkable manner.
The following table will illustrate the effect of the sun in accelerating the tide from springs to neaps, and in retarding it from neaps to springs, and how at neaps as well as springs it is coincident with the lunar wave.
It gives the time of high-water at Liverpool in the month of December, 1853, from the full moon on the 16th to the new moon on the 30th.
Column I. is the time of the lunar tide, varying from 44 to 51 minutes daily. Column II. that of the actual combined solar and lunar tides. Column III, the difference from day to day of the time of the actual tide. Column IV. the amount which the actual tide is before the lunar tide. Column V. the amount which the actual tide is behind the lunar tide.
Now here it will be observed, that from two days after spring tide till two days after neap tide, the differences are in Column IV., or the actual tide is in advance of the lunar tide. After that, the differences are for four days in Column V., or the actual tide is in arrear of the lunar tide. The irregularities are consequent upon the changes of declination and parallax which take place within the fortnight. Now it is clear that these variations in the times, being dependent upon the same causes as the variations in the heights of the tides, can be treated in the same manner as the observations of height. Each observation being referred to its group, tables may be formed from which the time of any future tide may be predicted.
This has been done, and the result has been equally successful with the result of the predictions of height.
With regard to the calculations that might be made to predict the time and height of the tidal wave at any particular spot, from the position of the earth and the heavenly bodies, and applied to a globe covered with a uniform thickness of water, it will at once be seen that the earth we live on is totally different from such a globe ; and the tidal wave instead of moving on steadily and regularly, is on our earth obstructed and distorted in various ways by the various forms of the land, such as promontories and peninsulas, islands, inland seas, reefs, rivers, &c.; and the obstructions from these relate not only to the immediate configuration of the land between high and low water, but to the shelving shores stretching out to a distance into the sea, where it forms probably a kind of submarine country with its hills and valleys. When the main body of the travelling tidal wave approaches the shores of islands and projecting continents, it becomes checked on the diminished depth of water long before it is perceptible on any shore. The direction of what may be termed the branch of the wave, as it curves round the shores of an island or peninsula, may assume that of a line at right angles to the line of the summit of the wave. This alteration will be in height and time as well as in direction.
Not only it may assume this right-angled direction, but it may, and even does assume a rotatory or retrograde motion in some instances.
Even along a straight line of shore parallel to the direction of the tidal wave, the different depths of water will produce different ratios of speed in the tide as it approaches the land; and this approach may be in a series of curves of greater or less curvature, according to different depths of water off the shore, the sharper curvature probably corresponding to a less depth of water. Supposing the tidal wave to travel along the Atlantic from south to north, at a rate of 700 miles per hour, it was supposed the sea was there five or six miles deep, which has since been verified.
The impediments formed by extensive coral reefs round the shores of islands, are often such as to afford inlets to the tides only at certain places; the direction and time of the tide-wave may thus be entirely changed, and therefore give no idea of the tidal movements outside these bars, and variations are thus caused to the amount of several hours, and when they extend to twelve bours, it is doubtful whether the tide under observation is due to one transit of the moon or to another,
The "age of the tide” represents the time elapsed since the heavenly bodies were in such position as to form it, and includes both the time in forming the tide, as well as that during which it has been rolling about at sea. At places where the tides are,