be underneath the moon. compelled to obey also the earth's rotation; and that too, as the pupil knows, with a velocity in accordance with its particular latitude; so that the exact place in the oval outline, which the attraction due to each drop's individual distance from the moon would have led it to assume, could not be taken by it; and in addition to this, the precise spot towards which the water had been attracted was no longer the spot of attraction, for, in consequence of the earth's rotation, the moon was only for an instant in the zenith there.

But meanwhile, each drop was

*

*

*

*

The whole consequence of these circumstances, was the production of "an immensely broad and excessively flat wave (not a circulating current). When the higher or lower parts of this wave strike the coasts, they experience what we call high or low water."* The question arises, what became of this state of disturbance of the equilibrium of the ocean so caused? Has it yet subsided? It has not, for the same cause that the vibrations of a pendulum cannot at once subside-the existence of inertia (D, p. 207). The undulations of the body of water so raised, are even now being propagated, by impression from body to body of the waters of our globe. The moon which now, (Monday, six P.M.,) is beginning similarly to trouble the less expanse of the Atlantic, (to the middle of which she will be vertical in two hours' time,) beholds the consequence of her morning work in the Pacific, in the transmission of a portion of the swell she then caused around Cape Horn, into the Atlantic; and she may view it, during her operations of the next four hours over that sea, at one time combining with and augmenting, at another time tending to oppose and efface, that very wave which is the immediate consequence of her present attraction there.

The great tidal wave is of course imperceptible to those who may be navigating its surface, except near the shores, on account of its great extent and excessive flatness; for it stretches from Africa to America, and dispenses high water to the shores of each; but it will still hold on its

* Sir John Herschel.

*

northward way with great velocity, (preceded and followed, at equal pace, by similar waves of earlier and later origin,) until having, on Tuesday afternoon, reached the northwestern coast of France, its eastern edge will find an interruption on the southern coasts of Great Britain and Ireland, and divide into portions, which will proceed (at different rates, because of the difference of impediment,) up and around the coasts of our islands, to lift the cargoes of our ships and furnish, at London, the Wednesday business of our wharfs with its " nerves and sinews."

M The moon, if new or full at the noon or midnight of any place, must be crossing the plane of the meridian of the place at that time. The interval between such a culmination of the moon at any port and the next "high water” there, is called the establishment of that port:-The establishment of London is about two hours.

But although it is usual thus to refer the time of high water to the transit of the moon next preceding it, as if her latest approach were the immediate cause of the phenomenon, such is not the case, as we have seen; for as she ceases to have any sensible influence on the tidal wave after its arrival in the narrower seas, in a river like the Thames both the present swell, and that which will be its successor after the lapse of another twelve hours, must already have travelled a considerable distance unchanged by the attraction of the moon, even before the time of her rising.

* The pupil will need again to be reminded, that it is not so much the body of water that travels, but the impression of its motion that is propagated or communicated (see G, p. 207).

MR. LUBBOCK'S TABLES.

349

Mr. Lubbock, who, as well as Mr. Whewell, has been much occupied in investigations on this intricate subject, gives* a table, from which the following is extracted, referring to the operations of the sun and moon at various angular distances from each other, and under average circumstances of declination, nearness, &c.; but at an interval of more than two days before the effect of those operations is discerned in London river in the flow of our "tide."

TABLE.

The angular distance of the sun and moon from each other, may be inferred from the time of the moon's coming to the meridian. The interval given shews, when added to the time of the moon's culmination, the time of high water at the London Docks :-ten minutes more are to be added for the time of high water at London Bridge.

* See "Elementary Treatise on the Tides," by J. W. Lubbock, Esq., Treas. R. S.

PROBLEM M.

CELESTIAL GLOBE.

To find the time of high water at the London Docks, or certain other places, on a given day.

RULE.-1. Find the time of the moon's " southing" at Greenwich on the day next but one before the given date.

2. Look out, in the left-hand column of the little table given on p. 349, for the time agreeing most nearly with this time of the moon's southing, and against it will be seen the interval to be added to shew the time of high water at the London Docks on the given day.

*

** If the time of the moon's southing, so found for the day next but one, was in its forenoon, and the addition of the interval produces more than two days twelve hours, the excess will, of course, shew the time of high water in the afternoon of the proposed day; but if the moon's southing was of the afternoon, and the addition of the interval produces more than two days twelve hours, the excess shews the time of high water in the morning of the day succeeding the proposed one. The time of the preceding tide may be found nearly, by deducting twelve hours twenty-five minutes.

Ex. 1. What was the time of high water at London Bridge on the 22d June, 1841, the moon having "southed" at nineteen minutes past one P.M., of June 20th?

Here, looking in the table for the nearest time, I take the interval placed against one hour thirty minutes, and adding it to one hour nineteen minutes, I get two days four hours ten minutes, shewing the time of high water at the London Docks on the 22d of June, to be ten minutes past four P.M. I afterwards add ten minutes to this, for the time of high water at London Bridge, and the result differs only nine minutes from the time given in the ephemeris.

Ex. 2. Find the time of high water at London Bridge on the 2d of July, 1841; the moon having “southed," or

TIME OF HIGH WATER.

351

come to the meridian of Greenwich, on the 30th of June, at nine hours forty-three minutes P.M.

I find in the table against ten hours, the interval of two days three hours forty-five minutes; and adding it to nine hours forty-three minutes, I get two days thirteen hours twenty-eight minutes. This takes me to the 3d of July, one hour twenty-eight minutes A.M., for high water at the London Docks, and one hour thirty-eight minutes,* for high water at London Bridge. The high water of the afternoon of the 2d of July, was twelve hours twenty-five minutes before this, or at one hour thirteen minutes P.M. (very nearly).

Ex. 3. What was the time of high water at the London Docks, and what was its height there, on the 24th of September, 1841, the moon having culminated at six hours P.M., on the 22d of September ?

Ex. 4. What was the time of high water at London Bridge on the 5th of December, 1841, the moon having "southed" at four hours two minutes A.M., on the 3d of December?

Ex. 5. What will be the time of high water at London Bridge, on the 27th of December, 1841, the moon "southing" at nine hours thirty-eight minutes in the afternoon of Christmas day? (see * * * following the Rule.)

Ex. 6. The moon's longitude on the 7th of August, 1841, was 11° 28'; at what time† did she culminate on the 8th of August, and what was the time of high water at London Bridge on the 10th of August?

Ex. 7. The moon's longitude on the 30th of August, 1841, was 19° 34'; at what time was her southing on that day, and what was the time and height of high water at the London Docks on the 1st of September?

The time of high water at London Bridge being ascertained, the times of tide at other places are to be found by the addition or deduction of certain differences given in "tide tables;" but local circumstances frequently occasion irregularities, and no such table can predict correctly for every given place.

Thus, having the time of high tide at London Bridge, for the time of high water at

* Within eight minutes of the true time, as given in the almanac. The southing must be found by Problem D, p. 312.