only when two tides in succession attain the same high-water level and the same low-water level, as at springs.

921. By the Establishment of the Port* has been commonly understood the apparent time of the first high water that takes place in the afternoon of the day of full or change. This Dr. Whewell has called the Vulgar Establishment.

922. The interval between the moon's transit and the high water next following is called a lunitidal interval.

The lunitidal interval varies from day to day during the fortnight between full and change.

923. The correct establishment is the lunitidal interval corresponding to the day on which the moon passes the meridian exactly at noon (with the sun) or at midnight. This is found by taking the mean of all the times of H. W. for a fortnight. The Vulgar Estab. may thus be an hour, or considerably more, in error when used as representing the H. W. on any day of the fortnight.

The tide caused by the united actions of the sun and moon, when each of these bodies is in one of the positions most favourable for raising the water, is identified by its superior height. And it is thus found (as observed in No. 919) that the interval by which the tide follows the moon on the day when the full or change occurs at 12 o'clock, or the lunitidal interval corresponding to that particular transit, is not the interval actually observed on that day.

The establishment of the port, and also the height of the tide, appear to be subject to change.

924. The difference between the lunitidal interval at each transit of the moon and the correct establishment is called (by Sir J. Lubbock), from the period of its recurrence, the semi-menstrual inequality.

This inequality is found to be different for different places; hence the time of high water at any place cannot, generally, be accurately deduced from that at any other place by merely applying the difference of time between the two establishments.

925. The tide is subject, in like manner, to a semi-menstrual inequality in the height. This inequality being, like that in the time, different for different places, the height of a tide at any one place cannot always be correctly inferred from the given height at any other.

It

* The term Tide-hour has been adopted, in Table 13, in preference to the Establishment of the Port, which, besides its inconvenient length, and the foreign and awkward appearance which it makes amongst our other technical terms, is objectionable on important grounds. The word "establishment," in English, has already certain received senses. implies, generally, a building or institution; it is an abbreviated expression for the Episcopal Church. In the naval departments of Government it implies the regulations which determine the equipment of the ships, dimensions and weight of stores, and the number of officers and men. The addition of the term port, intended to limit the vague term "establishment," restricts the sense too much; for not the ports only, but every point of the coast, and often many places in the same port, have severally their proper "establish. ments." The German name Hafenzeit (Harbour-time), on the other hand, is, to us at least, a misnomer, since its natural meaning is the proper time for entering the harbour The term Tide-hour is short and unequivocal; these are the main points. It is English sufficiently exact, and will accordingly be employed till a better is suggested.

Y

926. It has been found that the morning and afternoon tides do not rise to the same height; the difference is called the Diurnal Inequality.

This irregularity is the consequence of the sun and moon not being always on the equator. Thus, suppose the moon in 20° N. declin. then the summit of the superior tide is in 20° N. lat., and of the inferior tide in 20° S. lat., each alternate tide having thus its greatest elevation in the other hemisphere. The diurnal inequality is subject to steady rules, and may be predicted.-Phil. Trans.

1837.

927. The maximum of the diurnal inequality corresponds to the moon's greatest declination, though it may not appear till after the time of the greatest declination. In like manner, it disappears with the moon's declination, but not till some time after she has crossed the equator. For example, the age, as it may be termed, of this inequality is, at Liverpool, six days; at Singapore, a day and a half. -Phil. Trans. 1837.

928. A diurnal inequality appears in the times, as well as in the heights, of the morning and afternoon tides. Thus, near Cape Florida, the diurnal inequality of the time was found, at its maximum in June 1835, to be 24 hours.-Phil. Trans. 1836, p. 308.

929. Strong winds affect the time and height of the tide, but chiefly the former, especially in rivers and narrow seas.*

The pressure of the atmosphere also affects the height of the tide, the water being in general higher as the barometer is lower.†

930. Though high and low water may succeed each other regularly as to time, yet the water does not always rise and fall at the same rate. Thus, for ex., the water in some places falls faster during the first of the tide than afterwards.

Irregularities both in the duration of the tide and in the rate at which the water rises or falls, are, however, most conspicuous in rivers.§

At Limerick and New Ross, the fall of the water occupies a longer time than the rise; at most other stations the rise appears to occupy a little longer time than the fall. This last, however, appears less certain. Phil. Trans., 1845, "Law of Tides."

* Adm. Beechey acquainted me that he considered strong winds do not raise the water more than two feet, even in the Bristol Channel, where the range is above forty feet.

† It has been established that a rise in the barometer of an inch is accompanied by a fall in the height of the water of twelve or fourteen inches. This opposite motion of the water and the mercury due to the atmospheric pressure was established by Mr. Daussy in discussing the tide-observations made at Brest.

The observations on the coasts of Ireland in 1842 agree with those of Mr. Daussy, Dr. Whewell, and Mr. Bunt, in shewing a contrary motion in the water to that of the mercury, and from twelve to fourteen times the amount.

The tide at Courtown exhibits extraordinary irregularities: the tide-hour does not increase constantly, as elsewhere, but oscillates backwards and forwards, &c. (pp. 117, 121.) § At Limerick, after low water, the water sometimes rises as much in ten minutes as it nad previously dropped in two hours. Such irregularities cause considerable difficulty in

ascertaining the true state of the case

II. RULES FOR FINDING THE TIME OF HIGH WATER.

931. The first of the two following rules, which is the old method of finding the time of high water by the moon's age, affords merely a rough estimate, as it may be in error nearly two hours. The second, which involves the semi-menstrual inequality, will be found a tolerable approximation on our own coasts, being generally within 15 or 20; but as each place has a different semi-menstrual inequality, the degree of accuracy which it may possess as applied to other parts of the world than those for which the table is constructed, cannot be pronounced.

Complete rules for computing the time and the height of the tide involve, also, corrections for parallax and declination, and require special tables for each port.*

932. Rule I. for a rough estimate. (1.) For the moon's age. Το the epact of the year, Table 14, add the epact of the month, and the day of the month. The result, if less than 29d 13h, is the moon's age at noon; if it exceed 29d 13h, subtract 29d 13h.

In leap-years, in January and February, deduct 1 day.

(2.) For the moon's meridian passage.+ Multiply her age, to the nearest day, by 8, and point off one decimal: the result is the time of the merid. passage nearly.

(3.) For the time of high water. To the time of merid. pass. add the establishment of the port (or tide-hour).

(4.) If the sum be less than 12 hours, it is the time of high water P.M.; if it exceed 12 hours, it is the time of high water nex morning; and, to obtain the time for P.M. on the present day, suk tract 12h 24m.

If the sum exceed 24 hours, it is the apparent time of high water P.M. the next day; for the time P.M. on the proposed day, subtract 24h 48m.

Note. This rule supposes that the tide always follows the moon by the same interval; but this interval, generally speaking, is different for each day of the fortnight. See No.

923.

* Such tables are given in the Tides published annually by the Hydrographic Office. The errors of the predicted times do not appear to exceed five or ten minutes, except in gales of wind, when the time of high water may be altered upwards of half an hour.

This is often called southing; but as in south latitude the moon passes the meridian

to the northward, this term is not adapted to general use.

The moon's age thus found may be more than a day in error, but her merid. pass. will generally be less than an hour in error.

Ex. 3. Find the time of high water at Liverpool, March 10th, 1870.
Tide-hour 11h 23m

TIME OF H.W. 10th, 5 23 P.M.

Ex. 4. March 31st, 1870, find the time of high water at Portsmouth.
Tide-hour 11h 41m

TIME OF H.W. 10 5 P.M.

Ex. 5. June 2d, 1870, find the time of high water at Liverpool.
Tide-hour, 11h 23m

TIME OF H.W. 1h 23 P.M.

933. Rule II. (1.) Take from the Nautical Almanac the M.T. of the moon's meridian passage, and correct it for the longitude by Table 28.

(2.) Take from Table 15 the semi-menstrual inequality corresponding to this time, and apply it to the reduced time of mer. pass. as directed in the table. To this result add the tide-hour, and the sum is the time of high water.

(3.) When this time exceeds 12 hours, it is the time of high water past midnight, that is, A.M. the next day.

When, therefore, the P.M. tide preceding is required, it is necessary to employ the inferior transit of the moon. This is obtained by taking the mean of the given transit and the next preceding.

Ex. 1. Aug. 6th, 1870, find the times of high water at Shields. Long. 1° 25′ W.; tide-hour, 3h 30m

Ex. 2. Aug. 28th, 1870, find the time of H.W. at Portsmouth. Tide-hour, 11h 41m; tr. 27th, oh 40m; 28th, 1h 32m; sem. ineq. 28th, -21; do. for mean tr. 14. HIGH WATER 28th, 12h 52m; or 29th, oh 52m A.M.; and oh 13m P.M. on 28th.

Ex. 3. March 9th, 1870, find the time of high water at Cherbourg.

Tide-hour, 7 49m. HIGH WATER 9th, 12h 10m; or 10th, oh 10 A.M. No tide 9th P.M.

(4.) When the time of the moon's transit on the given day exceeds 12 hours, the transit occurs A.M. on the next day (civil

time). It is evident, therefore, that to obtain the times of high water on the same day, we must, in such cases, employ the transit of the preceding day.

Subtract 12 from the time of transit, to enter the table of the semi-menstrual inequality.

To find the other tide, we must employ the inferior transit as already directed.

Ex. 4. March 30th, 1870, find the times of high water at Shields.

934. When the range of tide is considerable, and the depth not great, and it is required to identify the place of the ship by the soundings, or when about to enter a harbour in a vessel whose draught of water is nearly equal to the depth, it is necessary to find the height of the tide as exactly as circumstances permit. If the place is one of those of which particulars are given in the tidetables published by the Hydrographic Office, the depth is found by the rules there given. When such tables are not at hand, it may be found approximately by Table 16.

935. It is proper to remark that the age of the tide is necessary to the computation of its height. Thus, suppose it is H. W. at 2h 30m P.M. on Monday, the day of change. Now, if this H. W. is the tide really corresponding to the transit of the sun and moon together (No. 919), it will also be that which gives the spring range; the next range, therefore, will be less, and each range in succession will go on decreasing to the neap-tide. But if the age of the tide, in the supposed case, is 2 days, that is, if the highest tide does not follow till 2 days later, or till Wednesday afternoon, then the range on Monday will not be so high as on Wednesday; that is, the range, instead of decreasing continually to the neap-tide, will go on increasing for the next 2 days; after which it will begin to decrease until the neap-tide, which will take place 2 days after the 1st quarter, and not on the day of the 1st quarter.