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is below the horizon than when she is above it; and at a place in south latitude it will be just the contrary.

377. Position and motion of the tide wave. The full effect of the moon's action at any place, occurring after her passage over the meridian, the tide wave or cotidal line in the open ocean is always to the east of the moon, and generally at the distance of about 30°. It must, therefore, have a westwardly motion, following the moon in her apparent diurnal motion round the earth; and it would thus, if the whole earth was covered with water, make a complete circuit in the course of a lunar day. This motion of the tide wave is not, however, a continued forward motion of the same portion of water, but merely an undulation of successive portions.

It follows from the preceding, that in the open ocean it must be high water about two hours after the moon's passage over the meridian. This is, however, subject to some variation, depending on the relative positions of the sun and moon.

378. Tides not perceptible in lakes and inland seas. As the tides result from the unequal actions of the sun and moon on different parts, it requires a great extent of surface to render them sensible. No perceptible tides are, therefore, observed even in the largest lakes of this continent or in the inland seas of the eastern continent.

379. Tides in bays, rivers, &c. The tides in bays, rivers, narrow seas, and generally on shores far from the main body of the ocean, are not produced by the direct actions of the sun and moon, but are derivative waves propagated from the great tide wave. These derivative waves are usually attended by a current, which in some situations is quite rapid. Its velocity is, however, far less than that of the tide wave.

The interval between the moon's passage over the meridian, and the time of high water at places situated on the shores of continents, or on bays and rivers, depends principally on the distances the derivative tide waves have to pass, and on the less or greater obstructions to their motions, resulting from shoals and indentations of the coast. It is, therefore, very different at different places. At the same place, however, this interval has a mean value, from which it seldom deviates more than an hour; the devia·

tion depending mainly on the moon's position with reference to the sun.

380. Establishment of a port. The mean interval between the moon's passage over the meridian and high water at any port on the days of new and full moon, is called the establishment of the port. When, by careful observations at any port or other place on tide water, the establishment has been determined, the time of high water at that place, on any given day, may be easily computed. This is done by adding the value of the establishment to the time of the moon's passage over the meridian, obtained from the Nautical Almanac, and then applying the correction due to the moon's position with regard to the sun. The correction is obtained from a small table calculated by a formula deduced by Laplace.*

381. Rise of the tides at different places. The rise of the tide, or difference between the heights of high and low water, is very different at different places, being affected by various local causes. Thus, at New York, the mean rise of the spring tides is about 5ft. ; at Boston, 11ft.; at Brest in France, 19ft.; at Bristol in England, 42ft.; and at Cumberland at the head of the Bay of Fundy, 71ft.

According to Professor Whewell, the great tide wave of the South Atlantic Ocean moves northwardly along the coast of North America to the mouth of the Bay of Fundy, where it is met by another tide wave, moving in the opposite direction; this accounts for the extraordinary high tides in that Bay.

The height of the tides in many situations is considerably influenced by the direction of the wind on the coast, especially when it is strong, and continues for a length of time in the same direction.

382. Unit of altitude. The unit of altitude of a place, is the mean rise of the spring tides at that place, that is, it is the rise of the tide about a day and a half after the syzygies, on the supposi

* The theory of the tides, a subject of great difficulty, has been elaborately treated by Laplace in the 4th Book of the Mécanique Céleste. The formula referred to, is contained in the 42d sect. of the 3d chap. of the book.

The table of corrections and another table containing the establishment of the port for various places, are given in treatises on Navigation.

tion that the sun and moon are then both in the plane of the equator, and at their mean distances from the earth. When, by a series of observations, the unit of altitude of a place has been determined, the rise of the spring tides, as affected by the distances and declinations of the sun and moon, may be computed by a formula deduced for the purpose.**

In many places it is of great importance to be able thus to know, by previous computations, when unusually high spring tides are likely to occur, in order to guard against damages which might otherwise be the result.



383. Calendar. The Calendar is a distribution of time into periods of different lengths, as years, months, weeks, and days.

384. Julian Calendar. It has been shown that the tropical year contains 365d. 5h. 48m. 48sec. (145). But, in reckoning time for the common purposes of life, it is most convenient to have the year contain a certain number of whole days. In the calendar established by Julius Cæsar, and thence called the Julian Calendar, three successive years are made to consist of 365 days each; and the fourth, of 366 days. The year which contains 366 days, is called a Bissextile year. It is also frequently called Leap year. The others are called common years. The added day in a bissextile year is called the Intercalary day.

According to the Julian calendar, and reckoning from the epoch of the Christian era, every year, the number of which is exactly divisible by 4, is a bissextile; and the others are common years.

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* Méc. Cél. Bk. 4, Chap. 3, Sect. 41. The American Almanac contains tabular numbers for all the spring tides that occur in the year. The product of the unit of altitude of a place, by any of the numbers, is the height of the corresponding spring tide.


385. Julian Year. It is evident that the reckoning by the Julian calendar supposes the length of the year to be 365 days. A year of this length is called a Julian Year. A Julian year, therefore, exceeds the true astronomical year by 11m. 12sec. This difference amounts to about 3 days in the course of 400 years.

386. Gregorian Calendar. At the time of the Council of Nice, which was held in the year 325, the vernal equinox fell on the 21st of March, according to the Julian calendar. But by the latter part of the 16th century, in consequence of the excess of the Julian year above the true solar year, it came ten days earlier, that is, on the 11th of March. It was observed that, by continuing to reckon according to the Julian calendar, the seasons would fall back, so that in process of time they would correspond to quite different times of the year. This reckoning also led to irregularity in the times of holding certain festivals of the church. The subject, claiming the attention of Pope Gregory XIII., he, with the assistance of several astronomers, reformed the calendar. To allow for the 10 days, by which the vernal equinox had fallen back from the 21st of March, he ordered that the day following the 4th of October, 1582, should be reckoned the 15th instead of the 5th. And in order to keep the vernal equinox to the 21st of March, in future, it was concluded that three intercalary days should be omitted every four hundred years. It was also concluded that the 'omission of the intercalary days should take place in those centurial years, the numbers of which were not divisible by 400. Thus, the years 1700, 1800, and 1900, which, according to the Julian calendar, would be bissextile, would, according to the reformed calendar, be common years.

The calendar, thus reformed, is called the Gregorian Calendar. It is easy to perceive, by a short calculation, that time reckoned by the calendar, agrees so nearly with that reckoned by true solar years, that it will require 3600 years to produce a difference of one day.

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387. Adoption of the Gregorian calendar. The Gregorian calendar was at once adopted in Catholic countries; but, in those where the Protestant religion prevailed, it did not obtain a place till some time after. In England and her colonies, it was not in

troduced till the year 1752.* It is now used in all Christian countries except Russia.

388. Old and New Styles. The Julian and Gregorian calendars are also designated by the terms Old Style and New Style. In consequence of the intercalary days, omitted in the years 1700 and 1800, there is now 12 days difference between them.

389. Months. The year is divided into 12 portions, called calendar months. Each of these contains either 30 or 31 days, except the second month, February, which in a common year contains 28 days, and in a bissextile, 29 days; the intercalary day being added at the last of this month.

390. Dominical Letter. It was formerly customary to designate the days of the week in the calendar, by the first seven letters of the alphabet, always placing them so that A corresponded to the first day of the year, B to the second, C to the third, D to the fourth, E to the fifth, F to the sixth, G to the seventh, A to the eighth, B to the ninth, and so on. According to this arrangement, whatever letter designates any given day of the week in the first part of the year, continues to designate the same throughout the year. The letter designating the first day of the week, or Sunday, is called the Dominical Letter.

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As a common year consists of 365 days, or 52 weeks and 1 day, the last day of each common year must fall on the same day of the week as the first, and the next year must commence one day later in the week. Consequently, the day of the week which was

* At this time there was a difference of 11 days between the Julian and Gregorian calendars, in consequence of the suppression, in the latter, of the intercalary day in 1700. It was, therefore, enacted by parliament, that 11 days should be left out of the month of September, of the current year, 1752, by calling the day following the 2d of the month, the 14th, instead of the 3d.

Previous to this, years commencing at two different times had been in use in England. The historical year commenced on the 1st of January, as at present. But the civil or legal year commenced on the 25th of March. Dates in the interval between these times, were frequently expressed by naming both years. Thus, in books printed prior to 1752, we often meet with dates expressed as follows: Feb. 2d, 1735–6, or 1735. The same act that introduced the Gregorian calendar, established the 1st of January, as the commencement of the civil, as well as of the historical year.

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