of different countries were crowned, and the length of their reigns; the dates and places of memorable battles, the number of men engaged, and loss on each side; the dates of the treaties between nations; and other incidents analogous in their character. These remarks may even be extended to the regions of history and biography. A mass of facts thus collected from year to year, not only will have some interest at the moment, but will at length become a useful storehouse for future recurrence. A brief outline of our political progress may also be easily introduced, such as a summary of the proceedings of Congress and of the legislature of the several states for each year, so far as they give rise to any new results either in the promulgation of laws, or the establishment of institutions, or aiding schemes of improvement. All the particulars of this sort, when divested of their extraneous accompaniments, may be brought together within a narrow compass. Notice may also be taken of charitable and religious societies, and associations for promoting the objects of humanity, morals, knowledge, and social order. A comparison of the extent of such efforts might communicate correct views of their effects, and serve as a guide in future undertakings of a like nature. But in all this we have again to confess, that we are only hinting at what may be done, within the scope of our plan, and what we hope will be done, but not what we have actually accomplished or attempted in the present volume. The astronomical part, we believe, will be found more full and accurate, than any thing of a similar kind which has appeared in the United States. It is intended to answer all the essential purposes of a nautical almanac, in addition to the usual calculations of an almanac and ephemeris. Should the work be continued, great care will be devoted to this part, and new matter will annually be given illustrating in a simple manner the practical topics in the science of astronomy. We have to acknowledge our obligation to the Companion to the British Almanac for many of the particulars, contained in the fourth part of the present work, relating to foreign countries. THE rising and setting of the Sun and Moon are given for five places in the United States, situated in different latitudes: the Almanac is thus adapted to the inhabitants of every part of the country, as these particulars depend simply on the latitude, and are wholly independent of the longitude. The column headed Boston, &c. will answer for all places north of latitude 41° 32', that is, British Continental North America, Maine, New Hampshire, Vermont, Massachusetts, and Michigan; all but the southern extremity of New York and Rhode Island, the northern half of Connecticut, the northern third of Pennsylvania, the Connecticut Reserve in Ohio, and the northern extremities of Illinois and Indiana. The column headed New York, &c. is intended for places situated between latitude 41° 32′ and 39° 48', that is, the southern extremities of New York and Rhode Island, all but the northern third of Pennsylvania, all but the southern extremity of New Jersey, the central parts of Ohio, Illinois, and Indiana, and the northern third of Missouri. The column headed Washington, &c. may be used between latitude 39° 48' and 35° 52', that is, throughout Maryland, Virginia, Delaware, the District of Columbia, and Kentucky, the northern half of Tennessee, the southern extremity of New Jersey, the southern third of Ohio and Indiana; the southern half of Illinois, all but the northern third of Missouri, and the northern third of North Carolina and Arkansas. The column headed Charleston, &c. is suited to places between latitude 35° 52' and 31° 24', namely, South Carolina, all but the southern extremity of Georgia, Alabama, and Mississippi, all but the northern_third of North Carolina and Arkansas; the southern half of Tennessee; the northern half of Louisiana. The column headed New Orleans, &c. is adapted to places south of latitude 31° 24', that is, all Florida and Texas, the southern half of Louisiana, and the southern extremities of Georgia, Alabama, and Mississippi. The setting of the Moon is given from new moon to full, and the rising from full moon to new; the letters M. A. m. a., to be found in these columns and in other parts of the Almanac, are used to denote Morning and Afternoon. The time of the Phases of the Moon is computed for the meridian of Washington, but may be readily reduced to that for any other meridian, by adding or subtracting the difference of the longitude according as the same is east or west of that city. The time of the moon's southing is computed for the same meridian. The variation, however, even in a remote part of the United States, will be inconsiderable. The time of High Water is corrected for the difference of the Right Ascension of the Sun and Moon, and the distance of the Moon from the Earth. The small corrections depending on their declinations and our distance from the Sun, have been neglected as unimportant; indeed it has been ascertained from a series of several hundred observations, that the corrections we have introduced will, in calm weather, give the time of high water within fifteen minutes, and, generally, much nearer. The difference between the time of high water at New York, Charleston, and Boston, was derived from the best authorities; but perhaps it has not been ascertained with the degree of accuracy that is to be desired. If our authorities are correct, the time of high water along the coast of Maine, New Hampshire, and Massachusetts, as far as Nantucket, is nearly the same as at Boston. Moreover, when it is high water in New York, it is nearly so in Long Island Sound, along the coast of New Jersey, Delaware, Maryland, Virginia, and North Carolina, as far as Cape Lookout, (with the exception of Sandy Hook and the entrance of Chesapeake Bay;) whilst along the coast of the southern part of North Carolina, of South Carolina, Georgia, and Florida, at Sandy Hook and the entrance of the Chesapeake, the time agrees very nearly with that in the column for Charleston; when greater accuracy is desired, reference should be had to the Tide Table on the 15th page. The time of the tide immediately preceding the southing of the inoon, only, having been given, it should be corrected by the addition of half the difference when the time of the other tide is required. The Planets are placed in the order in which they pass the meridian on the first day of each month, and their declinations are computed for the moment of their passage over the meridian of Washington. The places of the four new planets are not given, we believe, in any English or French Almanac. All the calculations in this Almanac, with the exception of the Occultations and the eclipses of Jupiter's Satellites, are expressed in apparent time; but in our large cities the mean time is more generally used. Apparent time, however, is readily converted into mean. by applying the equation of time, according to the direction at the head of the column; and mean into apparent, by applying the same equation with the contrary sign. The longitude, latitude, declination, semidiameter, and horizontal parallax of the Sun and Moon, the Moon's distance from the Sun, the equation of time, and the obliquity of the Ecliptic, being intended rather for the navigator and astronomer than the public generally, are adapted to apparent time for the meridian of Greenwich, whence we reckon our longitude. By comparing the Sun's longitude and his distance from the Moon as here given, with that in the Nautical Almanac, they will be found to differ, by a quantity varying from two to eleven seconds. This difference, according to Bessel, is the error of Delambre's Tables of the Sun, used in the computation of the Nautical Almanac. The lunar distances are placed in a manner, which it is hoped, will be found convenient for the formation of differences. The Sun's declination, being copied from the Nautical Almanac, is not strictly correct, but the error never exceeds three seconds, and is, for the most part, less than half that quantity; if greater accuracy is desired, the declination, as well as the right ascension can be readily computed from his longitude and latitude and the obliquity of the ecliptic. The longitude and latitude of the Moon being given for intervals of twenty-four hours, the proportional of their variation in that term, for any intermediate time, will not be strictly accurate; but must be corrected for the differences of the second, third, and fourth orders, when great accuracy is required. These corrections may be computed by the following formulæ, R being the 2d, 3rd, or 4th difference, and a the time from the first interval. In these formulæ, it will be noticed, that when the second or fourth differences are positive, the correction is negative, and vice versâ ; but that the correction for the third difference has the sign of that difference. If, for example, the longitude of the moon at midnight on the first of January were required, it will be found that the above formulæ give as the correc tion of half her motion between the first and second, +8.6; hence her longitude at that time is 9° 46′ 7′′.6. The Occultations (pages 4,5,6,) were computed with the greatest strictness, and so very nearly accurate are the Lunar Tables, that these interesting phenomena can be predicted with the certainty that they will take place almost at the precise moment. Indeed, that of Aldebaran, on the 18th of September last, actually happened at Boston, at the very second; that of the 21st of August within three seconds, and that of the 12th of November within ten, although the last took place near the edge of the moon, and in a position to be most affected by an error in her tabular longitude. We cannot refrain from expressing to M. Encke, our great obligation for the assistance we have received from his Astronomical Year-Book for 1830. "This work" (says Mr. Baily, first Vice-President of the London Astronomical Society)" should be hailed as the harbinger of a general improvement in the mode of arranging and forming the ephemerides of different nations. M. Encke, disdaining the trammels of former and less enlightened times, and relying on his own excellent judgment and abilities, has nobly and boldly struck out a new path for himself, which, there can be no doubt, will soon be followed by every nation pretending to encourage the science of Astronomy." Although it is mortifying to reflect that this country cannot, or will not, attempt to attain eminence in this and other scientific pursuits, yet we should be grateful for information, wherever it can be found, and hope we may be able, eventually, to emulate the splendid example that has thus been set us. To the English Nautical Almanac we are indebted for some of the elements here published. This work, though not to be compared with that of which we have just spoken, is, we apprehend, harshly mentioned by Mr. Baily, when he calls it "an unnecessary expense" and "a disgrace to the nation;" although it must be confessed to be singular, that, for a period of nearly thirty years after the discovery of four new planets, not the least notice should be taken of any one of them, and that the longitude of the Sun and his distance from the Moon (so important in the determination of terrestrial longitude) should still be computed from Delambre's tables, even after their errors had been pointed out, and the amount of them in 1829 actually calculated, in the Supplement to the Almanac for that year. Perhaps, however, it may be thought, that Americans have not the least right to complain of the defective state of the English Nautical Almanac, when they, so far from having ever attempted to produce a better, have done little to advance the noble science of Astronomy. Although great care has been taken to avoid errors, a few escaped notice until the opportunity for correcting them had passed; perfect accuracy, it would seem, cannot be attained, since even in the Berlin Year-Book, computed and edited, as it was, by the greatest astronomers, a considerable number of typographical errors is to be met with. Moreover, the time of the passage over the meridian of all the planets, as therein given, is for the most part incorrect; that of Mercury and Venus being one day too late, when they south before noon, and that of all the others being correct, only, when they south about midnight. The year 1831 will be distinguished for astronomical phemonena worthy of the attention of our astronomers. Besides the eclipse of the Sun on the 12th of February, which will be very large throughout the United States, and annular in some part of Louisiana, Mississippi, Alabama, Georgia, North Carolina, Virginia, and Massachusetts, there will be eight visible occultations of Aldebaran, three of Jupiter, three of Saturn, two of Regulus, one of Venus, and one of Uranus, as well as of a great number of the smaller stars. |