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 in Buzzard's Bay and Narraganset Bay, 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 20th page. The time of the tide immediately preceding the southing of the moon, 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 Ephemeris of the Sun is taken from the celebrated Almanac of Professor Encke. It contains the Sun's Semidiameter, the time (mean) occupied by the Semidiameter in passing the meridian, his declination, the mean ti.ne at the instant his centre is on the meridian of Berlin, the Sidereal time, and the obliquity of the ecliptic. The epoch of the Sidereal time is noon mean time, and that of the declination and of the equation is noon apparent time, of the meridian of Berlin, which is Oh. 53' 35.4" east of Greenwich.

The quantity in the column of the mean time at apparent noon at Berlin is constantly to be added to apparent time to reduce it to mean; indeed, with the exception of the epoch of the equation and declination of the Sun, mean time has been altogether used in the Almanac for 1833.

The apparent places of twenty-five stars, as determined by Professor Bessel at Königsberg, will be found very useful for ascertaining the time or the latitude. The Declination in some instances will be found to differ from that given in the English Nautical Almanac, more than was to be expected in the present improved state of astronomical instruments. This difference sometimes amounts to four seconds; a quantity too great to be altogether ascribed to the use of different tables of refraction.

The table of Refractions is that computed on principles explained by the late Dr. Thomas Young, and is recommended by its great simplicity; moreover, it is said to agree as closely as any other with the latest observations; nevertheless had not Professor Bessel's new table required the use of logarithms, it would have been preferred.

In the year 1834 will happen several very important astronomical phenomena in the United States, the most interesting of which will be the eclipse of the Sun, in the afternoon of Sunday, November 30th; which will be very large throughout the whole country, and total in some part of the States of South Carolina and Georgia.

Boston, October 4, 1832.

R. T. P.