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the Eclipses of Jupiter's Satellites, for 1824 and the following Years, from DELAMBRE's new Tables. For the Configurations, HALLEY'S Tables have been hitherto employed; and they appear, with proper corrections of the epochs, to be sufficiently accurate for the purpose. The obliquity of the Ecliptic has been corrected, from the Observations of the Astronomer Royal, since the beginning of 1822.

The Moon's Right Ascension and Declination are computed to seconds, for the more convenient observation of the Moon's place on shore, and for the calculation of occultations and many other purposes. At the suggestion of a very distinguished practical navigator, the differences of the Sun's Declination from day to day have been added, for the convenience of seamen. Whether any advantage would be gained from the insertion of the Moon's distance from Jupiter, must depend on the precision of the tables of that planet; a point which is expected to be very shortly determined from the most accurate obser

vations.

The attention of the BOARD has been particularly directed to the determination of the conditions, under which rewards are to be proposed for the improvement of Astronomical Tables and of Timekeepers; but all who are acquainted with the present state of this department of science must be aware, that a considerable time will be required, before it will be practicable to ascertain, with sufficient precision, how much has actually been effected, and how much is still required, with respect to both these objects. In the mean time it must be remembered, that the BOARD possesses ample powers to reward any improvement, which they may judge sufficiently important, either in the theory or in the practice of any part of Navigation or Nautical Astronomy. As far, however, as the existing Tables of the Sun and Moon have been examined, they appear to be already sufficiently accurate for every purpose of practical Astronomy.

EXTRACT FROM

DR. MASKELYNE'S PREFACE.

"MAYER's last Manuscript Tables of the Sun and Moon, and his curious and elaborate Theory of the Moon, were received by the Board of Longitude, after his decease, for which his Widow received a Reward of Three Thousand Pounds, by Act of Parliament; and the celebrated Mr. LEONARD EULER the Sum of Three Hundred Pounds, for having furnished the Theorems made use of by Mr. MAYER in his Theory. Both the Tables and Theory were printed under my inspection, and published in 1770.

"MAYER'S Tables of the Sun were used in the Computations of the NAUTICAL ALMANAC, from its first beginning in 1767 to that of 1804, inclusive. From the NAUTICAL ALMANAC of 1767 to that of 1776, both inclusive, or the first ten years, MAYER'S Lunar Tables were made use of. But from the NAUTICAL ALMANAC of 1777 to that of 1788, both inclusive, or the next twelve years, the Moon's Place was inserted as calculated from new Tables, improved from MAYER'S Tables composed by the late Mr. CHARLES MASON, under my direction, from calculations made by Order of the Board of Longitude upon the Series of Lunar Observations made by the late Dr. BRADLEY, and published in the NAUTICAL ALMANAC of 1774; in which new Tables the Epoch of the Moon's mean Longitude is 1" less, that of the Apogee is 56" less, and that of the ascending Node 45′′ more than in MAYER'S printed Tables, and the Equations are calculated to tenths of a second; and moreover, one new Equation is introduced, whose argument is the mean Distance of the Moon from the Sun's Apogee, and maximum is 16", 4. But from the NAUTICAL ALMANAC of 1789 to that of 1804, both inclusive, the Moon's Place was inserted as calculated from new Tables still further corrected by Mr. MASON, entitled by him, TABLES of 1780, as having been completed about that time, being rendered more exact than the former by the addition of eight Equations to the Number in MAYER'S Table, taken from MAYER'S Theory as to the Arguments, but settled as to the Maxima, from the said Observations, and the whole being calculated to Tenths of a Second. However the 18th Equation of these Tables was not used, as it was doubtful whether such an Equation should arise from the Theory of Gravity. Moreover, the Epochs of the Sun's Longitude in MAYER'S Tables, and of the Moon's Longitude and mean

anomaly contained in MASON's Tables of 1780, were diminished at the rate of 10" in a hundred years, reckoned from the year 1756, in the Calculations of the NAUTICAL ALMANACS from 1797 to 1804, both inclusive. Also the Longitudes of the Stars, used in computing their distances from the Moon, were carried on from Dr. BRADLEY's Catalogue of the year 1760, by subtracting 50", 35 from it, for each year between 1756 and 1760; to reduce that Catalogue back to the beginning of 1756, and then adding at the rate of 50", 20 for the Precession of the Equinoxes, for each year elapsed after 1756, and applying the Correction of Secular Motion derived from the 44th of the folio Tables annexed to the First Volume of my Astronomical Observations.

"The Distances of the Stars from the Moon had been computed, till the end of the EPHEMERIS of 1802, from a set of folio Tables, constructed for each Star, according to its respective Latitude in 1780; but the Distances in the EPHEMERIS from 1803 to 1808 were computed from the Latitudes corrected by my 45th Table, by making use of TAYLOR'S Tables of Logarithmic Sines and Tangents to every Second of the Quadrant.

"The Distances of the Moon from the nine principal fixed Stars are, in this Ephemeris, as they were from that of 1809, computed from their Longitudes and Latitudes, which I have settled from late Observations, and their annual variations, including their proper motions, by comparing them with Dr. BRADLEY'S places of them, settled about the year 1756. The Catalogue is inserted at the end of the Explanation of the Ephemeris, p. 162.

"The Calculations of the Planets' Places were made for the EPHEMERIS from 1780 to 1804, by the Tables contained in the Second Edition of M. DE LA LANDE'S Astronomy; and those of the Eclipses of Jupiter's Satellites were made from Mr. WARGENTIN'S Tables, which make a part of those Tables: excepting the Eclipses of Jupiter's Second Satellite, which were computed, from the EPHEMERIS of 1781 to that of 1804, from new Tables of Mr. WARGENTIN, published at the end of the Nautical Almanac of 1779.

"In the year 1792, came out the Third Edition of M. DE LA LANDE'S Astronomy, which he was pleased to make me a present of, containing new Tables of the Sun, Moon, and Planets, and of the Eclipses of Jupiter's Satellites. These Tables are constructed upon the best Observations, and upon the Physical Theories of M. LA GRANGE and M. DE LA Place, founded upon Sir ISAAC NEWTON'S Principles of Gravity. The Tables of the Sun were constructed by M. DE LAMBRE, entirely from my Observations: the Tables of the Moon are the same with Mr. CHARLES MASON'S Tables of 1780, only substituting M. DE LA PLACE'S Acceleration instead of MAYER'S, and diminishing the mean Secular Motion by 23". The Tables of Mercury, Venus, and Mars, were constructed by M. LA LANDE, The Tables of Jupiter and Saturn were constructed by M. DE LAMBRE from the Theory of M. De la PLACE, who has accounted for the great Inequalities of their Motion

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EXTRACT FROM DR. MASKELYNE'S PREFACE.

vii

to great exactness. The Tables of the Planet Herschel, called the Georgian Planet by us, were also calculated by M. DE LAMBRE, according to the Method of M. DE LA PLACE'S Theory of Jupiter and Saturn. The Tables for calculating the Eclipses of Jupiter's Satellites were constructed by M. DE LAMBRE upon M. DE LA PLACE'S elaborate Theory, and agree with Observation to surprising exactness. The learned world are much indebted to Mr. CHARLES MASON, M. LA GRANGE, M. DE LA PLACE, M. LA LANDE, and M. DE LAMBRE, for these valuable improvements in the Astronomical Tables. May I flatter myself, that I also have contributed my share to this great Work, by directing Mr. MASON in the improvement of the Lunar Tables by precise Rules, and pointing out to him the Equations contained in MAYER'S Theory, though omitted in his Tables, to be ascertained by BRADLEY'S Observations, and by supplying a variety of Observations, from which, in conjunction with others, this great Work has been completed.

"In the year 1806, the French Board of Longitude published further improved Tables of the Sun by M. DE LAMBRE; and improved Tables of the Moon by M. BURG, founded on M. DE LA PLACE'S Theory, with the maxima of the equations stated according to my observations, and the epochs principally from my observations and Dr. BRADLEY'S. In these, besides M. DE LA PLACE'S other improvements, is introduced a new equation of the Moon's longitude, of the long period of 180 years, depending at once on the Moon's Apogee and Node and on the Sun's Apogee, whose maximum he states at 14", but of great consequence in settling the mean motions of the Moon. Mr. BURG has introduced six new Equations, in addition to eight Equations pointed out by MAYER's Theory, but whose maxima had been settled by Mr. MASON, from Dr. BRADLEY'S Observations. These Tables had been long expected, and our Board of Longitude had anticipated the important use which they should be applied to in the calculations of the Nautical Almanac.

"I was moreover furnished with several copies of the same, by the favour of the French Board of Longitude. These I immediately put into the hands of our computers; and the publication of the Nautical and Astronomical Almanac for 1813 came out, for the first time, distinguished with this considerable improvement.

"The epochs of these Tables having been adapted to the civil reckoning of time, and to the Midnight with which the last day of the former year ends, and the new one begins, instead of the noon of the last day of the former year, as generally used in Astronomical Tables, I tried to adopt this method for the Nautical Almanac, but afterwards thought it best to relinquish it, and to retain the astronomical time, fearing it would be attended with inconvenience, both in keeping the Register of the Greenwich Observations, and in puzzling the sailors by changing the method of using the Nautical Almanac.

"The Places of the Planets, and the Times of the Eclipses of Jupiter's Satellites, beginning in the year 1805, have been calculated from the Tables annexed to the third edition of M. LA LANDE'S

Astronomy, and the Eclipses of the Satellites set down to mean time, instead of apparent time, as formerly.

"The Rev. SAMUEL VINCE, Plumian Professor of Astronomy at Cambridge, having had an early communication of the new French Tables, and of the errata discovered in them by the comparer of the Nautical Almanac and myself, and having also noted several errata himself, has lately re-published them in a neat, elegant, and accurate manner, according to astronomical time, together with the Tables of the Planets (taking those of Mars from M. LE FRANCAIS LA LANDE'S Tables in the Connaissance des Tems of the 12th year) and the Eclipses of Jupiter's Satellites from the third edition of M. LA LANDE'S Astronomy. These will be used for the calculations of the Nautical Almanac for succeeding years.

"All the Articles of the EPHEMERIS were computed by two separate Persons, and examined by a third, except the Moon's Longitude, Latitude, Right Ascension, Declination, Semidiameter, and Parallax, with its proportional Logarithm, which for Noon, were computed by one Person, and for Midnight by another, and the Truth of these Calculations ascertained by Means of Differences, which, for the Moon's Longitude, were carried as far as the Fourth Order.

"NEVIL MASKELYNE,

"ASTRONOMer Royal."

"GREENWICH,

September 25, 1810."

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