the mean time; those with the sign, are to be subtracted from the apparent for the mean time. TABLE VII. shews the moon's diameter to every 10" of the equatoreal parallax; by it we may also find the equatoreal parallax to different diameters. Where great precision is wished for, the equatoreal parallax must be reduced to the horizontal parallax in any given latitude, or the contrary. This may be done with all desireable accuracy by the following theorem: put the semi-axis major, c = { the semi-axis minor, s and r the sine and co-sine of the latitude of the place of observation, and p the sine of the horizontal polar parallax, the equatoreal parallax being always to the polar parallax, as 10c438 tcp to 100000; then √t's2 + c2 r22 zontal parallax at the given latitude. The parallax obtained by this theorem will sometimes be nearly 16" less than the equatoreal parallax; but this is in high latitudes: in the latitude of London, the reduction can never exceed 10", on the supposition that t is to c, as 230 to 229. ... See also Art. 553. the sine of the hori TABLE VIII. contains the mean astronomical rcfractions, as calculated by Dr. Bradley, according to the theorem given in Art. 105.: the use of this table is so manifest, that it needs no example, the refraction, it is well known, being always subtracted from the apparent, to find the true, altitude. This table shews the refractions in the medium state of the atmosphere, i. e. when the barometer stands at 29.6 inches, and Fahrenheit's thermometer at 50 degrees. The refractions agree very nearly with those in Dr. Maskelyne's table, given with his Observations, 1796. TABLE IX. contains the right ascensions (both in time and degrees) and the declinations of sixty-four of the principal fixed stars for the beginning of the year 1800, with their annual variations in right ascension and declination, where such variations were well ascertained. The greater part of this table was taken from Dr. Zach's catalogue of 381 stars, given in Dr. Hutton's Dictionary. Some errours are corrected, and most of the variations in declination supplied, from a comparison of the tables of Dr. Masketyne, La Caille, Mayer, and others of acknowledged accuracy. When the places of these stars are wanted for any time after the beginning of the year 1800, multiply the annual variation, both in right ascension and declination, by the years and decimals which have elapsed since that time; the product arising from multiplying the R. A. must be added to the R. A. for 1800, for the R. A. sought: but the product arising from multiplying the declination must be added or subtracted, according as the signor is found against the annual variation in the last column; the sum or difference gives the declination. But if the places of the stars be wanted for any time previous to the year 1800, the variation in R. A. must be subtracted from the R. A. found in the table (except in one instance where the variation is), and the variation in declination must be applied with a contrary sign to that which stands against it. In this table the mean places of the stars are exhibited; and, to obtain their apparent places, the mean places should be corrected for aberration, and the equation of equinoctial points; this we merely mention, to shew the reason of the difference between the tabular and the observed places. TABLE X. shews the mean longitudes and the latitudes of sixty stars for the beginning of the year 1800 their mean longitudes for any other time may be found, if 504 seconds (Art. 57.) be added for each succeeding, or subtracted for each preceding, 50" for parts years. year, and proportional parts The latitudes vary by such insensible degrees, that the table will answer pretty well for a few years, of of without regarding the variations. By means of this table, and a table of the moon's longitude for every twelve hours, we may ascertain how often a given fixed star may be eclipsed by the moon in a given year; for instance, spica virginis, or am in the year 1801 the longitude of the star for 1801 is nearly 21° 4' of, the latitude 2° 2' 11"S. Now, on Mar. 30, at 12 P.M. the long. Dis 19° 37′ 44′′ of ^, and the lat. 58′ 14′′S. and the long. and lat. are so incrcasing, that at about 2h past midnight the moon and star are in conjunction, and the difference of their latitudes is less than 57'; whence (Art. 545.) it appears there will be an occultation about that time. In a similar manner it may be found that there will be occultations of the same star behind the moon on May 24, between eight and ten o'clock, P.M. and on July 18, about noon: either of these occultations may then be calculated, by following the precepts in Art. 546, et seq. INDEX. [The figures denote the Articles referred to.] ABERRATION A. BERRATION, Art. 630.-646. Acceleration of the moon, 444- Achronical rising and setting, 185. Altitude, of the pole, 25.; of the equator, 26.; of the nonagesi- Amplitude, east and west, 51. Angle, of commutation, 292.; under which the sun would appear Annual parallax, 630. Anomaly, mean, 299.; true, 299.; excentric, 300.; to find the Antarctic circle, 31. Antecedentia, 296. Antipode, 23. Aphelion, and Apsides, 296. Apparent diameter, of the sun, 387.; of the moon, 461.; of the planets, 387. 388. Apogee, 297. Arctic circle, 31. Argument of latitude, 298. Ascending and descending points, 156.; signs, 45. Ascension, right and oblique, 4+. Ascensional difference, 44. 184. Asterisms, 68. Astronomy, 1. 2. Astronomical tables, 377. Atmosphere, cause of refraction, 94; of twilight, 107. Autumnal equinox, 53. Axis of the earth, 14.; of the heavens, 17.; parallelism of, 205. B Boscovich's method of finding the refraction, 10 C. Calculation of the geocentric and heliocentric places of a planet, Cardinal points, 50. Cassini's ellipsis, 288. Chronology corrected by eclipses, 544. Circles, greater and less, 12.; of longitude, 24. 46.; of declina- Comets, their orbits, 584.-586.; tails, 624-628.; parallaxes, Commutation, 292. Conical shadow, 521. Conjunction, inferiour and superiour, 250. 328. Copernican System, 205. Cosmas Indopleustes, his opinion, 4. Cosmical rising and setting, 184. Constellations, 68.; tables of, 71. Crepusculum, or twilight, 107.; when shortest, 138.-141. Culminating point, 160. Culmination of the stars, 171. Curtate distance, 293. 374. Cusps, 166. 470. D. Days and nights, their inequality, 52. Day solar, 111.; sidereal, 112. Declination, north and south, 42.; of a star, to find, 61. Density of the planets, 389. Diameter, see Apparent. Real, of sun, moon, and planets, 387. Dichotomy, 471. Difference of longitude, 20. Digits, 527. Dip of the horizon, 680. Distance, of the sun, 325.; of planets from the sun, 360. Dog-star and dog-days, 189. E. Earth, its figure and magnitude, 3.-10.; annual motion, 219. East, 50.; east and west longitude, 20. |