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computation of an observed occultation of a star, using the data for the star instead of those for the sun.*
* The formulæ for computing an observed eclipse or occultation, have been derived from an excellent Tract by Prof. Bessel, Astr. Nach. Nos. 151 and 152. In this tract, the investigations are extended so as to notice errors in some of the other elements obtained from the tables.
For all important eclipses of the sun, the values of N and n are given in the Berlin Ephemeris, for several consecutive whole hours, near to the time of
Catalogue of the Tables, with occasional observations.
TABLES I. and II.
Logarithms and logarithmic Sines and Tangents, to four decimal figures. To avoid an extra line of figures, the 10 in the index of the tangents and cotangents has been rejected, when the index exceeded 10.
TABLES III., IV., and V.
Log. tangent of the Obliquity of the Ecliptic.-Log. A = log. cosine of obliquity of the ecliptic less log. of the difference of the moon's and sun's parallaxes, and log. Barith. comp. log. sine of difference of the parallaxes.—Log. tangent of sun's semidiameter.
Latitudes of a number of places with their longitudes from the meridian of Greenwich.
The latitudes and longitudes of several of the places in the United States are given according to the determinations of R. T. Paine, the former editor of the astronomical part of the American Almanac, a valuable work, published annually in Boston.
Mean Refractions with the corrections due to given changes in the states of the barometer and thermometer.
Sun's Parallax in Altitude.
Mean Right Ascensions and Declinations of 30 principal Fixed Stars for the beginning of the year 1850, with their Annual Variations; also, auxiliary quantities to facilitate the computations of their aberrations and nutations. North declination is indicated by the sign plus, and South declination by the sign minus.
TABLES X. and XI.
These serve to convert intervals of mean solar time into equivalent intervals of sidereal time, and the contrary.
TABLES XII. to XV., inclusive.
Auxiliary tables, for the computations of Solar Eclipses, and Occultations.
Reductions of the Moon's Parallax and of the latitude of a place, and also the logarithms of the earth's radius, according to the compression.
Logarithms to be added to the logarithmic cosine and sine of the geographic latitude of a place, to obtain the logarithms of p cos p' and p sin o'; in which p is the radius of the earth at the place, and p' the geocentric latitude.
TABLES XVIII. to XXI., inclusive.
These serve to find the time of New or Full Moon in any mately, or within a few minutes of the true time.
The time of mean new moon in January of each year, as given in tablɛ XVIII., has been diminished by 15 hours. These 15 hours have been
added to the equations in table XXI. Thus, 4h. 20m. has been added to the first equations; 10h. 10m. to the second; 10 minutes to the third; and 20 minutes to the fourth. By this means, the equations are all made additive.
TABLES XXII. to XXXI., inclusive.
These are approximate Solar Tables, by which the sun's true longitude, hourly motion, semidiameter and radius vector, and the apparent obliquity of the ecliptic, may be determined for a given time, very nearly.
The Sun's Mean Longitude, the longitude of the perigee, and Arguments for finding some of the small equations of the sun's place given in table XXII., are all computed for mean noon at the meridian of Greenwich, on the first of January for common years, and on the second of January for bissextiles. The sun's longitudes and the longitudes of his perigee have each been diminished by 2°. As each is diminished by the same quantity, the mean anomaly, which is obtained by subtracting the longitude of the perigee from the sun's longitude, and which is the argument for the equation of the centre, is not affected. The Argument I. is for the equation depending on the action of the moon; Argument II. is for that depending on the action of Jupiter; Argument III. is for that depending on the action of Venus; and Argument N, is for the Nutation, or equation of the equinoxes.
Of the 2° which has been subtracted from the sun's mean longitudes, 1° 59′ 30′′ is added to the equation of the centre, and 10′′ to each of the small equations due to the actions of the Moon, Jupiter, and Venus.
TABLES XXXII. to LXIV., inclusive.
Approximate Lunar Tables, by which the moon's true longitude, latitude, horizontal parallax, semidiameter and hourly motions in longitude and latitude for a given time, may be determined, very nearly.
The Epochs of the Moon's Mean Longitude, and of the Arguments for finding the Equations which are necessary in determining the True Longitude and Latitude of the Moon given in table XXXII., are all computed for mean noon at the meridian of Greenwich, on the first of January for common years, and on the second of January for bissextiles. The Argument for the Evection is diminished by 29', the Anomaly by 1° 59′, the Argument for the Variation by 8° 59′, the Mean Longitude by 9° 44′, and the Supplement of the Node is increased by 7'. This is done to balance the quantities which are applied to different equations to render them affirmative.