« PreviousContinue »
PREFACE TO THE FOURTH EDITION.
THE great and steadily increasing favour bestowed on this work, as modified by its author in 1842, would seem to indicate that no further changes were needed, or would be acceptable to teachers: the undersigned has therefore, in revising the third edition for the press, thought it best to confine himself principally to a correction of typographical, and other errors; and to such additions as the recent progress of the science demanded. Some additions have been made in the chapter on instruments; and, throughout the First Part, such changes and modifications of the formulæ and demonstrations introduced, as have been dictated by eight years' experience in the use of this work as a class book. The tables of the elements of the planetary orbits, have been arranged in a more convenient form, and extended so as to include those of the new planets, as far as they are at present known. These elements have been invariably derived from the most reliable sources. In the Second Part, very many inaccuracies have been corrected, and several problems and examples of a practical nature inserted. In connection with one of these problems, a table of reductions to the meridian has been given at the end of the book. With this exception, and that of an alteration in Table IX., adapting it to the present time, the tables are the same as those in the third edition.
E. O. KENDALL.
Central High School, Philadelphia, February 1, 1851.
PREFACE TO THE THIRD EDITION.
IN preparing this edition, the greater part has been written anew and so modified as to increase the value of the work as a text book. Several of the more abstruse investigations of the First Part have been omitted, references being made to larger works, and others have been transferred to the Appendix. Many of the figures illustrating the text have been rendered more perspicuous by a change in the construction, and a number of new ones are added. The progressive state of the science has claimed attention, and notices of recent results have been introduced.
The Appendix, in addition to the other matter, contains Professor Bessel's late investigation of formulæ for computing Solar Eclipses, Occultations and Transits, reduced to a more elementary form. In the Second Part, the formulæ are applied in the computation of these phenomena.
The Tables are nearly the same as in the last edition. Instead, however, of some small ones, which have been omitted, a table of Logarithms, and one of Logarithmic Sines and Tangents to four decimal figures, have been inserted. These are convenient in many computations not requiring greater precision.
Haverford School, 9mo. 1842.
CHAP. II. Astronomical Instruments
CHAP. III. To place an Instrument in the Plane of the Meridian
-Sidereal Time-Terrestrial Meridian-Latitude and Longi-
CHAP. IV. Figure and Dimensions of the Earth-Geocentric Lati-
CHAP. VI. Apparent and True Places of a body-Parallax-Me-
thod of finding the Parallax of a body-Parallaxes and Dis-
tances of the Moon and Sun-Their Apparent and Real
CHAP. VII. Polar Distance of a Body-Apparent Diurnal Motions
of the Fixed Stars, uniform-Motion of the Earth on its Axis
CHAP. VIII. Sun's apparent Path-Earth's Annual Motion-
Definitions-Positions of the Fixed Stars-Constellations-
Catalogues of the Fixed Stars.
CHAP. IX. Precession of the Equinoxes-Aberration--Nutation .
CHAP. X. Sidereal and Solar Time-Tropical Year-Sun's Appa-
rent Orbit-Kepler's Laws-Solar Tables-Equation of Time
-Sun's Spots, and Rotation on his Axis-Zodiacal Light
CHAP. XI. Parallelism of the Earth's Axis-Variations in the
Lengths of Day and Night-Seasons-Astronomical Problems
CHAP. XIII. Eclipses of the Sun and Moon-Occultations
CHAP. XIV. General Remarks on the Planets-Definitions--Ele-
ments of the Orbits of the Planets-Conversion of the Helio-
centric Place of a Planet into its Geocentric Place-Retrograde
Motion of the Planets-Real Distances, &c., of the Planets .
CHAP. XV. Inferior Planets, Mercury and Venus-Transits-
CHAP. XVIII. Classification of the Fixed Stars-Clusters and
Nebula-Variable and Temporary Stars-Double Stars-
Binary Systems-Proper Motions of some Stars, and Motion
of the Solar System-Annual Parallax and Distance of the
CHAP. XIX. Different Methods of finding the Longitude of a Place
CHAP. XXII. Universal Gravitation-Tables of the Elements of
the Orbits of the Planets, and of their Masses and Densities.
To find the times of longest and shortest Twilight at a given place
To find the Annual Variations of a Star in Right Ascension and
To find the Aberration of a Star in Right Ascension and Declination
To find the Lunar Nutation in Right Ascension and Declination.
Given the Eccentricity of the Orbit of a Planet and the Mean
Anomaly, to find the True Anomaly
PROB. I. To work a proportion by logistical logarithms
PROB. II. From a table in which quantities are given for each
sign and degree of the circle, to find the quantity correspond-
ing to signs, degrees, minutes, and seconds
PROB. III. To convert degrees, minutes, and seconds of the Equa-
PROB. IV. To convert time into degrees, minutes, and seconds
PROB. V. The longitudes of two places and the time at one of
them being given, to find the corresponding time at the other
PROB. VI. To find the sun's longitude, &c., from the tables
PROB. VII. To find the sidereal time corresponding to a given
PROB. VIII. To find the sidereal time corresponding to a given
mean time, using the Nautical Almanac
PROB. IX. To find the mean time corresponding to a given side-
real time, using the Nautical Almanac
PROB. X. To find the Moon's longitude, latitude, &c., from the
PROB. XII. To find the approximate time of New or Full Moon,
PROB. XIII. To determine what Eclipses may be expected to oc-
cur in any given year, and the times, nearly, at which they
PROB. XIV. To calculate an Eclipse of the Moon
PROB. XV. Given the latitude of a place, to find the logarithms
of P sin p' and p cos p', in which o' is the geocentric latitude
and p the radius of the earth, for the given place .
PROB. XVI. To calculate an Eclipse of the Sun for a given place,
using the tables of the sun and moon, contained in this work.
PROB. XVII. To find a series of places at which an eclipse of the
PROB. XVIII. The value of a quantity at three consecutive whole
hours, T — 1, T, and T+ 1, being given, to find its value at
an intermediate time T', and its hourly variation at that time
PROB. XIX. To calculate an Eclipse of the Sun for a given place,
PROB. XX. To find the longitude of a place from an observed
PROB. XXI. To calculate an Occultation of a fixed star
PROB. XXII. To find the longitude of a place from an observed
PROB. XXIII. To find the Heliocentric Longitude, &c., of the
PROB. XXIV. The Heliocentric Longitude, &c., of Mercury being