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A SYSTEMATIC AND COMPREHENSIVE EXPOSITION OF THE
THEORY, AND THE MORE IMPORTANT PRACTICAL
PROBLEMS; WITH SOLAR; LUNAR, AND

OTHER ASTRONOMICAL TABLES.

Designed for ase as a Tert-Book in Colleges and Academies.

BY WILLIAM A: NORTON,

LATE PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY

IN THE UNIVERSITY OF THE CITY OF NEW YORK.

PUBLISHED BY

WILEY & PUTNAM, NEW YORK ; THOMAS, COWPERTHWAITE

& Co., PHILADELPHIA ; C. C. LITTLE & CO., Boston.

1839.

P

Entered according to an Act of Congress, in the year 1839, by

WILLIAM A. NORTON,

in the Clerk's Office of the District Court of the Southern District of New York.

J, P, Wright, Printer: 74 Cedar Street, N. Y.

PREFACE.

The object in writing the present treatise, has been to provide a suitable text book for the use of the students of Colleges and the higher Academies, and at the same time to furnish the practical astronomer with rules or formulæ, and accurate tables for performing the more important astronomical calculations.

The work is divided into four Parts. The first three Parts contain the theory: the First Part treating of the determination of the places and motions of the heavenly bodies; the Second, of the phenomena resulting from the motions of these bodies, and of their appearances, dimensions, and physical constitution; and the Third, of the theory of Universal Gravitation. The Fourth Part consists of practical problems, which are solved with the aid of the tables appended to the work. An Appendix is added, containing a large collection of useful trigonometrical formulæ, and such investigations of astronomical formulæ as, from their length, could not, consistently with the plan of the work, be admitted into the text, and which it was still deemed advisable to retain for the benefit of the few who might wish to pursue them.

The chief peculiarities of the present treatise are, 1. The adoption of the Copernican System as an hypothesis at the outset, leaving it to be established by the agreement between the conclusions to which it leads and the results of observation. 2. A connected exposition of the principles and methods of astronomical observation, embracing the doctrine of the sphere, the construction and use of the principal astronomical instruments, and the theory of the corrections for refraction, parallax, aberration, precession, and nutation. 3. The exhibition of the methods of determining the motions and places of the different classes of the heavenly bodies in one connection. 4. The explanation of the principles of the construction of astronomical tables. 5. The addition of a chapter on the measurement of time, embracing the explanation of the different kinds of time, the processes by which one is converted into another, the methods of determining the time from astronomical observations with the transit instrument and sextant, and the calendar. 6. The contemplation of the phenomena of the aspect and apparent motions of the heavenly bodies as consequences of their motions in space,

and the deduction of the various circumstances of these phenomena from the theory of the orbitual motions previously established. 7. A comprehensive view of the theory of Universal Gravitation, followed out into its various consequences. 8. An exposition of the operations of the disturbing forces in producing the perturbations of the motions of the Solar System. 9. The solution of practical problems by means of loga

rithmic formulæ instead of rules. 10. The addition of lunar, solar, and other astronomical tables of peculiar accuracy and improved arrangement. It may further be mentioned, that many of the inves

, tigations have been materially simplified, and that the aim has been to introduce into all of them as much sim-' plicity and uniformity of method as possible. Particular attention has also been paid to the diagrams, it being of great importance that they should convey correct notions to the mind of the student.

The problems in the Fourth Part are principally for making calculations relative to the Sun, Moon, and Fixed Stars. The tables of the Sun and Moon, used in finding the places of these bodies, have, for the most part, been abridged and computed from the tables of Delambre, as corrected by Bessel, and those of Burckhardt; and the tables of epochs have all been reduced to the meridian of Greenwich. These tables will give the places and motions of the Sun and Moon within a fraction of a second of the tables from which they were derived. But as this degree of accuracy will not generally be required, rules are also given in the Fourth Part for obtaining approximate results. The entire set of tables has been stereotyped, and great pains has been taken, by repeated revisions and verifications, to render them accurate.

The principal astronomical works which have been consulted in writing the present treatise, are those of Vince, Gregory, Woodhouse, Delambre, Biot, Laplace, Herschel, and Gummere; also Francæur's Uranogra

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