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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.


Central High School, Philadelphia, February 1, 1851.


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.




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