SOLD BY HILLIARD AND BROWN, CAMBRIDGE, AND BY HILLIARD, GRAY, & CO. NO. 134 WASHINGTON STREET, BOSTON. 1827. DISTRICT OF MASSACHUSETTS, TO WIT. District Clerk's Office. Be it remembered, that on the twenty-third day of March, 1827, in the fifty-first year of the Independence of the United States of America, Hilliard, Gray, & Co., of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, viz: “An Elementary Treatise on Astronomy, adapted to the Present Improved State of the Science, being the Fourth Part of a Course of Natural Philosophy, compiled for the use of the Students of the University at Cambridge, New England. By John Farrar, Professor of Mathematics and Natural Philosophy." In conformity to the act of the Congress of the United States, entitled " An act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned ;" and also to an act, entitled, “An act supplementary to an act, entitled, 'An act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned,' and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints." JNO. W. DAVIS, Clerk of the District of Massachusetts. ADVERTISEMENT. THE following treatise was selected from Biot's Traité Elémentaire d' Astronomie Physique, 2d edition, printed at Paris in 1811. Although the original is in three volumes octavo, all the body of the work is retained in this translation, except what relates to a description of astronomical instruments, the construction of tables, the temperature of the earth, the determination of certain astronomical periods, used in chronology, and two or three other topics anticipated in the parts of this course already published. A few only of the notes are given, and these are subjoined at the end in the form of an Appendix. The centesimal notation of the original has been changed to the sexagesimal; and alterations and additions have, in a few instances, been made for the purpose of adapting the work to the latest discoveries and improvements. Cambridge, March, 1827. Of the Uniform Motion of the Heavens and its Use in Measur- Exact Determination of the Meridian by the Measure of Time. Axis of Rotation of the Heavens Exact Determination of the Laws of Diurnal Motion. Proof that this Motion is circular, and that it is uniform.-Mea- sure of Time by Celestial Arcs Of the Celestial Sphere and its principal Circles Terrestrial Equator.-Meridians and Parallels.-Different Aspects of the Celestial Sphere above the Horizon of differ- Physical Consequences of the Earth's Oblateness.-Length of |