ELEMENTS OF SURVEYING, AND NAVIGATION; WITH A DESCRIPTION OF THE INSTRUMENTS AND THE NECESSARY TABLES. BY CHARLES DAVIES, LL. D. AUTHOR OF ARITHMETIC, ELEMENTARY ALGEBRA, ELEMENTARY GEOMETRY, PRACTICAL REVISED EDITION. NEW YORK: PUBLISHED BY A. S. BARNES & CO. No. 51 JOHN STREET. COURSE OF MATHEMATICS. DAVIES' FIRST LESSONS IN ARITHMETIC-For Beginners. DAVIES' ARITHMETIC-Designed for the use of Academies and Schools. KEY TO DAVIES' ARITHMETIC. DAVIES' UNIVERSITY ARITHMETIC-Embracing the Science of Numbers and their numerous Applications. KEY TO DAVIES' UNIVERSITY ARITHMETIC. DAVIES' ELEMENTARY ALGEBRA-Being an introduction to the Science, and forming a connecting link between ARITHMETIC and ALGEBRA. KEY TO DAVIES' ELEMENTARY ALGEBRA. DAVIES' ELEMENTARY GEOMETRY.-This work embraces the elementary principles of Geometry. The reasoning is plain and concise, but at the same time strictly rigorous. DAVIES' ELEMENTS OF DRAWING AND MENSURATION — Applied to the Mechanic Arts. DAVIES' BOURDON'S ALGEBRA-Including STURM'S THEOREM-Being an abridgment of the Work of M. BOURDON, with the addition of practical examples. DAVIES' LEGENDRE'S GEOMETRY AND TRIGONOMETRY-Being an abridgment of the work of M. Legendre, with the addition of a Treatise on MENSURATION OF PLANES AND SOLIDS, and a Table of LOGARITHMS and LOGARITHMIC SINES. DAVIES' SURVEYING-With a description and plates of the THEODOLITE, COMPASS, PLANE-TABLE, and LEVEL; also. Maps of the TOPOGRAPHICAL SIGNS adopted by the Engineer Department-an explanation of the method of surveying the Public Lands, and an Elementary Treatise on NAVIGATION. DAVIES' ANALYTICAL GEOMETRY- Embracing the EQUAtions of THE POINT AND STRAIGHT LINE-of the CONIC SECTIONS-of the LINE AND PLANE IN SPACE; also, the discussion of the GENERAL EQUATION of the second degree, and of SURFACES of the second order. DAVIES' DESCRIPTIVE GEOMETRY—With its application to SPHER ICAL PROJECTIONS. DAVIES' SHADOWS AND LINEAR PERSPECTIVE, DAVIES' DIFFERENTIAL AND INTEGRAL CALCULUS. Entered, according to Act of Congress, in the year 1835, by CHARLES DAVIES, in the Clerk's Office of the District Court of the United States, in and for the Southern District of New York. Conservation 1988 PREFACE. THE Elements of Surveying, published by the author in 1830, was designed especially as a text-book for the Military Academy, and in its preparation little regard was had to the supposed wants of other Institutions. It was not the aim of the author to make it so elementary as to admit of its introduction into academies and schools, and he did not, therefore, anticipate for it an extensive circulation. It has been received, however, with more favor than was anticipated, and this circumstance has induced the author to re-write the entire work. In doing so, he has endeavored to make it both plain and practical. It has been the intention to begin with the very elements of the subject, and to combine those elements in the simplest manner, so as to render the higher branches of plane-surveying comparatively easy. All the instruments needed for plotting have been carefully described; and the uses of those required for the measurement of angles are fully explained. The conventional signs adopted by the Topographical Beaureau, and which are now used by the United States Engineers in all their charts and maps, are given in plates 5 and 6. Should these signs be generally adopted in the country, it would give entire uniformity to all maps and delineations of ground, and would establish a kind of language by which all the peculiarities of soil and surface could be accurately represented. An account is also given of the manner of surveying the public lands; and although the method is simple, it has, nevertheless, been productive of great results, by defining, with mathematical precision, the boundaries of lands in the new States, and thus settling their titles on an indisputable The method was originated by Col. Jared Mansfield, whose great acquirements in science introduced him to the notice of President Jefferson, by whom he was appointed surveyorgeneral of the North-Western Territory. May it be permitted to one of his pupils, and a graduate of the Military Academy, further to add, that at the organization of the institution in 1812, he was appointed Professor of Natural and Experimental Philosophy. This situation he filled for sixteen years, when he withdrew from the academy to spend the evening of his life in retirement and study. His pupils, who had listened to his instructions with delight, who honored his learning and wisdom, and had been brought near to him by his kind and simple manners, have placed his portrait in the public library, that the institution might possess an enduring memorial of one of its brightest ornaments and distinguished benefactors. At the solicitation of several distinguished teachers here is added, in the present edition, an article on Plane Sailing, most of which has been taken, by permission of the author, from an excellent work on Trigonometry and its applications by Professor Charles Hackley. HARTFORD, March, 1841. |