OF SURVEYING AND LEVELLING; WITH DESCRIPTIONS OF THE INSTRUMENTS AND THE By CHARLES DAVIES, LL.D., ༔ AUTHOR OF A FULL COURSE OF MATHEMATICS. A. S. BARNES & COMPANY, NEW YORK AND CHICAGO. TA54 DAVIES' MATHEMATICS. THE WEST POINT COURSE, And Only Thorough and Complete Mathematical Series. IN THREE PARTS. I. COMMON SCHOOL COURSE. Davies' Primary Arithmetic.-The fundamental principles displayed in Davies' Intellectual Arithmetic.-Referring all operations to the unit 1 as Davies' Elements of Written Arithmetic.-A practical introduction to the whole subject. Theory subordinated to Practice. Davies' Practical Arithmetic.*-The most successful combination of Theory and Practice, clear, exact, brief, and comprehensive. II. ACADEMIC COURSE. Davies' University Arithmetic.*-Treating the subject exhaustively as a science, in a logical series of connected proposition. Davies' Elementary Algebra.*—A connecting link, conducting the pupil easily from arithmetical processes to abstract analysis. Davies' University Algebra.*-For institutions desiring a more complete but not the fullest course in pure Algebra. Davies' Practical Mathematics.-The science practically applied to the useful arts, as Drawing, Architecture, Surveying, Mechanics, etc. Davies' Elementary Geometry.-The important principles in simple form, but with all the exactness of vigorous reasoning. Davies' Elements of Surveying.-Re-written in 1870. The simplest and most practical presentation for youths of 12 to 16. III. COLLEGIATE COURSE. Davies' Bourdon's Algebra.*-Embracing Sturm's Theorem, and a most exhaustive and scholarly course. Davies' University Algebra.*-A shorter course than Bourdon, for Institutions have less time to give the subject. Davies' Legendre's Geometry.-Acknowledged the only satisfactory treatise of its grade. 300,000 copies have been sold. Davies' Analytical Geometry and Calculus.-The shorter treatises, combined in one volume, are more available for American courses of study. Davies' Analytical Geometry. The original compendiums, for those deDavies' Diff. & Int. Calculus. siring to give full time to each branch. Davies' Descriptive Geometry.—With application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces. Davies' Shades, Shadows, and Perspective. A succinct exposition of the mathematical principles involved. Davies' Science of Mathematics. For teachers, embracing I. GRAMMAR OF ARITHMETIC, II. OUTLINES OF MATHEMATICS, III. LOGIC AND UTILITY OF MATHEMATICS, * Keys may be obtained from the Publishers by Teachers only. Entered, according to Act of Congress, in the year 1870, by In the Office of the Librarian of Congress at Washington. S. PREFACE. THE Elements of Surveying, first published in 1830, was designed as a text-book for the pupils of the Military Academy, and in its preparation little regard was had to the supposed wants of other institutions. The work, however, was received by the public with more favor than was anticipated, and soon became a leading textbook in the Colleges, the Academies, and the higher grade of Schools. For the purpose of adapting it more fully to the supposed wants of these institutions, many changes have been made since its first publication; and the present edition will be found to differ, in many respects, from those which have preceded. 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 Bureau, 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 common language by which all the peculiarities of soil and surface could be accurately represented. A full account is also given of the system adopted in the survey of 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 basis. This 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 Surveyor-general of the Northwestern Territory, in the early part of the present century. Among the changes which have been made in the present edition, and which must be very acceptable to Practical Surveyors, are the methods of laying down Railroad Curves, Section Levelling for Excavation and Embankment, and the article on Mining Engineering. For the first of these, I am mainly indebted to Professor Plympton, of the Brooklyn Polytechnic Institute, who has happily combined science and art, both in his methods of teaching and in his practical operations in the field; and for the latter, to Professor Peck, of Columbia College, to whom education and science are indebted for much valuable labor. FISHKILL-ON-HUDSON, June, 1870. |