This textbook is a course in elementary surveying. It has been the intention of the author 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, and which are now used by the United States Engineers in all their charts and maps, are provided. 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 basis.