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XI. The Tables comprise a Traverse Table, computed for this volume, nd giving increased accuracy in one-fifteenth of the usual space; a Table of Chords, appearing for the first time in English, and supplying he most accurate method of platting angles; and a Table of natural Sines and Tangents. The usual Logarithmic Tables are also given. The tables are printed on tinted paper, on the eye-saving principle of Babbage.

XII. The great number of engraved illustrations, most of them crig. inal, is a peculiar feature of this volume, suggested by the experience of the author that one diagram is worth a page of print in giving clearness and definiteness to the otherwise vague conceptions of a student.

XIII. The practical details, and hints to the young Surveyor, have been made exceedingly full by a thorough examination of more than fifty works on the subject, by English, French and German writers, so as to make it certain that nothing which could be useful had been overlooked. It would be impossible to credit each item (though this has been most scrupulously done in the few cases in which an American writer has been referred to), but the principal names are these: Adams, Ainslie, Baker, Begat, Belcher, Bourgeois, Bourns, Brees, Bruff, Burr, Castle, Francoeur, Frome, Galbraith, Gibson, Guy, Hogard, Jackson, Lamotte, Lefevre, Mascheroni, Narrien, Nesbitt, Pearson, Puille, Puissant, Regnault, Richard, Serret, Simms, Stevenson, Weisbach, Williams.

Should any important error, either of printer or author, be discovered (as is very possible in a work of so much detail, despite the great care used) the writer would be much obliged by its prompt communication.

The present volume will be followed by another on LEVELLING AND HIGHER SURVEYING: embracing Levelling (with Spirit-Level, Theodolite, Barometer, etc.); its applications in Topography or Hill-drawing, in Mining Surveys, etc.; the Sextant, and other reflecting instruments; Maritime Surveying; and Geodesy, with its practical Astronomy.


As it is desirable to obtain, at the earliest possible period, a sufficient knowledge of the generQA principles of Surveying to commence its practice, the Student at his first reading may omit the vortions indicated below, and take them up subsequently in connection with his review of his studies. The same omissions may be made by Teachers whose classes have only a short time for this study. In PART I, omit only Articles (46), (47), (48), (51), (72), (84), (85).

In PART II, omit, in Chapter IV, (127), (128), (129), (130); and in Chapter V, learn at first ander each Problem, only one or two of the simpler methods

In PART III, omit only (225), (226), 232), (233), (244), (251), (280), (297), (322)

Then pass over PART IV; and in PART V, take only (379), (380); and (391) to (395),

Then pass over PART VI; and go to PART VII, (if the student has studied Trigonometryn

and omit (423); (431) to (438); and all of Chapter IV, except (439) and (440).

PART VIII may be passed over; and PARTS IX and X may be taken in full.

An PART XI, take all of Chapter I; and in Chapters II and III, take only the simpler con ructions, not omitting, however, (517), (518) and (538).

In PART XII, take (560), (561), (565), (566).

Appendix C, on LEVELLING, may conclude this abridgea course.








(1) SURVEYING is the art of making such measurements as will determine the relative positions of any points on the surface of the earth; so that a Map of any portion of that surface may be drawn, and its Content calculated.

(2) The position of a point is said to be determined, when it is known how far that point is from one or more given points, and in what direction there-from; or how far it is in front of them or behind them, and how far to their right or to their left, &c; so that the place of the first point, if lost, could be again found by repeating these measurements in the contrary direction.

The "points" which are to be determined in Surveying, are not the mathematical points treated of in Geometry; but the corners of fences, boundary stones, trees, and the like, which are mere points in comparison with the extensive surfaces and areas which they are the means of determining. In strictness, their centres should be regarded as the points alluded to.

(3) A straight Line is "determined," that is, has its length and its position known and fixed, when the points at its extremities are determined; and a plane Surface has its form and dimensions determined, when the lines which bound it are determined. Consequently, the determination of the relative positions of points is all that is necessary for the principal objects of Surveying; which are to make a map of any surface, such as a field, farm, state, &c., and to calculate its content in square feet, acres, or square miles. The former is an application of Drafting, the latter of Mensuration.

(4) The position of a point may be determined by a variety of methods. Those most frequently employed in Surveying, are the following; all the points being supposed to be in the same plane.

(5) First Method. By measuring the distances from the re quired point to two given points.

Fig. 1.

Thus, in Fig. 1, the point S is "determined," if it is known to be one inch from A, and half an inch from B: for, its place, if lost, could be found by describing two arcs of circles, from A and B as centres, and with the given distances as radii. The required point would be at the intersection of these arcs.



In applying this principle in surveying, S may represent any station, such as a corner of a field, an angle of a fence, a tree, a house, &c. If then one corner of a field be 100 feet from a second corner, and 50 feet from a third, the place of the first corner is known and determined with reference to the other two.

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There will be two points fulfilling this condition, one on each side of the given line, but it will always be known which of them is the one desired.

In Geography, this principle is employed to indicate the posi tion of a town; as when we say that Buffalo is distant (in a straight line) 295 miles from New-York, and 390 from Cincinnati, and thus convey to a stranger acquainted with only the last two places a correct idea of the position of the first.

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