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III. A complete system of Surveying with only a chain, a rope, or any substitute, (invaluable to farmers having no other instruments,) is very fully developed in Part II.
IV. The various Problems in Chapter 5, of Part II, will be found to constitute a course of practical Geometry on the ground. As some of their demonstrations involve the "Theory of Transversals, etc," (a beautiful supplement to the ordinary Geometry), a carefully digested summary of its principal Theorems is here given, for the first time in English. It will be found in Appendix B.
V. In Compass Surveying, Part III, the Field work, in Chapter 3, is adapted to our American practice; some new modes of platting bearings are given in Chapter 4, and in Chapter 6, the rectangular metho of calculating contents is much simplified.
VI. The effects of the continual change in the Variation of the mag netic needle upon the surveys of old lines, the difficulties caused by it and the means of remedying them, are treated of with great minuteness of practical detail. A new table has been calculated for the time of "greatest Azimuth," those in common use being the same as the one prepared by Gummere in 1814, and consequently greatly in error now from the change of place of the North Star since that date.
VII. In Part IV, in Chapter 1, the Transit and Theodolite are explained in every point; in Chapter 2, all forms of Verniers are shewn by numerous engravings; and in Chapter 3, the Adjustments are elucidated by some novel modes of illustration.
VIII. In Part VII, will be found all the best methods of overcoming obstacles to sight and to measurement in angular Surveying.
IX. Part XI contains a very complete and systematic collection of the principal problems in the Division of Land.
X. The Methods of Surveying the Public Lands of the United States, of marking lines and corners, &c., are given in Part XII, from official documents, with great minuteness; since the subject interests so many land-owners residing in the Eastern as well as in the Western States.
XI. The Tables comprise a Traverse Table, computed for this volume,
XII. The great number of engraved illustrations, most of them crig-
XIII. The practical details, and hints to the young Surveyor, have
Should any important error, either of printer or author, be discovered.
The present volume will be followed by another on LEVELLING AND
[A full Analytical Table of Contents is given at the end of the volume.]
CHAPT. 4. SURVEYING BY THESE METHODS COMBINED.
TO TEACHERS AND STUDENTS.
As it is desirable to obtain, at the earliest possible period, a sufficient knowledge of the genera
In PART II, omit, in Chapter IV, (127), (128), (129), (130); and in Chapter V, learn at first
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 Trigonometry
DEFINITIONS AND METHODS.
(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.