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Entered, according to the Act of Congress, in the year 1855, by

WILLIAM MITCHELL GILLESPIE,
In the Clerk's Office of the District Court of the United States for the Southern

District of New-York.

PREFACE.

LAND-SURVEYING is perhaps the oldest of the mathematical arts. Indeed, Geometry itself, as its name—“Land-measuring”-implies, is said to have arisen from the efforts of the Egyptian sages to recover and to fix the land-marks annually swept away by the inundations of the Nile. The art is also one of the most important at the present day, as determining the title to land, the foundation of the whole wealth of the world. It is besides one of the most useful as a study, from its striking exemplifications of the practical bearings of abstract mathematics. But, strangely enough, Surveying has never yet been reduced to a systematic and symmetric whole. To effect this, by basing the art on a few simple principles, and tracing them out into their complicated ramifications and varied applications (which extend from the measurement of “a mowing lot " to that of the Heavens), has been the earnest endeavor of thepresent writer.

The work, in its inception, grew out of the author's own needs. Teaching Surveying, as preliminary to a course of Civil Engineering, he found none of the books in use (though very excellent in many respects) suited to his purpose. He was therefore compelled to teach the subject by a combination of familiar lectures on its principles and exemplifications of its practice. His notes continually swelling in bulk, gradually became systematized in nearly their present form, and in 1851 he printed a synopsis of them for the use of his classes. His system has thus been fully tested, and the present volume is the result.

A double object has been kept in view in its preparation ; viz. to produce a very plain introduction to the subject, easy to be mastered by the young scholar or the practical man of little previous acquirement, the only pre-requisites being arithmetic and a little geometry; and at the same time to make the instruction of such a character as to lay a foundation broad enough and deep enough for the most complete superstructure which the professional student may subsequently wish to raise upon it

For the convenience of those wishing to make a hasty examination of the book, a summary of some of its leading points and most peculiar features will here be given.

I. All the operations of Surveying are deduced from only five simple principles. These principles are enunciated and illustrated in Chapter 1, of Part I. They will be at once recognized by the Geometer as familiar systems of " Co-ordinates;" but they were not here arbitrarily assumed in advance. They were arrived at most practically by analyzing all the numerous and incongruous methods and contrivances employed in Surveying, and rejecting, one after another, all extraneous and non-essential portions, thus reducing down the operations, one by one and step by step, to more and more general and comprehensive laws, till at last, by continual elimination, they were unexpectedly resolved into these few and simple principles; upon which it is here attempted to build up a symmetrical system.

II. The three operations common to all kinds of Land-surveying, viz. Making the Measurements, Drawing the Maps, and Calculating the Contents, are fully examined in advance, in Part I, Chapters 2, 3, 4, so that when the various methods of Surveying are subsequently taken up, only the few new points which are peculiar to each, require to be explained.

Each kind of Surveying, founded on one of the five fundamental prin. ciples, is then explained in its turn, in the successive Parts, and each carefully kept distinct from the rest.

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 bear-
ings are given in Chapter 4, and in Chapter 6, the rectangular method
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,
and giving increased accuracy in one-fifteenth of the usual space; a
Table of Chords, appearing for the first time in English, and supplying
the most accurate method of platting angles; and a Table of natural
Sines and Tangents. It was thought best not to increase the size of
the volume with Logarithmic Tables, not absolutely necessary for its
purposes, and to be found in all Trigonometries. The tables are printed
on tinted paper, on the eye-saving principle of Babbage.

XII. The great number of engraved illustrations, most of them orig-
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, Castie, Fran-
coeur, Frome, Galbraith, Gibson, Guy, Hogard, Jackson, Lamotte,
Lefevre, Mascheroni, Narrien, Nesbitt, Pearson, Puille, Puissant, Reg-
nault, 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, Theodo-
lite, 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.

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