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SAMUEL ALSOP,

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AUTHOR OF A TREATISE ON ALGEBRA, ETC.

THIRD EDITION.

PHILADELPHIA:
E. C. & J. BIDDLE, No. 508 MINOR ST.
(Between Market and Chestnut, and Fifth and Sixth Sts.)

1865.

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PREFACE.

The favor shown to this treatise by the author's colaborers in the educational field having called for another edition of it, he has carefully revised the work, and made such amendments as to him seemed desirable. These are not numerous, but he believes have somewhat improved the work.

His aim has been to present the subject, in its practical as well as its theoretical relations, in a manner adapted to the capacity of every student, by presenting the theory plainly and comprehensively, and giving definite and precise directions for practice; and to embrace in the work every thing which an extensive business in land-surveying would be likely to require. How nearly his object has been attained, others must determine: he trusts, however, that the treatise will be found to possess merit sufficient to commend it to the favorable notice of his fellowteachers. The following brief synopsis of its contents presents the plan and scope of the work.

Chapter I. consists of a short explanation of the nature and use of Logarithms.

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Chapter II. contains the geometrical definitions and constructions needed in the subsequent part of the work.

In Chapter III. is presented a treatise on Plane Trigonometry, including a great variety of examples illustrative of the solution of triangles. In this chapter will also be found a full description of the Theodolite and Surveyor's Transit, and directions for their use.

In Chapter IV. the principles of surveying by the Chain are explained. This method is little employed by practical surveyors in this country. Since, however, the measurements require no other instrument than a tape-line, or a cord, or some other means of determining distances, it is of importance to the farmer, who frequently desires to know the contents of particular fields, or of portions of enclosures. The second and third sections of this chapter contain a pretty full treatise on Field Geometry, or the method of performing on the ground, with the chain or measuring line only, those operations which are needed in fixing the positions of points or in locating lines. In Great Britain, Chain Surveying is almost exclusively employed.

Chapter V. is devoted to Compass Surveying. Under this head are included all those methods which require the use of an instrument for determining the bearings of lines, whether that instrument be a Compass, a Transit, or a Theodolite. This chapter contains a full account of the methods to be employed in locating lines by means of such instruments.

The numerous difficulties with which the surveyor will be likely to meet from obstructions on the ground are stated, and the modes of overcoming them explained.

This chapter, with that on Plane Trigonometry, constitutes, in fact, a full treatise on Surveying as practised in this country. In selecting the methods to be employed in overcoming the difficulties both in Compass and in Chain Surveying, care has been taken to adopt such only as may be conveniently employed in the field.

Chapter VI. contains the general principles of Triangular Surveying. This is the method employed in extensive geodetic operations.

The details of this method are so complex that a volumenot a chapter—would be required for their development. All that has been attempted is to give some of the more simple priuciples.

Chapter VII. treats of Laying out and Dividing Land. It is believed that many of the demonstrations in this chapter will be found to be much more simple than those usually given, almost all of them having been reduced to the development of a single principle. On a subject of this kind, which has so long occupied the attention of mathematicians, any thing new could hardly be expected. It has been the aim of the author to select the best methods, not to introduce any thing merely because it

was new.

Chapter IX. contains a treatise on Practical Astronomy, embracing all that is needed for the surveyor's purposes or is practicable with his instruments. Various methods of running meridian lines, and of determining the latitude and the time of day, are fully explained.

The concluding chapter (X.) is devoted to the subject of the Variation of the Compass. In it will be found information of great value to the practical surveyor. The tables of variation are in all cases drawn from the most recent and authentic

sources.

In the preparation of this treatise the author has consulted various well-known English and American mathematical works. To Professor GILLESPIE's excellentTreatise on Land Surveying," (D. Appleton & Co., New York,) especially, the author is indebted for very valuable hints, particularly in the directions for practice, the descriptions of the instruments, and various new methods of presenting important points. Some of these are referred to in their places. The typographical peculiarities of this volume, in the headings of articles, &c., were also suggested to the publishers by those of the work of Dr. Gillespie.

In each department of the subject treated of in this volume

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