ADVERTISEMENT.

THIS Edition of Mr. Gibson's Treatise of Practical Surveying, is in some particulars, different from the copy published by the Author,

Alterations have been made, adapting it to our country. Some articles of little or no importance have been entirely omitted; and others of more utility introduced: amongst which are a complete set of tables of latitude and departure to the distance of 100, and to every 15 minutes of the quadrant; a table of logarithms from 1 to 10,000; and a table of artificial sines, tangents, and secants; also, an example of calculating the contents of a survey, according to the method commonly practised in the Surveyor-General's office of Philadelphia.

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PREFACE.

THE

HE word Geometry imports no more than to measure the earth, or to measure land; yet in a larger and more proper sense, it is applied to all sorts of dimensions. It is generally supposed to have had its rise among the Egyptians, from the river Nile's destroying and confounding all their land-marks by its annual inundations, which laid them under the necessity of inventing certain methods and measures to enable them to distinguish and adjust the limits of their respective grounds, when the waters were withdrawn. And this opinion is not entirely to be rejected, when we consider that Moses is said to have acquired this art when he resided at the Egyptian court. And Achilles Tatius, in the beginning of his introduction to Aratus's Phænomena, informs us, that the Egyptians were the first who measured the heavens and the earth (and of course the earth first) and that their science in this matter was engraven on columns, and by that means delivered to posterity.

It is a matter of some wonder, that though surveying appears to have been the first, or at least one of the first of the mathematical sciences, that the rest have met with so much greater improvements from the pens of the most eminent mathematicians, while this seems to have been neglected; insomuch that I have not been able to meet with one author who has sufficiently explained the whole

art in its theory and practice for the most part, it has been treated of in a practical manner only; and the few who have undertaken the theory, have in a great measure omitted the practice

These considerations induced me to attempt a methodical, easy, and clear course of Surveying ; how far I have succeeded in it, must be determined by the impartial reader: the steps I have taken to render the whole evident and familiar are as follow:

In section the first, you have decimal fractions, the square root, geometrical definitions, some necessary theorems and problems;. with the nature and use of the tables of logarithm numbers, sines, tangents, and secants.

The second section contains plain trigonometry, right angled and oblique, with its application in determining the measures of inaccessible heights and distances.

The third section gives an account of the chains and measures used in Great-Britain and Ireland, methods of surveying and taking inaccessible distances by the chain only, with some necessary problems; also a particular description of the several instruments used in surveying, with their respective

uses.

The fourth section contains two methods of finding the areas of maps from their geometrical construction, more concise than any heretofore made public.

The fifth section contains a new, and much more concise method of determining the areas of surveys

from the field-notes, or by calculation than any hitherto published; and I venture to assert, that it is impossible (from the nature of right-lined figures) that any method or methods more concise than this can be investigated.

To these methods is annexed a short table of difference of latitude and half departure, to every degree and quarter of a degree of the quadrant, the stationary distance being one chain; which will be found as ready, by a little practice, and perhaps more exact, than those already published.

Truth calls upon me to acknowledge, that the methods by calculation, herein set forth, got their rise from those of the late Thomas Burgh, Esq. who first discovered an universal method for determining the areas of right lined figures, and for which he obtained a parliamentary reward. I hope therefore it cannot be construed as an intention in me to take from his great merit, when I say, that the methods herein contained are much more concise and ready than his.

Section the sixth contains the nature of off-sets, and the method of casting them up by the pen: the nature and application of enlarging, diminishing, and connecting of maps: variation of the compass by amplitudes and azimuths, with some of its uses : to which is added, a table of the sun's declination : how to find by what scale a map is laid down, having the map and area given: how to find the content of a ground that is surveyed by a chain that is too long or too short: the method of dividing lands: And the whole concludes with some necessary directions and remarks on surveys in general.