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The great utility of Land-Surveying, without which it is impossible to conduct the affairs of civilised life, induced many of the most celebrated philosophers and mathematicians of antiquity to study its principles; and to Thales, Pythagoras, Socrates, Plato, Aristotle, Euclid, Archimedes, &c. we are indebted for many substantial improvements. The ancient Romans, likewise, it is said, held this art in such high veneration, that they accounted no man capable of commanding a legion, who was incapable of measuring a field.

The increasing value of land, and the consequent necessity of ascertaining its dimensions and content with accuracy, have lately called forth many Treatises on this subject; the principal of which we owe to Dix, Davis, Talbot, Crocker, and Cotes; but as these Works take a very limited view of the subject, and are, in my opinion, very deficient in practical information, and consequently not well adapted either for Schools or private Learners, I have been induced to write the following Work, which, I hope, will be found to contain every necessary instruction both on theoretical and

practical Surveying.

I have carefully studied the Works of my predecessors and contemporaries; selected from them such matter as I thought most useful; and combined it with the information that I have received from some of the first Land-Surveyors in the kingdom, and with my own practical experience for upwards of twenty-five years.

The Work thus compiled and composed, I have divided into Seven Parts, upon each of which I shall make a few observations.

PART THE FIRST contains such Definitions, Problems, and Theorems in Geometry, as I conceived to be indispensably necessary in Land-Surveying. Those who desire to see the subject more fully treated, are referred to the Elements of Simpson, Emerson, Bonnycastle, Keith, Playfair, and Leslie ; to Simson's Euclid, Hutton's Course of Mathematics, and Reynard's Geometria Legitimą. The last Work is well adapted to the capacities of Youth; and contains a number of Quæstiones Solvendæ, at the end of each Book ; to which an excellent Key has lately been published by the Author.

PART THE SECOND contains a description of the Chain, CrossStaff, Offset-Staff, Compass, and Field-Book; also directions and cautions to young Surveyors, when in the field; and a few observations relating to Scales, laying down Figures, &c. &c.

The description of the Compass, together with an account of the variation of the Needle, has been given, under the conviction that the exact range of some line ought always to be taken, in the field, in order to determine the true situation of the estate.

PART THE THIRD treats of the method of surveying with the Chain and Cross ; and of measuring Meres, Woods, and Lines upon which there are Impediments.

I am aware that Professional Surveyors seldom or never use a Cross; but I am of opinion that every Learner should be taught the use of this instrument, in order to make him acquainted with the method of forming a right-angle in the field; and to give him a just idea of the nature and properties of the base and perpendicular of a triangle.

In this Part I have exhibited the absurdity of the processes fre. quently adopted by unskilful Surveyors, in computing the contents of Narrow Pieces of Land, and of Offsets. Methods leading to such erroneous results, ought to be discarded by every one who is ambi. tious of obtaining the appellation of a correct Surveyor.

I have also introduced the method of computing the contents of Narrow Pieces of Land, and of Offsets, by means of Equidistant Ordinates, which will be found more easy, expeditious, and accurate, than finding their areas by a succession of triangles and trapezoids.

No previous Writer with whom I am acquainted, has given this method in such a manner as to make it applicable to general practice; but the Rules which I have laid down may be applied with success in all cases when the fences are not very irregular, without first measuring the base, in order to divide it into an even number of equal parts, which is a general rule given by all former Writers on this subject.

PART THE FOURTH treats of the method of surveying with the Chain only; and of measuring Meres, Woods, Roads, Rivers, Canals, Distances, Lines upon which there are Impediments, and Hilly Ground.

The method of measuring Proof-Lines, in surveying single fields, which I have not observed in any preceding publication, forms a portion of the subject of this Part. Before I discovered this method, I frequently incurred the disagreeable necessity of repeating my survey, when disputes took place concerning the measurement. In large surveys, however, I am aware, it has long been known and practised by Professional Surveyors.

In this Part, likewise, I have treated largely upon the surveying of Hilly Ground, which seems to have been hitherto little regarded, and still less understood by the generality of Writers on Land-Surveying; and, to the method of preserving the horizontal line by elevating the chain, I have subjoined the description and use of King's Quadrant, as well as the mechanism and application of one of my own invention. I have also added a few directions for finding the hypothenusal measure of Hilly Ground, for paring, reaping, &c. ; but this generally depends upon dividing it into proper figures.

This subject is closed with Remarks on the impropriety and injustice of returning the hypothenusal measure of Hills, universally; although it has been long and strenuously contended for, by Theoretical and Superficial Writers. These Remarks, together with the following Observation, which I have since met with, in Professor Leslie's Geometry, Second Edition, Page 401, will, I think, tend to set this subject completely at rest : “In surveying Hilly Grounds, it is not the absolute surface that is measured, but the diminished quantity which-would result, had the whole been reduced to a hori. zontal plane. This distinction is founded on the obvious principle, that since plants shoot up vertically, the vegetable produce of a swell

a

ing eminence can never exceed what would have grown from its levelled base. All the sloping or hypothenusal distances are, therefore, reduced invariably to their horizontal lengths, before the calculation is begun.” Thus we see the opinion and practice of Professional Surveyors approved and supported by one of the most profound Mathematicians and Philosophers in the United Kingdom.

PART THE FIFTH contains four of the most approved methods of surveying large Estates or Lordships; general and particular Rules for planning them; and copious Directions for finding their Contents.

The use of the Parallel Ruler, in straightening crooked fences, is also given, in twelve entirely new Problems, comprising every possible case that can occur in Practice. Several methods of copying and reducing Plans have likewise been introduced, particularly the description and use of the Pentagraph, which instrument far surpasses any other, for that purpose.

Three different methods of embellishing Plans are given, containing directions for shading and colouring Meadows, Pastures, Cornfields, Moors, Marshy Grounds, Sands, Rocks, Trees, Lakes, Rivers, Sea-Shores, Hills, Pleasure-Grounds, Gardens, and the Bases and Elevations of Buildings.

This Part also contains directions for making Compartments; Observations on Penmanship; and a Plan of a New Town, laid out in such a manner as to form straight streets, at right angles with each other, which is by far the most eligible method of laying out Building-Ground. An Architectural Elevation of a House is like. wise given, in order to show the young Surveyor how to proceed, if he should be requested to give a view of the buildings belonging to an Estate.

This Part is fully and clearly illustrated by numerous Wood Cuts, Copper Plates, and a neatly Engraven Field-Book; and, it may not be improper to state, that the ESTATES contained in PLATES EIGHT AND TEN, are actual SURVEYS taken by the AUTHOR.

PART THE Sixth contains Rules and Directions for Laying-out, Parting-off, and Dividing Land; illustrated by a greater number of examples than I have met with in any other Treatise. If any

of them should appear superfluous to experienced Surveyors, they will please to recollect for whom the Work is designed.

In parting-off, and dividing land, by means of guess-lines, as a difficult branch of the art, I have been particularly explicit; and have exemplified the method by numerous examples, illustrated by figures exhibiting the various lines used in each process.

The method of dividing a Common among various Proprietors, according to the different qualities of the Land, has also been introduced; and copious directions have been given for valuing land, and conducting an Inclosure. I have likewise inserted an Abstract of the General Inclosure Act, which will be found to throw more light on the subject of Inclosures, than was ever before given to the Public, in any Treatise on Surveying.

Indeed, the only Work that takes any notice of Inclosures, is one published by Mr. Stephenson, (price sixteen shillings,) in which the Author appears to have treated the subject with considerable ability. This Work, however, is not at all adapted either for Schools or Private Learners, as the first principles of Land-Surveying are not clearly elucidated.

Various Customary Measures, formerly prevailed in different Counties of England, and also in Scotland and Ireland ; and, although all Customary Weights and Measures were abolished by the Act 5 & 6 Will. IV., Chap. 63., still the Author has found it necessary to give the Methods of reducing Customary Measures of Land, to Statute Measure; as, in many Old Surveys and Old Plans, the Contents are given in Local or Customary Measures. — Besides, there is an absolute necessity that our Young Surveyors should be made acquainted with those Local Land-measures which long prevailed in different Parts of the Kingdom; but, which will soon become only Matters of History.

This Part also contains a few Remarks on the Advantages of Leases, both as regards Landlords, Tenants, and the Public; and, to these Remarks are added a few Observations on the Improvement that may still be expected in Agriculture, from Scientific Modes of Cultivation ; and from the Resources and General Application of AGRICULTURAL CHEMISTRY.

The Subject of Leases is now engaging the attention, not only of the Public in general, but also of many Agricultural and Scientific Writers; and, the Reader will find an excellent Article on the Granting of Leases, the Purchasing of Leases, the Reversion of Leases, and the Renewal of Leases, in PART THE SECOND OF NESBIT'S PRACTICAL ARITHMETIC.

PART THE SEVENTH of the Land Surveying, contains the method of measuring and planning Villages, Towns, and Cities ; directions

; for surveying and planning Building-Ground, and dividing it into convenient lots for sale; and Miscellaneous Questions relating to surveying, laying-out, parting-off

, and dividing Land in general. Nothing has been said on the method of measuring, planning, and laying-out Building-Ground, by any former Writer ; but as it is a subject of great public importance, in the vicinity of large and improving towns, it ought by no means to be omitted in a Treatise on Land-Surveying

The Miscellaneous Questions at the end of this Part, will serve to exercise the genius of the Learner, after he has acquired a competent knowledge of the principles of surveying and dividing Land, by carefully studying the former part of this work. Such Questions tend to rouse the latent energies of youth ; and to give them a relish for making interesting calculations; and a delight in discovering unknown truths. They also call into action those abilities which might otherwise lie dormant, for want of objects of sufficient importance to excite the curiosity of the ingenious; and put the powers of their minds into motion.

The greater part of the Examples for single fields, have been taken from my own Field-Books; consequently, they are such as the Learner will generally meet with in taking actual Surveys. Hence, in going through this Work, he will become familiar with the method of keeping the Field-Book; so that when he commences Field-Practice, he will find no embarrassment in entering his Notes.

Copious directions have been given, in various parts of the Work, for taking the dimensions of all kinds of figures that can possibly be met with in the Practice of Surveying. This is of the greatest importance in measuring ; for it is evident that if the dimensions be improperly taken, the results must, of course, be incorrect; notwithstanding the greatest care may be taken in laying down the figures, and finding their contents.

The engraven Field-Book, being detached from the Surveying, will also be found extremely convenient in laying down the large Surveys; as it will, probably, be necessary for Learners to refer to the lines and stations upon the Rough Plans.

In composing the following Work, I have endeavoured to consult the wants of the Learner, in every possible way; consequently, no information that I conceived to be necessary, has been withheld. In order, however, to make a Complete Surveyor, the Rules and Directions which I have laid down, must be brought into actual use by Field Practice; not only in measuring single Fields, but also in surveying large Estates : in laying-out, parting-off, and dividing Land, and in performing every process that occurs in Practical Operations.

Being daily employed in the education of youth, I have had many opportunities of observing the numerous difficulties which Tutors have to surmount; it is, therefore, my highest ambition, that the following Work may be found well adapted for the use of Schools; and be a means of rendering a most useful and delightful science familiar to the rising generation. Such as it is, I respectfully commit it to the world ; trusting that slight mistakes will be pardoned, that serious ones have not been incurred, and that the forbearance which I have exercised towards the labours of others, will be exercised towards mine in return.

ANTHONY NESBIT.

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Kenninglon, near London, October, 1847.

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